Hard sphere, cross-linking

Cross-linked copolymers of polystyrene and divinylbenzene are usually used. These polymers are hard enough to resist pressure in the column and are made of small spheres with a diameter of a few micrometres (Fig. 4.2). 

In Section 8.2 we found that the reaction cross section provides the link between the rate constant and collision dynamics. However, Q , i,J) is just a function of the collision energy and the internal states of the reactants. The outcome of a single collision also depends upon the impact parameter, as demonstrated for the simple hard-sphere model of reaction cross section discussed in Section 8.4. The probability of a specific result p(b, e, i, j) is dependent on all these variables. In Section 8.4 we showed that the relative importance of a collision with impact parameter between b and b + db % proportional to the annular area Inb db. The reaction cross section is found by multiplying the weighting factor for a particular b by the probability of a specific result and integrating over all values of the impact parameter... 

The idea to coarse-grain the description of a system containing a very large number of polymer chains such that each chain is represented by a single effective particle dates back to the Asakura Oosawa model [189 191] of polymer colloid mixtures. In this model, the colloidal particles (e.g., cross-linked polystyrene spheres with radii in the size range 100 nm < < 1 /im) are represented as hard... 

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