Size-Distribution of Polymer-Free Voids in Frozen Polymer Solutions

In this chapter we address a question about a functional form of the distribution of sizes of polymer-free voids in frozen solutions of long polymer chains. We show that when the polymers can be considered as statistically independent, the problem can be solved exactly by mapping it onto the Target Problem. We present exact results for Gaussian chains in three- and two-dimensional systems. For chains of arbitrary conformations (but still independent), the probability of polymer-free voids is determined using some heuristic arguments. We show that the fact that all the monomers are linked into the chains causes a significant departure of the distribution of sizes of polymer-free voids from the Poisson distribution, and generically leads to a very uneven spatial distribution of the polymer fraction.