科研之友
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摘要
The second virial coefficient A(2) (A(2)(theta(1))) for ring polymers in dilute solution at the theta temperature of the corresponding linear polymers, theta(1), is investigated. It is interesting that the ring polymers at theta(1) show a positive value of A(2)(theta(1)), although the excluded volume of the polymer segments apparently disappears at theta(1). This is a consequence of the topological interaction due to a constraint that the topological state of each of the ring polymers is to be conserved. The value of A(2)(theta(1)) can be directly derived from the linking probability P-link, which is defined by the probability that two ring polymers are mutually entangled so that they make a nontrivial link type. Recently, we have numerically evaluated P-link precisely for random polygons (RPs) with several different values of the step number N. We have found a good approximate formula for P-link as a function of N which should be valid for arbitrary values of N. Consequently, we obtained a theoretical curve of A(2)(theta(1)) as a function of N through this formula. Rather recently, Takano et. al. obtained extremely pure ring polystyrenes by using liquid chromatography at the critical condition (LCCC) and measured the dependence of A(2)(theta(1)) on their molecular weight M-w. In this paper, we compare the theoretical curve of A(2)(theta(1)) vs. N calculated by P-link with the experimental data of A(2)(theta(1)) vs. M-w. Here we assume that M-w should be proportional to N. The qualitative behavior of the theoretical curve is consistent with the experimental data; quantitatively, however, the theoretical values are slightly larger than the experimental values. This result suggests that we should take into account some other effects also in the theory such as the three-body interaction (A(3)), as well as the topological interaction.
- 出版日期2011
