DOCSLIB.ORG

Tips & Tricks GPC/SEC: Product Registration and REACH

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Tips & Tricks GPC/SEC: Product Registration and REACH Tips & Tricks GPC/SEC: Product Registration and REACH Daniela Held, PSS Polymer Standards Service GmbH, Mainz, Germany Molecular mass is one of the central parameters required for product registration. Compared to low molar mass substances, the molar mass determination of macromolecular products is more diffi cult because the product is a mixture of chains with different lengths and, therefore, molar masses. Gel permeation chromatography/size-exclusion chromatography (GPC/SEC) is the standard technique to separate macromolecules by size and to measure the complete molar mass distribution as well as the molar mass averages. This technique therefore provides crucial information for product registration, including REACH. (High) performance polymers comprise widely environment. Of concern, however, are varying molecular weights, structures, and unreacted monomers, oligomers, and compositions. These molecular parameters adjuvants and additives, which are added to infl uence the macroscopic properties of the improve the processability, the stability, and resulting product and are adjusted during the the quality of the fi nal product. Leaching development process. of these (potentially toxic) components can A big advantage of polymers and cause severe (health) issues. Registration macromolecules is that they can be agencies therefore require comprehensive considered as non-toxic, even when characterization with detailed molar mass produced from toxic monomers. As a result information and, for some products, also of their size and the fact that reactive extractables and leachables studies. functional groups are reacting during The molar mass of a product is polymerization, polymers are usually traditionally measured using gel permeation considered to be (bio)chemically inert and chromatography/size-exclusion Photo Credit: saicle/Shutterstock.com do not pose a threat to humans and the chromatography (GPC/SEC) and the results 2 Q&A:Q&A: HorieHorie 6 NewsNews 9 TipsTips andand TricksTricks 14 HPLCHPLC EventEvent PPreviewreview 9 16 AndersonAnderson eett aal.l. 22 SchadSchad andand IwataIwata 27 HPTLCHPTLC EventEvent PreviewPreview 28 TrainingTraining & EventsEvents 30 StaffStaff The Column www.chromatographyonline.com Tips and Tricks Figure 1: Chromatogram of a polyol with 8+ automatically identifi ed single chains with 1–8 repetition units (compare Table 1 for detailed results). are of the utmost importance because REACH the molar mass can infl uence which REACH, Registration, Evaluation, registration category will apply for a Authorisation, and Restriction of Chemicals, new product, for example, the molar is an EU regulation that came into force on mass determines whether new products 1 June 2007. It addresses the production of fall into the category “polymer of low chemicals and their impacts on human health concern” (PLC) or if a product is subject for and the environment. For Europe, all polymers registration or not (EU REACH). Accordingly, are exempt from registration and evaluation the generation of detailed and appropriate under REACH. A polymer is here defi ned molar mass data that satisfi es regulatory using three criteria: guidelines is a key component of successful • The molecules must be distributed over a registration. molecular weight range. 2 Q&A:Q&A: HorieHorie 6 NewsNews 9 TipsTips andand TricksTricks 14 HPLCHPLC EventEvent PPreviewreview 1010 16 AndersonAnderson eett aal.l. 22 SchadSchad andand IwataIwata 27 HPTLCHPTLC EventEvent PreviewPreview 28 TrainingTraining & EventsEvents 30 StaffStaff The Column www.chromatographyonline.com Tips and Tricks Table 1: Molar mass and weight percentage results for the peaks from Figure 1 show that this Figure 2: Molar mass distribution determined for a typical polymer product. Since Mw is product is a polymer based on REACH criteria above 10000 Da and the fraction below 500/1000 Da are below 2/5%, this product fulfi ls Molar Mass M Content the molar mass requirements for a polymer of low concern. Example Polyol p Comment Polymer? (Da)* (%) Peak H 200 0.20 R-M, Yes, Less than 50% + Peak G 490 13.4 R-M-M below (3M 1) Peak F 790 15.7 R-M-M-M Peak E 1090 14.8 Yes, no individual Peak D 1400 13.3 chain > 50% Peak C 1810 11.0 Yes, molar mass distribution Peak B 2190 9.30 Peak A 2550 22.3 * Polystyrene equivalents • The weight percentage of molecules If the molar mass of a product is containing three monomer units or above suffi ciently low, GPC/SEC separations often should exceed 50% (3M+1 rule). show a nice oligomeric profi le as shown in • The weight percentage of any molecule the chromatogram in Figure 1. Identifi cation of the same molecular weight shall not of the single peaks is possible by overlaying exceed 50%. the data with at least one known reference to resolve this into single peaks. This the substance is a polymer according to the material. The single peaks can then be behaviour is very typical for GPC/SEC where defi