Compressibility, osmotic

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

In dispersions of particles and nonadsorbing polymer, flocculation may be induced at certain concentrations (11). At low concentrations the presence of free polymer has no effect on the dispersion stability, but as the concentration is raised flocculation occurs. As two particles approach each other, at separations corresponding to twice the radius of gyration of the polymer, polymer becomes excluded from the volume of solution between the particles. The particle separation is such that polymer is prevented from entering the interparticle space. The gap can now be considered as an osmotic membrane, permeable only to solvent molecules. The bulk solution thus exerts a compressive osmotic pressure and solvent drains from the space between the particles causing the particles to flocculate. 

The themiodynamic properties calculated by different routes are different, since the MS solution is an approximation. The osmotic coefficient from the virial pressure, compressibility and energy equations are not the same. Of these, the energy equation is the most accurate by comparison with computer simulations of Card and Valleau [ ]. The osmotic coefficients from the virial and compressibility equations are... 

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. 

A third exponent y, usually called the susceptibility exponent from its application to the magnetic susceptibility x in magnetic systems, governs what m pure-fluid systems is the isothennal compressibility k, and what in mixtures is the osmotic compressibility, and detennines how fast these quantities diverge as the critical point is approached (i.e. as > 1). 

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

If the dmg itself cannot provide the osmotic driving force, then a push-puU design of the osmotic system is available with other salts as the osmotic force. This system is schematized in Eigure 5. The outer surface is a rigid semi-permeable membrane that surrounds the osmotic layer of salt (propeUant). Inside the osmotic layer is a compressible membrane that surrounds the dmg solution. As the salt layer sweUs with water, the inner membrane compresses and pushes out the dmg solution. 

Now suppose this brought to unit concentration by compressing with an osmotic piston. Work done... 

Two mechanisms of steric stabilization can be distinguished entropic stabilization and osmotic repulsion. Entropic stabilization arises when two opposing adsorbed polymer layers of adjacent particles overlap, resulting in compression and interpenetration of their... 

Two repulsive contributions, osmotic and elastic contributions [31, 32], oppose the van der Waals attractive contribution where the osmotic potential depends on the free energy of the solvent-ligand interactions (due to the solvation of the ligand tails by the solvent) and the elastic potential results from the entropic loss due to the compression of ligand tails between two metal cores. These repulsive contributions depend largely on the ligand length, solvent parameters, nanopartide radius, and center-to-center distance ... 

High Sugar Yeasts. These are products specially produced to work under the high osmotic pressures in products like Danish pastries. These yeasts are available in the form of IADY products. There are also some Japanese strains of compressed yeast that can stand high osmotic pressures. 

Accordingly to (19) the osmotic compressibility dlt / dc into diluted solutions does not depend on the concentration of macromolecules (dft / dc = RT) on the contrary, in semi-diluted solutions it becomes (as it follows from (25)) as linear function of relative concentration ... 

It follows that the osmotic compressibility C7i / dc = von / dtp will be equal to... 

In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

As demonstrated in a previous section the osmotic compressibility can be obtained from the forward scattering of light... 

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