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Explains the correlation between the physical properties and structure of polymer gels
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.
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:
Autorentext
Takamasa Sakai, PhD 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.
Inhalt
Preface xi
Acknowledgements xiii
Part I Theories 1
1 Single Polymer Chain **3
**Takamasa Sakai
1.1 General Features 3
1.1.1 Conformation of a Polymer Chain 3
1.1.2 Coarse-Graining of a Polymer Chain 4
1.1.3 Free Rotation Model 5
1.2 Statistics of a Single Polymer Chain 7
1.2.1 End-to-End Distance of a 1D Random Walk 7
1.2.2 End-to-End Distance of a 3D Random Walk 10
1.2.3 Force Needed to Stretch an Ideal Chain 12
1.3 Scaling of a Single Polymer Chain 15
1.3.1 Stretching of an Ideal Chain 17
1.3.2 Real Chains 18
1.3.3 Stretching of a Real Chain 19
Column 1: Miscible Gels and Immiscible Gels 21
References 22
2 Polymer Solution **23
**Takamasa Sakai
2.1 Polymer Chains in Solution 23
2.1.1 Chain Swelling in a Good Solvent 23
2.1.2 Existing Conditions of an Ideal Chain and a Real Chain 25
2.2 Effect of Concentration on the Polymer Conformation 26
2.2.1 Overlapping Concentration 26
2.2.2 Semidilute Solution 28
2.2.3 Blobs in Semidilute Solution 29
2.3 Osmotic Pressure of a Polymer Solution 32
2.3.1 Entropy Change in Mixing 33
2.3.3 Basic Equation of Osmotic Pressure 36
2.3.4 Phase Separation of the Polymer Solution 37
2.3.5 Scaling of Osmotic Pressure 40
Column 2: Blob Size of a Polymer Gel 42
References 43
3 Definition of Polymer Gels and Rubber Elasticity **45
**Takamasa Sakai
3.1 Elasticity of Gels 45
3.2 Definition of Polymer Gels 46
3.2.1 Criterion for Gelation by Rheology 47
3.2.2 Criterion for Gelation by Scattering 48
3.3 Mesh Size of a Polymer Gel 49
3.4 Elastic Modulus 51
3.4.1 Affine Network Model 51
3.4.2 Phantom Network Model 54
3.5 Network Strands and Crosslinks 60
3.5.1 Percolate Network Model 62
3.5.2 Bethe Approximation 63
3.6 Topological Interaction 67
3.7 SolGel Transition 69
3.7.1 Gelation Threshold of Bethe Approximation 69
3.7.2 Gelation Threshold from the Percolation Model 70
3.8 Heterogeneity of Polymer Gels 71
Column 3: Elastic Deformation and Plastic Deformation 73
References 74
4 Swelling and Deswelling **77
**Takamasa Sakai
4.1 Changes in the Elastic Modulus Due to Swelling/Deswelling 77
4.1.1 Statistical Model for Networks Consisting of Ideal Chains 78
4.1.2 Scaling for Networks Consisting of Nonideal Chains 79
4.1.3 Scaling for Highly Deswollen Networks 82
4.2 Equilibrium Swelling 85
4.2.1 Scaling Prediction of the Equilibrium Swelling 86
4.2.2 Statistical Mechanics of Equilibrium Swelling 87
4.3 Volume Phase Transition 91
4.3.1 Electrically Neutral Gels 91
4.3.2 Electrically Charged Gels 94
4.4 Swelling/Shrinking Kinetics 95
4.5 Degradation of Polymer Gels 102
4.5.1 Degradation by Cleavage of Specific Bonds 102
4.5.2 Degradation by Cleavage of Nonspecific Bonds 104
Column 4: Diffusions of Polymer Network During Swelling 105
References 106
5 Deformation and Fracture **109
**Takuya Katashima and Takamasa Sakai
5.1 Description of Deformation 109
5.1.1 Displacement Vector 109
5.1.2 Strain Tensor 110
5.1.2.1 Normal Strain 110
5.1.2.2 Shear Strain 111
5.1.3 Principal Direction and Strain 113
5.2 Phenomenological Description of the Strain Energy Density Function 115
5.2.1 Estimation of the Strain Energy Density Function 116 5.3 Molecular Models for the Strain Energy Densit...