Surface models Rigidity control

The percolation model suggests that it may not be necessary to have a rigid geometry and definite pathway for conduction, as implied by the proton-wire model of membrane transport (Nagle and Mille, 1981). For proton pumps the fluctuating random percolation networks would serve for diffusion of the ion across the water-poor protein surface, to where the active site would apply a vectorial kick. In this view the special nonrandom structure of the active site would be limited in size to a dimension commensurate with that found for active sites of proteins such as enzymes. Control is possible conduction could be switched on or off by the addition or subtraction of a few elements, shifting the fractional occupancy up or down across the percolation threshold. Statistical assemblies of conducting elements need only partially fill a surface or volume to obtain conduction. For a surface the percolation threshold is at half-saturation of the sites. For a three-dimensional pore only one-sixth of the sites need be filled. 

Wittke and Chao [187] considered heat-transfer-controlled condensation on a moving bubble. They assumed that the bubble was a rigid sphere that moved with a constant velocity. They assumed that potential flow theory was valid. Isenberg et al. [188] corrected this model for no slip at the bubble surface and arrived at ... 

Fig. 2 Coexistence curve for CO2 in the temperature-density plane (a), vapor pressure at coexistence (b), and surface tension versus temperature (c). Dashed curves are the experimental data, while solid curves describe the prediction of the simple (truncated and shifted) LJ model (5), where the critical temperature and density are adjusted to coincide with experiment to fix the two parameters Sgs and as for Fig. 1. Stars and crosses denote the results of [131] for the parameter q Tc) that controls the strength of the quadrupolar interaction being chosen as q Tc) = 0.387 or q(Tc) = 0.47, respectively (see Sect. 2.2). Plus symbols and triangles are the result of atomistic models called EPM and EPM2 [146]. Small circles near the pluses are the results for flexible monomers [146], which give essentially the same results for the thermodynamic properties as the model for rigid molecules. Big circles and squares are simulation results [156] for two ab initio potentials [146,150]. Note that the interaction parameters of the EPM2 models have similarly been rescaled to fit the critical density and temperature of the experiment as done in Fig. 1, and that no prediction for the liquid-vapor surface tension from the atomistic models is available. From Mognetti et al. [131]...

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