Understanding Composition–Structure– Bioactivity Correlations

Understanding Composition–Structure– Bioactivity Correlations in Bioactive Glasses Yang Yu Academic dissertation for the Degree of Doctor of Philosophy in Physical Chemistry at Stockholm University to be publicly defended on Wednesday 12 December 2018 at 13.00 in De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14.

Abstract Bioactive glasses integrate with bone/tooth tissues by forming a layer of hydroxy-carbonate apatite (HCA), which mimics the composition of bone mineral. In the current thesis, we investigated composition–structure–bioactivity correlations of phosphosilicate and borophosphosilicate (BPS) glasses. Bioactive phosphosilicate glasses extend the compositional space of the ”45S5 Bioglass®”, which has been in clinical use for decades. Recently developed bioactive BPS glasses with SiO2→B2O3 substitutions transform more completely into HCA and their glass dissolution behaviors can be tuned by varying the relative contents of B and Si. It is known that the average silicate network connectivity NSi and the phosphate content (x(P2O5)) affect the apatite formation (in vitro bioactivity) of phosphosilicate glasses, but the details remain poorly explored. Three series of phosphosilicate glasses were designed by independently varying NSi and x(P2O5). After immersion of the glasses in a simulated body fluid (SBF) for 24 hours, different degrees of their apatite formation were quantified by Fourier-transform infrared (FTIR) spectroscopy. The results revealed that a high P content widened the NSi range that generated optimum amounts of apatite and also mitigated the detrimental effects associated with using glass particles with < 50 μm. The amounts of apatite derived from FTIR agreed with those from 31P magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. The growth of apatite at bioactive glass surfaces was found to follow a sigmoidal growth model, in which the precursor phase, amorphous calcium phosphate (ACP), formed in the induction period and then crystallized into HCA in the following proliferation period, with an improvement in the structural ordering of HCA in the maturation period. This formation process closely resembles the apatite precipitated spontaneously from supersaturated Ca/P-containing solutions. The simultaneous growth of ACP and HCA is discussed in conjunction with a previously proposed mechanism for explaining in vitro bioactivity and apatite growth from bioactive glasses. The short- and medium- range structures of bioactive borophosphosilicate (BPS) glasses were investigated by solid-state MAS NMR. Two series of BPS glasses were designed by gradually replacing SiO2 with B2O3 in the 45S5 glass, as well as another base glass featuring a more condensed glass network. As the B2O3 content is increased, the glass networks become more polymerized, together with decreased fractions of the dominating BO3 and orthophosphate units. Borate groups are homogeneously mixed with the isolated orthophosphate groups, while the remaining phosphate groups exhibit a slight [3] [4] preference for bonding to BO4 over SiO4 units. Linkages among borate groups are dominated by B –O–B linkages at the expenses of B[3]–O–B[3] and B[4]–O–B[4] linkages, with the latter B[4]–O–B[4] motifs disfavored yet abundant. A similar fashion of borate mixing was observed in P-free Na/Ca-based borosilicate glasses that span a large compositional space. [4] [4] The content of B –O–B linkages was found to be controlled by the relative fractions of BO4 groups and non-bridging oxygen ions.

Keywords: Bioactive glasses, Phosphosilicate glasses, Borophosphosilicate glasses, Solid-state NMR spectroscopy, Glass structure, Fourier-transform infrared spectroscopy, Hydroxyapatite, Amorphous calcium phosphate, Apatite formation, In vitro bioactivity testing.

Stockholm 2018 http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-161477

ISBN 978-91-7797-458-1 ISBN 978-91-7797-459-8

Department of Materials and Environmental Chemistry (MMK)

Stockholm University, 106 91 Stockholm

UNDERSTANDING COMPOSITION–STRUCTURE–BIOACTIVITY CORRELATIONS IN BIOACTIVE GLASSES

Yang Yu

Understanding Composition– Structure–Bioactivity Correlations in Bioactive Glasses

Yang Yu ©Yang Yu, Stockholm University 2018

ISBN print 978-91-7797-458-1 ISBN PDF 978-91-7797-459-8

Printed in Sweden by Universitetsservice US-AB, Stockholm 2018 To my beloved families and in memory of my father

谨以此论文献给我亲爱的母亲和已过世近十二年的父亲！

Abstract

Bioactive glasses integrate with bone/tooth tissues by forming a layer of hydroxy- carbonate apatite (HCA), which mimics the composition of bone mineral. In the current thesis, we investigated composition–structure–bioactivity correlations of phosphosilicate and borophosphosilicate (BPS) glasses. Bioactive phosphosilicate glasses extend the compositional space of the “45S5 Bioglassr”, which has been in clinical use for decades. Recently developed bioactive BPS glasses with SiO2→B2O3 substitutions transform more completely into HCA and their glass dissolution behaviors can be tuned by varying the relative contents of B and Si. Si It is known that the average silicate network connectivity NBO and the phosphate content (x(P2O5)) affect the apatite formation (in vitro bioactivity) of phosphosilicate glasses, but the details remain poorly explored. Three series Si of phosphosilicate glasses were designed by independently varying NBO and x(P2O5). After immersion of the glasses in a simulated body ﬂuid (SBF) for 24 hours, different degrees of their apatite formation were quantiﬁed by Fourier- transform infrared (FTIR) spectroscopy. The results revealed that a high P Si content widened the NBO range that generated optimum amounts of apatite and also mitigated the detrimental effects associated with using glass particles with < 50 µm. The amounts of apatite derived from FTIR agreed with those from 31P magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. The growth of apatite at bioactive glass surfaces was found to follow a sigmoidal growth model, in which the precursor phase, amorphous calcium phosphate (ACP), formed in the induction period and then crystallized into HCA in the following proliferation period, with an improvement in the structural ordering of HCA in the maturation period. This formation process closely resembles the apatite precipitated spontaneously from supersaturated Ca/P-containing solutions. The simultaneous growth of ACP and HCA is discussed in conjunction with a previously proposed mechanism for explaining in vitro bioactivity and apatite growth from bioactive glasses. The short- and medium- range structures of bioactive borophosphosilicate (BPS) glasses were investigated by solid-state MAS NMR. Two series of BPS glasses were designed by gradually replacing SiO2 with B2O3 in the 45S5 glass, as well as another base glass featuring a more condensed glass network. As the B2O3 content is increased, the glass networks become more polymerized, together with decreased fractions of the dominating BO3 and orthophosphate units. Borate groups are homogeneously mixed with the isolated orthophosphate groups, while the remaining phosphate groups exhibit a slight preference for bonding to BO4 over SiO4 units. Linkages among borate groups are dominated by B[3] O B[4] linkages at the expenses of B[3] O B[3] and B[4] O B[4] linkages, with the latter B[4] O B[4] motifs disfavored yet abundant. A similar fashion of borate mixing was observed in P-free Na/Ca- based borosilicate glasses that span a large compositional space. The content of B[4] O B[4] linkages was found to be controlled by the relative fractions of BO4 groups and non-bridging oxygen ions.

Key Words: Bioactive glasses, Phosphosilicate glasses, Borophosphosili- cate glasses, Solid-state NMR spectroscopy, Glass structure, Fourier-transform infrared spectroscopy, Hydroxyapatite, Amorphous calcium phosphate, Ap- atite formation, in vitro bioactivity testing List of Papers

The following papers, referred to in the text by their Roman numerals, are included in this thesis. Reprints were made with permission from the publishers.

PAPER I: Quantitative Composition-Bioactivity Relationships of Phos- phosilicate Glasses: Bearings From the Phosphorus Content and Network Polymerization. Y. Yu, R. Mathew, and M. Edén, J. Non-Cryst. Solids, 502, 106– 117 (2018). DOI: 10.1016/j.jnoncrysol.2018.07.060

PAPER II: Contrasting In Vitro Apatite Growth From Bioactive Glass Surfaces with that of Spontaneous Precipitation. Y. Yu, Z. Bacsik, and M. Edén, Materials, 11, 1690 (2018). DOI: 10.3390/ma11091690

PAPER III: Structure-composition Relationships of Bioactive Borophos- phosilicate Glasses Probed by Multinuclear 11B, 29Si, and 31P Solid State NMR. Y. Yu, and M. Edén, RSC Adv., 6, 101288–101303 (2016). DOI: 10.1039/c6ra15275a

PAPER IV: Medium-Range Structural Organization of Phosphorus-Bearing Borosilicate Glasses Revealed by Advanced Solid-State NMR Experiments and MD Simulations: Consequences of B/Si Substitutions. Y. Yu, B. Stevenson, and M. Edén, J. Phys Chem. B, 121, 9737– 9752 (2017). DOI: 10.1021/acs.jpcb.7b06654

PAPER V: Direct Experimental Evidence for Abundant BO4–BO4 Mo- tifs in Borosilicate Glasses From Double-Quantum 11B NMR Spectroscopy. Y. Yu, B. Stevenson, and M. Edén, J. Phys. Chem. Lett., 9, 6372–6376 (2018). DOI: 10.1021/acs.jpclett.8b02907

The following papers are not included in this thesis.

PAPER VI: Two Heteronuclear Dipolar Results at the Price of One: Quan- tifying Na/P Contacts in Phosphosilicate Glasses and Biomimetic Hydroxy-Apatite. B. Stevensson, R. Mathew, Y. Yu, and M. Edén, J. Magn. Re- son., 251, 52–56 (2015). DOI: 10.1016/j.jmr.2014.12.002

PAPER VII: Multicolor Fluorescent Labeling of Cellulose Nanoﬁbrils by Click Chemistry. J. R. G. Navarro, G. Conzatti, Y. Yu, A. B. Fall, R. Mathew, M. Edén, and L. Bergström Biomacromolecules, 16, 1293–1300 (2015). DOI: 10.1021/acs.biomac.5b00083

PAPER VIII: Proton Environments in the Calcium Phosphate Layer Grown from Mesoporous Bioactive Glasses in Simulated Body Fluid: Insights from Solid-State NMR. R. Mathew, C. Turdean-Ionescu, Y.Yu, B. Stevensson, I. Izquierdo- Barba, A. García, Daniel Arcos, M. Vallet-Regí, and M. Edén, J. Phys. Chem. C, 121, 13223-13238 (2017). DOI: 10.1021/acs.jpcc.7b03469

PAPER IX: Structure–Composition Trends in Multicomponent Borosilicate- Based Glasses Deduced from Molecular Dynamics Simula- tions with Improved B–O and P–O Force Fields. B. Stevenson, Y. Yu, and M. Edén, Phys. Chem. Chem. Phys., 20, 8192–8209 (2018). DOI: 10.1039/C7CP08593A Contents

1 Introduction to Glasses 1 1.1 What Are Glasses? ...... 2 1.2 Structural Views of Oxide-Based Glasses ...... 2 1.2.1 The Short-Range Structure ...... 3 1.2.2 Spatial Arrangements of the Building Units ...... 9

2 Bioactive Glasses 13 2.1 What Are Bioactive Glasses? ...... 13 2.2 The Origin of In Vitro Bioactivity ...... 14 2.2.1 Water–Silicate Glass Interaction ...... 14 2.2.2 Apatite Formation at BG surfaces ...... 16 2.2.3 Hench Mechanism ...... 18 2.3 Assessing the In Vitro Bioactivity ...... 18 2.4 Predicting the In Vitro Bioactivity of Phosphosilicate Glasses From Their Compositions ...... 20 2.5 Other Types of Bioactive Glasses ...... 21 2.5.1 Introducing New Glass Components ...... 21 2.5.2 Modiﬁcations In Microstructures ...... 22

3 In Vitro Bioactivity of Phosphosilicate Glasses—Summary of Pa- pers I and II 23

4 Application of Solid-State Nuclear Magnetic Resonance (NMR) Spec- troscopy in Understanding Glass Structures 27 4.1 Basic NMR Concepts ...... 27 4.2 Internal Spin Interactions ...... 33 4.2.1 Chemical Shift Interaction ...... 33 4.2.2 Direct Dipole–Dipole Coupling ...... 36 4.2.3 Electric Quadrupole Coupling ...... 39 4.3 NMR Techniques ...... 42 4.3.1 Spin-Echo and Spin Lock ...... 42 4.3.2 Recoupling of Homonuclear Dipolar Interactions . . . 43 4.3.3 Recoupling of Heteronuclear Dipolar Couplings . . . 44 4.3.4 Multiple-Quantum MAS ...... 45

5 Structures of Bioactive Borophosphosilicate Glasses—Summary of Papers III, IV, and V 47 5.1 A Brief Summary of Borosilicate Glass Structures ...... 47 5.2 Short-Range Structure of Borophosphosilicate Glasses (Paper III)...... 49 5.3 Medium-Range Structure of Borophosphosilicate Glasses (Paper IV)...... 51 5.4 Abundant B[4] O B[4] Linkages in Borosilicate Glasses (Paper V)...... 52

6 Sammanfattning 57

7 Acknowledgements 61

References 63 Abbreviations

2QF Double Quantum Filter BO Bridging Oxygen BPS Borophosphosilicate BS Borosilicate CFS Cation Field Strength CPMG Carr-Purcell-Meiboom-Gill CSA Chemical Shift Anisotropy DHMQC Dipolar-based Heteronuclear Multiple Quantum Correlation FTIR Fourier-transform Infrared Spectroscopy HA Hydroxyapatite HCA Hydroxy-Carbonate Apatite MAS Magic Angle Spinning MD Molecular Dynamics NBO Non-Bridging Oxygen NMR Nuclear Magnetic Resonance PXRD Powder X-ray Diffraction REAPDOR Ratational Echo Adiabatic DOuble Resonance REDOR Rotational Echo DOuble Resonance SEM Scanning Electron Microscopy

1. Introduction to Glasses

Development of glasses is intimately connected with human history. Long before owning the ability to manufacture glasses, naturally occurring ones such as obsidians1 formed by fast cooling of volcanic lava, were used to make tools with sharp edges. It was later discovered in Egypt, probably by sheer luck, that when sand was burnt together with sea salts and animal bones shiny particles formed, which are nowadays known as soda-lime silicate glasses and widely used for windows. In the middle ages, with more advanced technologies for fabricating glasses, people started to pursue their aesthetic aspects, as illustrated by the magniﬁcent stained glasses in St. Vitus Cathedral Prague (see Figure 1.1).

Figure 1.1: Glass windows in St. Vitus Cathedral, Prague (photographed by the author)

Advances in the glass industry are stimulated by in-depth understanding of glass chemistry/physics and inventions of new glass manufacturing technologies. For instance, window glasses were initially made by the crown method, where glass melts were ﬂattened by centrifugation, but that process led to uneven thicknesses of glass plates. By introducing the novel ﬂoat pro-

朱 cess, glasses were manufactured on a bath of molten tin under reducing atmo- sphere, and the ﬂatness was signiﬁcantly improved. More advanced technologies include lithography,2 which was used to “draw” desired patterns on the glass substrates, and 3D-printing of bioactive glass scaffolds that is especially promising for drug delivery applications.3

1.1 What Are Glasses?

As discussed by E. D. Zanotto and J. C. Mauro,4 “Glass is a non-equilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent super-cooled liquids (SCL), and they spontaneously relax toward the SCL state.”, glass, in a broad view, can be any materials that exhibit glass transition behaviors. Provided that the cooling rate is faster than the rate of structural reorganization, most materials can be trapped in a glassy state regardless of bonding nature. Many of the research interests nowadays are how to fight against crystallization,5 rather than showing a new glass-forming system. Defining a glass transition temperature usually involves some technicali- ties, such as using viscosity of a glass melt. Here, a more qualitative picture is provided instead of the strict definition. When a glass melt is cooled, its enthalpy/volume decreases with the temperature, as displayed in Figure 1.2. If the cooling rate is low and the glass melt has enough time to reorganize itself, it crystallizes with a sudden drop in the enthalpy/volume. However, if the cooling rate is considerably higher, there is not sufficient time for the melt to reorganize, and it ends up freezing itself in the preceding state. The ideal linear enthalpy/volume–temperature correlation is violated, and the decrease in the enthalpy per temperature unit diminishes resulting in more energies preserved in the glasses. In the present thesis, we use the term “glasses” interchangeably with “oxide- based glasses”, whose backbone consists of covalently bonded networks with O as the sole anion species. Oxide-based glasses include the most common glasses such as screens for electronic gadgets, window glasses, and optical fibers.

