Aided Design of Phase Change Materials from Blends

Phase Equilibrium- aided Design of Phase Change Materials from Blends

For Thermal Energy Storage

SAMAN NIMALI GUNASEKARA

Doctoral Thesis 2017 KTH Royal Institute of Technology Industrial Engineering and Management Department of Energy Technology Division of Heat and Power Technology SE-100 44 Stockholm, Sweden

ISBN 978-91-7729-484-9 TRITA-KRV Report 17/05 ISSN 1100-7990 ISRN KTH/KRV/17/05-SE © Saman Nimali Gunasekara, 2017

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknisk dok- torsexamen fredagen den 22 september 2017, kl. 13:00 i sal B1, Kungliga Tekniska Högskolan, Brinellvägen 23, Stockholm. Avhandlingen försvaras på engelska.

To Tharaka and my family, for all your love.

Abstract

Climate change is no longer imminent, but eminent, and the influence of anthropogenic activities in that is irrefutable. Energy is an integral part of society, however, energy processes are culpable for major anthropogenic environmental degradation, triggering climate change. Therefore, effective energy use, improved energy efficiencies, and smart energy management are imperative. Thermal energy storage (TES) is one attractive choice to realize this, with for example the high-density storage alternatives: phase change materials (PCMs). The most common, abundant, and cheap PCM is the water-ice system, known to humans for thousands of years. To accommodate the many heating and cooling demands today within a wide range of temperatures, innovative design of PCMs is essential. With the precondition of suitable phase change temperatures, enthalpies, and other thermal and physicochemical properties, the PCMs should also have robust phase change, be non-toxic, environmental-friendly, and cost-effective.

In realizing large scale TES systems with PCMs, the key challenges remain in achieving cost-effectiveness and robust function over many cycles. Cost- effective PCMs can be realized in natural or industrial bulk materials, which are essentially blends. Then again, to engineer PCMs for specific applications in the absence of suitable pure materials, blending is the key. Blends however have complex phase change, and unless chosen articulately, do not have robust phase change. This doctoral thesis bridges the gap between bulk blends and robust, cost-effective and/or fine-tuned PCMs, by means of the systematic design of blends as PCMs involving phase equilibrium evaluations with phase diagrams. This necessitates the comprehension of relevant fundamental phase equilibrium theory, thorough thermal and physicochemical characterizations, and generally applicable theoretical evaluations, as shown herein.

This thesis specifies the existing phase equilibrium theory into the PCM- context, to accurately select robust PCMs within blends. It is here established that a congruent melting composition, where all the phases in equilibrium have the same composition, is the most PCM-ideal among blends. Congruent melting could occur in a solid solution or a compound, either of which equally ideal as a PCM. Eutectic compositions are almost as ideal as PCMs, if supercooling is absent. Thereby, pure material-like blends with a sharp, reversible phase change with no phase separation can be obtained. In contrast, as phase diagrams indicate, any incongruent melting composition, including peritectics, are unsuitable as PCMs. This thesis serves as a basis in Saman Nimali Gunasekara establishing such vital fundamental phase equilibrium knowledge that is a prerequisite in designing PCMs in blends. Through a comprehensive state- of-the-art evaluation of the phase equilibrium-based PCM design, the underinvestigated PCM-ideal blends such as congruent melting compositions, and material categories like metal alloys, polyols and fats, are exposed herein. As the thesis shows, in PCM design so far, eutectics have been in the lime- light, although their unsuitability upon supercooling has not been acknowledged. It also discovered that the peritectics have already been considered as PCMs (e.g. Glauber salt and sodium acetate trihydrate), despite their in- feriority causing phase separation and eventual storage capacity degradation.

A key contribution of this thesis is the specification and establishment of the fundamental theory as well as techniques, approaches and conditions essential for a comprehensive and transparent phase equilibrium assessment, for the design of PCMs in blends for TES. With this as a basis, the phase diagrams of the systems: erythritol-xylitol and dodecane-tridecane, with PCM potential for low-temperature heating (60-120 °C) and freezing (-10 °C to -20 °C), are comprehensively evaluated. The erythritol-xylitol system is found to contain a eutectic in a partially isomorphous system, rather than in a non-isomorphous system as previous literature proposed. The dodecane-tridecane system is found to form a probable congruent minimum-melting solid solution (ideal as a PCM), unlike the previous literature proposing a maximum-melting liquidus or a eutectic in the system. By scrutinizing the theoretical phase equilibrium evaluations in PCM literature, a generic approach (the so-called CALPHAD method) is chosen here to complement the erythritol-xylitol experimental phase diagram. This generic method can appraise any material and phase change type, unlike a majority of the previ- ously employed methods limited to material types or chemical features. This theoretical study further corroborates the solvus, solidus, eutectic point, and altogether the erythritol-xylitol phase diagram thermodynamically.

This thesis in addition investigates the sustainability aspects of a PCM-based TES system by focusing on renewable, food-grade and cost-effective materials (e.g. polyols and fats) as PCMs. There, as examples, the food-grade, renewable materials erythritol and olive oil are investigated. Erythritol could become a cost-effective PCM (163 USD/kWh) if produced from glycerol coming as a by-product in bio-diesel/bioethanol production. Olive oil is already cost-effective (144 USD/kWh), and is found with potential PCM compositions with suitable phase change characteristics for cold storage.

From a methodology point of view, this thesis demonstrates that a critical need exists in the standardization of employed techniques and approaches, and transparent results reporting, of the phase equilibrium investigations in the PCM-context. This is here proposed to be achieved e.g. through international TES collaboration platforms.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Keywords: thermal energy storage (TES); phase change material (PCM); phase diagram, congruent melting, compound, solid solution, eutectic, peritectic

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Saman Nimali Gunasekara

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Sammanfattning

Energi är en integrerad del av samhället men energiprocesser leder till mil- jöbelastning, och klimatförändringar. Därför är effektiv energianvändning, ökad energieffektivitet och smart energihantering nödvändigt. Värmeener- gilagring (TES) är ett attraktivt val för att bemöta detta behov, där ett lag- ringsalternativ med hög densitet är s.k. fasomvandlingsmaterial (PCM). Ett exempel på ett billigt, vanligt förekommande PCM är systemet vatten-is, vilket har använts av människor i tusentals år. För att tillgodose de många värme- och kylbehov som idag uppstår inom ett brett temperaturintervall, är det viktigt med innovativ design av PCM. Förutom lämplig fasföränd- ringstemperaturer, entalpi och andra termofysikaliska egenskaper, bör PCM också ha robust fasändring, vara miljövänlig och kostnadseffektiv.

För att förverkliga storskaliga TES system med PCM, är måste kostnadsef- fektivitet och robust funktion under många cykler bland de viktigaste utma- ningarna. Kostnadseffektiva PCM kan bäst erhållas från naturliga eller in- dustriella material i bulkskala, vilket i huvudsak leder till materialblandningar, snarare än rena ämnen. Blandningar uppvisar dock komplexa fasföränd- ringsförlopp, underkylning och/eller inkongruent smältprocess som leder till fasseparation. Denna doktorsavhandling ger ny kunskap som möjliggör att bulkblandningar kan bli kostnadseffektiva och robusta PCM-material, med hjälp av den systematiskutvärdering av fasjämvikt och fasdiagram. Ar- betet visar att detta kräver förståelse av relevanta grundläggande fasjäm- viktsteorier, omfattande termiska och fysikalisk-kemiska karakteriseringar, och allmänt tillämpliga teoretiska utvärderingar.

Denna avhandling specificerar befintlig fasjämviktsteori för PCM-samman- hang, men sikte på att kunna välja robusta PCM blandningar med specifika egenskaper, beroende på tillämpning. Analysen visar att blandningar med en sammansättning som leder till kongruent smältande, där faser i jämvikt har samma sammansättning, är ideala bland PCM-blandningar. Kongruent smäl- tande fasta faser som utgör föreningar eller fasta lösningar av ingående kom- ponenter är därför ideala. Eutektiska blandningar är nästan lika bra som PCM, så länge underkylning inte förekommer. Därmed finns en stor potential för att finna och karakterisera PCM-ideala blandningar som bildar kongruent smältande föreningar eller fasta lösningar. Därigenom kan blandningar med en skarp, reversibel fasändring och utan fasseparation erhållas – egenskaper som liknar rena materialens fasändringsprocess. Vidare kan man,

Saman Nimali Gunasekara via fasdiagram, påvisa de blandningar som är inkongruent smältande, inklu- sive peritektiska blandningar, som är direkt olämpliga som PCM. Denna avhandling ger grundläggande kunskap som är en förutsättning för att designa PCM i blandningar. Genom en omfattande state-of-the-art utvärdering av fas-jämviktsbaserad PCM-design lyfter arbetet de PCM-idealiska blandning- arna som hittills inte fått någon uppmärksamhet, såsom kongruenta smäl- tande blandningar, och materialkategorierna metallegeringar, polyoler och fetter. Resultatet av arbetet visar dessutom att vissa PCM-material som ibland föreslås är direkt olämpliga då fasdiagram undersöks, bl a pga underkylning och även peritektiska system med fasseparation och degradering av kapaciteten (t ex Glauber-salt och natriumacetat-trihydrat).

Denna avhandling specificerar och upprättar grundläggande teori samt tekniker, tillvägagångssätt och förhållanden som är nödvändiga för en omfattande och genomsynlig fasjämviktsbedömning, för utformning av PCM från blandningar för energilagering. Med detta som bas har följande fasdiagram- tagits fram fullständigt: för erytritol-xylitol och för dodekan-tridekan, med PCM-potential för låg temperaturuppvärmning (60-120 °C) respektive frys- ning (-10 °C till -20 °C) utvärderas fullständigt. Erytritol-xylitol systemet har funnits vara eutektiskt i ett delvis isomorft system, snarare än ett icke-isomorft system vilket har föreslagits tidigare litteratur. Dodekan-tridekan systemet bildar ett system med kongruent smältande fast lösning (idealisk som en PCM) vid en minimumtemperatur, till skillnad från tidigare litteratur som föreslagt en maximumtemperatur, eller ett eutektiskt system.

Teoretisk modellering av fasjämvikt har också genomförts för att komplet- tera det experimentella fasdiagrammet för systemet erytritol-xylitol. Efter granskning av de metoder som använts tidigare i PCM-litteraturen har här valts ett generiskt tillvägagångssätt (CALPHAD-metoden). Denna generiska metod kan bedöma vilken typ av material och fasändring som helst, till skillnad från en tidigare använda metoder som är specifika för materialtyper eller kemiska egenskaper. Denna teoretiska studie bekräftar termodynamiskt solvus, solidus, eutektisk punkt och erytritol-xylitol fasdiagrammet i sin hel- het.

Vad gäller hållbarhetsaspekter med PCM-baserad TES, lyfter denna avhandling fokus på förnybara och kostnadseffektiva material (t.ex. polyoler och fetter) som PCM. Som exempel har här undersökts erytritol och olivolja, med förnybart ursprung. Erytritol skulle kunna bli ett kostnadseffektivt PCM (163 USD/kWh), om det produceras av glycerol vilket är en biprodukt från biodiesel/bioetanolframställning. Olivolja är ännu ett kostnadseffektivt material (144 USD/kWh), och som här har påvisats innehålla potentiella PCM sammansättningar med lämpliga fasändringsegenskaper för kylatill- lämpningar.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

En övergripande slutsats från denna avhandling är att det finns ett behov av att standardisera tekniker, metoder och transparent resultatrapportering när det gäller undersökningar av fasjämvikt och fasdiagram i PCM-samman- hang. Internationella samarbetsplattformar för TES är en väg att koordinera arbetet.

Nyckelord: termisk energilagring; fasändringsmaterial; fasdiagram; kongruent smältande, förening, fast lösning, eutektisk, peritektisk

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Preface

This PhD thesis presents the outcomes of a doctoral research conducted on thermal energy storage using phase change materials, at the department of Energy Technology (EGI), School of Industrial Engineering and Manage- ment (ITM), KTH Royal Institute of Technology, Sweden. This work includes three published journal articles, one accepted journal manuscript in press, one submitted journal manuscript, and four peer-reviewed conference publications. The work presented therein consists of: the state-of-the art assessment of phase equilibrium-based PCM design on phase equilibrium characteristics, material categories as well as experimental and theoretical methods; experimental binary phase diagram investigations; theoretical phase diagram modelling; and the exploration of sustainability of potential PCMs via cost- and thermal property appraisals.

Acknowledgements My foremost gratitude is expressed to the Swedish Energy Agency for funding this PhD research (project nr. 34948-1). Particularly to Mr. Conny Ryytty for awarding the funding, and Mr. Mattias Törnell, Ms. Jennica Broman, Ms. Emina Pasic at the Swedish Energy Agency, for their collaborations. My heartfelt gratitude is expressed to my principal supervisor Prof. Viktoria Martin, for welcoming me onboard on this stimulating research, and for being the best supervisor I could ever wish for. Without her guidance, con- structive criticism, mutual trust and the freedom to explore to shape the research, this thesis would not be possible. I wish to sincerely thank Prof. Torsten Fransson, for recruiting me as a PhD candidate and for being a co- supervisor, and to Prof. Andrew Martin and Prof. Björn Palm for the inspiring work-environment we are provided at the Energy Technology department (EGI). My heartfelt gratitude goes to Dr. Justin Chiu, for being the best mentor ever, and for his invaluable guidance as a co-supervisor. I express my sincere appreciation to all the thermal energy storage experts, researchers and industrialists for the fruitful discussions, inspiration and the lasting friendships acquired though the International Energy Agency- En- ergy Conservation through Energy Storage Annexes 24 and 29. My heartfelt gratitude goes to Prof. Halime Paksoy for her valuable feedback and reflec- tions on my mid-term seminar. I greatly appreciate Prof. Björn Palm’s contributions in improving this thesis by being my internal quality reviewer.

Saman Nimali Gunasekara

Special thanks to my final seminar committee: Assoc. Prof. Rahmatollah Khodabandeh, Dr. Samer Sawalha and Dr. Jeevan Jayasuriya.

Special thanks go to the heads of the laboratories, Dr. Jens Fridh and Mr. Peter Hill at HPT and ETT. Thank you very much dear friend Monika Ig- natowicz, for the generosity in sharing your lab space and instruments, emer- gency experimental help, invaluable assistance with the thermal conductivity evaluations, and for your friendship. My heartfelt appreciation also goes to the workshop engineers, especially to Mr.’s Micke, Göran and Leif for manufacturing the experimental accessories, and to Mr.’s Benny, Bosse, and eve- ryone else at both divisions, for your kind and generous help always. Thank you Mr.’s Tony, Birger and Johan for all the IT help. My sincere gratitude goes to Dr. Jeevan Jayasuriya, who introduced me to EGI and encouraged me with his best wishes for my achievements all the way, and also to Ms. Chamindie Senaratne for her best wishes and friendship every day. Special thanks to Ms. Anneli Ylitalo for all the administrative help and her friendship. I sincerely appreciate Dr. Peter Hedström, Dr. Huahai Mao, Ms. Sedigheh Bigdeli, and Dr. Rafael Borrajo Pelaez at the Material Science and Engineering Department; and Ms. Rebecca Hollertz at the Chemical Engi- neering Department; at KTH, for the fruitful collaborations. Thanking Thermo-Calc for the free access on the academic version, and Mr.’s Måns, Florian, Mårten, Archit and Guillaume for developing an automated calculation tool for the T-history measurements evaluations.

Heartfelt appreciation goes to my best friends Sara Ghaem, Justin Chiu, and Amir Vadiee, for being amazing office-mates, encouraging, inspiring, cheer- ing, and sharing. Because of you, I always look forward to come to work. Special thanks to my friends at the TES group: Ruijun Pan, José Fiacro and Amir Abdi, and at the department, particularly, Mahrokh, Jorge, Maria, Eye- rusalem, Mazyar, Sujee, Tobi, Mauri, Trang, Patri, Wujun, Fumi, Hanna, Monica, Nora, Eunice, Gaby, Rebecka, Viggy, Abhi, Dimitris, Costas, Pavel, Natalia, David, Willem, Ana-Martha, Daniel, Marco, Davide, Adhemar, Evelyn, Fabi, Jhonny, Louis, Nelson, Dillip, Brijesh, and all the other friends (sorry, but I’m sure I forgot a few!). You’ve all made my stay at the department simply amazing. An enormous thank you especially to: Susantha, Ananda, Lakshika, Hedbys family, Piyasena family, Duleeka, Charaka, Uth- pala, Ravin, Rebecca aunty, Chathuri, Sanuri, Chanuka, Kuley uncle, among others, for being our family in Sweden. I thank with all my love: my parents, especially my mother for making who I am today; and my two sisters, brother, and their families for their unwavering love. Also a big thank you to my mother-in-law, brother-in-law and family for all their support and love. Last but not in the least, my overwhelming gratitude and love goes to my husband Tharaka, for his patience, understanding and above all, undying love that I am privileged to have every day. Without you, this amazing ad- venture is not possible. Thank you very much to all of you, who have supported me in each and every way. x

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Publications This PhD thesis is based on the following papers. All these papers are appended at the end of the thesis.

Journal Publications

I S. N. Gunasekara, V. Martin and J. N. Chiu, "Phase Equilibrium in the Design of Phase Change Materials for Thermal Energy Storage: State-of-the-Art," Renewable and Sustainable Energy Reviews, Vol 73, pp. 558-581, 2017.

Work Input: Literature review and analysis, and Writing of the paper.

II S. N. Gunasekara, J. N. Chiu and V. Martin, "Polyols as Phase Change Materials for Surplus Thermal Energy Storage," Applied Energy, Vol. 162, pp. 1439-1452, 2016. [Developed starting from the conference article VII]

Work Input: Literature review, Experimental work, Results analysis and Writing of the paper.

III S. N. Gunasekara, J. N. Chiu, V. Martin, and P. Hedström. "The Ex- perimental Phase Diagram Study of the Binary Polyols System Eryth- ritol-Xylitol," Solar Energy Materials and Solar Cells, Accepted Man- uscript In Press, DOI: 10.1016/j.solmat.2017.08.005, 2017.

Work Input: Literature review, All the experimental work using the T-history method and assistance in the XRD and FESEM experiments, Results analysis, and Writing of the paper.

IV S. N. Gunasekara, H. Mao, S. Bigdeli, J. N. Chiu, and V. Martin. "Thermodynamic Assessment of Binary Erythritol-Xylitol Phase Di- agram for Phase Change Materials Design," Calphad, Submitted Man- uscript CALPHA_2017_96, 2017.

Work Input: Part of the modelling work, All of the results analysis, and Writ- ing of the paper.

V S. N. Gunasekara, S. Kumova, J. N. Chiu and V. Martin, “Experi- mental Phase Diagram of the Dodecane-Tridecane System as Phase Change Material in Cold Storage," International Journal of Refrigera- tion, Vol. 82, pp. 130-140, 2017. [Developed based on the conference contribution X]

Saman Nimali Gunasekara

Work Input: Literature review, Experimental work, Results analysis, and Writing of the paper.

Peer Reviewed Conference Publications

VI S. N. Gunasekara, V. Martin, and J. NW. Chiu, "Phase Diagrams as Effective Tools in Thermal Energy Storage De- sign Using Phase Change Materials", the 5th International Conference on Applied Energy- ICAE2013, July 1-4, 2013, Pretoria, South Africa.

Work Input: Literature review and analysis, and Writing of the paper.

VII S. N. Gunasekara, R. Pan, J. NW. Chiu, and V. Martin. "Polyols as Phase Change Materials for Low-grade Excess Heat Storage", Energy Procedia, Vol. 61, pp 664-669, 2014. [Proceedings of the 6th Interna- tional Conference on Applied Energy- ICAE2014, May 30-June 2, 2014, Taipei, Taiwan].

Work Input: Literature review and analysis, Most of the experimental work, All the Data Analysis, and Writing of the paper.

VIII S. N. Gunasekara, J. N. Chiu and V. Martin, "Binary Phase Equilib- rium Study of the Polyols Blend Erythritol-Xylitol with the T-History Method for Phase Change Materials Design", the 13th International Conference on Energy Storage- Greenstock 2015, May 19-21, 2015, Beijing, China.

Work Input: Literature review and analysis, The experimental work, Data Analysis, and Writing of the paper.

IX S. N. Gunasekara, J. Stalin, M. Marçal, R. Delubac, A. Karabanova, J. N. Chiu, and V. Martin. “Erythritol, Glycerol and Olive Oil as Re- newable, Safe and Cost-Effective Phase Change Materials”, the 11th International Renewable Energy Storage Conference- IRES2017, March 14-16, 2017, Düsseldorf, Germany. [Accepted and In press in Energy Procedia]

Work Input: Parts of the literature review, Supervision of the cost-evaluation and experimental analysis work, Results synthesis, and Writing of the paper.

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Conference Contributions

X S. N. Gunasekara, J. N. Chiu and V. Martin, “Experimental Phase Equilibrium Study of Dodecane-Tridecane System for Phase Change Materials Design for Thermal Energy Storage", the 4th International Symposium on Innovative Materials for Processes in Energy Systems IMPRES 2016, October 23-26, 2016, Sicily, Italy.

Work Input: Literature review and analysis, the experimental work, Data Analysis, and Delivering an oral presentation.

Publications Not Included in this Thesis

I A. Vadiee, J. NW. Chiu, S. N. Gunasekara, and V. Martin “Thermal Energy Storage Systems in Closed Greenhouse with Com- ponent and Phase Change Material Design”, the 2nd International Conference on Sustainable Energy Storage in Buildings, June 19-21 2013, Dublin, Ireland.

II Alenka Ristić, Simon Furbo, Christoph Moser, Hermann Schranzho- fer, Ana Lazaro, Monica Delgado, Conchita Peñalosa, Laurent Zalew- ski, Gonzalo Diarce, Cemil Alkan, Saman N. Gunasekara, Thomas Haussmann, Stefan Gschwander, Christoph Rathgeber, Henri Schmit, Camila Barreneche, Luiza Cabeza, Gerard Ferrer, Yeliz Konuklu, Halime Paksoy, Holger Rammelberg, Gunther Munz, Thomas Her- zog, Jochen Jänchen, and Elena Palomo del Barrio, “IEA SHC Task 42 / ECES Annex 29 WG A1: Engineering and Processing of PCMs, TCMs and Sorption Materials”. Energy Procedia, Vol. 91, pp. 207– 217, 2016. [Proceedings of the 4th International Conference on Solar Heating and Cooling for Buildings and Industry (SHC 2015)]

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Contributions to the Appended Papers

The author of this thesis is the main author of the papers appended I to IX. In those, the literature review and analysis, most of the experimental measurements and data analyses, part of the theoretical modelling (when relevant), as well as the writing of the papers were performed by her. All these contributions were conducted under the supervision and guidance of Prof. Viktoria Martin, and Dr. Justin NW Chiu.

The journal articles I, II, and V are published and III is accepted and in press, while IV is a submitted manuscript under review. The author has contributed for the journal paper I with comprehensive literature review and critical analysis, and writing of the paper. For the journal article II, she has contributed by performing a comprehensive literature review, experimental work and results analysis, and writing of the paper. In the journal article III, the author’s contributions are, literature review, conducting all of the T-history experiments and the assistance in the XRD and SEM evaluations, results analysis, and writing of the paper. The author contributed on the journal manuscript IV with part of the numerical modelling work, and, all of the results analysis and the writing of the paper. For the journal article V, the author contributed with the experimental work, the results analysis and writing of the paper.

For the peer reviewed conference publications VI-VIII the author performed the literature reviews, conducted experiments and evaluated results, wrote the articles and performed oral presentations. For the conference contribution IX she performed parts of the literature review, supervised the cost-evaluation and experimental studies conducted by project- and intern- ship- students, wrote the paper, and performed an oral presentation. For the conference contribution X she conducted the experimental work and results analysis, and performed an oral presentation. The conferences that were at- tended and oral presentations were performed by the author are: the 11th International Renewable Energy Storage Conference IRES 2017, March, Düsseldorf-Germany; the 4th International Symposium on Innovative Ma- terials for Processes in Energy Systems IMPRES 2016, October, Sicily-Italy; the 13th International Conference on Energy Storage- Greenstock 2015, May, Beijing-China; the 6th International Conference on Applied Energy ICAE2014, May-June, Taipei-Taiwan; the 5th International Conference on Applied Energy ICAE2013, July, Pretoria-South Africa; and the 2nd Inter- national Conference on Sustainable Energy Storage in Buildings, June 2013, Dublin, Ireland.

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Abbreviations and Nomenclature Symbols

A Heat transfer area m2

A, B, C, … Elements or compounds or cationic salts a Component activity cp Specific heat capacity at constant pressure kJ/(kg·K), J/(mol·K)

Cp Heat capacity at constant pressure J/K

Fr Freezing

G Gibbs free energy J

Gm Molar Gibbs free energy J/mol

E Gm Excess molar Gibbs free energy J/mol

° GEt Molar Gibbs free energy of erythritol J/mol

° GXy Molar Gibbs free energy of xylitol J/mol

γ Activity coefficient h Specific enthalpy J/g, kJ/kg, J/mol

H Enthalpy J hm Molar enthalpy J/mol i, j, k Any component k Thermal conductivity W/(m·K) k1 Constant W/K k2 Constant W l Characteristic length m

Saman Nimali Gunasekara

L Liquidus lmtd Log mean temperature difference K, °C ln k Solubility product of a salt hydrate based on molality

ln Ksp Solubility product of a salt hydrate based on mole fraction

ν Li, j Interaction parameter of components i and j

λ Interaction parameter m Mass kg

M Molar mass, melting, cation g/mol, -

N Mole number

ν Stoichiometric coefficient

Ωij Interaction parameter between salts i and j

Q Heat J

Q Power W

Ṙ Gas constant J/K·mol ri BET parameter of the salt i

S Solidus

S Entropy J/K

SEt A solid solution of erythritol

SXy A solid solution of xylitol

S-S Solvus

S-Se Solid-solid phase change end

S-Ss Solid-solid phase change start xvi

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

T Temperature K, °C t Time s

ΔT Temperature difference K, °C

Δt Time difference s

U Overall heat transfer coefficient W/(m²·K) x Mole fraction

X- Anion

Xi Equivalent fraction of component i

Subscripts/superscripts amb Ambient config Configurational liq Liquid max Maximum

M, m Melting p Number of excess Gibbs free energy coefficients phys Physical q+ Ionic number of cations

R Reference

S Sample

SL Between solid and liquid phases

SSTT Stainless steel test-tube srf Surface tr Transition

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Saman Nimali Gunasekara v Adjustable parameter, =0, 1, 2,…, w Water

Abbreviations

BCC Body-centered Cubic

BET Brunauer-Emmett-Teller

CALPHAD CALculation of PHAse Diagrams

CC Congruent melting compound

CIS Conformal ionic solution

COP21 Paris Climate Conference

Cu-ETP Electrolytic copper

DSC Differential Scanning Calorimetry

DTA Differential Thermal Analysis

E Eutectic

ECES Energy Conservation through Energy Storage

Er or Et Erythritol

FCC Face-centered Cubic

FESEM Field-Emission Scanning Electron Microscopy

FT-IR Fourier Transform Infra-Red Spectroscopy

GC Gas Chromatography

HPLC High-Pressure Liquid Chromatography

HT High-temperature

HTXRD High-temperature X-Ray Diffraction

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Hypo-P Hypo-Peritectic

ICM Isomorphous Congruent Minimum-Melting

ICMx Isomorphous Congruent Maximum-Melting

IEA International Energy Agency

IPCC Intergovernmental Panel on Climate Change

IR Infra-Red

IRT Infra-Red Thermography

MPA Melting Point Apparatus

NPG Neopentyl glycol

NRTL Nonrandom Two-Liquid

P Peritectic

PCM Phase change material

PE Pentaerythritol

PG Pentaglycerine ph. eqm. Phase equilibrium pICM Partially Isomorphous Congruent Minimum-melting

PLM Polarized Light Thermo-Microscopy

PSC Pitzer–Simonson–Clegg

PTFE Polytetrafluoroethylene

RBCs Repeated Batch Cultures

RT Room-temperature

RTDs Resistance Temperature Detectors

RTXRD Room-temperature X-Ray Diffraction

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Saman Nimali Gunasekara

SAT Sodium Acetate Trihydrate

SEM Scanning Electron Microscopy

SLE Solid-Liquid Equilibrium

SS Stainless-steel

S-SPC Solid-solid Phase Change

STA Simultaneous Thermal Analyzer

TE Trimethylol ethane

TEM Transmission Electron Microscopy temp Temperature

TES Thermal energy storage

TGA Thermogravimetric Analysis

T-history Temperature-history

TPS Transient Plane Source

UNIFAC UNIQUAC Functional Group Activity Coeffi- cients

UNIQUAC Universal Quasi Chemical Activity Coefficients

XRD X-Ray Diffraction

Xy Xylitol

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Table of Contents

ABSTRACT ...... I SAMMANFATTNING ...... V PREFACE ...... IX ACKNOWLEDGEMENTS ...... IX PUBLICATIONS ...... XI ABBREVIATIONS AND NOMENCLATURE ...... XV TABLE OF CONTENTS ...... XXI INDEX OF FIGURES ...... XXIII INDEX OF TABLES ...... XXVII INTRODUCTION...... 1 MOTIVATIONS ...... 3 AIM AND OBJECTIVES ...... 3 METHODOLOGY AND SCOPE ...... 4 THESIS STRUCTURE...... 5 STATE-OF-THE-ART IN PHASE EQUILIBRIUM-BASED PCMS DESIGN ...... 7 PHASE EQUILIBRIUM- THEORETICAL BACKGROUND FOR PCM DESIGN ...... 8 2.1.1 Congruent Melting Systems ...... 11 2.1.2 Eutectics ...... 12 2.1.3 Peritectics ...... 13 PHASE EQUILIBRIUM-BASED PCM DESIGN: STATE-OF-THE-ART..... 14 2.2.1 Organics ...... 16 2.2.2 Inorganics ...... 24 2.2.3 Phase Equilibrium Knowledge from Non-PCM Studies ...... 29 PHASE DIAGRAMS IN PCM DESIGN- CONCLUDING REMARKS ...... 32 METHODS FOR ESTABLISHING PHASE EQUILIBRIUM OF PCM BLENDS ...... 37 EXPERIMENTAL PHASE DIAGRAM DETERMINATION ...... 38 3.1.1 Experimental Methods: State-of-the-Art ...... 38 3.1.2 Experimental Methods for the Selected Blend Systems Investigations ...... 45

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THEORETICAL PHASE DIAGRAM DETERMINATION ...... 51 3.2.1 Theoretical Phase Equilibrium- Basis ...... 52 3.2.2 Theoretical Methods: State-of-the-Art ...... 55 3.2.3 Thermodynamic Phase Diagram Assessment with CALPHAD ... 61 PHASE EQUILIBRIUM DERIVATION METHODOLOGIES- CONCLUDING REMARKS ...... 63 EXPERIMENTAL PHASE DIAGRAMS DETERMINATION ...... 65 EXPERIMENTAL PHASE DIAGRAM OF THE ERYTHRITOL-XYLITOL SYSTEM ...... 65 4.1.1 Erythritol-Xylitol Study: Materials and Methods ...... 68 4.1.2 Erythritol-Xylitol Study: Results and Discussion ...... 70 EXPERIMENTAL PHASE DIAGRAM OF THE DODECANE-TRIDECANE ALKANES SYSTEM ...... 85 4.2.1 Dodecane-Tridecane Study: Materials and the T-history Method ...... 87 4.2.2 Dodecane-Tridecane Study: Results and Discussion ...... 88 EXPERIMENTAL PHASE DIAGRAMS- CONCLUDING REMARKS ...... 94 THEORETICAL PHASE DIAGRAM DETERMINATION ...... 97 EXPERIMENTAL UNARY AND BINARY DATA ...... 97 THERMODYNAMIC OPTIMIZATION ...... 98 ERYTHRITOL-XYLITOL THEORETICAL PHASE EQUILIBRIUM ...... 98 THEORETICAL PHASE EQUILIBRIUM- CONCLUDING REMARKS ...... 104 TOWARDS SUSTAINABLE TES WITH PCMS ...... 105 POLYOLS AS PCMS OF RENEWABLE ORIGIN ...... 105 THE POTENTIAL IN OLIVE OIL AS A SUSTAINABLE PCM ...... 108 6.2.1 Thermal Properties of Olive Oil ...... 109 SUSTAINABLE PCMS- CONCLUDING REMARKS ...... 111 DISCUSSION ...... 113 EXPERIMENTAL PHASE DIAGRAM CONSTRUCTION ...... 114 THEORETICAL PHASE DIAGRAM EVALUATION ...... 117 PHASE EQUILIBRIUM FOR DESIGNING COST-EFFECTIVE PCMS FROM BLENDS ...... 118 SUSTAINABLE TES WITH PCMS...... 119 SPECIFIC THESIS CONTRIBUTIONS ...... 120 CONCLUSIONS ...... 123 FUTURE WORK ...... 125 GLOSSARY ...... 127 REFERENCES ...... 131

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Index of Figures Figure 1-1 Hand-warmers using PCMs ...... 2

Figure 2-1. Typical phase diagrams of binary systems of PCM-interest: a) an isomorphous system with a congruent minimum melting solid solution; b) an isomorphous system with a congruent maximum melting solid solution; c) a partially isomorphous system with a congruent minimum melting solid solution; d) a partially isomorphous system containing a eutectic; e) a partially isomorphous system containing a peritectic; f) a partially isomorphous system containing congruent melting compounds (also with eutectic and peritectic compositions); g) a non-isomorphous system containing a eutectic; h) a non-isomorphous system containing a peritectic; and i) a non-isomorphous system containing a congruent melting compound (also with eutectic and peritectic compositions) (Based on [31], [41], [53], [54], and [60])...... 9

Figure 2-2. The peritectic Glauber Salt in the Na2SO4-H2O system (based on [24], [40], [42] and [67]) ...... 14

Figure 2-3 Summary on phase equilibrium studies of the literature surveyed (1977 to 2015) on PCM TES design per, (a) phase change characteristics categories and, (b) material categories...... 15

Figure 2-4. PCM-potential of fatty acids blends (Eutectics-E, and Peritectics-P, found, with their temperatures plotted against available melting enthalpies) ...... 17

Figure 2-5. PCM-potential of alkanes blends (Eutectics-E, Peritectics-P and Isomorphous congruent minimum melting solid solutions- ICM found, with their their temperatures plotted against available melting enthalpies) ...... 19

Figure 2-6. PCM-poetntial of other organic blends (excluding fatty acids and alkanes), and the only organic-inorganic blend evaluated. (Eutectics-E, Peritectics-P, Isomorphous congruent minimum melting solid solutions- ICM, Isomorphous congruent maximum melting solid solutions- ICMx, and Congreunt melting compounds-CC with their their temperatures plotted against available melting enthalpies) ...... 21

Figure 2-7. PCM-potential of salt hydrates shown in: a) all potential points, and b) enlargement of those between -30 to 90 °C which lack the enthalpy data (Eutectics-E, Peritectics-P, Hypo-peritectic compositions- Hypo-P, and Congreunt melting compounds-CC with their their temperatures plotted against available melting enthalpies)...... 26

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Figure 2-8. PCM-potential of salts blends (Eutectics-E, Peritectics-P, Isomorphous congruent minimum melting solid solutions-ICM and such with miscibility gaps-pICM, with their their temperatures plotted against available melting enthalpies) ...... 27

Figure 2-9. PCM-potential of metal alloys (Eutectics-E, and Congreunt melting compounds-CC, with their their temperatures plotted against available melting enthalpies) ...... 28

Figure 2-10. PCM-interesting characteristics within various blends (numerous organics, and even a salt system: LiCl-CaCl2) found presented by several non-PCM studies, with a) all potential points, and b) enlargement of those between -40 to 110 °C which lack the enthalpy data ...... 30

Figure 2-11. The solidus and the liquidus representation on the melting and freezing temperature-history curves, with (a) temperature-history, (b) phase diagram ...... 34

Figure 3-1. Characterization of a eutectic and a peritectic, in a complex phase diagram (above), using a Tammann plot (below), with the surrounding curves (a)-(d) indicating the corresponding typical cp profiles during heating (Adapted from Rycerz et al. [206]) ...... 43

Figure 3-2. The T-history set-up used (Left: a photograph, Right: a schematic) ...... 46

Figure 3-3. The variation of enthalpy (H) and Gibbs free energy (G) with temperature for the solid and liquid phases of a pure metal. (Here, L: latent heat of melting, Tm: equilibrium melting temperature) (Redrawn based on [55])...... 54

Figure 3-4. The phase diagram derivation (shown in (d)) of a system with a miscibility gap in the solid region, using the Gibbs free energy diagrams for the system at temperatures (a)T1, (b)T2 and (c)T3 (Redrawn based on [55])...... 54

Figure 4-1. The chemical structures of erythritol and xylitol ...... 68

Figure 4-2. The specific heat profiles evolution of the erythritol-xylitol system for the pure and many blend compositions, for chosen melting cycles. (Here, the cp axis uses arbitrary units (a.u.), and the profiles are shifted by 10 a.u. intervals for illustrative clarity. The gap between the minor gridlines nevertheless is similar to 4 kJ/(kg·K). M1-M4 indicate the 1st to 4th melting, while Er is erythritol and Xy is xylitol) ...... 71

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Figure 4-3. The phase diagrams of the erythritol-xylitol system, comparing: the selective average (over 2nd-4th melting), with a) first melting, and b) each 2nd-4th cycles, respectively (The expanded uncertainties of the temperature and composition are 0.4 ºC and 1.3 mol% Er respectively, with 0.95 confidence)...... 73

Figure 4-4. Tammann plots summary of the erythritol-xylitol system, comparing the selective average of 2nd-4th melting (in a dashed-line), with each melting cycle, 1st-4th (in dotted-lines) ...... 76

Figure 4-5. HTXRD characteristics of 5 and 95 mol% Er samples, with the erythritol (Er) and xylitol (Xy) characteristic peak positions indicated by arrows...... 78

Figure 4-6. Slow-XRD characteristics on 80 mol% Er sample (xylitol peaks denoted by arrows) ...... 79

Figure 4-7. FESEM micrographs of a) 5 mol% Er, b) 95 mol% Er, and, c) 80 mol% Er specimens, which underwent: long-term annealing (a) 1, b) 1,2, and c) 2; short-term annealing (c) 1; and quench-annealing (c) 2, after the T-history cycling...... 80

Figure 4-8. The proposed erythritol-xylitol phase diagram: a partially isomorphous system with a eutectic ...... 82

Figure 4-9. Sensitivity analysis of the enthalpy uncertainty against the temperature uncertainty ...... 84

Figure 4-10. The cp profiles for melting and freezing, of the examined C12-C13 compositions for chosen cycles (Here the cp is shown using arbitrary units (a.u.), at 50 a.u. intervals- which are nevertheless similar to 50 kJ/kg·K- for illustrative clarity) ...... 89

Figure 4-11. The C12-C13 system’s (a) Tammann plot for the ‘probable eutectic’ during heating compared with, (b) the phase diagrams for freezing and melting. (The expanded uncertainties with 0.95 confidence for temperature, enthalpy and composition are: 0.4 °C, 10% and 0.013) ...... 90

Figure 4-12. The phase diagram proposal for the dodecane-tridecane binary system ...... 92

Figure 5-1. The specific heat of solid (BCC) and liquid erythritol in the full temperature range of stable and metastable states ...... 100

Figure 5-2. The molar enthalpy (Hm) variations of erythritol (solid: BCC, and liquid) with reference to room temperature ...... 100 xxv

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Figure 5-3. The specific heat of solid (FCC) and liquid xylitol in the full temperature range of stable and metastable states ...... 101

Figure 5-4. The molar enthalpy (Hm) variations of xylitol (solid: FCC, and liquid) with reference to room temperature ...... 101

Figure 5-5. The thermodynamically optimized erythritol-xylitol phase diagram (BCC is the crystal structure of the stable solid phase of erythritol or its solid solution SEt, and FCC is the stable solid phase of xylitol or its solid solution SXy). For comparison, the calculated results in literature are also plotted using dotted-lines: in green the liquidus and solidus from the modified UNIFAC model by Diarce et al. [93]; and in magenta the liquidus from the ideal solutions approach by Del Barrio et al. [97]...... 102

Figure 6-1. Erythritol production process: potential adaptation alternatives for cost reduction ...... 107

Figure 6-2. Specific heat characteristics of olive oil (S1) during (a) heating and (b) cooling; and (c) the temperature profile of olive oil (S1) during cooling, showing slight supercooling...... 110

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Index of T ables Table 1-1 Outline of the Papers complying with the Research Objectives .. 5

Table 2-1. The eutectics proposed in some example systems, along their composition, temperature and enthalpy change (NA: not available) ...... 13

Table 3-1. Experimental techniques employed in phase equilibrium determination and verification in the PCM-context (PC: phase change, temp: temperature, h: enthalpy, cp: specific heat) ...... 39

Table 3-2. T-history procedural differences between this work and Chiu and Martin [209] ...... 46

Table 3-3. Thermal properties of the reference and the sample holder materials ...... 47

Table 3-4. Operating conditions for the XRD tests conducted ...... 50

Table 3-5. The employed theoretical phase equilibrium study methodologies in the PCM-context ...... 56

Table 4-1. Literature-based thermal properties and crystallography of dodecane and tridecane ...... 86

Table 4-2. The comparison of the pure components’ obtained thermal properties with literature ...... 91

Table 6-1. Simplified economic analysis of a batch production process of erythritol (adapted from ethanol production [290]) ...... 107

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Saman Nimali Gunasekara

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES Introduction

Climate change is no longer imminent but eminent, as also acknowledged by the Intergovernmental Panel on Climate Change (IPCC) [1]. At the Paris Climate Conference (COP21) in December 2015, 195 countries agreed upon a universal and legally binding climate treaty to limit the global warming to only 2 ºC from today’s levels [2]. Energy-related anthropogenic activities, largely owing to fossil fuels combustion, have a major effect on accelerating climate change. Better energy management, improved energy efficiencies, and the utility of renewable energies in the energy mix are therefore valued as never before.