nition of REACH. Different REACH-like regulations around evaluated with respect to molar mass and for higher molar masses broader peaks are the world have adopted this defi nition, weight percentage. The example shows observed. Polymers of Low Concern although the regularity requirements about a polyol with a molar mass distribution Table 1 shows the numerical results Product registrations often require the Mw the consequences may differ. For example, (criteria 1 met) and eight automatically for the eight identifi ed species and a (weight average molecular weight) and the polymers are not exempt for China-REACH. identifi ed peaks for chains with 1–8+ comparison with REACH polymer defi nition mass fractions below a defi ned molar mass, The preferred method to determine whether a repetition units. For higher molar masses criteria. By comparing the REACH criteria such as 500 or 1000 Da. This is required to substance falls under the defi nition of a polymer (longer chains, 8+ repetition units), the with the GPC/SEC results, it is seen that all classify a product as a PLC. Unfortunately, is GPC/SEC with referral to OECD TG 118 (1). resolution of GPC/SEC was not suffi cient three REACH criteria are met. Consequently, the defi nitions for PLCs in different countries 2 Q&A:Q&A: HorieHorie 6 NewsNews 9 TipsTips andand TricksTricks 14 HPLCHPLC EventEvent PPreviewreview 1111 16 AndersonAnderson eett aal.l. 22 SchadSchad andand IwataIwata 27 HPTLCHPTLC EventEvent PreviewPreview 28 TrainingTraining & EventsEvents 30 StaffStaff The Column www.chromatographyonline.com Tips and Tricks can vary as well as the required actions— Please note that there are some general Molar mass distribution determined for a polymer product that does not fulfi l the nevertheless GPC/SEC is able to provide the exclusions for polymers, which are generally Figure 3: molar mass requirements for a polymer of low concern (fraction < 1000 Da is above 5%). required information. not exempted. Cationic or potentially cationic In addition, the measurement uncertainty is displayed, which is quite high here and can be In addition to the area percentage values polymers, high-molecular-weight water improved. for each well separated peak, GPC/SEC absorbing polymers, and polymers that results include the molar mass distribution, degrade, decompose, or depolymerize are which allows Mw to be determined and not eligible for exemption. Reactive groups the required fractions deduced. The molar can also be a problem; as a consequence, mass distribution is obtained from the a polymer would not be exempted from chromatogram when a calibration curve is regulations, even if the mass results indicate available (or more precisely, when the molar that it is a polymer of low concern. mass information for each elution volume In addition, the mass fraction for every is available) (2). As a result of the special molar mass slice (sometimes referred to transformations required in GPC/SEC analysis as slice list) can be required for product it is important to ensure that the results for registration. An additional slice list can easily registration are taken from a true molar mass be created once the molar mass distribution distribution and not from a chromatogram is available. From this slice list the required where only the elution volume is replaced by parameters discussed above can be directly the molar mass (3). determined. Figure 2 shows an example for a sample with a broad molar mass distribution (no resolution Measurement Uncertainty and into single peaks) with graphical molar mass Infl uence of Analytical Parameters distribution and molar mass averages as well Analytical scientists producing data for as the fractions below 500 Da and above product registrations should refl ect on at least highest concern, mass spectrometry (such as Partially related to calibration, the 1000 Da. According to the defi nitions in the two important parts of GPC/SEC analysis. electrospray ionization mass spectrometry measurement uncertainty is the second part US and China, this sample is a polymer of low First, all analysts must make the right [ESI-MS] or matrix-assisted laser desorption– to be reviewed (6). Quality of raw data, concern because the Mw is above 10,000 Da, choice for calibration. GPC/SEC, as a relative ionization [MALDI]) can be a valuable addition analytical conditions, and calibration quality less than 2% are below 500 Da, and less than method, always requires a calibration, either for products where no chemically matching infl uence the results, and the measurement 5% are below 1000 Da. For a polymer of Mw using reference materials or an additional reference materials are available (5). If uncertainty can help to identify random error between 1000 Da and 10,000 Da, the fractions detector that allows the molar mass to be chemically matching reference materials are sources to improve the quality of the data. below 500 Da should be below 10% and measured directly (4). In case of registrations, available, it is recommended to select these Figure 3 shows an example of a molar below 1000 Da 25%, respectively.