1.2 Structural Views of Oxide-Based Glasses

Glasses are disordered solids that are devoid of the long-range structural ordering and the glass structure is usually classiﬁed as the short-range (. 0.3 nm) 6 and the medium-range (. 1 nm) structures. Certain glasses may exhibit structural features at longer length-scales, but they are beyond the scope of the cur-

朲 Figure 1.2: The change of the enthalpy/volume of the glass against temperatures. Tm is the melting temperature, whereas Tg,1 and Tg,2 are the glass transition temperatures for the two glasses with rapid and slow cooling rates, respectively. The glass transformation region is indicated by the gray-shaded ellipse. rent thesis. For instance, phase separations emerge in some modiﬁer-poor and silicate-rich compositional regions in borosilicate glasses7, 8 and “archipelago- like” arrangements appear in the silicate glasses, where connected silicate tetrahedra constitute the islands and metal ions are waters around them.9

1.2.1 The Short-Range Structure In 1932, Zachariasen10 published a paper on the atomic arrangements of oxide glasses and which metal-oxide systems that may form glasses. His initial attempt was largely limited by the fact that powder X-ray diffraction (PXRD) was the main characterizing method. In his continuous random network (CRN) model, which was based on the then-well-known silicate/phosphate/borate glass- forming systems, glasses were described as solids that lacked long-range structural order, which was consistent with the absence of sharp Bragg peaks in the PXRD patterns. Another argument was that both crystalline compounds and the corresponding glasses shared the same basic building blocks, and it was rooted in their very similar mechanical properties and thus the bond energies. Zachariasen claimed that although the basic building units of crystals

朳 and glasses comprised the same number/type of elements, those in glasses exhibited variations in bond angles and bond lengths.

The Basic Building Units. SiO2 glass possesses a three-dimension structure constituted by inter-connecting Si tetrahedra (SiO4) through O atoms on the vertex. Si atom is a network former, which constitutes the glass skeleton, and the oxygen atom connecting two tetrahedra is referred to as a bridging oxygen (BO). In the soda-silicate glasses, the network modiﬁer Na cleaves the Si O Si bond, which forms two non-bridging oxygen (NBO) atoms, each with one negative charge. Such a reaction can be described by

– + Si O Si + Na2O 2 Si O Na . (1.1) BO NBO Network formers are usually cations with large cation ﬁeld strength (CFS) values,

2 CFS j = z j/R j , (1.2) where z j and R j are the valence and the radius of the cation j, respectively. Network modifiers are electropositive metal ions associated with much lower CFS values than the network formers . However, such a classification is rather arbitrary, and in reality, there are no strict boundaries between the network formers and the network modifiers.6, 11–13 For instance, Mg2+ can act in both roles. Generally speaking, the majority of Mg2+ ions balance the charge of NBO ions, and the remaining is incorporated into the glass network as MgO4 units.12 On introducing network modifiers into a silicate glass, the silicate network 4 3 becomes less polymerized. The primary silicate units undergo QSi → QSi → 2 1 0 n QSi → QSi → QSi transformations, where QF denotes the structural unit FO4 with n BO ions. The dominating motifs alter from a 3D structure to a planar one and subsequently to chains/rings and dimers of lower dimensionality, which finally disintegrates into isolated Si tetrahedra. Note that in the glass systems discussed in the current thesis, only four-coordinated Si atoms exist. However, five-coordinated Si atoms can be found in glasses prepared under extreme conditions,14 and six-coordinated silicate units coexist with other network formers with even higher CFS.15 Unlike crystalline silicates which are n often dominated by one specific QSi unit, silicate glasses always exhibit a dis- n 16–20 tribution of QSi units due to the following equilibrium,

n n+1 n−1 QSi QSi + QSi . (1.3) The equilibrium is shifted to the right side when the amount and CFS value of

朴 6, 16–20 n the modiﬁer increase. The relative fractions of QSi units may be deter- n mined experimentally. The QF notation can be extended to phosphate glasses, 0 1 where QP units denote the orthophosphate groups, and QP units are the PO4 units with 1 BO which can connect to either another P atom or other network formers, such as Si and B.

Figure 1.3: The B, Si, and P structural units of relevance to the present thesis 0 are listed. Phosphate atoms exist mainly as orthophosphate (QP) groups, and a 1 minor portion is QP. Both BO3 and silicate units can have up to 3 NBO ions. Since the four-coordinated B has one negative charge, having another NBO ion in the ﬁrst coordination sphere is not very likely, although BO4 unit with NBO has been observed in molecular dynamics simulations (see Refs21, 22 and Paper VI).

Although additions of metal cations in SiO2/P2O5 glasses depolymerize the glass networks, this is not the case for vitreous B2O3, where instead the transformation B[3] → B[4] occurs,23–29

BO3 + NBO BO4. (1.4) This unusual behavior is termed the “B anomaly”—viz., the addition of metal cation increases the polymerization degree of the glass network, rather than reducing it. A further increase in the cation content reduces the relative fraction [3] of BO4 and leads to the formation of B (nNBO) units with n number of NBO ions.26, 27 The B/Si/P structural units that are relevant for the present thesis are shown in Figure 1.3. They can also be visualized in the context of glass fragments as shown in Figure 1.4, in which displays two fragments of borophosphosilicate

朵 Figure 1.4: Two fragments extracted from the molecular dynamic simulations of borophosphosilicate glasses with compositions of 24.1Na2O–23.3CaO–34.0SiO2–14.6B2O3–4.0P2O5 and 24.1Na2O–23.3CaO–24.3SiO2–24.3B2O3–4.0P2O5, respectively. Cations are not shown.(Paper IV, reproduced with permission from American Chemical Society.) 朶 (BPS) glasses obtained by molecular dynamics (MD) simulations. The frag- 2 3 4 ments consist of three types of silicate units, QSi, QSi, and QSi, and two kinds 0 1 [4] of phosphate units, QP and QP, with the latter bonding to B unit through a BO atom. The borate units, BO3 and BO4, and all three possible linkages— B[3] O B[3],B[3] O B[4], and B[4] O B[4]—are observed in the MD simulation.

The Network Polymerization Degree. Two approaches can provide insights into the glass network polymerization degrees. The ﬁrst one is an “average approach” that takes all the network formers as a whole. Assume a glass with composition

(nM1 M1 nM2 M2 ···)nF1 F1 nF2 F2 ···nOO, (1.5) where {F1, F2, ···} and {M1, M2, ···} are the network formers and modiﬁers, respectively, and nE is the atomic fraction of element E. Each network former

Fn is associated with a coordination number ZFn , and the average coordination number Z over the Fn ensemble is the weighted mean of {ZF1 , ZF2 , ···}. The average number of O over all network formers is n r = O . (1.6) nF1 + nF2 + ··· The average numbers of BO and NBO atoms are,

NNBO = 2r − Z, (1.7) and NBO = 2(Z − r). (1.8) The second approach treats each network former separately and calculate its associated numbers of BO atoms and NBO ions, which is referred to as the split network approach.30, 31 The glass composition can be organized into

(n M n M ···)n F O n F O ··· , (1.9) M1 1 M2 2 F1 1 rF1 F2 2 rF2 where O is distributed among the various network formers Fi. If all rFi = 1 F ZFi − 2 NBO are known, except for rF1 , rF1 can be derived by

r = n−1(n − n r ), (1.10) F1 F1 O ∑ Fi Fi i=2,3,··· with

F1 NNBO = 2rF1 − ZF1 , (1.11)

朷 and F1 NBO = 2(ZF1 − rF1 ). (1.12) F NBO denotes the average number of BO atoms per network former F and is called the average network connectivity. Note that since the average network connectivity is derived from glass compositions, it is a theoretical value, which contrast its counterpart obtained from experiments. For glasses with a single network former, the two approaches are equivalent. For instance, the set of pa- F F rameters {rF , NNBO, NBO} for SiO2 and the sodium metasilicate glass Na2SiO3 are {2, 0, 4} and {3, 2, 2}, respectively. For glasses that contains more than one network former, the two approaches distinct predictions, and the difference grows with the increasing discrepancies between the NBO-afﬁnities of the network formers. One example is to employ the split network approach to understand the glass structure of phosphosilicate bioactive glasses.30 “45S5 Bioglassr” is the most well-known bioactive glass (BG) that has been in clinic use for decades,32, 33 with a molar composition of 24.6Na2O–26.7CaO–46.1SiO2–2.6P2O5. Experimental studies suggested that in the 45S5 structure, P exists predominantly as orthophosphate 0 34–39 1 1 groups (QP), while the remaining QP (its relative population xP amounts 39–41 1 Si 39 to ≈ 0.05) form Si O P bonds, with xP increasing with growing NBO. 2 Silicate units are dominated by the chains/rings motifs (QSi) with minor frac- 1 3 tions of QSi and QSi units. The relative fragmented glass networks and a dom- 0 2+ inating fraction of QP groups ensure that phosphate and Ca ions are readily released and facilitate the formation of hydroxyapatite (HA). P Assuming that P exists solely as orthophosphate groups, i.e., NBO = 0, the average silicate network connectivity can be calculated using equations 1.10 and 1.12,

Si nO − 4nP NBO = 2(4 − ) (1.13a) nSi x(NaO ) + x(CaO) + 2x(SiO ) − 3x(P O ) = 8 − 2 2 2 2 5 , (1.13b) x(SiO2) where nE denotes the atomic fraction of element E, and x(M) denotes the molar Si fraction of oxide M. Equation 1.13 provides an estimate NBO of 2.11 and is consistent with the experiment-derived results.30, 33, 34 A rational approach to Si design the bioactive phosphosilicate glasses is to separately vary the NBO and the (ortho)phosphate content separately, as illustrated in Refs30, 39 as well as in Paper I. The split network approach can be applied to bioactive BPS glasses, whose short- and medium-range structures were extensively explored in Papers III

朸 0 and IV. In the bioactive BPS glasses, P exists also mainly as QP Papers III, which resembles the role of P in the phosphosilicate glasses and ensures the readily releasing properties. To the ﬁrst-order approximation, the BPS P glass network can be split into a phosphate sub-network with NBO = 0 and a borosilicate sub-network (see Chapter 5). However, in a multi-component F glass with several network formers, the task of obtaining NBO for each former is formidable. A way to obtain the NBO distributions is to invoke the MD simulations.42, 43

1.2.2 Spatial Arrangements of the Building Units Medium-range glass structures are the consequences of set of rules for arrang- ing basic structural units such as SiO4, PO4, BO3, and BO4 that is similar to assembling Legor bricks. Assuming that bricks with the same shape but various colors are available, there are several scenarios to assemble the bricks: (i) picking bricks randomly and assembling them together; (ii) following the same procedures as in scenario (i) but avoiding putting the bricks with two specific colors—Ca and Cb—adjacent to each other; (iii) first making small units which contains a few bricks using the same formula and linking them together; (vi) repeating the same procedures as in scenario (iii), but excluding the case where the linking bricks of the adjacent units are the two specific colors, Ca and Cb. Various rules such as random assembly, avoiding bricks with colors of Ca and Cb connecting to each other, as well as making identical units first, render the final products with distinct appearances. The CRN model from Zachariasen suggested a totally random mixing of the basic units.10 However, later studies suggested that glasses usually exhibited a certain ordering in the medium range,44 in terms of preferential linking of certain polyhedra6, 45 and the formation of rings motifs46–51 and superstructural units.23, 24, 52 It is still interesting to explore that to what extent the structural orderings are preserved in glass structures. Note that due to the limitations of current characterization methods, some motifs cannot be unambiguously resolved, and their existence is only supported by the circumstantial evidences, such as fitting experimental outputs with hypercritical models or using the ‘ad hoc” way to compare with crystalline compounds(1).

Preferential Connection of Polyhedra. Although arrangements of basic structural units tend to be randomized in glasses, some types of linkages are inevitably favored compared with the statistic model. A typical example is the [4] [4] – direct Al O Al linkages. Since each [AlO4] unit is associated with

(1)The responses from the glass are sometimes signiﬁcantly broader, which make direct com- parisons less reliable

朹 one negative charge, their direct connections are energetically disfavored due to accumulations of negative charges locally, but its existence was proven by 17O nuclear magnetic resonances.45 An equivalent question—the direct B[4] O B[4] linkage in the Na/Ca borosilicate glasses—was addressed in Pa- per V. However, such a question is more controversial than the aluminum case. On one hand, such direct linkages are usually assumed to be absent,6, 28, 53–55 especially for borosilicate glasses with monovalent modiﬁers such as Na+; on the other hand, since the superstructural units that contain direct B[4] O B[4] linkages are assumed to exist in borate glasses,23, 24, 52 the very idea is applied to borosilicate glasses by some researchers27, 56–58 but without providing convincing experimental evidences. On the contrary, some linkages are favored due to opposite charges associated with network formers. For instance, if all O atoms are BO, the formal charges on the central P and B atoms are −1 and +1 for PO4 and BO4 units, respectively,and their linkages are favored. Such bondings are abundant in 59–61 borophosphate glasses, albeit a small portion of PO4 units inevitably bond 62 to BO3 units. For the BPS glasses in Paper IV, the MD simulations revealed that direct linkages of PO4 and BO3 were minimal, except for the compositions which were rich in B.

The Ring Motifs. Ring structures are commonly encountered in the sili- (1) cate/borate glasses. SiO2 glasses consist primarily of 5–8 member rings 46, 47 with 6 member ring motif being the most abundant. Unlike vitreous SiO2 which exhibits a ring-size distribution, vitreous B2O3 is dominated by a well- 48, 49 ◦ deﬁned structure—the boroxol ring with ∠B O B of 120 and the B O length of 1.365 Å. The relative content of B in boroxol rings was estimated to be 0.8048 and 0.70–0.73.49–51

Superstructural Unit. A superstructural unit, in my opinion, is a fancy term that is likely intended to convey the idea of “structural hierarchies” or “structure of the basic structure”. In the context of borate glasses,52 superstructural units are ring/connected-ring motifs that are composed of basic BO3 and BO4 structural units, and many superstructural units occur in crystalline borate compounds.63–65 One can ﬁnd a thorough list of various superstructural units in Wright’s review,52 such as triborate, pentaborate, and diborate groups. Superstructural units can be also viewed as rings, and the reasons why it is separated from the discussion of ring motifs are that: (i) they are well-ordered and usually expand in a large space that challenges the common understanding of glass structure; (ii) their existence is not supported by sound experimental

(1) The ring size refers to the minimum number of SiO4 units forming the ring.

朱朰 proofs.23, 24, 66 Wright invoked the term “stabilization energy” to support the existences of superstructural units,52 but as he pointed out himself that such stabilization effects has hitherto not been proved by theoretical calculations. Raman spectroscopy remains as the primary method to identify the superstructural units,66 but since their Raman bands are broad and greatly enhanced,44 both the assignment and the quantiﬁcation of such units are problematic.

