Stockmayer formula

Equation (11) is the well known Stockmayer formula for the DP of randomly crossllnked chains (11). It will be2noticed that the equation (12) for the structure factor S (q ) cem be obtained from equation (11) sluply by replacing the weight-average degree of polymerization of the prlmatry chain y by its structure factor"... 

The introduction of branching in the Kirkwood formula and the KR calculations can be accomplished in a relatively easy way if Gaussian statistics corresponding to ideal chains are maintained. This description cannot, however, be very accurate in molecules with centers of high functionality because of the presence of cores with a high density of polymer units, which profoundly perturbs the internal distribution of distances. Stockmayer and Fixman [81 ] employed the Kirwood formula and Gaussian statistics to calculate h in the case of uniform stars, obtaining an analytical formula. They also performed a KR evaluation of the viscosity and proposed that g could be evaluated from the approximation... 

A useful compendium of formulas for estimating the interaction parameters e and cr in the Lennard-Jones or Stockmayer potentials has been presented by Svehla [389]. His work... 

Pgf values of the various distributions with respect to the counts of monomer units, bonds, or unreacted functional groups can be obtained from Eq. (98) by setting equal to one the molecular weight of the species in question and to zero the molecular weights of all the other species. Analytical inversion by computing derivatives with respect to dummy Laplace variables on s = 0 is feasible with the simplest chemical systems, for which the resulting recurrence formulae are not too complex, as happens with the Stockmayer distribution. 

The data bank on basic physical and chemical properties of individual substances stores the following data the name of the substance, molecular mass, the structural formula of the molecule and the number of carbon atoms, melting and boiling temperatures at atmospheric pressure, critical parameters, acentric factor and polarity, parameters of the Lennard-Jones and Stockmayer potentials, the coefficients of an equation for calculation of isobaric heat capacity in the ideal-gas state and some other properties. The content of the bank is enlarged continuously by input of information on new substances. 

In the original formula of Flory, a = 2.6(3/27t). Stockmayer suggested that the choice of a = 4/3(3/2ti) gives the exact result of first order perturbation theory near 6 temperature and the result of equation (23) in good solutions. With this choice of a, equation (24) is called the modified Flory formula which can be derived in a systematic way. Many approximate closed expressions for a exist in the literature which are adequately reviewed. ... 

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