Load more

Recommended publications
  • GPC - Gel Permeation Chromatography Aka Size Exclusion Chromatography- SEC
    GPC - Gel Permeation Chromatography aka Size Exclusion Chromatography- SEC Wendy Gavin Biomolecular Characterization Laboratory Version 1 May 2016 1 Table of Contents 1. GPC Introduction………………………………………………………. Page 3 2. How GPC works………………………………………………………... Page 5 3. GPC Systems…………………………………………………………… Page 7 4. GPC/SEC Separations – Theory and System Considerations… Page 9 5. GPC Reports……………………………………………………………. Page 10 6. Calibrations of GPC systems………………………………………... Page 14 7. GPC preparation……………………………………………………….. Page 16 8. Alliance System………………………………………………………… Page 17 9. GPC columns…………………………………………………………… Page 18 2 1. GPC Introduction Gel permeation chromatography (GPC) is one of the most powerful and versatile analytical techniques available for understanding and predicting polymer performance. It is the most convenient technique for characterizing the complete molecular weight distribution of a polymer. Why is GPC important? GPC can determine several important parameters. These include number average molecular weight (Mn), weight average molecular weight(Mw) Z weight average molecular weight(Mz), and the most fundamental characteristic of a polymer its molecular weight distribution(PDI) These values are important, since they affect many of the characteristic physical properties of a polymer. Subtle batch-to-batch differences in these measurable values can cause significant differences in the end-use properties of a polymer. Some of these properties include: Tensile strength Adhesive strength Hardness Elastomer relaxation Adhesive tack Stress-crack resistance Brittleness Elastic modules Cure time Flex life Melt viscosity Impact strength Tear Strength Toughness Softening temperature 3 Telling good from bad Two samples of the same polymer resin can have identical tensile strengths and melt viscosities, and yet differ markedly in their ability to be fabricated into usable, durable products.
    [Show full text]
  • Fundamentals of Reversible Addition– Fragmentation Chain Transfer
    Chemistry Teacher International 2021; 3(2): 3–17 Review article Catherine L. Moad and Graeme Moad* Fundamentals of reversible addition– fragmentation chain transfer (RAFT) https://doi.org/10.1515/cti-2020-0026 Received September 15, 2020; accepted December 14, 2020; published online December 30, 2020 Abstract: Radical polymerization is transformed into what is known as reversible addition–fragmentation chain transfer (RAFT) polymerization by the addition of a RAFT agent. RAFT polymerization enables the preparation of polymers with predictable molar mass, narrow chain length distribution, high end-group integrity and provides the ability to construct macromolecules with the intricate architectures and composition demanded by modern applications in medicine, electronics and nanotechnology. This paper provides a background to understanding the mechanism of RAFT polymerization and how this technique has evolved. Keywords: addition–fragmentation; radical polymerization; RAFT; reversible-deactivation. Introduction This paper aims to provide an understanding of the mechanism of reversible addition–fragmentation chain transfer (RAFT) polymerization without going into full detail on the actual chemicals (i.e., monomers, ini- tiators and control agents) used. It is intended for undergraduates who have some understanding of organic or polymer chemistry and already know about reactive intermediates (e.g., carbon-centered radicals, carbanions), reaction types (e.g., addition reaction, fragmentation reaction, substitution reaction) and polymerization. Radical polymerization is a versatile process that sees widespread use in industry for production of many commodity polymers that include poly(methyl methacrylate) (PMMA, Perspex®), polystyrene, low density polyethylene (LDPE), poly(vinyl chloride) (PVC) and many others. It is compatible with a vast range of monomers, it is tolerant of functionality in the monomers and the polymerization medium, and it can be carried out under a wide range of polymerization conditions (Moad & Solomon, 2006c).
    [Show full text]
  • Polyethylene Loss of Ductility During Oxidation: Effect of Initial Molar Mass Distribution Armando F
    Polyethylene loss of ductility during oxidation: Effect of initial molar mass distribution Armando F. Reano, Alain Guinault, Emmanuel Richaud, Bruno Fayolle To cite this version: Armando F. Reano, Alain Guinault, Emmanuel Richaud, Bruno Fayolle. Polyethylene loss of ductil- ity during oxidation: Effect of initial molar mass distribution. Polymer Degradation and Stability, Elsevier, 2018, 149, pp.78-84. 10.1016/j.polymdegradstab.2018.01.021. hal-01741541 HAL Id: hal-01741541 https://hal.archives-ouvertes.fr/hal-01741541 Submitted on 23 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Polyethylene loss of ductility during oxidation: Effect of initial molar mass T distribution ∗ Armando F. Reano, Alain Guinault, Emmanuel Richaud , Bruno Fayolle Laboratoire PIMM, Ensam, CNRS, Cnam, 151 Boulevard de l'Hôpital, 75013 Paris, France ARTICLE INFO ABSTRACT Keywords: This paper reports a study of thermal oxidation induced embrittlement in several polyethylene grades differing Polyethylene mainly by the broadness of the molar mass distribution (ranging for lower than 3 to more than 30). Thermal Oxidation oxidation was monitored at macromolecular scale (Gel Permeation Chromatography, Differential Scanning Loss of ductility Calorimetry) and macroscopic scale (tensile tests).
