Details

Physics of Polymer Gels


Physics of Polymer Gels


1. Aufl.

von: Takamasa Sakai

124,99 €

Verlag: Wiley-VCH
Format: EPUB
Veröffentl.: 27.02.2020
ISBN/EAN: 9783527346554
Sprache: englisch
Anzahl Seiten: 304

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Beschreibungen

Explains the correlation between the physical properties and structure of polymer gels<br> <br> This book elucidates in detail the physics of polymer gels and reviews their unique properties that make them attractive for innumerable applications. Geared towards experienced researchers and entrants to the field, it covers rubber elasticity, swelling and shrinking, deformation and fracture of as well as mass transport in polymer gels, enabling the readers to purposefully design polymer gels fit for specific purposes.<br> <br> Divided into two parts, Physics of Polymer Gels starts by explaining the statistical mechanics and scaling of a polymer chains, and that of polymer solutions. It then introduces the structure of polymer gels and explains the rubber elasticity, which predicts the solid-like nature of polymer gels. Next, it describes swelling/deswelling, which can be understood by combining the rubber elasticity and the osmotic pressure of a polymer solution. Large deformation and fracture, and the diffusion of substances in polymer gels, which are essential for practical applications, are also introduced. The last half of the book contains the authors' experimental results using Tetra-PEG gels and provides readers with the opportunity to examine and compare it with the first half in order to understand how to utilize the models to experiments. This title:<br> <br> * Is the first book dedicated to the physics of polymer gels<br> * Describes in detail the properties of polymer gels and their underlying physics, facilitating the development of novel, polymer gel-based applications<br> * Serves as a reference for all relevant polymer gel properties and their underlying physics<br> * Provides a unified treatment of the subject, explaining the physical properties of polymer gels within a common nomenclature framework<br> Physics of Polymer Gels is a must-have book for experienced researchers, such as polymer chemists, materials scientists, organic chemists, physical chemists, and solid-state physicists, as well as for newcomers to the field.
<p>Preface xi</p> <p>Acknowledgements xiii</p> <p><b>Part I Theories </b><b>1</b></p> <p><b>1 Single Polymer Chain </b><b>3<br /></b><i>Takamasa Sakai</i></p> <p>1.1 General Features 3</p> <p>1.1.1 Conformation of a Polymer Chain 3</p> <p>1.1.2 Coarse-Graining of a Polymer Chain 4</p> <p>1.1.3 Free Rotation Model 5</p> <p>1.2 Statistics of a Single Polymer Chain 7</p> <p>1.2.1 End-to-End Distance of a 1D Random Walk 7</p> <p>1.2.2 End-to-End Distance of a 3D Random Walk 10</p> <p>1.2.3 Force Needed to Stretch an Ideal Chain 12</p> <p>1.3 Scaling of a Single Polymer Chain 15</p> <p>1.3.1 Stretching of an Ideal Chain 17</p> <p>1.3.2 Real Chains 18</p> <p>1.3.3 Stretching of a Real Chain 19</p> <p>Column 1: Miscible Gels and Immiscible Gels 21</p> <p>References 22</p> <p><b>2 Polymer Solution </b><b>23<br /></b><i>Takamasa Sakai</i></p> <p>2.1 Polymer Chains in Solution 23</p> <p>2.1.1 Chain Swelling in a Good Solvent 23</p> <p>2.1.2 Existing Conditions of an Ideal Chain and a Real Chain 25</p> <p>2.2 Effect of Concentration on the Polymer Conformation 26</p> <p>2.2.1 Overlapping Concentration 26</p> <p>2.2.2 Semidilute Solution 28</p> <p>2.2.3 Blobs in Semidilute Solution 29</p> <p>2.3 Osmotic Pressure of a Polymer Solution 32</p> <p>2.3.1 Entropy Change in Mixing 33</p> <p>2.3.3 Basic Equation of Osmotic Pressure 36</p> <p>2.3.4 Phase Separation of the Polymer Solution 37</p> <p>2.3.5 Scaling