In that, thermal energy storage (TES) plays a key role, for example: through better energy management and increased efficiencies by means of storing industrial excess heat or cold (e.g. [3]-[10]); and by meeting the energy demands at different locations or time (e.g. [3], [4], [11]-[13]) thus alleviating CO2 emissions ( [14], [15]). It can also be the storage of heat of a concentrated solar thermal power plant for power production at night (e.g. [16]). With TES, load shifting and peak shaving can be achieved ( [17]-[20]) permitting financial benefits for the right type of electricity tariff, on top of emissions reduction.

Phase change materials (PCMs) are one attractive material category for TES, that change phase from solid to liquid and reverse and thereby store latent heat of fusion. The ice-water system is the oldest and the most- abundant PCM. For applications at temperatures other than 0 ºC, different PCMs are needed. PCMs, with large storage densities and the ability to regulate the temperature of the storage using the narrow phase change temperature window, are competitive against sensible TES. Commercial- ized applications of PCMs include e.g. hand-warmers [21], [22] (c.f. Figure 1-1), and pharmaceuticals transportation container insulations [23].

Even with numerous commercialized PCMs, there are still several material challenges to address such as, phase separation, supercooling, and material cost. Supercooling reduces the expected storage capacity, as the latent heat is replaced by an increased portion of sensible heat, with poor temperature regulation. Phase separation compromises the robust functionality of the TES, as the separated material often does not fully recom-

Saman Nimali Gunasekara bine. Several preventive solutions exist to lower the supercooling by ini- tiating the crystallization by adding nucleators [24], [25], or using Peltier elements [24], and to lessen the phase separation effect by mixing, gelling and/or thickening [24], and micro/macro encapsulation, e.g. [26]-[29]. Nevertheless, these phenomena could be avoided by considering the fun- damentals of phase change in the design of materials, something that is presently not common. With such an understanding, the PCM-ideal blends within e.g. natural blends or chemical-industrial by-products can be distinguished, despite their complex phase change. This will lower the cost of the PCM, and thus facilitate the commercial use of this storage technology.

Figure 1-1 Hand-warmers using PCMs

Understanding phase equilibrium evaluations is one key aspect in manag- ing the phase change complexities of blends. A phase diagram is a pow- erful tool to visualize a system’s phase equilibrium behavior. It indicates the number of phases that exist in a blend system and at which temperature intervals, plus the composition and the proportion of all the phases [30]. To use a blend as a PCM, only the compositions which have sharp reversible phase changes similar to pure materials are ideal. This means that in a blend system, based on the phase diagram, only congruent melting compositions are ideal as PCMs, while those having pseudo congruent melting (e.g. eutectics) can also be suitable as PCMs. Therefore, to find a PCM out of a blend system, a vital and a compulsory step is the study of its phase diagram.

Hence, in this thesis, the study of phase equilibrium in material blends is introduced as a central part of a newly developed systematic methodology to find ideal blend-PCMs for TES. Using this new methodology in PCM design enables finding cost-effective and technically robust PCM blends, in place of more expensive high-purity components or as those tailor- made for specific applications.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Motivations PCM research has been ongoing for more than four decades. Starting with pure components e.g. from paraffins, and binary systems like salt hydrates, it has evolved to the present context that has a number of commercial applications. However, PCM-based large-scale TES systems are still not common. Then again, the material issues such as supercooling, phase separation and material cost challenge the search for robust PCMs. Pure materials have simpler phase change, but often their high-purity adds to the cost. Blends can be competitive against high-purity components if realized from e.g. natural mixtures or chemical industrial by-products. However, one cannot use such a bulk blend as it is as a PCM, until it is proven to have sharp and reversible phase change for a great number of cycles. This is why a systematic study of blends is of utmost importance. Another advantage of blending is the ability to tailor-make PCMs for specific applications for which pure materials cannot cater to. Rather than an ad-hoc selection of mixtures and attempting cycling tests only to conclude on their robustness as a PCM, a standard methodology is essential.

Hence, a phase equilibrium study, most-conveniently using a phase diagram, becomes very pertinent. In a phase diagram, PCM-ideal characteristics can be identified distinctively from those that are unsuitable (e.g. congruent melting against peritectic, c.f. Chapter 2). Although several text-books and publications have emphasized these facts, a large awareness gap still exists within the applied TES scientific community, as found in the state-of-the-art assessment presented herein (detailed in section 2.2). Despite that, even amongst those who employ phase diagram evaluations for PCM design, to derive the diagram, a lack of standards and agreements on approaches exist (c.f. section 2.2). To address this gap, the experimental and theoretical methods that are used today are evaluated herein (Chapter 3). Based on this analysis, several methods are chosen and detailed for the phase equilibrium investigation of certain chosen systems (sections 3.1.2 and 3.2.3). To exemplify the utility of these chosen methods, also addressing several methodological aspects needing standardization, two selected blend systems are then appraised (erythritol-xylitol and dodecane-tridecane, Chapters 4 and 5). To combine the climate change mitigation contributions with sustainable development, the TES system should fulfill sustainability criteria. Hence, herein the use of renewable and safe materials with potential for cost-reduction, like polyols and olive oil, as PCMs, is also exemplified (Chapter 6).

Aim and Objectives The aim of this thesis is to establish a phase equilibrium evaluations-based systematic design methodology to find cost-effective PCMs in blends for

Saman Nimali Gunasekara

TES. In-line, the following objectives are attempted to be met, so as to cover multi-faceted aspects of instituting such a methodology.

1. Identify and describe the PCM-ideal, as well as unsuitable, blend compositions based on fundamental phase equilibrium characteristics. 2. Comprehensively analyze the state-of-the-art of phase equilibrium-based PCMs design concerning PCM-ideal compositions and material categories, and thereby identify research gaps. 3. Present and critically analyze the state-of-the-art of phase equilibrium determination methodologies employed in the PCM- context, for deriving the phase diagrams experimentally and theoretically. Thereby, select several suitable methods to evaluate certain selected blend systems and describe these methods. 4. Demonstrate the experimental determination of phase diagrams on the selected binary systems: the polyols erythritol-xylitol and the alkanes dodecane-tridecane. 5. Appraise the utility of a chosen theoretical method in predicting the binary phase diagram of the erythritol-xylitol system. 6. Evaluate the material aspects of achieving a sustainable thermal energy storage system using PCMs. 7. Define the key aspects for a systematic design methodology employing phase equilibrium evaluations to design cost-effective and robust PCMs from blends.

Methodology and Scope To appraise the state-of-the-art on phase equilibrium-based PCM design, including the experimental and theoretically methods used, a rigorous sur- vey and critical analysis of the literature was performed. For materials characterizations, polyols and alkanes were chosen, polyols as an emerging PCM-category with renewable origin, and both polyols and alkanes as categories with phase diagram discrepancies in literature. These blends were primarily characterized with the Temperature-history (T-history) method, to determine the thermal properties, melting temperatures, enthalpies and specific heat. In addition, X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) were used to evaluate the physical characteristics of materials (of the polyols), like the crystallography and the microstructural characteristics respectively. Employing these experimental techniques coupled with the analysis of Tammann plots, two experimental phase diagrams were determined. Tammann plots, constructed using thermal properties obtained via T-history, characterize the 4

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES eutectics and the miscibility levels of the blends. The experimental thermal properties of one of these binary systems were optimized by employing the CALPHAD theoretical method using Thermo-Calc software, to propose and thereby to better verify the system’s phase diagram. To put things into a sustainability perspective, certain materials of renewable origin (i.e., erythritol and olive oil) are evaluated for their production, cost-effectiveness and thermal properties as potential PCMs. Finally, as a whole, these various aspects covered in the thesis are put into the context of a systematic PCMs design methodology with phase equilibrium evaluations. The contributions to attain the stated objectives 1-6 (c.f. section 1.2) from each appended paper are identified in Table 1-1.

Table 1-1 Outline of the Papers complying with the Research Objectives Objective Papers

1 I

2 I

3 I, II, III, IV, V, VI

4 III, V, VIII

5 IV

6 II, IX

Thesis Structure In the thesis, the state-of the-art in using phase equilibrium evaluations in the design of PCMs for TES is presented (Chapter 2). This is complemented with a fundamental background on phase equilibrium using binary phase diagrams, distinguishing ideal and unsuitable behaviors, as relevant to PCM design. In addition, a comprehensive literature-review identifying phase change behavior types and material categories as blends that lack PCM-attention is discussed. Then, methodological aspects in deriving phase diagrams in the PCM-context, via a comprehensive assessment of the experimental as well as theoretical methods used in the PCM-context, are detailed (Chapter 3). Given this as a basis, several experimental techniques and approaches and a theoretical method are chosen and detailed (also in Chapter 3). The experimental phase diagrams determination of two chosen binary systems: erythritol-xylitol and dodecane-tridecane,

Saman Nimali Gunasekara employing the experimental techniques detailed in Chapter 3 is exemplified (Chapter 4). This is followed by the theoretical modelling of the phase diagram of the erythritol-xylitol system (Chapter 5). The sustainability aspects of a TES based on the material choices, and such potential choices (e.g. erythritol and olive oil) are investigated (Chapter 6). Then a holistic discussion over the fundamental, experimental and theoretical aspects of deriving the engineering tool- phase diagrams, and using these to select a pure material-like PCM blend is elaborated (Chapter 7). Therein, the key methodological aspects of the systematic design of PCMs from blends, employing phase equilibrium evaluations, are specified (Chapter7). Fi- nally, the key conclusions and the way forward are expressed (Chapter 8).

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES State-of-the-art in Phase Equilibrium-based PCMs Design

A phase diagram is an engineering tool that visualizes a material or a material blend’s phase equilibrium. Phase diagrams depict the phase changing temperature interval, and the number, composition and proportion of phases in equilibrium. Phase diagrams can thus indicate incongruent melting causing phase separation, and even details on metastable states (c.f. section 2.1) formed upon supercooling1 [31]- two undesirable features of many commercial PCMs today. For decades, phase equilibrium has been employed in PCM design, although not with the systematic approach which is the aim of this dissertation. All this work is therefore comprehensively reviewed in Paper I, with highlights from that paper presented in this chapter along with an in-depth discussion on previous work – essential findings and knowledge gaps. This chapter thus addresses the thesis objectives 1 and 2.

The phase equilibrium study of bulk blends, natural or coming as industrial by-products, is the key to determine their PCM-suitability, since they can be cost-effective PCM-alternatives to high-purity materials. In addition, to systematically engineer new PCM blends with a specific desired melting temperature, in-depth phase equilibrium studies are required (e.g. [32]- [39]). The known phase equilibrium characteristics of a certain material facilitate the phase change prediction of unknown materials of similar chemical constitution. This can be very useful in finding new suitable materials, as acknowledged by early-stage research (e.g. [31], [40]-[43]). To present the state-of-the-art of phase equilibrium-based PCM evaluations performed over the years, the following are examples of topics included: evaluating the PCM-suitability [40], [44]; investigating specific material categories, e.g. fatty acids [45], [46], salt hydrates [42], [47], and alkanes [48], [49]; and melting points adjustments [33], [50].

1 As the phase rule and the liquidus, solidus principles are valid also at these metastable states [31].

Saman Nimali Gunasekara

Notwithstanding numerous PCM-interesting findings, a majority of these studies were concentrated on identifying and predicting eutectic blends. On the other hand, some even more PCM-ideal characteristics, like congruent melting solid solutions or compounds, have gained very little attention. Also, the unsuitability of peritectics as PCMs has still not been fully comprehended and described. In addition, the understanding on phase separation and supercooling which can be provided by a phase diagram remains under-utilized, and blends displaying these issues are instead managed with additives or other preventive measures. Therefore, there is a need for a systematic approach in selecting PCM blends through addressing the material issues from a fundamental phase equilibrium point-of-view.

P hase Equilibrium- Theoretical Background for PCM Design Herein, the existing general phase equilibrium studies e.g. [30], [41], [51]- [59], are complemented by explaining the phase equilibrium-based knowledge into the PCM-context.

The simplest material system is a pure component, displaying reversible phase change at a specific temperature (or an extremely narrow range). Blends contain several components, and often tend to change phase within a wide temperature range. The simplest blend is a binary system (i.e., contains two components). Thus, a multicomponent study starts with binary phase equilibrium assessments, and is the main focus of this work. Certain phase change characteristics of blends are perfect as PCMs, which exhibit reversible phase change at a specific temperature, like a pure component. Such PCM-ideal (i.e., perfectly suitable as a PCM) characteristics in binary systems are concisely presented along nine typical binary phase diagrams, as outlined in Figure 2-1. All the systems in Figure 2-1 are completely miscible in the liquid state, and are condensed systems considered at constant (atmospheric) pressure and ignoring the vapor phase.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Miscible liquid Miscible liquid A+ B Miscible liquid A+ B A+ B

Temperature S Temperature Solid solution Temperature S S A + B Solid solution Solid solution A + B A + B Solid A + Solid B

0 XB, Component B 1 0 XB, Component B 1 0 XB, Component B 1 1 XA, Component A 0 1 XA, Component A 0 1 XA, Component A 0 (a) (b) (c)

SA3B + Miscible Liquid Liquidus Tm,A CC Miscible liquid Miscible Liquid Liquid A+B A+ B A + B Solidus SAB + Liquid SA+ Liquidus SA + Liquid Liquid CC TmA TP Solid P SA3B Solidus E SB+ Solution Liquid + Liquid Temperature E Solid SAB Solid SA Solid SB SA3B P T solution S E solution Solution SA T A E + Solidus SB Solid m,B SB + TmB + SAB SB SA Solid Solution SAB Solid solution S + Temperature SA+

A Temperature SB Solution SB SA3B 2 Solid solution SB B 3 A AB AB

solvus SAB4 X1 X X2 XE P XE1 X1 XE2 X2 XP X4 0 X , Component B 0 1 B 1 XB, Component B 0 XB, Component B 1 1 XA, Component A 0 1 XA, Component A 0 1 XA, Component A 0 (d) (e) (f)

Miscible Liquid Miscible liquid Tm,A Miscible Liquid TmA A+B A+ B A+ B Solid A CC TCC Solid A + + Liquid Solid Solid B Solid A Liquid + Liquid TP P AB + Solid B Solid B + Liquid + Liquid Liquid Solid AB E Solid P TE1 + Liquid Tm,B E + Liquid TE + Liquid P Temperature AB TP P TE Solid A + Liquid + Solid A E Solid T Solid AB3 mB Solid A + Temperature + Solid P Solid B Solid AB AB + TE2

Solid B Temperature + Solid P Solid E

3 Solid B +

AB3 AB Solid AB3

XE XP X1 XE XE1 X1 XP X2 XE2 0 XB, Component B 1 0 XB, Component B 1 0 nB, Component B 1 1 XA, Component A 0 1 XA, Component A 0 1 nA, Component A 0 (g) (h) (i)

Figure 2-1. Typical phase diagrams of binary systems of PCM-interest: a) an isomorphous system with a congruent minimum melting solid solution; b) an isomorphous system with a congruent maximum melting solid solution; c) a partially isomorphous system with a congruent minimum melting solid solution; d) a partially isomorphous system containing a eutectic; e) a partially isomorphous system containing a peritectic; f) a partially isomorphous system containing congruent melting compounds (also with eutectic and peritectic compositions); g) a non-isomorphous system containing a eutectic; h) a non- isomorphous system containing a peritectic; and i) a non-isomorphous system containing a congruent melting compound (also with eutectic and peritectic compositions) (Based on [31], [41], [53], [54], and [60]).

Saman Nimali Gunasekara

Binary solid systems typically consist of one or more of the characteristics: 2 3 solid solutions , eutectic and compound [61]. The most PCM-ideal of all are congruent melting compositions, respectively forming a solid solution (e.g. Figure 2-1 a)-c)) or a compound (e.g. the points CC in Figure 2-1 f) and i)). By definition, congruent melting is when all the solid and the liquid phases in equilibrium have the same composition [31]. Eutectics (points E in Figure 2-1) d), and f) to i)) are also ideal as PCMs, if no supercooling occurs. A eutectic contains two solid phases in equilibrium with the liquid, and if one of the solids supercools, phase separation occurs due to their compositional differences. This is clearly identifiable by applying the lever rule4 on the phase diagram for the supercooled phases. Peritectics (points P in Figure 2-1) e), f), h) and i)), are already in use as PCMs (e.g. Glauber Salt), even though they are unsuitable as PCMs. This is because, a peritectic will always supercool (due to solidification with ‘coring’), and consequently will always phase separate (due to compositional differences) [31]. All these characteristics are further detailed in sections 2.1.1-2.1.3. The distinction of these phase change characteristics, e.g. congruent melting from a eutectic, is quite important for PCM design. For instance, supercooling causes phase separation in a eutectic, but not in a congruent melting composition.

The degree of solid-state miscibility of the components determines the systems’ level of being isomorphous. Isomorphous means that all components are completely mutually miscible in liquid and solid states [31], [51]. A system completely miscible in the liquid state, is isomorphous when the components are completely miscible in the solid state, and is non-isomorphous when they are completely immiscible. Then, those having partial miscibility are partially isomorphous. The isomorphous level of the system, specified by the solid-state miscibility, already indicates PCM-prospects of a blend system. For instance, a non-isomorphous system will always have at least one eutectic [31], thus at least one PCM-ideal point.

Phase diagrams represent the stable equilibrium of systems. A system can exist in stable, metastable or unstable equilibrium. Stable equilibrium is

2 A solid solution contains at least two types of atoms, where the solute occupies the solvent lattice, while retaining the solvent crystal structure. Its composition is homogeneous [62], [63], but the atoms’ spatial arrangement is variable [31], [62]. A solution is a single phase made of more than one component, while a mixture is a material containing more than one phase [61], [64]. 3 In a compound, atoms of more than one element are chemically bonded in fixed stoichiometry (this varies in a solid solution), and arranged in a characteristic lattice [62]. 4 See e.g. Callister and William (pages 261-262) [30].

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the lowest Gibbs free energy state. Metastable equilibrium is a local minimum in Gibbs free energy [30] and needs additional energy to reach stability [53]. Unstable equilibrium requires no additional energy to reach stability or metastability [53]. Comprehending metastability is vital to understand peritectics (a metastable phase [30], [31]), and other nonequilibrium phase changes. In standard literature (e.g. [30]) the term nonequilibrium refers to any equilibrium state other than the stable equilibrium state. Stable equilibrium is usually attained with extremely slow heating and cooling rates, while the application-rates are often faster, giving rise to metastable phases. Such metastabilities include the phase change shifts to lower temperatures in cooling (supercooling) and to higher temperatures in heating (superheating) [31].

2.1.1 Congruent Melting Systems During congruent melting, a single liquid phase is formed out of a single solid phase, which is either a solid solution or a compound. These solid and liquid phases, in equilibrium at the congruent melting point, have the same composition [31]. Congruent melting compositions are ideal as PCMs, melting at a specific temperature (in reality an extremely narrow range), with no phase separation.

A congruent melting solid solution can exist at a temperature minimum (e.g. Figure 2-1 a) and c)), or a maximum (e.g. Figure 2-1 b)). This solid solution is characterized by the tangential intersection of the liquidus 5 and solidus 6 curves at the congruent melting point. The congruent maximum melting solid solutions are however rare [31]. Here, the systems a) and b) in Figure 2-1 are isomorphous, while c) is partially isomorphous due to the immiscible region (i.e., a miscibility gap, the darker region) at lower temperatures. The alkanes system pentadecane-heptadecane [36], is an example of an isomorphous congruent minimum melting system, congruently melting at around 12.5 mol% Heptadecane and 8 °C.

A congruent melting compound always exists at a temperature maximum. The partially isomorphous system in Figure 2-1 f) contains two congruent melting compounds: A3B and AB, at the compositions X1 and X2 respectively. A completely stable compound, with no dissociation in the liquid state, is formed at a temperature maximum at which the liquidus curves intersect at an acute angle [31]. The narrower the angle, the more stable the compound [31]. The non-isomorphous system in Figure 2-1 i) forms

5 The locus of temperature points at which alloys of various compositions begin freezing upon cooling, or finish melting upon heating [57]. 6 The locus of temperature points at which alloys of various compositions finish freezing upon cooling, or start melting upon heating [57]. 11

Saman Nimali Gunasekara

a congruent melting compound AB at the composition X1. As an example, the salt-hydrate system Mn(NO3)2-H2O [65], contains two congruent melting compounds: Mn(NO3)2·6H2O, Mn(NO3)2·4H2O. These melt at the approximate temperatures, 26 °C and 38 °C, with the melting enthalpies 140 kJ/kg and 120-126 kJ/kg respectively [65]. These systems (Figure 2-1 f) and i)) in addition also contain eutectics and peritectics, as further detailed in sections 2.1.2 and 2.1.3.

2.1.2 Eutectics Eutectics are not congruent melting by definition [30], [31], as they contain solids of different compositions in equilibrium with the liquid. These solids however form in an intimate mix, and therefore their combined composition is the same as the liquid. Hence, in the absence of supercooling, eutectics behave similar to congruent melting. This is often the case, and such eutectics are PCM-ideal [31]. But, if one of the solids supercools, while the other solidifies, such eutectics are not PCM-ideal. This is because, upon supercooling, phase separation occurs due to their compositional differences. Although the reasons why a eutectic may supercool are not exactly apprehended, the consequent phase separation is understood using the lever rule on the supercooled phases in the phase diagram.

The systems displaying eutectics (points E) in Figure 2-1 are: d), f), g), h) and i), where d) and f) are partially isomorphous and the rest non-isomorphous. The non-isomorphous eutectics are the most abundant, compared to any other type [31]. Eutectics do not occur in isomorphous systems, and conversely, congruent melting solid solutions do not occur in non- isomorphous systems. A system containing merely a eutectic as in Figure 2-1 d) or g) is also called a ‘simple eutectic’ [54], [55]. In such, the eutectic solid in fact is a physical mixture of: the two pure solid components in a non-isomorphous system (e.g. Figure 2-1 g)), or the two terminal solid solutions in a partially isomorphous system (e.g. SA and SB in Figure 2-1 d)).

Non-isomorphous systems are unique, as they will always contain at least one eutectic [31]. This is caused by the complete immiscibility of the two components, which lowers the melting point of each other. Nevertheless, a special case of this otherwise general rule also exists, in monotectics (e.g. [64]). In a monotectic, the expected lowest melting point of the blend coincides with that of the lower melting pure component. Therefore the solidus is horizontal while the liquidus starts from the lower meting component and increases monotonously towards the higher melting pure component, in a non-isomorphous system [64].

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Eutectics are found in abundance. Table 2-1 summarizes several binary organic and inorganic eutectics and their properties. In Table 2-1, the systems maltitol-water and lauric acid-1-tetradecanol are non-isomorphous simple eutectic type. Whereas, the other systems shown there, each contain a peritectic in more complex phase diagrams. The Mn(NO3)2-H2O system contains three eutectics as well as two congruent melting compounds (c.f. section 2.1.1).

Table 2-1. The eutectics proposed in some example systems, along their composition, temperature and enthalpy change (NA: not available) System Eutectic characteristics Sources Composition Tempera- Enthalpy (w/w% or mmol%) ture (°C) change (kJ/kg) Mn(NO3)2- 42, 65, 78 Mn(NO3)2 -35, 25, 25 NA [65] H2O Maltitol-water m3-5 maltitol -19 NA [66] Na2SO4-H2O 4.5 Na2SO4 A bit below 0 NA [24], [40], [42], [67] Lauric acid-1- 57, 59 1-tetradecanol 24, 26-28 161, 163 [68], [69] tetradecanol Stearic-lauric m85-86 lauric 34 152 [70]

2.1.3 Peritectics In a peritectic transformation, a solid and a liquid transform into a solid compound [55]. Peritectics form metastable phases, and undergo incongruent melting, yielding phase separation [30], [31], [55]. In Figure 2-1, the partially isomorphous systems e), f) and the non-isomorphous systems h) and i) all contain peritectics, denoted with P. In practice, peritectic transformations hardly reach completion [30], [55], as they undergo nonequilibrium freezing caused by coring. With coring, upon solidification of the melt, an increasingly higher melting-point core is encircled by layers of lower melting-point material [31]. Thus the melt needs to be cooled increasingly below the expected freezing point. This causes supercooling, and thus hinders reaching equilibrium. Therefore, a peritectic freezes over a temperature range instead of at a definite temperature, in- stigating phase separation both on a crystalline and a bulk scale [31] (due to the consequent compositional differences, as the phase diagram shows).

One or more peritectics are common in many complex phase diagrams [31]. However, partially isomorphous systems with merely a peritectic as in Figure 2-1 e) are not as common. In a non-isomorphous system, even if peritectics may exist, at least one eutectic will always exist [31]. The Na2SO4-H2O system is such an example with a peritectic and a eutectic ( [24], [40], [42], [67]), as shown in a conceptual phase diagram in Figure 2-2. There, the peritectic compound Na2SO4·10H2O (Glauber salt) exists

Saman Nimali Gunasekara

at around 32 °C and about 43 w/w% of Na2SO4, and the eutectic exists at around 4.5 w/w% of Na2SO4 and a temperature slightly below 0 °C. As a peritectic, Glauber salt is unsuitable as a PCM, despite the fact that it has been implemented as a PCM for years ( [71]-[73]).

60 Liquid Solution + 50 Liquid Solution Solid Na2SO4

40 Peritectic

° C ) temperature ( 30

20 Solution Liquid Solution + Solid Na2SO4.10H2O + + Ice Solid Na SO 10 Solid Na2SO4.10H2O 2 4 Temperature

Composition of 0 Ice + Eutectic + Na2SO4.10H2O Eutectic (compound) -10 Solid Na2SO4.10H2O 0 10 20 30 40 50 60 70 80 90 100 Weight % of Na2SO4 Figure 2-2. The peritectic Glauber Salt in the Na2SO4-H2O system (based on [24], [40], [42] and [67])

Upon supercooling, the liquid solution and solid Na2SO4 remain even below the peritectic temperature, rather than forming the stoichiometric peritectic compound. As these phases are of different compositions according to the lever rule (see the phase diagram in Figure 2-2, where, the composition of the liquid solution follows the solvus curve while the solid Na2SO4 remains at the pure composition) these will phase separate. In addition, this system experiences inverse solubility effects [24], as implied by the leftward bent liquidus, for compositions higher than about 34 w/w% Na2SO4 at above the peritectic temperature. Due to this, upon further cycling, an increasing amount of Na2SO4 remains insoluble in liquid at higher temperatures, thereby reducing the long-term stability of the material over many cycles of use.

P hase E quilibrium- based PCM D esign: State- of- the- Art For commercial TES applications, pure materials are generally more expensive than bulk blends (e.g. industrial by-products). On one hand, bulk materials come with great opportunities as PCMs. For instance, commercial-grade metals and their binary eutectics [74], or other industrial-grade blends [75], could be used as PCMs for harvesting industrial waste heat [5]. On the other hand, by blending, pure materials can be engineered to

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES fulfill the conditions of specific applications. Hence, multicomponent systems are of major interest for PCM design. Understanding the blend’s complex phase change behaviors necessitates comprehensive phase equilibrium evaluations. Once the phase equilibrium of a material system is comprehended, reasonable predictions on other blends of similar chemical constitution can be made.

This state-of-the-art assessment considered the phase equilibrium evaluations of blends in the PCM-context over the last four decades (1977- 2016). The findings include phase equilibrium characteristics of many solid-liquid PCMs (hereon referred to as PCMs), and of a few evaluated examples on solid-solid PCMs and PCM slurries and dispersions. The state-of-the art of phase equilibrium-based PCM design is classified pro- portionately, in Figure 2-3 a) and b), respectively according to phase change characteristics and material categories investigated.

Figure 2-3 a) indicates that eutectic is the most-investigated phase equilibrium characteristic. Peritectics have had considerable interest, though lack in-depth assessment of their metastability. Congruent melting systems, forming solids solutions (in isomorphous or partially isomorphous systems, c.f. [48], [76]- [79]) or compounds (in partially or non-isomorphous systems, c.f. [42], [65], [80]-[82]) are almost neglected. Hence, a major knowledge gap concerning these PCM-ideal systems exists.

Binary metastables: avoiding Binary organic- Binary congruent Binary metal supercooling inorganic blends Binary isomorphous melting alloys congruent melting compounds

Binary isomorphous incongruent melting Other binary/ ternary organics Binary-quinary Binary non/ partially fatty acids isomorphous Binary polyols incongruents Eutectics (binary- Binary benzenes quaternary) Binary/ Peritectics ternary (binary- Binary-quaternary alkanes ternary) salt hydrates/ salts

(a) (b) Figure 2-3 Summary on phase equilibrium studies of the literature surveyed (1977 to 2015) on PCM TES design per, (a) phase change characteristics categories and, (b) material categories.

As shown in Figure 2-3 b), the salts-based (salts and salt hydrates) systems, fatty acids, and alkanes have had the most attention in literature. The salts-based studies are dominated by CaCl2·6H2O ( [47], [65], [83]- [87]), Na2SO4·10H2O ( [40], [42], [65], [88]), and NaNO3-KNO3 ( [5], [78], [89]- [92]). Fatty acids followed-by alkanes dominate the organics PCM contributions, while other organic categories have had much less

Saman Nimali Gunasekara attention. Polyols are still emerging ( [93]-[97]), whereas organic-inorganic combinations have seen extremely minor interest so far ( [98]). Metal- alloys have experienced a major negligence as PCMs. However, their phase equilibrium is well-ascertained in the metallurgy field (e.g. [99]- [102]) and thus could provide useful insights for PCM design. All these under-investigated categories, e.g. polyols, various organic blends, organic-inorganic blends, and metal alloys all have ample room for PCM explorations.

Complying with one major aspect sought-after in this state-of-the-art assessment, some investigations aimed to obtain a global understanding of a material category as a whole, concerning: fatty acids ( [70], [103]-[106]); alkanes ( [36], [39], [49]); benzenes ( [34], [35], [107]); fatty acid derivatives [108]; n-alkanols [77]; naphthalene and benzene derivatives [76]; and salts and their hydrates [31], [65]. A few have even proposed generic phase diagrams of systems with PCM-ideal compositions ( [31], [41], [43]), put- ting the phase equilibrium evaluations into the PCM-context.

The state-of-the-art is further elaborated below, classified along material categories, and exemplifying lessons to be learnt from studies conducted on both PCM and non-PCM applications.

2.2.1 Organics The organics’ phase equilibrium findings in the PCM-context are discussed here along: fatty-acids (section 2.2.1.1), alkanes (section 2.2.1.2) and, other organics (section 2.2.1.3). The average7 temperatures, and enthalpies (if available) of their PCM-interesting phase change characteristics are compiled into Figure 2-4, Figure 2-5, and Figure 2-6 respectively. (The specific details of these systems are found in Paper I) The only organic-inorganic blend found is also discussed along the ‘other organics’. In these figures, the characteristics that lack the enthalpy data are still plotted along the temperature axis, for comparison.

The other organics constitute of chemically similar and dissimilar blends, and interestingly also contain several congruent melting compounds [80], [82], and solid solutions [36], [39], [49], [76], [109]. Numerous studies on engineering PCM blends have prioritized a temperature criterion (c.f. section 2.2.1.2), using alkanes [36], [39], [49], [109]-[111], and various organics [34], [35], [76], [77], [107], [112]. The distinction of the stable and metastable equilibrium is crucial, as e.g. the stearic acid-acetamide system indicates, exhibiting different phase changes when stable and metastable

7 Considering the simple average of all the values presented per invariant point. 16

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

[82]. Tammann plots (explained in section 3.1.1) are an employed approach ( [44], [69], [103], [105], [106], [113]-[116]), which is quite effective for PCM design to precisely characterize e.g. eutectics and peritectics.

