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《高分子物理》课程教学资源（书籍文献）Polymer Physics——A Molecular Approach, Springer, 2013 polymerphysics

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3 Conformation Statistics and Entropic Elasticity . . . . . . . . . . . . . . . 33 3.1 Gaussian Distribution of End-to-End Distances of Polymer Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Statistical Mechanics of Rubber Elasticity . . . . . . . . . . . . . . . . . 35 3.2.1 Mechanics of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.2 Thermodynamics of Elasticity . . . . . . . . . . . . . . . . . . . . 35 3.2.3 Entropic Elasticity of a Deformed Polymer Coil . . . . . . . 37 3.2.4 Statistical Thermodynamics of a Cross-Linked Polymer Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 Scaling Analysis of Real-Chain Conformations . . . . . . . . . . . . . . . . 43 4.1 What Is the Scaling Analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Single-Chain Conformation in Polymer Solutions . . . . . . . . . . . . 44 4.2.1 An Introduction of Polymer Solutions . . . . . . . . . . . . . . . 44 4.2.2 Single-Chain Conformation in Athermal Dilute Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.3 Single-Chain Conformation in Athermal Concentrated Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.4 Single-Chain Conformation in Thermal Dilute Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Single-Chain Conformation in Polyelectrolyte Solutions . . . . . . . 59 4.4 Single-Chain Conformation Under External Forces . . . . . . . . . . 66 4.4.1 Stretching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4.2 Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4.3 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Part II Chain Motion 5 Scaling Analysis of Polymer Dynamics . . . . . . . . . . . . . . . . . . . . . . 77 5.1 Simple Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Short Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.3 Long Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6 Polymer Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1 Characteristics of Polymer Deformation . . . . . . . . . . . . . . . . . . . 93 6.2 Relaxation of Polymer Deformation . . . . . . . . . . . . . . . . . . . . . 97 6.2.1 Relaxation Via Molecular Motions . . . . . . . . . . . . . . . . . 97 6.2.2 Boltzmann Superposition Principle . . . . . . . . . . . . . . . . . 100 6.2.3 Time–Temperature Superposition Principle . . . . . . . . . . . 103 6.2.4 Dynamic Mechanical Analysis . . . . . . . . . . . . . . . . . . . . 105 6.3 Glass Transition and Fluid Transition . . . . . . . . . . . . . . . . . . . . 109 6.3.1 Glass Transition Phenomena . . . . . . . . . . . . . . . . . . . . . 109 6.3.2 Glass Transition Theories . . . . . . . . . . . . . . . . . . . . . . . . 111 x Contents

6.3.3 Chemical-Structure Dependence of Glass Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.3.4 Fluid Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.4 Conventional Mechanical Analysis . . . . . . . . . . . . . . . . . . . . . . 119 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7 Polymer Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.1 Introduction to Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.1.1 What Is Rheology? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.1.2 Classification of the Flow . . . . . . . . . . . . . . . . . . . . . . . . 127 7.1.3 Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.1.4 Non-Newtonian Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.2 Characteristics of Polymer Flow . . . . . . . . . . . . . . . . . . . . . . . . 132 7.3 Viscoelastic Phenomena of Polymer Flow . . . . . . . . . . . . . . . . . 140 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Part III Chain Assembly 8 Statistical Thermodynamics of Polymer Solutions . . . . . . . . . . . . . 147 8.1 Polymer-Based Multi-Component Systems . . . . . . . . . . . . . . . . 147 8.2 Flory-Huggins Lattice Theory of Polymer Solutions . . . . . . . . . . 149 8.2.1 Advantages of the Lattice Model . . . . . . . . . . . . . . . . . . 149 8.2.2 Basic Assumptions of Flory-Huggins Lattice Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 8.2.3 Calculation of Mixing Entropy . . . . . . . . . . . . . . . . . . . . 152 8.2.4 Calculation of Mixing Heat and Free Energy . . . . . . . . . . 155 8.3 Developments of Flory-Huggins Theory . . . . . . . . . . . . . . . . . . 156 8.3.1 Simple Additions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.3.2 Compressible Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.3.3 Dilute Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8.3.4 Concentration Dependence of Interaction Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.3.5 Lattice-Cluster Theory Considering Molecular Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.3.6 Semi-Flexible Polymers . . . . . . . . . . . . . . . . . . . . . . . . . 163 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 9 Polymer Phase Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.1 Thermodynamics of Phase Separation . . . . . . . . . . . . . . . . . . . . 167 9.2 Kinetics of Phase Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.3 Microphase Separation of Diblock Copolymers . . . . . . . . . . . . . 179 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 10 Polymer Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.1 Thermodynamics of Polymer Crystallization . . . . . . . . . . . . . . 187 10.2 Statistical Thermodynamics of Polymer Crystallization . . . . . . . 192 Contents xi