of Osmotic Pressure 40</p> <p>Column 2: Blob Size of a Polymer Gel 42</p> <p>References 43</p> <p><b>3 Definition of Polymer Gels and Rubber Elasticity </b><b>45<br /></b><i>Takamasa Sakai</i></p> <p>3.1 Elasticity of Gels 45</p> <p>3.2 Definition of Polymer Gels 46</p> <p>3.2.1 Criterion for Gelation by Rheology 47</p> <p>3.2.2 Criterion for Gelation by Scattering 48</p> <p>3.3 Mesh Size of a Polymer Gel 49</p> <p>3.4 Elastic Modulus 51</p> <p>3.4.1 Affine Network Model 51</p> <p>3.4.2 Phantom Network Model 54</p> <p>3.5 Network Strands and Crosslinks 60</p> <p>3.5.1 Percolate Network Model 62</p> <p>3.5.2 Bethe Approximation 63</p> <p>3.6 Topological Interaction 67</p> <p>3.7 Sol–Gel Transition 69</p> <p>3.7.1 Gelation Threshold of Bethe Approximation 69</p> <p>3.7.2 Gelation Threshold from the Percolation Model 70</p> <p>3.8 Heterogeneity of Polymer Gels 71</p> <p>Column 3: Elastic Deformation and Plastic Deformation 73</p> <p>References 74</p> <p><b>4 Swelling and Deswelling </b><b>77<br /></b><i>Takamasa Sakai</i></p> <p>4.1 Changes in the Elastic Modulus Due to Swelling/Deswelling 77</p> <p>4.1.1 Statistical Model for Networks Consisting of Ideal Chains 78</p> <p>4.1.2 Scaling for Networks Consisting of Nonideal Chains 79</p> <p>4.1.3 Scaling for Highly Deswollen Networks 82</p> <p>4.2 Equilibrium Swelling 85</p> <p>4.2.1 Scaling Prediction of the Equilibrium Swelling 86</p> <p>4.2.2 Statistical Mechanics of Equilibrium Swelling 87</p> <p>4.3 Volume Phase Transition 91</p> <p>4.3.1 Electrically Neutral Gels 91</p> <p>4.3.2 Electrically Charged Gels 94</p> <p>4.4 Swelling/Shrinking Kinetics 95</p> <p>4.5 Degradation of Polymer Gels 102</p> <p>4.5.1 Degradation by Cleavage of Specific Bonds 102</p> <p>4.5.2 Degradation by Cleavage of Nonspecific Bonds 104</p> <p>Column 4: Diffusions of Polymer Network During Swelling 105</p> <p>References 106</p> <p><b>5 Deformation and Fracture </b><b>109<br /></b><i>Takuya Katashima and Takamasa Sakai</i></p> <p>5.1 Description of Deformation 109</p> <p>5.1.1 Displacement Vector 109</p> <p>5.1.2 Strain Tensor 110</p> <p>5.1.2.1 Normal Strain 110</p> <p>5.1.2.2 Shear Strain 111</p> <p>5.1.3 Principal Direction and Strain 113</p> <p>5.2 Phenomenological Description of the Strain Energy Density Function 115</p> <p>5.2.1 Estimation of the Strain Energy Density Function 116</p> <p>5.3 Molecular Models for the Strain Energy Density Function 120</p> <p>5.3.1 Neo-Hookean Model 120</p> <p>5.3.2 Inverse Langevin Model 121</p> <p>5.4 Scaling for Large Deformation 125</p> <p>5.5 Fracture Behavior of Polymer Gels 126</p> <p>5.5.1 Griffith Model 127</p> <p>5.5.2 Lake–Thomas Model 128</p> <p>5.6 Mesh Size Estimated from Elastic Modulus and Finite Extensibility 130</p> <p>Column 5: Linear Viscoelasticity and Nonlinear Viscoelasticity 134</p> <p>References 134</p> <p><b>6 Mass Transport in Polymer Gels </b><b>137<br /></b><i>Xiang Li and Takamasa Sakai</i></p> <p>6.1 Thermal Motion and Brownian Motion 137</p> <p>6.1.1 Diffusion Coefficient and Relaxation Time 138</p> <p>6.1.2 Diffusion and Migration 139</p> <p>6.2 Diffusion in Dilute Polymer Solutions 139</p> <p>6.2.1 Diffusion of a Hard Sphere 139</p> <p>6.2.2 Rouse Model 140</p> <p>6.2.3 Zimm Model 141</p> <p>6.3 Diffusion in Semidilute Polymer Solutions and Polymer Gels 142</p> <p>6.3.1 Obstruction Model 142</p> <p>6.3.2 Hydrodynamic Model 144</p> <p>6.3.3 Free Volume Model 145</p> <p>6.3.4 Reptation Model 146</p> <p>6.3.5 Entropic Trapping Model 147</p> <p>Column 6: Effects of Mesh Sizes on Mass Transport 149</p> <p>References 149</p> <p><b>7 Tetra Gel as a Near-Ideal Polymer Network </b><b>153<br /></b><i>Takamasa Sakai</i></p> <p>7.1 Ideal Polymer Network 153</p> <p>7.2 Tetra-PEG Gel 155</p> <p>7.3 Structure Tuning of Tetra-PEG