    [Show full text]
  • Devoted to Polyolefin Science Your Partner in Polyolefin Characterization
    Years of Innovative Thinking Corporate Overview Devoted to Polyolefin Science Your Partner in Polyolefin Characterization With headquarters in Valencia, Spain, Polymer Char offers a broad range of modern instruments and analytical services for Polyolefin Analysis, standing out in GPC/SEC with GPC-IR®, in Chemical Composition Distribution with CRYSTAF, TREF or CEF, in Cross Fractionation Chromatography with CFC, and in Soluble Fraction analysis with CRYSTEX® QC and CRYSTEX® 42. More recently, two instruments were added to the portfolio: GPC-QC for measuring molar mass distribution in a plant environment, and IVA for the analysis of intrinsic viscosity in a wide range of polymers. Also in the solutions offered is LabAID, a line of accessories for facilitating daily operations. With equipment installations in leading petrochemical companies, government laboratories and universities in over 25 countries and analytical services provided to 35 countries, Polymer Char has clearly become the leader in research, engineering, software and service in Polyolefin Characterization. After dedicating 25 years to polyolefins, the company is now starting to transfer its expertise and innovative approach to the analysis of other polymers as it broadens its scope of solutions. For over two decades Polymer Char has been the sole instrumentation company in the world fully dedicated to the microstructural characterization of polyolefins. We stay ahead in the industry by developing new technologies that help polymer researchers know more about their polyolefin products. Overview Company Profile Founded: September, 1992. Headquarters: Valencia, Spain. Products: Instrumentation for Polymer Analysis, Infrared Detectors, Software and Accessories. Services: Analytical and Fractionation Services, Training and Consulting. Markets served: Petrochemicals.
    [Show full text]
  • Disentangled Polyethylene with Sharp Molar Mass Distribution : Implications for Sintering
    Disentangled polyethylene with sharp molar mass distribution : implications for sintering Citation for published version (APA): Talebi, S. (2008). Disentangled polyethylene with sharp molar mass distribution : implications for sintering. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR639413 DOI: 10.6100/IR639413 Document status and date: Published: 01/01/2008 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
    [Show full text]
  • Basics of GPC (SEC) Separation Including Calibration Options
    FOR INTERNAL USE ONLY 9/20/2016 FOR INTERNAL USE ONLY Basics of GPC (SEC) separation including calibration options Dr. Harry J.A. Philipsen Workshop at the International Symposium on GPC/ SEC and related techniques Amsterdam, September 26, 2016 FOR INTERNAL USE ONLY Some words on myself.. - 2016-now: Senior Scientist/ Project Director and Competence Lead Molecular Structures and Quantification of Synthetic Polymers. - 2011-2016: Resources manager Polymers Cluster at DSM Resolve, Geleen. - 2014-now: Project director “(Bio)Macromolecular Characterization” – part of the DSM corporate Analysis & Characterization program. - 2009-2012: Visiting scientist capacity group Polymer Chemistry (SPC) at TU/e and lecturer Analytical Chemistry at TU/e. - 2007-2010: New Business Development Manager at DSM Resolve, Geleen. - Until 2007: Researcher/ group leader (analytical chemist) at Océ Technologies, Venlo. -1997-now: Chairman Discussion group Separation methods of Polymers (DSP) of KNCV. - 2002-now: Board member and chairman Section Analytical Chemistry (SAC) of KNCV. - 1998: PhD Analytical Chemistry (polymer characterization), TU/e. Page 1 1 FOR INTERNAL USE ONLY 9/20/2016 FOR INTERNAL USE ONLY SEC in industrial applications - 2016 o Big gap between academic research and industrial practice on polymer separations. o SEC: one of the most used techniques for polymer characterization in industry. o Considered as simple, but still many pitfalls. o Real life accuracy and precision often cumbersome.. Page 2 FOR INTERNAL USE ONLY What is GPC/ SEC? GPC and SEC are different names for the same technique; • GPC: Gel Permeation Chromatography. • SEC: Size Exclusion Chromatography: the official IUPAC name. • Liquid chromatography technique that separates molecules according to their size (but only when performed properly).
