Volume fraction of solute

Figure 8. The reduced excess free energy of mixing x versus the volume fraction of solute for a) flexible chain polymers (18) a and b) rodlike chains (17). The chains have 100 segments in both cases.

The cloud point is close to, but not necessarily equal to the lower consolute solution temperature for polydisperse nonionic surfactants (97). These are equal if the surfactant is monodisperse. Since the lower consolute solution temperature is like a critical point for liquid—liquid mixtures, the dilute and coacervate phases have the same composition, and the volume fraction of solution which the coacervate comprises is a maximum at this temperature (98). If a coacervate phase containing a high concentration of surfactant is desired, the solution should be at a temperature well above the cloud point. 

The coefficient v is a limiting ratio, determined by extrapolation to zero volume fraction of solute. In making this extrapolation, it is... 

The theory relates parameters a and to directly measurable physical quantities. The product, volume fraction of solute at which aggregation occurs while a2 is a measure of the sharpness of the transition. For a given value of the product, measurable physical properties in terms of the potential energies of interaction and partition functions of the individual molecules. However, the precise definitions of these parameters are in terms of a rather crude lattice model. Consequently, errors in this model will be taken up by corresponding errors in the experimental assignment of values of these parameters. 

From the theory, one can calculate three different concentrations 0i, the number of lattice sites occupied by solute molecules divided by N, the total number of sites (the volume fraction of solute molecules) 02, the number of contiguously occupied sites, divided by N (the moles of aggregate per unit volume), and 03, the number of lattice sites filled with isolated molecules but surrounded by solvent divided by N (the moles of unassociated molecules per unit volume). These concentrations are calculated from the partition function, E, by the equations,... 

One of the interesting predictions of the theory is that the abruptness of the transition above the critical concentration depends on which property is being measured. This point is illustrated in Figure 5, where Z)w and (Z2)w are plotted against 0i (volume fraction of solute molecule) for various values of a. Quantities which depend upon (Z2)w will show a much more abrupt change above the transition point. 

One can multiply all the occupation variables 5, and collect terms in powers of s,. The result yields a constant term that just redefines the zero of energy for the system, a linear term that multiplies the average volume fraction of solute molecules (which is either fixed or determined by a chemical potential), and a quadratic term. Adding and subtracting terms linear in, the net interaction in the system can be written... 

The above expression for 4AEiast is that of I cm of polymer (dry). If rii moles of solvent are added to I cm of polymer, then the volume fraction of solute ( 2) is given by... 

The parameter will vary with PS molecular weight and with the free energy of dilution (Flory, 1953), kT jj2 — Q/T)v, where is the entropy of dilution, 9 is the Flory theta temperature, and V2 is the volume fraction of solute. 

This, in turn, will affect the patterns of solubilization by cosolvents. Furthermore, a high concentration of solutes may invalidate the log-linear model, which presumes negligible volume fraction of solute and no solute-solute interactions. For solid solutes, solvent induced polymorphism may also bring additional changes in their solubilization profile. 

For steels with Ni levels < 1.2wt% there are significant data on the development of Cu clusters with fluence, irradiation temperature, flux and composition. It has been demonstrated that, as the irradiation proceeds, the number density and size of the clusters build up to a plateau value. There are limited data on the microstructure formed at high fluence, but there is now some evidence for over-ageing of the clusters. The size and number density of Cu clusters formed at a given fluence before the plateau are strongly dependent on the flux and material composition, but only weakly dependent on irradiation temperature. Finally, Ni and Mn may have a profound effect on the development of CECs. At high bulk Ni levels > 1.2wt%, the volume fraction of solute clusters may not reach a plateau (in the dose range of interest). 

Although the Flory-Huggins theory is not truly valid at low-volume fractions of solute, it is useful to examine the dilute limiting law for the osmotic pressure. The expression In (l - x) = -x - / 2--is used ... 

Fig. 9 (a) Structural models of the three enzymes. A is an overview of the tunnel network B is a close-up of the tuimel near the active site in the WT. C, D and E are close-ups of the MM and FI mutants, as indicated. In C, an arrow points to the second conformation of M122. A conserved hydrophilic cavity is shown in blue in E. (b) Comparison of the kinetics of CO inhibition of H2 oxidation in PFV experiments. The current (i) has been normalised by its value I o, measured before CO was added. Left shows the short-term change in current, whereas the end of the relaxation is shown on Right. The dimensionless volumic fractions of solutions saturated under 1 atm of CO at 25°C and injected at time 0. Electrode rotation rate 2 krpm, pH 7. Adapted with permission from [77]. Copyright (2008) PNAS... 

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