Virial coefficients measurement

Saunders, A.E. and Korgel, B.A. (2004) Second virial coefficient measurements of dilute gold nanocrystal dispersions using small-angle x-ray scattering. Journal of Physical Chemistry B, 108 (43), 16732-16738. 

The second virial coefficients measured in various solvents at room temperature after heating are given in Table I. In the absence of aggregation and selective adsorption, a ranking by quality of solvents for PVB would follow the order of A2 values. The higher A2, the better the solvent. However, since these effects were not completely absent in the data used to construct Table I (particularly in the 9 1 solvent mixture), the solvent ranking given in this table must be considered tentative. 

TABLE 11.7 SPECIFIC SURFACE AREA FROM BET AND THIRD VIRIAL COEFFICIENT MEASUREMENTS... 

These data were obtained by estimating the chain expansion factor a from viscosity and osmotic second virial coefficient measurements, through the combined use of equations (10) and (11). These results tend to confirm the main predictions of the theory presented by the above mentioned authors both as regards the steep decrease in with... 

The results of virial coefficient measurements are also discussed by E. A. Guggenheim.il For an interesting recent discussion of the data concerning intermolecular forces between unlike molecules see A. Michels and A. J. M. Boerboom. The relationship between virial coefficients and intermolecular forces has also been discussed in some detail by Guggenheim, and by J. S. Rowlinson. ... 

Fig. 16i. Values of the second virial coefficient measured at various temperatures in the vicinity of Trr(S). (From Strazielle and Benoit4.)...

This section discusses how spectroscopy, molecular beam scattering, pressure virial coefficients, measurements on transport phenomena and even condensed phase data can help determine a potential energy surface. 

Note added in proof. Table 5 is a summary of interaction virial coefficient measurements reported since the manuscript was first submitted. A review of the chromatographic method has appeared and a compilation of Bifs for hydro-... 

TABLE 12.8 Second Virial Coefficients Measurements by Gas Chromatography... 

As a first approximation the second virial coefficient measures the size of the sugar molecule. However, there are two sugars which have the same molecular weight, and are stereoisomers xylose and ribose. It turns out that a 1 M solution of ribose is as near as can be ideal, it has a zero second virial coefficient, whereas xylose has quite... 

The third virial coefficient C(7) depends upon tliree-body interactions, both additive and non-additive. The relationship is well understood [106. 107. 111]. If the pair potential is known precisely, then C(7) ought to serve as a good probe of the non-additive, tliree-body interaction energy. The importance of the non-additive contribution has been confimied by C(7) measurements. Unfortunately, large experimental uncertainties in C (7) have precluded unequivocal tests of details of the non-additive, tliree-body interaction. 

Equation (8.97) shows that the second virial coefficient is a measure of the excluded volume of the solute according to the model we have considered. From the assumption that solute molecules come into surface contact in defining the excluded volume, it is apparent that this concept is easier to apply to, say, compact protein molecules in which hydrogen bonding and disulfide bridges maintain the tertiary structure (see Sec. 1.4) than to random coils. We shall return to the latter presently, but for now let us consider the application of Eq. (8.97) to a globular protein. This is the objective of the following example. 

The parameter a which we introduced in Sec. 1.11 to measure the expansion which arises from solvent being imbibed into the coil domain can also be used to describe the second virial coefficient and excluded volume. We shall see in Sec. 9.7 that the difference 1/2 - x is proportional to. When the fully... 

Krigbaumf measured the second virial coefficient of polystyrene in cyclohexane at several different temperatures. The observed values of B as well as some pertinent volumes at those temperatures are listed below ... 

Here eK, gk are the force constants for the pure solute K, which can be determined from measurements of its second virial coefficient, and q, oq are similar, but as yet unknown, constants characteristic for the / -hydroquinone lattice. 

Equation 8 may be fitted to those results just described for which the vapor pressure of the pure solid is known. We show graphically the second virial coefficients derived from such fitting and those derived from conventional p-V-T measurements. 

Figure 15 shows the second virial coefficients derived independently by us and by Reuss and Beenakker66 from the measurements of solubility by Dokoupil, van Soest, and Swenker,18 and the coefficients at room temperature from the conventional measurements of Verschoyle,86 Michels and Wassenaar,49 and Michels and Boer-boom.47 These results are sufficient to give unambiguously the parameters of a 12-6 potential... 

Figure 17 shows two sets of virial coefficients—derived by us and by Reuss and Beenakker56 from the measurements of Dokoupil,... 

The virial coefficients at 190°K have been calculated from Ewald s results22 and may be combined with the measurements at room temperature of Michels and Boerboom,47 of Cottrell and his colleagues,11 12 and of Harper and Miller,32 to give the parameters for helium + carbon dioxide... 

The second virial coefficients at 155°K are, respectively, +15, —9, and —19 cm3/mole for these three systems.22 There are no measurements at room temperature. 

Intrinsic viscosity measurements revealed a conformational transition upon heating from 26 to 40 °C, while the UV absorbance of the solution was insensitive to the change. The entropy parameters for PA were also discussed in light of the Flory-Krigbaum correlation between the second virial coefficient and theta temper-... 

The same measurements also provide values of the second virial coefficient, which corresponds to the repulsive energy between micelles. The coefficient of the Na methyl a-sulfomyristate decreases from 7.30 x 10 3 to 3.05 x 10"4 ml/ g with increasing concentration of the electrolyte. The second virial coefficient of the calcium salt is small and changes to a negative value in 0.01 N Ca(N03)2. 

The second virial coefficient B in Eq. 17 refers to the static case. In the ultracentrifuge the measured value can show a speed dependence [39], an effect which can be minimized by using low speeds and short solution columns. If present it will not affect the value of after extrapolation to zero concentration. 

Theta temperature (Flory temperature or ideal temperature) is the temperature at which, for a given polymer-solvent pair, the polymer exists in its unperturbed dimensions. The theta temperature, , can be determined by colligative property measurements, by determining the second virial coefficient. At theta temperature the second virial coefficient becomes zero. More rapid methods use turbidity and cloud point temperature measurements. In this method, the linearity of the reciprocal cloud point temperature (l/Tcp) against the logarithm of the polymer volume fraction (( )) is observed. Extrapolation to log ( ) = 0 gives the reciprocal theta temperature (Guner and Kara 1998). 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

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