Second virial coefficient light scattering

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... 

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. 

For accuracy in light-scattering measurement the proper choice of solvent is necessary. The difference in refractive index between polymer and solvent should be as large as possible. Moreover, the solvent should itself have relatively low scattering and the polymer-solvent system must not have too high a second virial coefficient as the extrapolation to zero polymer concentration becomes less certain for high A2. Mixed solvent should be avoided unless both components have the same refractive index. 

The intrinsic viscosity of PVB is shown as a function of solvent composition for various MIBK/MeOH mixtures in Figure 6. Since [ij] increases with a (see Equation 8), the higher [ly] the better the solvent. Apparently, most mixtures of MIBK and MeOH are better solvents for PVB than either pure solvent. Based on Figure 6, PVB should have a weak selective adsorption of MIBK in a 1 1 solvent mixture and weak adsorption of MeOH in a 3 1 MIBK/MeOH solvent mix. These predictions are in accord with light scattering data discussed previously. The intrinsic viscosity data is also consistent with the second virial coefficient data in Table II in indicating that the 1 1 and 3 1 MIBK/MeOH mixtures are nearly equally good solvents for PVB, the 9 1 mix is a worse solvent, but still better than pure MeOH. 

Because all the above deductions are valid for infinite low polymer concentrations but practical measurements have to be carried out at finite values of c, it is necessary to include the second virial coefficient A2. Thus the equation according to which evaluation of light-scattering experiments can be done is ... 

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).

It is important to note that the values of the second virial coefficients determined by light scattering are weight-average quantities. The general expression for the second virial coefficient of a polydisperse polymer is as follows (Casassa, 1962) ... 

The advantage of static light scattering over some other methods of determining the second virial coefficient is the capability to measure both thermodynamic (A2) and structural parameters (Mw, Rq) in a single... 

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.

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. 

Figure 6.11 Effect of ionic strength on (a) weight-average molar weight, Mw ( ), and second virial coefficient, A2 ( ), of p-casein in solution at pH = 5.5 and 22 °C, as determined by static light scattering and (b) average droplet diameter, c/43 (A.), and extent of gravity creaming ( ) of p-casein-stabilized emulsion (11 vol% oil, 0.6 wt% protein, pH = 5.5, 22 °C).

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... 

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. 

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