10.3 Crystalline Structures of Polymers . . . . . . . . . . . . . . . . . . . . . . 197 10.3.1 Hierarchical Crystalline Structures . . . . . . . . . . . . . . . 197 10.3.2 Unit Cells of Polymer Crystals . . . . . . . . . . . . . . . . . . 198 10.3.3 Folded-Chain Lamellar Crystals . . . . . . . . . . . . . . . . . 200 10.3.4 Morphology of Polymer Crystals . . . . . . . . . . . . . . . . 203 10.4 Kinetics of Polymer Crystallization . . . . . . . . . . . . . . . . . . . . . 208 10.4.1 Nucleation of Polymer Crystallization . . . . . . . . . . . . . 208 10.4.2 Microscopic Mechanism of Polymer Crystal Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 10.4.3 Overall Kinetic Analysis of Polymer Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 11 Interplay Between Phase Separation and Polymer Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11.1 Complexity of Polymer Phase Transitions . . . . . . . . . . . . . . . . 223 11.2 Enhanced Phase Separation in the Blends Containing Crystallizable Polymers . . . . . . . . . . . . . . . . . . . . . 226 11.3 Accelerated Crystal Nucleation in the Concentrated Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 11.4 Accelerated Crystal Nucleation at Liquid Interfaces . . . . . . . . . 230 11.5 Accelerated Crystal Nucleation in the Single-Chain Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 11.6 Interplay of Phase Transitions in Diblock Copolymers . . . . . . . 235 11.7 Implication of Interplays in Biological Systems . . . . . . . . . . . . 236 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 xii Contents

Chapter 1 Introduction 1.1 What Are Polymers? Polymers are our molecular views on certain chemical substances. The views have been established in our long-lasting exploration and exploitation of materials in nature. The term “polymers” is commonly used to describe a broad range of materials, from synthetic materials, such as plastics, rubbers, fibers, coatings, filtration membranes, adsorption resins and adhesives; to natural materials, such as cellulose, starches, natural rubbers, silks, hairs, and chitins; and even to the prototypes of bio-macromolecules, such as DNA, RNA and proteins, which are the basic substances for highly diverse creatures. There is a long history for us to recognize polymers. Let us start with the early evolution of our molecular views (Rupp 2005). As early as in the middle of 500 BC, the Greek philosopher Leucippus and his follower Democritus suggested that, an indivisible minimum substance called atoms constituted our world. Almost at the same time, Empedocles proposed that the world was formed by four elements, i.e., water, air, fire, and earth. Later on, Plato set up the Academy at Athens, inherited the atomic theory, and also advocated the four-element theory on the basis of the formal logic system of geometries. In the next 2,000 years, the alchemists discovered more and more elements. Till to eighteenth century, Lavoisier named the elements of oxygen and hydrogen, and proved the mass conservation in chemical reactions (Lavoisier et al. 1783). This milestone delivered the birth of chemistry. At the beginning of nineteenth century, Dalton proposed that each molecule contains a fixed ratio of atoms among several elements (Dalton 1808). This theory was another milestone that opened the gate to modern chemistry. Since then, the atomic and molecular theory became the main stream of chemistry. In the field of physics, in 1880s, Boltzmann invented statistical thermodynamics according to the Maxwell’s theory of the motions of atoms (Boltzmann 1872). In 1905, Einstein elucidated that the stochastic Brownian motions of atoms are mainly W. Hu, Polymer Physics, DOI 10.1007/978-3-7091-0670-9_1, # Springer-Verlag Wien 2013 1