    [Show full text]
  • The FULL PICTURE of Your POLYOLEFIN
    The FULL PICTURE of your POLYOLEFIN MOLAR MASS DISTRIBUTION PRODUCTS Contents An Overview 05 Instruments 07 Molar Mass Distribution 11 Chemical Composition Distribution 19 Bivariate Distribution 23 Soluble Fraction Measurement 27 Intrinsic Viscosity 31 Preparative Fractionation LabAID 35 Analytical Services 45 Molar Mass Distribution 47 Chemical Composition Distribution 51 Bivariate Distribution 53 Soluble Fraction Measurement 55 Intrinsic Viscosity 57 Preparative Fractionation Comparative Table 61 Users Training Meeting 63 Contact 65 02 AMPLIFYING YOUR POLYOLEFIN EXPER- 03 Overview THE MOST COMPLETE RANGE OF TOOLS FOR POLYOLEFIN CHARACTERIZATION TO GET THE FULL PICTURE OF YOUR RESIN At Polymer Char we have strived for over 25 years to become the expert company in the development of innovative and automated solutions for polyolefin characterization. The pursuit of this goal has resulted in a solid portfolio of 14 instruments that cover several different separation techniques necessary for a full characterization. All of the analytical equipment can integrate any of three Infrared Detectors developed in-house, as well as other types of detection systems such as Viscometry and Light Scattering. Every instrument’s technique is also available in the form of analytical services provided to our customers according to their specific needs. All the analyses are performed in a cutting-edge laboratory that has served over 35 countries worldwide. More recently, we launched LabAID, a line of accessories that solves the inconvenient tasks performed in the laboratory that are too manual and too time-consuming. Now, we are beginning to take our expertise into the analysis of other polymers, and with this latest venture we continue expanding our portfolio to become the top all-round solutions provider in polymer analysis.
    [Show full text]
  • Molar Mass Determination
    Polymers in Solution Dresden, 25th November 2020 Silvia Moreno Pinilla Bioactive and Responsive Polymers Institute of Macromolecular Chemistry Leibniz-Institut für Polymerforschung Dresden e.V. 5. Molar mass determination 2 5. Molar mass determination 1. Overview Size exclusion Osmometry chromatography End group analysis molar mass distribution, χ, Mn dispersity Light scattering and diffraction Conformations, Chemical composition and dynamics, crystal molecular structure structure Thermal transitions Spectroscopy (Tm, Tc, Tg) Differential scanning calorimery dilarometry 3 polymer coils 5. Molar mass determination 1. Overview Molar Mass in Polymers Number average molar weight MMD (polydispersity) is with Mw/Mn σ푖 푐푖 σ푖 푁푖푀푖 Mn= = For monodisperse samples Mw/Mn = 1 σ푖(푐푖/푀푖) σ푖 푁푖 Polydisperse polymers have Mw/Mn > 1 Weight average molar weight σ푖(푐푖푀푖) Mw= σ푖 푐푖 z-average molecular weight 2 σ푖(푐푖푀푖 ) σ푖 푧푖푀푖 Mz= = σ(푐푖푀푖) σ 푧푖 4 polymer coils 5. Molar mass determination 2. Methods for determining the molar mass of macromolecules Method Molar mass average Molar mass range Absolut method 3 Ebulliometry, cryoscopy Mn M < 5 x 10 4 6 Membrane osmometry Mn 10 < M > 10 4 Isothermal distillation Mn M > 5 x 10 2 Sedimentation velocity Mn, Mw, Mz M> 10 2 Equilibrium sedimentation Mw, Mz M > 10 4 Vapor pressure osmosis Mn M < 2 x 10 2 Static Light Scattering Mw M > 5 x 10 2 Turbidity measurements Mw M > 5 x 10 2 Small-angle X-ray scattering Mw M > 5 x 10 2 Small-angle neutron scattering Mw M > 5 x 10 2 Dynamic Light Scattering Mw M > 5 x 10 Mass spectroscopy- MALDI-TOF Mn, Mw, Mz M > 5 x 10 Equivalent method 4 End-group analysis- (titration, NMR, IR) Mn M < 5 x 10 Relative method 2 Dilute solution viscometry Mn M > 10 7 Gel Permeation chromatography Mn, Mw, Mz M < 10 7 Supercritical fluid chromatography Mn, Mw, Mz M < 10 Field-flow fractionation M M M M > 103 5 polymer coilsn, w, z 5.