2.2.1.1 Fatty Acids Fatty acids (i.e., carboxylic acids) studies in the PCM-context have so far been concentrated on binary blends ( [33], [38], [45], [46], [70], [103]- [106], [117]-[128], [129] in [130], [131]-[133]), with minor attention on higher-order systems ( [46], [133]). Their PCM design highlights include: phase diagram generalizations for even, straight-chained blends ( [70], [103]-[106]); a methodology for engineering blends with adjustable melting temperatures [33]; and all the PCM-ideal (mainly eutectic) points identified.

As the temperature-enthalpy plot, in Figure 2-4, of the proposed eutectics and peritectics indicate, many of their enthalpies are still unknown (plotted here along the temperature axis). Overall, the reported fatty acid eutectics and the peritectics respectively exist within the temperatures 4-53 °C and 8-57 °C, with the reported phase change enthalpies within 130- 220 kJ/kg, and 84-106 kJ/kg. These fatty acid eutectics thus have potential for cooling and low-temperature TES. The highest enthalpy change of 220 kJ/kg among these (Figure 2-4) is encountered in the lauric- myristic-stearic ternary eutectic, at 30 °C [46].

Fatty Acids Blends E P 240 200 160 120 80 H,E or P (kJ/kg) Δ 40 0 0 10 20 30 40 50 60 70 Temperature (°C) Figure 2-4. PCM-potential of fatty acids blends (Eutectics-E, and Peritectics-P, found, with their temperatures plotted against available melting enthalpies)

Many presented fatty acids phase diagrams however were only preliminary, made of merely a ‘melting points curve’ but no ‘freezing points

Saman Nimali Gunasekara curve’8 ( [46], [117], [118], [124]-[128], [131]-[133]). Hence these cannot confirm the system’s level of miscibility, the shapes of the phase boundaries, and thus their specific characteristics (e.g. the eutectics, or, congruent melting solid solutions or compounds). Besides, it was rarely specified whether these ‘melting points curves’ correspond to the start or the completion of melting, and hence to the solidus or the liquidus. Some studies (e.g., [38], [119]-[123]) proposed ‘potential’ eutectics merely based on melting ranges found for a number of blend compositions and one intermediate, sharp and the lowest, melting point. This is however not as accurate or valid as a phase diagram-based deduction. To confirm the eutectic, a phase diagram must contain all the essential phase boundaries (i.e., the liquidus, solidus and the solvus if it exists).

To engineer fatty acids with adjustable melting points, blending was proposed suitable, exemplified by combining theoretical predictions with experimental data [33]. A generalized phase diagram for even, straight- chained fatty acids was proposed to contain a eutectic and a peritectic [70], similar to Figure 2-1 (h). Another globalized phase diagram was proposed on even, straight-chained fatty acids blends differing by two [103], four [105] and six [106] atoms in the molecules. This contained a eutectic, peritectic, metatectic9, and in addition, polymorphic transitions10 in the systems with less than six carbons difference between the components. Tammann plots (c.f. section 3.1.1), of molar enthalpy versus composition, verified the eutectics and the peritectics. Owing to their broad and systematic approach, these presented phase diagrams ( [103]- [106]) can serve as valuable benchmarks for other PCM fatty acids investigations.

2.2.1.2 Alkanes The alkanes’ (CnH2n+2, i.e., n-alkanes) phase equilibrium evaluations were focused on either, engineering PCM blends prioritizing an application temperature ( [36], [39], [49], [109]-[111], [134]), or selecting PCM-suitable compositions such as congruent melting or eutectic points ( [48], [135]- [139]). Those prioritizing the application temperature sought for compositions that store 95% of the total latent heat within a narrow temperature window. However, the chosen compositions were not always PCM-ideal compositions (c.f. section 2.1), and therefore risk e.g. phase separation. Their thermal cycling purportedly yielded negligible phase separation. This, however, maybe related to the use of commercial-grade materials,

8 and if applicable solvus curves (the phase boundaries for the first solid-solid transformations after melting), and other relevant phase boundaries. 9 A single solid phase transforming into a mixture of another solid phase (of different composition and crystal structure) and a liquid, during cooling [140]. 10 The same chemical substance existing in more than one crystalline form [31]. 18

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES where their impurities may have formed a multicomponent blend composition with less phase separation.

The temperatures and available enthalpies of the proposed PCM-interesting compositions of various alkanes blends from C8H18 to C44H90 are plotted in Figure 2-5. Evidently, only a handful are reported with their determined phase change enthalpies. The alkane eutectics, peritectics, and the isomorphous congruent minimum melting solid solutions occur (Fig- ure 2-5): within the temperatures -60 °C to 35 °C, -22 °C to 82 °C and - 27 °C to 69 °C; with the reported enthalpies within 130-166 kJ/kg, 158- 227 kJ/kg and 170 kJ/kg, respectively. A majority melts within -40 °C to 40 °C. From these, the eutectic in the C14H30-C16H34 system, melting at 2 °C with an average enthalpy of 166 kJ/kg [48], [137], and the ICM point on the C32H66-C36H74 system, melting at 69 °C with an enthalpy of 170 kJ/kg [39] are highlights.

Alkanes Blends E P ICM 250

200

150

100 H,E or P (kJ/kg) Δ 50

0 -80 -60 -40 -20 0 20 40 60 80 100 Temperature (°C) Figure 2-5. PCM-potential of alkanes blends (Eutectics-E, Peritectics-P and Isomorphous congruent minimum melting solid solutions- ICM found, with their their temperatures plotted against available melting enthalpies)

The PCM-ideal isomorphous congruent melting solid solution systems were rare among all the material categories analyzed in the PCM-context. They were found among the alkanes systems: C11H24-C13H28, C15H32- C17H36, C17H36-C19H40 and C32H66-C36H74. These congruent melting compositions, and eutectics of alkanes can serve as potential PCMs for cooling and low-temperature heating.

Systematic evaluations of alkanes ( [49], [109], [134]) identified, common crystal structures respectively in odd and even numbered carbon chains, and that this influences their solid-state miscibility [110]. For instance, the blends of consecutively odd and even alkanes with a higher difference in the number of carbons will be more miscible in solid-state [109]. Com- plete miscibility is possible: for the rotator phases when the components

Saman Nimali Gunasekara have the same stable phase; and for the ordered phases only when the number of carbon atoms between the components differ by two [49]. Many explored n-alkane systems contain polymorphic features, as well as a mesostate [49]. This mesostate is a crystalline state with properties intermediate to that of the normal ordered solid state and the liquid [49]. Many of the studied alkanes systems were either completely or almost- completely isomorphous, with the rest being partially isomorphous. Some isomorphous systems had ascendant phase diagrams, hence which lack congruent melting or eutectic compositions. As a highlight, no presented alkanes system was non-isomorphous.

The C14H30-C16H34 system was explored the most ( [48], [49], [136], [137]), however, with discrepancies among the presented phase diagrams. It was proposed with: a eutectic [137]; an isomorphous congruent minimum melting solid solution [48]; or a eutectic and a peritectic in a partially isomorphous system [49]. This could be a probable confusion between a eutectic in a partially isomorphous system, and an isomorphous congruent minimum melting solid solution. In addition, a general assumption that a blend of components with similar crystal structures will be isomorphous [48], was shown invalid for this system [49]. Nevertheless, the various proposed minimum melting points and the liquidus curves of the C14H30-C16H34 system are comparable. The C12H26-C13H28 system also was proposed differently: with only the liquidus which indicated a maximum melting trend [135], or with a eutectic and polymorphs, using a detailed phase diagram [109]. These confirm that the systematic evaluations of the pure components and their blends coupled with crystallographic and miscibility analyses (e.g. [49], [109], [134]), are crucial for a comprehensive phase equilibrium understanding.

2.2.1.3 Other Organics The phase equilibrium of numerous organics beyond fatty acids and alkanes (hereon referred to as other organics), have been explored as PCMs. These include: alkanols (aliphatic alcohol, CnH2n+1OH) [77]; the derivatives of: β.R-substituted naphthalene [76], benzenes [34], [35], [76], [107], [141], and fatty acids [108], respectively; polyols [93]-[96]; organic salt hydrates [80]; fatty acids with alkanes or alkanols [50], [68], [69], [113], [115], [142]; alkanes-alkanols [44], [112], [143]; ethers-phenyls [144]; and others [82], [114], [116], [145]. The only organic-inorganic blend evaluation found in the PCM-context [98], is also discussed herein. Figure 2-6 com- piles the temperatures and available enthalpies of the eutectics, peritectics, isomorphous congruent minimum melting solid solutions, isomorphous congruent maximum melting solid solutions (ICMx), and congruent melting compounds (CC), in these systems.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

a) Alkanols Blends P b) Benzenes and their E ICM Derivatives, and β.R- P E Substituted Naphthalene ICM Derivatives Blends ICMx

30 40 50 60 70 0 10 20 30 40 50 60 70 80

Temperature (°C) Temperature (°C) c) Fatty Acid Derivatives, Polyols, Polyols-Urea, Organic Salt Hydrates and Organic-Inorganic Blends E CC 400

300

200

100 H,E or CC (kJ/kg) Δ 0 0 20 40 60 80 100 120 140 160 180 200 Temperature (°C)

d) Fatty Acids with Alkanes, Alkanols, Naphthalenes, or Amides; Alkanes-Alkanols; and Ethers-Phenyls E P CC 300 250 200 150 100 H,E or P (kJ/kg)

Δ 50 0 0 20 40 60 80 100 120 140 Temperature (°C)

As in Figure 2-6 c), the blends of fatty acid derivatives, polyols, erythritol- urea, and urea-NaNO3 contain many eutectics, within 17.5-177.5 °C with the enthalpies 121-282 kJ/kg. The investigated polyols contain many eutectics and a few monotectics. The eutectics with the highest available enthalpies among the fatty acid derivatives and polyols exist in the sys-

Saman Nimali Gunasekara tems ethyl palmitate-ethyl stearate [108] and mannitol-galactitol [94], respectively, melting at 18 °C and 156 °C, with the enthalpies 193 kJ/kg and 282 kJ/kg.

Congruent melting compounds (CC) were rare among organics. There- fore, the CC’s in the Pinacone-water system (C6H12(OH)2·6H2O and C6H12(OH)2·4H2O), and in the stearic acid-acetamide system (in (Figure 2-6 c) and d) respectively), are highlights. These melt at the temperatures: 41 °C, 45.5 °C and 66 °C, with the enthalpies: 134 kJ/kg, 302 kJ/kg and 194 kJ/kg, respectively. The Pinacone-water CC’s were referred to as ‘dystectics’ [80] (a temperature maximum of which the occurrence and the degree of phase separation is described by the Gibbs-Duhem equation [146]). A dystectic hence seemingly is any compound.

The eutectics of the blends of: fatty acids with alkanes, alkanols, naphthalenes, or amides; alkanes-alkanols; and ethers-phenyls, (Figure 2-6 d)) occur at the temperatures 6.5-65 °C with the enthalpies between 93-245 kJ/kg. The eutectics with the best enthalpies are found in the systems octadecane-lauryl alcohol [44], stearic acid-decanediol [50], [142], n-octadecane-myristic acid, and n-octadecane-palmitic acid [115], with the melting temperatures and enthalpies respectively: 19 °C, 245 kJ/kg; 64 °C, 236 kJ/kg; 27 °C, 236 kJ/kg; and 27 °C, 238 kJ/kg.

All in all, the congruent melting compositions and the eutectics from these various organics have potential in low to moderately high temperature TES, some with considerable enthalpies.

A systematic assessment of alkanols blends from C15 to C20 [77] yielded congruent melting solid solutions in some isomorphous and partially isomorphous systems, and a eutectic and several peritectics in other partially isomorphous systems (Figure 2-6 a)). Narrow solid-liquid regions within several isomorphous incongruent melting systems were chosen as PCMs [77]. Although these close-to-congruent compositions will have minimal phase separation, they are not completely congruent melting. A systematic investigation of fatty acid derivatives exhibited eutectics in many same-acid based fatty acid derivative blends [108]. The disparate acid’s derivative blends in contrast indicated polymorphism, with eutectics in some, and partially or completely isomorphous solid solutions in some others [108]. Converting natural blends such as fats and oils into PCMs, was proposed by separating them into their single acid derivatives [108]. Along this concept, natural multicomponent bulk blends can be derived into PCM-ideal blends by systematic compositional refinements using their phase diagrams.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Comprehensive experimental and theoretical phase equilibrium evaluations were employed on the systems: alkane-fatty acids [113]; fatty acid- alkanols [69]; and alkanes-alkanols [44], [112], [143], some also combined with Tammann plots [44], [69], [113]. The fatty acid-alkanol systems indicated partial solid-state miscibility, as well as phase changes below the eutectic temperatures which may be metastable transformations that may later revert to peritectics or metatectics [69]. The many eutectics identified in these systems encourage further exploration of dissimilar organic blend systems as PCMs. Such investigations could benefit from the likely trends identified within the analysis here.

2.2.1.4 Concluding Summary on Organics Comprehensive evidence (e.g. [70], [103], [105], [106]) indicates that fatty acids blends deliver eutectics, often accompanied by peritectics and possibly other solid-solid phase changes. These eutectics are ideal as PCMs, in the absence of supercooling. Systematic and comprehensive evaluations are essential for a holistic understanding of a material category’s PCM-potential, as shown for alkanes (e.g. [49], [109], [134]). These investigations confirm that the thermal, crystallographic and miscibility characteristics of the pure components and their blends, collectively, are crucial for a complete phase equilibrium understanding. Alkanes blends are full of PCM-opportunities, including the rare type: isomorphous congruent melting solid solutions. Hence, novel fatty acids blends and alkanes are worth future explorations.

Various other organic systems are rich in PCM-prospects, with: many non-isomorphous eutectics; several isomorphous congruent melting solid solutions; and even a few congruent melting compounds. Some of their enthalpies are however unknown, and should be determined for TES design. Systematic evaluations of miscellaneous organic blends offer valuable insights for PCM design. Such systematic evaluations of materials in ‘families’ (or genres) than as random isolated systems enable better phase change predictions [39]. In organics, these predictions would be associated with their functional groups, which cause molecular interactions forming e.g. van der Waals bonds or hydrogen bonds. Therefore, aiming towards holistic understanding of material categories would greatly benefit PCM design.

A noticeable lack of in-depth exploration of: the systems forming congruent melting solid solutions and compounds; multicomponent systems; the material categories like alkanols, polyols and organic salts; and organic-inorganic combinations, exists. Congruent melting compositions, though were not abundant among organics, are even better than eutectics,

Saman Nimali Gunasekara as they do not phase separate even with supercooling. Exploring chemically dissimilar component blends is of major interest for bulk, cost-effective PCM design, e.g. blended to mimic industrial by products.

2.2.2 Inorganics The inorganic materials’ phase equilibrium studies in the PCM-context are concentrated on salts and salt hydrates, with only a few metal alloy explorations. Salts and metal alloys were hardly ever considered until 2015, where after a renewed interest surged. Numerous inorganic congruent melting compounds are found, however, almost exclusively among salt hydrates, besides one metal alloy system. The studied salts systems in contrast contain two isomorphous congruent melting solid solution systems (NaCl-KCl, and possibly NaNO3-KNO3), also PCM-ideal. The PCM design highlights of these salt hydrates, salts and metal alloys are discussed in the sections: 2.2.2.1, 2.2.2.2, and 2.2.2.3, with their PCM- interesting characteristics summarized in Figure 2-7, Figure 2-8, and Fig- ure 2-9 respectively (with their specific details found in Paper I). In these figures, when the enthalpy data are missing, the points are plotted along the temperature axis for comparison.

2.2.2.1 Salt Hydrates The salt hydrate evaluations consist of: many binary systems ( [40], [42], [47], [65], [83]-[88], [147]-[152]); several ternary systems ( [65], [148], [153]- [157]); and a few quaternary ( [148], [155]) systems. The most frequently studied are the CaCl2-H2O ( [42], [47], [65], [83], [84], [86], [87]) and Na2SO4-H2O ( [40], [42]) systems, where CaCl2·6H2O is studied the most, and exemplifies the degree of benchmark a system can gain. Salt- hydrates have experienced the most PCM-attention among all the material categories. As a whole, around twenty congruent melting hydrates of the salts: Zn(NO3)2, CaBr2, LiClO3, KF, Mn(NO3)2, LiNO3, Ca(NO3)2, Cd(NO3)2, NaOH, Ba(OH)2, Mg(NO3)2, NH4Al(SO4)2, MgCl2, ( [42], [65], [86], [152], [156]) are identified (c.f. Figure 2-7), which are all PCM- ideal. Many of these were proposed within an impressive compilation of binary salt hydrate phase diagrams [65]. These are unique, as congruent melting compounds are a rarity among the other material categories.

Generally, two typical binary salt hydrate phase diagrams exist: one with eutectics together with congruent melting and peritectic hydrates; and the other with a eutectic and a peritectic in a system where the solubility decreases with temperature [31]. Thus, salt hydrates have plenty of PCM- ideal compositions.

A peritectic is technically incongruent melting [83], however close it may be to the congruency, and is a metastable phase (section 2.1.3). Both

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

CaCl2·6H2O and Na2SO4·10H2O (Glauber Salt) are peritectics, and thus are prone to supercooling and phase separation. To minimize the incongruency of these peritectics, the use of a slightly hypo-peritectic compound (i.e., with excess water) was proposed [40], [47], [84], [87]. Thereby, improved thermal cycling was observed in: Glauber Salt using a mixture of 68.2 w/w% Na2SO4·10H2O and 31.8 w/w% H2O [40], and with CaCl2·6.11H2O [47], [84]. Using such a hypo-peritectic composition appears to have potential benefits for peritectics in other systems as well. For reversible phase change with no phase separation in peritectic, it was recommended to [83], [84], [87]: - avoid the metastable compound(s) formation or keep it unstable within the desired temperature range - accelerate the stable phase nucleation while impeding the metastable nucleation. Nucleators make a peritectic salt hydrate more congruent [47], [83], [87], however, only temporarily, as the metastable phases can nucleate if the system is held supercooled long-enough [84].

As Figure 2-7 a) and b) show, the identified salt hydrate congruent melting compounds (CC), eutectics, and peritectics, and a few hypo-peritectic (Hypo-P) compositions, melt within the average temperatures, 6-68 °C, 11-93 °C, -22-205 °C and 29-30 °C, possessing the enthalpies (of those reported) 106-289 kJ/kg, 133-220 kJ/kg, 170-272 kJ/kg, and 244 kJ/kg respectively. From these, the CCs, eutectics and potentially the hypo- peritectics could serve as PCMs for cooling and low-temperature heating. The highest enthalpies among the CC’s and the eutectics respectively are recognized in the compound LiNO3·3H2O (melting at 8 °C with an enthalpy 283-295 kJ/kg [65]) and the Na2CO3·10H2O-Na2HPO4·12H2O system (melting at 27 °C with an enthalpy 220 kJ/kg [157]).

The effects of using exact or marginal compositions of the compounds that melt congruently or close-to-congruently were investigated on the systems CaCl2·6H2O [86] and CaBr2·6H2O [86], [152], respectively. Both compounds indicated noticeable enthalpy decreases (of 11% and 17%), even at slight concentration variations (of about 1%) [86], [152]. The supercooling of the peritectic sodium acetate trihydrate (Na- CH3CO2·3H2O, SAT) was aimed to be used for seasonal TES [150]. There, to achieve stable supercooling, the SAT should be heated above the upper liquidus temperature at the peritectic composition (83 °C) [150], only above which it is fully soluble (c.f. its phase diagram [151], [158]).

Saman Nimali Gunasekara

a) Salt Hydrates E P Hypo-P CC 350 300 250 200 P or CC (kJ/kg) - 150 100 50 H,E, P, Hypo

Δ 0 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 Temperature (°C)

b) Salt Hydrates (enlarged temperature-only points E P -30 to 90 °C) Hypo-P CC

-30 -20 -10 0 10 20 30 40 50 60 70 80 90

Temperature (°C) Figure 2-7. PCM-potential of salt hydrates shown in: a) all potential points, and b) enlargement of those between -30 to 90 °C which lack the enthalpy data (Eutectics-E, Peritectics-P, Hypo-peritectic compositions- Hypo-P, and Congreunt melting compounds-CC with their their temperatures plotted against available melting enthalpies)

A valuable simplification of multicomponent systems’ partial phase diagrams into phase diagrams of lesser components is found ( [148], [154]- [156]). There, e.g. ternary and quaternary salt hydrate systems were simplified to their quasi-binary and quasi-ternary partial phase diagrams respectively. Among these salt hydrates, several ternary simple eutectics [156], and ternary and quaternary eutectics [155] were identified. These prove that considering binary blends is just the start in exploring blends suitable for PCM TES applications.

2.2.2.2 Salts The salts blends (i.e., anhydrous) investigations contain: several binary systems ( [5], [78], [89], [91], [92], [159]-[162]), and a few ternary ( [159], [163], [164]) and quaternary ( [78], [165]) systems. Their PCM-interesting characteristics are summarized in Figure 2-8, along with melting temperatures and enthalpies (if found reported). These include several eutectics, two congruent melting solid solutions (isomorphous: ICM, or with a miscibility gap: pICM), and a few peritectics, within the respective temperatures 123-424 °C, 222-655 °C and 143-360 °C.

The enthalpies of the eutectic salts (c.f. Figure 2-8) vary between 136-190 kJ/kg, with the highest: 190 kJ/kg encountered in a eutectic in the NaCl- 26

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

CaCl2-MgCl2 system at 424 °C [163], [164]. From the congruent melting solid solutions in NaCl-KCl [31], [78], and NaNO3-KNO3 [5], [78], only the melting enthalpy of that in NaNO3-KNO3 was found, on average to be 102 kJ/kg, melting at 222 °C. Although without indicating their phase diagrams, the KCl-NaCl, CaCl2-MnCl2 and CaCl2-SrCl2 were also proposed as forming isomorphous congruent melting solid solutions with an immiscible solid region at a lower temperature [31]. All these eutectics and congruent melting compositions in salts appear attractive for high- temperature TES.

Salts Blends E P ICM/pICM 200

150

100

50 H,E, P, ICMor pICM (kJ/kg)

Δ 0 0 100 200 300 400 500 600 700 Temperature (°C) Figure 2-8. PCM-potential of salts blends (Eutectics-E, Peritectics-P, Isomorphous congruent minimum melting solid solutions-ICM and such with miscibility gaps-pICM, with their their temperatures plotted against available melting enthalpies)

The NaNO3-KNO3 system ( [5], [78], [89]- [92]) dominates the studied binary systems. In contrast, the remainder of the systems (LiNO3-KNO3, NaNO3-NaCl, Ca(NO3)2-NaNO3, AgNO3-KNO3, NaNO3-TlNO3, and NaCl-KCl) were evaluated by only a few studies each. Even though no hypo-peritectic compositions were proposed in place of the peritectics in the salts blends, that would be an interesting follow-up similar to the salt hydrate investigations (section 2.2.2.1). Eutectics were found in the systems NaNO3-NaCl [78], [166], KNO3-KCl [78], and NaCl-CaCl2- MgCl2 [163]. The NaCl-KCl-NaNO3-KNO3 system only contains a peritectic [78], and therefore unsuitable as a PCM.

The NaNO3-KNO3 system was proposed as containing a eutectic [89], but was later proven, comprehensively, to contain a congruent minimum melting solid solution, with a miscibility gap and polymorphs at lower temperatures [78]. This, therefore, is a perfect example of confusing an isomorphous congruent minimum melting system with a partially isomorphous system with a eutectic. A comparison of the experimental eutectic points of the systems LiNO3-KNO3, and LiNO3-KNO3-NaNO3 yielded

Saman Nimali Gunasekara discrepancies and gaps in the error reporting [159]. This is a clear indication of the necessity for a systematic and standardized phase equilibrium appraisals in the PCM-context.

2.2.2.3 Metal Alloys Metal alloys are extremely deprived of PCM-attention, with no own phase diagrams derivations in the PCM-context. Those investigated compose of several binary systems ( [5], [81], [166]-[169]) and a few ternary systems ( [170], [171]). Their PCM-ideal characteristics are summarized in Figure 2-9, indicating their temperatures and enthalpies (when available). These include, a congruent melting compound in the Mg-Bi system melting at 825 °C, though its phase change enthalpy is unknown, and several eutectics: within the temperatures 177-755 °C and having the enthalpies between 104-479 kJ/kg. A eutectic in the Al-Si system, melting at 577 °C, has the highest melting enthalpy of 479 kJ/kg [5] (from those available) among all the PCM-ideal blend compositions recognized within this state- of-the-art assessment.

Metal Alloys E CC 600

400

200 H,E or CC (kJ/kg) Δ 0 0 100 200 300 400 500 600 700 800 900 Temperature (°C)

Figure 2-9. PCM-potential of metal alloys (Eutectics-E, and Congreunt melting compounds-CC, with their their temperatures plotted against available melting enthalpies)

The only metal alloy congruent melting compound found (among the phase equilibrium evaluations in the PCM-context), exists in the Mg-Bi system, together with two eutectics ( [81], [172]). However, to verify its PCM-suitability, the heat of fusion needs to be determined. Interestingly, instead of these PCM-ideal compositions, some intermediate compositions were chosen as potential PCMs [81]. As the phase diagram indicates, these intermediate compositions unfortunately will phase separate. Eu- tectics exist also in the systems: Al-Si [169]; Sn-Pb [166]; Mg-Zn [173]; Cu-Mg-Si [170]; and Mg-Zn-Al [171]. These have potential in high-temperature TES as PCMs e.g. in direct steam generation in concentrated solar power (CSP) plants [167], [168], [171]; or, in a dish Stirling TES system [170].

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

The PCM-ideal compositions in metal alloys are clearly attractive as PCMs for high-temperature TES, with attractive enthalpies, as well as higher thermal conductivities of metals. However, their high melting temperatures also may have been a reason for their lack of PCM-attention so far, also coupled with relatively high price and competition against other metal applications. Metal alloy phase equilibrium is well-comprehended in non-PCM functional areas (e.g. [99]-[102], [174]), which can benefit PCM design, for the emerging high temperature applications.

2.2.2.4 C oncluding Summary on Inorganics Some frequently investigated salt hydrates demonstrate how a comprehensive study enables in-depth understanding of their suitability in PCM applications. The use of hypo-peritectics to avoid phase separation in peritectics is a valuable recommendation, also worth attempting on the anhydrous peritectics. The multitude of salt hydrate systems presented imply a general trend to form eutectic(s), peritectic(s) and most-likely at least one congruent melting compound- i.e., great PCM-prospects. Tech- nical-grade salt hydrates are potentially cheap PCMs, but are essentially multicomponent systems. Phase equilibrium evaluations of multicomponent salt-water systems will significantly aid in realizing these as PCMs.

Salts blends are underinvestigated, despite their attractive melting temperatures for high-temperature applications, large enthalpies, and PCM-ideal characteristics including congruent melting compositions and eutectics. Corrosion of metals is a common issue with most salt hydrates and salts, which needs to be addressed with e.g. smart heat exchanger design. Metal alloys are almost neglected over the past four decades. This is so, in spite of their very attractive melting temperatures, enthalpies, thermal conductivities, and the PCM-ideal compositions: congruent melting compounds and eutectics. Metal alloys and salts are undeniably material categories worth many future explorations for e.g. integrating TES into renewable energy alternatives like CSP.

2.2.3 Phase Equilibrium Knowledge from Non- PCM Studies An abundance of mature phase equilibrium evaluations outside PCM applications (termed non-PCM studies hereon) contain numerous lessons for PCM design. These can complement PCM research to: 1) benchmark PCM phase equilibrium studies against non-PCM studies; 2) complement preliminary PCM findings with available comprehensive non-PCM phase equilibrium findings; and 3) identify PCM-prospects of novel systems.

Saman Nimali Gunasekara

Some non-PCM examples ( [61], [175]-[189]) are discussed here, high- lighting their material and methodological aspects valuable for PCM design. Their eutectics, congruent melting compounds and peritectics are compiled into Figure 2-10 (specific details found in Paper I). Many studies have omitted the heat of fusion, however, their phase diagram evaluations are still insightful. A eutectic in the LiCl-CaCl2 system at 485 ºC [189], could be attractive for high-temperature TES. The many eutectics found within these various organics melt at the temperatures -38 ºC to 104 ºC with the enthalpies 11-184 kJ/kg, with the highest melting enthalpy found on the naphthalene–catechol eutectic at 74 ºC [188]. The organic congruent melting compounds found (Figure 2-10), melt from -18 ºC to 8 ºC, with the (available) enthalpies 243-281 kJ/kg. A CC in the nonan-1-ol- 1,3-diaminopropane system (at -7 ºC) [183] has the largest reported fusion enthalpy among these.

a) Many Organics and the LiCl-CaCl2 System E P CC 300

200

100 H,E P, or CC(kJ/kg) Δ 0 -100 -50 0 50 100 150 200 250 300 350 400 450 500 550 Temperature (°C) b) Many Organics (enlarged temperatre-only points E P -40 to 110 °C)

-40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 Temperature (°C) Figure 2-10. PCM-interesting characteristics within various blends (numerous organics, and even a salt system: LiCl-CaCl2) found presented by several non-PCM studies, with a) all potential points, and b) enlargement of those between -40 to 110 °C which lack the enthalpy data

Fats are renewable and non-toxic, hitherto unexplored as PCMs. They are however, multicomponent blends with complex phase change, mainly composed of triglycerides (triacylglycerols, TAGs) [190]. Fats’ phase change complexities include: metastable liquid crystals (like the meso- states on alkanes [49]) and polymorphism in all long-chain compounds [61]. Among typical binary TAG systems, a partially isomorphous type with a eutectic is of PCM-interest, and is the most common type [190]. This occurs between components that differ in molecular volume and polymorphic structures, but not much in melting points [190]. 30

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

‘Kinetic’ phase diagrams [61], [176] is a concept extremely relevant for TES design, which is frequently used in non-TES applications. Unlike a phase equilibrium diagram, the kinetic phase diagram includes metastable phases triggered by fast heating/cooling rates, which often represent the application conditions. The kinetic and equilibrium phase diagrams of several TAGs [61], [176], and binary sitosteryl ester blends [178] are such examples. The thermodynamic stability of the stable and metastable phases in the TAGs were distinguished related to the heating/cooling rates [61], [176]. The long-chained saturated binary sitosteryl esters contained eutectics [178]. Their shorter chained blends displayed complex behaviors including mesophases11, e.g. a smectic and an exothermic phase [178]. All sitosteryl ester blends exhibited supercooling [178], making their eutectics’ PCM-suitability questionable.

Binary perfluoro-alkanes and n-alkanes blends have displayed solid solutions, eutectics, or a combination of both [177]. As PCMs, the eutectics are suitable, but not the solid solution systems as they are the incongruent melting ascendant type. When the van der Waals length of the taller alkane is larger than the lattice length of the shorter alkane, a non-isomorphous eutectic is formed [177]. When the components have a critical chain-length difference, the phase change is rate-dependent, and forms partially isomorphous systems [177]. PCM design can greatly benefit from these generalizations to predict binary alkanes’ phase change.

Several comprehensive binary fatty acids blends evaluations [64], [179]- [181] provide benchmark for those studied in the PCM-context (section 2.2.1.1). The monotectic systems oleic-stearic and oleic-behenic [64] are exemptions of the general rule that non-isomorphous system always contain a eutectic. A peritectic formation in fatty acids blends was associated with the number of carbon atoms in the pure acids [181]. Several binary fatty acid eutectics underwent phase separation at the stable state [179], hence violating another expectation on a eutectic. These components were partially miscible at the nonequilibrium conditions, and became immiscible when reaching stability upon annealing [179]. This signifies the value of distinguishing stability and metastability in deriving the phase diagrams.

A systematic evaluation of the alkanol-amine systems yielded a general trend of a congruent melting compound between two eutectics [183]. This compound was a consequence of the strong intermolecular interactions between the alcohol and 1,3-diaminopropane [183]. An investigation of effects of high pressure on the liquiduses of the alkanes systems

11 A mesophase is a liquid crystal phase, while A smectic phase is a specific structure of a liquid crystal state (depending on the crystal orientation) [191]. 31

Saman Nimali Gunasekara

C14-C15 and C14-C16 [185], sheds light on the confusions on the C14-C16 system discussed in section 2.2.1.2. The system has a eutectic and a peritectic, together with a rotator (R) phase that is a mesophase [49], [185], and a triclinic phase [185]. The mesophase was stable only between the eutectic and the peritectic, while was metastable elsewhere, and became stable by forming the triclinic phase [185].

Phase Diagrams in PCM design- Concluding Remarks The key to find robust, cost-effective and/or specifically engineered PCMs in blends, is the study of their phase equilibrium. A phase diagram is a perfect engineering tool to visualize a blend’s phase equilibrium. In a blend system, only compositions with sharp and reversible phase change are ideal as PCMs. Thus, only congruent melting solid solutions, congruent melting compounds, or eutectics are PCM-ideal. Congruent melting compositions are the most PCM-ideal, as these, made of a solid and liquid of the same composition, do not phase separate even upon supercooling. Eutectics, are not ‘technically’ congruent melting, as they contain (e.g. in a binary system) two solids in equilibrium with a liquid. Nonetheless, as the solids form in an intimate mix, with a combined composition the same as the liquid, eutectics usually do not phase separate. However, if one solid supercools, the eutectic will phase separate. Hence, in the absence of supercooling, eutectics are PCM-ideal. Peritectics have been already considered as PCMs (e.g. Glauber salt), although they are unsuitable as PCMs. This is because peritectics always undergo supercooling causing phase separation, are metastable, and never reach complete transformation in practice.

This state-of-the-art assessment for 1977-2016 discloses major PCM-attention on eutectics, and considerable attention on peritectics despite their unsuitability as PCMs. In contrast, only negligible attention has so far been dedicated to the PCM-ideal congruent melting solid solutions or congruent melting compounds. Besides, numerous evaluations choosing e.g. hypo- or hyper-eutectic or incongruent melting blend compositions as PCMs exemplify a phase equilibrium awareness gap. In this respect, this state-of-the-art assessment establishes the relevant phase equilibrium facts such as: a eutectic is not the only minimum melting-type blend (could as well be a congruent melting solid solution); the only PCM-suitable minimum melting blend is not a eutectic (could as well be a congruent melting solid solution), peritectics are unsuitable as PCMs; supercooling eutectics are also unsuitable as PCMs (as they will phase separate); and congruent melting compositions are the most-desirable, of all blends, as PCMs.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Salt hydrates, fatty acids and alkanes are the most-frequently evaluated material categories. Salts blends have only had moderate PCM attention, with ample room for explorations. However, the renewable materials like polyols and fats, and metal-alloys which consist of both high melting temperatures and thermal conductivities, are extremely under-investigated. The phase equilibrium evaluations of chemically disparate component blends (organic-organic and organic-inorganic), chosen e.g. to mimic industrial by-products, have a great unrealized potential to unveil cheap and robust PCMs for large-scale TES.

For a share of the numerous potential PCM-ideal points recognized herein, certain TES design criteria such as heat of fusion and thermal conductivity are still unknown. These properties need to be characterized to realize those blends as PCMs. A majority of the known heats of fusion of the PCM-ideal blends lie within 100-300 kJ/kg, with a few even reaching up to 480 kJ/kg (e.g. in metal alloy eutectics). Generally, a fusion enthalpy larger than 200 kJ/kg is attractive, however, the definition of an adequate enthalpy depends on the application. Each application has its own speci- fications on the storage capacity and power. The fusion enthalpy may be sometimes less prioritized over the phase change temperature, thermal conductivity (influencing the heat/cold charging/discharging rate); cost- effectiveness; non-toxicity; non-flammability; or, better stability.

As evidenced within the literature assessment, PCM design has so far experienced very comprehensive to very preliminary phase equilibrium evaluations. To decide the PCM-suitability of a blend, its phase equilibrium must be known comprehensively. For that, the blend’s complete phase diagram must be determined, with all the relevant phase boundaries (e.g., the liquidus, solidus, and solvus if applicable). As the most comprehensive studies indicate, only the combined use of thermal and physicochemical property evaluations can confirm a phase diagram. Phase equilibrium predictions of unknown systems can be achieved with respect to known materials of similar chemical constitution. Thus, effective phase equilibrium predictions are possible only via the systematic evaluations of material categories instead of isolated material systems.

Among valuable PCM design lessons found, the simplification of multicomponent systems into partial systems of lesser components [156], [192], is an effective approximation. Thereby e.g. a ternary system can be presented using quasi-binary phase diagrams. Then, to identify the overall PCM-potential in the complete multicomponent system, all the quasi- phase diagrams should be derived and finally combined.

