Membrane entropic pressures

We initially consider the temperature-induced increase in fluid spacing between liquid-crystalline EPC membranes as functions of the underlying pressure (Pj, = o exp(—df/A)), the attractive van der Waals pressure (Py), and the bilayer undulation pressure (P ). For our calculations, we use for Pj, the repulsive pressure measured for DPPCsg bilayers (Fig. 3), where entropic pressures are small [22], Evans [33] asssumed that the van der Waals pressure decays as df and has a magnitude characterized by the Hamaker constant ( h). and that the undulation pressure is characterized by the Helfrich energy scale , Eh = 1.6n. Evans plotted 2/deq versus Ah/Eu for... 

Let us now assume that the functional form for the entropic contribution, eq 10, holds even when the membrane is subjected to an arbitrary potential, U(u), with a minimum at u = 0. Therefore, the Gibbs free energy of the membrane per unit area at a constant external pressure II is given by... 

When the system is subjected to an external pressure pcxi, the undulations of the membranes occur in such a manna- to minimize the total Gibbs free energy of the system, which is the sum between the enthalpy of the system and the entropic contribution provided by Eq. (10) (see Appendix B) ... 

A practically useful predictive method must provide quantitative process prediction from accessible physical property data. Such a method should be physically realistic and require a minimum number of assumptions. A method which is firmly based on the physics of the separation is likely to have the widest applicability. It is also an advantage if such a method does not involve mathematics which is tedious, complicated or difficult to follow. For the pressure driven processes of microfiltration, ultrafiltration and nanofiltration, such methods must be based on the microhydrodynamics and interfacial events occurring at the membrane surface and inside the membrane. This immediately points to the requirement for understanding the colloid science of such processes. Any such method must account properly for the electrostatic, dispersion, hydration and entropic interactions occurring between the solutes being separated and between such solutes and the membrane. 

Membrane equilibria give rise to a pressure difference between the two phases. For three-dimensional systems this is the osmotic pressure 77, for two-dimensional systems it is the surface pressure, n. For osmosis the driving force is the fact that the chemical potential of the water is lower on the side containing the molecules that cannot pass the membrane. As a result, water is imbibed and this process continues until the water transport has resulted in a pressure compensating n. The driving force is primarily entropical and stems from the mixing entropy the osmotic pressure follows from see [1.2.12.15],... 

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