The self-diffusion coefficients of Ar, Kr, Xe, and CH4 have been measured as functions of temperature and pressure and the data used to examine critically the current theories of diffusion. It is found that: (1) The self-diffusion coefficients of Ar, Kr, and Xe fit one corresponding states relationship, and this relationship differs from that needed to fit the observed diffusion coefficients of CH4. For Ar, Kr, and Xe: logD̃=0.05+0.07p̃−(1/T̃)(1.04+0.1p̃),with D̃, T̃, and p̃ the reduced diffusion coefficient, temperature and pressure. (2) The free volume theory of diffusion is inadequate to describe our observations. (3) The volume of activation for CH4 is one third of the molar volume, while for Ar, Kr, and Xe it is one molar volume or larger. This observation is related to the steepness of the intermolecular repulsion, as is the deviation of CH4 from the corresponding states curve determined by Ar, Kr, and Xe. (4) The dominant temperature dependence of D arises from the correlation between successive increments in momentum. In describing molecular motion it is necessary to include negative portions of the momentum autocorrelation function. A simple fluid continuum model appears to be accurate in describing momentum correlations. Calculations of D and (d lnD/dT) are in good agreement with experiment. (5) The dense square-well fluid provides a zeroth-order approximation to real fluids. The computed temperature dependence of D is in quantitative agreement with experiment, but the computed values of D are in error by about 30%.

We have reviewed the general principles of interfacial constraint on highly concentrated polymers near sharp interfaces. First, chains are constrained by their inability to penetrate the boundary. Second, at high concentration, polymers are also constrained by interactions with neighboring chains. Third, one additional constraint depends on the chain length: (a) for long chains, a symmetry condition arises from the indistinguishability of segments k and k + 1, whereas (b) for shorter molecules, wherein the segments are distinguishable, the length of the chains is fixed. Subject to these restraints, chains at equilibrium will be configured to maximize their entropy, and hence their configurational disorder. The physical properties of chains at interfaces are often quite different from those of bulk polymers. In most such systems, the conformational ordering is dissipated within only 5-10 A from the interface, but some physical properties depend on effects that are propagated over much longer distances. The currently available theory is found to be in quite good general agreement with a large number of conformational and mixing properties of polymers at interfaces, in semicrystalline polymers, in alkane crystals, in stationary phases used in reversed-phase liquid chromatography, and in amphiphilic aggregates including bilayer membranes and micelles.

Nonintersecting ring polymers of step number (chain length) 6–118 have been produced by the Monte Carlo method on a tetrahedral lattice. The mean square radius of gyration and its standard deviation for each sample have been determined. A log-log plot of the mean square radius of gyration 〈S2〉 vs N, the number of steps, gives the usual straight line with a slope of 1.218. The deviation of this exponent from reported values for the mean square end to end distance of linear polymers (1.200) lies within the margin of error and is unlikely to be due to the ring geometry of the polymer. The data are also compared with similar results on linear polymers; in particular, the ratio of the two radii of gyration 〈S2〉lin/〈S2〉ring in the presence of excluded volume is discussed, and its asymptotic value is compared with the value predicted from existing theory.

No abstract

The free volume theory of diffusion for hard spheres, earlier developed by Cohen and Turnbull, is modified for simple van der Waals type liquids. The modified theory fits the self-diffusion data for argon, krypton, and xenon fairly well and predicts glass transition for these liquids at approximately one-third of their normal boiling points. It is found that a more accurate model for the free volume diffusion in liquids should include a redistribution energy for voids arising from the nonlinear behavior of the pair potential. The agreement found by Cohen and Turnbull between their hard sphere theory and the self-diffusion data of some large organic molecules is interpreted as evidence that the simple Lennard-Jones potential does not accurately describe their interaction with each other. This situation is reflected in the failure of these molecules to obey the same corresponding states relationship as the simple liquids of argon, krypton, and xenon.