The heating/cooling rates regulation is vital to derive phase diagrams, as faster rates often trigger metastability. In-relation, a kinetic phase diagram

Saman Nimali Gunasekara is a key concept for applied PCM design, however, not yet employed in the PCM-context. Kinetic phase diagrams include metastable states, thus are constructed using the system’s rate-dependent phase change behavior (i.e., for faster heating/cooling rates). Therefore, the real behavior of a blend PCM under the application conditions can, and should, be mapped in a kinetic phase diagram. Nevertheless, the phase equilibrium diagram of the system must also be determined, to comprehend the system’s standard behavior, and to predict other similar systems.

It was seen within this state-of-the-art assessment that many PCM investigations had an ambiguous distinction of the experimental solidus and the liquidus derivation. Therefore, to clarify, the relevant definition is explained in Figure 2-11. The phase diagram can be constructed using the phase changes during either the heating or the cooling, respectively. There, the start of melting Sh in heating, or the end of freezing Sc in cooling, as in Figure 2-11 a), each corresponds to the solidus, as in Figure 2-11 b). Conversely, the end of melting Lh or the start of freezing Lc in Figure 2-11 a) correspond to the liquidus in Figure 2-11 b). By repeating this for each composition, the complete phase diagram can be constructed.

Liquidus: Miscible liquid End of melting in A+ B heating (Lh)

Start of freezing Liquidus (Lh or Lc) in cooling (Lc)

Lh S Lc Solidus: Temperature h Sc Start of melting in Temperature Solid heating (Sh) Solidus (S or S ) solution h c SAB End of freezing in 0 1 cooling (Sc) Time nA, Component A 1 0 (a) (b) Figure 2-11. The solidus and the liquidus representation on the melting and freezing temperature-history curves, with (a) temperature-history, (b) phase diagram

Systems undergo supercooling more often than superheating, while hysteresis usually entails a lower temperature for freezing. Hence, the heating-based phase diagram is more preferred [31]. Nevertheless, the comparison of the phase diagram for heating and for cooling will better-verify the phase change of the system. For PCM design, it is crucial that the studies distinguish which of the two are represented in their phase diagrams, also because the two options yield rather different temperatures. As identified, many studies only presented the liquidus, which alone has limited value.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

In conclusion, a phase diagram is one of the most effective tools to describe a system’s phase equilibrium behavior. To conveniently use this tool in the applied design of PCMs, a prerequisite is the correct distinction of PCM-ideal phase equilibrium characteristics versus the unsuitable types. This chapter is laying the fundamental basis for such prerequisite knowledge required by a PCM designer. In addition, the categories worth many future explorations: the PCM-ideal congruent melting compositions; as well as materials like metal alloys, polyols and fats; are highlighted herein. For the correct distinction of the phase equilibrium characteristics, a valid phase diagram is indispensable. In-relation, the three succeeding chapters analyze, discuss, and exemplify the multifaceted aspects of comprehensively determining phase diagrams for PCM design.

Saman Nimali Gunasekara

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES Methods for Establishing Phase Equilibrium of PCM Blends

The past four decades encountered numerous phase equilibrium evaluations for PCM design. Although with varying comprehensiveness as identified in Chapter 2, the experimental and theoretical methodologies employed by these evaluations have lessons that can benefit PCM blends design. Along that, this section addresses the thesis objective number 3, synthesizing the methodological aspects of the literature that encompass the Paper I, that are complemented with details from the Papers II-VI. The state-of-the-art of phase equilibrium determination methodologies, categorized into experimental and theoretical aspects (sections 3.1.1, 3.2.1, and 3.2.2), is analyzed here. Thereby, a methodology appraisal is made on the methods that can provide a comprehensive phase equilibrium understanding in combine, to identify the combination that can lead to the most robust knowledge. With this as a basis, certain selected blend systems of PCM-interest were evaluated in this thesis work (later presented in Chapters 4 and 5). The specific methodologies of the employed experimental techniques and theoretical method therein are also detailed in this chapter (sections 3.1.2 and 3.2.3 respectively).

A vast majority of PCM evaluations has determined phase equilibrium employing experimental techniques. Many of these were also complemented with theoretical modelling, using semi-empirical approaches based on the pure components’ experimental data. Comparing the methods is beneficial in standardizing the design approaches. In a nut-shell, many experimental-only evaluations ( [34], [35], [47], [50], [70], [80], [82]- [85], [87], [91], [94], [96], [98], [103], [105], [106], [111], [112], [124], [128], [135]-[137], [142], [145], [153], [156], [157], [159], [160], [193], [194]), as well as many employing both experimental and theoretical evaluations in combine ( [33], [39], [44], [46], [48], [49], [68], [69], [77]-[79], [93], [95], [97], [108]-[110], [113]- [117], [125], [127], [131], [133], [134], [141], [143], [144], [147], [148], [151], [154], [155], [161]-[163], [192], [195]-[197]) exist. This chapter discusses and comparatively analyzes the methodological highlights of these studies (also including a few solid-solid PCM examples). 37

Saman Nimali Gunasekara

Purely theoretical, i.e., ab-initio (first principles [198]) calculations may also be employed for deducing a system’s phase diagram. These however, have not been employed in the PCM-context so far. The ab-initio calculations require extensive efforts, and specific knowledge per system and are purely theoretical. Thus, it may not be the most economical approach in the engineering application of phase diagrams to design PCMs. Hence, ab-initio calculations are excluded in this thesis.

Experimental Phase Diagram Determination Numerous experimental techniques have been employed in deriving phase diagrams of PCM-interesting blends. Their interesting methodological aspects are concisely highlighted, and their insights to derive correct phase diagrams are analyzed, in section 3.1.1. Thereby, several techniques were chosen to study two chosen blends of PCM-interest in this thesis work. The methodologies of these chosen techniques are described in section 3.1.2.

3.1.1 Experimental Methods : State- of- the- Art The experimental techniques employed in deriving the phase diagrams of numerous blends of PCM interest are summarized in Table 3-1. These techniques characterize either the thermal, physical, or the chemical properties of materials. The thermal properties include: the melting and freezing temperatures and enthalpies; the material’s specific heat (cp) variations; and thermal degradation effects. The physical characteristics are such as: crystallography (structures and crystallization rates); phases and solid-sate miscibility details; morphologies, and microstructures. The chemical characteristics include: chemical structural changes and degradation, and compositions, among others.

The evaluations over the years have employed at least one thermal property characterization technique. DSC is the most-employed, while a considerable fraction has employed in-house calorimetric apparatuses. These include: thermostat-based own apparatuses ( [36], [87], [92], [127], [135], [137], [148], [154], [155], [159]), non-stirred continuous thermal methods ( [47], [82]-[84], [87]), and the T-history method ( [50], [151], [156], [194]). All these calorimetric techniques characterize the melting/freezing temperatures, enthalpies, and specific heats.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Table 3-1. Experimental techniques employed in phase equilibrium determination and verification in the PCM-context (PC: phase change, temp: temperature, h: enthalpy, cp: specific heat) Thermal Property Evaluation Techniques (and Measured Materials Sources Characteristics) DSC (Differential Scanning Calorimetry) Fatty acids/ alkanes/ alkanes-monohydric alco- [33], [38], [46], [70], [103], [105], [106], [117], [120]-[123], (PC temp, h, cp) hols/alkanes-fatty acids/ fatty acid derivatives/ [125]- [127], [131], [133], [145], [199]/ [36], [39], [48], [49], benzene derivatives/ alkanes, fatty acids, alcohols [79], [109]- [111], [134]- [138]/ [44], [112]/ [113], [115]/ blends/ fatty alcohols (alkanols)-fatty acids/ salt hy- [108]/ [35], [76], [107], [141]/ [50]/ [68], [69], [142]/ [78], drates, salts/ organometallics/ polyols/ other or- [91], [92], [147], [148], [153], [155]- [157], [159], [163], [192], ganics/metal alloys/ organic-inorganic blends [194], [195], [197], [200]/ [201]/ [93]-[96], [144], [202], [203]/ [76], [77], [82], [114], [116], [143]/ [167], [168]/ [98] Thermostat-based own calorimetric apparatuses (PC temp, h, c p) Alkanes/ fatty acids/ salt hydrates, salts [36], [135], [137]/ [127]/ [87], [92], [148], [154], [155], [159] Non-stirred continuous thermal methods; Conventional cool- Salt hydrate/ other organics [47], [83], [84], [87], [153]/ [82] ing curves (PC temp) T-history (Temperature-history) method Salt hydrates/ alkanes-fatty acids, alkanes-monohy- [151], [194]/ [50]/ [156] (PC temp, h, c p) dric alcohols, fatty acids-diols/ organic salt hydrate TGA (Thermogravimetric Analysis) (mass changes with temp) Fatty acids/metal alloys/ other organics [117]/ [167], [168]/ [114] STA (Simultaneous Thermal Analyzer); DTA (Differential Salts [78], [160]-[162] Thermal Analysis); STA-DTA (PC temp) MPA (Melting Point Apparatus); Binocular microscope MPA Salts/fatty acids [92]/ [46] (PC temp) Visual polythermal; synthetic method using thermal sensors Fatty acids/ other organics/organic-inorganic [145]/ [116]/ [98] with samples in thermostat-baths (PC temp) blends IRT (Infra-Red Thermography) method (PC temp) Polyols [95], [97] Physical/Chemical Characterization Techniques (and Materials Sources Measured Characteristics) XRD (X-Ray Diffraction) Benzene derivatives/ alkanols-fatty acids/ polyols/ [76], [141]/ [69]/ [93], [94]/ [103], [105], [117], [199], [204]/ (crystallography, phases present, solid-state miscibility) fatty acids/ metal alloys/ alkanes/ other organics/ [167], [168]/ [39], [49], [109]- [111], [134]/ [76], [77], [82], salts, salt hydrates/ organic-inorganic blends [112], [114], [116], [143]/ [78], [157], [161], [162]/ [98] IR (Infra-Red) /FT-IR (Fourier Transform IR) Spectroscopy Fatty acids/ organometallics/ polyols/ other organ- [70], [103], [105], [117], [123], [126], [133], [193], [199]/ (chemical structures and their changes, solid phases/polymorphs) ics [201]/ [94], [203]/ [82] PLM (Polarized Light (thermo-) Microscopy) (PC temp, crystalli- Polyols/ fatty acids/ other organics [93]/ [103], [105], [106]/ [116] zation rate) SEM (Scanning Electron Microscopy) (morphology, microstructures, Fatty acids/ alkanols- fatty acids/ salt hydrates [46], [117]/ [69]/ [157] phases and phase transitions, solid-state miscibility) Optical Microscopy (morphology, melting fractions and microstructures) Alkanols -fatty acids/ other organics [69]/ [76] GC (Gas Chromatography) (compositions) Fatty acids [145]

Saman Nimali Gunasekara

Thermogravimetric Analysis (TGA) measures the mass changes with temperature, thus the thermal degradation effects ( [114], [117], [167], [168]). The melting/freezing temperatures are identified using: Melting Point Apparatus (MPA) or Binocular Microscope MPA ( [46], [92]); by visual observations in a thermostat-based apparatus with temperature measurements ( [98], [116], [145]); or with conventional cooling curves [153] (Table 3-1). The melting temperatures can also be determined by examining: the mass change and heat flux in Simultaneous Thermal Anal- ysis (STA); and heat fluxes in Differential Thermal Analysis (DTA) (Table 3-1). In the IR Thermography (IRT) method, IR emissivity changes are measured of material droplets deposited on small cavities on an aluminum plate mounted on a heating/cooling plate [95], [97]. The droplets’ phase change temperatures are determined by mathematically interpreting the IR emissivity changes during heating [95]. This method is proposed as suitable for fast estimation of phase diagrams [95], however, appears more suitable for obtaining kinetic phase diagrams.

In general, the techniques DSC, TGA, STA and DTA are of a more standard construction, however, can evaluate only very small sample sizes. Whereas, the in-house built calorimetric apparatuses have own, yet simple and cheap construction, and allow larger sample sizes testing. There, for the T-history method, the standardization is proposed e.g. through the International Energy Agency (IEA) Energy Conservation through Energy Storage (ECES) Annex 24 and 29 platforms [205]. An adequate sample size is crucial to identify the container geometry-independent behavior of the material, particularly if it is inhomogeneous and/or supercools. This explains the complementary use of both types of techniques by some, e.g. DSC complemented with T-history [50], [80], [156], [194], and other methods [36], [82], [98], [116], [135], [145], [167], [168].

In deriving phase diagrams, essentially, the thermal property-based phase diagram judgments can be confirmed only with supplements from physicochemical characterizations [206] (e.g. crystallographic, chemical and microstructural). There, XRD, followed by IR-spectrometric and microscopic techniques are the most commonly employed. The comprehensive phase equilibrium studies in the PCM-context have employed several of these thermal, physical and chemical characterizations extensively in combine, to verify the phase equilibrium (e.g. [69], [103], [105], [106], [113], [144], [199]).

XRD is the most straightforward technique for identifying the crystallography, including the crystal structures, cell parameters and space groups. With XRD, the polymorphs of the pure components can be identified [199], [204]. By comparing the pure components’ XRD peaks to that of

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the blends, the systems’ solid phases and thus solid solubility can be determined (e.g. [39], [69], [82], [103], [105], [110], [116], [117], [134], [199], [204]). The blend XRD peaks corresponding only to pure components indicate an immiscible system, while new peaks that appear correspond to compounds formation. In a blend, the disappearance of the XRD peaks of a pure component over certain temperatures indicates the formation of a solid-solution of the other component. By operating XRDs at isothermal conditions at different temperatures, step-wise crystallographic evaluations enable correct solid-phase characterization (e.g. [39], [49], [76], [77], [109]-[112], [134], [141], [199], [204]). Thereby, e.g., reduced solid-state miscibility is indicated by a number of solid forms all stabilizing within narrow composition ranges [199], [204].

The Infra-Red (IR) or Fourier Transform IR (FT-IR) spectra comparison of the pure and blend compositions indicates important phase change details. These include: their chemical structures and degradation ( [82], [94], [117], [123], [133], [193]); the variations in the functional groups’ (e.g. –OH) absorption bands shifts ( [70], [82], [133], [203]) and vibrational modes [82], [103], [105]; and, the specific solid phases formed for the pure components [133], [199]. Different vibrational modes in FT-IR spectra correspond to different crystal structures and the melting [103], [105]. The IR spectra for various functional groups of the pure and blend compositions can indicate the stable polymorphs of the pure components, and hence the partial miscibility of their eutectic blend [70]. In blends, identical FT-IR vibration bands to that of its pure components indicate a physical mixture of the pure ones, while dissimilar bands indicate vice-versa [103], [105]. Identical FT-IR peaks at the same frequency bands, before and after thermal cycling, indicate the absence of chemical degradation [117], [123], [126]. Wave number correlations proposed to the solid-solid phase transition temperatures of several polyols, based on their –OH absorption bands shifts in the IR spectra, are also available [203].

Polarized Light (thermo-) Microscopy (PLM), Scanning Electron Micros- copy (SEM) and optical microscopy are all microscopic techniques. With PLM, the crystallization rates and different solid regions in the phase diagram are determined ( [93], [103], [105], [106], [116]). SEM indicates the morphology of the existing various phases and their transitions ( [46], [69], [117], [157]). SEM evaluations are often coupled with in-situ compositional mapping of the specimens, e.g. with Energy Dispersive Spec- troscopy (EDS) to further verify the identified microstructures. With optical microscopy, melting fractions and the various microstructures that occur during heating can be determined ( [69], [76]).

Saman Nimali Gunasekara

The thermal and physicochemical property characterizations can be optimized by accompanying with valuable approaches such as: thermal cycling tests ( [34]- [36], [82], [87], [92], [94], [114], [117], [121], [123], [137], [154], [155], [159], [202]); thermal annealing ( [68], [142]); ‘strain induced transformations’ [143]; and Tammann plots ( [69], [98], [103], [105], [106], [112]-[116], [144]).

Thermal cycling tests verify: the predominant phase change behavior of the blends, and thus their phase diagram; the variations in the fusion enthalpy under different conditions; and material homogeneity [35]. The cycled samples are often evaluated with XRD or FT-IR to analyze the variations. In thermal annealing, the solidified samples are heated at a controlled rate to the annealing temperature (above the expected melting), maintained at that for a given time, and then cooled below the melting temperature [142]. Thereby, sufficiently slow heat transfer rates and enough time for the material to reach the stable equilibrium are allowed. This appears useful on materials that tend to yield metastable phases. Strain induced transformations can produce the stable crystal structures of materials prone to supercooling and which therefore preserve higher- temperature phases at room temperature [143]. With this approach, the samples are kept chilled for a given period of time (e.g. at -20 °C for 12 hours [143]), and then using a piston subjected to a large strain inside a small cylinder.

Tammann plots map the enthalpy variation of blend systems’ invariant transitions like eutectics and peritectics against composition [206]. The shapes of the plot along the compositions range verifies e.g. the eutectics, and indicates the extent of solid-state miscibility of the blends. A characteristic triangle in a Tammann plot for the eutectic enthalpy change sum- mits at the eutectic composition. If this eutectic enthalpy triangle spans over the whole compositional range (i.e., reaching zero only at the pure components), this indicates complete solid-state immiscibility [69], [206]. Several investigations confirmed their eutectics and peritectics, and the system’s level of miscibility via Tammann plots ( [69], [98], [103], [105], [106], [113]-[116], [144]).

To determine the phase change temperatures, a correct interpretation of the cp, enthalpy and temperature profiles is crucial. In literature, particularly the cp profiles are extensively employed in identifying the various phases in the systems. Hence, correct cp profile interpretations are extremely significant. There, Tammann plots are an effective supplement. Rycerz [206] offers valuable insights on cp profile interpretations and Tamman plots construction to characterize e.g. eutectics and peritectics in phase diagrams. To exemplify, the Tammann plot of a eutectic (E1) and a peritectic (P) in the system A-B (has two eutectics and a peritectic),

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES is shown in Figure 3-1. There, in addition, the surrounding curves (a)-(d) indicate the cp profiles expected in this system for: pure A; hypo-eutectic (for E1); the exact eutectic (for E1); and a hypo-peritectic (preceded by a small hyper-eutectic peak) compositions respectively. For a pure component containing polymorphs, more than one cp peaks occur (unlike in the cp profile (a) in Figure 3-1), which may also be overlapping [69], [108], [112].

(a) (a)(b) (c) (d) Phase Diagram

E1 (d) )

(b) K ( P T

(c)

) Tammann Plot mol / kJ ( . Inv H Δ

A XE1 XP B X (Mole fraction of) B Figure 3-1. Characterization of a eutectic and a peritectic, in a complex phase diagram (above), using a Tammann plot (below), with the surrounding curves (a)-(d) indicating the corresponding typical cp profiles during heating (Adapted from Rycerz et al. [206])

The systems beyond merely completely isomorphous or simple eutectic transformations, contain complex cp profiles (e.g. Figure 3-1). For instance, three consecutive cp peaks at heating (or cooling) could occur for several successive compositions. These peaks could be: a eutectic, a peritectic, followed-by melting (e.g. Figure 3-1 (d)); or a solid-solid transition, a eutectic, followed-by melting, among other possibilities. A eutectic or a peritectic each occurs at a constant temperature, for all the compositions they exist. Whereas, melting or solid-solid phase change temperatures change along compositions, and are respectively above and below that of the eutectic. Relying on such trends, followed by plotting these phase changes in a preliminary phase diagram, they can be approximately distinguished. Then a Tammann plot could strongly suggest the possible eutectics and peritectics, by means of an enthalpy triangle with the exact compositions found at the peak enthalpy. However, without knowing the physicochemical characteristics of the blends, it is impossible to confirm their corresponding phase changes, and thus the exact precise phase diagram.

Among further phase change complexities, small phase change cp peaks between the melting and eutectic phase changes of some fatty acids were

Saman Nimali Gunasekara deemed probable metastable molecular formations, which could eventually turn to peritectics of metatectics [69]. In these, a third cp peak below the eutectic temperature was considered a solid-solid phase change, attributed to the system by the pure component polymorphs [69]. Similarly, for complicated cp curves obtained for the blends of hexane-hexadecanol, isothermal XRD evaluations indicated a metatectic phase change [112]. Solid-state compounds formation or decomposition can trigger metastable states, while incongruent melting compounds can cause DSC thermo- gram misinterpretations [206]. With DSC, the material homogeneity is qualitatively related to the cp peaks evolution at different temperatures [35]. A peak, becoming wider or narrower indicates the width of the solid- liquid or phase separation interval (if it happens) [35]. Such knowledge is of practical significance for PCM design, beneficial for all calorimetric methods in general.

However, blends’ DSC cp profiles interpretations in the PCM literature do not always exactly converge. Therefore, a common consensus on this is essential, which is equally beneficial for all the calorimetric methods- based phase change deductions. For instance, in heating, the diphenyl ether-biphenyl blends contained two cp peaks (except for the pure component and eutectic compositions), the first independent of the composition and the second dependent [144]. This is similar e.g. to the cp profile (b) in Figure 3-1, which becomes like (c) at the eutectic. With the increase of e.g. diphenyl ether, the area of the first peak increased while for the other it decreased. These observations were attributed to complete solid- state immiscibility (c.f. [207], [208]), and thus the system a non-isomorphous simple eutectic ( [69], [93], [144]). In contrast, from two DSC cp peaks observed in other systems for both heating and cooling, it was deduced that the first (in heating) is a solid-solid phase change, and the second is the melting [136]. For cooling curves, it was the vice versa.

In summary, the thermal property evaluations (using e.g. DSC, TGA, STA and DTA, T-history, TGA, STA, MPA, other calorimetric methods, heating/cooling studies and IRT), must be complemented with physicochemical characterizations (e.g. with XRD, FT-IR, SEM, PLM, optical microscopy and GC) to confirm a phase diagram. There, to precisely determine the eutectic or peritectic compositions, a Tamman plot is crucial. With thermal cycling tests, the standard phase change of the system should be known to derive its phase diagram, and the robustness of any identified compositions suitable as PCMs. With thermal annealing or strain induced transformations stable states can be obtained of the systems which tend to undergo supercooling or metastability.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

3.1.2 Experimental Methods for the Selected Blend Systems Investigations To evaluate two chosen blend systems of PCM-interest in this thesis work, several methods are chosen as explained herein. The selected systems are the binary polyols erythritol-xylitol and the binary n-alkanes dodecane-tridecane systems. These were chosen because of their attractive properties as potential PCMs and for the inconsistent phase diagrams proposed in literature. These systems are further described in later sections 4.1 and 4.2.

As the experimental methodology appraisal in section 3.1.1 indicated, thermal property evaluations must be combined with physical and/or chemical properties of the system, to confirm the phase diagram. For both blend systems, for thermal property characterizations, the T-history method was chosen. This is due to its advantages of a larger sample size (e.g. versus DSC and DTA, to have less supercooling effect) and the flex- ibility in operation. Tammann plots were chosen to further confirm the thermal properties of their potential invariant points. To complement these thermal properties, several physical characterization techniques were also chosen. XRD is the most straightforward technique found employed to characterize crystallography. The erythritol-xylitol system was rather novel ( [93], [97], and Paper VIII), with only room-temperature XRD and no SEM evaluations available [93]. In addition, this system indicated complex phase change during pre-evaluations in Paper VIII. Hence, XRD and SEM were selected to extensively characterize the erythritol-xylitol system’s phase change. The complementary use of these techniques were expected to better-verify its phase diagram.

The alkanes system dodecane-tridecane has also been evaluated only by a few, using DSC, thermostat-based cooling studies, and crystallographic characterizations [109], [135]. Hence, the T-history coupled with Tam- mann plots here were expected to enable further understanding on the system. Considering the crystallographic characteristics of the system as well-defined in the earlier literature, these were excluded here.

3.1.2.1 Temperature- History Method The T-history method employed follows the same basis as in Chiu and Martin [209], with some procedural modifications. These modifications are compared in Table 3-2. As indicated in Table 3-2, the reference and the containment box were altered to expand the T-history working temperature range to be within -35 °C to 150 °C. The sample holders were constructed from stainless-steel (SS), primarily as the polyols’ crystallization and melting inclined to crack glass. The references were chosen to be solid metal (copper or stainless-steel) blocks, because unlike distilled

Saman Nimali Gunasekara water, they remain a single phase (solid) within -35 °C to 150 °C. The Horizontal orientation was chosen following Chiu [210] to minimize the buoyancy effect. Hence the SS sample holders (cylindrical test-tubes) were constructed with an arm (close to its open end) to insert the temperature sensors, and with screw-fitting lids. Their effective volume (till the arm’s height) is 10.1 ml.

Table 3-2. T-history procedural differences between this work and Chiu and Martin [209] Criteria This work Chiu and Martin [209] Reference Solid blocks of stainless-steel Distilled water and/or copper (of geometry identical to the samples) Sample orientation Horizontal Vertical Sample holders Stainless-steel test-tubes Glass test-tubes Sample volume ~10 ml ~50 ml Heating, cooling program Fixed slow rates, plus isother- Maintaining under a mally maintaining for ~3-5 fixed temperature ramp hours at the highest and lowest (variable heating/cool- cycle temperatures. ing rates) Sample and reference hold- Stainless-steel box Polystyrene box ers containment (for minimal convection)

The smaller sample volumes were a result of test-tubes with smaller di- ameters, to obtain a large length to diameter ratio (>10). Thereby, only the radial temperature distribution can be considered (according to Mazo et al. [211]), assuming the samples to be in infinitely long cylinders. The fixed cooling and heating rates were utilized because, achieving symmetric temperature-gradients before and after melting (or freezing) for materials prone to large supercooling was challenging by using a fixed ramp. Then, isothermal conditions (for ~3-5 hours) were maintained at the highest and lowest cycle temperatures to further ensure thermal equilibrium.

Climate Chamber SS Containment Data Logger

PCM

Reference Computer

PCM

Figure 3-2. The T-history set-up used (Left: a photograph, Right: a schematic)

As shown in Figure 3-2, the sample and reference holders were insulated with HT-Armaflex of 19 mm thickness. T-type thermocouples were used as temperature sensors, of which the temperatures were logged using a 46

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES data logger (Keithley 2701) recording data via a computer. This set-up was calibrated, and has an average expanded uncertainty of 0.4 °C with 0.95 confidence12. The complete T-history set-up, inserted inside the SS containment (as in Figure 3-2 (Left)), was placed inside a temperature- programmable climate chamber (ACS Hygross 1200) and thermally cycled for four or more cycles (specified for each blend in Chapter 4). With the SS containment, convective heat transfer due to possible air currents inside the climate chamber is avoided. The sample and reference weights were measured using a weighing scale of an expanded uncertainty of 0.04 g with 0.95 confidence. The copper used for the references is electrolytic copper (Cu-ETP), and the stainless steel used for the sample holders and the SS reference is SS 316. Their thermal properties are given in Table 3-3. The weights of the reference blocks are: 162.66± 0.04 g (Cu-ETP), and 145.8 ± 0.04 g (SS1) and 144.81± 0.04 g (SS2).

Table 3-3. Thermal properties of the reference and the sample holder materials Mate- Specific Heat Thermal conduc- Remarks Source rial kJ/(kg·K) tivity W/(m·K) ETP 0.39 389.1 Average be- [212] copper tween 20-100 C SS 316 0.50 *16.2 Between 0-100 [213] ⁰C/ *At 100 C 0.452, 0.486, 0.528 -- At 20, 90, 200 [214] and 0.548a and⁰ 320 C ⁰ a used in the polyols’ evaluation which spanned over a broader temperature range ⁰ The T-history method fulfills the ‘lumped capacitance’ conditions. Thereby, it is ensured that the heat conduction dominates over the convection, and a uniform temperature profile is maintained within the sample during the transient process. To verify this, the Biot number, as expressed in Eqn. 3-1, of the sample as well as the reference, is maintained below 0.1 [209]. This condition was achieved by increasing insulation, and by using small heating/cooling rates. In Eqn. 3-1, U is the overall heat transfer coefficient (W/(m2.K)), k is the thermal conductivity (W/(m.K)), and r/2 is the characteristic length (m) (r is the inner-radius (m) of the test-tube).

U ⋅ r Bi = << 1 Eqn. 3-1 2 ⋅ k

12 All the uncertainties (for temperature, mass, composition and enthalpy) provided are the expanded uncertainties, with 0.95 level of confidence, unless specified.

Saman Nimali Gunasekara

To determine the unknown thermal properties of the sample, the known thermal properties of the reference are used, as follows. The total heat  gained by the reference SS block (QR ) during the sampling time is determined using its specific heat cp, R (known), mass mR (measured), and the temperature difference ΔTR (calculated using measurements) according to Eqn. 3-2. Here, ∆hR (kJ/kg) is the enthalpy change, and Δt (s) is the sampling time.

 QR = mR ⋅ ∆hR / ∆t = mR ⋅ cP,R ⋅ ∆TR / ∆t Eqn. 3-2

The total heat gain by the reference is also expressed as a curve-fit of the heat versus logarithmic mean temperature difference (lmtd) plot [209], as expressed in Eqn. 3-3. The lmtd is defined for the reference and the sample in Eqn. 3-4 and Eqn. 3-5 respectively.

 QR = k1 ⋅lmtdR + k2 Eqn. 3-3 [(T n−1 −T n−1 )− (T n −T n )] R amb R amb Eqn. 3-4 lmtdR = n−1 n−1 n n ln[(TR −Tamb )/(TR −Tamb )] [(T n−1 −T n−1 )− (T n −T n )] S amb S amb Eqn. 3-5 lmtdS = n−1 n−1 n n ln[(TS −Tamb )/(TS −Tamb )]

The sample and its containment SS test-tubes (SSTTs) are assumed to be at the same temperature. Therefore, their overall lmtd is considered the same as that of the sample, as indicated in Eqn. 3-6.

TSSTT = TPCM ⇒ Eqn. 3-6 lmtdOverall = lmtd SSTT = lmtd S

As in Eqn. 3-7, the overall heat transfer coefficient U can be found with respect to the slope of the curve-fit k1 (Eqn. 3-3) and the heat transfer area A (m2) of the reference or the sample in an SS test-tube. The sample has the same: overall heat transfer coefficient U; heat transfer area A; and the curve-fit intercept k2; as the reference, owing to their identical geom- etries and measurement conditions [24], [209]. Consequently, by solving Eqn. 3-7 and Eqn. 3-8, the total heat accumulated by the sample and its  holder SS test-tube (QTot ), at each time step Δt (s) is found. Because the SS test-tube’s mass mSSTT (g), specific heat cpS S (J/(kg·K)), and the temperature difference dTSSTT (ºC) are known, heat gain by the SS test-tube   QSSTT can be calculated. Thus, the heat gained by the sample QS can be determined, using Eqn. 3-9.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

    QR − k2 QTot − k2 (QS + QSSTT )− k2 k1 = U ⋅ A = = = Eqn. 3-7 lmtdR lmtdTot lmtdS    Eqn. 3-8 QTot = QSSTT + QS = k1 ⋅lmtdS + k2   QS = k1 ⋅lmtdS + k2 − QSSTT Eqn. 3-9 = k1 ⋅lmtdS + k2 − (mSSTT ⋅ cP,SSTT ⋅ dTSSTT ∆t)

 Using the calculated heat gain QS , similar to Chiu and Martin [209], the enthalpy and thereby the specific heat change of the sample can be determined based on Eqn. 3-10 and Eqn. 3-11 respectively. By employing Eqn. 3-12, the overall thermal energy storage capacity of the sample over the temperature range T1-T2 can also be calculated.  QS ⋅ ∆t hS = Eqn. 3-10 mS dh(T ) c (T )⋅dT = P Eqn. 3-11 dt dt

T2 T2 = ⋅ = ⋅ ⋅ QS ∫ m dhS (T ) ∫ m cP,S (T ) dT Eqn. 3-12 T1 T1

To verify that the T-history conditions are met, it is necessary to perform the experiments first. These experimental data are then used to calculate the Biot number and validate the hypothesis that it is below 0.1. Before testing the chosen materials, the T-history method was verified with benchmark tests with distilled water and octadecane. The identical insulations were verified with identical temperature profiles obtained for distilled water. Phase change enthalpies consistent with literature were obtained for octadecane, which verified the validity of the employed T-history method. There, enthalpy and cp measurements with the respective expanded uncertainties 10% and 6%, at 0.95 confidence level were obtained.

3.1.2.2 Tammann Plots In the studied systems, Tammann plots (plotting molar enthalpy changes of potential invariant points against mole fraction) were employed when the following conditions were met: 1. More than one phase change was observed, per blend composition, within the studied temperature ranges. 2. One of such transitions occurred rather isothermally, for several consecutive blend compositions.

Saman Nimali Gunasekara

For the eutectic transformation, the molar enthalpy evolution along the composition takes a triangular shape, peaking at the exact eutectic composition. The exact eutectic composition exists at the intersection of the linear-regression fits of the eutectic molar enthalpy change, respectively until and after the measured eutectic composition. The same applies also for a peritectic. In addition, if the molar enthalpy change of the eutectic becomes zero at compositions between the pure components, this indicates partial miscibility [69], [206]. Accordingly, the Tammann plots- based analysis of the studied systems used when applicable, are detailed along the results, in the sections 4.1.2 and 4.2.2.

3.1.2.3 X - Ray Diffraction (XRD) By comparing the XRD patterns of the blends to those of the pure components, details on the existing phases and the level of miscibility of the system can be obtained. Hence, with XRD, it was aimed to better explain the phase change characteristics of the chosen system erythritol-xylitol (c.f. section 3.1.2), identified via the T-history-based thermal properties.

There, three main types of XRD evaluations were employed. The first type was conducted at room temperature, thus referred to as RTXRD. The second type was conducted under controlled heating from room temperature to about 5 ºC above the end of the melting temperature as identified by the T-history. This is referred to as HTXRD. The third type of testing involved room temperature (RT) and high temperature (HT) evaluations, however conducted with extremely slow heating and measurements. This is called slow-XRD. The operating conditions employed for the RTXRD and HTXRD are detailed in Table 3-4.

Table 3-4. Operating conditions for the XRD tests conducted Operating Conditions RTXRD HTXRD Sample holder Polymeric material Stainless steel holder with a Kapton Window Radiation Cu Kalpha Detection type 1D SI strip detector, 192 strips Furnace None Antoon-Paar dome furnace DHS1100 Temperature calibration None Using pure erythritol and xylitol as references Step size 0.03 degrees 0.03 degrees Time per step (s) 1 0.3 Sample illumination Fixed illumination of 10 mm Heating rate, Isothermal holding None 1 °C/min, 5 min. (plus measurement time ~3 min) Selected temperatures (°C) Room temperature At ~5 °C intervals from RT to ~5 °C above melting 2-θ range (scanning) 10-80 29-45

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

For the slow-XRD, besides the RT and HT conditions as in Table 3-4, 10 hours of isothermal maintenance followed by measurements over another 10 hours at each chosen temperature step was used. These 10 hours were considered as sufficient to allow the system to reach stable equilibrium.

All the samples were investigated in powder form, prepared by grinding the solid specimens using a porcelain mortar and pestle. These were then investigated in the XRD contained in a special sample holder (specified in Table 3-4).

3.1.2.4 Scanning Electron Microscopy (SEM) Microstructural evaluations of the blends and their pure components can also shed light on their phase transitions, and hence the phase diagram, as evidenced in section 3.1.1. Particularly the SEM micrographs can indicate the phase’s morphology and the transitions that occurred throughout the heating/cooling sessions. Therefore, microstructural evaluations were also selected as part of the methodology of the phase diagram scrutiny. In this work, the microstructural characteristics of the erythritol-xylitol system was thus evaluated. Pre-studies of the erythritol-xylitol system using optical microscopy and a table-top SEM indicated a need for stronger magnifications. Hence, an advanced SEM technique: Field-Emission SEM (FESEM), was chosen for the study.

All the samples examined via the FESEM were flakes broken off from the solid samples (prepared under different conditions detailed in 4.1.1.2). These flakes were coated with a layer of Pt/Pd or gold/Pt, using a sputter or a vacuum coater respectively, depending on the available coater type. The thickness of the coating was around 5-8 nm with the Pt/Pd, or a few nanometers with gold/Pt (from 30 s cycle of coating). The coating is necessary to protect the specimens from charging under the electron beam, for conductivity improvements, and to improve the topographical contrast particularly of these polyols which are of lower density [215]. Thicker coatings were used on the specimens that exhibited a deterioration ten- dency.

Theoretical Phase Diagram Determination A considerable share of theoretical phase equilibrium evaluations have been performed on many PCM-interesting blends over the years. These have always been complements to their pre-determined experimental phase diagrams. The methodological insights of these various theoretical methods are discussed in section 3.2.1. Based on this analysis, a generic

Saman Nimali Gunasekara theoretical approach, suitable to represent any chemical system and any phase change type, was chosen to theoretically optimize the experimental phase diagram of the erythritol-xylitol system. The thermodynamic evaluation theory of this phase diagram is described in section 3.2.3.

