Second virial coefficients from light scattering

In principle, there is agreement between values of second virial coefficients from light scattering or X-ray scattering. Okano et applied SAXS to semidilute solu-... 

Aside from the difference just noted, the interpretation of the second virial coefficient in light scattering is exactly the same as that developed in Section 3.4. It should be noted, however, that Equation (39) does not apply to charged systems. The reason for this lies in the... 

This theoretical form is the basis of the Zimm plot that yields the molecular weight, the mean-squared radius of gyration, and the osmotic second virial coefficient from measurements of the excess light scattering as a function of angle and concentration. A typical Zimm plot is shown in Figure 5.2. 

A graphical method, proposed by Zimm (thus tenned the Zinnn plot), can be used to perfomi this double extrapolation to detemiine the molecular weight, the radius of gyration and the second virial coefficient. An example of a Zinnn plot is shown in figure Bl.9.6 where the light scattering data from a solution of poly... 

The alternative value, which describes the polymer-solvent interaction is the second virial coefficient, A2 from the power series expressing the colligative properties of polymer solutions such as vapor pressure, conventional light scattering, osmotic pressure, etc. The second virial coefficient in [mL moH] assumes the small positive values for coiled macromolecules dissolved in the thermodynamically good solvents. Similar to %, also the tabulated A2 values for the same polymer-solvent systems are often rather different [37]. There exists a direct dependence between A2 and % values [37]. 

Tables VI and VII give results corresponding to two series of lignin fractions obtained with a flow-through reactor (3). (The units for dn/dc and A2 are respectively ml.g-1 and mole.ml.g-2). These results show that LALLS allows the determination of low Mw values. The dn/dc values differ from sample to sample but vary only slightly for a given set of fractions. The second virial coefficient exhibits no definite trend. Negative values indicate perhaps some association effects but light scattering alone is not sufficient to ascertain this point.

Figure 3.5 Demonstration of correlation between the stickiness of protein-coated droplet pair encounters in shear flow (left ordinate axis) and viscoelasticity of concentrated emulsions (right ordinate axis) with the strength of protein-protein attraction as indicated by the second virial coefficient A2 determined from static light scattering , percentage capture efficiency (0%) A, complex shear modulus (G ) for emulsions stabilized by asl-casein or (3-casein (pH = 5.5, ionic strength in the range 0.01-0.2 M).

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.

Deszczynski, M., Harding, S.E., Winzor, D.J. (2006). Negative second virial coefficients as predictors of protein crystal growth evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients. Biophysical Chemistry, 120, 106-113. 

The diffuse part of the double layer is of little concern to us at this point. Chapters 11 and 12 explore in detail various models and phenomena associated with the ion atmosphere. At present it is sufficient for us to note that the extension in space of the ion atmosphere may be considerable, decreasing as the electrolyte content of the solution increases. As micelles approach one another in solution, the diffuse parts of their respective double layers make the first contact. This is the origin of part of the nonideality of the micellar dispersion and is reflected in the second virial coefficient B as measured by osmometry or light scattering. It is through this connection that z can be evaluated from experimental B values. 

From low-angle-laser-light-scattering measurements, one can take the absolute average molecular weight and the second virial coefficient A, which is an indication... 

Here BLS is the second virial coefficient of the polymeric solute in the original solution before ultracentrifugation. BLs is a quantity which can be obtained in light-scattering experiments (17, 25, 30) or in Archibald experiments (31), provided it is calculated from a plot of l/MWapp° vs. c. Here 1/Mw pp° is obtained from values of Mw pp (at rm or rb) that have been extrapolated to zero time. The reason for using Equation 75 is that it leads to a simple method of estimating the MWD in nonideal solutions. 

The mass-average molar mass of the block copolymer solute, M , and the second virial coefficient, A2, can be obtained from SLS. These quantities can be determined from the concentration dependence of the scattered light intensity using the relationship (cf. Section 1.4.10)... 

The second virial coefficient A2 from osmometry, light scattering, and sedimentation experiments were found in the same range, 4-10-10-7 molTg-2 for DADMAC contents 8-100 mol %. The change is mainly influenced by the changes in charge density [46,67,131]. 

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