朱朱朱朲 2. Bioactive Glasses

2.1 What Are Bioactive Glasses?

A biomaterial exhibits in vivo bioactivity—viz., it can “trigger the biological response from the body and induce the bonding between the living tissue (usually bone) and the material”.67 Bioactive glass (BG) is the intersection of biomaterials and glasses, which has several intrinsic favorable glass properties, such as readily varied compositions that make it feasible to incorporate other elements (see Section 2.5) and being shapable into various forms such as fibers and scaffolds. However, at the same time, the drawbacks of glass also manifest themselves in BGs such as brittleness and a susceptibility to crystallization.13, 33 The research of bioactive glasses was initiated by Hench and his colleagues at the University of Florida. He happened to meet an Army colonel during a bus trip, who asked him whether he could develop a material for repairing bone fractures of wounded soldiers.68 Implant materials used at the time were mainly “inert”, such as metals and polymers, that lead to scar tissue formed around the implant. The physical separations from the host tissues resulted in failures of the implants. One of the fruits of Hench’s pioneering research was a soda-lime-phosphosilicate bioactive glass, the “45S5 Bioglassr”, with 32, 69 a molar composition of 24.6Na2O–26.7CaO–46.1SiO2–2.6P2O5. Distinct to other inert implants, the 45S5 Bioglass dissolves partially in body fluids and the dissolution products are “essential for metabolic processes, formation and calcification of bone tissue”.70 A layer of hydroxy-carbonate apatite (HCA) forms between the glass surface and the surrounding tissues, which mimics the composition of bone mineral.32 HCA conforms to the calcium hydroxya- 3– patite (“HA”) structure (Ca5(PO4)3OH) with the trivalent PO4 ions partially 2– 2– 71 replaced by the divalent CO3 and HPO4 ions. Note that we use the terms “HCA”, “HA”, and “apatite” interchangeably in the current thesis. Assessments of the in vivo bioactivity usually involve animal testing, which is costly and may bring ethical concerns. As a substituted screening approach for the resource-consuming in vivo bioactivity testing, an in vitro equivalent using (buffered) water was proposed, which was later evolved into the simulated body fluid (SBF) solution.72, 73 The SBF solution mimics the inorganic compo-

朱朳 sition of blood plasma and is buffered by tris(hydroxymethyl)aminomethane (TRIS). After their immersion in the SBF solution for a sufﬁcient period, a layer of HCA is generated at the BG surfaces, which resembles its counterpart formed under the in vivo conditions,32, 33 as well as the biogenic bone min- erals.71 The ability to form a HCA layer without biological surroundings is referred to as the in vitro bioactivity or the in vitro apatite formation. The mechanism of HA formation will be discussed in Section 2.2. Despite that the usage of SBF is accepted by the BG community,33, 72–77 the direct relationship between the in vivo and in vitro bioactivities was ques- tioned by Bohner and Lemaitre.78 As summarized by Zadpoor,77 although a general correlation between the two bioactivities may be questionable, they do correlate well for silicate-based bioactive glasses, as those studied in Papers I and II. Morphologies of apatite formed at BG surfaces and those from supersaturated P/Ca-containing solutions are similar, as well as their formation kinetics, which is characterized by a sigmoidal growth model79–82 (see Section 2.2.2). The apatite may form through an amorphous calcium phosphate (ACP) pre- cursors, which subsequently crystallizes into (nano)crystalline particles with crystalline cores covered by amorphous surface layers83–85 (see Section 2.2.2).

2.2 The Origin of In Vitro Bioactivity

The formation of HCA at BG surfaces usually involves two major steps: (i) the glass dissolution and repolymerization; (ii) the growth of ACP followed by its transformation into the crystalline HCA.32, 33

2.2.1 Water–Silicate Glass Interaction

Several coupled reactions are responsible for the water–glass interactions, in- cluding the glass hydration, the hydrolysis of the covalent glass network, and + + 86 the exchanges of network modiﬁers with H or H3O . The exact reaction mechanism may depend on the solution pH values: when the pH value is larger than 9, the hydrolysis of glass network dominates and silicate glasses dissolve congruently into the solution,87, 88 whereas in the lower pH solution which is relevant for assessing the in vitro bioactivity, glasses undergo a selective dissolution of metal cations via the exchange processes (a.k.a. selective leaching), leaving a layer of silica gel at the glass surfaces.

Hydration and Hydrolysis. Hydration occurs when water molecules penetrate into the glass network, whereas hydrolysis is the cleavage of covalently-

朱朴 bonded network formers, as shown by the following schematic reaction,29, 86

Si O Si + H2O 2 Si OH. (2.1)

A hydrated network former in the form of Si(OH)3 may be removed by the nucleophilic attacks of OH– groups via29, 86

– – Si O Si(OH)3 + OH Si O + Si(OH)4. (2.2)

Silicate glasses are able to heal themselves by repolymerizing silanol groups and forming Si O Si bonds, during which process released water molecules may penetrate further into the glass structure:89

2 Si OH Si O Si + H2O. (2.3)

For glasses containing boron, the B speciation comprises BO3 and BO4 units. Since BO3 units are planar, the central boron is readily accessible to a nucleophilic attack by OH– ions; hence, any bonds involving 3-coordinated boron atoms are easily hydrolyzed. A neutral Si O Si bond is more stable than Si O B[4] with negative charges; see the caption of Figure 2.1.

Ion Exchange Silicate glasses with large amounts of network modiﬁers are susceptible to water attack through ion exchange processes:

– + + – Si O Na + H2O Si OH + Na (aq) + OH (aq). (2.4) At near neutral pH conditions, such a process is favorable compared to network hydrolysis,86 and it leads to an increase of the solution pH value,32, 33 which may trigger the formation of ACP and HCA. This explains why bioactive phosphosilicate glasses are usually rich in modifiers, which are mirrored in their relative confined compositional region, with 0.35 ≤ x(SiO2) ≤ 0.60 and x(P2O5) ≤ 0.06. Glasses that involve several network modifiers, sometimes exhibit a non- linear behavior when varying the relative modifier amounts which is called the mixed cation effect,92, 93 where a minimum of dissolution rate may appear. One may expect that relative Na/Ca ratios have bearings on the dissolution behaviors of BGs, but to a (much) lesser extent.

2.2.2 Apatite Formation at BG surfaces Due to their relevance to bone mineral,71 the structure and formation kinetics of apatite have been intensively studied by spontaneously precipitating apatite from a supersaturated Ca/P containing solution. It is generally accepted that

朱朵 Figure 2.1: Relative propensities for bond cleavage by a water molecule: Si O Si>Si O B[4]>Si O B[3] linkages.29, 90, 91 Any bond containing BO3 units are readily attacked by the water molecular due to its planar geometry. The formal charge of the central O atom of the Si O B[4] bond is –0.25, which makes it more vulnerable to the electrophilic attack than the Si O Si bond.

HCA is formed via a precursor phase of ACP, which features a composition 2– similar to Ca3(PO4)2 with some minor components such as HPO4 ions and water molecules.82, 83, 85, 94 The final product HCA is characterized by a crystalline core with Ca2+ and/or OH– deficiencies,95 covered by an amorphous 2– 83–85 surface layer which is HPO4 /H2O-rich. The exact mechanism of ACP→HCA transformation does not reach a con- sensus, where both the surface-meditated growth82, 96–99 and the solid–solid transformations100–102 have been identified. Although their transformation mechanism is not well understood, the kinetic aspects of HCA formation are more accepted to follow a sigmoidal growth model:79–82 ACP forms during the “induction period”, whereas HCA forms during the “proliferation period”, which are followed by the improvement of the structural ordering of HCA in the “maturation period”. Our semi-qualitative FTIR investigations of a phosphosilicate glass in conjunction with the concentration measurements revealed a similar growth model for apatite formed at BG surfaces (see Figure 2 and 3 of Paper II). Our study also indicated a simultaneous growth of ACP and HA, which has hitherto not been pointed out in the BG community, albeit the sup-

朱朶 porting data has been just buried in the literature. Both aspects are discussed together with the Hench mechanism32 (HM) (see the left panel of Figure 2.2) in Section 2.2.3.

Figure 2.2: Schematic illustration of the Hench mechanism32 for HCA formation from a melt-prepared Na–(Ca)–Si–O–(P) glass exposed to SBF; the five HM stages are identified with the induction, proliferation, and maturation stages associated with sigmoidal growth (arrows; left panel). The first three HM steps involve (1) exchange of Na+/Ca2+ cations with protons from the solution, and (2) hydrolysis of Si–O–Si bonds, together leading to a high abundance of silanol (SiOH) surface groups, a portion of which (3) form Si–O–Si linkages by water removal. As depicted in the right panel, the HM stages (1)–(3) together produce a silica-gel layer, which comprises SiOH groups and water, but is nearly devoid of Na+/Ca2+ species. Next follows (4) a heterogenous nucleation of ACP, which then (5) crystallizes into HCA. The two last HM steps proceeds in parallel, with co-existing ACP/HCA components of the CaP layer (bottom, right), where HCA crystallizes from the interior of the ACP particles.101, 102 ( Reprinted from Paper II with permission from MDPI))

32 In the original HM, the vague term “amorphous CaO–P2O5-rich film” was used to represent the precursor of the crystalline HCA, and such a term is widely used. In part of the BG community, “amorphous CaO–P2O5-rich film” is identified as ACP103–110 due to their very similar structural features. In the current thesis, we use the explicit term ACP instead of the implicit one,

朱朷 “amorphous CaO–P2O5-rich ﬁlm”.

2.2.3 Hench Mechanism The original ﬁve-step Hench Mechanism (HM) that describes the apatite formation at the BG surface is as followings:32

(1) Rapid exchanges of Na+ or Ca2+ cations at the glass surface with H+ + or H3O ions from the solution (as shown by reaction 2.4); (2) Cleavage of Si O Si bonds and formation of silanol groups at glass surfaces (see reactions 2.1 and 2.3);

(3) Repolymerization of silanol groups that generates a layer of a highly polymerized (NBO-poor) silica gel;

2+ 3− (4) Diffusing of Ca and PO4 ions through the silica gel layer and forming an amorphous CaO P2O5 rich layer, which continues to grow by 2+ 3− incorporating Ca and PO4 ions from solution; – 2− (5) Crystallization of the amorphous layer by incorporating OH and CO3 ions from the solution and formation of crystalline HCA;

The as-proposed HM is largely consistent with later studies though a few studies showed that some of its details are not fully correct.108, 111, 112 When putting HM into the context of a sigmoidal apatite growth model (see Figure 2.2), it is clear that the first three steps of HM belong to the induction period, as well as formation of first ACP embryos, whereas the growth of those embryos and their further transformations into HCA happen primarily in the proliferation and maturation periods. The simultaneous growth of ACP and HCA discussed in Section 2.2.2 and in Paper II led to a small modification of the HM where step (4) and step (5) are merged due to their simultaneous occurrences, as illustrated in Figure 2.2 (see Chapter 3 for details).

2.3 Assessing the In Vitro Bioactivity

The in vitro bioactivity, i.e., the extent of apatite formation can be characterized by either the onset of the HCA crystallization or the amount of HCA formed. Powder X-ray diffraction (PXRD)38, 113–115 can address both aspects, where the quantiﬁcation of ACP and HCA is achieved by Rietveld-based methods.116, 117 31P magic angle spinning (MAS) NMR,114, 116, 118–120 on the other hand, can be used to obtain the relative amounts of ACP and HA, due to their

朱朸 different degrees of structural ordering and thus the widths of the corresponding NMR peaks. The challenging part is that the signals from ACP and HA appear at very similar positions in the NMR spectrum and a careful deconvolution is usually needed. Both HCA and ACP also appear at similar positions in the Fourier-transform infrared (FTIR) spectra of SBF-treated BG.38, 111, 113–115, 121–126 The onset of HA can be identified by the splitting in the P–O bending vibrations region around ≈600 and ≈560 cm−1, whereas ACP showing a featureless peak at ≈ 580 cm−1. Due to the broadness of IR bands and relative similar spectral positions of ACP and HCA, the quantification of HCA is always affected by ACP, with the interference diminishing as the SBF-immersion period increases. Scanning electron microscopy (SEM)76, 115, 122–124, 127–129 can be used to identify the onset of HA, but EDX is always required to identify whether the crystalline phase are formed by other compounds such as NaCl, which is abundant in the SBF solution.130 SEM can measure the thickness of the “CaO P2O5 film”, which is largely restricted to bulk glass pieces and the nature of the surface layer cannot be identified by SEM alone. Except for a few exceptions,116, 117, 120 nearly all of previous studies on apatite formation from BGs are qualitative rather than quantitative, which reflects a general research interest of the induction period. In Papers I and II, we quantified the apatite formation using FTIR with an internal reference compound K3Fe(CN)6, which featured a sharp C N band isolated from the FTIR bands stemming from the glass and the calcium phosphate. The usage of a reference compound allowed compensating variations in the thickness of mixture pellets.131 Although such a method itself provides an accurate quantification of the constant of phosphate anions in SBF-treated BGs, it does not alleviate the interferences from ACP. In Paper I, the apatite formation was evaluated after immersing BGs in SBF for 24 hours (h). As shown in the collection of IR spectra of Figure S2 in Paper I, similar degrees of splittings in the P–O bending vibration regions for all glasses giving a significant apatite formation. While the conclusions in Paper I could be affected by small amounts of ACP, those are expected to be (nearly) the same among the various glass compositions which should give insignificant bearings on the composition–bioactivity correlations. As shown in refs,116, 120 the relative amounts of ACP and HCA can be quantified by 31P MAS NMR for SBF-treated mesoporous bioactive glasses (MBGs), under the assumption that the release of P is nearly instantaneous from MBG featuring a high surface area, and that the amounts of P units preserved in glass matrixes have little bearings on the quantification procedures. However, it is not the case for melt-prepared BGs since PO4 units not leached from glass matrixes remain as a dominating component for the SBF testing of glasses when using

朱朹 a short SBF-immersing periods.

2.4 Predicting the In Vitro Bioactivity of Phosphosilicate Glasses From Their Compositions

The composition–bioactivity relationship can be investigated by systematically varying the glass composition.76, 113, 121, 127, 132, 133 A rational way is to first understand the glasses structures and use it to tie the glass composition and its associated bioactivities together. One can also resort to data-driven methods(1), which efficiently explore a large compositional space.122, 128 At a very early stage, composition–bioactivity studies were mainly performed on glasses with varying amounts of silicon yet low and nearly constant 132, 134 P content. Hench and his coworkers found that glasses with SiO2 content ≥ 60 mol% were not bioactive. Brink et al. proposed a surface activity index based on a large series of Na2O–K2O–MgO–CaO–B2O3–P2O5–SiO2 glasses, and they found that only glasses with SiO2 content ≤ 59 mol% were bioactive. The first attempt to use the glass structure as a linkage between the glass composition and its bioactivity was performed by Strnad,135 who correlated the BG bioactivity to a composition-derived average number of BO atoms of all network formers (NBO; see equation 1.12), a parameter equivalent to the Y 136 parameter proposed by Stevels. The NBO parameter can be derived by

nO NBO = 8 − 2 = Y, (2.5) nP + nSi where nE denotes the atomic fraction of element E. The deﬁnition of NBO is built on the assumption that BO atoms evenly distributed among two network formers—P and Si and it is inconsistent with later studies.34–39 In those stud- 2 3 ies, Si existed mainly as QSi and QSi structural units, and P was dominated by 0 0 QP units. Note that due to the dominating role of QP units with its fractional 0 population xP & 0.80, the orthophosphate content is approximately equal to 0 the P2O5 content, i.e., x(P2O5)xP ≈ x(P2O5) (see Section 1.2.1). An improved Si version NBO that accounts for the different afﬁnities of the different network formers F to bind to NBO ions (see equation 1.13 and the corresponding discussions) was proposed.30 It thereby provides predictions that was consistent with experimental 29Si MAS NMR results.30, 33, 34, 39 Si Since the development of NBO, it has been used to predict the the in vitro Si bioactivity. Although it is generally accepted that NBO and x(P2O5) affect the

(1)A more funky approach is to invoke machine learning such as the convolutional neural network, and solve the problem in a high-dimensional space (using the fractions of each component for instance).

