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

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.

Supercooled liquids and the glass transition

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...

Molecular Transport in Liquids and Glasses

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

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.

Mechanical properties of solid polymers

A novel, light-weight, portable strip biaxial skin transducer was built to measure the stress-strain behavior of human skin in vivo. The experimental setup, test protocol and transducer calibration are discussed in detail. Data are analyzed in the context of the finite elasticity theory using a pseudo stored-energy function. For stress relaxation experiment, both ascending steps and descending steps were performed. A peculiar effect is seen that in descending steps, stress relaxation almost disappears.

In vivo study of human skin rheology

In the previous paper, the detailed experimental set-up and procedures were described for tubeless siphon or Fano flow, from which the tensile viscosity, ηT, is calculated Here we investigate the simultaneous effects of temperature and concentration on tensile viscosity A semi-empirical scaling law has now been established to relate the concentration, c, temperature, T, and deformation rate, e, by a reduced deformation rate variable to bring all ηT together Furthermore, ηT has been compared with the steady and dynamic shear data The onset of high ηT occurs in the vicinity of the onset of non-Newtonian viscosity observed in a simple shear flow experiment Finally, the asymtotic solution of Hassager’s kinetic theory of a bead-rod model for macromolecular solutions2 has been compared with experimental data It indicates that ηT depends strongly on the molecular weight, and the higher the molecular weight, the more sensitive the tensile viscosity in terms of e

Extensional Flow of Dilute Polymer Solution

The relationship between network chain concentration and the maximum value of the extension ratio at break is discussed. Experimental data obtained from the literature are then used to test the theoretically derived dependence.

Relationship between maximum extensibility of networks and the degree of crosslinking and primary molecular weight

Volume-extension data for an SBR-peroxide vulcanizate are presented. It is shown that Gee's expression, in conjunction with the experimental stress-strain response for the vulcanizate, lea...

Dependence of Relative Volume on Strain for an SBR Vulcanizate

A single master logarithmic stress relaxation curve of reduced modulus as a function of reduced time is established for a styrene-butadiene rubber (SBR) system, accounting for the effects of crosslinking density, temperature, and time. The results from recent tests involving uniaxial and various biaxial strain states at finite strain levels may be represented by a unique strain-energy function W of the Valanis-Landel separable symmetric type, 



where the λi are principal extension ratios. These two representations demonstrate that the mechanical response of whole families of elastomeric materials may be predicted once a single member of the family is fully characterized.

Robert F. Landel

Papers

In vivo study of human skin rheology

Extensional Flow of Dilute Polymer Solution

Relationship between maximum extensibility of networks and the degree of crosslinking and primary molecular weight

Dependence of Relative Volume on Strain for an SBR Vulcanizate

Reduced‐variable mechanical characterization of styrene‐butadiene rubber with varying crosslink density, temperature, and finite strain states