A method is presented here by which orientation distribution of crystallites in anisotropic polycrystalline samples can be derived from a set of plane-normal distributions obtained by x-ray diffraction measurements. It is the generalization of the similar procedure proposed previously for analysis of samples having fiber texture. It thus represents a completely general solution to the problem of pole figure inversion, applicable to samples having any arbitrary symmetry elements. The plane-normal distribution function is expanded in a series of spherical harmonics, the coefficients of which, Qlmi, can be determined by numerical integration of experimental diffraction data. The crystallite distribution function is expanded in a series of generalized spherical harmonics which appear as solutions to the Schrödinger wave equation of a symmetric top. The coefficients of the crystallite distribution function, Wlmn, are then obtained as linear combinations of Qlmi. Symmetry properties of Wlmn arising from crystallographic or statistical symmetry elements existing in the sample are examined. The methods of estimating the series truncation errors and of minimizing the experimental error by a least-squares method, previously proposed in connection with fiber texture analysis, are still applicable here with appropriate generalizations. In addition it is shown that the effect of diffraction line broadening due to finite size or imperfection of crystallites can also be allowed for at least approximately.

Molecular dynamics simulation of bulk liquid and glass oflong-chain molecules has been performed. The system consists of linear chains of up to 50 spherical segments, each subject to forces due to bond stretching, bending, and torsion, and to nonbonded interaction, according to a truncated Lennard-Jones potential, between segments in neighboring chains and between segments separated by more than three bonds along the chain. The parameters are chosen to mimic polymethylene, the segment representing a CH 2 unit. Behaviors suggestive of liquid-toglass transition were exhibited by (i) cessation of trans-gauche conformational transitions, (ii) changes in the temperature coefficients of the density and internal energy, and (iii) effective vanishing of the segmental self-diffusion coefficient. The "freezing in" of these properties occurs at decreasing temperatures in the order given above, indicating the decreasing size of domains of cooperative motion required. The dependence of the transition temperature on the chain length and on the flexibility of the chain (effected by switching of the torsional potential off) obtained is in accord with experimental observations. Below the transition temperature the system behavior depends on the path through which the state was reached, suggesting that simulation of relaxation effects could be achieved in longer runs.

The light scattering technique was utilized to measure the phase separation temperatures (cloud points) of mixtures containing a polystyrene and a polybutadiene of various molecular weights and also of mixtures containing a polystyrene and a random or block copolymer of styrene and butadiene. The data was analyzed to obtain the polymer-polymer interaction parameter for the styrene-butadiene pair as a function of temperature and concentration. The value of the parameter deduced from the homopolymer mixtures agrees well with that obtained from the mixtures containing a copolymer. The polymer-polymer interaction parameter thus evaluated was compared with a theoretical expression derived on the basis of the Flory equation-of-state theory. The effect of free volume disparity between the two components was found to play a relatively minor role in determining the interaction parameter when the two polymers lack any specific interactions which would make them mutually miscible.

A molecular dynamics simulation of bulk atactic polystyrene was performed. A united atom model and an all atom model were developed, in both of which the bond lengths were held fixed and the phenyl group was represented by a rigid, planar hexagon. The degree of success of the simulation was examined by comparing the calculated X-ray scattering intensity curve with experiment. The united atom model reproduces the so-called "polymerization peak", and the calculated curve agrees well with one of the most recently published experimental data. The degree of agreement achieved is in fact comparable to the degree to which two published experimental curves agree with each other. The agreement in the radial distribution function between the calculated and experimentally derived one is good in the r range smaller than 9 Á but deteriorates somewhat for larger r. There are again uncertainties in the experimental radial distribution function itself at large distances, however, as can be seen by comparing experimental curves obtained by two different groups. In contrast to the united atom model, the all atom model was found to give a result which clearly disagrees with experimental results, and one of the commercially available software gave an even worse result. The nature of smearing that accrues in the experimentally determined radial distribution function, as a consequence of the differing q dependencies of C and H atomic scattering factors and the limited q range accessible to experiment, has been examined by calculating the radial distribution function directly from the simulation result.

No abstract