朲朰 bioactivity of bioactive glasses13, 30, 33, 137 with the in vitro apatite formation 0 growing with an increasing P content (provided that P exists as QP groups and Si apatite indeed forms), the bearings of NBO are poorly understood. This is for instance reflected by two conflicting results:30, 137 where Hill predicted that Si Si the bioactivity to drop monotonically as NBO is increased, with an upper NBO limit of 2.4, above which no significant amount of apatite forms. In contrast, Si Edén predicted a non-monotonic NBO–bioactivity relationship, with consider- Si able apatite formation when NBO < 2.7. Our study in Paper I extends the current understanding of composition– Si bioactivity correlations by showing the complex influences of x(P2O5) and NBO on the in vitro bioactivity. Different from a commonly assumed decreasing Si 13, 33, 137 bioactivity with increasing NBO, Figure 3 in Paper I exhibited a range Si of NBO values that produced equally large amounts of apatite, with the range being expanded as the P content is increased. We also found a high P content also mitigated the negative influences of using (too) small glass particles for SBF testing. Our results suggest another approach for designing bioac- Si tive glasses by combining a (relative) high P content and a large NBO, while exploiting the beneficial effect of a lower crystallization tendency associated Si with large NBO.

2.5 Other Types of Bioactive Glasses

Since the emergence of the “45S5 Bioglassr”, the BG research ﬁeld have witnessed a boom in the development, where one main focus is to improve BG properties by introducing new glass components and modifying their microstructures.

2.5.1 Introducing New Glass Components A new glass component can be either a network modifier or a network former. The beneficial effects of a new glass network modifier are usually to promote the new bone formation70 or to improve glass processing abilities,13, 138, 139 whereas a new network former may alter dissolution behaviors of the base glass,3, 140–145 thus offering tools for tailoring its bioactivity. Due to their “anabolic effects in bone metabolism”,70 the leching of elements like Sr, Cu, or Co may participate in meditating the bone growth. Other modifiers, such as Zn which provides anti-inflammatory effects146 and Ag that can eliminate bacteria to a very high extent,147 offer a healthy environment for the new bone to grow. The 45S5 glass is known to have an unfavorable processing abilities, since it crystallizes during processing.13 The temperature

朲朱 difference between glass transition temperature and crystallization temperature is referred to as the processing window. Oxides like K2O and MgO are found to increase the processing window, such as in “13-93”138 and “ICIE16” glasses.139 Moreover, the design of “13-93” adopted a dual approach—not only introducing K2O and MgO, but also increasing the polymerization de- 138 Si gree of silicate networks. That glasses featuring high NBO usually have low bioactivity is commonly assumed.13, 33 However, we demonstrated in Paper Si III that a high P content made BGs with NBO up to 2.5–2.6 bioactive, which offered another approach for controlling BG crystallization yet without (too much) compromising the bioactivity. A partial substitution of Si by another network former, i.e., B, in some phosphosilicate glasses such as 45S532, 33 and “13-93”138 are promising for bone-grafting applications. B substitutions change dissolution behaviors of the base glasses29, 90 (see Section 2.2.1) and convert the glass more completely into HCA without leaving a Si-rich core.3, 140–145 The glass dissolution behaviors may be adjusted by varying the relative contents of Si and B.140–142 The doping of B may also promote angiogenesis3, 148 and RNA synthesis in ﬁbrob- last cells,70 which is beneﬁcial to bone growth. A more thorough description of the structural role B in the bioactive is presented in Chapter 5.

2.5.2 Modifications In Microstructures Another research thread in BG field is to modify their synthetic routes. Ini- tially, BG were mainly prepared by melt-quench methods, and finial glass products were either bulk glass pieces or glass powders. An obvious way to improve the in vitro bioactivity is to increase the specific surface areas, which is possible by using the sol–gel145, 149–151 and evaporation-induced self- assembly (EISA).107, 152, 153 Due to the homogeneous mixing at the atomic level is achieved in the gelation process, a low glass synthesizing temperature is required for sol–gel glasses/MBGs.33 With the above-mentioned approaches, BGs can be fabricated with compositions that would not be possible to be synthesized by the traditional melt-quench method. Low-temperature synthesis of BG not only provides a way to alter the in vitro bioactivity, but also makes it feasible to fabricate inorganic–organic hybrid materials, whose mechanical properties may be tailored.154 The other microstructure modification involves producing BG scaffolds. Such meso/macro-porous structures assist new bone growth and are promising for drug delivery applications.3, 155 The high porosity can be made with melt-prepared glasses using sacrificial templates composed of (foam) polymer particles156, 157 or ice crystals.158

朲朲 3. In Vitro Bioactivity of Phosphosilicate Glasses— Summary of Papers I and II

Si It is generally accepted that the average silicate network connectivity NBO and the phosphate content x(P2O5) affect the in vitro bioactivity of phosphosilicate glasses,30, 33, 137 but the details remain poorly understood. This is reflected by some conflicting predictions in the literature:30, 137 Hill predicted a monotonic Si decrease of the apatite formation for increasing NBO values and an upper limit of 2.4, above which the apatite formation became insignificant.137 In contrast, Edén suggested a non-monotonic dependence of the apatite formation against Si Si NBO with the condition NBO < 2.7 as being necessary for a non-negligible apatite formation.30 Most studies in the BG research field were qualitative and mainly focused on determining the onset of HCA crystallization rather than the amounts of HCA that formed. In Paper I, we presented a quantitative study Si of the apatite formation to understand the bearings of NBO and x(P2O5) on the composition–in vivo bioactivity correlations. A large series of glasses, with Si 2.0 . NBO . 2.9 and x(P2O5)={0.026, 0.040, 0.060} were prepared (see Table 3.1), which comprised both bioactive and non-bioactive glasses. The P content was found to primarily affect the apatite formation (provided Si that the apatite formation was not inhibited by an “unfavorable” NBO value of the glass), which was reflected by their nearly linear relationship (see Figure Si 7 in Paper I). At each P content, there was a range of NBO values, for which equally large amounts of HCA were formed; the range increased for growing P content (see Figure 3 in Paper I). The upper limits for a considerable Si Si apatite formation were NBO = 2.6 and NBO = 2.7 for glasses with 2.6 mol% and 4.0 mol% P2O5, suggesting a slightly higher upper limit as the P content of the glass was increased. Our main conclusion was that a higher P content Si expanded the NBO range associated with a near optimal apatite formation.

朲朳朲朴 a Table 3.1 Na2O CaO SiO2 P2O5 Glass Compositions Exposed to SBF Si label NBO x(Na2O) x(CaO) x(SiO2) x(P2O5) BG2.6(2.0) 2.00 0.252 0.274 0.448 0.026 BG2.6(2.1) 2.11 0.246 0.267 0.461 0.026 BG2.6(2.2) 2.20 0.241 0.261 0.472 0.026 BG2.6(2.3) 2.30 0.235 0.255 0.484 0.026 BG2.6(2.4) 2.40 0.228 0.248 0.498 0.026 BG2.6(2.5) 2.50 0.222 0.240 0.512 0.026 BG2.6(2.6) 2.60 0.214 0.233 0.527 0.026 BG2.6(2.7) 2.70 0.207 0.224 0.543 0.026

BG4.0(2.1) 2.10 0.254 0.275 0.431 0.040 BG4.0(2.2) 2.20 0.248 0.270 0.442 0.040 BG4.0(2.3) 2.30 0.243 0.263 0.454 0.040 BG4.0(2.4) 2.40 0.237 0.257 0.466 0.040 BG4.0(2.5) 2.50 0.230 0.250 0.480 0.040 BG4.0(2.6) 2.60 0.223 0.243 0.494 0.040 BG4.0(2.7) 2.70 0.216 0.235 0.509 0.040 BG4.0(2.9) 2.90 0.200 0.218 0.542 0.040

BG6.0(2.0) 2.00 0.269 0.291 0.380 0.060 BG6.0(2.1) 2.10 0.264 0.286 0.390 0.060 BG6.0(2.2) 2.20 0.259 0.281 0.400 0.060 BG6.0(2.3) 2.30 0.254 0.275 0.411 0.060 BG6.0(2.4) 2.40 0.248 0.270 0.422 0.060 BG6.0(2.5) 2.50 0.243 0.263 0.434 0.060 BG6.0(2.6) 2.60 0.236 0.257 0.447 0.060 a Si Si Nominal BGp(NBO) glass compositions, where p represents the P2O5 content (mol%) and NBO is the silicate network connectivity, whose precise values are listed in the second column. Note that all glasses feature the same x(Na2O)/x(CaO) molar ratio as “45S5 Bioglass”.32 These apatite-formation trends were corroborated by 31P MAS NMR results, Si which also indicated that the inhibited apatite growth for high NBO values was mainly due to an insufﬁcient glass dissolution. We also found that the P concentration, which exhibits a strong inverse correlation with the apatite formation, may be used as a convenient screening tool for the in vitro bioactivity before attempting more elaborate analytical techniques, such as FTIR and 31P MAS NMR. Si Besides challenging the commonly assumed high NBO–low apatite formation correlation, the composition–bioactivity relationships derived from Paper I signiﬁcantly facilitates the design of glasses with low crystallization ten- Si dency by combining a relative high NBO value (2.5–2.6) and P content (> 4 mol% P2O5).

In Paper II, we focused on the apatite formation process of a specific phosphosilicate glass, which was monitored by PXRD and FTIR for increasing SBF-exposure periods. The corresponding P/Ca concentrations and pH values were also measured (see Figure 2 and 3 of Paper II). The FTIR-derived apatite formation revealed that HCA started to crystallize after immersing the glass in an SBF solution for 16 hours, and it continued to grow out to 72 hour, which was then followed by a slight improvement of the structural ordering of the HCA phase. The corresponding P concentration measurements revealed insignificant consumptions of P during both the induction and maturation periods, whereas the major consumption of P ocurred during the proliferation period. Overall, these results suggested that the formation process of apatite at a BG surface was consistent with a sigmoidal growth model, which is the widely established formation kinetics of apatite precipitated spontaneously from a supersaturated Ca/P-containing solution.80–82, 159 However, since most studies in the BG field are qualitative in their nature, this apatite formation behavior has hitherto remained unnoticed. Besides a sigmoidal growth model, we also identified that the growth of HCA and ACP were largely coincident, where both phases were found to grow within a 16–20 hour SBF-treatment, with the growth of ACP being sur- passed by the ACP→HCA transformation at the longer SBF-exposure periods. The coincident formation of ACP and HCA during the proliferation period agreed with the considerable P consumption observed during the same period. Our findings were also supported by results “buried” in the literature,103, 104, 111, 113, 160–162 albeit their implications were never pointed out. We also partially revised the currently prevailing “Hench mechanism”32 (see Section 2.2.3) that describes the in vitro apatite formation from BGs by merging its last two stages. Moreover, when viewing the Hench mechanism

朲朵 in the context of the sigmoidal growth model, its ﬁrst three steps may be in- terpreted as the “induction period”, which involves the glass dissolution and glass network repolymerization stages. Hence, those may be combined into a single step that represents all reactions occurring at the BG surface to facilitate the subsequent HCA formation. The last two HM steps (see Section 2.2.3) may be equated to the proliferation and maturation periods of the sigmoidal apatite growth model; these are merged into a single step, due to their largely simultaneous occurrences.

朲朶 4. Application of Solid-State Nuclear Magnetic Resonance (NMR) Spectroscopy in Understanding Glass Structures

Solid-State Nuclear Magnetic Resonance (NMR) is a technique that probes the local chemical environment of a nucleus, which is especially useful for understanding structures of disordered materials such as glasses.6, 163, 164 Due to the lack of long-range structural ordering, diffraction techniques based on the Bragg’s law such as powder X-ray diffraction (PXRD) cannot be easily applied. Pair distribution functions (PDF) derived from neutron/X-ray diffraction using synchrotron light sources can partially settle the problem,48, 165, 166 but as the number of glass components increases, the associated PDF becomes increasingly complex due to the overlaps of various responses. A full structural solution usually requires aids of some simulation techniques such as fittings to a hypothetical model or invoking the reverse Monte Carlo.36, 167 However, the element-selective NMR techniques make it possible to investigate the medium range arrangements of specific glass element(s) by using dipolar couplings which reflect their spatial intervals.

4.1 Basic NMR Concepts

A Classical Picture. In the classical picture, for a small particle with a magnetic moments ~µ, its magnetic energy associated with the surrounding magnetic ﬁeld ~B is168

Emag = −~µ ·~B, (4.1) where the magnetic moment relates to the angular momentum J~ by

~µ = γJ~, (4.2)

朲朷 where the coefﬁcient γ is the gyromagnetic ratio and its sign is determined by whether the two vectors, ~µ and J~, are parallel or anti-parallel(1). Both vectors ~B and J~ can be expanded using the {~ex, ~ey, ~ez} base vectors of a cartesian coordinate system,

~B = Bx~ex + By~ey + Bz~ez, (4.3) and

J~ = Jx~ex + Jy~ey + Jz~ez, (4.4) where {Bx, By, Bz} and {Jx, Jy, Jz} are the projections of ~B and J~ on each coordinate axis, respectively. In the following discussions, we simplify the case by only considering a magnetic ﬁeld along the z-axis in the laboratory frame (LAB)—i.e., Bx = By = 0 and ~B0 = B0~ez. The small particle acquires a torque ~τ and it changes the direction of its angular momentum J~ by dJ~ ~τ = = ~µ ×~B , (4.5) dt 0 which results in a rotation around the z-axis. Based on the geometry shown in Figure 4.1, the altering rate of its angular momentum(2) relates to its angular velocity ω by dJ = ωJsinθ, (4.6) dt where θ is the angle between J~ and the z-axis. Combining equations 4.5 and 4.6, one can derive that J ω = B = γB , (4.7) µ z 0 where the angular velocity of the small particle depends on the product of the magnetic ﬁeld strength it feels and its gyromagnetic ratio. Precession can be visualized via a spinning top which rotates along its rotational axis. Since the spinning top is also affected by gravity, its rotational axis is tilted from the normal direction of the horizontal plane where it rotates. Therefore, the rotational axis of the spinning top changes continuously while it spins and such a fashion of motion is referred to as the procession.

A Quantum Mechanics Picture. Spin is an intrinsic property of a nucleus, the same as the mass and the electric charge.168 However, “spin” is more subtle

(1)h¯ was omitted from the right side of the equation for simplicity (2)The right arrow over the vector was dropped to denotes its magnitude.

朲朸 Figure 4.1: Under the magnetic ﬁeld B~z, a small particle with magnetic moment ~µ feel the torque perpendicular to the plane determined by B~z and ~µ, which changes the direction of angular momentum J~ continuously. Note that ~µ and J~ are in the same direction or the opposite, which depends on the gyromagnetic ratio γ. This render the particle precessing along the Bz with angular velocity ω. During the interval ∆t, the angular momentum alters from J~ to J~0 and the corresponding variation amounts to Jωsinθ, where J refers to the magnitude of J~ and θ the angle between B~z and J~. The angular velocity which gives ω = γBz. than some other intrinsic properties, as it is hard to be imagined, although its existence was fully supported by experimental evidences.169 Spin is also a form of the angular momentum and one may draw an analogy between a spinning top and a spin, as both share the precessional motions, where the spin polarization axis of a spin rotates around the direction of the magnetic ﬁeld. In the quantum mechanics picture, the magnetic energy, i.e., the eigenval- ˆ ues of the Hamiltonian operator (Hˆmag) and magnetic moment ~µ have similar mathematical representations as those for a magnetized small objected de- ˆ scribed in the classical view. Hˆmag and ~µ are the quantum mechanical operators, which are denoted using a caret ( ˆ ). These quantum mechanical operators operate on the wavefunctions, which describe states of quantum systems. Equations 4.1 and 4.2 can be expressed as,168

ˆ Hˆmag = −~µ ·~B, (4.8)

朲朹 and

~µˆ = γ~Iˆ, (4.9) where ~Iˆ is the spin angular momentum vector operator. The spin angular momentum operator ~Iˆ is similar to angular momentum operator J~ˆ, and it can be expressed with {~ex,~ey,~ez} by ˆ ~I = Iˆxex + Iˆyey + Iˆzez, (4.10) ˆ where {Iˆx, Iˆy, Iˆz} are the projections on the x, y, and z-axis of~I, respectively.

