Constant surface pressure ensemble

To show this, we will present and discuss some typical results readily available in the literature. Here we will select systems simulated in the constant-pressure constant-surface-tension ensemble, i.e. with a temperature, pressure and surface tension control. 

Venable, R. M., Brooks, B. R. and Pastor, R. W. (2000). Molecular dynamics simulations of gel phase lipid bilayers in constant pressure and constant surface area ensembles, J. Chem. Phys., 112, 4822-4832. 

One can now also investigate other ensembles for the single vesicle adhered to a substrate such as the ensemble in which besides the volume also the surface area A is kept constant. As we discussed previously, this is the ensemble for which Seifert and Lipowsky constructed their phase diagrams of the vesicle unbinding transition. Another ensemble one might wish to consider is the constant pressure ensemble, for which Q is the appropriate free energy, in which instead of the vesicle volume the Laplace pressure difference Ap is... 

A more quantitative measure of the effect of the surface on crystal nucleation we obtained from a direct calculation of the crystal-nucleation barrier. We performed Monte Carlo simulations in the constant normal-pressure NP T) ensemble where we used N = 13824 particles and simulated 2 10 cycles for every window. The result for the free energy barrier calculated at a pressure AP = 0.63 is shown in Fig. 34 (dots). At this pressure, the estimated barrier height is AG = llksT at a critical cluster size c = 150. 

In what follows, the two fluctuating interfaces will be replaced by many small, independent surfaces of area S, separated by a distance z (see Figure 4). The (metastable) distribution of the distances between the surfaces, in an ensemble subjected to a constant pressure, will be assumed Boltzmannian. It will be also assumed that the fluctuating interfaces have constant total areas and an elastic bending modulus Kq. Let us first consider that the interfaces interact per unit area through a harmonic potential... 

In the canonical ensemble approach, the adsorbed phase is treated as a separate phase with a known volume and containing a fixed number of molecules at constant temperature. This approach is somewhat unrealistic even though the results obtained can be successfully correlated with experimental data [8]. If we consider that the gas—solid interactions induce a smooth gradient in the density of the gas as the surface is approached, another formahsm is necessary. The solution is obtained by adopting the grand canonical ensemble, in which the fixed variables are the volume, temperature and chemical potential. The unknown quantities would be, e.g., the number of molecules, energy, and pressure. The chemical potential of the adsorbed phase, once the equifibrium condition has been achieved, is equal to the chemical potential of the gas phase, which is determined from the density at a point far from the surface. The amount adsorbed, can be defined as the difference between the total number of molecules in the system, N, and N, the number of molecules in a hypothetical system of equal volume but with no gas—solid interactions. 

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