Spherically symmetric problems state ordering

In order to calculate the maximum rate of the bimolecular reaction, the assumption is made that every time two molecules collide, a chemical reaction occurs. Consider the diffusion of a system of A molecules into stationary B molecules. If every time A collides with B a reaction occurs, the concentration of A at the surface of B must equal zero, while the concentration at a large distance from B is equal to the bulk concentration C o In order to simplify the problem mathematically, the molecules are assumed to be spherical, so that the diffusion process is spherically symmetric, and the potential energy U is assumed to be a function of r only. This model is depicted in Fig. 2-13. A general solution of Eq. (2-85) is still not possible, but if a steady state is assumed (that is, dCJdt = 0), the total flux through the surface of a sphere of radius r around B is constant for all values of r and is... 

For the symmetric diblock copolymer a second-order transition between lamellar and disordered phase was predicted, while at all other compositions a first-order transition between disordered state and a body-centered cubic phase of spherical domains formed by the minority component was predicted, which changes into hexagonally packed cylinders and finally into lamellae upon further increasing xN. It has already been noted by Leibler s that his approach does not include fluctuation effects, which become important for finite degrees of polymerization (74). Fredrickson and Helfand accounted for this problem by modifying Leibler s theory in the following way (90) ... 

---