I Introduction for their().The epoch-markin ideas above,along with the flourishing of quantum mechanics created a solid foundation for atomic and molecular views of chemical substances.The atomic view has been reinforced by modern techniques,for example,scanning tunneling microscopy,which is capable of visualizing and even manipulating individual atoms (Binnig and Rohrer 1986).Nowadays,we define the molecules,including ions and mono-atomic molecules,as the smallest units that maintain the chemical properties of pure substances,and define the atoms as the smallest units that rep nt the prop s of eleme nts in molecules and in chemical reactior Molecule al na the che cal operties, imply tha their mola too l ase Th hen Stau cromolecules"in 1920(St from the whole academic community.However,he unflinchingly fought for his argument,and collected various concrete evidences to prove that the chemical compounds in his hand contained more than 1.000 atoms,and their molar masses reached more than 10 kilograms per mole.He eventually persuaded his colleagues in the community and won the Nobel Prize in Chemistry in 1953 for his work on romolecules.Nowadays.it has been well known that the molar msof ould he ral P rem rep wouldno affec their or physical properties concep of Macromolecules"has indeed challenged our common sense that molecules are the smallest structural units maintaining the properties of pure substances. In 1996,the International Union of Pure and Applied Chemistry (IPUAC) published the recommendation of polymer terms (Jenkins et al.1996).It provided the definition below: Macromol ecule:polymer molecule A m which ess of low relative molecular mass Notes: (1)In many cases,especia ally for synthetic polymers,a molecule can be regarded as having macromolecu for which the properties may a high relativ mass a and e ntiall tition of units ed actu mocuof lowreive molecular mass it may be describedeithr lar or polymeric.or by polymer used adjectivally. The definition above is flexible enough to accommodate the diverse macromo lecular compounds encountered by chemists.But such a definition is not satisfac tory to physicists,because it does not reflect the basic molecular structure that determines most of the unique physical behaviors of polymers

responsible for their self-diffusion in the liquid (Einstein 1905). The epoch-marking ideas above, along with the flourishing of quantum mechanics, created a solid foundation for atomic and molecular views of chemical substances. The atomic view has been reinforced by modern techniques, for example, scanning tunneling microscopy, which is capable of visualizing and even manipulating individual atoms (Binnig and Rohrer 1986). Nowadays, we define the molecules, including ions and mono-atomic molecules, as the smallest units that maintain the chemical properties of pure substances, and define the atoms as the smallest units that represent the properties of elements in molecules and in chemical reactions. Molecules, as the minimal units maintaining the chemical properties, imply that their molar mass could not be too large. Therefore, when Staudinger proposed the concept of “Macromolecules” in 1920 (Staudinger 1920), he met a strong objection from the whole academic community. However, he unflinchingly fought for his argument, and collected various concrete evidences to prove that the chemical compounds in his hand contained more than 1,000 atoms, and their molar masses reached more than 10 kilograms per mole. He eventually persuaded his colleagues in the community and won the Nobel Prize in Chemistry in 1953 for his work on macromolecules. Nowadays, it has been well known that the molar mass of polymers could be so large that, removing several repeating units would not significantly affect their chemical or physical properties. The concept of “Macromolecules” has indeed challenged our common sense that molecules are the smallest structural units maintaining the properties of pure substances. In 1996, the International Union of Pure and Applied Chemistry (IPUAC) published the recommendation of polymer terms (Jenkins et al. 1996). It provided the definition below: Macromolecule; polymer molecule A molecule of high relative molecular mass, the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass. Notes: (1) In many cases, especially for synthetic polymers, a molecule can be regarded as having a high relative molecular mass if the addition or removal of one or a few of the units has a negligible effect on the molecular properties. This statement fails in the case of certain macromolecules for which the properties may be critically dependent on fine details of the molecular structure. (2) If a part or the whole of the molecule has a high relative molecular mass and essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass, it may be described as either macromolecular or polymeric, or by polymer used adjectivally. The definition above is flexible enough to accommodate the diverse macromolecular compounds encountered by chemists. But such a definition is not satisfactory to physicists, because it does not reflect the basic molecular structure that determines most of the unique physical behaviors of polymers. 2 1 Introduction

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