How different coarse-grained models can be compared

From the previous discussions it should be clear that there is no unique model description of a polymer chain system in fact, for different physical questions somewhat different coarse-grained models are optimal. For example, while the bond fluctuation model is very well suited to the study 

This question is similar to the question of how to compare simulations and experiment or to compare Monte Carlo work with MD work, of course. But a need for such a conversion arises even when somewhat different Monte Carlo models need to be compared. This question was addressed 

Gerroff et al argue that it is the universal scaling limit that can be extracted from different models and which must be identical so, when one considers the scaling limit N oo, 0- 0 (or N — oo, 0 — 0), one must obtain the same scaling function for (/ g(0))/(i (0 = 0)) versus iV/ATbiob(0) oc which describes the crossover from the dilute to 

Differences in the nonuniversal prefactors like the persistence length lead to the necessity of mapping different chain lengths onto one another. In the dilute limit, we write for the mean square gyration radius (i g) 

Now the two models are mapped onto each other defining N = otN and fixing the conversion factor a such that the amphtude factors in eqs (1.14a) and (1.14b) then are equal, Ca = Cbf- From the numerical results C = 0.24, Cbf = 0.164 it was found that a 0.274, i.e., the range from iV = 8 to iV = 64 was mapped to a range from iV pa 11 to iV 88 in the bond fluctuation model. 

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