Second virial coefficient comparison

Figure 5. Ethylene second virial coefficient comparison. AB2=B2 (Dous-lin) — B2 (this chapter) (%), Douslins graphical value (O), least-squares value from Douslins data.

Let us now consider some actual numerical data for specific mixed biopolymer systems. Table 5.1 shows a set of examples comparing the values of the cross second virial coefficients obtained experimentally by static laser light scattering with those calculated theoretically on the basis of various simple excluded volume models using equations (5.32) to (5.35). For the purposes of this comparison, the experimental data were obtained under conditions of relatively high ionic strength (/ > 0.1 mol dm- ), i.e., under conditions where the contribution of the electrostatic term (A if1) is expected to be relatively insignificant. 

Table 5.1 Comparison of the cross second virial coefficients obtained experimentally by static laser light scattering with those calculated from theory on the basis of the excluded volume contribution only.

Table 3.3 also includes an approximation for the case in which the concentration of the salt exceeds that of the colloid, but not to the swamping extent, mM > mP. Comparison of that case with the result given in Equation (34) suggests that the contribution of charge to the second virial coefficient of the solution is given by... 

These examples, and the previous summaries of the results for other dimers7,8, demonstrate that the pair potentials from ab initio SAPT calculations are indeed accurate. Another, more global, comparison with experiment which confirms this finding was made by computations of the (pressure) second virial coefficients of all of these dimers over a wide range of temperatures364. 

Simulations of the liquid water properties have been the subject of many papers, see Ref. (374) for a review. Recently a two-body potential for the water dimer was computed by SAPT(DFT)375. Its accuracy was checked375 by comparison with the experimental second virial coefficients at various temperatures. As shown on Figure 1-16, the agreement between the theory and experiment is excellent. Given an accurate pair potential, and three-body terms computed by SAPT376, simulations of the radial 0-0, 0-H, and H-H distribution functions could be... 

Most interesting is the comparison among the three systems. We have seen that the various potential energy surfaces look different topographically however, similar results are obtained for some specfroscopic observables, in spife of fhe fact that geometry and values of well depfhs and positions differ significantly, but what varies is their ability to reproduce other experimental data (integral cross-sections and second virial coefficient). These quantities are therefore most sensitive probes of dimer sfructure and dynamics. 

The independence of and of T must be expected in those regions of the phase diagram, where the attraction between the rods is negligible in comparison with their mutual repulsion. Since the high-temperature corridor of the phase diagram is situated at i 1/p I, i.e. in the region of validity of the second virial approximation, this statement can be reformulated as follows the values of and do not depend on temperature if the contribution of the attraction to the second virial coefficient, Ba, is much less than that of the repulsion, B,. 

This is confirmed by a recent comparison [90] of calculated and experimental values of second virial coefficient in the temperature range 298-373 K, which turned out underestimated by as much as 300 % by the TIP4P model. 

The enthalpy of micelle formation of various mixed sodium dodecylsulfate (NaDDS) and sodium deoxycholate (NaDOC) systems was measured by calorimeter In aqueous systems. The heat of micelle formation, AH, showed a maximum around NaDDS NaDOC molar ratio 1. These data are analyzed In comparison to the aggregation number of mixed micelles and the second virial coefficient, Bg. 

Figure 1 Temperature dependence of the second virial coefficient of water as predicted by six models in comparison with experimental data...

Comparison of the ab initio and experimental second virial coefficients. The solid and dashed lines represent second virial coefficients generated from the original and scaled a6 initio potentials, respectively, while the dotted line shows the second virial coefficient calculated using the isotropic component of the ab initio potential. Circles and squares are experimental points from Refis. (74) and (73), respectively. 

In Figure 5, we present a comparison of our preferred values for the ethylene second virial coefficient with comparable state of the art results obtained by Douslin and Harrison (2). The experimental method and data analysis used by Douslin are independent from ours. In Douslin s experiment, all of the variables required for the calculation of the compressibility factor are measured, whereas in the Burnett method only two variables are measured. Aslo, in this experiment the same sample of gas is retained for the entire experiment in the Burnett isothermal method, the sample is changed for each sequence of measurements. Furthermore,... 

We have already in this and the previous sections made a number of comparisons between the various theories of fluids and the machine computations for the hard sphere system. Unfortunately, many recent developments in theory have been evaluated numerically only to the extent that the fourth and fifth virial coefficients can be compared. The table below lists the values of the fourth and fifth virial coefficients for the three-dimensional hard sphere fluid in units of the second virial coefficient b [cf. Eq. (33)]. The bases of calculation have been identified already in Section III except for the older "netted-chain approximation of Rushbrooke and Scoins. ... 

Polyelectrolyte molecules in highly dilute aqueous solutions exert strong electrical repulsions on each other. These repulsive forces are long range (proportional to l/r ) by comparison with normal dispersion forces (proportional to 1/r ), and as a consequence the intermolecular interactions persist down to the lowest measured concentrations. In osmotic-pressure measurements on polyelectrolytes, the Donnan membrane equilibrium must be satisfied and experimental results indicate that the second virial coefficient in the osmotic-pressure equation (p. 915) becomes very large. 

Table 2. Comparison of second virial coefficients for argon...

The acoustic virial coefficient ofQH was determined from the pressure dependence of the sound velocity in the temperature range of 270 K-380 K The second virial coefficient B(T) was calculated from these acoustic virial coefficients and literature values available for B(T) n r 270 K. The resulting temperature dependence and a comparison with data reported by Douslin and Harrison and by Waxman and Davis is shown in Fig. 16. The maximum deviation is 0,8cm /mole at 373 K. 

Table III. Comparison of Calculated and Corresponding States Values of the Second Virial Coefficient for Methane—Nitrogen System in cc/mole...

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