Stockmayer model

Binary Mixtures—Low Pressure—Polar Components The Brokaw correlation was based on the Chapman-Enskog equation, but 0 g and were evaluated with a modified Stockmayer potential for polar molecules. Hence, slightly different symbols are used. That potential model reduces to the Lennard-Jones 6-12 potential for interactions between nonpolar molecules. As a result, the method should yield accurate predictions for polar as well as nonpolar gas mixtures. Brokaw presented data for 9 relatively polar pairs along with the prediction. The agreement was good an average absolute error of 6.4 percent, considering the complexity of some of... 

The basis of model calculations for copolymerization, branching and cross-linking processes is the stochastic theory of Flory and Stockmayer (1-3). This classical method was generalized by Gordon and coworkers with the more powerful method of probability generating functions with cascade substitution for describing branching processes (4-6). With this method it is possible to treat much more complicated reactions and systems (7-9). 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

Figure 9,1 Molecular interaction potentials in Stockmayer s (1941) model for H2O vapor, (a) antiparallel dipolar moments (b) parallel dipolar moments. Reprinted from D. Eisemberg and W. Kauzmann, The Structures and Properties of Water, 1969, by permission of Oxford University Press.

The value of calculated from Wg and corresponding to the polystyrene Interpretation is 0.72 ns which is in good agreement with the time scale of the Jones and Stockmayer model. 

Since none of the lattice models is now clearly superior, the choice for interpretation of spin relaxation in polymers is arbitrary. Familiarity leads us to select the Jones and Stockmayer model so we will now consider application of this model to several well studied polymer systems in order to compare dynamics from polymer to polymer. Also the equations required to consider anisotropic Internal rotation of substituent groups and overall molecular tumbling as independent motions in addition to backbone rearrangements caused by the three-bond jump are available for the Jones and Stockmayer model (13). 

Modelization of the System. Theoretical treatment of polyfunctional monomers condensation polymerization has been firstly proposed by Flory and Stockmayer (22.23 and later by Gordon, Bruneau, Macosko and others (24-26. These theories lay out the basic relation between extent of reaction and average molecular weight of the resulting non linear polymers. 

The molar cyclization equilibrium constants, Kx, of PDMS are measured. Using the Jacobson and Stockmayer equilibrium theory of macrocyclization, the dimensions of PDMS chains with 40-80 chemical bonds in the bulk polymer at 383 K are deduced. Dilution effects in the PDMS systems are contrasted with predictions of the Jacobson-Stockmayer theory, and the experimental molar cyclization equilibrium constants of the smallest siloxane rings are discussed in terms of the statistical properties of the corresponding oligomeric chains using tire RIS model of PDMS of Flory, Crescemi, and Mark [S 116]. 

Cyclic oligomers with x - 2-9 are found to be present in poly(1,3-dioxolane) samples prepared by monomer-polymer-equilibrations using boron trifluoride diethyl etherate as catalyst. The molecular cyclization equilibrium constants 7fx are measured and the values are in agreement with those calculated by the Jacobson-Stockmayer theory, using an RIS model to describe the statistical conformations of the corresponding chains and assuming that the chains obey Gaussian statistics. 

A theoretical model to determine the probability of loop formation, based on an elaborated form of the Jacobson-Stockmayer theory of cyclization equilibria, is developed and used on RNA chains of homogeneous puckering and lengths up to 2 residues. 

Orwoll, R. A., Stockmayer, W. H. Stochastic models for chain dynamics. Advan. Chem. Phys. 15,305-324 (1969). 

Verdier,P.H., Stockmayer, W.H. Monte Carlo calculations on the dynamics of polymers in dilute solution. J. Chem. Phys. 36, 227-235 (1962). See also Verdier,P.H. Monte Carlo studies of lattice-model polymer chains. 1. Correlation functions in the statistical-bead model. J. Chem. Phys. 45,2118-2121 (1966). 

Chain Dynamics, Stochastic Models for (Orwoll Stockmayer). 15 305... 

Baur and Stockmayer (13) have recently observed a low frequency dielectric dispersion zone in liquid poly(propylene) oxide which is dependent upon molecular weight in the manner of Eqs. (2.8) and (2.9). Due to the method of synthesis of their samples, there are only infrequent reversals of dipolar sense along the chain, and the model discussed above... 

Polymer systems containing copolymers call for a further extension of the thermodynamic model. The interaction function for statistical copolymers was originally derived by Simha and Branson [34], discussed by Stockmayer [35] et al., and experimentally verified by Glbckner and Lohmann [36]. 

This article deals with one of the above mentioned subjects already treated in the 1940 s branched polymers. We present a survey of a number of scattering functions for special branched polymer structures. Hie basis of these model calculations is still the Flory-Stockmayer (FS) theory1,14,15) but now endowed with the more powerful technique of cascade theory which greatly simplifies the calculations. 

Stockmayer and Hecht (1953) have developed an additional mathematical theory of the heat capacity of chain polymeric crystals. Their theory is based on the concept of strong valence forces between atoms in the polymeric chain and of weak (non-zero) coupling between chains. This model corresponds to that also proposed by Tarassov (1952). There are not many low temperature specific heat data on polymers, but the Stockmayer-Hecht theory can be tested by calculating the Tm constant... 

They calculated the value of k by using mathematical models and found a value of 5/s for hard spheric particles. This value was obtained in an equivalent manner many years ago for a gas composed of hard spheric molecules (31). They derived this equation from osmotic pressure measurements and showed the parallelism between these virial coefficients and those obtained from light scattering. Stockmayer et al. (32) made an... 

---