3.2.1 Theoretical Phase Equilibrium- Basis A component system that does not decompose into sub-systems can be thermodynamically considered as a unary system. In a purely theoretical sense, such a unary system is an element, and a binary, ternary, and other higher-order systems respectively are made of two, three or more elements. However, in engineering design, often a system made of two components is termed a binary system, and so forth. This in-fact is a multicomponent system made of the number of elements in the system. Such a two component system nevertheless can be considered a pseudo-binary system, if no chemical decomposition or new sub-components formation occurs. In the engineering application of PCM design, and hence in this thesis, for instance such a pseudo-binary system will be referred to as a binary system.

During melting or at the solid-liquid equilibrium (SLE) of a unary system, the solid and liquid phases have equal Gibbs free energy. The phase diagram of a binary system made of such unary systems can be determined by minimizing the Gibbs free energy of the whole system ( [55], [56]). The Gibbs free energy G is defined as in Eqn. 3-13 ( [53], [55], [57]), where H is the enthalpy, T is the absolute temperature, and S is the entropy, of the system.

G = H − TS Eqn. 3-13

For a closed system at constant temperature and pressure, its G is a minimum at equilibrium ( [53], [55], [56]), implying (Eqn. 3-14)

dG = 0 Eqn. 3-14

A transformation is possible if it can decrease G, and hence the necessary criterion for a phase transformation is, as expressed in Eqn. 3-15. Here, G1 and G2 are the initial-state and final-state G of the system [55].

∆G = G2 − G1 < 0 Eqn. 3-15

The change in G for the changes between equilibrium states is given by Eqn. 3-16, where, P is the pressure and V is the volume [56].

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

∂G ∂G dG = dT + dP = −SdT +VdP Eqn. 3-16 ∂T ∂P

In constructing the phase diagram of a material system, its phases in equilibrium at different temperatures need to be determined. This is done by determining the system’s G variations with temperature. To calculate G, the thermal properties of the system such as the heat capacity at constant pressure CP, and the entropy should be determined. The system’s enthalpy variation with temperature is obtained by integrating Eqn. 3-17, where, CP is equal to the slope of the H versus T plot. The entropy S is found by using Eqn. 3-18, setting the entropy at 0 K as zero [55]. T = Eqn. 3-17 H ∫ C p dT 298 T C p S = ∫ dT Eqn. 3-18 0 T

Applying constant pressure conditions on Eqn. 3-16 produces Eqn. 3-19. This indicates a decrease in G at increasing T, at a rate of –S [55].  ∂G    = −S Eqn. 3-19  ∂T  p

In Figure 3-3, the variation of G and H are plotted on the same diagram, as exemplified for both solid and liquid phases of a metal. At all temperatures, the liquid state contains a higher enthalpy (c.f. Figure 3-3) and thus higher internal energy than the solid. Thus at lower temperatures, the G of the liquid is larger than that of the solid (i.e., GL> GS). Then again, the entropy of the liquid is much larger than that of the solid. This causes a rapid decrease of GL, as compared to GS, when the temperature increases. Therefore, the solid is more stable at temperatures up to the melting temperature Tm, and the liquid becomes more stable at temperatures above Tm. At Tm, both the solid and liquid coexist, as they have the same value of G [55].

The phase diagram construction using the G curves is exemplified on a binary system with a miscibility gap, in Figure 3-4. In this system, T1 > T2 > T3. At T1 (Figure 3-4 (a)), the liquid is stable for all the compositions, as the phase diagram shows in Figure 3-4 (b). In this system (Figure 3-4), the liquid phase is almost ideal (i.e., the enthalpy change of liquid mixing ΔHmix,liquid is zero), whereas the solid phase is nonideal (i.e., ΔHmix,solid>0). Therefore, at a lower temperature like T3, the GS curve has a negative curvature as in Figure 3-4 (c). Hence, the solid is stable at T3 as a

Saman Nimali Gunasekara

physical mixture of two solid solutions SA and SB at the compositions e and f.

H d H ( Liquid)

H (Solid) c L b 0 T (K) 298 Tm a G (Solid) e

Solid Liquid stable stable G G ( Liquid) f Figure 3-3. The variation of enthalpy (H) and Gibbs free energy (G) with temperature for the solid and liquid phases of a pure metal. (Here, L: latent heat of melting, Tm: equilibrium melting temperature) (Redrawn based on [55]).

At T1 At T2 liquid XB a c d XB b G G solid solid liquid

A (a) B A (b) B liquid At T3 T1 b c T2 liquid a d Solid solution SAB G XB T solid e Solid sol. SA+ f f T3 Solid sol. SB e A B A XB B (c) (d) Figure 3-4. The phase diagram derivation (shown in (d)) of a system with a miscibility gap in the solid region, using the Gibbs free energy diagrams for the system at temperatures (a)T1, (b)T2 and (c)T3 (Redrawn based on [55]).

At higher temperatures, e.g. T1 and T2 shown in Figure 3-4 (a) and (b), the value of –TΔSmix (ΔSmix is the entropy change of the mixture) increases. Hence, the points e and f (Figure 3-4 (c)) approach each other and eventually disappear, forming a single solid solution SAB as in Figure 3-4 (d). A positive enthalpy of mixing at solid state gave rise to the minimum point mixture as seen in the phase diagram [55].

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

3.2.2 Theoretical Methods: State- of- the- Art The theoretical phase equilibrium evaluations conducted for PCM design so far are all semi-empirical. Hence, they have used the pure components’ (and occasionally of the involved solutions) experimentally determined thermal properties. These theoretical approaches are summarized in Ta- ble 3-5. Overall, many organic systems mostly proposed with eutectics, and several organic and inorganic systems with a variety of phase equilibrium characteristics, have been analyzed in the PCM-context.

Amid these PCM investigations, several studies relied purely on the fundamental Gibbs free energy minimization of the system (c.f. Table 3-5), to determine the stable phases. These constructed the phase diagrams adhering to the fundamental approach explained along Figure 3-4 in section 3.2.1. A great share of the theoretical investigations in the PCM-context however, in contrast have used specific SLE expressions restricted to certain material characteristics. These are categorized as ‘thermodynamic SLE related to the activity coefficients’ and the specific simplification into the ‘Shröders Equation’, in Table 3-5. All these approaches in literature, along the used SLE expressions, are concisely analyzed here.

A majority of organics and several inorganics were investigated, in the PCM-context, using SLE expressions which accounted the non-idealities in mixing with activity coefficients (c.f. Table 3-5). The corresponding complete SLE expression based on which many organics were evaluated, is given in Eqn. 3-20 [69].

∆h  1 1  n ∆h  1 1   i  −  + tr  −   L L   ∑    x γ  R  Ti Tm  tr=1  R  Ttr Tm  i i =   S S exp  Eqn. 3-20 xi γ i ∆c  T T  + p,i  i − ln i −1   R  T T     m m  

L S L S In Eqn. 3-20, xi , xi are the mole fractions, while γ i and γ i are the activity coefficients, of the main component in the liquid and solid state. Δhi (J/mol) and Ti (K) are, the latent heat of fusion and the melting temperature respectively, of the pure component i. Tm is the melting temperature of a mixture containing component i (K), and R is the gas constant (8.314 J/K·mol). Furthermore, Δhtr and Ttr are the enthalpy change and temperature of solid-solid transitions of the pure component i, while

∆c p,i is the specific heat of the pure component i at its melting temperature. Eqn. 3-20 however was subjected to several simplifications in the evaluations in the PCM-context. These are detailed here below.

Saman Nimali Gunasekara

Table 3-5. The employed theoretical phase equilibrium study methodologies in the PCM-context SLE Theorya Details Sources Schröder’s equation Binary-quinary fatty acids, binary fatty [33], [44], [46], [68], [69],

(Shroders, Shraeders, Schrodervan Laar, Schröeder-Van Laar, acid-alkanols, fatty acids-amides, fatty acid [93], [95], [108], [113], ‘freezing point depression theory for independent crystal for- derivatives, and polyols systems. [114], [117], [125], [127], mation’, or no specific name) [129] & [216] in [130], [131], [133], [136], [144]

imple eutectic ** Wilson, NRTL and UNIQUAC models Binary alkane-alkanol/alkane-fatty acid [44]/ [113]

systems.

Wilson, NRTL and UNIFAC models Binary diphenyl ether-biphenyl system. [144] liquidus

Organics and other UNIFAC, UNIFAC-Dortmund, and Binary alkanol-fatty acid systems. [69]

* Margules 2 and 3-suffix models isomorphous s

UNIFAC Dortmund/Pharma UNIFAC - Binary polyols/urea-polyol systems. [93]/ [116] Specific models Non

similar models **Buchowski (λh) equation, and UNIFAC Ideal liquid solution assumption Binary alkane-fatty acid systems. [115] Group contribution, UNIFAC, *Won, and *Pedersen’s models IC Binary alkanes’ solidus prediction. [48]

regular solution M

activity coefficients Conformal ionic solution (CIS) theory ( [217], [218]), Salt-salt interac- Ternary salts system [163] E and assuming ideal liquid solutions tions Pitzer–Simonson–Clegg (PSC) model Solubility, water Ternary/quaternary salt [154]/ [148]

Thermodynamic SLE related to the Modified Brunauer-Emmett-Teller (BET) model activity, & salt- hydrates systems [155] Inorganics [219] salt interactions

ph. eqm. Calculating the phase diagram by minimizing the total Using: Thermo-Calc PARROT module on poly- [143], [196]; [161], [162]/ Organics , or, E , for phases in equilibrium, by iteratively ols; salts/ a LIQFIT program and a Txy-CALC [49], [77], [109], [110], Gm Gm

& Inor- haracteristics program on binary and ternary organic systems/ [134], [141]/ [78] optimizing the experimental data. c Generic ganics Various OptiSage optimization on a salts system a SLE- Solid-Liquid Equilibrium, ph. eqm.- Phase Equilibrium, G - Molar Gibbs free energy, E - Excess molar Gibbs free energy, NRTL- Nonrandom two- m Gm liquid, UNIQUAC- Universal quasi chemical activity coefficient, UNIFAC- UNIQUAC functional group activity coefficients, CIS- Conformal ionic solution, SAT- Sodium acetate trihydrate, ICM- Isomorphous congruent minimum-melting, E- Eutectic, org.- Organic, Inorg.- Inorganic.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

A component’s functional groups (e.g. –OH, –CH3, –COOH) have a unique contribution to its properties [220], expressed in terms of the activity coefficients. In the PCM-context, the activity coefficients were determined using ‘group-contribution models’ such like: Wilson, NRTL [44], [113], [144]; UNIQUAC [44], [113]; UNIFAC [48], [69], [115], [144]; UNIFAC-Dortmund [69], [93]; Pharma UNIFAC [116]; and Margules 2 & 3-suffix [69], and the regular solution models: Won, and Pedersen’s [48]. In the regular solution models, the activity coefficients were determined using the pure component’s solubility parameters for the liquid and solid phases. All these group-contribution approaches used in the PCM- context neglected the correction terms for the solid-solid transitions and specific heat in Eqn. 3-20. This was because, they were small compared to the uncertainty in the activity coefficents.

Eqn. 3-20 was further simplified by certain studies, for the systems com- S S pletely immiscible in the solid state, and hence xi γ i =1 [69]. Then the systems contain the two pure solids in a physical mix, and hence also nul- lifies the solid-solid correction in Eqn. 3-20. The resultant SLE expression, Eqn. 3-21, is the most-employed among the group contribution approaches in the PCM-context. It exclusively yielded non-isomorphous simple eutectics in these binary organic systems.

∆h  1 1  Lγ L = i  −  xi i exp   Eqn. 3-21  R  Ti Tm 

Most group contribution-based investigations in the PCM-context compared the nonideal behavior of the system to that for an ideal liquid solu- L tion. Hence, it was assumed that γ i =1(for an ideal liquid solution) [93]. This simplifies Eqn. 3-21 to Eqn. 3-22, which in fact is the so-called Shrö- der’s equation (among other similar names). In that, xi is the mole fraction of the main component i of the mixture.

∆h  1 1  = i  −  ln xi   Eqn. 3-22 R  Ti Tm 

Eqn. 3-22 yielded non-isomorphous simple eutectics in numerous binary- quinary organic systems examined within PCM literature. Eqn. 3-22 was further simplified for fatty acid systems, e.g. assuming the excess molar E Gibbs free energy ( Gm ) of the components to be zero, and for components with large-enough molecular weight [33], [129], [216]. Buchowski (λh) equation in Eqn. 3-24, is another SLE expression proposed to be suitable on most systems [115]. Here, the equation parameters λ and h

Saman Nimali Gunasekara were determined by an iterative optimization between the calculated and experimental data [115]. Although this is not based on activity coefficients, it is rather similar, and hence is categorized among such methods in Table 3-5 for simplicity.

 λ −    (1 xi ) 1 1 ln1+  = λh −  Eqn. 3-23  xi   Ti Tm 

The inorganics’ evaluations in the PCM-context employing activity coefficients have utilized other specific SLE expressions (c.f. Table 3-5). For instance, the ternary salts system NaCl-CaCl2-MgCl2, based on the conformal ionic solution (CIS) theory ( [217], [218]), was considered as AX- + + + qA qB q BX2-CX2. Hence the system contains the cations A , B and C C , and a common anion X- [163]. Thereby, the SLE of the mixture can be expressed for each salt, related to the activity coefficient γ i of each component i, e.g. for the salt AXqA as in Eqn. 3-24 [163].

RT lnγ A = qA X B (X B + X C )λAB − qA X B X CλBC Eqn. 3-24 + qA X C (X B + X C )λAC

In Eqn. 3-24, Xi is the equivalent fraction of component i, and λij is the binary interaction parameter for each binary sub-system. The detailed interaction parameter determination is found in Wei et al. [163]. The system’s SLE was also modelled assuming ideal non-electrolyte solutions13 [163].

The salt-water systems can be considered as electrolytic solutions [221]. Their activity coefficients were correlated to the water activity, salt-solubility and salt-salt interactions ( [148], [154], [155]), and hence determined for water (the solvent), the cation M (e.g. NH4+, Ca2+, K+, Mg2+) and the anion X- (e.g. Cl- and NO3-). For that, the models Pitzer–Simonson– Clegg (PSC) [148], [154], or modified Brunauer-Emmett-Teller (BET) [155] were employed.

With the PSC model, as in Eqn. 3-26, the (solubility) phase diagram of the binary and ternary salt-water systems were derived [148], [154]. Here, an infinitely dilute solution is assumed [148], [154]. In Eqn. 3-26, ln k and ln Ksp are the solubility products of the salt hydrate, respectively with re- 14 spect to molality and mole fraction. ν+ and ν- are the stoichiometric

13 An electrolytic solution forms anions and cations when in solution [221]. 14 i.e., the amount of moles of solute in 1000 g of solvent 58

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES coefficients of the positive ions and negative ions of the salt in Mν+Xν- ·nH2O(s). MA is the molar mass of the solvent. The corresponding activities are ai,x and ai,m (i= anion or cation), based on mole fraction and molality respectively, and were determined by fitting the experimental water activity and solubility data via regression. ln k and ln Ksp were determined by calculating the component activity of the saturated solution in equilibrium with the solid Mν+Xν-·nH2O(s) [148], [154].

ln K − ln k spMν +Xν − ⋅nH2O(s) Mν +Xν − ⋅nH2O(s)

=ν + (ln a + − ln a + )+ν − (ln a − − ln a − ) M ,m M ,x X ,m X ,x Eqn. 3-25   1000  = (ν + +ν − )ln   M A 

The modified BET model is expressed as in Eqn. 3-26 and Eqn. 3-27 for a multicomponent salt-water system. These are expressed in terms of the activities of salt i: ai and water: aw. The extra salt-salt interactions were accounted as a regular solution in Eqn. 3-27 [155].

N w − ∑ Ni(M ) i Eqn. 3-26 aw = N w

  r  N r N − N  i  Ω  = i i i i(M )  ij  ai    ∏exp x j  Eqn. 3-27  ∑ Ni  ri Ni  j≠i  RT   i 

15 Here, Nw, Ni and Ni(M) are the mole number of: water, salt i, and the water bound to the salt i, respectively. ri is a BET parameter of the salt i,

Ωij is an empirical interaction parameter between the salt i and j, and xj is the mole fraction of the salt j in the anhydrous mixture. The phase diagram was determined by finding the BET parameters and the chemical potential of the solid salt·nH2O. The latter was found based on Eqn. 3-27, by determining the salt and water activities at the binary liquidus [155].

Overall, in the PCM literature, the approaches detailed along Eqn. 3-20 to Eqn. 3-27 always relied on certain chemical characteristics of the ma-

15 The number of ‘particles’ per chemical species (i.e., salts and water), which would yield a consistent amount of the species when taken in an Avogadro constants’ amount, that corresponds to its molar mass M [219]. In other words, a ‘particle’ here is a single molecule within a unit molar mass which has an Avogadro constants’ amount of molecules. 59

Saman Nimali Gunasekara terials. In contrast to these specific approaches, several other phase equilibrium evaluations in the PCM-context depended solely on the fundamental Gibbs free energy minimizations, as was pointed earlier (also in E Table 3-5). There, to find the stable phases, the system’s Gm ( [49], [77], [109], [110], [134], [141]) or the total molar Gibbs free energy (Gm) ( [78], [143], [161], [162], [196]) was minimized. Thereby, several organic systems and a few inorganic systems, containing various phase equilibrium characteristics, were appraised (c.f. Table 3-5).

The total Gm consists of the contributions from the pure component (i.e., E the reference state), ideal liquid solution behavior, and Gm [78], [161], E [162]. For the Gm minimization in the PCM-context, the experimental liquidus of binary and ternary organic systems were optimized using LIQFIT ( [49]16, [77], [109], [110], [134], [141]), and Txy-CALC ( [109], [110], [134]) programs, respectively. With these optimizations, the equal Gibbs-energy curves for the ideal (calculated) and experimental phase di- E agrams are localized approximately [77]. The Gm optimizations for the solid-liquid solution phases in binary systems, assuming ideal liquid solutions and neglecting heat capacities, yielded a Redlich-Kister polynomial as shown in Eqn. 3-28 ( [77], [109], [110], [134], [141]).

p E SL n−1 ∆ Gm = x j (1− x j )∑Gm,n (1− 2x j ) Eqn. 3-28 n=1

E SL E There, ∆ Gm is the excess Gibbs free energy ( ∆ Gm ) difference between the liquid and solid solution phases, xj is the mole fraction of the second component (i.e., with higher molecular weight or the most carbons), and p is the number of excess Gibbs free energy coefficients. Red- lich-Kister polynomials were obtained by the Gibbs free energy minimizations of salts-based systems using the programs FactSage (OptiSage module) [78], and Thermo-Calc (PARROT module) [161], [162] and for the polyols systems using Thermo-Calc (PARROT module) [143], [196]. E The solid-state Gm was determined by some, by assuming temperature independence, or linear temperature dependence ( [77], [109], [110], [134]). Some others expressed the excess properties: Gibbs energy, enthalpy and entropy, in terms of several system dependent parameters (A,

16 They have employed WINIFIT software, the Window’s version of LIQFIT.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

E B and θ) ( [49], [77]). For ternary systems, the Gm minimizations fol- E lowed the Kohler’s method yielding a Gm expression as given in Eqn. 3-29 [110]. Here, i and k superscripts denote the various components.

3 2 E,ternary  2 E  x x  = +  i k  Eqn. 3-29 Gm ∑∑ (xi xk ) Gik  ,  k>i i=1   xi + xk xi + xk 

On the whole, these fundamental Gibbs free energy minimization approaches (detailed along Eqn. 3-28 and Eqn. 3-29) are not bound by specific, chemical or phase equilibrium, characteristics of the systems. Hence only these in the PCM-context appear universally capable of evaluating organic and inorganic systems with various phase equilibrium behaviors. As shown, the Shröder’s equation (Eqn. 3-22) is limited to non-isomorphous simple eutectics. The activity coefficients-based approaches (Eqn. 3-21, Eqn. 3-24-Eqn. 3-27) also have limitations, only apt for material- systems of which the activities can be appropriately expressed. The regular solution theory [48] and the Buchowski (λh) equation (Eqn. 3-23) were so far only limited to organic systems with simple phase diagrams. Hence, herein, the fundamental Gibbs free energy minimization approach (the so-called CALPHAD method) was chosen as a nonspecific method suitable to evaluate any material system and any phase diagram. To conduct these iterative calculations, the optimization tool Thermo-Calc [222] was chosen, already successfully applied on both organic and inorganic systems.

3.2.3 Thermodynamic Phase Diagram Assessment with CALPHAD To exemplify the utility of the chosen thermodynamic phase diagram modelling approach CALPHAD (CALculation of PHAse Diagrams) [198], the erythritol-xylitol system was selected. Here, the employed thermodynamic optimization method using the iterative software Thermo- Calc [222], is explained briefly. Thereby it is aimed to consider the thermodynamic properties (enthalpy and heat capacity) and the experimental phase diagram data to generate a self-consistent thermodynamic dataset, and by using that, predict the phase equilibrium diagram of the system. The CALPHAD method follows the theory explained in section 3.2.2 (Eqn. 3-28-Eqn. 3-29), to propose the thermodynamically correct phase diagram. This is different to a purely mathematical curve-fitting in that, it thermodynamically re-evaluates each individual experimental point to ensure that is an equilibrium point in the system (e.g. shown in Figure 3-4 in section 3.2.1).

Saman Nimali Gunasekara

The stable states of erythritol and xylitol are respectively tetragonal [223], and orthorhombic [224]. In the thermodynamic assessment, their structures were approximated, for simplified notation, to be BCC (body-centered cubic) and FCC (face-centered cubic) respectively. The experimental phase diagram analysis of the erythritol-xylitol system indicated (later presented in section 4.1), the liquid phase and solid-solutions of erythritol and xylitol having mutual solubility at the pure component-rich compositions. These solid solutions, namely SEt and SXy, (of erythritol and xylitol respectively), also consist of the structures BCC and FCC respectively, because a solid solution retains the crystal structure of the solvent (i.e., the host) [30]. The phase equilibrium of these three solution phases (the liquid, SEt and SXy) can be described by the Gibbs free energy minimization of the entire system [198]. In that, their molar Gibbs free energy was described using the substitutional solution models [198], [225] as in Eqn. 3-30-Eqn. 3-33.

srf config E phys Gm = Gm + Gm + Gm + Gm Eqn. 3-30 srf ° ° Gm = xEt GEt + xXy GXy Eqn. 3-31 config Gm = RT(xEt ln xEt + xXy ln xXy ) Eqn. 3-32 n E ν ν Eqn. 3-33 Gm = xEt xXy ∑ LEt,Xy (xEt − xXy ) ν ° ° Here, GEt and GXy represent the molar Gibbs free energy of erythritol srf and xylitol, Gm is the average energy related to the reference surface, config and Gm expresses the influence of configurational entropy on the Gibbs free energy due to chemical mixing. The physical contributions (e.g. from magnetic transitions) to the Gibbs energy are denoted with phys Gm , and this was considered negligible for the erythritol-xylitol system. To express the system’s deviations from an ideal solution, the excess E Gibbs free energy Gm is used in-terms of a Redlich-Kister polynomial ν as Eqn. 3-33 shows. In Eqn. 3-33, the interaction parameters LEt,Xy , with v=0, 1, 2,…, are adjustable parameters, expressed as linear functions of temperature, and optimized in line with the experimental data.

The experimental data employed in the erythritol-xylitol phase diagram modelling will be described later in Chapter 5. Coupling the experimental thermal property data of the pure components with the temperature- composition data of the binary system, the thermodynamic parameters of

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the pure components followed by the binary system were optimized using the PARROT module in Thermo-Calc [222].

Phase Equilibrium Derivation Methodologies- Concluding Remarks The phase equilibrium evaluations over the past four decades have numerous lessons for the benefit of PCM design. For instance, experimental phase diagram derivation needs to be a thorough process, which com- bines the information from thermal, physical and chemical evaluations of the pure components and the blends. The methods such as DSC, TGA, DTA and STA, T-history, and other calorimetric methods indicate the phase change temperatures and enthalpies. The physical characterizations can be achieved using XRD, SEM, PLM, and optical microscopy techniques, and chemical characterizations using e.g. IR or FT-IR. No single technique is superior over another, whereas, a combination of thermal and physicochemical characterizations is definitely superior over any single technique. To understand the complex phase change of material systems, such a combination is a must.

Thermal cycling indicates the standard phase change behavior of the system, and the robustness of the chosen PCM compositions. To overcome metastability, thermal annealing and strain induced transformations are effective. Tammann plots are invaluable to precisely characterize eutectics and peritectics, and thereby to determine the system’s solid-state miscibility. One major requirement in the PCM design however, is the standardization of these experimental techniques and approaches used to derive phase diagrams, and the relevant results reporting in a transparent and repeatable manner. Based on the state-of-the-art evaluation, several experimental approaches were selected here to evaluate the chosen PCM- interesting blend systems (erythritol-xylitol, and dodecane-tridecane) in this thesis work. Therein, the T-history method combined with Tammann plots, XRD, and FESEM were selected and explained.

The T-history method was adapted here to an operational mode with a controlled heating/cooling rate, essential to yield equilibrium conditions. In the XRD assessment, especially the high-temperature and very slow heating and measurement conditions were involved to ensure that the equilibrium behavior is captured. The FESEM investigations were conducted on specimens subjected to various cooling processes, to capture the dependence of the system’s stability particularly on the cooling process.

The theoretical phase equilibrium evaluations in the PCM-context have thus far been semi-empirical only. Purely theoretical assessments require 63

Saman Nimali Gunasekara extensive efforts and hence may not be the foremost step in deriving a novel phase diagram for the engineering application of PCM design. Thermodynamically, the Gibbs free energies of phases in a system are equal in equilibrium, while that of the system should be a minimum. Based on this, the phase diagrams have been derived using various semi- empirical methods, such as group-contribution approaches, regular solution theory, Schröder’s equation, PSC model, and BET model. Most of these approaches however, bound by several assumptions, were limited to specific material types such as organics or inorganics, or specific material characteristics such as those having functional group contributions. Another approach in the PCM-context identified the equilibrium phases by minimizing the Gibbs free energy of the system. With this, purely based on the phase change behavior of the system, regardless of e.g. its chemical characteristics, complex phase diagrams have been evaluated.

Therefore, in this thesis work, such a fundamental Gibbs free energy minimization approach- CALPHAD, was chosen to further evaluate one of the chosen blend systems, erythritol-xylitol. The employed methodology is also briefly explained herein. This is considered superior to other specific theoretical phase equilibrium derivations for its nonspecificity. CAL- PHAD, by evaluating the thermodynamically viable equilibrium phases in the system, proposes the thermodynamically correct phase boundaries with respect to the experimental data.

The combination of experimental phase diagram results with thermodynamic phase equilibrium evaluations altogether produces more confirmed descriptions. Deriving a novel blend’s phase diagram indeed is a continuous development process. Therefore, standard methods and approaches, and transparent and repeatable data reporting, are imperative to make the blends-based PCM design cost-effective. The current state-of-the-art of PCM design using phase diagrams, however, clearly lacks such a common consensus on the type and the number of characterization techniques needed to confirm a phase diagram. In addition, a dire necessity exists in defining standard procedures per technique, to obtain consistent, repeatable and comparable phase diagrams.

The comprehensive methodological synthesis in this chapter clarifies their various key aspects in achieving consistent and comparable phase equilibrium determinations of blend systems of PCM-interest. These are expected to serve as guidelines in achieving phase equilibrium derivations standardization in the PCM-context. Only by realizing such standardizations can the extensive and continuous development process of ascertain- ing a novel blend phase diagram be time- and cost-effective. This will contribute to realizing cost-effective and robust PCM blends.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES Experimental Phase Diagrams Determination

This chapter exemplifies the utility of the selected experimental techniques and approaches detailed in 3.1.2, to derive the phase diagrams of two binary blends systems: erythritol-xylitol, and dodecane-tridecane. This section addresses the thesis objective number 4, mainly based on the Papers III, V, and VIII, and supplemented with the relevant details from Paper II.

The state-of-the-art analysis of PCM design in Chapter 2 shows that a fundamental study with a phase diagram is the foremost step in defining a blend’s suitability as a PCM for TES applications. In that, consistent and repeatable phase diagram data are crucial to proceed with the TES design. However, the evaluations conducted so far in the PCM-context (section 2.2) also contain methodological discrepancies. The selected blend systems erythritol-xylitol and dodecane-tridecane are rather novel systems of PCM-interest, also reported with inconsistent results. Hence, with the case studies as a basis, this chapter discusses and highlights the crucial experimental methodological requirements to obtain consistent and repeatable phase diagrams. As the polyols system and the alkanes system have somewhat different background and approaches, these are detailed separately under the sections 4.1 and 4.2. Then, an overall reflection on the experimental methodologies is given in section 4.3.

Experimental Phase Diagram of the Erythritol- Xylitol System Polyols (poly-alcohols) are gaining PCM-interest ( [93]- [95], [97], [226]- [234]), as renewable and non-toxic materials, melting around -15 °C to 245 °C with the enthalpies 100-413 kJ/kg. A number of polyols blends have been explored as PCMs ( [66], [93]-[96], [202], [235]-[238]). There, the erythritol-xylitol blend system was proposed to be a non-isomorphous simple eutectic type [93], [97]. Among other polyols systems: many non-isomorphous simple eutectics [93]-[95], [97], [232]; several monotectics [66], [95], [97], [236]; a co-crystalline behavior [236]; and systems with miscibility gaps and even complete miscibility [235] were identified.

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The literature as a whole propose the stable melting of erythritol and xylitol to occur respectively within the temperatures 111-129 °C ( [93], [230], [239]-[246], and, Papers I and VIII) and 87-100 °C ( [93], [224], [240], [243]-[245], [247]-[249], and, Papers I and VIII). Their proposed enthalpies however vary considerably between the studies, ranging between 281-370 kJ/kg for erythritol, and 219-280 kJ/kg for xylitol. This diversity in the proposed enthalpies could be related to the considerable differences in their employed measurement methods, cooling/heating rates and particularly the number of cycles investigated. Metastable phases were also reported on these two polyols, with the predominant one identified: for erythritol between around 105-108 °C ( [246], Paper II) or 102-112 °C [230]; and for xylitol at 61-61.5 °C [224], [249]. Erythritol has displayed a melting process (regardless of the heating rate) which strongly depended on the preceding solidification process [246]. For instance, erythritol, solidified under different conditions, yielded a metastable polymorph before the stable melting, for the same heating rate, between 15-43 °C, at 75 °C or, at around 65 °C respectively [246].

Pure xylitol is amorphous, and thus undergoes glass transition (vitrification) ( [66], Paper II). Crystallization could be induced in such glassy polyols by seeding or undercooling for long durations [66]. Erythritol and xylitol ( [233], Paper II), among other polyols [229], have displayed thermally activated change or degradation (browning and thickening/tan- ning). This has intensified with cycling and lowered their melting temperatures and enthalpies [229], [233], [250]. It was deemed as an oxidation occurring in air but absent in inert conditions [229]. Findings from studies on other polyol systems indicate similar complexities. For example, the FT-IR spectra of myo-inositol, galactitol and D-mannitol indicated that the initial thermal treatment caused chemical changes in their C=O bonds, which were retained thereafter through cycling [229]. For pentaerythritol (PE), trimethylol ethane (TE), neopentyl glycol (NPG) and their blends, the chemical changes were explained, with FT-IR, to be solid- state transitions that reversibly break the nearest hydrogen bonds [251]. Blending of ring-structured polyols apparently improve the thermal stability of polyols [232].

The erythritol-xylitol phase diagram was proposed as a non-isomorphous simple eutectic type using: DSC [93], [97]; PLM [93]; XRD [93]; IRT [97]; and, thermodynamic modelling [93], [97]. In contrast, a preliminary study of the system with the T-history method in Paper VIII yielded a possible eutectic with more complex phase changes. The proposed eutectic point was also different between the studies: at 25 [93], 25-30 (Paper VIII), or 36 [97] mol% erythritol; and at 82 °C [93], [97] or 80-82 °C (Paper VIII), respectively. In these evaluations, the erythritol-xylitol blends were first grinded by mortar and pestle ( [93], [97], and Paper VIII). Thereafter, the

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES samples were prepared by: desiccation for 24 hours (Paper VIII); melting and cooling to room temperature [97]; or, sieving, moisture measurements, and adding minor quantities of diethyl-ether (a volatile solvent) [93]. Diethyl ether was expected to partially dissolve the pure components and enable the formation of potential new phases [93]. Nevertheless, its removal was not discussed. To realize freezing, Diarce et al. [93], and in Paper VIII small amounts of the starting material were seeded to the glassy compositions. The evaluated erythritol-xylitol samples were: a ‘droplet’ in the IRT method [97]; about 4-6 mg [93], or 10 mg in the DSC [97]; or about 50 g in the T-history method (Paper VIII).

Using PLM, Diarce et al. [93] justified the use of DSC cp peak offset temperature as the liquidus, determined a slow heating/cooling rate to use in the DSC for thermal equilibrium, and evaluated the blends’ crystallization rates and the pure component polymorphs. Seeing no new or disappearing peaks in the blends’ XRD spectra at room temperature, the system was deduced to be completely immiscible, and thus a non-isomorphous simple eutectic type [93]. To derive their phase diagram, Del Barrio et al. [97] primarily used the IRT method and theoretical modelling using pure component data from the DSC. In the preliminary T-history study (Paper VIII), the phase diagram was deduced using three melting cycles. The others, however, did not specify the number of cycles their phase diagram represents. They only explain: in DSC, the first melting (no seeding indicated) [93], [97]; in PLM, the first melting, freezing with seeding, and another melting [93]; and in the IRT, only the 2nd melting (i.e., melting of a pre-molten blend droplet solidified under room temperature) [97]. A heating rate of 1 °C/min in the DSC [93], [97] and the IRT [97]; and cooling from 152 °C under room temperature in the IRT [97]; or, heating/cooling rates of 0.1 °C/min, in the T-history method (Paper VIII) were employed.

To understand and explain the discrepancies observed in the erythritol- xylitol system’s phase change, the system was then thoroughly evaluated experimentally in Paper III, using the methods: T-history combined with Tammann plots analysis and Transient Plane Source (TPS) method; XRD; and FESEM. In the following, this detailed methodology is explained and the results are discussed, to determine the erythritol-xylitol phase diagram. Furthermore, the benefits, challenges, and requirements in utilizing multiple characterization methods to derive experimental phase diagrams for PCM design are discussed.

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4.1.1 Erythritol- Xylitol Study: Materials and Methods In this work, meso-erythritol (C4H10O4, CAS number 149-32-6) and xylitol (C5H12O5, CAS number 87-99-0) each of 99% purity were used [252]. Their chemical structures are shown in Figure 4-1.

OH OH HO OH HO OH OH OH OH Erythritol Xylitol

Figure 4-1. The chemical structures of erythritol and xylitol

Two separate T-history tests were conducted for temperature and enthalpy determination, later explained in section 4.1.1.1. There, the pure components and the blend compositions within 10 mol% intervals as well as the 217, 5, 25, 35, 95 and 98 mol% erythritol (referred to as mol% Er) were investigated. These samples were prepared by weighing the relevant erythritol and xylitol amounts (with 0.04 g expanded uncertainty with a 0.95 confidence), and by grinding and mixing using porcelain mortars and pestles. The overall mixing ensures a composition with an expanded uncertainty of 1.3 mol% with a 0.95 confidence.

These mixtures were then desiccated for 24 hours to remove moisture. A simple thermogravimetric analysis of the prepared pure components, 25 mol% Er, and 80 mol% Er yielded weight losses less than 0.05%. Hence, succeeding desiccation, negligible moisture content was assumed in all the samples. The desiccated samples were then transferred into the SS test- tubes, for T-history experiments: in powder form for temperature-tests; and in liquid form, after melting in an oven at 135 ºC for 5 hours, for enthalpy-tests. The sample weights used were within 10-11.5 g and 14-16 g for the temperature- and enthalpy-tests respectively. The references used were Cu-ETP1 and SS1 (c.f. section 3.1.2.1).

