Table of Contents
Foreword v
Lessons xi
Literature Basis xiii
1 Introduction to polymer physical chemistry 1
1.1 Targets of this book 1
1.2 Definition of terms 2
1.3 Irregularity of polymers 5
1.3.1 Nonuniformity of monomer connection in a chain 5
1.3.2 Polydispersity in an ensemble of chains 6
1.3.2.1 Derivation of the Schulz-Flory distribution 11
1.3.2.2 Derivation of the Schulz-Zimm distribution 13
1.3.2.3 Characteristic averages of the Schulz-Flory and Schulz-Zimm distribution 14
1.4 Properties of polymers in contrast to low molar mass materials 16
1.5 Polymers as soft matter 18
1.6 History of polymer science 20
2 Ideal polymer chains 25
2.1 Coil conformation 26
2.1.1 Micro- and macroconformations of a polymer chain 26
2.1.2 Measures of size of a polymer coil 29
2.2 Simple chain models 31
2.2.1 The random chain (phantom chain, freely jointed chain) 31
2.2.2 The freely rotating chain 33
2.2.3 The chain with hindered rotation 33
2.2.4 The Kuhn model 34
2.2.5 The rotational isomeric states model 36
2.2.6 Energetic versus entropie influence on the shape of a polymer 38
2.2.7 The persistence length 39
2.2.8 Summary 40
2.3 The Gaussian coil 42
2.4 The distribution of end-to-end distances 43
2.4.1 Random-walk statistics 43
2.5 The free energy of ideal chains 49
2.6 Deformation of ideal chains 49
2.6.1 Entropy elasticity 49
2.6.2 A scaling argument for the deformation of ideal chains 53
2.7 Self-similarity and fractal nature of polymers 55
3 Real polymer chains 59
3.1 Interaction potentials and excluded volume 60
3.2 Classification of solvents 64
3.3 Omnipresence of the Θ-state in polymer melts 66
3.4 The conformation of real chains 68
3.4.1 Coil expansion 68
3.4.2 Flory theory of a polymer in a good solvent 70
3.5 Deformation of real chains 74
3.6 Chain dynamics 78
3.6.1 Brownian motion and diffusion 78
3.6.2 The Rouse model 80
3.6.3 The Zimm model 82
3.6.4 Relaxation modes 84
3.6.5 Subdiffusion 86
3.6.6 Validity of the models 87
4 Polymer thermodynamics 89
4.1 The Flory-Huggins mean-field theory 89
4.1.1 The entropy of mixing 93
4.1.2 The enthalpy of mixing 96
4.1.3 The Flory-Huggins parameter as a function 99
4.1.4 Microscopic demixing 102
4.1.5 Solubility parameters 103
4.2 Phase diagrams 106
4.2.1 Equilibrium and stability 106
4.2.2 Construction of the phase diagram 112
4.2.3 Mechanisms of phase transitions 118
4.2.3.1 Spinodal decomposition 118
4.2.3.2 Nucleation and growth 119
4.3 Osmotic pressure 121
4.3.1 Connection of the second virial coefficient, A2, to the Flory-Huggins parameter, X, and the excluded volume, Ve 125
5 Mechanics and rheology of polymer systems 129
5.1 Fundamentals of rheology 129
5.1.1 Elementary cases of mechanical response 129
5.1.2 Different types of deformation in rheology 131
5.1.3 The tensor form of Hooke's law 133
5.2 Viscoelasticity 135
5.2.1 Elementary types of rheological experiments 136
5.2.1.1 The relaxation experiment 136
5.2.1.2 The creep test 136
5.2.1.3 The dynamic experiment 137
5.3 Complex moduli 138
5.4 Viscous flow 141
5.5 Methodology in rheology 145
5.5.1 Oscillatory shear rheology 145
5.5.2 Microrheology 146
5.5.2.1 Active microrheology 146
5.5.2.2 Passive microrheology 147
5.6 Principles of viscoelasticity 149
5.6.1 Viscoelastic fluids: the Maxwell model 149
5.6.2 Viscoelastic solids: the Kelvin-Voigt model 156
5.6.3 More complex approaches 157
5.7 Superposition principles 159
5.7.1 The Boltzmann superposition principle 160
5.7.2 The thermal activation of relaxation processes 162
5.7.3 Time-temperature superposition 163
5.8 Viscoelastic states of a polymer system 167
5.8.1 Qualitative discussion of the mechanical spectra 167
5.8.2 Quantitative discussion of the mechanical spectra 169
5.9 Rubber elasticity 172
5.9.1 Chemical thermodynamics of rubber elasticity 173
5.9.2 Statistical thermodynamics of rubber elasticity 174
5.9.3 Swelling of rubber networks 182
5.10 Terminal flow and reptation 185
5.10.1 The tube concept 186
5.10.2 Rouse relaxation and reptation 187
5.10.3 Reptation and diffusion 190
5.10.4 Constraint release 192
6 Scattering analysis of polymer systems 193
6.1 Basics of scattering 193
6.2 Scattering regimes 196
6.3 Structure and form factor 197
6.4 Light scattering 202
6.4.1 Static light scattering 202
6.4.2 Dynamic light scattering 210
7 Closing remarks 213
Index 215
