Zimm technique

Light scattering data were evaluated by the Zimm technique (15). A computer program was developed in this laboratory to generate the Zimm plot where double extrapolations were required. 

Equation (29) was previously derived by Zimm and Stockmayer [49] who used another technique. Figure 12 shows a plot of the theoretical increase of the radii of the stars as a function of the number of arms. 

Since the Zimm-Bragg parameters o and s of the naturally occurring amino acids (In water) cannot be obtained from studies of the helix-coil transition in homopolymers, because of experimental difficulties, a technique Is developed to circumvent these problems. It involves the study of the thermally induced transition curves for random copolymers of "guest amino acid residues in a water-soluble host" po y(amino acid). The data may be interpreted with the aid of suitable theories for the helix-coil transition in random copolymers to obtain a and s for the "guest" residues. It is shown in this paper that, for the usual ranges of parameters found for polylamino acids), one of the two lowest order approximations (corresponding to earlier treatments by Lifson and Allegra) is completely adequate. In essence, the low-order approximations hoid if o and s for the two constituents of the copolymer do not differ appreciably from each other. 

Dynamic light scattering, coupled with modern computer programs and auxiliary equipment, automatically graphs Zimm plots and computes Mw, Rg, , Cl, and flow rates. New techniques have expanded the method to the semidilute and concentrated regimes (Barth and Sun, 1991). 

Although Equation 5.61 describes a three-dimensional surface for the variation of Kc/R0 with c and 0, it is usual to plot the experimental data in two dimensional using an elegant technique devised by Zimm. In the Zimm plot, Kc/Re is plotted against the composite quantity sin2(0/2) + k c where k is an arbitrary constant the value of which is chosen so as to give a clear separation of the data points (usually k is taken as 0.1 when the units of c are g dm-3). 

The MALS measurements which eliminate the need for column calibration and all of its subsequent aberrations also permit the direct evaluation of branching phenomena in macromolecules because the basic quantitation of branching may only be achieved from such measurements as shown in the article by Zimm and Stockmayer [7]. Empirical approaches to quantitate branching, using such techniques as viscometry, have been shown to yield consistently erroneous results especially when long-chain branching becomes dominant. 

The Zimm-plot technique, like q.l.s., also involves a difficult extrapolation to zero angle. Another difficulty is that its qiplication assumes that the particles are Rayleigh-Cans-Debye scatterers (namely, that there is no change of phase or other distortions of the incident radiation by the particle). For the larger mucins in particular, this may not be the case. 

The first approach assumes that the sample is composed of a discrete number or a specific distribution of components. Then the deviations from linearity for the proposed model can be included as higher order c-orrections in Equations 25 or 27. Current techniques are limited to the consideration of two discrete size populations of particles or to a size profile defined by two parameters such as the Schulz-Zimm distribution (7,26,27,28,29,30). If there is evidence that such a model describes the sample, it is certainly the best way to proceed. This approach has been applied recently to polydispersity analysis based on the assumption of a particular distribution model by Chen et al. (35, 36) and McDonnell et al. (26,37). 

FIGURE 9.7 A typical Zimm plot showing the double extrapolation technique, where - O-represents the experimental points and - - represents the extrapolated points. 

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