17 For the temperature-tests of the 2 and 98 mol% samples, the expanded uncertainty (with 0.95 confidence) of weights were 0.14 g, and of the composition were: 5% and 4%.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

4.1.1.1 T- history and Transient Plane Source (TPS) Methods, and Tammann Plots Two separate T-history tests were conducted, to determine the melting temperatures (temperature-tests) and the enthalpies (enthalpy-tests). The temperature-tests started from powder samples, thus captured their very first melting. Whereas, the enthalpy tests started with liquid samples (powders pre-molten in the oven, section 4.1.1), to ensure sample volumes similar to the reference. Thereby, the correct T-history conditions for the enthalpy calculations were met in the enthalpy-tests. There however, the first melting was skipped, while the rest of the enthalpy changes were calculated according to section 3.1.2.1. Both the temperature and enthalpy tests underwent the same temperature program, using heating/cooling rates of 0.2 ºC/min, with isothermal stabilization at the end- temperatures 0 ºC and 139 ºC for 5 hours, each. All the compositions underwent 5-9 heating/cooling cycles. Because 0-60 mol% Er compositions failed to readily crystallize, small amounts (5-10 mg) of the starting powders were seeded onto their supercooled liquid. Thereby, for those compositions, four melting instances were obtained: the first independent, and three more induced by seeding. As seeding interrupted the cooling cycles, these were excluded in the investigation.

The blends’ thermal conductivities are unknown, yet necessary to verify the T-history conditions (i.e., Bi<0.1). Hence, as estimates, the thermal conductivity of pure erythritol, pure xylitol, 25 mol% Er, and 80 mol% Er were measured, using the Transient Plane Source (TPS) method with a Hot Disk Thermal Constants Analyzer TPS-2500S [253]. The employed Hot Disk sensor 7577 (2 mm radius) was insulated with polytetrafluoroethylene (PTFE). The sample holder used was an aluminum one, built in- house [253].

To compare the very first melting with the remainder, the Tammann plots were constructed using the approximate enthalpy change from the T-history temperature-test measurements. There, it was assumed that the sample and reference volumes are equal, and the associated volumetric-error is equal for each calculated enthalpy. These approximate enthalpy and cp curves were also employed together with the temperature profiles to deduce the phase change temperatures to plot the phase diagram.

4.1.1.2 X - Ray Diffraction Analysis For the XRD scrutiny, the liquid T-history end-products were poured into glass test-tubes at room temperature, and then maintained at room temperature for 3 months (for RTXRD and HTXRD, c.f. section 3.1.2.3), or 1.5 months (for slow-XRD). The resultant solids were then grinded

Saman Nimali Gunasekara into powders. These were evaluated using: pure components and 5-95 mol% Er compositions in RTXRD; 5, 25, 30, 80 and 95 mol% Er compositions in HTXRD; and 2 and 80 mol% Er compositions in slow-XRD.

The RTXRD followed by HTXRD were conducted employing the conditions detailed in section 3.1.2.3, Table 3-4. In the HTXRD, heating conditions that are close (but not exactly the same) to the T-history conditions were achieved. Both RTXRD and HTXRD results failed to fully explain the T-history observations, possibly due to heating rates still faster than desired. Therefore, slow-XRD investigations were then conducted with isothermal temperature steps and measurements for 10 hours each (c.f. section 3.1.2.3), to reach conditions allowing better thermal equilibrium. There, the chosen temperature steps were: room temperature for both samples, and 70 ºC and 76 ºC for the 80 mol% Er. These temperatures and the compositions were chosen using the preliminary phase diagram of the system constructed using the T-history results (detailed in section 4.1.2.1).

4.1.1.3 Scanning Electron Microscopy Analysis All the samples investigated by the FESEM were also liquid T-history end products. Most of these (5-95 mol% Er) were prepared by quenching the liquids at room temperature followed by about 3 months room-temperature annealing. These are referred to as ‘long-term annealed’ samples. The compositions 70 and 80 mol% Er were also investigated after keeping the quenched T-history products under room temperature just one day. These are termed ‘short-term annealed’ samples. A few more samples were prepared, aiming to preserve the eutectic structure around the grain- boundaries, if it exists in the system. There, the molten T-history products of the compositions 5, 25, 32.5 and 80 mol% Er were: annealed at 78 °C for 5 hours (and 80 mol% Er also annealed at 139 °C for 2 hours); quenched in liquid N2; and then annealed at room temperature for 3 hours. These are the ‘quench-annealed’ samples.

4.1.2 Erythritol- Xylitol Study: Results and Discussion Here, the phase equilibrium of the erythritol-xylitol system is comprehensively evaluated, combining the thermal, crystallographic and microstructural evidences. In parallel, the novel understanding obtained on the system is compared to the previous study results ( [93], [97], and Paper VIII).

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

4.1.2.1 Thermal Properties To exemplify the various phase changes in the erythritol-xylitol system, the cp profiles of a number of compositions at a chosen melting cycle are shown in Figure 4-2. These were obtained from the T-history temperature-tests. The phase change onset and offset temperatures were chosen at the intersection of the tangents, drawn to the baseline, and respectively to the leading and the backward edge of the cp peaks. Many peaks lacked a straightforward leading edge. Hence, the cp, temperature and enthalpy profiles were compared as whole to ultimately deduce the onsets and offsets.

The cp Profiles Evolution in the Erythritol-Xylitol System 156

136

116 Er,M2 Er,M1 96 95Er,M4 80Er,M4 76 70Er,M3 60Er,M4 56 40Er,M2

(arbitrary units) (arbitrary units) 25Er,M2 p

c 36 10Er,M3 5Er,M3 16 2Er,M2 Xy,M4 Xy,M3 -4 Xy,M1 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Temperature (°C) Figure 4-2. The specific heat profiles evolution of the erythritol-xylitol system for the pure and many blend compositions, for chosen melting cycles. (Here, the cp axis uses arbitrary units (a.u.), and the profiles are shifted by 10 a.u. intervals for illustrative clarity. The gap between the minor gridlines nevertheless is similar to 4 kJ/(kg·K). M1-M4 indicate the 1st to 4th melting, while Er is erythritol and Xy is xylitol)

Clearly, the system exhibited one, two or three phase change cp peaks per heating, as Figure 4-2 indicates. The peak at the highest temperature was considered melting, except for blends with just one peak. A single peak appeared was considered: as the melting, on the pure components and e.g. 95, and 98 mol% Er; and, as a potential eutectic on the blends e.g. 25- 30 mol% Er. A low temperature peak below the potential eutectic temperature, occurred for several compositions (e.g. 2, 5, 10, 60, 70 and 80 mol% Er), was considered as a solid-solid phase change (S-SPC). The eutectic peak consistently appeared for the blends 20-60 mol% Er. Often superheating preceded the S-SPC, causing a negative cp in the increasing part of the peak (e.g. 2, 70 and 80 mol% Er, Figure 4-2).

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The system also exhibited possible liquid crystalline behavior, partially crystalline behavior, and thermal decomposition (interpreted according to a DSC guide [254]), respectively on certain compositions. The browned and thickened T-history products also implied thermal decomposition. Succeeding the first melting, pure erythritol and xylitol alternately contained some random minor cp humps before the stable melting peak. This is seen e.g. in Figure 4-2, during the 2nd and 3rd melting of erythritol and xylitol respectively. These could be consequent of thermal decomposition and glass transition, while may even be metastabilities such as those encountered in erythritol [246] (section 4.1). Nonetheless, the stable melting was consistently achieved in all the heating cycles for both pure polyols. Therefore, these minor cp variations were considered trivial, and that overall, the system attained stability.

The melting offsets or the offsets of the single peaks of the potential eutectic compositions were chosen as the liquidus. The eutectic onset or the melting onset were chosen as the solidus. This is despite different approaches found employed in literature, choosing e.g. the eutectic offset as the solidus [93], or the melting peak as the liquidus [66]. With choices as such (e.g. [66], [93]), some material still in the eutectic transition will remain below the eutectic isotherm, or, some of the melting solid will remain above the liquidus. Here in contrast, it was ensured that all that is eutectic or melting were encompassed between the solidus and liquidus. The solvus was chosen to be the S-SPC offset, so that the phase region above this contains only the intended solid solution phase. Using these interpretations, the phase diagram of the erythritol-xylitol system (phase change temperatures versus the molar composition) was plotted.

During the first melting, the powdered components melted and dissolved for the first time, but it was not a single solid (i.e., the real blend) that melted. Thus the system’s phase diagrams are derived for the 2nd-4th melting cycles in Figure 4-3. Here, nevertheless, the temperature-composition plot for the first melting is also plotted for comparison, although it is not a phase diagram. In Figure 4-3, the average over the 2nd-4th melting (the selective average) is respectively compared with the 1st melting (in Figure 4-3 a)), and each 2nd-4th melting cycles (in Figure 4-3 b)). The liquidus, solidus and the S-SPCs are denoted with L, S and S-S respectively, followed by the cycle number, or by 2-4 for the selective average. In Figure 4-3, the dotted lines in a) and the dashed lines in both a) and b) are smoothened data point connections drawn to guide the eye. The dotted lines in Figure 4-3 b) are obtained using point-by-point interpolation of the selective average, denoted using a suffix ‘int’.

As a whole, the liquidus trends in Figure 4-3 indicate a temperature minimum in the system. The solidus exists at a rather constant temperature

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES for many intermediate compositions for the 2nd-4th melting cycles. This is possibly a eutectic isotherm, with the temperature minimum a eutectic. However, this cannot be confirmed with merely the thermal properties of the system.

a) The selective average (dashed lines) compared to the 1st melting (dotted lines)

A W shape in the liquidus that may indicate co-crystals

b) The selective average (in dashed lines, with the trends in dotted lines) compared to the 2nd to 4th melting Figure 4-3. The phase diagrams of the erythritol-xylitol system, comparing: the selective average (over 2nd-4th melting), with a) first melting, and b) each 2nd-4th cycles, respectively (The expanded uncertainties of the temperature and composition are 0.4 ºC and 1.3 mol% Er respectively, with 0.95 confidence).

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Several compositions (e.g. 80, 90, 95 and 98 mol% Er) experienced a random appearance and disappearance of a eutectic cp peak during different cycles. This peak completely disappeared at later cycles for certain compositions, e.g. 95 and 98 mol% Er. This could be an implication that the erythritol-xylitol system, in the long-run, is partially isomorphous at these compositions. Similar observations were reported on the pentaglycerine (PG)-NPG system, where, an initially immiscible behavior has given-in to a partially miscible behavior dominant through extensive cycling [202].

The system’s phase diagram, represented by the selective average, is clearly different to the temperature-compositions plot of the 1st melting as in Figure 4-3 a). Only the temperature-compositions plot for the 1st melting corresponds to a non-isomorphous simple eutectic shape similar to that of Diarce et al. [93] and Del Barrio et al. [97]. The erythritol-xylitol phase diagram in-contrast, implies partial miscibility at pure component- rich compositions (c.f. Figure 4-3). That is, the S-SPCs observed possibly indicate an incomplete solvus. This S-SPCs indicating partial miscibility agrees with the observations in the earlier preliminary T-history study (Pa- per VIII). The variations between each melting cycle, 2nd, 3rd and the 4th, and the selective average are negligible, except for 90-98 mol% Er, as seen in Figure 4-3. The larger variations at 90-98 mol% Er, and the incom- pleteness of the solvus could be due to glassy interferences.

Based on just the trend of the liquidus in Figure 4-3, the average eutectic point exists around 30 mol% Er, with the onset at 77 °C. A possible ‘W’ shape around this eutectic (between 20-40 mol% Er) can be seen on the liquidus, e.g. in Figure 4-3 b). In the preliminary T-history study (Paper VIII) a similar ‘rise-and-fall’ in the liquidus was suspected to be a possible congruent melting compound. This behavior reflects a co-crystal formation, as was e.g. reported on the xylitol-D-sorbitol system [236]. A co- crystal is made of two or more molecules bound by non-covalent bonds in fixed stoichiometry [255]. It appears as a temperature maximum between two eutectics in a typical W shape [255]. To confirm if the ‘w’ shape in the erythritol-xylitol liquidus is also a co-crystal, crystallographic or other physical characterizations are a must. All-in-all, the erythritol-xylitol phase equilibrium is complex, and needs experimental evidences from multiple assessments to verify the correct phase diagram.

Thermal Conductivity The TPS analysis yielded the thermal conductivities of erythritol, xylitol, 25 mol% Er, and 80 mol% Er to be: 0.32, 0.43, 0.40 and 0.36 W/m·K in the liquid state; and 0.59, 0.37, 0.39 and 0.54 W/m·K in the solid state, respectively (with an expanded uncertainty of up to 5% with a 0.95 confidence level). Hence, the lowest thermal conductivity in the system is of liquid erythritol. Even this smallest thermal conductivity produced Biot

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES numbers smaller than 0.1 in the T-history calculations. Therefore, the lumped capacity conditions were met, thus confirming the validity of the T-history evaluations.

Enthalpy Characteristics The phase change enthalpies of the pure and blend compositions were calculated using the T-history enthalpy-tests. The maximum melting enthalpies of erythritol and xylitol were found to be: 229±64 kJ/kg and 164±46 kJ/kg (within 112.6-128.0 °C and 90.6-97.7 °C). These, having excluded the first melting, are not exactly comparable with many of the literature which examined only the first melting or an unspecified number of cycles (c.f. Paper III). Nonetheless, in comparison, these values are lower than a majority, but are rather close to the lowest of the literature values: 286 kJ/kg [239], and 219-222 kJ/kg [247], for erythritol and xylitol respectively. The lower enthalpies identified herein are possibly caused by thermal degradation, glass transition and some minor pre-melting metastabilities. Thermal degradation is in fact promoted by ambient conditions in the T-history, in contrast to inert atmospheres in DSCs (c.f. [229]). Besides, even with DSC, a 20% and 8% decrease in erythritol and xylitol melting enthalpies have been experienced, after 2 hours at 40 °C above the melting temperatures [233]. Although thermal degradation is to be avoided, the above findings are important inputs to designing TES using polyols.

The compositions closest to the eutectic, 25 and 30 mol% Er respectively contained: the maximum eutectic enthalpies of 59.5±17 kJ/kg and 45±13 kJ/kg (between 80.6-101.6 °C and 80.0-91.1 °C respectively); and a total enthalpy change (accounting glass transition and the intermediate sensible heat as well) of 172±48 kJ/kg and 200±56 kJ/kg (between 38-102 °C and 27-91 °C respectively). These enthalpies, being heavily masked by glass transition, are perchance not their best eutectic enthalpies. The highest eutectic enthalpy change of the system was however observed on 40 and 50 mol% Er compositions. These are larger possibly due to less glassy- influence.

Tammann Plots The Tammann plots constructed with the approximate 18 eutectic enthalpies from the temperature-tests of the erythritol-xylitol system, are summarized in Figure 4-4. There, the selective average (over the 2nd-4th cycles) eutectic enthalpy change is compared to that of each 1st to 4th melting. In Figure 4-4, the eutectic enthalpy change ΔhE (in kJ/mol) for each cycle is represented with h,E, followed by the cycle number, or by

18 Because of the volumetric error incurred in the T-history temperature tests.

Saman Nimali Gunasekara

2-4 for the selective average. As the 1st melting is not the real blend melting, its enthalpy-composition plot (but not truly a Tammann plot) is used here merely for comparison. The eutectic enthalpy change of several compositions fluctuates very much between the cycles, and hence a linear- regression was not performed here.

Figure 4-4. Tammann plots summary of the erythritol-xylitol system, comparing the selective average of 2nd-4th melting (in a dashed-line), with each melting cycle, 1st-4th (in dotted-lines)

As was explained in section 3.1.2.2, in a Tammann plot, a eutectic is characterized by a triangular shape. This triangle ends: at the pure compositions for a non-isomorphous simple eutectic; and where the solid-miscibility begins (and the eutectic disappears) for a partially miscible system [206]. The erythritol-xylitol Tammann plot (Figure 4-4) lacks a straightforward triangle for any of the four cycles. Complexities in Tamman plots occur due to systems with intricate phase change, which may even make it impossible to create the plot [206]. Therefore, the erythritol-xylitol system appears to have a behavior more complex than a non-isomorphous simple eutectic. The real blend melting, at the 2nd-4th cycles in Figure 4-4, imply partial miscibility at pure component-rich compositions, where the eutectic enthalpy change reaches zero. Only the trend for the 1st melting indicates a completely immiscible system, which however does not represent the real blend melting.

From the measured values, the maximum enthalpy change exists at the 25 mol% Er composition, for all the cycles as well as the selective average. Hence, the Tammann plots imply that the eutectic lies the closest to 25 mol% Er from those measured. However, as the temperature minimum on the liquidus in Figure 4-3 lies around 30 mol% Er, the exact eutectic 76

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES could be between 25 and 30 mol% Er, yet closer to 25 mol% Er. This is comparable with the ~25 mol% Er composition Diarce et al. [93] concluded, but different to the 36 mol% Er Del Barrio et al. [97] concluded.

4.1.2.2 Crystallographic Characteristics The RTXRD characteristics of the erythritol-xylitol blends only contained a mixture of the pure component peaks, with no new or disappearing peaks. This also agrees with Diarce et al. [93]. Hence, the RTXRD implies that at room temperature the system is only a physical mixture of erythritol and xylitol, i.e., is completely immiscible. Thus the minimum melting composition in the system, surrounded by an isothermal phase change for several compositions, is more likely a eutectic. The system could be a non- isomorphous simple eutectic; or a eutectic in a system which is partially miscible at higher temperatures, and undergoes complete de-mixing around room temperature.

The absence of any disappearing peaks in RTXRD implied that no solid solutions are detected in the system. This however contradicts the S-SPCs identified during the T-history study. Therefore, aiming to capture the solid solutions behavior at the higher temperatures, the HTXRD was conducted, maintaining conditions rather close to the T-history. The HTXRD of the 5 and 95 mol% Er characteristics are shown as examples, in Figure 4-5.

With HTXRD, all the five compositions displayed only a mixture of pure component peaks, without any new or disappearing peaks (e.g. Figure 4-5). Hence, the HTXRD also could not explain S-SPCs observed in the T-history. The reason for this was considered as the ~5 times faster heating rate: 1 °C/min in HTXRD, instead of the 0.2 °C/min used in the T- history method. Although the isothermal steps (c.f. section 4.1.1.2) were expected to promote better thermal equilibrium, these seem inadequate to surpass the very slow phase change kinetics of this glassy system. Be- sides, the counting statistics (e.g. the time per step) used in HTXRD may have been insufficient to clearly indicate the exact disappearance of certain peaks of some compositions (e.g. 5 and 95 mol% Er).

Saman Nimali Gunasekara

a) 5 mol% Er, HTXRD heating from room temperature to above 94 °C

b) 95 mol% Er, HTXRD heating from room temperature to above 124 °C Figure 4-5. HTXRD characteristics of 5 and 95 mol% Er samples, with the erythritol (Er) and xylitol (Xy) characteristic peak positions indicated by arrows.

Consequently, the slow-XRD was then conducted, allowing significantly more measurement duration at each temperature. The slow-XRD characteristics of the 80 mol% Er sample are summarized in Figure 4-6. With slow-XRD, the 80 mol% Er exhibited several xylitol peaks (indicated by black arrows), which existed at room temperature and 70 ºC, disappearing at 76 ºC. This principally specifies that the 80 mol% Er sample was a mixture of the solid solutions of the pure components till 70 ºC, but became a single solid solution of erythritol above 76 ºC19. This confirms the solid-solid phase change at e.g. 80 mol% Er. The slow-XRD of the 2

19 The crystal structure of a solid solution SA between two components A and B, becomes the crystal structure of A, if A is the host (solvent) and B is the guest (solute).

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES mol% Er sample yielded already at the room temperature only the xylitol characteristics. This is potentially due to the very small volume fraction of erythritol in 2 mol% Er.

Figure 4-6. Slow-XRD characteristics on 80 mol% Er sample (xylitol peaks denoted by arrows)

Ultimately, the slow-XRD corroborated the S-SPCs in the T-history, with e.g. the solid solutions formation for the 80 mol% Er with slow-XRD. Therefore, the system is partially miscible in the solid-state (i.e., partially isomorphous), with a solvus through the 60-80 mol% Er compositions. Interestingly, from the three XRD evaluations, the slow-XRD represented the conditions closest to the stable equilibrium. Therefore, the T- history conditions also appear to have met the stable equilibrium conditions. The overall XRD results also verify that the polymorphic changes were absent in the system. Therefore, the blend system’s stability was un- affected by the probable minor metastabilities seen on the pure components (c.f. section 4.1.2.1). Since none of the XRD evaluations yielded new peaks, the system does not form any compounds. Hence, the system does not have any co-crystals, as was suspected earlier based on the T- history only.

4.1.2.3 Microstructural Characteristics The first SEM evaluations in literature on the erythritol-xylitol system are presented here, to complement the T-history and XRD characteristics. From those evaluated, a few selected FESEM micrographs are compiled into Figure 4-7, for a) 5 mol% Er, b) 95 mol% Er and, c) 80 mol % Er specimens. Their magnifications are shown at the bottom, and the regions of interest are marked in light-yellow. In this microstructural analysis, the most-stable crystal structure of erythritol and xylitol respectively was considered to be tetragonal [223], and orthorhombic [224]. Furthermore, the interpretations start at the findings so far, that the erythritol-xylitol system

Saman Nimali Gunasekara is a partially isomorphous system, miscible at and above 60 mol% Er, and at extremely xylitol-rich compositions, and contains a eutectic between 25 and 30 mol% Er.

1) 2)

1 μm

1) 2)

1) 2) 3)

As Figure 4-7 a) 1) and 2) show, both the long-term annealed and quench- annealed specimens of 5 mol% Er consist of alike morphology. This includes a microconstituent20 (small blocks-like regions as indicated by a yellow arrow in Figure 4-7 a) 2)) of a smaller proportion, precipitated on the grain-boundaries of a matrix microconstituent/phase (i.e., the continuous regions in Figure 4-7 a)). Similar morphologies existed on the 10 mol% Er and 95 mol% Er specimens, the latter shown in Figure 4-7 b), with precipitates zoomed-in on 2). Hence, the pure component-rich compositions 5, 10 and 95 mol% Er imply a secondary microconstituent precipitating on a primary solid solution phase, stable at room temperature. This implies the solid-solutions formation and thus the partial-miscibility of the system. This primary phase would be a solid solution: of xylitol (SXy) for 5-10 mol% Er; and of erythritol (SEt) for e.g. 95 mol% Er.

20 A portion within a microstructure with a distinct structure [256], e.g. a eutectic. 80

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Whereas, the precipitated microconstituent would be the eutectic portion of a hyper- or hypo-eutectic composition.

The molten T-history products of the 70, 80 and 90 mol% Er formed cube-like crystalline blocks when quenched from 138 ºC to room temperature. These cube-like structures were retained even after one day in room temperature, as e.g. seen in the 80 mol% Er specimen in Figure 4-7 c) 1). The microstructure of this 80 mol% Er sample however became completely different after long-term annealing, as in Figure 4-7 c) 2). There, the cube-like structures were replaced by a darker microconstituent/phase surrounded by another lighter microconstituent precipitation (circled in light-yellow). The quench-annealed 80 mol% Er specimen in Figure 4-7 c) 3) also exhibited a morphology very different to both 1) and 2). Because the long-term annealed sample underwent the longest room temperature annealing, this has to be the most stable structure of all, for 80 mol% Er. Then, the short-term annealed cube-like structure and the quench-annealed structure of 80 mol% Er (Figure 4-7 c) 1 and 3)) are most-likely dissimilar metastable structures.

As a whole, the FESEM evaluations indicate solid-solutions formation and thus support a partially isomorphous phase diagram for the erythritol-xylitol system. The system’s crystallization is cooling-rate dependent, yielding various metastable structures, e.g. for 80 mol% Er, under different cooling. This rate-dependent crystallization is important to be understood for TES design, irrespective of the phases it encompasses.

4.1.2.4 Erythritol- Xylitol Phase Diagram The complementary results from the three experimental methods employed confirm the erythritol-xylitol phase diagram to be a partially isomorphous system containing a eutectic. Determining the complete solvus in the system requires further interpretations. Nonetheless, combining the experimental evidences so far, the erythritol-xylitol phase diagram is proposed in Figure 4-8. This represents the selective average of the 2nd-4th melting instances, manually drawn with the most-fitting phase boundary trends to guide the eye. In Figure 4-8, the liquidus, solidus and the solvus points are chosen to be the: melting offsets (or the eutectic offset, if only this exists); eutectic onsets; and the S-SPC offsets respectively. The first melting is excluded as it was not the real blend that melted there, but only the pure component powders.

The T-history results in both Paper III and Paper VIII comply. The phase diagram here is however different to that identified based on merely the preliminary T-history results (Paper VIII). This discrepancy clearly indicates the misinterpretations that arise when the physical and/or chemical

Saman Nimali Gunasekara characteristics of the system are unknown. The extensive physical characterizations of the system herein confirmed the eutectic and the solid solutions formation, and ruled-out the possibility of a compound formation. The pure polyols exhibited some minor, and perhaps metastable phase change variations prior to the stable melting peak, after the very first melting. These changes could be triggered by thermal decomposition and glass-transition. Nonetheless, as the XRD verified, these minor metastabilities in pure polyols did not affect the overall stability of the blend system.

Figure 4-8. The proposed erythritol-xylitol phase diagram: a partially isomorphous system with a eutectic

The eutectic point of the erythritol-xylitol system exists between 25-30 mol% Er and 77 °C (onset), as the Tammann plots and the liquidus trends indicate in-combine. The partially isomorphous phase diagram with a eutectic for the erythritol-xylitol system (Figure 4-8) does not comply with the non-isomorphous simple eutectic type the other evaluations ( [93], [97]) presented. Only the temperature-composition plot (but not a phase diagram) of the first melting here indicates such a non-isomorphous simple eutectic shape. Therefore, the proposed eutectic point or the enthalpies are not directly comparable with the present study results. After- all, the eutectic was proposed at the compositions 25 [93] or 36 [97] mol% Er, and an onset temperature of 82 °C [93], [97] by the others, hence with considerable disparities. The eutectic enthalpy obtained here is between around 45-60 kJ/kg, with the total phase change and glass-transition enthalpy between around 172-200 kJ/kg. This eutectic enthalpy is possibly smaller than the actual value, being heavily influenced by glass-transition 82

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES and thermally-activated change. Glass transition distributes the otherwise concentrated enthalpy of fusion over a continuous heating/cooling range. Thermally-activated change is incident after the first melting, and decreases the fusion enthalpy. The eutectic enthalpies proposed by the other studies, 249 kJ/kg [93] or 270 kJ/kg [97] also are rather different.

The main reason for the differences between the studies is possibly the use of the cycled behavior of the system here, compared to an unspecified number of cycles used by the others ( [93], [97]). Some other procedural differences between the studies also may have affected the results. For instance, the mixing of a volatile solvent during samples preparation, without disclosing its removal [93] instead of using merely the polyols as here. If the solvent remained, it could influence the blend’s phase change as an impurity. The sample size used here is at least 1000 times larger, while the heating/cooling rates were 5 times slower, than those employed in the other studies [93], [97]. Thus, in the present investigation, the phase change behavior of a more bulk sample, and conditions closer to the equilibrium were likely. As a whole, it is not clear how comparable is the overall property assessment methodology employed here to those employed by the other evaluations ( [93], [97]), because those lacked such detail.

This work excludes the freezing-based phase diagram, as the cooling cycles were interrupted during seeding. However, if the freezing-based diagram was realized, it could further verify the phase change trends in the system, and thereby the phase diagram. Besides, the freezing temperatures and enthalpies, as well as the level of supercooling and hysteresis should be known to design the TES system. For blend systems freezing on their own, the comparison of the phase diagrams based on both melting and freezing will be feasible and beneficial.

The enthalpy uncertainty here is rather considerable (i.e., 28%). However, this does not affect the phase diagram, which is only affected by the temperature and compositional uncertainties, that are small (0.4 °C and 1.3 mol% Er expanded uncertainties respectively with 0.95 confidence). Nev- ertheless, as the sensitivity analysis in Figure 4-9 indicates, the enthalpy accuracy improves significantly, e.g. to 7%, with only smaller improvements in the temperature accuracy, e.g. with 0.1 °C. This can be achieved by using thermal sensors with higher accuracy, e.g. Resistance Tempera- ture Detectors (RTDs) instead of thermocouples. Furthermore, accounting corrections related to the thermal conduction along the temperature sensors would also improve the temperature accuracy.

The identified erythritol-xylitol eutectic is a renewable and safe material with an attractive melting temperature as a PCM e.g. for district heating. However, it’s extremely glassy nature and consequently the low melting

Saman Nimali Gunasekara enthalpy are challenges in realizing its PCM benefits. Besides, the thermally activated change and its effects on the long-term cycling need to be thoroughly understood, before using it as a PCM. For that, the blend’s reactivity, e.g. in terms of its chemical characteristic changes, under the real environmental conditions of the TES system (e.g. oxygen atmos- phere, and high temperatures and humidity) should also be investigated. Even for a TES system favoring supercooling, a supercooling eutectic cannot work as a robust PCM because it will phase separate. Also, this system will require an external mechanism to trigger freezing, every time. Thus, initializing the crystallization, avoiding thermal degradation, and extensive cycling tests coupled with chemical characterizations, are explorations required in future to make the eutectic application-ready. Determin- ing the exact composition of the eutectic and the exact spread of the solvus necessitate further evaluations allowing higher compositional resolution.

80 70 70 63 60 56 49 50 42 40 35 28 30 21 20 14 7 10 4 Enthalpy Uncertainty (%) 0 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Temperature Uncertainty (°C) Figure 4-9. Sensitivity analysis of the enthalpy uncertainty against the temperature uncertainty

On one hand, distinguishing if the erythritol-xylitol phase diagram is a partially isomorphous type with a eutectic or a non-isomorphous simple eutectic does not matter much. While on the other hand, it is a must. On the one hand, once a eutectic (or a congruent melting composition) is confirmed, it is only the eutectic (or the congruent melting composition) that is relevant as a PCM. On the other hand, to confirm the eutectic, the complete phase diagram must be confirmed. To verify the phase diagram, the complements from thermal and physicochemical characteristics of the system, obtained using multiple techniques, while ensuring equilibrium conditions and the long-term standard behavior of the system, are crucial. A TES design supplement to the phase diagram is its kinetic phase diagram, derived for the application-specific conditions.

To determine the actual phase equilibrium of the erythritol-xylitol system, the T-history method has been indispensable. It consistently displayed the S-SPCs, while presented the temperature, enthalpy and the cp profiles

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES simultaneously, enabling a more effective phase change diagnosis. XRD effectively complemented in verifying the eutectic as well the solid-solutions. FESEM also implied the solid solutions formation, and exemplified the system’s susceptibility to metastability. This cooling/heating rate-dependence of the system and the expected metastable phases are extremely relevant inputs for the TES system design. Such phases can be plotted in a kinetic phase diagram to understand the system’s PCM potential under metastability. As experienced, each experimental method requires a certain maturity over a novel system, to yield its correct phase diagram.

Understanding a novel blend’s phase change completely is an extensive continuous development process, requiring complementary contributions over time. This, however, should not compromise the objectives of a phase equilibrium study for the engineering purpose of PCM design, necessitating timely and cost-effective information. Then again, it should not undermine the significance of obtaining an accurate and a comprehensive phase equilibrium diagram. Though discrepancies are observed between the studies ( [93], [97], and the present work) the erythritol-xylitol phase diagram progressed, with benefits towards PCM design. This is indeed a continuous development process through which a novel systems’ phase equilibrium understanding reaches maturity, delivering cost-effective and robust PCM blends. Each investigation has specific scientific contributions, which will be complemented by upcoming findings, essentially building up a database per blend. However, as it is shown here, to collectively build-up complementary findings, it is extremely critical to standardize the property evaluation techniques, methodologies, and transparent results reporting, used in PCM design. The present investigation is based on an in-depth understanding of the state-of-the-art in methodologies, and then clearly identifies the procedure as to how input from various methodologies together bring forward the phase equilibrium aspects of a binary system.

Experimental Phase Diagram of the Dodecane- Tridecane Alkanes System Alkanes have been extensively investigated in the PCM-context, concerning many pure components (e.g. [257]-[263]), and blends (e.g. [36], [39], [48], [49], [109], [110], [135]). Alkanes are attractive as PCMs, with rather stable phase changes, negligible supercooling, moderate enthalpies and satisfactory compatibility with metals [24]. Their drawbacks include, being of non-renewable origin, having rather low thermal conductivities (often around 0.1-0.4 W/m·K, as compared to 0.5-1.5 W/m·K typical to inorganics), and incompatibility with plastics [24].

Saman Nimali Gunasekara

Among the phase equilibrium studies of alkanes blends for PCM design, as detailed in section 2.2.1.2, phase diagram disparities exist for several systems. One such is the dodecane-tridecane (C12H26-C13H28) binary system, proposed with a liquidus increasing towards a temperature maximum [135], or to contain a eutectic in a partially isomorphous system [109]. The phase change of pure dodecane (C12H26, referred to as C12) and tridecane (C13H28, referred to as C13) are characterized in literature, as summarized in Table 4-1. The melting phase of the pure even alkanes including C12 is an ordered triclinic phase (TP), while, that of the odd alkanes including C13 is a rotationally disordered orthorhombic phase (RI) [109].

Table 4-1. Literature-based thermal properties and crystallography of dodecane and tridecane Parameter Dodecane (C12H26) Tridecane (C13H28) Fusion/Melting tem- -10 [49], [109]; -9.6 -5.5 [49], [109], [264]; -4, -6 perature (ºC) [135], [264] [135] Fusion enthalpy 210 [49], [109]; 216 157 [49], [109], [135]; 196 [264] (kJ/kg) [135], [264] Melting phase TP [49], [109] RI [49], [109]

Yilmaz et al. [135] presented a preliminary phase diagram of the C12-C13 system, based on the liquidus only. This liquidus had an increasing trend towards a maximum and then decreasing, such like the liquidus in the system in Figure 2-1 (b) (Chapter 2). This was determined using the freezing onsets of the blends determined using the cooling curves obtained using a thermostat-bath, and the DSC. The DSC, used with a cooling rate of 1 ºC/min, also yielded their phase change enthalpies in addition. To determine the solidus, it was stated that the crystallographic evidences are required. The maximum melting point in the preliminary phase diagram exists at 80% w/w C13 (~78.7 mol% C13) and around -3 ºC to -5 ºC, with a freezing enthalpy of 126 kJ/kg [135].

In contrast, Ventolà et al. [109] proposed the system to be partially isomorphous type, containing a eutectic at around 17 mol% C13 and -17 ºC. Their proposed system’s SLE is of the type in Figure 2-1 (d) (Chapter 2), followed by solid-solid phase changes including a eutectoid21. Their phase diagram derivation was based on DSC measurements complemented with the solid phases’ crystallography obtained through XRD, and thermodynamic modelling. However, the detailed experimental methodology is unknown, of which the original literature ( [265]) is unavailable openly. In their phase diagram, the eutectic isotherm and the solvus curves were presented in discontinuous lines, though not explained as to why. The melting enthalpy of the eutectic was not disclosed, however, for the 50 mol%

21 A eutectoid is a solid-solid phase change, shaped like a eutectic in the phase diagram, but forming a eutectoid mixture of two solids out of a single solid.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES blend, it was reported to be 146 kJ/kg. Pure C13 has a polymorph, which is an orthorhombic phase (a face centered Bravais lattice) [266]. Hence, by its influence, the C12-C13 phase diagram also includes polymorphic phase changes, forming a eutectoid at lower temperatures [109].

Hence, both studies can be said to only present part of the results needed to establish the phase diagram. Furthermore, there is a major discrepancy between the two studies as to the liquidus, such that, it is worthwhile to re-evaluate the C12-C13 system. Therefore, with the main objective of confirming the phase diagram of the C12-C13 system, and to understand why some discontinuous phase boundaries were identified in the phase diagram by Ventolà et al. [109], the system was re-evaluated in this work. In addition, it was aimed to determine the melting and freezing enthalpies of the PCM-potential compositions in the system and characterize their supercooling and hysteresis. Here, the T-history method, combined with a Tammann plot analysis, is used, also enabling larger sample sizes investigation as compared to e.g. a DSC. The crystal structures were not evaluated here, given that they are ascertained in literature ( [109], [266]).

4.2.1 Dodecane- Tridecane Study: Materials and the T- history Method Using n-dodecane (CH3(CH2)10CH3, CAS number 112-40-3) and n-tridecane (CH3(CH2)11CH3, CAS number 629-50-5) of 99% and 99+% purity [267], thirteen blend compositions and the pure components were investigated using the T-history method. There, the blend compositions: 5, 10, 15, 17.7, 20, 25, 30, 40, 50, 60, 70, 80 and 90 mol% C13 were analyzed, with the samples weighing between 7.10-7.73 g (with 1.3 mol% and 0.04 g compositional and mass expanded uncertainties with a 0.95 confidence level respectively).

