Partial Enumeration Schemes

3) The ratio of the coarse-grained parameters, R o and % defines an additional nticroscopic scale, p = J eo/V, whichisdenotedaspacldnglength.Thisscaleisproportionaltothetubediameterofthe reptation motion of the long, flexible macromoleciiles in a melt. 

Given the single-chain density, c])] [vpa], one obtains improved estimates for the external fields and this cycle of calculations is repeated until self-consistency of Eq. (5.25) (or Eq. (5.37)) is obtained. Typically, one uses the same set of singlechain conformations in each iteration such that the noise in 4 a[w a] due to the finite number, Nc, of conformations does not interfere with the convergence of the self-consistency condition. Calculating the single-chain density, (])a[w a] is computationally expensive, but it can be easily implemented on parallel computers, where each processor evaluates the Boltzmann weight of a subset of chain conformations. 

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Mean Field Theory for Non-Gaussian Chain Architectures 5.3.2.1 Partial Enumeration Schemes... 

Fig. 38. Temperature dependence of the interfacial tension of the pure polymer for chain length N = 10. Circles correspond to MC results and the solid line to the SCF ealculations. The line with diamonds shows the the result of a density functional calculation, which uses the TPTl-equation of state, decomposes the interaction free energy functional into a repulsive short-ranged and an attractive long-ranged contribution, and employs a partial enumeration scheme to take due account of the chain conformations on all length scales [154]. The dashed line shows the result of density functional calculations which do not use the decomposition of the free energy functional, but employ the same equation of state and chain model [99]. The inset compares the free energy densities / = F/VkgT of the SCF calculations and the accurate TPTl equation of state. Adapted from [99,154]...

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