A molecular‐kinetic theory, which explains the temperature dependence of relaxation behavior in glass‐forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region, is presented. The size of this cooperatively rearranging region is shown to be determined by configuration restrictions in these glass‐forming liquids and is expressed in terms of their configurational entropy. The result of the theory is a relation practically coinciding with the empirical WLF equation. Application of the theory to viscosimetric experiments permits evaluation of the ratio of the kinetic glass temperature Tg (derived from usual ``quasistatic'' experiments) to the equilibrium second‐order transition temperature T2 (indicated by either statistical‐mechanical theory or extrapolations of experimental data) as well as the hindrance‐free energy per molecule. These parameters have been evaluated for fifteen substances, the experimental data for which were available. Hindrance‐free energies ...

On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids

A review of dielectric data for a wide range of solids proves the existence of a remarkable ‘universality’ of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations. Certain unique features of the universal behaviour strongly suggest the dominant role of many-body interactions.

The ‘universal’ dielectric response

A brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law. It is shown that the universal law is indeed found in a remarkable variety of physical and chemical situations, and this is deemed to merit a special attempt at finding a suitably general theoretical model. Several such models are briefly described, and a novel very general approach based on the so-called energy criterion is introduced. It is concluded that it is not yet possible to establish with certainty the validity of any of the models. >

The universal dielectric response

Block copolymers are macromolecules composed of sequences, or blocks, of chemically distinct repeat units. The development of this field originated with the discovery of termination-free anionic polymerization, which made possible the sequential addition of monomers to various carbanion-ter­ minated ("living") linear polymer chains. Polymerization of just two dis­ tinct monomer types (e.g. styrene and isoprene) leads to a class of materials referred to as AB block copolymers. Within this class, a variety of molec­ ular architectures is possible. For example, the simplest combination, obtained by the two-step anionic polymerization of A and B monomers, is an (A-B) dioblock copolymer. A three-step reaction provides for the preparation of (ABA) or (BAB) triblock copolymer. Alternatively, "living" diblock copolymers can be reacted with an n-functional coupling agent to produce (A-B)n star-block copolymers, where n = 2 constitutes a triblock copolymer. Several representative (A-B)n block copolymer architectures

Block Copolymer Thermodynamics: Theory and Experiment

We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

Reptation of a Polymer Chain in the Presence of Fixed Obstacles

The Nature of Viscoelastic Behavior. Illustrations of Viscoelastic Behavior of Polymeric Systems. Exact Interrelations among the Viscoelastic Functions. Approximate Interrelations among the Linear Viscoelastic Functions. Experimental Methods for Viscoelastic Liquids. Experimental Methods for Soft Viscoelastic Solids and Liquids of High Viscosity. Experimental Methods for Hard Viscoelastic Solids. Experimental Methods for Bulk Measurements. Dilute Solutions: Molecular Theory and Comparisons with Experiments. Molecular Theory for Undiluted Amorphous Polymers and Concentrated Solutions Networks and Entanglements. Dependence of Viscoelastic Behavior on Temperature and Pressure. The Transition Zone from Rubberlike to Glasslike Behavior. The Plateau and Terminal Zones in Uncross-Linked Polymers. Cross-Linked Polymers and Composite Systems. The Glassy State. Crystalline Polymers. Concentrated Solutions, Plasticized Polymers, and Gels. Viscoelastic Behavior in Bulk (Volume) Deformation. Applications to Practical Problems. Appendices. Author & Subject Indexes.

Viscoelastic properties of polymers

Mathematical Structure of the Theories of Viscoelasticity

Viscoelastic Properties of Polymers

The frequency dependences of the intrinsic storage and loss shear moduli can be predicted from molecular theories for flexible random coil polymers (bead-spring models) and for rigid elongated macromolecules. Comparison with various experimental data extrapolated to infinite dilution shows good agreement with both these extreme types. For semi-rigid helical macromolecules, and for highly charged polyelectrolytes, experimental data correspond to hybrid relaxation spectra which are attributed to rigid-body rotation together with certain internal motions – probably flexural modes for the helices, configurational rearrangements for the polyelectrolytes. At high frequencies or in high-viscosity solvents, additional energy dissipation mechanisms appear in random coil polymers, whose nature is still conjectural.

Viscoelastic properties of dilute polymer solutions

A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (Mw/Mn <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of Mw/Mn and the Mark-Houwink exponent a. The resulting value of S2/S (where S1 = Στp/τ1, S2 = Σ(τp/τ1)2, the τp's being the relaxation times and τ1 the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.

John D. Ferry

Papers

Viscoelastic properties of polymers

Mathematical Structure of the Theories of Viscoelasticity

Viscoelastic Properties of Polymers

Viscoelastic properties of dilute polymer solutions

Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties