Boltzmann constant size-dependent diffusion

The size-selectivity factor, which depends on the permeant s volume and the lateral pressure exerted by the membrane, is formulated as the reverse work done required to accommodate the permeant in the membrane. In this sense, it is analogous to the cavitation term in models of water solvation. Based on molecular dynamic simulations of membrane diffusion of small molecules, the calculated diffusion coefficients display small deviations across the membrane barrier. Assuming that the rates of diffusion in the membrane barrier are similar to those of bulk solvent with similar viscosity, or at least that they correlate strongly, the barrier diffusion coefficient is estimated using the size-dependent Stokes-Einstein relation, where kg is the Boltzmann constant, T is temperature, is membrane viscosity and is the radius of the permeant. 

It is expected that the jump distance 8 will be relatively constant from one polymer to the next, and that variations in the diffusion constant are caused primarily by differences in the jump frequency c ). This fiequency depends on the probability of collecting a sufficient number of packets of free volume to give a hole of volume V of sufficient size that the diffusing molecule can move into it. The creation of a hole in the polymer requires the expenditure of a certain quantity of energy E, and the probability of forming such a hole can be calculated from Boltzmann statistics to be proportional to exp(—Application of this theory to both polymeric and small-molecule liquids has given jump distances 8 which conespond roughly to the dimensions of small molecules (i.e., 2-20... 

---