Zeeman Interaction. If only a magnetic field along the z-direction of the laboratory frame is considered, i.e., Bx = By = 0 and ~B0 = B0~ez, a case relevant for the main magnetic field used in NMR spectrometers, the interaction between a spin and its surrounding magnetic field B0 is referred to as the Zeeman interaction. The Hamiltonian of the Zeeman interaction is derived by substituting equation 4.10 into equation 4.8168 ˆ HˆZ = −γ~I ·~B0 = −γIˆzB0 = ω0Iˆz, (4.11) where ω0 = −γB0 is referred to as the Larmor frequency. The Zeeman interaction Hamiltonian can be diagonalized by using the Zeeman basis set,

HˆZ |I,mi = EI,m |I,mi (4.12) where I and m (m = −I,−I + 1,...,I − 1,I) are the spin quantum number and the azimuthal quantum number, respectively. The energies EI,m are the eigen- values associated with the eigenstates |I,mi, the wavefunctions that describe spin systems. 1 1 13 29 31 A nuclide with spin quantum number I = 2 , such as H, C, Si, and P, 1 is termed spin- 2 , and its Zeeman basis of such a nucleus comprises two eigen- 1 1 1 1 states, |+ 2 ,+ 2 i and |+ 2 ,− 2 i, which are abbreviated as |αi and |βi. The 1 1 corresponding Zeeman interaction energies are + 2 ω0 and − 2 ω0, respectively. 1 Any nuclide with the spin quantum number > 2 is termed quadrupolar nu- 11 3 3 3 3 1 3 1 cleus. For B with I = 2 , four eigenstates—|+ 2 ,+ 2 i, |+ 2 ,+ 2 i, |+ 2 ,− 2 i, 3 3 |+ 2 ,− 2 i—constitute the Zeeman basis. A Macroscopic property of a spin system such as the “magnetization vector” is an ensemble average of expectation values of all spins in a sample,170

M~ z = h~µz, ji, (4.13) where h~µz, ji denotes the expectation value of the vector operator ~µz, j. When the magnetic ﬁeld is absent, the spin polarization directions are randomly

朳朰 distributed—viz., there is no net magnetization. However, with the magnetic ﬁeld, a net magnetization is generated, as may be visualized from Figure 4.2. Note that the population difference between the two energy levels |αi and |βi are exaggerated, which, in reality, amounts to around 1 over 105. Such a small population difference makes NMR an insensitive method relative to most other spectroscopic techniques.

Figure 4.2: An illustration of two energy levels—|αi and |βi—associated with 1 a spin- 2 in a magnetic ﬁeld along the z-direction of the laboratory frame. Note that the population difference is exaggerated. The net magnetization reﬂects a collective behavior of all spins.(Adapted with permission from Wiley.168)

Interaction with Radio Frequency (RF) Pulses. Another electromagnetic ﬁeld that interacts with a spin ensemble is generated by a radio-frequency (RF) pulse, which oscillates at the spectrometer reference frequency ωrf. The mathematical representation of the interaction between the spin ensemble and the RF pulse can be simpliﬁed if one views it in a rotating frame which revolves around ~B0 at the same frequency as ωrf. Under such an assumption, the Hamil- tonian of the RF interaction may be expressed as,168

HˆRF = ωnut(Iˆxcosφp + Iˆysinφp), (4.14)

1 with the nutation frequency ωnut = 2 γBRF, where BRF is the magnetic ﬁeld (1) strength generated by the RF pulse, and φp is the phase of the RF pulse . An RF pulse is usually associated with a ﬂip angle βp,

βp = ωnuttp, (4.15) where tp is its duration. The magnetization vector may be rotated by the RF pulse. For instance, the z-magnetization generated at the thermal equilibrium,

(1) ◦ In the NMR jargon, x-pulse is the pulse with phase φp of 0

朳朱 where there is no net ﬂow of thermal energy between the spin system and its surrounding environment, can be rotated to the x-direction by a pulse with the ◦ ﬂip angle φp = 90 . Such a rotation of the magnetization vector to the xy- plane creates a transverse magnetization, which is more formally referred to as single-quantum coherence (1QC) (see Figure 4.3). The coherence is created when a spin is a superposition state of |αi and |βi.

Figure 4.3: When the spins are randomly polarized in the xy-plane, there is no net transverse magnetization, i.e., no 1QC. However, if the spins are partially polarized to a certain direction, the net polarization indicate the existence of 1QC. (Adapted with permission from Wiley.168)

A rotating magnetic dipole produces a rotating magnetic field, which, according to the Maxwell’s electromagnetic theory, introduces an electric field. Under the influence of such an electric field, electrons in the coil form an oscillating current, which is detected by an RF receiver. The oscillating current diminishes due to the relaxation and the corresponding decaying NMR signal is referred to as the free induction decay (FID). The time domain NMR signal FID can be Fourier transformed (FT) into the frequency domain and results in the “NMR spectrum”, which involves amplitude as function of frequency; see Figure 4.4 The recorded FID is mixed with a reference signal oscillating at ωrf in the receiver of the NMR spectrometer,168 with the resulting frequency difference named the resonance offset frequency Ω j,

Ω j = ω j − ωrf. (4.16)

To make the NMR spectrum irrespective of the experimental conditions, a chemical shift in the ppm scale is introduced. By using a speciﬁed reference compound, the chemical shift of a resonance j is deﬁned as168

朳朲 Figure 4.4: Transformation of a time domain FID into a frequency domain spectrum using a Fourier transform (FT).

Ω j + ωrf − ωref δ j = , (4.17) ωref where ωref is the resonance frequency of a selected site in the reference compound.

4.2 Internal Spin Interactions

4.2.1 Chemical Shift Interaction The chemical shift interaction represents an indirect interaction between an external magnetic field (~B) and the spin of the nucleus via its surrounding electrons. The current introduced by an external magnetic field generates an induced magnetic field ~Binduced, as illustrated in Figure 4.5. ~Binduced relates to the ~ 168 LAB external magnetic field B through a second-rank chemical shift tensor δcs , where

  δxx δxy δxz ~ LAB~ ~ Binduced = δcs B = δyx δyy δyzB. (4.18) δzx δzy δzz It is always possible to choose three mutually perpendicular vectors to represent the chemical shift tensor, where the applied external magnetic ﬁeld and the induced magnetic ﬁeld are parallel. These three vectors constitute the principle axis frame (PAF) and the representation of the chemical shift tensor in PAF 168 the PAF frame δcs is   δXX 0 0 PAF δcs =  0 δYY 0 , (4.19) 0 0 δZZ

朳朳 where δXX , δYY , and δZZ are the three principle values along the x, y, and z axes of the PAF, respectively.

Figure 4.5: The external magnetic field ~B0 introduces a flow of electrons that generates an induced magnetic filed ~Binduced. (Reproduced with permission from Wiley.168)

j In the PAF, the isotropic chemical shift δiso of a spin j in the ppm scale is the average of the three principle values,168 1 δ j = (δ j + δ j + δ j ). (4.20) iso 3 XX XX XX where the three principle values are allocated according to the following relationship, j j j j j j |δZZ − δiso| ≥ |δXX − δiso| ≥ |δYY − δiso|. (4.21) The chemical shift anisotropy (CSA) may be deﬁned as168 j j j δaniso = δZZ − δiso, (4.22) and the asymmetry parameter of the chemical shift tensor

j j j δYY − δXX ηaniso = j . (4.23) δaniso The chemical shift interaction Hamiltonian in the laboratory frame is

ˆ full ~ ~ˆ PAF −1~~ˆ HCS = −γBinducedI = −γR(ΘLP)δcs R(ΘLP) BI, (4.24) where R(ΘLP) is the rotation matrix that transforms the chemical shift tensor from the PAF into the laboratory frame. Recall that ~Iˆ has three components {Iˆx, Iˆy, Iˆz}, which does not commute with each other. For example,

[Iˆx,Iˆz] ≡ IˆxIˆz − IˆzIˆx 6= 0. (4.25)

朳朴 The chemical shift Hamiltonian interaction becomes simpliﬁed due to the dominating Zeeman interaction, and after the Zeeman truncation,171 the sum of the chemical shift and Zeeman interactions are171

Hˆ = HˆZ + HˆCS = [ω0 + ωcs(Θ)]Iˆz, (4.26) where

ωcs(Θ) = ω0δiso + ωCSA(Θ), (4.27) and Θ denotes the orientation dependence. Such an orientation dependence can be simpliﬁed by two polar angles (θ, φ)(1). The z-axis in the laboratory frame may be expressed in the PAF as (sinθcosφ,sinθsinφ,cosθ)(2). By using 170 such a representation, ωCSA(θ,φ) can be expanded as 1 ω (θ,φ) = ω δ {3cos2θ − 1}, (4.28) CSA 0 aniso 2 for the axial symmetry case where δXX = δYY and

1 ω (θ,φ) = ω δ {3cos2θ − 1 + η sin2θcos2φ}, (4.29) CSA 0 aniso 2 aniso represents a general case, i.e., no specific relationship between the three principle components. For a given spin site in a single crystallite of a given compound, the NMR peak occurs at a specific position which is determined by the two polar angles (θ, φ) as suggest by equation 4.29. However, in a poly-crystalline compound, a static NMR spectrum is characterized by a powder pattern, which represents a superposition of NMR signals from randomly orientated crystallites, as shown in Figure 4.6. The powder pattern with broadenings from ◦ CSA can be narrowed√ by a spinning of the sample at an angle θMAS ≈ 54.74 (cos(θ) = (1/ 3) (with respect to the direction of the main magnetic field B0), which is referred to as magic angle spinning (MAS). The MAS technique was introduced independently by E. R. Andrew et al.172 and by I. J. Lowe.173 Nowadays, the availability of ultra-fast MAS up to 110 kHz make it possible to average out strong homonuclear dipolar couplings between protons, thereby allowing detections of alpha and side-chain protons in fully protonated proteins.174

(1) θ is the angle between B0 and the direction of δZZ and φ the angle between the projection of B0 and the direction of δXX . (2) This vector represents the third column of the rotation matrix R(ΘLP), and other elements of the matrix are immaterial when calculating the Zeeman-truncated chemical shift interaction.

朳朵 Under MAS, equation 4.27 becomes(1)

0 0 ωcs(Θ ,t) = ω0δiso + ωCSA(Θ ,t), (4.30) where Θ0 represents the orientation dependence. Here the time-dependent term 0 0 ωCSA(Θ ,t) oscillates at the MAS frequency ωrot and 2ωrot. If ωCSA(Θ ,t) >ωrot, the power pattern is split into a set of spinning sidebands, where each 0 sideband is separated by ωrot (see Figure 4.7). If ωCSA(Θ ,t) ωrot, the powder pattern becomes one narrow peak, which is referred to as the center band, and is positioned at ω0δiso. Unlike well-crystalline compounds, the isotropic chemical shifts from glasses exhibit a Gaussian distribution due to a plethora of coexisting local chemical environments induced by variations in bond angles and bond lengths, as illustrated in Figure 4.8.

Figure 4.6: The NMR “powder pattern” represents a superposition of NMR signals from crystallites that are randomly orientated. (Reproduced with permission from Wiley.168)

4.2.2 Direct Dipole–Dipole Coupling For two spins j and k, the magnetic ﬁeld generates by j interacts with k and vice versa. Such a mutual spin interaction is referred to as the direct dipole– dipole interaction (DD), as illustrated in Figure 4.9. The strength of the DD interaction is dictated by the dipolar coupling constant168

µ0 γ jγkh¯ b jk = − 3 , (4.31) 4π r jk where r jk is the distance between the two interacting spins j and k, and µ0 = 4π × 10−7N/A2 is the vacuum permeability. Since the dipolar coupling con- 3 stant is inversely proportional to r jk, the DD interaction diminishes rapidly as

(1) The time dependence of ωcs in the laboratory frame originates from the transformation of rotor frame→LAB and Θ0 are angles used to for the transformation, PAF→rotor frame→LAB.

朳朶 13 13 Figure 4.7: C MAS NMR spectra of 99%- C2-labeled glycine recorded at spinning speeds of (a) 0 kHz, (b) 1 kHz, (c) 3 kHz, (d) 7 kHz, (e) 15 kHz, and (f) 30 kHz using a 9.4 T magnet. Each spectrum is scaled by the number list to its right side. (Reproduced with permission fromR. Mathew.175)

朳朷 Figure 4.8: The NMR responses of a poly-crystalline sample with long-range order and an amorphous sample devoid of that order, and assuming only Zeeman and chemical shift interactions. The crystalline sample produces a Lorentzian NMR lineshape, which corresponds to a single signal component exhibiting an exponentially decaying FID. However, for the amorphous counterpart, the inde- pendent variations in bond-angles and bond-lengths introduce a Gaussian distribution of chemical shifts. the internuclear distance is increased. The DD interaction Hamiltonian depends on if two nuclei are alike or unlike. In the case of alike nuclei, the homonuclear dipolar interaction between the two spins j and k is represented by168

jk 1 2 Hˆ = b jk (3cos θ − 1)(3IˆjzIˆkz − IˆjIˆ ), (4.32) DD 2 k where θ is the angle between the inter-nuclear vector and the direction of the main magnetic ﬁeld ~B0. In the case of unlike nuclei, the heteronuclear dipolar interaction has a simpler form due to the much larger differences in the Zeeman interactions of spins I and S (compared to heteronuclear DD interaction),168

ˆ IS 2 ˆ ˆ HDD = bIS(3cos θ − 1)IzSz. (4.33) The direct homonuclear/heteronuclear dipole–dipole interactions are extensively employed in Paper III-V using dipolar recoupling techniques under MAS conditions (as discussed in Section 4.3.2) for the purpose of better un-

朳朸 Figure 4.9: Mutual interactions between two spins j and k. (Reproduced with permission from Wiley.168)

derstanding the preferential connectivities among various BO3, BO4, and PO4 polyhedra in BPS glasses. However, the existence of DD interactions denotes solely the spatial vicinity. A more convincing proof of linkages among structural units in BPS glasses is the offered by detecting the existence of an indirect dipole–dipole interaction (J coupling),176 which is more directly related to the presence of chemical bonding.

