Potential, chemical osmotic

It is conventional to let 1/2 zAw = RT, where x is called the Flory-Huggins interaction parameter. Note that 1/2 Aw is the energy change per 1,2 pair according to Equation (69) therefore, wiih the coordination number z absorbed, the parameter x measures this in units of RT. Finally, Equation (21) establishes the connection between chemical potential and osmotic pressure according to this equation,... 

The term in the second derivative of the free energy with respect to composition (or first derivative of the chemical potential or osmotic pressure), brings in a virial equation, usually expressed in a slightly different form than we used in our discussion of osmotic pressure (Equation 12-35) ... 

Osmosis is similar to diffusion in that the molecules move from a location of high chemical potential to one of low chemical potential. An osmotic pressure is generated in a colloidal solution when it is separated from its solvent by a barrier that is impermeable to the solute but is permeable to the solvent. The pure solvent will flow across the membrane, diluting the colloidal dispersion and, as the colloidal material cannot flow in the opposite direction, a pressure difference (osmotic pressure) will be created between the two compartments. Osmotic pressure is a colligative... 

In chemical thermodynamics, osmotic pressure should be determined as follows [8]. Consider the equilibrium between a solution whose chemical potential is jji and a solvent whose chemical potential is fi". The solution and the solvent are separated by a semi-permeable membrane. The chemical (osmotic) equilibrium between them occurs under the condition... 

Minimizing G with respect to the variables and Ni implies that in equilibrium one has equality of the chemical potentials and osmotic pressure. We thus have ... 

Free Energy, Chemical Potentials, and Osmotic Pressure... 

Because in an equilibrium state the solvent chemical potential must be the same on both sides of the semipermeable membrane, there is a relation between chemical potentials and osmotic pressure given by... 

It is also possible to relate differences in chemical potential to osmotic pressure which can be used to measure number-average molar masses of polymers. 

The criterion for phase equilibrium is given by Eq. (8.14) to be the equality of chemical potential in the phases in question for each of the components in the mixture. In Sec. 8.8 we shall use this idea to discuss the osmotic pressure of a... 

FIG. 21 Dependence of the average density on the configurational chemical potential. The solid line denotes the grand canonical Monte Carlo data, the long dashed fine corresponds to the osmotic Monte Carlo results for ZL = 40, and the dotted line for ZL = 80. (From Ref. 172.)... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

Panagiotopoulos et al. [16] studied only a few ideal LJ mixtures, since their main objective was only to demonstrate the accuracy of the method. Murad et al. [17] have recently studied a wide range of ideal and nonideal LJ mixtures, and compared results obtained for osmotic pressure with the van t Hoff [17a] and other equations. Results for a wide range of other properties such as solvent exchange, chemical potentials and activity coefficients [18] were compared with the van der Waals 1 (vdWl) fluid approximation [19]. The vdWl theory replaces the mixture by one fictitious pure liquid with judiciously chosen potential parameters. It is defined for potentials with only two parameters, see Ref. 19. A summary of their most important conclusions include ... 

The chemical potential of associating systems has also been studied more recently by Bryk et al. [2]. They have extended the usual GEMC method for studying osmotic equihbrium by including four simulation cells in series, rather than the usual two compartments, but with osmotic equilibrium established between only two adjacent compartments (e.g. I and II, II and III, or IV and I). Each semi-permeable membrane was made permeable to only one species as shown and described below ... 

P. Bryk, A. Patrykiejew, O. Pizio, S. Sokolowski. The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations. Mol Phys 92 949, 1997 A method for the determination of chemical potential for associating liquids. Mol Phys 90 665, 1997. 

R. L. Rowley, M. Henrichsen. Calculation of chemical potential for structured molecules using osmotic molecular dynamics simulations. Fluid Phase Equil 137 15, 1997. 

The swelling pressure or osmotic deswelling data can be, therefore, described as the functions of n(w) by either of the theories [115]. This description can be then applied to determining the network parameters (see, for example, Ref. [22]). On the other hand, the swelling pressure which is directly connected with the chemical potential of water in the gel ... 

To survive freezing, a cell must be cooled in such a way that it contains little or no freezable water by the time it reaches the temperature at which internal ice formation becomes possible. Above that temperature, the plasma membrane is a barrier to the movement of ice crystals into the cytoplasm. The critical factor is the cooling rate. Even in the presence of external ice, most cells remain unfrozen, and hence, supercooled, 10 to 30 degrees below their actual freezing point (-0.5 °C in mammalian cells). Supercooled cell water has a higher chemical potential than that of the water and ice in the external medium, and as a consequence, it tends to flow out of the cells osmotically and freeze externally (Figure 1). 

From the chemical potential we may at once set down expressions for the activity ai of the solvent and for the osmotic pressure tz of the solution, using standard relations of thermodynamics. For the activity... 

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