Molecular weight and second virial coefficient

Archibald (1947) showed that measurement of c and dc/dr at the cell boundaries permit Molecular weight determination at any stage in the equilibrium process. However, when measurements are made early enough, before the molecular species have time to redistribute in the cell, the weight-average Molecular weight and second virial coefficient can be evaluated. In practice, measurements can be made... 

Some of the experimental details of osmometry and the use of osmometry for determining molecular weights and second virial coefficients are discussed in Section 3.3. 

What is the relation between the Rayleigh ratio and the molecular weight and second virial coefficient of a dispersion of colloids or macromolecules ... 

A different line of approach has been used by Flory and Brant for the evaluation of the characteristic ratio of four polypeptides on the basis of intrinsic viscosity, molecular weight and second virial coefficient data 53). 

In order to extract information on the single chain structure from SLS data, it is necessary to fulfill the condition of a single mode scattering, similarly to the extraction of molecular weight and second virial coefficient from SLS data (see Sec. VII). A further condition is that the scattering from polyions should not be influenced by intermolecular interference due to intermolecular interactions, i.e., the solution structure factor S(0) = 1. In this case the total... 

Molecular weight and second virial coefficient (A 2) measurements were made on a KMX-6 fixed low-angle light-scattering (LALLS) spectrometer at 25 °C. The refractive index increments (dnldc) in 2% NaCl were 0.163 for NVP/NaAMPS (50/50), 0.136 for NVP/SPE (50/50), 0.159 for NVP/SPE (80/20), and 0.139 for NVP/SPE (10/90), as measured on a KMX-16 differential refractometer at 25 C. Quasi-elastic light scattering measurements were made on a Brookhaven apparatus. 

DETERMINATION OF MOLECULAR WEIGHT AND SECOND VIRIAL COEFFICIENT... 

FIGURE 14.6 Determination of molecular weight and second virial coefficient. 

A practical use of theoretical estimates of. 43 is to facilitate reliable extrapolation of osmotic and light-scattering data to zero concentration in determining molecular weights and second virial coefficients. Substituting A in terms of y and A 2 into equation (63) and taking the square root gives... 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

Kobayashi, H. Molecular weight dependence of intrinsic viscosity, diffusion constant, and second virial coefficient of polyacrylonitrile. J. Polymer Sci. 39, 369-388 (1959). 

Table 1.3 summarizes molecular weights (Mn) and second virial coefficient (A2) data for various fractions of this polymer. 

Here, R is the gas constant, Mj is the solvent s molecular weight, and P 22 are the saturated vapour pressure and second virial coefficient of the pure solvent at temperature T, respectively. The required vapour pressures and virial coefficients can be calculated or estimated from known relationships [473-477]. Other treatments for the determination of y , which include a term to correct for the free volume contribution due to differences in the size of the solute and solvent, have also been used [478, 479]. The temperature dependence of the resulting solute activity coefficient is related to the infinite dilmion partial molar excess Gibbs energy (AG ) through Eq. (9). 

Table 1. Molecular weights, interaction parameter and second virial coefficient AA2 for PS-PDMS, PMMA-PDMS and PS-PVAc mixtures at mass fraction y = cJ(Ca+Cb) = 0.5. M = (Ma + Mb)/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... 

In the next section we shall describe the use of Eq. (8.83) to determine the number average molecular weight of a polymer, and in subsequent sections we shall examine models which offer interpretations of the second virial coefficient. 

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