4.2.3 Electric Quadrupole Coupling A quadrupolar nucleus possesses a non-spherical electrical charge distribution. The electric quadrupole moment (eQ) of a quadrupolar nucleus interacts with a surrounding electric ﬁeld gradient (eq) and this interaction is characterized by the quadrupolar coupling constant CQ

2 CQ = eQ · eq/h = e qQ/h. (4.34)

CQ which reflects charge distribution in the vicinity of the quadrupolar nucleus. For instance, the two BO3 and BO4 units in BPS glasses have distinct NMR responses (see Figure 3 from Paper III). The planar configuration of BO3 units lead to uneven charge distributions around the BO3 unit, whereas the charges disperse more evenly around the more symmetric tetrahedral symmetry of the 26, 27, 177, 178 BO4 unit. The distinct geometries are mirrored in their distinct values of CQ, with 2–3 MHz and < 0.5 MHz being typical for BO3 and BO4 units, respectively. The electric field gradient (EFG) is characterized by a second-rank EFG tensor, whose three principle values, VXX , VYY , and VZZ obey VZZ ≥ VXX ≥ VYY , with the largest component VZZ = eq. The asymmetry parameter is defined by168

ηQ = (VXX −VYY )/VZZ. (4.35)

朳朹 The strength of the quadrupolar interaction is proportional to CQ, which is reﬂected by its quadrupolar frequency179

2πC ω = Q . (4.36) Q 2I(2I − 1) and If ωQ ω0, the quadrupolar interaction is treated within perturbation theory as as a perturbation to the (dominating) Zeeman interaction (1) according to171

ˆ ˆ ˆ ˆ (1) ˆ (2) HZ + HQ ≈ HZ + HQ + HQ , (4.37) ˆ (1) ˆ (2) where HQ and HQ are the Hamiltonian of the first-order and the second order quadrupolar interaction, respectively. The bearings from the first- order and second-order quadrupolar interactions on Zeeman interaction are 3 displayed in Figure 4.10. For a spin- 2 , the transition between two energy lev- 3 1 3 1 els |+ 2 ,+ 2 i and |+ 2 ,− 2 i is referred to as the central transition (CT), while 3 3 3 1 3 1 3 3 |+ 2 ,+ 2 i → |+ 2 ,+ 2 i and |+ 2 ,− 2 i → |+ 2 ,− 2 i are the satellite transitions 3 3 1 3 (ST). Note that symmetric transitions like |+ 2 ,+mi and |+ 2 ,−mi (m = 2 , 2 ) are not affected by the first-order quadrupolar interaction.168 If the nutation frequency of an RF pulse is much smaller than the quadrupolar frequency of the quadrupolar nucleus, i.e., ωrot ωQ, only CT is excited. Such an excitation scenario is termed as CT-selective excitation, with the nutation frequency CT of the CT (ωnut ) given by 1 ωCT = (I + )ω . (4.38) nut 2 rot When probing the internuclear connectivities involving quadrupolar nuclei, CT-selective excitation is always used (see Sections 4.3.2 and 4.3.3). ˆ (1) 179 The first-order quadrupolar Hamiltonian HQ is,

(1) (1) 1 Hˆ = ω (Θ) {3I2 − I(I + 1)1ˆ}, (4.39) Q Q 2 z where Θ represents a set of angles that transforms the PAF into the laboratory (1) frame, and ωQ (Θ) is the ﬁrst-order quadrupolar frequency. By using two (2) ˆ (1) 179 polar angles (θ, φ) and equation 4.36, HQ may be expressed πC {3cos2θ − 1 + η sin2θcos2φ} ω(1)(θ,φ) = Q aniso . (4.40) Q 2I(2I − 1)

(1) In the other regime when ωQ ω0, it is better to treat the Zeeman interaction as a perturbation to the quadrupolar interaction, or to use nuclear quadrupole resonance (NQR) to investigate the quadrupolar interaction. (2) see the descriptions of ωCSA and equation 4.29

朴朰 3 Figure 4.10: The zeeman energy levels of an I = 2 spin are perturbated by ﬁrst- and second- order quadrupolar interactions. Note that the energy differences 3 3 1 between the two energy levels—|+ 2 ,+mi and |+ 2 ,−mi with m = 2 (a.k.a CT- 3 transition), 2 —are not affected by the ﬁrst-order quadrupolar interaction. (Re- produced with permission from Wiley.180)

Note that equations 4.40 and 4.29 have similar forms, i.e.,the similar orientation dependence. The second-order quadrupolar frequency contains two terms,179

2 (2) Q Q CQ f (I) ωQ = ωiso + ωaniso(Θ) ∼ 2 , (4.41) γB0[I(2I − 1)] Q Q where ωiso represents the isotropic term and ωaniso(Θ) represents the anisotropic frequency. Unlike the CSA, the anisotropic second-order quadrupolar interaction cannot be completely averaged out by MAS. Here, multiple quantum MAS (MQMAS) offers a way to get a spectrum free of second-order quadrupolar broadenings (see Section 4.3.4). The isotropic second-order quadrupolar part Q results in the isotropic second-order chemical shift δiso, 3π2C2 (1 + η2/3)[(3 − 4I)(I + 1)] Q = Q , (4.42) δiso 2 2 2 40ω0 I (2I − 1) 179 and the center of gravity (δCG) of a quadrupolar site j is derived ,

j j Q j δCG = δiso + (δiso) . (4.43)

For well-crystalline sample, CQ and η may be derived by equations 4.42 and 4.43, whereas for a glass sample, (due to broadenings induced by a structural

朴朱 disorder), CQ and η cannot be determined separately. Here the parameter CQη is used179 , q 2 CQη = CQ 1 + η /3. (4.44)

11 Equation 4.43 was used in Paper III to determine the average CQη of BO4 sites.181

4.3 NMR Techniques

This section introduces several NMR techniques that are relevant to the current thesis. They either increase the spectral resolution for quadrupolar nuclei (Sections 4.3.4), or bring back the dipolar interactions that were averaged by MAS for the purpose of understanding the medium-range structure (Sections 4.3.2 and 4.3.3).

4.3.1 Spin-Echo and Spin Lock

The Spin-Echo182 is widely utilized in the solid-state NMR experiments, which refocuses inhomogeneous broadenings due to inhomogeneities of the main magnetic field B0, uneven distributions of the susceptibility across the sample, as well as isotropic chemical shift dispersions as encountered from structurally discussed samples like glasses. Spin-echo is also served as a component for complex pulse sequence, as those in Section 4.3.3 or used to record broad spectra where the FID decays significant during the “ringing”, a short period that is required to let the RF pulse dissipate. The extended version, Carr-Purcell- Meiboom-Gill (CPMG), has been used to enhance the signal-to-noise ratio.183 Spin-echo and the multiple quantum MAS to be described in Section 4.3.4 belongs to a general coherence-transfer echo.184, 185 Spin lock186 (“spin-locking”) can serve as a constituting block of complex NMR experimental, like the cross polarization.187 During the spin lock, the spin magnetization vector is “locked” by a RF field which is parallel to it and the decay of spin magnetization is characterized by a longitude relaxation time in the rotating frame T1ρ . Spin lock can accurately measure the 188 1 RF nutation frequency based on the 2Q-HORROR condition ωnut = 2 ωrot (as a special case of rotary resonance recoupling (R3)) or R3 conditions189 ωnut = nωrot (where n is a small integer, n < 3) restoring CSA and DD interactions. This feature is particularly useful for optimizing dipolar recoupling techniques relying on 2Q-HORROR/R3 RF conditions (see Sections 4.3.2 and 4.3.3.

朴朲 Figure 4.11: The representation of IjxIkx operator. For each spin pair, the spin polarization directions of two spin are all have projections along +x or −x direction (Reproduced with permission from Wiley.168)

4.3.2 Recoupling of Homonuclear Dipolar Interactions

Under the MAS condition, some relative week homonuclear dipolar couplings are averaged out, such as 11B 11B couplings in the BPS glasses. To bring it back, one may resort to the recoupling techniques where the rotation of spin operators by RF pulses interfere with their rotations induced by macroscopic sample spinnings, thus preventing dipolar interaction from averaging out.170 The Homonuclear dipolar recoupling sequences can be used to generate double quantum coherences (2QC) and the coherence itself can be pictured as that the spin polarization directions of two spins in a spin pair pointing to similar directions, as displayed in Figure 4.11. A homonuclear recoupling sequence usually contains the excitation and the reconversion blocks, where the transitions Z-magnetization→2QC and 2QC → Z-magnetization occur, respectively.6, 190 A short excitation duration is required if one wants to suppress the contributions to the 2QC from distant spins. Such an sequence can be arranged in a 2D fashion (double-quantum–single- quantum correlation, a.k.a. 2Q–1Q correlation), as illustrated in Figure 4.12. Assume a spin system with two j and two k spins, with their relative positions shown in the ﬁgure. During the acquisition, i.e., t2 period, two j and two k evolve at the frequencies of ω j and ωk, respectively, and if spins in the vicinity are correlated with each other, the corresponding frequencies of the spin pairs are 2ω j, ω j +ωk, and 2ωk. After a FT transformation from (t1, t2) to (F1, F2), where F1 represents the indirect dimension and F2 the direct dimension, the individual frequencies appears in the F2 dimension, whereas their sum frequencies appear in the F1 dimension. The corrections between the individual

朴朳 frequencies and the sum frequencies of spin pairs jk can be used to identify their spatial intervals. 1191 In Paper IV and V, we employed the SR22 sequence for the excitation and recoupling blocks, as well as a “short” excitation period to investigate the intermixing of borate groups in boro(phospho)silicate glasses. Due to the unlike average b jk (b jk) associated with each spin pair and the relative weak quadrupolar couplings of B[4], the excitation efﬁciencies of 11B[p] O 11B[q] (p, q = 3, 4) are different and a correction is needed to derive the corresponding pq xB populations (see the discussions in SI of Paper V).

Figure 4.12: A “carton” scheme for 2QC–1QC correlation experiments (2Q– 1Q). It contains the excitation block and the reconversion block, during which the transitions of Z-magnetization→2QC and 2QC→Z-magnetization occur. During the t2 evolution time, two j and two k spins evolve at their frequencies of ω j and ωk, respectively and during the t1 evolution period in between the two blocks, the recoupled spin pair evolve at frequencies of2ω j, ω j + ωk, and 2ωk. Such corrections can be used to identify the spins that are in vicinity.

4.3.3 Recoupling of Heteronuclear Dipolar Couplings Utilizing the heteronuclear dipolar interaction under the MAS condition requires dipolar recoupling techniques. For heteronuclear spin pairs, several options are available, such as R3,189 rotational echo double resonance (RE- DOR)192 (or rotational echo adiabatic passage double resonance (REAPDOR)193 ν ν as a variant for the quadrupolar nuclei), and symmetry-based RNn and CNn pulse sequences.194 A REDOR experiment between two distinct spin species S and I comprises a reference experiment with an integral S0 and a dephasing experiment whose signal is attenuated by the recoupled IS heteronuclear dipolar couplings,192 with the reduced amount ∆S. The recoupling is achieved by one π pulse per half rotational period (2π/ωrot) and the recoupling period (τrec) is deﬁned by ◦ 8nπ/ωrot with n the number of 180 pulses. ∆S/S0 increases with increasing τrec and it reaches a maximum value, upon which it exhibits an oscillation behavior if spin pair IS is isolated. The ∆S/S0 −τrec correlation can be simulated

朴朴 to extract the internuclear distance.195 For samples where the internuclear distance exhibit a distribution, the extraction of internuclear distance of each spin pair is formidable, and a van Vleck dipolar second moment196, 197 is usually used to ﬁt the ∆S/S0 − τrec curve with 0 ≤ ∆S/S0 ≤ 0.2 − 0.3. Heteronuclear dipolar couplings interactions can be also probed by the dipolar-based heteronuclear multiple quantum correlation (D-HMQC) tech- 198, 199 2 niques, where heteronuclear dipolar couplings are recoupled by SR41 RF blocks.200

4.3.4 Multiple-Quantum MAS As discussed in Section 4.2.3, the anisotropic second-order quadrupolar inter- Q action ωaniso(Θ) cannot be totally averaged out by MAS. That problem has been addressed by the dynamic-angle spinning (DAS) and the double rota- 201, 202 tion. In the DAS, sample spins around different axises during the t1 and t2 periods, respectively, resulting in a echo free of anisotropic second-order quadrupolar interactions. Such an issue can be also solved by the Multiple- Quantum MAS (MQMAS)203, 204 which is similar to the DAS, where the multiple quantum coherence (MQC) evolved during t1 are correlated to the 1QC 205, 206 during t2. Later modiﬁcations are shifted-echo MQMAS, where whole- echo acquisition207 is exploited to enhance the S/N208 and Z-ﬁlter MQMAS,208–210 with the latter one used in Paper III to resolve various BO3 sites.

朴朵朴朶 5. Structures of Bioactive Borophosphosilicate Glasses— Summary of Papers III, IV, and V

This chapter summaries the contents from Papers III and IV, which presented the ﬁrst comprehensive study of composition–structure correlations in the recently proposed borophosphosilicate (BPS) glass system (see Sections 5.2 and 5.3); it also summarizes Paper V that provided experimental evidence for abundant B[4] O B[4] groups in Na (Ca) B Si O glasses across a large compositional span (see Section 5.4). Before diving into explaining our ﬁnd- ings of the BPS glass structure, we will get across some important structural aspects in the widely investigated borosilicate glasses. As discussed in Section 1.2.1, given that the P speciation in BPS glasses are dominated by orthophos- 0 phate groups (QP; see Section 5.2), a BPS glass network can be viewed as P a borosilicate sub-network and a phosphate sub-network with NBO ≈ 0 (see equation (1) in Paper III)(1).

5.1 A Brief Summary of Borosilicate Glass Structures

The structure of borosilicate glasses can be described by the Yun–Dell-Bray- Xiao (YDBX) model,26, 27 which provides adequate predictions of the relative (2) [3] [4] populations of the BO3 and BO4 units, i.e., xB and xB , respectively. The YDBX model was derived by ﬁtting the experimentally determined fractional populations to a series of reactions, which described how the various structural units varied with the glass compositions. There are also some other structural models for the borosilicate glass, where topology211 and thermal dynamics212 approaches are invoked. For a borosilicate M2O B2O3 SiO2 glass with M representing a mono-

(1)Its exact value can be derived from the experimentally determined fractional population 0 1 0 1 of QP and QP, i.e., xP and xP, respectively (2) [4] xB is equivalent to “N4” that are widely used in the literature.

朴朷 valent metal cation, the YDBX model parametrizes the glass composition as RM2O B2O3 KSiO2, where R = x(M2O)/x(B2O3) denotes the ratio of the molar fractions between the metal oxide (M2O) and B2O3, and K=x(SiO2) /x(B2O3) denotes the ratio of the molar fractions between SiO2 and B2O3. 213 For the modifier-free borosilicate glasses, B exists solely as BO3 units, and the addition of M2O leads to the transformation BO3 → BO4 within the first YDBX region (0 < R < 0.5). The authors mentioned the possible formation of diborate rings, which consist of two BO3 and two BO4 groups, but they were not the prerequisites for the YDBX model. In region II that follows when R is 1 K increased, 0.5 ≤ R ≤ RMAX = 2 + 16 , a part of the diborate groups are transformed into reedmergnerite groups, which consists of only BO4 groups. Within regions I and II, there is no formation of NBO, and the relative BO4 fraction is [4] 1 K equal to the R value, xB = R. In region IIIl, i.e., for which RMAX ≤ R ≤ 2 + 4 , [4] the YDBX model predicts a constant xB value and NBO formation at the reed- 1 K mergnerite groups. In region IV with 2 + 4 ≤ R ≤ 2 + K, the additional modifiers generate BO3 and SiO4 units, both having 2 NBO ions. Several structural features have been addressed by later studies:

(1) The YDBX model was originally derived from sodium borosilicate glasses,26, 27 and its application to borosilicate glasses with glass mod- iﬁers featuring large-CFS values is much less successful.214–219 The large-CFS modiﬁers promote the formation of NBO and lead to lower 214–218, 220 BO4 fractions than those predicted by the YDBX model; this is due to two competing process, i.e., NBO formation and BO3 → BO4 transformation. This generally results in a more randomized glass structure,215, 216, 218, 220 as well as non-negligible NBO formation on glass compositions that are predicted to be NBO-free.219

(2) Manara proposed that in the YDBX region II, the addition of mod- iﬁers forms a mixture of reedmergnerite (NaBSi3O8) and danburite (CaB2Si2O8) groups, which feature B:Si ratio of 1:3 and 1:1, respectively.221 The existence of danburite rings was also assumed in other studies,57, 217, 222 support thereof was mainly obtained from poorly resolved Raman spectroscopy. Note that danburite units are not the sole borosilicate motifs with equal amounts of B and Si: the 223 sodium-based equivalent to danburite, malinkoite (NaBSiO4), features six-member rings which are constituted by alternating SiO4 and [4] [4] BO4 units, i.e., there are no B O B linkages. (3) The YDBX model invokes the “diborate” superstructural unit that involves direct B[4] O B[4] linkages. However, such linkages are energetically disfavored due to accumulations of negative charges locally

朴朸 and they are by many researchers28, 215, 216, 224–227 assumed not to exist for borosilicate glasses involving glass modiﬁers with low CFS values; yet, cations with high CFS values could promote their formation.215, 216, 218, 220

(4) Many structural models suggest a (sub)nanometer heterogeneity in the borosilicate glass structure (see Refs.25, 57, 217, 221, 222, 228 as well as Pa- per IV). Such a heterogeneity is also implied by the YDBX model,27 where diborate rings and reedmergnerite groups are suggested to coexist. However, the details of such a “domain structure” differs in later studies, where a borate domain comprising boroxol rings48, 49 and a borosilicate domain composed of interlinked BO4 and SiO4 groups were favored,57, 228 at least for NBO-poor glass compositions. Possi- bly, the underlying reason for the formation of domain structure may be the preferential mixing between Si and borate units, which follows the trend B[4] > B[3](non-ring) > B[3](ring),28, 54, 55 where ring and non- ring refer to B in the boroxol ring or not involved in such ring motif.

