Malcolm L. Williams

Bio: Malcolm L. Williams is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Relaxation (physics) & Creep. The author has an hindex of 14, co-authored 16 publications receiving 6857 citations.

Extensions of the Rouse Theory of Viscoelastic Properties to Undiluted Linear Polymers

Abstract: The Rouse theory for viscoelastic properties of very dilute solutions is modified for application to undiluted linear polymers. With the effective segment mobility expressed in terms of steady‐flow viscosity, the theory is applied to polymers of rather low molecular weight essentially without further change. In high molecular weight polymers, it is assumed that for modes of motion with relaxation times above a critical value the effective segment mobility drops abruptly, in accordance with the effect of entanglement coupling on steadyflow viscosity as described by Bueche. Properties in both the transition region between glasslike and rubberlike consistency and the rubberlike or plateau region are predicted semiquantitatively with no arbitrary parameters. In an alternative application to the transition region, the average effective friction coefficient per monomer unit can be calculated for both linear and lightly cross‐linked systems.

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

Abstract: 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 ...

Supercooled liquids and the glass transition

Abstract: Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

Molecular Transport in Liquids and Glasses

Abstract: We have derived, by using simple considerations, a relation between the diffusion constant D in a liquid of hard spheres and the ``free volume'' vf. This derivation is based on the concept that statistical redistribution of the free volume occasionally opens up voids large enough for diffusive displacement. The relation is D=A exp[−γv*/vf], where v* is the minimum required volume of the void and A and γ are constants. This equation is of the same form as Doolittle's [J. Appl. Phys. 22, 1471 (1951)] empirical relation between the fluidity φ of simple hydrocarbons and their free volume. It has been shown [Williams, Landel, and Ferry, J. Am. Chem. Soc. 77, 3701 (1955)] that the Doolittle equation also can be adapted to describe the abrupt decrease in molecular kinetic constants with decreasing temperature that accompanies the glass transition in certain liquids. Our result predicts that even the simplest liquids would go through this glass transition if sufficiently undercooled and crystallization did not oc...

Mechanical properties of solid polymers

Abstract: A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.