S. F. Edwards

Theory of spin glasses

A new theory of the class of dilute magnetic alloys, called the spin glasses, is proposed which offers a simple explanation of the cusp found experimentally in the susceptibility. The argument is that because the interaction between the spins dissolved in the matrix oscillates in sign according to distance, there will be no mean ferro- or antiferromagnetism, but there will be a ground state with the spins aligned in definite directions, even if these directions appear to be at random. At the critical temperature the existence of these preferred directions affects the orientation of the spins, leading to a cusp in the susceptibility. This cusp is smoothed by an external field. Although the behaviour at low t needs a quantum mechanical treatment, it is interesting to complete the classical calculations down to t=0. Classically the susceptibility tends to a constant value at t=0, and the specific heat to a constant value.

The computer study of transport processes under extreme conditions

A method is developed to investigate the behaviour of a liquid under the action of a very high shearing force using computer simulated molecular dynamics. Values for the viscosity are calculated but these require more extensive computation for statistical accuracy. A short calculation is, however, sufficient to establish the nature of the processes involved, and to plot the velocity distribution curve; these graphs are presented. The method abandons the usual homogeneous isotropic cyclic conditions used so far in calculation of transport coefficients and can be applied to arbitrarily large shear.

The statistical mechanics of polymers with excluded volume

The probability distribution of the configurations of a polymer consisting of freely hinged links of length l and excluded volume v is studied. It is shown that the interaction of the polymer with itself can be represented by considering the polymer under the influence of a self-consistent field which reduces the problem to an equation like the Hartree equation for an atom. This can be solved asymptotically, giving the probability of the nth link of the polymer passing through the point r to be (L)exp[-27{r-(5/3)3/5(v/3πl)1/5L3/5}2(1/20Ll)] where L = nl is the length along the polymer and (L) the normalization. Thus the mean square of r, r2, is (5/3)6/5(v/3πl)2/5L6/5. The theory is extended to polymers of finite length, to the excluded random walk problem and to n dimensions.

Dynamics of concentrated polymer systems. Part 1.—Brownian motion in the equilibrium state

In this series of papers, the dynamics of polymers in melts and concentrated solutions are discussed with the eventual aim of constructing the rheological constitutive equation. The basic ideas are introduced in this paper. A mathematical model chain which describes the motion of the polymer in the fully entangled state is presented and its Brownian motion in equilibrium is studied. The model chain, called the primitive chain, shows much qualitatively different behaviour from that of the Rouse chain used in dilute solution theory.

Dynamics of concentrated polymer systems. Part 2.—Molecular motion under flow

The primitive chain model presented in Part 1 is extended to the case in which the system is macroscopically deformed. The molecular expression of the stress due to the primitive chain is given, and the stress relaxation after a sudden deformation is calculated as an example.

Dynamics of concentrated polymer systems. Part 3.—The constitutive equation

The rheological constitutive equation of a condensed polymer system is presented based on the primitive chain model presented in Parts 1 and 2. The constitutive equation has the form of a BKZ equation and gives an explicit form for the memory kernel with the dependence of the rheological parameters on molecular weight and concentration. An interesting point is that it predicts a stress superposition law in the regime of non-linear viscoelasticity. The general features agree with experiments fairly well.

The effect of entanglements in rubber elasticity

Abstract This paper presents a theory of rubber elasticity based on the concept of entanglements. It is shown that for small deformation the molecular mechanism of stretching is dominated by the slippage of chains. Hardening of the rubber at a high deformation is due to inextensibility as described by the tube concept. This free energy of deformation agrees well with experiment. The resulting free energy is F k B T = 1 2 N c ∑ i=1 3 (1−α 2 )λ i 2 1−α 2 Z λ i 2 − log 1−α 2 ∑ i=3 3 λ i 2 + 1 2 n s ∑ i=1 3 λ i 2 (1+η)(1−α 2 ) (1+ηλ i 2 )(1−α 2 σλ i 2 ) + log (1+ηλ i 2 ) − log (1−α 2 σλ i 2 ) where α is a measure of the inextensibility and η of the slippage, Nc is the number of crosslinks and Ns the number of slip links.

Theory of powders

Starting from the observations that powders have a large number of particles, and reproducible properties, we show how statistical mechanics applies to powders. The volume of the powder plays the role of the energy in conventional statistical mechanics with the hypothesis that all states of a specified volume are equally probable. We introduce a variable X - the compactivity - which is analogous to the temperature in thermodynamics. Some simple models are considered which demonstrate how the problems involved can be tackled using the concept of compactivity.

Dynamics of concentrated polymer systems. Part 4.—Rheological properties

The constitutive equation for polymer melts and concentrated solutions derived in the previous papers is applied to two typical rheometrical flows: steady and transient shear flow, oscillatory shear flow superposed on steady flow, steady and transient uniaxial elongational flow. The stress responses predicted are qualitatively in good agreement with experiments except for one case (the first normal stress in the transient shear flow). A particularly interesting result is that the constitutive equation suggests instability in steady shear flow and uniaxial elongational flow.

The theory of polymer solutions at intermediate concentration

It is argued that polymer solutions can be classified into three broad types which may be characterized in terms of N the total number of (micro) molecules, n the number of polymer chains, l the effective length of a micromolecule, v the excluded volume per micromolecule and V the total volume. The types are: (i) dense solutions in which V/N V/n > v or (Ll)1/2 > V/n > v according to the magnitude of v, i.e. L-1/10v-1/5l7/10 greater than 1 or less than 1, and (iii) dilute solutions in which V/n < L9/5v3/5l-3/5. The intermediate case is discussed in detail and the partial pressure of the molecules is found to be given by PV = NκT{(n/N) + ½(Nv/V) - ½π√3(N/V)½(v3/2/l3)}. A discussion is given of the way this expression fails as one enters regions (i) and (iii).