Zimm-Stockmayer equation

In an analogous fashion, the weight average long chain branching parameters per molecule (B ) and per 1000 repeat units (Xy) can be calculated. First Bu(V) can be determined from the Zimm-Stockmayer equation (20),... 

An experimental verification of Eqs. (65)-(67) has not yet been possible because the MALLS instrument that allows measurement of has only recently become available in laboratories. Furthermore, the combination of the MALLS with the Vise detector is not a trivial problem. Several experiments are, however, in progress. This work is of great importance since a quantitative estimation of the branching density would be possible if the Zimm-Stockmayer equations for the g-factor hold true. 

Fig. 26. Molar mass dependence of the g factor for three pregel and one postgel fraction of end linked PS stars. A good fit was obtained with the Zimm Stockmayer equation (Eq. 69) and an exponent in Eq. (70) of fi 0.63 [95] which agrees well with Kurata s estimation with b-0.6 [129]. Reprinted with permission from [129]. Copyright [1972] American Society...

At the 0 point, the self-repulsion of the monomers, due to the excluded volume, is just compensated for by the interactions with the solvent. While this tricritical point is well understood for linear chains, less is known about the properties of stars at Tff. Candau et alP assumed that at Tq all the arms can interpenetrate each other completely. This means that all virial coefficients vanish and the size of the star is given by the Zimm-Stockmayer equation. 

In Figure 29, gs values for several polymers in theta (filled S3rmbols) and good solvents (unfilled symbols) are plotted against /. The line represents the theoretical gs calculated according to the Zimm-Stockmayer equation ... 

Equation 1 compares the mean square radius of gyration of a regular star with /arms with the radius of gyration of the linear polymer having the same number of segments [14]. The Zimm-Stockmayer branching factor... 

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. 

The estimation of g then enables all the quantities in equation (43) to be evaluated, and hence allows a relation for a hypothetical, linear dextran g = 1) to be obtained. By this method, Wales and coworkers found g values which could not be reconciled with theoretical values calculated from the randomly branched model of Zimm and Stockmayer. This led to dextran s being assigned a herring-bone type of structure, that is, a linear backbone having branches of uniform length distributed uniformly along the chain. 

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