Expanded ensemble simulations polymeric systems

If a fiVT ensemble simulation can be turned into a ( quasi ) NPT ensemble-type simulation (e.g., a pseudo- FT ensemble), the inverse transformation (a pseudo-NPT ensemble) is also possible. The key relationship for a pseudo-NPT ensemble technique is Eq. (5.1) [78]. Such a reverse strategy can be practical only if molecular insertion and deletion moves can be performed efficiently for the system under study (e.g., by expanded ensemble moves for polymeric fluids). Replacing volume moves by particle insertions can be advantageous for polymeric and other materials that require simulation of a large system (due to the sluggishness of volume moves for mechanical equilibration of the system) such an advantage has been clearly demonstrated for a test system of dense, athermal chains [78]. 

Escobedo and de Pablo have proposed some of the most interesting extensions of the method. They have pointed out [49] that the simulation of polymeric systems is often more troubled by the requirements of pressure equilibration than by chemical potential equilibration—that volume changes are more problematic than particle insertions if configurational-bias or expanded-ensemble methods are applied to the latter. Consequently, they turned the GDI method around and conducted constant-volume phase-coexistence simulations in the temperature-chemical potential plane, with the pressure equality satisfied by construction of an appropriate Cla-peyron equation [i.e., they take the pressure as 0 of Eq. (3.3)]. They demonstrated the method [49] for vapor-liquid coexistence of square-well octamers, and have recently shown that the extension permits coexistence for lattice models to be examined in a very simple manner [71]. 

There has been some criticism of the study by Jang et a/., which address the importance of the equilibration procedure for polymeric systems. Elliott and Paddison have argued that the difference in density between the MD simulated system and the experimentally measured values are due to incomplete chain relaxation or an erratic force field. Since later MD simulations of Nafion using similar force field provided good agreement in density, the latter can probably be ruled out. Jang et al. used a rather complex equilibration process, were the MD boxes were heated, and expanded and compressed several times in the NPT ensemble. The resulting densities (1.60 and 1.67 g/cm ) are 5-10% lower than experimental values, which can partly be explained by the lack of semicrystalline domains in the MD box, which do exist in real membranes and contribute to a somewhat increased density. 

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