Both pure components are liquids at room temperature, and hence their corresponding weights for each composition were mixed directly in glass test-tubes by rigorous shaking. Thereby, a clear single liquid was ensured via visual observation. Then the contents were poured into the T-history SS test-tubes, and the total sample weights were measured. The T-history methodology as explained in section 3.1.2.1 was followed, while, here only the SS2 reference was used. The T-history cycling was conducted at a heating and cooling rate of 0.2 °C/min, between -29 °C to +10 °C, allowing 5 hours’ isothermal stabilization at the two end-temperatures. In total, each composition was subjected to five heating and cooling cycles. The Tammann plots, if and when relevant, were also plotted according to section 3.1.2.2.

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4.2.2 Dodecane- Tridecane Study: Results and Discussion Using a combined scrutiny of the temperature, enthalpy and cp profiles (similar to that in section 4.1.2.1) of the pure and blend compositions of the C12-C13 system, their phase change temperatures were determined. Unlike the erythritol-xylitol system, the C12-C13 system froze on its own, and therefore, both the heating and cooling cycles of the first four cycles were evaluated. Also, in the C12-C13 system, quite consistent phase change behavior per composition for all the four cycles including the first cycle were observed. To exemplify the overall phase change of the system, the melting and freezing cp profiles of the evaluated compositions, for a chosen cycle each, are shown in Figure 4-10. Although the T-history cycling started with a single liquid blend, the first melting was excluded in this study as well, when considering the average behavior of the system.

As shown in Figure 4-10, a polymorphic phase change precedes the melting and follows the freezing of pure C13 and 90 mol% C13, within the evaluated temperature range -29 °C to 10 °C. In contrast, within this range, pure C12 only has a single phase change (melting or freezing). These attributes comply with the results of Ventolà et al. [109]. According to the XRD characteristics from literature ( [109], [266]), solid C12 should be triclinic (TP), while the polymorphic C13 is orthorhombic and trans- forms into the rotator phase RI before melting.

The average melting and freezing temperatures of the pure C12 and C13 are found respectively to be: -11 °C to -9 °C and -7 °C to -4.5 °C (for melting), and -12 °C to -10.5 °C and -8 °C to -6 °C (for freezing). Thus the hysteresis is between 1-1.5 °C for each component. Supercooling was absent for many compositions, and was negligible for the others, with merely around 2 °C for pure C12 and 5% C13.

The melting or freezing cp peaks evolution in the system (e.g. Figure 4-10), indicates a minimum melting/freezing trend, agreeing with Ventolà et al. [109] but contrasting Yilmaz et al. [135]. For the compositions 5-20 mol% C13, except 17.7 mol% C13, two main cp peaks occurred during heating. From these, the lower temperature peak appeared at rather similar temperatures (c.f. Figure 4-10). This could be the eutectic in the system Ventolà et al. [109] suggested. However, such a secondary probable eutectic peak was absent during freezing for all the compositions except for 5 mol% C13. The 17.7 mol% C13 had only a very narrow single peak for both melting and freezing (e.g. Figure 4-10). Hence, if the system truly has a eutectic, 17.7 mol% C13 is the closest to the eutectic from those valuated. The compositions 25-81 mol% C13 had merely a single phase change cp peak for both heating and cooling over the evaluated temperature range, as Figure 4-10 shows.

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

(a) C12-C13 Melting: Specific Heat vs. Temperature 990

790 C13, M4 90 C13,M2 81 C13, M3 590 70 C13, M2 60 C13, M4 50 C13, M3 40 C13, M4 390 30 C13, M2 25 C13, M4 20 C13, M3

(arbitrary units) (arbitrary 190 17.7C13, M2

p 15 C13, M4

c 10 C13, M3 5 C13, M3 -10 C12, M2 -30 -25 -20 -15 -10 -5 0 5 10 Temperature (°C)

(b) C -C Freezing: Specific Heat vs. Temperature 1190 12 13

990

790 C13, Fr4 90 C13, Fr2 590 81 C13, Fr3 70 C13, Fr2 60 C13, Fr4 50 C13, Fr3 40 C13, Fr4 390 30 C13, Fr2 25 C13, Fr4 20 C13, Fr3

(arbitrary untis) (arbitrary 190 17.7C13, Fr2

p 15 C13, Fr4

c 10 C13, Fr3 5 C13, Fr3 -10 C12, Fr2 -30 -25 -20 -15 -10 -5 0 5 10 Temperature (°C)

By evaluating all the investigated compositions, the selective average phase diagram trends (over the 2nd-4th cycles) for the C12-C13 system are determined for freezing and melting. These, in Figure 4-11 b), are compared with a Tammann plot for the possible eutectic in Figure 4-11 a). In these phase diagrams, the liquidus, solidus, and the solid-solid phase changes start and end, are denoted respectively with L, S, S-Ss and S-Se. Here, the liquidus is made of the melting offset or the freezing onset (as defined in section 4.1.2.1). The solidus consists of either the onset of the melting (for the compositions between 25-100 mol% C13) or the ‘probable eutectic’ (for the remainder in melting), or the offset of freezing (for all except 5 mol% C13). The S-Ss and S-Se consists of the lower temperature and the higher temperature inflection of the polymorphic phase change cp peak, during both melting and freezing.

Saman Nimali Gunasekara

Clearly, the freezing-based phase diagrams are rather different to the melting-based diagrams, as Figure 4-11 b) shows. In addition, no phase boundaries to indicate the solvus were obtained in either melting or freezing, for any composition. A minimum melting trend is evident during both melting and freezing. However, the minimum melting temperature during freezing, observed at around 15-20 mol% C13 is clearly dissimilar to that seen in melting, at around 25-30 mol% C13. As a whole (c.f. Figure 4-11 b)), the freezing occurred in narrower temperature ranges (compared to melting), while 17.7 mol% C13 had the narrowest freezing.

40 38 (a) C12-C13 Tammann Plot (of the probable eutectic) 36 0.177; S,M 34 31.995 L,M 32 S-Ss,M 30 0.2; 31.4 S-Se,M 28 S,Fr 26 L,Fr 24 S-Ss,Fr (kJ/mol)

E 22 S-Se,Fr h 20 R² = 0.9598 Δ Avg,M2-M4-hE,m 18 16 14 12 10 8 6 4 2 0 -2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -4 -6 0.177; -15.1 -8 0.177; -12.400 C) ° -10 -12 -14 -16 -18 0.177; -15.733 -20

Temperature ( Temperature -22 0.177; -16.367 -24 -26 -28 (b) C12-C13 Phase Diagrams for Freezing and Melting -30 C H C H 12 26 Mole Fraction of C13H28 13 28

Figure 4-11 b) also indicates the levels of hysteresis each composition undergoes. There, a hysteresis of between around 1-5 °C can be identified. The Tammann plot was constructed using the molar enthalpy change of

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the probable eutectic identified just during heating (Figure 4-11 a)), to verify if the system truly contains a eutectic. In Figure 4-11 a), the regression analysis of the probable eutectic enthalpy indicates the maximum eutectic enthalpy change to be at a composition between 17.7 and 20 mol% C13, and closer to the 20 mol% C13. Hence, if a eutectic exists in the system, it should exist at a composition, larger than 17.7 mol% C13 and very close to 20 mol% C13. In contrast, the minimum melting composition in the melting-based liquidus exists between 25-30 mol% C13.

Due to this inconsistency of the composition of the probable eutectic, and the absence of solvus indications, the heating-based phase diagram cannot confirm the phase change behavior of the system. With strong evidence of low-temperature polymorphs in the system, this system cannot have a non-isomorphous phase diagram. Therefore, if there is a eutectic, it must be in a partially isomorphous system, and therefore, must have the solvus indicating the solid-solution formation. Therefore, as a whole, the cooling-based phase diagram is chosen as a better representative of the systems’ phase change.

4.2.2.1 Enthalpy Characteristics The average melting and freezing enthalpies (over the 2nd-4th cycles) of all the studied compositions were calculated using the T-history results. The pure components’ phase change temperatures and enthalpies, as compared to the literature values, agree rather well, as seen in Table 4-2.

Table 4-2. The comparison of the pure components’ obtained thermal properties with literature Mate- Fusion Melting/Freez- Fusion en- Melting/Freez- rial Temp. (°C) ing Temp. (°C)a thalpy ing enthalpy (kJ/kg) (kJ/kg)b Literature This work (avg.) Literature This work (avg.) C12 -10 [49], [109]; -11.4 to -8.8/ 210 [49], [109]; 216/ 230 -9.6 [135], -10.5 to -11.6 216 [135], [264] [264] C13 -5.5 [49], [109], -6.7 to -4.5/ -6.3 157 [49], [109], 182/ 208 [264]; -4, -6 to -7.9 [135]; [135] 196 [264] a, b expanded uncertainties with 0.95 confidence, of a 0.4 °C, and b 10 %

The minimum melting point among the investigated compositions lies at 17.7 mol% C13. It melts between -15.7 °C and -12.4 °C with an enthalpy of 185±19 kJ/kg, and freezes within -15 °C to -16.4 °C with an enthalpy of 165±17 kJ/kg. The 5 mol% C13 composition consists of the maximum melting and freezing enthalpies, 277±28 kJ/kg and 248±25 kJ/kg respectively. The enthalpy change from the polymorphic phase to melting (or freezing), for the 90 mol% C13 and the pure C13, is either similar to the 5 mol% C13 or larger, respectively being: 282±28 kJ/kg and 300±30 kJ/kg (during heating); and 245±25 and 287±29 kJ/kg (for cooling). 91

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4.2.2.2 Dodecane- Tridecane Phase Diagram Combining the experimental evidence of the study, the final phase diagram of the dodecane-tridecane (C12-C13) system is proposed in Figure 4-12. With a liquidus approaching a temperature minimum, and polymorphic phases, the phase diagram agrees more with Ventolà et al. [109], and disagrees completely with Yilmaz et al. [135]. However, having no eutectic phase change during freezing, and no solid-solutions formation to indicate the solvus, the system fails to indicate a partially isomorphous system with a eutectic. If a eutectic exists in this system with polymorphic changes, a solvus must exist.

Thus, such behavior points to the formation of a congruent melting solid- solution (instead of a eutectic), followed-by polymorphic phase changes at lower temperatures. If this is true, the C12-C13 minimum melting composition is an extremely PCM-ideal composition, and is even better than a eutectic, as was presented in section 2.1.1. Hence, the phase diagram obtained herein as a whole, also contrasts that proposed by Ventolà et al. [109].

Figure 4-12. The phase diagram proposal for the dodecane-tridecane binary system

Ventolà et al. [109] indicated that the 30 and 50 mol% C13 compositions melt from the RI phase, and hence that partial miscibility exists between the TP and RI phases in the C12-C13 phase diagram. However, the solvus that marks this partial miscibility was represented with discontinuous lines, without being explained why. Unless the reasons for this represen-

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES tation and their detailed evaluation methodology are uncovered, the dissimilarities between their phase diagram and Figure 4-12 here cannot be explained. Complete solid-state miscibility usually occurs between components of similar crystal structures [48]. However, exceptions of this rule also exist (e.g. the C14-C16 alkanes system [49], c.f. section 2.2.1.2). Thus, the RI phase identified on the blends [109] could be an exceptional case of a continuous (i.e., completely miscible) solid solution having the same structure as the melting phase of C13. Else, the system has a complex phase change, which masks the partial miscibility during thermal cycling. Another possibility is that either the continuous solid solution seen here, or the partially miscible eutectic seen by Ventolà et al. [109], is a metastable phase, which will become a eutectic or a continuous solid solution, at equilibrium. However, if it is a eutectic, it must contain the solvus indications for this system. A detailed crystallographic characterization of the blends (at least 10-20 mol% C13) are essential to verify these possibilities.

Extensive evaluations are necessary to understand why different phase change behaviors occurred in the C12-C13 system during heating and cooling. An opposite behavior was reported e.g. on pure hexadecanol, where a single DSC cp peak in heating has become two distinct peaks in cooling, explained as the S-SPC overlapping with melting in heating [112]. To verify if such overlapping occurs in the C12-C13 system, extensive crystallographic, chemical and microstructural assessments are necessary. Evalu- ating potential metastable phase changes in the system, and producing the corresponding kinetic phase diagrams is also valuable in a PCM applications perspective. This could confirm whether the RI phase seen on 30 and 50 mol% C13 is stable or not, and shed understanding on why e.g. Yilmaz et al. [135] obtained a maximum-melting liquidus for the system.

The potentially congruent melting solid solution composition in the system lies between 15-20 mol% C13, freezing around -17 to -15 °C and melting around -16 °C to -12 °C. The freezing and melting enthalpy of this varies between 187-192 kJ/kg and 220-222 kJ/kg. As the 17.7 mol% C13 exhibited the narrowest freezing, this could be considered as the most apt composition as a PCM (from those evaluated), freezing between -15.1 °C and -16.4 °C, and melting between -15.7 °C and -12.4 °C, with the freezing and melting enthalpies 165 kJ/kg and 185 kJ/kg. With no supercooling and only moderate hysteresis (1-3 °C), this appears ideal as a PCM for e.g. freezing refrigeration applications. If the polymorphic phase changes in the system indeed form a eutectoid (as Ventolà et al. [109] found), this would be attractive for solid-solid PCM developers.

This study as a whole indicates: the complexities of material blends; the phase diagram inconsistencies that arise due to the lack of standards in the techniques to be used and their individual approaches; the value of a

Saman Nimali Gunasekara combination of thermal and physicochemical characterizations to confirm a phase diagram; and, the necessity in the comparison of a system’s phase diagram based on heating as well as cooling, whenever possible.

Experimental Phase Diagrams- Concluding Remarks For novel PCMs design from blends, determining their phase diagrams must be time- and cost-effective, for the PCM to be cost-effective. The experimental derivation of the binary phase diagrams of the erythritol- xylitol and the dodecane-tridecane systems collectively have several interesting aspects and lessons along this. The complexities identified in the e.g. their cp profiles are proof that thermal properties alone have a limited input in deriving a phase diagram. Most-definitely, presenting a confirmed phase diagram using experimental data must involve multiple techniques that evaluate thermal, physical, and chemical properties of the system. It is a laborious process, however, essential as well.

Each employed experimental technique must reach maturity over each novel system to capture the system’s equilibrium phase change, and to avoid material changes caused by the technique. For the polyols system, the conditions for the T-history were decided based on pre-studies. Thereby, e.g. it was understood that a constant heating/cooling rate was necessary to avoid metastability in the system, instead of fixed ramps which caused different rates in heating and cooling, due to hysteresis. With the XRD study, the actual behavior of the system was obtained only after several measurement conditions. With microscopy, several low- magnification devices proved insufficient before moving-on to FESEM. The FESEM analysis also required a number of pre-evaluations e.g. to recognize the suitable measurement conditions. Systematic evaluations (e.g. [49], [109], [134]) that characterize material categories, are therefore invaluable and essential. Thereby, even if it is a novel blend, the characteristics of the material category and the details of the employed methodology enable the prediction of the expected behavior. Such complementary knowledge reduces the time and therefore the cost incurring in per- fecting a novel phase diagram.

Pure component properties already have indications on the expected blend phase change. For instance, pure component polymorphs will always continue into the blend phase diagram. Thus, if at least one of the components has a polymorph, the system will be more complex, where it cannot be e.g. merely a non-isomorphous simple eutectic or a completely isomorphous system with no solid-solid phase changes. The dodecane- tridecane phase diagram is such an example. A pure component’s metastable polymorphs will appear in its kinetic phase diagram obtained under 94

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES similar heating and cooling conditions, however, will be absent in the stable phase diagram. The erythritol-xylitol system is such an example, where even if pure xylitol contains a metastable polymorph, the stable system does not have polymorphic attributes as e.g. XRD verified.

Experimentally confirming whether the phases are stable or metastable is challenging, while defining stability in practice also depends on the phase diagram application. Literally all materials have metastable states. Some metastable states (e.g. diamond, a metastable state of carbon) take almost forever to reach its stable state, and if the application lifetime is shorter, this is a stable phase for the application conditions. A similar understanding is crucial on each and every pure material, as well as blend, considered as a PCM.

As particularly the erythritol-xylitol study indicated, systems could have considerable variations in their phase change over cycling. In certain erythritol-xylitol compositions, a eutectic portion randomly appeared and diminished in different cycles. Therefore, the cycled behavior of the phase change of the system must be known to derive its phase diagram. The comparison of the phase diagrams obtained using heating and cooling is also very important, as the dodecane-tridecane study exemplified. This system had quite unlike behaviors respectively during melting and freezing. Therefore, whenever possible, the cooling-based phase diagram must be compared with the heating-based one, to ultimately decide the phase diagram.

To confirm the phase diagram upon such complexities, well-specified standards and a common consensus on each technique, procedure and data analysis process are instrumental. Such standards should specify, e.g. how many cycles must be considered to derive an experimental phase diagram, and why e.g. it should exclude the first cycle. A consensus over the onset and offset temperature choices of various phase changes is also extremely necessary. As a whole, specifying how the phase equilibrium evaluation methods and results should be reported, in a transparent and repeatable manner, is extremely crucial. Thereby, all the results on each system presented by various researchers can be collectively maintained in a single database, to build the PCM design understanding per blend. This essentially makes a phase equilibrium study a cost-effective process, where building new understanding on a system can always rely on the database as a starting point.

Saman Nimali Gunasekara

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES Theoretical Phase Diagram Determination

The experimental phase equilibrium evaluation of the erythritol-xylitol binary system (Chapter 4), indicated a partially isomorphous phase diagram with a eutectic. However, confirming the system’s solvus and the solidus at the erythritol-rich side, and if its phase diagram represented the system’s stable equilibrium, requires further interpretations. To address these aspects, the system’s phase equilibrium is modelled using the CALPHAD method herein. This chapter is based on Paper IV supplemented with relevant details from Paper III, and addresses the thesis objective 5.

The CALPHAD method is applied in this investigation, due to the reasons and according to the method described in section 3.2. This is a nonspecific phase diagram derivation method applicable on any material and phase diagram type. This is in contrast to a majority of PCM-evaluations which were restricted to certain chemical characteristics (e.g. component activities), and almost exclusively to non-isomorphous simple eutectics, as discussed in section 3.2.2.

Experimental Unary and Binary Data The binary phase diagram of the system erythritol-xylitol system was proposed to be a non-isomorphous simple eutectic type ( [93], [97]). Whereas, in this thesis work it was found to be a partially isomorphous type with a eutectic (section 4.1, Papers III and VIII). Hence, although the solid-state miscibility of the system is under controversy, the existence of a eutectic is affirmed. The system’s eutectic temperature and composition were however proposed differently between the studies (see section 4.1.2.4), as at: 25 [93], 25-30 (Paper III), or 36 [97] mol% erythritol; and 82 °C [93], [97], or 77 °C (Paper III). As was explained in section 4.1, only the investigations in Papers III and VIII clearly included the cycled phase change behavior of the system, ensuring the phase change of the real blend. The comprehensive experimental phase equilibrium scrutiny of the system in Paper III confirmed the solid-solutions formation and hence the partial miscibility. Therefore, for this thermodynamic assessment of the erythritol-xylitol system, the binary phase diagram data proposed in Paper III are used as the basis. 97

Saman Nimali Gunasekara

For the thermodynamic analysis of the unary erythritol and unary xylitol, their cp and heats of fusion as measured by Tong et al. [239], [247] were employed. This is despite that the pure erythritol and pure xylitol thermal properties were available in Paper III, obtained using the T-history method. Tong et al. [239], [247] have measured the pure component cp in an adiabatic calorimeter using extremely slow heating rates. These adiabatic calorimetric measurements ( [239], [247]) produced larger signal to noise ratios, and hence smoother cp profiles and more accurate enthalpies rather than with the T-history measurements (Paper III). Thus the heat of fusion of erythritol and xylitol were considered as 37920 J/mol [239] and 33260 J/mol [247] respectively. The pure component’s enthalpies, with respect to room temperature, were also calculated using the measured cp [239], [247]. The pure erythritol and xylitol melting temperatures were chosen to be respectively 393.85 K and 368.32 K (i.e., 120.7 °C and 94.8 °C), according to Paper III. The eutectic composition of the blend was chosen here to be ~27 mol% erythritol, based on observing the maximum eutectic enthalpy on the 25 mol% erythritol and the minimum- melting point on the 30 mol% erythritol, experimentally (Paper III). The uncertainty of these temperatures was rather low (an expanded uncertainty of 0.4 °C within a 0.95 confidence), and hence were considered a suitable choice.

Thermodynamic Optimization In the thermodynamic assessment, the thermodynamic parameters of the unary erythritol and xylitol and their binary system were optimized using Thermo-Calc PARROT module (c.f. section 3.2.3). Firstly, the parameters of the stable solid phases of erythritol and xylitol, (i.e., BCC and FCC, c.f. section 3.2.3) were optimized based on the experimental data from Tong et al. [239], [247]. Secondly, the liquid phase of erythritol and xylitol respectively was optimized in par with its experimental melting temperature (from Paper III) and enthalpy ( [239], [247]). Lastly, the binary experimental data presented in Paper III were fitted using substitutional solution models, by the thermodynamic optimization of the interaction parameters in the liquid and the solid solution phases SEt and SXy (considered to be of BCC and FCC structures respectively, c.f. section 3.2.3). The interaction parameters 0L and 1L were adequate to fit this experimental phase diagram.

Erythritol- Xylitol Theoretical Phase E quilibrium The Gibbs free energy expression parameters obtained from the thermodynamic optimizations here for: the unaries erythritol and xylitol; and, for

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the BCC (i.e., SEt), FCC (i.e., SXy) and the liquid solution phases in the erythritol-xylitol system, are summarized in Table 5-1. The cp and enthalpies of the pure erythritol and xylitol calculated in this optimization are plotted along the available experimental data, in Figure 5-1, Figure 5-2 (for erythritol), Figure 5-3, and Figure 5-4 (for xylitol). As these figures indicate, the optimized data (shown using solid lines) agree well with the available experimental data (represented by triangular points).

Table 5-1. The Gibbs free energy expression parameters for the unary and binary systems (here, Comp: component, Et: erythritol, Xy: xylitol, BCC: the stable solid phase of Et or its solid solution SEt, and FCC: the stable solid phase Xy or its solid solution SXy) Unary systems Com Pha Molar Gibbs free energy expression parameters p. se Et BCC = GBCCET298.15−393.85K -23279.19 - 6062.77T - 5.56T lnT - 0.24T 2 GBCCET = -115815.33 - 4031.58T - 322.40T lnT 393.85−6000K +1.25 ⋅10 26 T −9 LIQ = + GLIQET298.15−393.85K GBCCET 30858.74 -75.37T UID -7.99 ⋅10-16 T 7

GLIQET393.85−6000K = -72409.69 -4140.39T -322.40T lnT Xy FCC 2 GFCCXY298.15−368.32K = -33566.85 -6060.23T -3.39T lnT -0.37T = GFCCXY368.32−6000K -144331.06 -3422.14T -422.00T lnT +7.64 ⋅10 25 T −9 LIQ = + GLIQXY298.15−368.32K GFCCXY 25401.72 -65.41T UID − -1.42⋅10 15T 7

GLIQXY368.32−6000K = -104945.94 -3527.40T -422.00T lnT Binary system LIQUID ° LIQUID SER GEt − H Et = GLIQET ° LIQUID SER GXy − H Xy = GLIQXY 0 LLIQUID = 70489.20 - 209.06T Et,Xy 1 LIQUID LEt,Xy = 6387.69 ° BCC (SEt) BCC SER GEt − H Et = GBCCET ° BCC SER G Xy − H Xy = GBCCXY = GFCCXY +1326.77 0 BCC LEt, Xy = 14848.62-34.66T ° FCC (SXy) FCC SER GEt − H Et = GFCCET = GBCCET + 461.04 ° FCC SER GXy − H Xy = GFCCXY 0 FCC LEt, Xy = 50424.00 −128.73T

Saman Nimali Gunasekara

Figure 5-1. The specific heat of solid (BCC) and liquid erythritol in the full temperature range of stable and metastable states

Figure 5-2. The molar enthalpy (Hm) variations of erythritol (solid: BCC, and liquid) with reference to room temperature

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES

Figure 5-3. The specific heat of solid (FCC) and liquid xylitol in the full temperature range of stable and metastable states

Figure 5-4. The molar enthalpy (Hm) variations of xylitol (solid: FCC, and liquid) with reference to room temperature 101

Saman Nimali Gunasekara

The erythritol-xylitol phase diagram calculated based on the thermodynamic optimizations, plotted along the binary experimental data from Pa- per III, is given in Figure 5-5. In Figure 5-5, the liquidus and solidus proposed theoretically by the previous studies ( [93], [97]) are also plotted, for comparison.

As seen, the calculated phase diagram in Figure 5-5 is in considerable agreement with most of the experimental solidus and liquidus data from Paper III. The calculated phase diagram thermodynamically verifies the partially isomorphous phase diagram of the erythritol-xylitol system forming a eutectic, as identified in Paper III. The thermodynamic optimization particularly verifies the propagation of the solidus between the compositions 80-98 mol% erythritol, and the solvus as a whole, where the experimental data (Paper III) had lager deviations. Most-importantly,

102

Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES the thermodynamic optimization confirms that the erythritol-xylitol system has attained stable equilibrium during the experimental conditions employed in Paper III.

Figure 5-5 shows that considerable differences exist between the previous proposals of the erythritol-xylitol phase diagram with a non-isomorphous simple eutectic ( [93], [97]), to the present study results presenting a partially isomorphous eutectic. In particular, their phase diagrams lack the indication of a solvus, and their eutectic temperature is considerably different. The calculated phase diagram of Del Barrio et al. [97] also lacks the solidus.

The calculated eutectic temperature and compositions via the thermodynamic optimizations here are compared to the literature results in Table 5-2. As seen, the calculated results in this work are in good agreement with the employed experimental data (from Paper III), and further verifies the exact eutectic point. As the other studies proposed the system to be a non-isomorphous simple eutectic ( [93], [97]), their proposed eutectic points are not directly comparable with the eutectic in a partially isomorphous system here. Besides, the previous studies have disparities between their experimental and calculated eutectic points, as Table 5-2 shows. Nevertheless, the calculated eutectic composition here numerically agrees reasonably with the theoretical results using ideal solution approach by Del Barrio et al. [97], or the DSC experimental results of Diarce et al. [93] (c.f. Table 5-2).

Table 5-2. The erythritol-xylitol eutectic transformation temperature and compositions summary, present study results compared to literature (experimental: onset temperature unless specified) Eutectic Temperature Composi- Comment Source Transfor- K °C tion (Mol% mation erythritol) Liquid→ 355.40/ 82.2/ 25 Experimental, DSC [93] FCC+ BCC 357.05a 83.9a (pure 358.05 84.9 ~28 Theoretical, Modified solids) UNIFAC 355.35 82.2 ~28 Experimental, IRT [97] 355.20 82.0 36 Experimental, DSC 359.45 86.3 27.4 Theoretical, Ideal solution approach Liquid→ 350.20 77.0 25-30 Experimental, T-His- Paper FCC+ BCC (~27b) tory III (solid 349.90c 76.7c 26.8d Theoretical, CAL- Paper solutions) PHAD IV a eutectic offset [93] b approximated to be 27 mol% erythritol (within the range: the highest eutectic enthalpy at 25 mol% erythritol, and the lowest liquidus point at 30 mol% erythritol) c, d with an expanded uncertainty of c0.1 K and d1 mol%, respectively with 0.95 confidence 103

Saman Nimali Gunasekara

Theoretical Phase Equilibrium- Concluding Remarks The erythritol-xylitol phase diagram is thermodynamically verified to be a partially isomorphous system containing a eutectic. This was achieved by using the CALPHAD method using substitutional solutions models, where, the experimental data on the system were thermodynamically optimized using Thermo-Calc PARROT module. The calculated solidus, liquidus and solvus are in good agreement with the experimental data proposed in Paper III (section 4.1.2.4). The calculated results, as expected, particularly verify the solvus, the erythritol-rich parts of the solidus, and the liquidus close to the eutectic point, where the experimental data had larger deviations. One crucial outcome of the assessment is the confirma- tion that the system has attained stable equilibrium in the experimental conditions in Paper III. The calculated eutectic point lies at 26.8 mol% erythritol and 76.7 °C, with considerable agreement to the experimental data considered: ~27 (i.e., between 25-30) mol% erythritol and 77 °C (Pa- per III). This eutectic point however is not directly comparable with the other studies which proposed the system to be non-isomorphous simple eutectic type.

As shown in section 3.2.2, in PCM design, a majority of phase equilibrium evaluations have been restricted to certain chemical characteristics of the materials, and almost exclusively to non-isomorphous simple eutectics. The present thermodynamic investigation based on the fundamental Gibbs free energy minimization (using e.g. CALPHAD) exemplifies the significance of such a method with no restrictions on chemical characteristics or phase change behaviors. When the relevant sub-systems’ (e.g. the binary system) phase diagrams are established, these approaches can be conveniently used to evaluate higher-order systems, which also could comprise of complex phase changes. Hence, such nonspecific methods are instrumental in cost-effective multicomponent PCMs design. This study also exemplifies the complementary nature of a semi-empirical phase diagram study towards PCM blends design.

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES Towards Sustainable TES with PCMs

As described in Chapter 1, TES with PCMs enables better management of energy systems also allowing higher efficiencies. In order to achieve a sustainable TES system, the PCMs themselves also need to be sustainable. Sustainable development, by definition, is the ability to meet today’s needs without compromising the future generations’ ability to meet their needs [268]. For that, the balanced fulfillment of the three pillars of sustainability: economic development, environmental conservation and so- cietal development is essential [268]. When interpreting sustainability into PCMs, on top of their energy benefits, they must be renewable, environmental friendly, non-toxic, and cost-effective. There, cheap, commercial- grade materials that are renewable, non-toxic and environmentally safe, have a great unrealized potential as sustainable PCMs. To exemplify this potential, in this chapter, the food-grade commercial materials: the polyol erythritol and the fatty-acid esters blend olive oil, are evaluated as potentially sustainable PCMs. This chapter is developed based on Paper IX and parts of Paper II, and addresses the thesis objective 6. Thereby, insights on how to achieve a sustainable TES system by integrating with sustainable PCMs are given.

Polyols as PCMs of Renewable Origin Polyols are an emerging renewable material category of PCM-interest, as identified in Chapters 2 and 4. Erythritol (C4H6(OH)4) is one example of a polyol. Many polyols, including erythritol and xylitol, are food-grade, often called sugar alcohols. These are thus also safe for humans and the environment. Polyols, like paraffins, are compatible with metals [264]. However, some polyols undergo autoxidation under higher temperatures, producing acidic products that could corrode metals [269]. Polyols tend to be more expensive than other organics like paraffins and fatty acids [270]-[272]. However, as polyols are produced by carbohydrates hydrogenation [24], [273]- [275], a potential exists for cost-reductions via mass- production. Polyols are still competitive against the non-renewable, fossil- based paraffins, and the less-metal compatible fatty acids.

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Erythritol is a sugar substitute, and serves as a flavor enhancer, stabilizer, thickener, humectant, and a formulation aid [276]. Erythritol has applications in pharmaceutical and cosmetics industries [276]. This polyol is currently rather expensive [277], however, potential cost-reductions can be foreseen as it is produced by starch hydrogenation [24], [278]. This potential is elaborated below.

Commercially, erythritol is produced by hydrolyzing starch (e.g. from maize) into glucose, which is then fermented using a fungus such as Mo- niliella pollinis [278]-[280]. This fermented broth is subjected to purification via adsorption and filtration, and then to controlled cooling to crystallize erythritol [279], [280]. With repeated crystallization, higher purity erythritol is achieved [279], [280]. The production costs and therefore the price of erythritol can be lowered by increasing the yield, by using: more productive fungi; glucose concentration control; alternative carbon sources; vitamin and mineral supplements; and the inhibitors and by- products removal [278], [281]. For example, a ten-fold erythritol yield increase was obtained by replacing maize with straw, combined with a ge- netically modified fungus Trichoderma reesei [282]-[284]. With straw instead of maize, the raw materials procurement competition is less because maize is a food-commodity while straw is an inedible and cheap by-product.

Erythritol can also be produced via chemical synthesis. In one commercial method, erythritol is produced from erythrose, formed by decarbon- izing ribonic acid or arabinonic acid (or certain hexose sugars) via elec- trolysis [285]. In the chemical synthesis of erythritol, higher yields are achievable at a lesser time, rather than with e.g. starch hydrolysis followed by fermentation [286]. While avoiding the starch processing, glucose can be replaced with crude glycerol (unpurified glycerol), then fermented using the yeast Yarrowia lipolytica to produce Erythritol [281]. Crude glycerol is a by-product in: transesterification (in biodiesel or bioethanol production) [287], [288]; saponification (in soap production); and hydrolysis [289], of fats and oils. Glycerol is already cost-effective, while, further cost-reductions can be anticipated. This is owing to the increasing production of glycerol due to the global increase of biodiesel and bioethanol production [287]. Crude glycerol fermentation to produce erythritol can be done in batch, fed-batch or repeated batch cultures (RBCs) [281]. All these potential alterations to the erythritol production process which can lower the costs are summarized in Figure 6-1.

In order to quantify the cost-savings in erythritol production by means of such alterations, a simplified production cost estimation was conducted. There, a batch production of erythritol using crude glycerol was assumed, which was approximated to a batch production of ethanol considered in

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2000 in U.S.A. [290]. This cost estimation is summarized in Table 6-1, which accounts the investment, utilities and process operations.

Ion exchange Enzymetic GM mold Starch resins, hydrolysis fungus Activated separation Fermentation Trichoderm carbon, < 99.5% Starch Glucose using yeast Ultrafiltration Straw a reesei purity

Biodiesel/ Purification, Sterilized crystallization Pure Bioethanol fermentation Erythritol Production broth Crystals Crude Soap Prodcution Glycerol Fermentation E.g. using yeast Fungus Fats or Oils Yarrowia Hydrolysis lipolytica Figure 6-1. Erythritol production process: potential adaptation alternatives for cost reduction

Table 6-1. Simplified economic analysis of a batch production process of erythritol (adapted from ethanol production [290]) Batch fermentation Fermenta- Crystalliza- Total annual Unit unit costs tion,$/yr tion and puri- cost, $/yr costs cost fication, $/yr $/Gal $/kg Total capital cost 27 591 826 19 519 985 47 111 811 0.942 0.168 Annualized capital 3 066 348 2 168 459 5 234 807 0.105 0.019 cost (over 9 years) Steam --- 3 342 621 3 342 621 0.067 0.012 Cooling water 230 947 430 094 661 042 0.013 0.002 Electric power 210 083 85 760 295 843 0.006 0.001 Annual utilities 441 030 3 858 476 4 299 505 0.086 0.015 Plant labor 1 102 216 778 458 1 880 674 0.038 0.007 Supplies 690 252 488 227 1 178 479 0.024 0.004 Glycerol cost 2 569 912 585 --- 2 569 912 585 51.398 9.174 General operational ex- 276 273 194 255 470 528 0.009 0.002 penses Annual operational 2 571 981 326 1 460 940 2 573 442 266 51.469 9.187 costs Annual cost, batch 2 575 488 704 7 487 874 2 582 976 579 51.660 9.221 production Other costs 1545293222 4 492 725 1 549 785 947 30.996 5.533 Total annual cost 4 120 781 927 11 980 599 4 132 762 526 82.655 14.754

Comparing the batch production of ethanol [290] or erythritol, fermentation is common. Whereas, the distillation and dehydration costs in ethanol production [290] were here assumed similar to the erythritol crystallization and purification costs. The ethanol costs for the year 2000 [290] were projected to 2017, accounting the inflation from 2000 to 2016 [291]. One batch produced per every 48 hours, and 365 days’ plant operation [290] was considered. The capital investment was annualized by assuming a payback period of 9 years [290]. The required amount of crude glycerol 107

Saman Nimali Gunasekara was calculated by considering an erythritol yield of 109 g/l (from crude glycerol) for a batch process [292]. The price of crude glycerol used was 800 USD/ton [293]. Assuming the total production volume of 50 million gallons per year [290], the equivalent weight of erythritol was found to be 280 kilo tons.

In Table 6-1, the ‘other costs’, taken as 60% of the annual batch production cost, include the specific costs in e.g. crude glycerol transportation and purification of erythritol up to 99% purity. The sum of the annual batch production cost and other costs produces the total annual cost. Thus the total annual production cost was found to be 14.75 USD/kg of high-purity erythritol. This is in the same range of the commercial-grade erythritol prices today: e.g. 1-10 USD/kg [294] or 5 USD/kg [295], but is about 130 times lower than the laboratory-grade (99% pure) erythritol which costs 1900 USD/kg [252]. Therefore, a remarkable potential exists in achieving lower costs in high-purity (99% pure) erythritol by producing with e.g. crude glycerol. Pure erythritol produced at a cost of 14.75 USD/kg corresponds to 163 USD/kWh22 stored energy, in contrast to the cost of pure erythritol today: 20 982 USD/kWh (at 1900 USD/kg [252]). Furthermore, by e.g. using 80% pure glycerol (44 USD/ton [287]) from biodiesel production, the pure erythritol cost can become 1.04 USD/kg. Thereby the pure erythritol production cost can become: the same as the cheapest of the current commercial-grade price; and more than 1820 times less than the laboratory-grade prices. Therefore, a palpa- ble potential appears in achieving cost-effective erythritol. This, nevertheless, is a simplified cost valuation, and thus a more specified cost assessment would enable a more accurate comparison. Evaluating the potential cost-reductions in the other production alternatives such as use of straw with special fungi could be useful future work.

