Second viral coefficient

For a more detailed and critical discussion of the second viral coefficient, the reader is referred to Section IV A. 

B. Guo, S. Kao, H. McDonald, A. Asanov, L.L. Combs, W.W. Wilson, Correlation of second viral coefficients and solubilities useful in protein crystal growth, J. Cryst. Growth 196 (1999) 424-433. 

One might also question whether the truncation of the expansion at the second viral coefficient level and the neglect of the protein-protein interaction term in Equation 30 is valid (24). While the inclusion of three-body terms (and of the protein-protein term) should improve the comparison with experiment quantitatively, we suspect that the trends predicted for the protein partition coefficient as a function of molecular weight would be the same. 

Second viral coefficient molcm g Nephila clavipes spider dragline 3.0 X 10 (13)... 

An increase in concentration Oion of added salt ions, leads to the penetration of salt ions into the star interior and a decrease in the differential osmotic pressure. When the concentration of added ions sufficiently exceeds the average concentration of counterions in the osmotic star, the polyion is found in the so-called salt-dominated regime. Here, the differential osmotic pressure of ions is equivalent to that created by binary monomer-monomer interactions with an effective second viral coefficient Ueff = a /24>ion. As a result, one recovers the same scaling dependence for the size of a PE star as that found for neutral star polymer under good solvent conditions, (4), with replacement u —> Uetr ... 

Dynamic light scattering is the most popular method. Results are usually expressed by the radius of gyration, Rg, the second viral coefficient, Aj, flic association number, p, and the number of arms, f, for starlike micelles. 

Some interesting results have been obtained for mixtures of glassy polymers which are similar in type and described in the literature as compatible. The coil dimensions of the copolymer of acrylonitrile and styrene (PSAN) dispersed in deuteropoly(methyl methacrylate) have been measured in those compositions in which the copolymer forms molecularly disperse mixtures. The coils are expanded as compared with the unperturbed coil dimensions. Measurements of the second viral coefficient at different temperatures show that the system is exothermic and has a negative excess entropy of mixing. Measurements of the coil dimensions in mixtures of poly(dimethyl siloxane) with the deuteriated polymer also show that the coil of the former expands compared to the 0-value as the... 

A. Baranowska, B. Fernandez, A. Rizzo, B. Jansik, The CO-Ne van der Waals complex ab initio intermolecular potential energy, interaction induced electric dipole moment and polarizability surfaces, and second viral coefficients. Phys. Chem. Chem. Phys. 11, 9871... 

A(Q,R,L, a) Form factor for an ensemble of isotropically oriented cylinders A, B and C Terms of the quadratic regression problem that relates the measured intensities to the scattering length densities A2 Second viral coefficient... 

Here A2 denotes the second viral coefficient, P(Q) the polymer form factor, and Vp the molar polymer volume. For a Gaussian coU ... 

The temperature dependence of many properties of methanol has been described in figures, tables, and equations. Plots of vapor pressure, liquid density, liquid heat capacity, vapor heat capacity, heat of vaporization, surface tension, liquid thermal conductivity, vapor thermal conductivity, liquid viscosity, and vapor viscosity against temperature have been given by Yaws [13] and by Flick [14]. Tables of vapor pressure [3,1517], liquid density [3,15,17], liquid volume [16], vapor density [15,17], vapor volume [16], liquid viscosity [15,18], vapor viscosity [15], surface tension [15,19], liquid heat capacity [15,17,20], vapor heat capacity [3,15,17], solid heat capacity [11], liquid thermal conductivity [15,17], vapor thermal conductivity [15], second viral coefficient [16], dielectric constant [21], refractive index [3], and heat of vaporization [16] have also been published. Thermodynamic properties of methanol in the condensed phases have been tabulated by Wilhoit et al. [11], and those in the gas phase have been given by Chao et aL [9]. 

For the time being, a rigorous characterization and modehng of particle interactions is only possible for simple model systems A nice and very recent example is the measurement of the second viral coefficient and structure factor of quantum dots in solution by three independent methods, namely small-angle X-ray scattering (SAXS), cryo-TEM, and centrifugation (Van Rijssel et al, 2014). Nevertheless, the above-described approach can be transferred to many technical applications in a qualitative and conceptual way. 

We then numerically integrate Equation (E4.10B) at different values of dimensionless temperature, and convert back to T and B, using the Lennard-Jones parameters in Table 4.2. The results are plotted as a solid curve in Figure E4.10A. The experimental data given earlier are also plotted for comparison. The second viral coefficient obtained from the Lennard-Jones potential reasonably represents the experimental data. 

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