5.2 Short-Range Structure of Borophosphosilicate Glasses (Paper III)

Two series of bioactive BPS glasses were synthesized by substituting SiO2 Si with B2O3 in two phosphosilicate base glasses with the calculated NBO values of 2.11 and 2.54, respectively (see Table 5.1). The former base glass was the 45S5 Bioglass, while the latter featured a more condensed glass network, as well as a higher P2O5 content (x(P2O5)=0.04). The B substitution degree (in %) f = 100x(B2O3)/[x(B2O3)+x(SiO2)], altered in the ranges of 0–100% and 0–80% in the glass series S46 and S49, respectively(1). In both BPS glass series, the P speciation was dominated by orthophos- 0 1 phate groups (QP), while the fractions of the remaining phosphate units (QP) increased across the ranges of 0.041–0.084 and 0.100–0.168 for the S46 and S49 glass series, respectively, as the B2O3 substitution degree was increased. 1 Note that, as compared with S46 base glass, the higher QP content of the base Si 39 glass in the S49 series stems from its higher NBO value. B existed as BO3 and BO4 groups, with the fraction of the latter units increasing to the respective asymptotical values of 0.34 and 0.43, for growing fractions of B2O3 (see

(1)The S49 glass series in Paper IV was complemented with three new members with high B2O3 substitution degrees. Our later studies on the glass formation region in the BPS glasses suggested the highest possible B substitution degrees were 40% and 10% for glasses with 5.0 mol% and 6.0 mol% P2O5, respectively, which consequently diminished for increasing P2O5 content.

朴朹 Figure 4 of Paper III). The NMR signals from two distinct BO3 sites were re- 11 solved by B 3QMAS, with one BO3 site having one silicate neighbor and the other BO3 unit in the borate rings. These assignments agreed with the double- quantum ﬁltered (2QF) 11B spectra and the domain-structure revealed by MD simulations (see Section 5.3).

Two factors affect the 29Si chemical shift: (i) for a more condensed sili- n cate network, the contributions from QB units with higher n values increase, which lead to a lower 29Si average shift; (ii) a change in the next nearest neigh- 29 bor from SiO4 to BO4 will increase the Si shift. Due to the two factors, the 29Si spectra of BPS glasses were of lower resolutions than the B-free counterparts, which made their deconvolution results unreliable. In Paper III, with 1 an assumption that the majority of QP groups was bonded to Si, we used a Si 1 linear relationship between NBO and xP determined previously for phospho- 39 Si silicate glasses to estimate the variations in the NBO values induced by the SiO2→B2O3 substitutions. The results revealed an increased silicate polymerization degree, and the conclusions were qualitatively correct, but the underlying assumption was later found out (Paper IV) to be inappropriate for B-rich 1 BPS glasses. Since QP has a slightly higher preference for bonding to BO4 1 than SiO4 (see Section 5.3), QP O Si bonds only dominated in the silicate rich sample. As discussed in Paper IV, the fundamental reason that led to an Si increase in the NBO was the equimolar substitution of SiO2 by B2O3, which led to a diminished number of NBO atoms on each glass network former. 0 1 The QP → QP and BO3→BO4 transformations accompanying the B2O3→SiO2 replacement is a direct consequence of the more condensed glass network. Although modifiers contents in the glasses were formally sufficient to charge- 0 1 compensating all the phosphates groups as QP units, QP formed and its content was found to increase for increasing (overall) network polymerization degree of the glass. Since all the BPS glasses were in the region IV of the YDBX [4] model, an decrease in the modifier content would increase xB . The find- ing of more condensed glass networks was consistent with the MD-derived xNBO trend (see Table 2 of Paper IV). The simulations also revealed that the preference of accommodating NBO ions on the structural units followed PO4 BO3 > SiO4 > BO4. In Paper III, we conjectured a domain structure for BPS glass, which BO3 groups associated with itself and form a sub-domain of boroxol rings. However, the relative strong ability of accommodating NBO on BO3 units limits the formation of boroxol rings; see discussions in Section 5.3. Besides the relative strong propensity of BO3 units for accommodating NBO ions, MD simulations indicated there was a non-negligible number of [4] [4] NBO ions on the BO4 unit as well. Similar to the B O B motifs to be discussed in Sections 5.3 and 5.4, such BO4 NBO contacts are energetically

朵朰 disfavored, and their bearing on the glass structure are currently under investigation.

5.3 Medium-Range Structure of Borophosphosilicate Glasses (Paper IV)

The intermixing between borate and phosphate units of the BPS glass networks was investigated using D-HMQC experiments (see Section 4.3.3), where the NMR signals from 11B and 31P appear along the direct dimension and the indirect dimension, respectively, of the 2D NMR spectrum; see Figure 6 of Paper IV. Two ridges stemming from the correlation signals of P–BO3 and P–BO4 were revealed. The projection of the P–BO3 ridge in the indirect dimension ex- 0 1 31 hibited similar fractions of QP, QP as those deduced by deconvoluting the P MAS NMR spectra, thereby indicating that BO3 units were homogeneously distributed with the PO4 units (see Figure 7a of Paper IV). However, the projection of the P–BO4 ridge revealed a significantly increased signal intensity 1 1 from the QP groups, suggesting that QP preferentially bonds to BO4 units rather than BO3 units. MD simulations also suggested an insignificant number of 1 QP BO3 linkages, except for the B-richest samples (see Table 2 of Paper IV). 1 We could then safely assume that QP units were distributed solely among the 1 [4] 1 BO4 and SiO4 groups and the abundances of the QP B and QP Si contacts were then possible to quantify by 31P{11B} REAPDOR NMR experiments. As 1 shown in Figure 8a of Paper IV, QP groups bonded slightly preferentially to [4] BO4 (rather than SiO4) as compared with statistically P O B and P O Si 1 bonds. Such a slight affinity of QP groups for bonding to BO4 groups would 1 [4] only lead to dominating QP O B contacts in the B-rich samples featuring 1 x(B2O3)& 0.25, which clarify our statement in Paper III that QP units form predominantly P O Si bonds. The mixing between the various borate groups were investigated by 2Q– 1Q correlation NMR experiments (see Section 4.3.2). As shown in Figure 3 of Paper IV, all three 2QCs stemming from the B[3] O B[3],B[3] O B[4], and B[4] O B[4] linkages appeared in the 2D NMR spectra. Table 3 of Paper IV lists the integrated 2QC signal intensities. But as discussed in Paper V, due to slight differences in the average distances among B[p] O B[q] spin pairs and the widely differing in the quadrupolar coupling constants between the B[3] and B[4] coordinations, the 2QCs from B[3] O B[4] and B[4] O B[4] motifs were excited less efficiently than those from the B[3] O B[3] motifs. Hence, pq a correction factor was required to derive the xB populations from their integrated 2D NMR peak intensities. Table 5.2 lists the “corrected” populations obtained from the NMR experiments, as well as the statistical predictions (see

朵朱 Section 5.4 for more details of the statistical model). Throughout the glasses, B[3] O B[4] were the most abundant linkages except for the glass with the [4] [4] [4] lowest xB . Although B O B linkages are energetically disfavored, they exist in large amount in the modiﬁer-rich BPS glasses.

pq Table 5.2: Corrected xB populations based on the procedures described in Section S3 of Paper V. The statistical populations are listed in the parenthesis, which were calculated by the statistical model (i); see Section 5.4 for details) NMR MD 33 34 44 33 34 44 xB xB xB xB xB xB S462.6(5) 0.56(0.61) 0.37(0.34) 0.07(0.05) 0.18 0.73 0.09

S462.6(37) 0.29(0.35) 0.55(0.48) 0.16(0.17) 0.21 0.63 0.16

S462.6(46) 0.30(0.36) 0.55(0.48) 0.15(0.16) 0.20 0.63 0.17

S494.0(7) 0.28(0.27) 0.56(0.50) 0.16(0.23) –––

S494.0(24) 0.22(0.25) 0.56(0.50) 0.22(0.25) 0.15 0.64 0.21

In Paper III, we conjectured a higher preference for B[4] O Si bonding than B[4] O B, which implies the formation of a “domain” structure, where a borosilicate subdomain comprising interlinked BO4 and SiO4 units is inter- leaved with another subdomain of boroxol rings built from BO3 units. Based on the experimental/MD-simulation results of the medium-range structure arrangements in the BPS glasses (see Paper IV), we modiﬁed the details of the previously proposed structure by two intermixed subdomain, one built from silicate rings/chains and the other one consisting of interconnected BO3 and BO4 units (see Figure 1.4).

5.4 Abundant B[4] O B[4] Linkages in Borosilicate Glasses (Paper V)

After improving the understanding of the borate-group mixing in the BPS glasses, we turned to exploring the widely utilized parent borosilicate glasses system. The presence of B[4] O B[4] linkages in the bioactive BPS glasses may not be overly surprising, since those glasses are abundant in the network modiﬁers and contain Ca2+ ions with a large CFS has been suggested to promote the formation of B[4] O B[4] linkages.215, 216, 218, 220 However, the existence of B[4] O B[4] linkages in borosilicate glasses is much more controversial; they have often been assumed not to exist in borosilicate glasses incorporating small-CFS cations, such as Na+,28, 215, 216, 224–227 while the B[4] avoidance (equivalent to the Al[4] avoidance6, 45) is expected to be relaxed in

朵朲 glasses containing large-CFS metal cations.215, 216, 218, 220 We designed eight borosilicate glasses with either Na as the sole modifier glasses (labelled as NK–R) or mixed Na/Ca modifiers (labelled as NCK–R). As illustrated in Table 5.3, this set of glasses covered wide ranges of the NBO frac- [4] tion (0.0 ≤ xNBO ≤ 0.40) and the relative BO4 fraction (0.270 ≤ xB ≤ 0.733). [4] xB values of the NK–R glasses accorded well with the YDBX model, while [4] those glasses with mixed modifiers possessed smaller xB fractions than the predicted values. The effects from modifiers are most clear when comparing a pair of glasses, N2.0–0.5/NC2.0–0.5, both of which share the same R and K values. As for the BPS glasses (Paper IV) borate-group mixing of the borosilicate glass networks was investigated by 2Q–1Q correlation NMR experiments. The 2D NMR spectra are shown in Figure 1 of Paper V. All samples revealed 2QCs stemming from all three types of B[3] O B[3],B[3] O B[4], and B[4] O B[4] linkages. The projection along the direct dimension (i.e., the MAS NMR result after 2QF) exhibited increased spectral intensities of both the higher-ppm 11 11 range of the resonances from the BO3 and BO4 groups, suggesting that those sites are surrounded by more B neighbors than the borate groups res- onating in with lower shifts. This observation was also consistent with the assignments of the 11B MAS NMR spectra. The relative population of each B[p] O B[q] linkage in the glass structure was estimated approximately by correcting the integral of the associated 2QC, with the correction factors obtained from numerical simulations (see details in Section S3 of Paper V). As for the BPS glasses (Paper IV), B[3] O B[4] linkages are dominating. Albeit B[4] O B[4] motifs were disfavored, they are present in considerable amounts throughout all investigated borosilicate pq glasses. We also compared the experimental-derived xB populations with those derived from various statistical models. Since the numbers of linking points at the BO3 and BO4 units that are occupied by NBO ions or by bonds to SiO4 units are unknown (and very difficult to assess experimentally), we evaluated three statistical models using data derived from MD simulations of the corresponding glass compositions. The statistical models were then con- structed by assuming a binomial distribution function, where p represents the probability that BO3 is the neighboring unit; this provided the relative popula- 33 34 44 2 2 tions of {xB , xB , xB } according to {p , 2p(1− p), (1− p) }. The probability p is given by

x[3]N[3] p = B BO , (5.1) [3] [3] [4] [4] xB NBO + xB NBO [3] [4] with NBO and NBO being the available “connecting points” at the BO3 and

朵朳 [3] [4] BO4 units, respectively. In statistical model (i), the B and B coordination [3] [4] numbers were used directly, i.e., NBO = 3 and NBO = 4. In models (ii) and (iii), the respective numbers of “connecting points” were reduced by accounting for the MD-derived NBO ions and “NBO plus silicon”. As shown in Table S3 of Paper V, the simplified statistical model (i) agreed well with the (presumably) “most correct” model (iii). This seemingly surprising result was attributed to compensating effects, where the lower NBO-preference of the BO4 units was compensated by its high preference for forming B[4] O Si bonds. Most important, this justified the usage of a simple model (i) for comparing against the experimentally determined fractional populations. This revealed that the B[3] O B[4] motifs are marginally preferred, whereas the B[3] O B[4] motifs are slightly disfavored. The B[4] avoidance is violated in B(P)S glasses by the presences of high- CFS metal cations and large amounts of NBO ions, both of which promote a randomized glass structure (see Figure 2b of Paper V). MD simulations suggested that the stabilization effect of B[4] O B[4] linkages by Ca2+ ions is “indirect”, and presumably stemming from the formation NBO ions at the BO3 units and which partially blocks their involvement in the borate networks. In turn, this feature leads to elevated relative B[4] O B[4] contents. We also found that the abundance of B[4] O B[4] linkages was primarily controlled [4] by xB and xNBO; see the correlation plot between the experimental values 44 [4] 2 and those derived from the best-fit equation (xB = 0.642(xB ) +0.362xNBO − 0.005nSi/nB) in Figure S2 of Paper V. The usage of square of the BO4 fraction in the equation could be justified by that the B[4] O B[4] linkage is a pairwise bonding and the weak dependence on the ratio of atomic fractions between B and Si is probably due to the poor sampling of such a parameter by the set of glasses in Paper V.

