Molecular weight from Zimm-plot

Polarizability of particles Molecular weights from Rayleigh ratios Use of Zimm plots... 

Fig. 9.— Double Log Plots of (a) Intrinsic Viscosity, (b) the Reciprocal of the Diffiision Coefficient, and (c) Sedimentation Coefficient Data versus Molecular Weight for Human Cervical Mucins. [Key and O, whole mucins and , subunits and A, T-domains. Molecular weights determined from Zimm plots (filled symbols) or the Svedbeig equation using QLS (open symbols). Values for the slopes are in all cases consistent with a random-coil model and not with a rigid sphere or a rod.]...

Thus, in dealing with large molecules, it is necessary to extrapolate data to = 0 to correct for this intermolecular interference effect. To get the proper molecular weight from a HcjR(q plot, one must carry out a double extrapolation , both to c - 0 and q- Q. One way of doing this is by a Zimm Plot . 

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... 

One of the most important fiinctions in the application of light scattering is the ability to estimate the object dimensions. As we have discussed earlier for dilute solutions containing large molecules, equation (B 1.9.38) can be used to calculate tire radius of gyration , R, which is defined as the mean square distance from the centre of gravity [12]. The combined use of equation (B 1.9.3 8) equation (B 1.9.39) and equation (B 1.9.40) (tlie Zimm plot) will yield infonnation on R, A2 and molecular weight. 

The weight-average Molecular weightin the inverse of the intercept at c = 0 and q = 0 in the Zimm plot. The second virial coefficient can be calculated from the slope of the lines at constant angle by eq. 8.34, and to a first approximation is independent of angle. The radius of gyration is... 

EXAMPLE 5.3 The Use of Zimm Plots Determination of Molecular Weight, Second Virial Coefficient, and Radius of Gyration of Cellulose Nitrate in Acetone. The following are the values of the intercept and slope from Figure 5.9 ... 

The determination of the molecular weight was complicated by the lack of data at low angles, and a simple Zimm plot analysis of the curve (Kc/Rq)c=0 could not be performed in a straightforward way (as suggested by Eq. 4), since it would lead to an underestimated value of the micelle molecular weight. However, from the downward curvature of these different plots we were able to deduce that the scattering particles present in solution had a rod-like shape. 

Table C gives the results of several series of measurements. The absolute value of dn/dc decreases with increasing HEMA content of the polymer. However, it was difficult to obtain reproducible results owing to the absorption of water vapor from the air. Where the angle and concentration lines of Zimm plots are nonlinear, there can be considerable error in determining the common zero intercept for polystyrene, where this is the case, the error in the intercept gave a variation of 30% in the molecular weight. However, for the copolymers the variation was of the order of 10%. The error in determining the radius of gyration and...

Thus from Eqs. (8.4.10) and (8.5.3) we see that the Zimm plot yields the weight average molecular weight of a polydisperse sample. 

The quantity K equals 4it X sin (9/2), where X is the neutron wave length and 9 is the angle of scatter. Thus, the Z-average mean square radius of gyration, R, and the polymer molecular weight, Mj, may be obtained from the slope and intercept respectively of a Zimm plot of [dZ/dn] vs. K. The values of and Rg were evaluated after appropriate subtraction of the scattering from an unlabeled polymer matrix (blank) from the samples containing different fractions of labeled molecules. 

Styrene-methyl methacrylate diblock copolymers have also been studied in a selective solvent, i.e. a solvent which is thermodynamically better for one or other block. For these experiments, p-xylene was used as the solvent since it had been previously reported as a theta solvent for polymethyl methacrylate at drca 40 °C. Separate SANS measurements were made on a copolymer with a deuterated styrene block dissolved in deuterated xylene and in hydrogenous xylene at tmperatures of 30 °C and 40 °C. Deutero xylene has the same scattering length density as deuterostyrene, consequently the scattered intensity is solely attributable to the methyl methacrylate block when the copolymer is dissolved in this solvent. At the two temperatures used conventional Zimm plots were obtained, however the methyl methacrylate block molecular weight obtained at 30 °C was twice that at 40 °C indicating the formation of a bimolecular multimer at 30 °C. From the radii of gyration obtained at both temperatures it appears that the methyl methacrylate block in the multimer... 

---