Second virial coefficients of oligo- and polystyrenes. Effects of chain ends

Abstract

The second virial coefficient Az was determined from light scattering measurements for atactic polystyrene in cyclohexane at 34.5 "C (e) and in toluene at 15.0 OC down to the oligomer region, including the monomer, in order to clarify the effect of chain ends on Az. The observed dependence of AZ on weightaverage molecular weight M, may well be explained by the Yamakawa theory that takes into account both the effects of chain ends and chain stiffness. It is shown that the observed nonvanishing of Az at 8 arises from the former effect. The excess effective binary-cluster integrals 81 and 82 associated with the chain end beads are estimated to be 16 and 260 A3 in cyclohexane and 220 and 270 Aa in toluene, respectively, taking the repeat unit as a single bead. These values are of reasonable order of magnitude compared to those for small molecules. It is then striking to find that the effect of chain ends exists even at relatively large M, ( N 103 in the good solvent toluene. For this system, however, the previous conclusion for the interpenetration function 9 still remains valid, since the contribution AiE) of the effect of chain ends to A2 is not very large in the ordinary range of M,. As the cubed radius expansion factor a,+ (or M,) is decreased, the (true) 9 including no effect of AiE) in toluene first increases gradually, then passes through a maximum and a minimum, and finally increases steeply, deviating significantly upward from the two-parameter theory values but being consistent with the Yamakawa theory. This is due to the effect of chain stiffness. As a,+ (or M,)is further decreased, the contribution of AiE) to Az or to the apparent interpenetration function 9ap as usually defined from the whole Az including AiE) becomes progressively large. It is shown that the rapid increase of 9'ap there with decreasing M, arises mainly from the effect of chain ends but not from that of chain stiffness, in contrast to the prevailing notion.

Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse‐grained hybrid molecular dynamics approach

“…19 Therefore, the accuracy level of our method appears to be quantitative close to that of more rigorous methods. In general, our simulation results are in good agreement with observations [45][46][47][48][49] and the reported values from other more rigorous theoretical methods. 19,33,50 Moreover, we also computed the diffusion coefficient of the solvents by using…”

Second and third virial coefficients of low-molecular-weight polystyrene with a benzyl end in toluene

“…The difference between theoretical and experimental values becomes larger with decreasing M w . By adding A 2 (E) with a 2,1 ¼2.5 cm 3 g À1 and a 2,2 ¼À200 cm 3 mol À1 , 5 we obtain the dashed line, which closely fits the experimental data for butyl-PS. The solid line calculated with a 2,1 ¼1.4 cm 3 g À1 and a 2,2 ¼À200 cm 3 mol À1 also closely fits the data for benzyl-PS.…”

“…The unfilled and filled circles represent the data points of A 2 for benzyl-and butyl-PS, 5 respectively, in toluene at 15 1C. The data points for benzyl-PS are systematically lower than those for butyl-PS.…”

“…3 The importance of the effects of chain stiffness on A 2 was discussed by Yamakawa. 4 Einaga et al 5 later showed that the effects of chain ends, as well as chain stiffness, must be considered to obtain a quantitative agreement between the theoretical and observed values of A 2 for polystyrene (PS) in toluene (a good solvent) for M w o10 4 , where M w denotes the weight-average molecular weight. The PS samples used by Einaga et al 5 had a butyl group at one end of the chain.…”

“…This enabled us to study the effects from the chain end and chain stiffness by comparing the results with the data for butyl-PS. 5 …”