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

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The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids

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.

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

Functional magnetic particles are formed by dissolving a mucopolysaccharide such as chitosan in acidified aqueous solution containing a mixture of ferrous chloride and ferric chloride. As the pH of the solution is raised magnetite is formed in situ in the solution by raising the pH. The dissolved chitosan is a polyelectrolyte and forms micelles surrounding the granules at pH of 8-9. The chitosan precipitates on the granules to form microspheres containing the magnetic granules. On addition of the microspheres to waste aqueous streams containing dissolved ions, the hydroxyl and amine functionality of the chitosan forms chelates binding heavy metal cations such as lead, copper, and mercury and the chelates in turn bind anions such as nitrate, fluoride, phosphate and borate.

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Functional magnetic microspheres

By using new invariants in the theory of finite elasticity an expression is obtained for the stored energy function of slightly compressible materials in which the effects of the distortional change (change of shape) and of the volume change are clearly separated. The volume-related terms are expressed as a function of the third invariant, the classical compressibility, and an induced anisotropy of the effective compressibility which is due to the large deformations. After evaluating the terms, using data on pressure, volume, uniaxial strain, and fractional volume change vs strain data on natural rubber from the literature, it is shown that the volume change contribution to the total stress observed in a simple tensile experiment can be clearly separated from the distortional contribution, even at finite strains.

Stored energy function and compressibility of compressible rubberlike materials under large strain

The mechanical properties of rubberlike composite propellants and similar filled elastomers are determined largely by the volume fraction of filler, the visco-elastic properties of the binder, and the interactions between the binder and filler particles. The ratio of the quasi-equilibrium modulus of the composite to that for the unfilled elastomer increases with the volume fraction of the filler, apparently according to an equation of the form proposed by Eilers and Van Dyck. However, the same ratio for the dynamic storage modulus decreases as the frequency is increased or the temperature is decreased. The time-dependent tensile properties can be characterized by stress-strain curves measured at different strain rates and temperatures. Both the small deformation and ultimate properties can be represented by master curves, which are functions only of the experimental time scale, along with a temperature function which is a near-universal function of the glass temperature. Propellants under constan...

Robert F. Landel

Papers

The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids

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

Functional magnetic microspheres

Stored energy function and compressibility of compressible rubberlike materials under large strain

Viscoelastic Properties of Rubberlike Composite Propellants and Filled Elastomers