    [Show full text]
  • Polymer Physics Chapter 1
    Polymer Physics Chapter 1 1.6 Molar mass ・Low molar mass substances (oligomers) : m. p.↑ with MW↑. ・High molar mass substances (polymers) : m. p. constant with MW↑ but, rheological properties : (ex.) melt viscosity ↑ with MW↑ Molar mass distribution (3 ~ 4 지수 정도의 범위로 분포) ∙ Number average molecular weight ∑ N M ∑W 1 M = i i = ∑n M = i = n N i i W w ∑ i ∑ i ∑ i Mi Mi Ni = # of molecules ni = numerical fraction or number fraction ( = mole fraction xi) Wi = mass of Mi wi = weight fraction or mass fraction Polymer Physics Chapter 1 ∙ Weight average molecular weight 2 ∑ NiMi ∑WiMi M w = = = ∑ wiMi ∑ NiMi ∑Wi ∙ Viscosity average molecular weight 1/ a ⎛ ∑ N M 1+a ⎞ 1/ a M = ⎜ i i ⎟ = w M a , 0.5 ≤ a ≤ 0.8 v ⎜ ⎟ ()∑ i i ⎝ ∑ NiMi ⎠ ⎛η −η0 ⎞ []η = lim ⎜ ⎟ c→0⎝ cη0 ⎠ η0 : η of pure solvent [η] : intrinsic viscosity c : concentration of polymer in solution Polymer Physics Chapter 1 ∙ Mark-Houwink rule (relationship betw. [η ] and M v ) a []η = K M v K, a : Mark-Houwink parameters, Unique for the combination of polymer & solvent ∙ M n ≤ M v ≤ M w ≤ M z M w ∙ Polydispersity index, PI (or heterogeneity index) ≡ M n Polymer Physics Chapter 1 M n ≤ M w 의증명: 2 ∑ Ni ()Mi − M n ≥ 0 이 성립하므로 풀어 쓰면 2 2 이된다 이식을 N 로나누면 ∑ NiMi +∑∑NiM n − 2 NiMi Nn ≥ 0 . ∑ i 2 ∑ NiMi 2 2∑ NiMiM n + M n − ≥ 0 이므로 ∑ Ni ∑ Ni 2 ∑ NiMi 2 ≥ M n 이된다. 이를 다음과 같이 처리하면 ∑ Ni 2 2 ∑ NiMi 1 ∑ NiMi ∑ Ni × ≥ M n ⇒ × ≥ M n 이 되므로 ∑ Ni M n ∑ Ni ∑ NiMi M w ≥ M n 이 성립한다.
    [Show full text]
  • Overview of Methods for the Direct Molar Mass Determination of Cellulose
    Molecules 2015, 20, 10313-10341; doi:10.3390/molecules200610313 OPEN ACCESS molecules ISSN 1420-3049 www.mdpi.com/journal/molecules Review Overview of Methods for the Direct Molar Mass Determination of Cellulose Josua Timotheus Oberlerchner, Thomas Rosenau and Antje Potthast * Christian-Doppler Laboratory “Advanced Cellulose Chemistry and Analytics”, Division of Chemistry of Renewable Resources, Department of Chemistry, University of Natural Resources and Life Sciences Vienna, Muthgasse 18, A-1190 Vienna, Austria; E-Mails: [email protected] (J.T.O.); [email protected] (T.R.) * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +43-1-47654-6454; Fax: +43-1-47654-6059. Academic Editor: Jun Araki Received: 10 March 2015 / Accepted: 27 May 2015 / Published: 4 June 2015 Abstract: The purpose of this article is to provide the reader with an overview of the methods used to determine the molecular weights of cellulose. Methods that employ direct dissolution of the cellulose polymer are described; hence methods for investigating the molecular weight of cellulose in derivatized states, such as ethers or esters, only form a minor part of this review. Many of the methods described are primarily of historical interest since they have no use in modern cellulose chemistry. However, older methods, such as osmometry or ultracentrifuge experiments, were the first analytical methods used in polymer chemistry and continue to serve as sources of fundamental information (such as the cellulose structure in solution). The first part of the paper reviews methods, either absolute or relative, for the estimation of average molecular weights.
    [Show full text]