The Potential in Olive Oil as a Sustainable PCM Olive oil is a popular food ingredient produced from olives, a crop flour- ishing in the Mediterranean climates. To obtain olive oil, the olives are crushed, and the resulting paste is mixed, from which the oil is separated by physical processes [296]. Olive oil essentially is a multicomponent blend, with the key components being triacylglycerols (triglycerides, TAGs). TAGs are formed by the esterification of fatty acids with glycerol [297], [298]. Olive oil TAGs typically are made of the fatty acids: Palmitic, palmitoleic, stearic, oleic, linoleic and linolenic acids [298]. These account

22 For an average heat of fusion of 326 kJ/kg (of the literature values: 281-370 kJ/kg).

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Doctoral Thesis- Phase Equilibrium- aided Design of PCMs from Blends for TES for 94-96 % of the total TAG weight [297]. Olive oil also contains minor proportions of free fatty acids and glycerol [298]. The exact composition of olive oil depends on the region it grows, and can be evaluated using e.g. High-Pressure Liquid Chromatography (HPLC). A composition analysis of an olive oil sample from Spain yields its major fatty acid constitu- ents to be linoleic, palmitic, oleic, margaric, and stearic acids [299].

The average price of olive oil during 2013 to 2016 was 4.2 USD/kg, with that predicted for 2017-2018 being 3.9 USD/kg [300]. Hence, Olive oil is rather cost-effective already, and mass production could lower the price further. Despite its renewable origin, and the food-grade, environmental friendly and cost-effective attributes, olive oil has not been considered as a PCM thus far. Therefore, using the T-history method, the thermal properties of olive oil were evaluated here to explore its PCM-potential.

6.2.1 Thermal Properties of Olive Oil Two identical samples of commercial-grade virgin olive oil from Spain (S1 and S2), each of 9.71 g were analyzed with the T-history method. Here the reference SS1 (c.f. section 3.1.2.1) was used. Four heating/cooling cycles between -30 ºC to 80 ºC, at a rate of 0.1 ºC/min, with isothermal conditions at the end temperatures for 3 hours each were utilized.

The T-history results indicate consistent phase change for both evaluated samples S1 and S2, for the four evaluated cycles. There, the phase change occurred with two distinct cp peaks, as shown using e.g. S1 in Figure 6-2 (a) and (b), for melting and freezing respectively. The secondary peak before melting or after freezing was the major phase change peak. A similar phase change behavior was also identified by using DSC [301], purportedly similar to the phase change of the TAG Triolein, which accounts for almost one third of olive oil. The secondary phase in Triolein is a polymorph, supposedly reflected in olive oil phase change as well [301]. How- ever, as olive oil indeed is a multicomponent blend, to verify if this truly is a polymorph, or is instead indicating e.g. a near-eutectic phase change in this blend, further thermal and physicochemical characterizations are necessary.

The evaluated olive oil samples underwent slight supercooling. As an example, this is shown in the temperature profile of S1 in Figure 6-2 (c). The total melting and freezing of the evaluated olive oil (averaged over the 4 cycles, and considering both S1 and S2) occur respectively within the temperatures -4.5 °C to 10.4 °C and -8 °C to -11.9 °C (0.4 °C uncertainty with 0.95 confidence), with the enthalpies 105±11 kJ/kg and 97±8 kJ/kg, respectively. These results are comparable with the DSC results from literature [301], reporting melting around -15 °C to 10 °C, with a

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Saman Nimali Gunasekara total melting enthalpy of around 90 kJ/kg. The investigated olive oil in the present work also exhibited considerable hysteresis, of up to 22 °C.

S1 Melting cp vs Temperature S1 Freezing cp vs Temperature 25 50 M1 Fr1 M2 Fr2 20 M3 40 M4 Fr3 Fr4 15 -6.0; 1.7; 2.4 30 5.5 -10.20; 10 10.4; 1.1 20 -11.64; 3.94 (kJ/kg·K)) (kJ/kg·K)) p 7.22 c p -8.01; 5 c 10 3.33

0 0 -26 -16 -6 4 14 24 34 44 54 64 74 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Temperature (°C) Temperature (°C) (a) (b) S1 Freezing Temperature vs. Time 0 Fr1 Fr2 -5 Fr3 -9.2 Fr4 C) ° -10

-10.9 -15

-20 Temperature ( Temperature

-25 160000 162000 164000 166000 168000 170000 172000 174000 Time (s) (c) Figure 6-2. Specific heat characteristics of olive oil (S1) during (a) heating and (b) cooling; and (c) the temperature profile of olive oil (S1) during cooling, showing slight supercooling.

On the whole, the phase change temperature and enthalpy of olive oil appear attractive for pre-cooling in chilling applications. Combining the olive oil’s heat of fusion for the average market price of 4 USD/kg over 2013-2018 [300] correspond to a moderate energy storage cost of 144 USD/kWh. Therefore, detailed compositional analysis coupled with a systematic evaluation of olive oil compositional refinements will be worthwhile to find a potentially PCM-ideal composition from olive oil. Thereby, it can be identified what olive oil can offer in designing sustainable multicomponent PCMs. Olive oil can be refined using e.g. activated carbon and other filters [302], which may yield a better blend composition in a phase-change perspective. Besides, several fatty acids can also be ex- tracted by e.g. the hydrolysis of olive oil at low temperatures with solid acid catalysts [303] or lipases [304]. These pure fatty acids could also serve as PCMs.

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Sustainable PCMs- Concluding Remarks In todays’ energy context, TES using PCMs can significantly contribute towards energy savings and better energy management. The integration of PCMs with sustainable attributes contribute towards achieving sustainability in a TES system. Therefore, on top of the PCM-suitable thermal properties, the materials should be: renewable, non-toxic, environmental friendly and cost-effective. To find such sustainable PCMs, food-grade materials like polyols, fats and fatty acids are attractive candidates. To exemplify the hidden potential of such food-grade materials, here erythritol and olive oil were evaluated as examples.

An appraisal of the erythritol production process and related costs exemplify great prospects in achieving lower prices. Erythritol can be produced using straw instead of as presently from maize, or using crude glycerol. A batch production of high-purity erythritol from crude glycerol indicated potential production costs up to 130-1800 times lower than today’s market prices of commercial- and laboratory-grade erythritol. For pure erythritol, an energy storage cost of 163 USD/kWh is feasible instead of the current cost around 20 982 USD/kWh. This reflects positively also on other rather expensive polyols e.g. xylitol, where process modifications and mass production indicate cost reduction potential.

Olive oil is a multicomponent blend, which is renewable, food-grade, and cost-effective. The T-history evaluations here show that olive oil has a phase change temperature (melting and freezing around -4.5 °C to 10.4 °C and -8 °C to -11.9 °C ) suitable e.g. for pre-cooling in chilling applications, with an enthalpy of 100 kJ/kg. Olive oil also indicated a secondary phase change before melting, or after freezing. This could be an indication of a polymorph, or even a near-eutectic in this multicomponent blend. Hence, it is worth exploring minor-adjustments to the olive oil composition systematically, to see if e.g. a eutectic composition could be found. As olive oil exhibited only minor supercooling, if a eutectic is found through slight compositional modifications, it could be ideal as a PCM. The energy storage cost of olive oil is around 144 USD/kWh, also encouraging further research to find suitable PCMs in it. Extracting the pure fatty acids in olive oil as potential PCMs is another opportunity. As a whole, this chapter indicates that food-grade renewable materials have plenty of opportunities in realizing sustainable PCMs.

Besides being renewable, food-grade, potentially cost-effective and com- prising of suitable thermal properties as potential PCMs, these organics need to fulfill other criteria. Primarily, many organics are biodegradable, meaning they are susceptible to environmental conditions in the long-run,

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Saman Nimali Gunasekara and thus could degrade. Hence, when designing PCMs out of bio-degradable organics (i.e., essentially all food-grade organics) their stability under various environmental conditions must be rigorously examined be- forehand. In addition, these should be generally safe, e.g. are non-flam- mable and non-corrosive. Normally, food-grade materials are not carcino- genic, mutagenic, or irritants (unless due to allergies). However, when dealing with large-scale, in a TES system, the materials handling and waste and spill management practices should comply with all the safety measures as relevant to any industrial chemical.

Sustainable PCMs make a TES system more sustainable. To achieve a sustainable TES system on the whole, the sustainability criteria should be met throughout its complete life-cycle. These include resource efficient, environmental friendly, cost-effective and safe practices involved with the PCM and other TES system components throughout the materials processing, manufacturing, transportation, application, and end-of-life waste management. Thereby a holistically sustainable TES system is realized.

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For a significantly positive impact in mitigating climate change, large-scale TES systems need to harvest excess heat and cold to substitute fossil- based heating and cooling. In realizing large-scale TES systems using PCMs, cost-effectiveness of the material is instrumental. Indeed, if a suitable and cost-effective pure (i.e., single) component PCM exists for a certain TES application, that can be used. For a pure component PCM to be robust, it must be extremely pure. This however, often makes pure components expensive as PCMs in large-scale. That is when bulk industrial- grade chemicals or natural blends become interesting as cost-effective PCMs. Then again, to obtain PCMs fine-tuned for specific TES application temperatures, in the absence of suitable pure materials, blending is instrumental. Such tailor-made PCMs are relevant in TES applications which prioritize functionality over cost. As highlighted in this thesis, the backbone of designing PCM-ideal blends lies in systematic phase diagram evaluations. This is equally true, whether the blend is a natural mixture, or, is tailor-made. This thesis comprehensively explores several key elements relevant to PCM blends design based on phase equilibrium evaluations. Those start by specifying the invaluable utility of the engineering tool: a phase diagram, to choose the right blend (i.e., with sharp, reversible phase change).

Sodium acetate trihydrate (SAT), a PCM used in hand-warmers (Chapter 1, Figure 1-1), is a perfect example that signifies a phase diagram’s utility in PCM design. After a number of freezing cycles, these hand-warmers lose their heating capacity. Then, when the molten PCM is kept supercooled, instead of remaining a liquid, it becomes a liquid-solid mixture. At this stage, when crystallization is initiated, only the remaining liquid solidifies with a much less heat release. This is however seen in the sodium acetate (SA)-water phase diagram (c.f. [305]), where SAT: CH3COONa·3H2O is in fact a peritectic compound. The SA-water phase diagram is rather similar to the Na2SO4-H2O phase diagram in Figure 2-2, with a eutectic and a peritectic, but, with a rightward bent liquidus. The peritectic SAT will always supercool and phase separate, without reaching complete transformation (c.f. section 2.1.3). Therefore, at each consecutive cycle, an increasing amount of sodium acetate (SA) remains insoluble in the liquid, precipitating in the supercooled liquid. Thus, SAT solidifies from an increasingly diluted liquid, producing a

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Saman Nimali Gunasekara lower amount of solid SAT, and hence the storage capacity is reduced. The rightward bent liquidus implies better solubility at higher temperatures, nevertheless, being a peritectic, SAT is not a robust PCM choice.

Obtaining a complete phase diagram of a novel blend requires extensive efforts and time, and is always a continuous development process. There- fore, to make the design of PCM blends cost-effective, their phase equilibrium results should be complementary. For that, the phase diagrams need to be presented using standardized techniques and approaches, and in a repeatable and transparent manner. However, this dissertation discloses that such standards and common consensus are greatly lacking within the current PCM design context. This thesis work also identifies that establishing phase diagrams requires multifaceted attention. In the following, based on the thesis as a whole, these aspects are analyzed and synthesized, to serve as guidelines in achieving the standardizations needed.

Experimental Phase Diagram Construction This work shows, particularly through the Papers I, II, III, V and VIII, the following experimental methodological deductions. As seen within all the blends’ phase diagram derivations analyzed in Paper I, determining a novel phase diagram for PCM design needs to start at its experimental phase diagram. It cannot start with the theoretical phase diagram derivations (which, as relevant in the PCM-context, are semi-empirical) because these depend on the experimental phase equilibrium data. For example, without knowing if the blend system forms a non-isomorphous simple eutectic, the use of a theoretical method specific to such systems is not valid. This is, however, something that until now has sometimes been erroneously done and reported in the literature.

Also, as illustrated by Papers III, V, and VIII, the experimental phase diagram investigation of a novel blend must start at the pure components. This is because, pure components indicate certain attributes expected in the blend phase diagram, e.g. due to stable polymorphs of the pure components. Pure components also indicate the expected conditions such as the heating/cooling rates in the evaluation. The various phase diagram discrepancies exposed via the state-of-the-art assessment herein (Paper I) verify that confirming the experimental phase diagram comprehensively is extremely important. This is even more significant because the semi- empirical assessments depend on the experimental phase equilibrium data.

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The phase diagram dissimilarities observed on the same system, e.g. in Papers I, III, and V indicate a vital PCM design lesson. That is, to verify an experimental phase diagram, a single characterization method, be it a thermal, physical or a chemical characterization, is never sufficient. A minimum of two and preferably ‘as many as possible’ techniques are necessary to confirm a novel blends’ phase diagram. Confirming all the stable phase boundaries of a phase diagram will be a continuous development process, complemented by a number of contributions over time. As understood through Papers III, V and VIII, thermal property evaluations, however, are the best way to start a novel blend’s phase equilibrium exploration. The information obtained, e.g. in terms of cp and temperature profiles, can then be explained using crystallographic characteristics followed by chemical structural and/or microstructural information. This is exemplified e.g. by the comparison of the conclusions in Paper VIII to those based on the comprehensive scrutiny in Paper III.

A prerequisite in thermal property evaluations is ensuring that the real blend’s phase change behavior is captured. This is one major conclusion brought through the discoveries in Paper III on the erythritol-xylitol experimental phase diagram. The IEA ECES Annex 24 (e.g. [306]) initiated pure component thermal property characterization standards with DSC, requiring such as: measurements on three samples per material, over at least three complete melting and freezing cycles, while ensuring thermal equilibrium. Along such standards, for the blend’s phase equilibrium explorations as well, it can be stipulated that at least three complete melting/freezing cycles must be examined to conclude on the systems’ phase diagram. As witnessed in Paper III, this characterization should always exclude the very first melting to ensure the real blend phase change on blends starting as solid mixtures. Whenever possible, the comparison between the melting-based phase diagram to that based on freezing must be achieved. In paper V the significance of such a comparison is illustrated. This comparison, on top of further verifying the system’s phase change, discloses the level of hysteresis, and both melting and freezing enthalpies if a calorimetric method is used, which are relevant for applications.

In studying the phase equilibrium of a multicomponent system, ensuring high purity of each component is extremely important. Upon blends preparation, no external materials should be combined into the system. Such externalities may also have influenced the phase diagram deduction of the erythritol-xylitol system in literature, as reflected in Paper III. An- other reflection therein is that the evaluated sample sizes should be representative of the materials’ general behavior, especially for materials of low homogeneity and/or prone to large supercooling.

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The knowledge assimilated from the Papers I, II, III, V and VIII indicate that, to obtain the phase (equilibrium) diagram, guaranteeing stable equilibrium when evaluating the pure components and blends is imperative. A universal condition e.g. in terms of heating/cooling rates does not exist that ensures stability in any material system. This always is material-specific, whereas, only by a systematic investigation per material system the best condition can be identified. During this investigation, the system’s metastability can also be characterized. For instance, the metastability of erythritol was witnessed in Paper II, based on which the T-history set-up was adapted to accommodate controlled cooling/heating. Consequently, the stable equilibrium was attained in pure erythritol, xylitol and their blends, presented in the Papers III and VIII. Via systematic rate-specific phase change explorations of the system, its metastable phases can be portrayed in a kinetic phase diagram: a valuable find within Paper I. The phase diagram indicates the standard behavior of the blend system, whereas the kinetic phase diagram indicates the application-specific behavior.

Tammann plots, also recognized within Paper I, should also be one analysis embedded into any phase diagram study of a system suspected to have e.g. eutectics or peritectics. Thereby, the exact eutectic or the peritectic composition can be identified, and the system’s solid-state miscibility can be confirmed.

A common consensus is crucial on the choice of phase change onset/offset/or peak temperatures, to plot the phase diagram. As it was explained in section 4.1.2.1 (and Paper III), e.g. for a partially isomorphous system with a eutectic: the melting offset; eutectic onset, or the melting onset when the eutectic disappears; and the solid-solution formation offsets, are better to represent respectively: the liquidus; solidus, and the solvus. Then, for a congruent melting solid solution, the liquidus and the solidus should be the offset and onset of melting, respectively. Certain investigations employed the phase change cp peak to represent a phase boundary in the phase diagram. However, it is neither the start nor the end of the phase change, and thus does not seem relevant in the phase diagram. Likewise, similar reasoning and agreements are needed on all the possible phase change characteristics. Only with such common agreements can the phase diagrams be comparable. As a whole, to obtain comparable phase diagrams, the data reporting must always be transparent with all the key information, hence making the evaluations repeatable.

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Theoretical Phase Diagram Evaluation For the engineering application of phase diagrams to design PCM blends, semi-empirical theoretical phase equilibrium assessments are preferable over purely-theoretical assessments. This is because, on top of extensive efforts and specific knowledge required by purely-theoretical assessments, these still cannot represent the exact actual phase change of the blend system. This is, however, crucial to be known before integrating the PCM into an application, and is achieved only by experimental evaluations. Experimental phase diagram alone, however, tends to include deviations from the standard behavior of the system, due to various experimental influences. Semi-empirical studies, in comparison, can indicate the thermodynamically correct phase diagram of the system and hence are a vital complement to the experimental phase diagrams. Therefore, the most effective approach for PCM design would be experimental evaluations coupled with semi-empirical studies.

As shown in section 3.2.2, all the theoretical phase equilibrium investigations performed thus far in the PCM-context are semi-empirical. Alt- hough numerous methods have been employed, most of these were limited to specific material characteristics (e.g. functional group activities or water-solubilities), and were often, bound by numerous assumptions, restricted to specific simple systems (i.e., almost exclusively to non-isomorphous simple eutectics). Several other evaluations however have employed a fundamental and nonspecific approach where the stable phases are determined by the Gibbs free energy minimizations. Only with such an approach can any material system be evaluated solely depending on its phase change behavior, irrespective of its chemical characteristics. An- other advantage of this generic approach is its ability to evaluate any type of a complex phase diagram. Starting from a simple blend system, the Gibbs free energy minimization approaches can predict the phase equilibrium of higher-order blend systems, which is invaluable in multicomponent PCMs design.

Therefore, a recommendation out of this thesis is also moving towards generic Gibbs free energy minimization approaches which have more freedom in the type of the system and its phase diagram. This is crucial to obtain comparable phase diagram evaluations, to build-up a database for continuous improvement of knowledge per material category.

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Phase Equilibrium for Designing Cost- effective PCMs from Blends In order to select the correct blend composition, besides deriving the correct phase diagram, knowing all the PCM-ideal composition possibilities is a prerequisite. This work, as in Paper I, has appraised the phase equilibrium in the context of functional PCMs. Thereby it is emphasized here that congruent melting solid solutions and congruent melting compounds are superior over any other blend composition as PCMs, because they do not phase separate even upon supercooling. Eutectics are the second-best choice, as, if supercooling is absent, they are similar to congruent melting compositions. Peritectic compounds have already been considered as PCMs, e.g. Glauber salt, SAT or CaCl2·6H2O, although they are unsuitable as PCMs. This is because they solidify with coring, which inevitably causes supercooling, phase separation, and incomplete transformation. Overall, any incongruent melting composition is unsuitable as a PCM, because of phase separation. Even if gelling and similar measures could reduce phase separation in an incongruent melting composition, these dilute the effective storage capacity of the PCM, and cannot completely eliminate the incongruency.

Comprehensive phase equilibrium evaluations require extensive efforts over a period of time. To make this extensive process still cost-effective, the novel understanding on a material system should be able to complement the existing knowledge. In addition, compiling the phase equilibrium knowledge per material category is the key to predict novel blends of the same chemical constitution. These are essentially continuous improvements to the existing knowledge per material system and category, which thereby makes the PCM blends design cost-effective. However, to achieve these complementary knowledge bases, phase equilibrium contributions must be presented abiding to standard techniques, approaches and data reporting methods.

In spite of this requirement, in the current PCM-context, the availability of such standards and common-consensuses are extremely limited, so far focused on pure materials and only a few techniques. Therefore, it is highlighted herein that there is an enormous need in acquiring standardization in phase equilibrium evaluations for PCM design23. This work presents the foundation for such a standard, by specifying the following:

23 Although no specific phase equilibrium standardizations are found, the organizations such as CALPHAD [307], SGTE [308], IUPAC [309], ASM International [310], NIST [311], and The American Ceramic Society [312], work towards achieving accurate and common results.

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• To confirm an experimental phase diagram, the minimum number of experimental techniques that are compulsory is two, and the type of characterizations these must include are thermal, and physical and/or chemical properties. • To complement the experimental phase diagram, the use of theoretical phase equilibrium evaluations that are generic to any system and phase change type is recommended (instead of specific, limited methods). • To achieve comparable phase equilibrium results, various methodological aspects are crucial, such as: using the cycled behavior of the system while excluding the first melting; the avoidance of external materials mixing into the intended blend; a consensus on the choice of the phase boundaries with respect to the phase change onset and offsets; and abiding to transparent and repeatable data reporting practices.

These standards should address each individual technique, the approaches in using a combination of techniques, and the specific requirements to present results in a transparent and repeatable manner. For that, international TES forums such like the IEA ECES Annex 24 and 29 [205] are instrumental.

S ustainable TES with PCMs By storing excess thermal energy for use at different times and locations, with e.g. PCMs, improved energy efficiencies and better energy management is achieved. To make a TES system using PCMs sustainable, the PCMs must also be sustainable. Hence, the PCMs should be of renewable origin, non-toxic to humans and the eco-system, safe for handling (e.g. nonflammable and non-irritant), and cost-effective. These attributes are fulfilled by many food-grade organic materials among e.g. polyols, fatty acids and fats. Some of these which are presently expensive, still have the potential in becoming cost-effective, as was exemplified in this work for the polyol erythritol (in section 6.1, Paper IX). Some others, like fats, come with complex phase change, as was exemplified with olive oil (section 6.2.1, Paper IX) in the first detailed thermal property characterization of this oil in the PCM-context. These blends, nevertheless, also come with attractive temperatures and enthalpies which encourage extensive phase equilibrium evaluations to find PCM-ideal compositions. The long-term stability of these food-grade organics, which are thus bio-degradable, should also be examined under the TES system conditions to conclude on their PCM-suitability. Despite the sustainability attributes a PCM has, the cradle-to-grave sustainable management of all the involved resources is essential to ultimately achieve a sustainable TES system.

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Specific Thesis Contributions In addition to the numerous phase equilibrium-aided PCM blends design guidelines discussed earlier, this thesis has the following specific scientific and/or engineering contributions.

• It comprehensively explained and pin-pointed the PCM-ideal compositions in material blends (congruent melting solid solutions and congruent melting compounds, and eutectics without supercooling), against the compositions unsuitable as PCMs (peritectics or any other incongruent melting composition). • It identified the knowledge and awareness gaps within the state- of-the-art in phase-equilibrium-based PCM design, and thereby highlighted the under-investigated: PCM-ideal phase change characteristics (e.g. the congruent melting solid solutions and congruent melting compounds); and attractive material categories (e.g. metal alloys, polyols, and fats). • It integrated a fixed heating/cooling rates-based operational mode to the T-history method, which is crucial for phase equilibrium investigations. • By means of a comprehensive experimental evaluation of the erythritol-xylitol phase diagram, it identified a eutectic in a partially isomorphous system, instead of a non-isomorphous simple eutectic as proposed by previous literature. In-relation, it highlighted several procedural aspects needing standardization in the PCM-context. • Through an experimental phase diagram appraisal of the alkanes system tridecane-dodecane, it verified a minimum melting liquidus in the system which is forming a probable congruent melting solid solution (the most PCM-ideal type), instead of a eutectic or a maximum-melting composition as proposed in literature. • By conducting a theoretical phase equilibrium assessment of the erythritol-xylitol system, it confirmed the erythritol-xylitol phase diagram thermodynamically. In doing so, it also exemplified the utility of a generic theoretical approach capable of evaluating any material and phase diagram type (unlike with specific methods). • It exemplified the potential in realizing sustainable PCMs within food-grade materials. There, it identified that erythritol could become cost-effective, and that olive-oil has attractive melting/freezing characteristics for freezing applications within which a potentially PCM-ideal composition is obtainable.

As a whole, herein, a foundation based on phase equilibrium evaluations- based systematic PCM blends design is set-forth, addressing: the suitable

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Thermal energy storage is a key element to address climate change. PCMs have the advantages of denser energy storage and hence requiring lesser volume, compared to sensible storage. To optimally realize the benefits in TES using e.g. PCMs, large-scale systems cost-effectively tailored to the applications are essential. Such cost-effective and robust PCMs can be realized in PCM-ideal compositions found within natural or industrial mixture systems, distinguished by a systematic evaluation of their phase equilibrium in a phase diagram. Besides, to engineer PCMs for specific application conditions for which suitable pure components do not exist, blending is the key. In the PCM-context, notwithstanding various phase equilibrium evaluations conducted over four decades, several aspects need improvements as identified in this thesis. These need to start at the fundamental phase equilibrium understanding of blends, where as well, certain knowledge gaps exist.

It is precisely explained in this thesis that among blends, the compositions ideal as PCMs are: congruent melting solid solutions, congruent melting compounds, and eutectics (if supercooling is absent). In contrast, any incongruent melting composition, including peritectics, are unsuitable as PCMs due to their inherent phase separation. The comprehensive state- of-the-art scrutiny revealed that the congruent melting compositions are extremely underinvestigated although they are the most PCM-ideal, and that the material categories metal alloys, polyols and fats, carry great potential for future TES design. The analysis of experimental and theoretical phase equilibrium derivation methods employed in the PCM-context thus far exposed considerable methodological discrepancies. This indicates a vital necessity in achieving a standardization of these methods and approaches in the PCM-context. Several experimental approaches and a theoretical method chosen based on the methodological assessment, have here altogether delivered novel phase equilibrium understanding on the two selected binary systems: erythritol-xylitol and dodecane-tridecane, for PCM design.

In the comprehensive experimental phase diagram study of the erythritol- xylitol system, the obtained thermal properties (using the T-history method), indicated a eutectic and solid-solid phase changes. However, the thermal properties alone were insufficient to confirm the phase diagram.

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Therefore, extensive XRD and FESEM investigations were incorporated, which verified the observed S-SPCs to be solid solutions formation in a partially isomorphous system. Thereby, the phase diagram was concluded. The FESEM in addition disclosed the rate-dependence of this polyols system yielding metastabilities at faster cooling. Such metastabilities must be mapped in kinetic phase diagrams, before integrating the PCM into a TES. For the characterization of the exact eutectic composition and the solid-state miscibility of the system, Tammann plots were valuable. As a whole, the erythritol-xylitol system was found to contain a eutectic in a partially isomorphous system, but not a non-isomorphous simple eutectic as the previous studies proposed. The discrepancies between this work and literature were reasoned as due to the number of cycles used to derive the results, missing procedural details, and overall methodological inconsistencies.

The dodecane-tridecane phase diagram was also presented with major dissimilarities in literature. When the system was investigated here using the T-history method and Tammann plots, a minimum melting liquidus and polymorphs were identified. These results agree with one of the literature, and discard the possibility of a maximum-melting liquidus presented by another study. However, the temperature minimum, lacking a solvus indication, is found possibly to be a congruent melting solid solution (thus PCM-ideal), but not a eutectic in a partially isomorphous system as the former study proposed.

As the methodological state-of-the-art analysis revealed, a majority of the theoretical phase equilibrium derivations in the PCM-context were limited to specific chemical interactions (e.g. activities of the molecules) or categories (e.g. organics or inorganics), and almost exclusively to eutectics. The remainder of the phase equilibrium assessments in PCM design, in contrast, employed the fundamental approach of the Gibbs free energy minimization of the system (commonly called the CALPHAD method). Only these generic approaches are able to evaluate a system of any material category and any type of phase diagram. Thus, the CALPHAD method, using Thermo-Calc, was employed to thermodynamically evaluate the identified erythritol-xylitol experimental phase diagram. Thereby, the erythritol-xylitol phase diagram was thermodynamically optimized, which verified the solvus and the solidus at the erythritol-rich compositions (which exhibited larger deviations in the experimental study), as well as the eutectic point. As a whole, the study exemplifies the necessity and the utility of a theoretical phase equilibrium assessment valid for any material type and phase change behavior, to confirm the experimental phase diagram.

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Overall, the conducted phase equilibrium appraisals (erythritol-xylitol and dodecane-tridecane) confirm the dire necessity in achieving standards and common consensus on the experimental and theoretical techniques, approaches, and transparent data reporting, to derive phase diagrams for PCM design. Confirming a novel phase diagram is an extensive, continuous development process, and requires collective phase equilibrium contributions over time, which essentially should be comparable. Designing cost-effective PCMs in blends through such extensive phase equilibrium evaluations profoundly relies on a build-up of databases per system. For building-up such knowledge, consistent data obtained by combining comparable and repeatable methods with transparent data reporting is crucial. This is achievable only by collectively adhering to common standards and consensuses.

A PCM-based TES system can contribute towards sustainable development. For that, the PCMs should be of renewable origin, non-toxic, safe, cost-effective, and have no negative impacts on the eco-systems. The food-grade, renewable organics erythritol and olive oil are potentially sustainable PCMs, however, currently expensive and with unknown thermal properties as a PCM, respectively. As shown here, producing high-purity erythritol from glycerol can result in costs one hundred and thirty times lower than the current laboratory-grade prices. Olive oil, under a T-history examination, exhibited melting/freezing and a solid-solid phase change, at a temperature attractive in refrigeration applications, with a reasonable enthalpy change and negligible supercooling. The multiple phase changes indicate the complex features of olive oil as a blend, however, the thermal properties inspire compositional refinements to find e.g. a eutectic. On the whole, these evaluations confirm that the food-grade renewable materials have a great potential to become cost-effective, and to come with PCM-suitable thermal properties. These therefore can serve as sustainable PCM candidates. Essentially, their long-term stability as bio-degradable organics also should be examined. Sustainable PCMs combined with cradle-to-grave sustainable management yield a sustainable TES system.

Future Work The experimental and theoretical assessments presented in this thesis can benefit from the following investigations and improvements, as future work.

In the T-history set-up employed here, the enthalpy accuracy improvements are proportional to the temperature accuracy improvements, as the sensitivity analysis indicated. The temperature accuracy can be improved by replacing the temperature sensors (e.g. using Resistance Temperature

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Detectors- RTDs, instead of thermocouples, with higher precision), and by including corrections related to the heat conduction along the sensors. The thermodynamic phase equilibrium modelling will also benefit from the improved enthalpy accuracy in the T-history method.

The erythritol-xylitol phase diagram can be further improved with a thorough slow-XRD investigation coupled with a chemical structural characterization (e.g. with FT-IR), particularly on the compositions 5-15 mol% Er and 60-95 mol % Er. Thereby, the solvus can be further confirmed, and possibly the large deviations encountered on e.g. the 80-98 mol% Er compositions can be better explained. A kinetic phase diagram study of the system for the application conditions would be also complementary.

A thorough study of the crystallographic and the chemical structural variations of the dodecane-tridecane system is needed to explain the major phase change differences observed during its melting and freezing. With these investigations, the system’s phase diagram can be confirmed. Fur- thermore, a thermodynamic assessment of the systems’ phase diagram would supplement for a comprehensive understanding.

The prediction of the phase diagrams of multicomponent blends derived from the binary erythritol-xylitol and dodecane-tridecane systems can possibly indicate PCM-ideal compositions in more real-life blends.

Fundamental and experimental investigations of the nucleation and solidification mechanisms and crystallization kinetics, of pure materials and their blends is a worthwhile continuation of this thesis work. Thereby, a systematic understanding of supercooling phenomena and hysteresis is anticipated, complementing the phase equilibrium understanding of these materials, that is greatly beneficial for PCM design.

To comprehend the reasons for the heat of fusion variations between materials, exploring their chemical and physical attributes (e.g. molecular interactions and bonding) from a fundamental point-of-view would be valuable. Thereby, reasonable predictions could be drawn to ascertain multicomponent blends with e.g. potentially large heats of fusion.

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Binary system– a material system made of two elements or a two components (which do not decompose into sub systems within the temperature range of interest). Composition- the proportion of each component (or element) in a multicomponent (or, multi-elemental) mixture. Compound- a phase where atoms of more than one element are chemically bonded in fixed stoichiometry (unlike in a solid solution), and arranged in a characteristic lattice. Congruent melting- when all the liquid and solid phases each have the same composition in equilibrium. Congruency- the attribute of congruent melting, which hence has no phase separation. Coring- an increasingly higher-melting point core is surrounded by layers of lower-melting point material, during solidification. Crystalline- when the atoms (in the material) are arranged in a repeating or a periodic array, within large atomic distances (i.e., maintains a long- range order). Eutectic- a mixture of two (for a binary system) or more solid phases, forming in an intimate mix, out of a single liquid. The total composition of the solids in the eutectic is the same as that of the liquid. Eutectic enthalpy- the phase change enthalpy change of a eutectic transition in a system (i.e., the enthalpy change corresponding to the eutectic phase change cp peak). Glass transition/Vitrification- a state transition where a supercooled liquid becomes like a glass (a very thick liquid that eventually becomes a transparent, rigid material). This occurs in materials that are amorphous in the solid-state, and these do not undergo phase transition, but instead glass transition. Hysteresis- the shift between the melting temperature and the freezing temperature, of the same material system. Isomorphous components- the components that solidify in the same crystal system, have similar crystal structures and dimensions, and consist of similar chemical constitution. To be able to form solid solutions, the involved components must be isomorphous. Isomorphous system- when all the components are completely mutually miscible in all proportions, both in liquid and solid states, and thus form a continuous solid solution.

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Kinetic phase diagram- a phase diagram that includes the rate-specific, i.e., metastable phase changes in the system. Liquidus- the locus of temperature points at which alloys of various compositions begin freezing upon cooling, or finish melting upon heating. Hence, all material above the liquidus are liquid. Metal alloy- a metallic substance made of two or more elements. Metastable equilibrium- a local minimum state in Gibbs free energy, which needs additional energy to reach stability. Miscibility- the ability to be mixed to form a liquid or a solid solution. The liquid and solid miscibility can be hence defined respectively. Mixture (or blend) - a material containing more than one phase. Multicomponent system- a system made of more than one component Noncrystalline/Amorphous- when the atoms in a material are arranged in a random, irregular manner, at relatively large atomic distances. Non-isomorphous system- a system (completely miscible in the liquid state) where in the solid state the components are completely mutually immiscible. Partially isomorphous system- a system (completely miscible in the liquid state) where a miscibility gap exists in the solid state, i.e., the components are mutually miscible in the solid-state only up to a certain proportion (but not 100%). PCM-ideal- perfectly suitable as a PCM Peritectic- an incongruent melting compound in a phase diagram, which is formed from a mixture of a liquid and a solid, during cooling (and vice- versa during melting). Phase diagram (Phase equilibrium diagram) - the plot of the phase changes in a material system at the thermodynamic equilibrium, of each composition, for different temperatures. Phase separation- physical separation/settling of the phases in a mixture due to compositional (and density) differences. Polymorphs- more than one, different crystalline solid forms that exist for a single chemical substance. A polymorph could be stable or metastable.

Solid solutions - a phase made of at least two types of atoms, where the solute occupies the solvent lattice, while retaining the solvent crystal structure. A solid solution has a homogeneous composition, but its atoms’ spatial arrangement is variable. Solidus- the locus of temperature points at which alloys of various compositions finish freezing upon cooling, or start melting upon heating. Hence, all materials below the solidus should be solid. Solution- a single phase made of more than one component. Solvus- the locus of the points that mark the solid solutions formation in e.g. a partially isomorphous system. Stable equilibrium- the lowest Gibbs free energy state in the system.

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Supercooling- when the system reaches temperatures below the expected freezing temperature, to start crystallization. Unary system- a single element, or, a single component (which is in fact only a pseudo unary system) provided that it does not decompose into sub-systems within the temperature range of interest. Unstable equilibrium- a state which requires no additional energy to reach stability or metastability.

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