朵朴 Table 5.1: Borophosphosilicate Glass Compositions, and B and P Speciationsa (Paper IV, reproduced with permission from American Chemical Society.) Oxide equivalents Molar Ratios b c c 0 d e label f /% x(Na2O) x(CaO) x(SiO2) x(B2O3) x(P2O5) xNa/xCa xB/xSi R K S462.6(0) 0 0.246 0.267 0.461 0.000 0.026 1.84 0.00 –– S462.6(5) 10 0.246 0.267 0.415 0.046 0.026 1.84 0.22 9.46 9.00 S462.6(9) 20 0.246 0.267 0.369 0.092 0.026 1.84 0.50 4.73 4.00 S462.6(14) 30 0.246 0.267 0.322 0.138 0.026 1.84 0.86 3.15 2.33 S462.6(18) 40 0.246 0.267 0.277 0.184 0.026 1.84 1.33 2.37 1.50 S462.6(28) 60 0.246 0.267 0.184 0.277 0.026 1.84 3.00 1.58 0.67 S462.6(37) 80 0.246 0.267 0.092 0.369 0.026 1.84 8.00 1.18 0.25 S462.6(46) 100 0.246 0.267 0.000 0.461 0.026 1.84 – 0.95 0.00

S494.0(0) 0 0.241 0.233 0.486 0.000 0.040 2.08 0.00 –– S494.0(2) 5 0.241 0.233 0.462 0.024 0.040 2.08 0.11 14.7 19.0 S494.0(5) 10 0.241 0.233 0.437 0.049 0.040 2.08 0.22 7.37 9.00 S494.0(7) 15 0.241 0.233 0.413 0.073 0.040 2.08 0.35 4.91 5.67 S494.0(10) 20 0.241 0.233 0.389 0.097 0.040 2.08 0.50 3.69 4.00 S494.0(15) 30 0.241 0.233 0.340 0.146 0.040 2.08 0.86 2.46 2.33 S494.0(19) 40 0.241 0.233 0.292 0.194 0.040 2.08 1.33 1.85 1.50 S494.0(24) 50 0.241 0.233 0.243 0.243 0.040 2.08 2.00 1.48 1.00 S494.0(39) 80 0.241 0.233 0.097 0.389 0.040 2.08 8.00 0.93 0.249 a Each glass is labeled SNp(q), where N = 100[x(SiO2) + x(B2O3)] is the sum of mol% of SiO2 and B2O3, whereas p and q are the mol% of P2O5 and B2O3, respectively. xE denotes the atomic fraction of element E, whereas x(···) is the molar fraction 0 1 of the as-indicated oxide. All glass-composition data and fractional populations of {QP, QP} and {BO3,BO4} groups—denoted 0 1 [3] [4] 91 {xP, xP} and {xB , xB }, respectively—are reproduced from Yu and Edén, except for the S462.6(46) and S494.0(39) specimens. The uncertainty of each fractional population is ±0.01. b f = 100x(B2O3)/[x(SiO2) + x(B2O3)] is the percentage of B2O3-for-SiO2 substitution. c Ratios of the atomic fractions of Na and Ca (xNa/xCa), and B and Si (xB/xSi), respectively. 朵朵 d 0 Ratio R = x(M2O)/x(B2O3) = xM/xB, with xM calculated from equation (1) in Paper III. e K = x(SiO2)/x(B2O3). 朵朶

Table 5.3: Glass Compositions and NMR/MD-Derived Structural Parametersa (Paper V, reproduced with permission from American Chemical Society.) b b c molar fractions NBO fraction BO4 fraction BOp–BOq connectivities 33 34 44 glass x(Na2O) x(CaO) x(B2O3) x(SiO2) NMR MD NMR MD xB xB xB N2.0–0.26 0.078 0.307 0.615 0.00 0.005 0.270 0.238 0.52(0.43) 0.44(0.54) 0.04(0.03) N2.0–0.5d 0.143 0.286 0.571 0.01 0.020 0.476 0.432 0.29(0.18) 0.60(0.71) 0.11(0.11) N4.0–1.2e 0.192 0.162 0.646 0.07 0.098 0.733 0.610 0.08(0.07) 0.57(0.65) 0.35(0.28)

NC0.5–0.5 0.124 0.124 0.501 0.251 0.03 0.055 0.419 0.387 0.26(0.21) 0.58(0.67) 0.16(0.12) NC2.0–0.5d 0.071 0.071 0.286 0.572 0.03 0.044 0.404 0.347 0.27(0.26) 0.58(0.65) 0.15(0.09) NC4.0–1.2e 0.096 0.096 0.162 0.646 0.10 0.121 0.552 0.464 0.17(0.15) 0.60(0.68) 0.23(0.17) NC4.0–2.0 0.143 0.143 0.143 0.571 0.22 0.227 0.591 0.527 0.13(0.09) 0.58(0.67) 0.29(0.24) NC4.0–3.3 0.199 0.199 0.120 0.482 0.40 0.397 0.472 0.461 0.18(0.14) 0.55(0.63) 0.27(0.23)

σ f 0.01 0.001 0.01 0.006 0.030(0.010) 0.030(0.014) 0.030(0.014) a Nominal Na2O–B2O3–SiO2 (NK–R) and Na2O–CaO–B2O3–SiO2 (NCK–R) glass compositions, with K = x(SiO2)/x(B2O3) 27 and R = x(Na2O)/x(B2O3) for the NK–R glasses, whereas R = [x(Na2O) + x(CaO)]/x(B2O3) for the NCK–R counterparts. b [4] [4] Fractional populations of NBO (xNBO) and B species (xB ) out of the total O and B speciations, respectively, as obtained by 11 B MAS NMR experiments or MD simulations. The fractions of BO and NBO species obey xBO + xNBO = 1. c 33 34 44 11 Fractional populations {xB , xB , xB } of {BO3–BO3, BO3–BO4, BO4–BO4} linkages derived either from 2Q–1Q B NMR experiments or by MD simulations (values within parentheses). dThe N2.0–0.5 and NC2.0–0.5 glasses only differ in their Na/Ca contents. eThe N4.0–1.2 and NC4.0–1.2 glasses only differ in their Na/Ca contents. fTypical data uncertainties (±1σ). 6. Sammanfattning

När “bioaktiva glaser” används som inplantat integreras de med ben/tandvävnad genom att bilda ett lager av hydroxidkarbonatapatit (HCA), vars kemiska sam- mansättning är mycket lik benmineralets. I den här avhandlingen undersökte vi sambanden mellan silikatbaserade glasers bioaktivitet, sammansättning och struktur. Sådana fosfosilikatglaser, som byggs upp av silikat (SiO4) och fosfat (PO4) grupper, används i kirurgi för att fylla hålrum i ben och tänder. Vi under- sökte också strukturen av nyligen utveklade bioaktiva borofosfosilikat (“BPS”) glaser, där SiO4 grupperna delvis är ersatta med boratgrupper (BO3 och BO4). Dessa glaser har högre löslighet i kroppsvätskor, där lösligheten kan anpassas genom att man varierar glasets relativa mängder av B och Si. Det är sedan tidigare känt att silikatnätverkets polymerisering samt fos- fathalten påverkar bioaktiviteten av ett fosfosilikatglas, men de detaljerade sambanden är oklara. För att utröna dessa samband, tillverkade vi tre serier av fosfosilikatglas genom att variera både glasets polymeriseringsgrad och fosfathalt. Efter att ha behandlat varje glas med en simulerad kroppsvätska under 24 timmar, kvantiﬁerades dess HCA innehåll med hjälp av Fourier- transform infrarödspektroskopi (FTIR). Resultaten avslöjade att en hög fosfathalt i glaset ger en hög apatitbildning även för fosfosilikatglas med relativt hög nätverkspolymerisering—vilket man tidigare inte trodde var möjligt. FTIR resultaten överensstämmde väl med andra spektroskopiska undersökningar som utnyttjade kärnspinnsresonans (“nuclear magnetic resonance”; NMR) i fasta tillståndet. Vi visade att tillväxten av apatit vid bioaktiva glasytor följer en “sigmoidal” tillväxts-modell, där en “prekursorfas” av amorft kalciumfosfat (ACP) bildas i “induktionsteget” och sedan omvandlas till HCA i det efterföl- jande “proliferationsteget”. Vi visade också att denna apatitbildningsprocess är mycket lik den där apatit spontant bildas från övermättade lösningar som innehåller kalcium och fosfat joner. Detta fenomen har inte uppmärksammats tidigare. Våra resultat visar också att bildandet av ACP och HCA på glasytor exponerade av simulerade kroppsvätskor sker samtidigt, i kontrast till den rådande mekanismen för apatitbildning som tidigare föreslagits. Denna doktorsavhandling omfattar också fastfas-NMR studier av bioaktiva BPS glaser. Två serier av BPS-glas konstruerades genom att gradvis ersätta SiO2 med B2O3 i två olika fosfosilikatglas med olika polymeriseringsgrader. Med avancerade fastfas-NMR metoder undersökte vi hur BPS-glasernas olika

朵朷 byggstenar var sammanlänkade, varav två viktiga slutsatser drogs: (i) Liksom i strukturer av fosfosilikatglaser, utgörs fosfatgrupperna huvud- sakligen av ortofosfater, som snabbt frigörs när glaset exponeras av (simulerade) kroppsvätskor: detta bidrar till glasens “bioaktivitet” genom en snabb apatitbildning. (ii) I motsats till gängse uppfattning, byggs BPS glaser delvis upp av di- rektlänkade BO4 grupper. Dessa BO4–BO4 strukturmotiv har ansetts som osan- nolika, eftersom varje BO4 tetraeder har en negativ laddning och oorganiska materials strukturer vanligtvis undviker “onödiga” lokala laddningskoncentra- tioner. Vi har också visat att direktbundna BO4 grupper inte bara existerar i BPS glaser, utan också i borosilikatglaser (som inte innehåller fosfatgrupper) med mycket viktiga tillämpningar, alltifrån mobiltelefonskärmar till material för lagring av radioaktivt avfall.

朵朸科科科普普普：：：生生生物物物活活活性性性玻玻玻璃璃璃

随着老龄化社会的到来，很多老人在罹患疾病之后，需要用人造的生物材料来代替失去功能的器官或组织，例如髋关节，牙齿和心脏瓣膜。生物活性玻璃是生物材料的一种，它可以用于填充骨头内的病变区域，或者附着在其他生物活性材料表面并加强其与周围骨或软体组织的粘结性。生物活性玻璃的概念最初由加利福尼亚大学的Hench教授提出，当时所用的生物材料会被人体排斥，并在材料周围产生伤痕组织而导致材料失效。而生物活性玻璃在被移植到活体之后，它会在体液中发生降解，并且其降解产物（主要包括硅和钙）可以作为生物信号，促进骨祖细胞的分化并形成成骨细胞,进而调节骨组织的矿物化以及重建。从玻璃中释放的以及体液中的钙和磷会重新沉积在生物活性玻璃表面，生成碳化羟基磷灰石，并与新生成的骨组织结合在一起，这种特性称之为体内生物活性。Hench教授提出的生物活性玻璃引发了这个领域的研究热潮，研究人员通过改变化学组成以及微观结构来提升生物活性玻璃的生物活性和可加工行，并使其释放的溶解产物有助于新骨的生成。检测生物活性玻璃的体内生物活性通常需要动物实验，但这类实验通常要耗费大量资源，而且会涉及到道德问题。而Kokubo等研究人员发明的模拟体液因其有于血浆相似的无机组分，可以用于生物活性材料的初步筛选。生物活性玻璃在模拟体液中浸泡之后，表面也会生成碳化羟基磷灰石，这种在不存在细胞的情况下生成碳化羟基磷灰石的特性称之为体外生物活性。对于对于硅酸盐生物活性玻璃而言，它们体外生物活性与体内生物活性有着很好的相关性。 Hench教授提出的生物活性玻璃是一种磷硅酸盐玻璃，并含有大量的氧化钠和氧化钙，具有很好的体内降解性。生物活性玻璃中的硅氧四面体主要是以链状，环状，或平面状的形式存在，而其中的磷则主要是以正磷酸盐的形式存在。磷的这种存在形式会使其很容易地从玻璃中释放出来，并促进玻璃表面碳化羟基磷灰石层的生成。先前有关磷硅酸盐生物活性玻璃的生物活性的研究表明，玻璃表面羟基磷灰石的生成量与正磷酸盐的含量以及硅氧四面体的聚合度有关，但对于这两者的具体影响还存在争议。本论文采用红外光谱定量的方式，研究了玻璃组成与体外生物活性之间的关系，并发现较高的正磷酸盐含量可以降低硅氧四面体的聚合度对于生物活性的影响。我们的研究提供了一种新的设计生物活性玻璃的方式，那就是同时使用较高的磷酸盐含量（摩尔含量在0.04和0.06之间）和硅氧四面体的聚合度，而且利用玻璃较高的聚合

朵朹度来降低其在加工过程的结晶的可能性。最近被提出的硼磷硅酸盐玻璃是在磷酸盐玻璃的基础上，逐渐将二氧化硅等摩尔替换成三氧化二硼。硼的加入不但可以改变磷硅酸盐玻璃的降解速度，还可以使其更完整地转化成碳化羟基磷灰石。硼本身也会促进血管新生和纤维母细胞中RNA的合成。本论文使用了固体核磁共振来和分子动力学模拟来研究磷硼硅酸盐玻璃的微观结构。磷硼硅酸盐中的磷以正磷酸盐为主，还有少部分的磷氧四面体会与硼氧以及硅氧四面体相连。玻璃中硅氧四面体会组成链状和环状，硼是以三角形硼氧BO3单元和硼氧四面体形式存在。虽然硼氧四面体之间的直接连接会导致负电荷的局部聚集，但是我们通过硼硼之间的偶极作用证明了他们的存在，而且含量仅稍微低于随机模型给出的预测值。同时，硼氧四面体之间的连接在硼硅酸盐玻璃中也广泛存在。

朶朰 7. Acknowledgements

I would like to express my tremendous thanks to my supervisor Mattias Edén. He is critical about the design of experiments, data collecting and paper writ- ing, which sets a good model for me to follow. His ample knowledge in NMR theory and practical experiences in optimizing NMR experiments benefitted me a lot in pursuing my PhD degree. Most importantly, I have learned from him how to analyze and solve problems in a systematic way. Without his kind- hearted help, I would not have finish my PhD study and have a chance to write this acknowledgment. I am grateful to my co-supervisor Baltzar Stevensson. Without his ded- icated work on the molecular dynamics simulations, we could not have presented a complete story of the borophosphosilicate glass structures. He is also an expert in mathematics and programming, and I can always get a satisfying answer from him. I would also like to express my sincere gratitude to the se- nior scientists in the physical chemistry division, Arnold Maliniak and Jozef Kowalewski, for their guidance and support. I want to express my gratitude to Renny Mathew, who helped me a lot at the beginning of my PhD study and gave me plenty hands-on experience on running the solid-state NMR. My sincere thanks to Zoltán Bacsik for his help with FTIR and UV–Vis, Jekabs Grins for his patience with all my XRD-related questions and help with the high-temperature furnace, and Kjell Jansson for his help and suggestions in running SEM experiments. A special thank to Wei-Chih Liao makes me think about my future career, a puzzle probably relevant to many PhD graduates. I would like also thank other (former) group members, Meng Ge, Hua Guo, Diana Bernin, Aleksander Jaworski, and Gholamhasan Teymoori, as well as all other staffs at the Depart- ment of Materials and Environment Chemistry, who has helped me in one way or another. I am really appreciated that Arnold Maliniak, Wei-Chih Liao, Baltzar Stevens- son, and Mattias Edén would like to spend your precious time on improving my thesis. The way to the doctoral degree is never flat and accompanied with many hard times. I really appreciate my family members being the most attentive listeners. They would like to hear my complaining and find all the ways to

朶朱 cheer me up again. Without their support, it is hard to believe that I can make the PhD degree come true. Special thanks to Patric, who help me with the Swedish summary “sammanfattning” and make my almost ﬁve-year life in Sweden colorful.

致谢

感谢我亲爱的家人，虽然我们相隔万里，但我一直感受到了你们的无微不至的关怀。读博的征途中充满荆棘，是你们的支持和鼓励，让我一路坚持下来。感谢母亲和已过世近十二年的父亲，是你们赋予了我生命，提供给了我无忧无虑的生活，让我茁壮成长。父亲，你是我化学的启蒙老师，在你工作的实验室里，我对化学产生了一些懵懂的想法。我还记得那块在岩石间结晶出的紫水晶原矿石，它让我感觉到了化学是如此的神奇。父亲，在得知你往生的那一瞬间，我哭了，那是一种如刀绞心脏般的痛苦。还好，我和母亲并没有被生活所击倒，那种丧失亲人的痛苦，只会让我们变得更加坚毅。父亲，您对我的生育和养育之恩，我此生无法报答，遂以此论文告慰您的在天之灵。

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