Molecular Dynamics Simulation of Atactic Polystyrene. 1. Comparison with X-ray Scattering Data

Abstract

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.

Molecular anisotropy effects in carbonK-edge scattering: Depolarized diffuse scattering and optical anisotropy

“…The / spectra were measured with = 30° using a silicon CCD subtending 0.062 sr at 2 = 100°, yielding a scattering vector q with magnitude q = 2.2 +/-0.07 nm -1 at 285 eV and oriented 20° off the surface normal. This q is well below the "polymerization" and "amorphous" peaks at 7 and 15 nm -1 measured with hard x-rays [23,[27][28][29], consistent with our observation of weak, flat intensity across the CCD, whose integrated signal is thus reported.…”

“…While clearly an oversimplification, assume each monomer is identical with ring axis strictly parallel to the backbone axis (Fig. 1), and with uniaxial scattering tensor = � While the q-dependence of / is usually of interest in x-ray scattering from polymers [27][28][29], the same spatial arrangement of scattering centers contributes to its hν dependence at fixed q, which thus is sensitive to the ensemble-average, 2-point density and orientation distribution of PS monomers. The polarized and depolarized elastic scattering contributions to / are related to spatial fluctuations in density and anisotropic orientation, respectively [1,2].…”

“…While beyond the scope of this work, we can anticipate some aspects of such 20 studies. Structural models from molecular dynamics and Monte Carlo simulations are readily resolved into intra-and intermolecular partial distribution functions and partial structure factors for phenyl-phenyl, backbone-backbone, and phenyl-backbone correlations for comparison with hard x-ray and neutron scattering results [29,52,53]. Extending these to include tensor scattering entities and evaluation of resonant polarized and depolarized scattering is possible at different levels of sophistication.…”

“…It is a disordered (amorphous) polymer containing 2 functional groups; highly anisotropic, rigid phenyl rings attached to the flexible polyethylene-like chain backbone as shown for a single monomer in Figure 1. The visible optical properties of aPS are well documented [19][20][21][22], as is its hard x-ray scattering in small-angle [23][24][25][26], wide-angle [23,[27][28][29], and surface sensitive [30][31][32] regimes. Spatially averaged anisotropy in C K-edge XAS has also been reported [12,13].…”

Orientation of Phenyl Rings and Methylene Bisectors at the Free Surface of Atactic Polystyrene

“…7 The use of coarse-grained models permits the construction of more thoroughly equilibrated, and larger, models than is possible using the atomistically detailed representation of the system. Bulk amorphous polystyrene has been the subject of several prior studies that employed fully atomistic detail [8][9][10][11] or a united atom description of the chain. 10 Roe's united atom model used five sites for each monomer unit.…”