Molecular weight Schulz-Zimm

To generate the necessary distribution functions, the ratio of is used to approximate the true molecular weight distribution by a Schulz-Zimm distribution. It is also assumed that the reactive functional groups are distributed randomly on the polymer chain. The Schulz-Zimm parameters used to calculate distribution functions and probability generating functions (see below) are defined as follows ... 

These parameters are used calculate the site and mass distribution functions assuming a Schulz-Zimm molecular weight distribution. The Schulz-Zimm parameters are calculated in lines 930-950. The weight fraction of diluent (as a fraction of the amount of polymer) is then sought. If there is no diluent enter 0. If there is a diluent, the functionality and molecular weight of the diluent is requested (line 1040). The necessary expectation values are computed (lines 1060-1150). 

The equations relating Mn and Mw to radiation dose which are most frequently used apply to all initial molecular weight distributions for Mn, but only to the most probable distribution (Mw/Mn = 2) for Mw. However, equations have been derived for other initial distributions, especially for representation by the Schulz-Zimm distribution equation. 

Using the Benoit-Doty expression for 0 of a monodisperse wormlike chain 121), the relationship between q and Z of polymers having a Schulz-Zimm type molecular weight distribution is derived as follows 67 ... 

The importance of molecular weight distribution in studies of polymerization, polymer processing and the physical and mechanical properties of polymers creates a need for mathematical description of the distribution. Several models are commonly used (Flory [1], Schulz-Zimm... 

Schulz-Zimm type molecular weight distribution,... 

Fig. 2.9 Relative changes in weight and number average molecular weights for random scission of polymers with a Schulz-Zimm molecular weight distribution at six values for initial heterogeneity [14a].

Fig. 1.3. Molecular weight distributions of the Schulz-Zimm type for / = 2 (left) and of the Poisson-type (right). Both correspond to the same number average degree of polymerization, Nn = 10 ...

One can then derive the relationship between the intrinsic viscosity and various molecular weight averages, if a distribution function is specified. For example, for the Schulz-Zimm distribution function (Eq. 2.61), we obtain the following relationships between [rj] and the weight and number average molecular weights. 

The theoretical treatments of Ajg discussed here were motivated by the question of the effects of molecular weight dispersion on measured second virial coefficients. Once Ajf Mjy Mj ) is available it is obvious in principle how to obtain A 2 or. 4 2 for any desired form of distribution. Detailed calculations using the hard-spherelike interaction model with the familiar Schulz-Zimm distribution indicate that the ratio of virial coefficients increase wi out limit with the... 

FOR [i l = k, /M > i USING WEIGHT-AVERAGE MOLE-CXrlAlf VEICHT FOR POLYMERS with a SCHULZ-ZIMM (SZ) DISTRIBUTION OF THE MOLECULAR WEIGHT... 

WITH A SCHULZ-ZIMM (SZ) DISTRIBUTION OF THE MOLECULAR WEIGHT... 

TABLE 46. POLYMOLECULARITY CORRECTION FACTORS qcyr (s ) M USING (S )j AND M FOR POLYMERS WITH A SCHULZ-ZIMM (SZ) "DISTRIBUTION OF THE MOLECULAR WEIGHT... 

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