Molecular weight and second virial

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. 

Next, we introduce the theory of Rayleigh scattering (Section 5.3), the first of many models covered in the chapter. The Rayleigh theory for dilute systems and solutions is developed here, with illustrative examples of the determination of molecular weight and the second virial coefficient. This is followed by a brief description of some of the basic experimental considerations and an introduction to absorbance and turbidity (Section 5.4). 

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... 

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

Mw is the weight-average molecular weigA the second virial coefncierRh, hydrodynamic radius. aTaken from Reddy et al. (1990). bTaken from Zhou and Chu (1988). 

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

M in Eq. (7-7) is the number-averaged polymer molecular weight, and A2 is the second virial coefficient for a theta solvent, A2 = 0, while in a good solvent, A2 > 0. The better the solvent, the stronger the depletion flocculation. 

In Equation 2, Vi and v2 are the probe molar volume and polymer specific volume, respectively M2 is the polymer molecular weight and R is the gas constant. Pi is the probe vapor pressure and Bn is its second virial coefficient in the gas phase. For work with high polymers, the third term of Equation 2 becomes negligible and may be omitted. 

The density of chlorobenzene is 1.10 g/cm. Calculate for the polymer (a) molecular weight and (b) the second virial coefficient. 

By experimentally measuring the turbidity as a function of concentration, one can obtain the molecular weight of solute and the second virial coefficient, B2, which characterizes interactions between solute molecules (or particles). In systems containing charged particles, such as e.g. micelles of ionic surfactants, the second virial coefficient describes the effective charge of particles. The molecular weight and the second virial coefficient can be determined by plotting the quantity Hc/x as a function of concentration, c. 

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