Gels 155</p> <p>References 158</p> <p><b>8 Sol-Gel Transition </b><b>161<br /></b><i>Takamasa Sakai</i></p> <p>8.1 Determination of Sol–Gel Transition by Rheometry 161</p> <p>8.2 Phase Diagram 161</p> <p>8.3 Fractal Dimension at the Critical Point 163</p> <p>8.4 Critical Behavior of Elastic Modulus 165</p> <p>8.5 Reaction Kinetics of a Gelling System 166</p> <p>8.5.1 Hydrolysis Kinetics of Tetra-PEG–OSu 167</p> <p>8.5.2 Gelation Kinetics of Tetra-PEG Gel 167</p> <p>References 169</p> <p><b>9 Structural Analysis by Light and Neutron Scattering </b><b>173<br /></b><i>Takamasa Sakai and Xiang Li</i></p> <p>9.1 Scattering Curves of Tetra-PEG Gels 173</p> <p>9.2 Scattering Curves of Stretched Tetra-PEG Gels 176</p> <p>References 177</p> <p><b>10 Elastic Modulus </b><b>179<br /></b><i>Takamasa Sakai and Yuki Yoshikawa</i></p> <p>10.1 Effect of Connectivity 179</p> <p>10.2 Effect of the Polymer Concentration and Network Strand Length 180</p> <p>References 182</p> <p><b>11 Large Deformation </b><b>183<br /></b><i>Takamasa Sakai and Takuya Katashima</i></p> <p>11.1 Estimation of Strain Energy Density Function 183</p> <p>11.1.1 Applicability of Neo-Hookean Model 184</p> <p>11.1.2 Finite Extensibility Effect 185</p> <p>11.1.3 Coupling Between Different Principal Axes 186</p> <p>11.1.4 Extended Gent Model 187</p> <p>11.2 Cross-Coupling 189</p> <p>11.2.1 Effects of the Fraction of Elastically Effective and Ineffective Chains 190</p> <p>11.2.2 Effects of Polymer Volume Fraction and Network Strand Length 191</p> <p>11.2.3 Effect of the Fraction of Guest Chains 193</p> <p>11.2.4 Conjecture on Origin of Cross-Coupling 196</p> <p>11.3 Stretchability in Uniaxial Stretching 196</p> <p>11.3.1 Kuhn Model 197</p> <p>11.3.2 Effect of Connectivity 197</p> <p>11.3.3 Effect of Polymer Concentration and Network Strand Length 198</p> <p>11.3.4 Semiempirical Model Based on Experiments 200</p> <p>References 201</p> <p><b>12 Fracture </b><b>205<br /></b><i>Takamasa Sakai and Takeshi Fujiyabu</i></p> <p>12.1 Estimation of Fracture Energy 205</p> <p>12.2 Conversion-Tuned Tetra-PEG Gels 207</p> <p>12.3 Effects of Network Concentration and Strand Length 208</p> <p>12.4 Bimodal Tetra-PEG Gels 209</p> <p>12.5 Summary 210</p> <p>References 211</p> <p><b>13 Mass Transport </b><b>213<br /></b><i>Takamasa Sakai and Takeshi Fujiyabu</i></p> <p>13.1 Diffusion of Water Molecules 213</p> <p>13.1.1 Estimation of Diffusion Coefficient of Water Molecules 213</p> <p>13.1.2 Effect of Structural Parameters 214</p> <p>13.1.3 Applicability of Theoretical Models 215</p> <p>13.1.4 Effect of Correlation Length on Diffusion 216</p> <p>13.2 Migration of Water Molecules in Hydrogels 217</p> <p>13.2.1 Water Permeation Through Hydrogel 217</p> <p>13.2.2 Effect of Structural Parameters on Friction Coefficient 219</p> <p>13.2.3 Effect of Correlation Length on Friction Coefficient 220</p> <p>13.3 Electro-Osmotic Flow in Electrically Charged Gels 221</p> <p>13.3.1 Electro-Osmosis in an Electrically Balanced System 221</p> <p>13.3.2 Electro-Osmosis in an Electrically Imbalanced System 222</p> <p>13.3.3 Sum Rule of Electro-Osmotic Flow and Electrophoretic Motion 224</p> <p>13.4 Migration of Small Double-Stranded DNAs 225</p> <p>13.4.1 Electrophoresis of dsDNA in Tetra-PEG Gels and Solutions 225</p> <p>13.4.2 Semiempirical Model 226</p> <p>13.4.3 Effect of Correlation Length on Electrophoretic Mobility 228</p> <p>13.4.4 Interaction Between Elastic Blobs and Contour of dsDNA 229</p> <p>13.5 Migration of Large Double-Stranded DNAs 229</p> <p>13.5.1 Electrophoresis of Large dsDNA in Tetra-PEG Gels and Solutions 230</p> <p>13.5.2 Transition of the Migration Mechanism 231</p> <p>References 233</p> <p><b>14 Osmotic Pressure </b><b>235<br /></b><i>Takamasa Sakai</i></p> <p>14.1 