The virial series of viscosity in polyelectrolyte concentration c can be obtained from Eq. (229) by iterating S(k) to the desired order in c and then combining with Eq. (38). To the leading order in c, Eq. (229) yields [Pg.47]

Bjemim parameter. The virial series is an expansion in the total ionic concentration c at a fixed value of [Pg.511]

A2.3.2.2 EQUATIONS OF STATE, THE VIRIAL SERIES AND THE LIQUID-VAPOUR CRITICAL POINT [Pg.441]

The extended virial equations are made up of a truncated virial series followed by a closure term or terms, hi the Benedict-Webb-Rubin (BWR) Equation (4.177), the closure term is an exponential. [Pg.312]

Developing the osmotic pressure in a virial series one obtains [Pg.180]

The coefficient of the first term of the virial series in Equation I is the inverse Henry constant for the temperature considered. From the graph of the isotherm in Figure 3 of the survey paper, it follows that the linearity of the initial section of the adsorption isotherm of ethane on zeolite LiX in accordance with the calculated Henry constant is observed for adsorption values not exceeding 0.7 mmole/g. According to K. N. [Pg.63]

Figure A2.3.4 The equation of state P/pkT- 1, calculated from the virial series and the CS equation of state for hard spheres, as a fimction of q = where pa is the reduced density. |

Since dilute solutions are considered we can expand the osmotic pressure in a virial series that is truncated at the second virial coefficients [Pg.134]

Both Fade approximant " and the more powerful Tova approximant" predictions of the tails of the virial series are consistent with the location of the first-order pole at the crystal close-packed density, as required by the closure for the virial series. In fact, Baram and Luban" give this as a conclusion of their work. The known virial coefficients in the soft-sphere, inverse twelfth power models also imply that the virial series contains information on the crystalline phase at very high pressure, but is unrelated to the freezing transition, the glass transition, or the amorphous solid equation of state. ° [Pg.447]

An approach based on the virial expansion suffers from the difficulty of evaluating higher coefficients for highly asymmetric particles and from the non-convergence of the virial series at the concentrations required for formation of a stable nematic phase Lattice methods therefore take precedence over the virial expansion as a basis for quantitative treatment of the liquid crystalline state. [Pg.3]

Occasionally, the temperature voltage coefficient is not expressed as a simple number, but as apower series in T (we generally call it a virial series, or expansion). For example, Equation (7.19) cites such a series for the cell Pt(S) H2(g) HBr(aq) AgBr(s) Ag(s) [Pg.297]

For low density (large Vm), the series (2.30) is expected to achieve useful accurary with only a few terms. Higher densities within the domain of convergence require additional terms to achieve a desired accuracy. For some densities, the virial series may not converge at all. [Pg.45]

In physical chemistry there are a number of applications of power series, but in most applications, a partial sum is actually used to approximate the series. For example, the behavior of a nonideal gas is often described by use of the virial series or virial equation of state. [Pg.170]

The nth virial coefficient = < is independent of the temperature. It is tempting to assume that the pressure of hard spheres in tln-ee dimensions is given by a similar expression, with d replaced by the excluded volume b, but this is clearly an approximation as shown by our previous discussion of the virial series for hard spheres. This is the excluded volume correction used in van der Waals equation, which is discussed next. Other ID models have been solved exactly in [14, 15 and 16]. [Pg.460]

In this section we shall explain somewhat the results which we have just presented. We are interested this time in the evolution equation for the one-particle distribution function. We write down the virial series expansion of the transport equation and we recall that every contribution to this equation is proportional to V n+d, where n is the number of particles which are involved [Pg.336]

Carbon dioxide. Collision-induced absorption in carbon dioxide shows a discernible density dependence beyond density squared, even at densities as low as 20 amagats [34]. Over a range of densities up to 85 amagats the variation of the absorption with density may be closely represented by a (truncated) virial series (as in Eq. 1.2, with I(v) replaced by a(v)) of just two terms, one quadratic and the other cubic in density. The coefficient of g3 is negative. Relative to the leading quadratic coefficient, it is, [Pg.106]

The stabilization of the collapsing coil comes from other terms of the interaction part of the free energy. The interaction energy per unit volume is an intrinsic property of any mixture, that is often expressed as a virial expansion in powers of the number density of monomers c [Eq. (3.8)]. The relevant volume of interest here is the pervaded coil volume R. The excluded volume term is the first term in the virial series and counts two-body interactions as vc. The next term in the expansion counts three-body [Pg.116]

It is detemrined experimentally an early study was the work of Andrews on carbon dioxide [1], The exact fonn of the equation of state is unknown for most substances except in rather simple cases, e.g. a ID gas of hard rods. However, the ideal gas law P = pkT, where /r is Boltzmaim s constant, is obeyed even by real fluids at high temperature and low densities, and systematic deviations from this are expressed in tenns of the virial series [Pg.441]

This value of kn is actually low by an order of magnitude for dilute suspensions of charged spheres of radius Rg. This is due to the neglect of interchain correlations for c < c in the structure factor used in the derivation of Eqs. (295)-(298). If the repulsive interaction between polyelectrolyte chains dominates, as expected in salt-free solutions, the virial expansion for viscosity may be valid over considerable range of concentrations where the average distance between chains scales as. This virial series may be approxi- [Pg.48]

We first consider the case of a two-component solution (biopolymer + solvent) over a moderately low range of biopolymer concentrations, i.e., C < 20 % wt/wt. The quantities pm x in the equations for the chemical potentials of solvent and biopolymer may be expressed as a power series in the biopolymer concentration, with some restriction on the required number of terms, depending on the steepness of the series convergence and the desired accuracy of the calculations (Prigogine and Defay, 1954). This approach is based on simplified equations for the chemical potentials of both components as a virial series in biopolymer concentration, as developed by Ogston (1962) at the level of approximation of just pairwise molecular interactions [Pg.82]

See also in sourсe #XX -- [ Pg.125 ]

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