Distribution equilibrium INDEX

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

In industrial reactors, the full equilibration of the chain length distribution is prevented by incomplete mixing, as well as by the residence time distribution, thus resulting in considerable deviations from the equilibrium polydispersity index. These deviations are generally higher for continuous plants than for batch plants and increase with increasing plant capacity as demonstrated in Figure 2.2. 

Evidently, correlation functions for different spherical harmonic functions of two different vectors in the same molecule are also orthogonal under equilibrium averaging for an isotropic fluid. Thus, if the excitation process photoselects particular Im components of the (solid) angular distribution of absorption dipoles, then only those same Im components of the (solid) angular distribution of emission dipoles will contribute to observed signal, regardless of the other Im components that may in principle be detected, and vice versa. The result in this case is likewise independent of the index n = N. Equation (4.7) is just the special case of Eq. (4.9) when the two dipoles coincide. 

MINTEQA2 http //www.epa.gov/ceampubl/mmedia/minteq/index.htm MINTEQA2 is an equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressures. 

Distribution ratio is the total analytical concentration of a substance in the organic phase to its total analytical concentration in the aqueous phase, usually measured at equilibrium. Symbol D. D shall be defined and, preferably, specified by an index if the distribution of mercury is measured, the distribution ratio is written D(Hg) or The term partition ratio is not used for the distribution ratio. 

While studying polymer distribution between the emulsion phases it was found that in the systems mentioned above obtained both by copolymerization of styrene with polybutadiene rubber and mixing styrene solutions of polymers when the composition is far enough from the critical mixing point, thermodynamic equilibrium is reached.At this thermodynamic equilibrium the ratio of polymer concentration (Cp) in rubber (index ) as well as in polystyrene (index ) phases is practically constant (table II),... 

Polymerization in the equilibrium regime does provide the control of the molecular weight and a narrow molecular weight distribution. The integration of the kinetic equations for the moments of the distribution (see section IV) leads to equations for the number-average degree of polymerization (An) and the polydispersity index PDI = A4 /A4 = Aw/An. 

Here the index I is used to denote a particular charge distribution (i.e. a particular electronic state of the system). The displacement field P/(r) represents a charge distribution p/(r) according to the Poisson equation V T>i = npi. In (16.79) D(r ) and the associated p(r) represent a fluctuation in the nuclear polarization, defined by the equilibrium relationship between the nuclear polarization and the displacement vector (cf. Eqs (16.14) and (16.15))... 

We consider especially ensembles of systems in which the index (or logarithm) of probability of phase is a linear function of the energ>. This distribution on account of its unique importance in the theory of statistical equilibrium, I have ventured to call... 

The study of the osmotic equilibrium between a polymer solution in two solvents and a mixture of these two solvents is quite instructive. In particular, we shall describe a limiting case in which we shall be able to define a coefficient characterizing the action of the polymers on the solvent distribution. First, let us attribute the index 0 to the main solvent, the index 1 to the second solvent, and the index 2 to the polymer. We have / = 1, m = 2. The numbers of molecules are N s, (jit = 0,1,2) in cell I of Fig. 5.1 and (,r/ = 0,1) in cell II. The chemical potentials of the solvents are, respectively,... 

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