Osmotic Pressure of Gels and Prepolymer Solutions 235</p> <p>14.2 Change in Osmotic Pressure During Gelation 235</p> <p>14.3 <i>c</i>* Theorem at the Gelation Threshold 237</p> <p>References 239</p> <p><b>15 Swelling </b><b>241<br /></b><i>Takamasa Sakai and Takeshi Fujiyabu</i></p> <p>15.1 Elastic Modulus of Swollen and Highly Deswollen Gels 241</p> <p>15.2 Equilibrium Swelling 243</p> <p>15.3 Swelling Kinetics 244</p> <p>15.3.1 Examination of Swelling Equation 244</p> <p>15.3.2 Cooperative Diffusion Coefficient 245</p> <p>References 246</p> <p><b>16 Degradation </b><b>249<br /></b><i>Takamasa Sakai and Takeshi Fujiyabu</i></p> <p>16.1 Cleavage of a Specific Site 249</p> <p>16.2 Cleavage of Nonspecific Sites 253</p> <p>16.2.1 Initial Swelling Equilibrium 254</p> <p>16.2.2 Degradation Behavior of Tetra-PEG Gels 254</p> <p>16.2.3 A Model for Degradation 255</p> <p>16.2.4 Estimation of Degradation Rate Constants 257</p> <p>References 258</p> <p><b>17 Control Over Swelling of Injectable Gel </b><b>26<br /></b><i>Takamasa Sakai and Takeshi Fujiyabu</i></p> <p>17.1 Nonswellable Gels 261</p> <p>17.2 Nonosmotic Gel 265</p> <p>17.3 Oligo-Tetra-PEG Gel 269</p> <p>References 275</p> <p>Index 277</p>
<p><b><i>Takamasa Sakai, PhD</i></b><i> is Professor in the Department of Bioengineering, Graduate School of Engineering, at The University of Tokyo, Japan. His research is focused on polymer physics and structural biomaterials and was recognized with numerous awards, including the Award for the Encouragement of Research in Polymer Science from the Japanese Polymer Society and the Sumitomo Bakelite Award.</i>
<p><b>Explains the correlation between the physical properties and structure of polymer gels</b> <p>This book elucidates in detail the physics of polymer gels and reviews their unique properties that make them attractive for innumerable applications. Geared towards experienced researchers and entrants to the field, it covers rubber elasticity, swelling and shrinking, deformation and fracture of as well as mass transport in polymer gels, enabling the readers to purposefully design polymer gels fit for specific purposes. <p>Divided into two parts, <i>Physics of Polymer Gels</i> starts by explaining the statistical mechanics and scaling of a polymer chains, and that of polymer solutions. It then introduces the structure of polymer gels and explains the rubber elasticity, which predicts the solid-like nature of polymer gels. Next, it describes swelling/deswelling, which can be understood by combining the rubber elasticity and the osmotic pressure of a polymer solution. Large deformation and fracture, and the diffusion of substances in polymer gels, which are essential for practical applications, are also introduced. The last half of the book contains the authors' experimental results using Tetra-PEG gels and provides readers with the opportunity to examine and compare it with the first half in order to understand how to utilize the models to experiments. This title: <ul> <li>Is the first book dedicated to the physics of polymer gels</li> <li>Describes in detail the properties of polymer gels and their underlying physics, facilitating the development of novel, polymer gel-based applications</li> <li>Serves as a reference for all relevant polymer gel properties and their underlying physics</li> <li>Provides a unified treatment of the subject, explaining the physical properties of polymer gels within a common nomenclature framework</li> </ul> <p><i>Physics of Polymer Gels</i> is a must-have book for experienced researchers, such as polymer chemists, materials scientists, organic chemists, physical chemists, and solid-state physicists, as well as for newcomers to the field.

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