Stockmayer

The methods we consider have been developed by Stockmayer and Flory and have been applied to quite a variety of polymer systems and phenomena. 

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

For both polar and nonpolar nonhydrocaihon gaseous mixtui es at low pressui es, the most accurate viscosity prediction method is the method of Brokaw. The method is quite accurate but requires the dipole moment and the Stockmayer energy parameter (e/A ) for polar components as well as pure component viscosities, molecular weights, the normal boding point, and the hq-uid molar volume at the normal boding point. The Technical Data Manual should be consulted for the fidl method. 

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... 

At the end of the 1930s, the only generally available method for determining mean MWs of polymers was by chemical analysis of the concentration of chain end-groups this was not very accurate and not applicable to all polymers. The difficulty of applying well tried physical chemical methods to this problem has been well put in a reminiscence of early days in polymer science by Stockmayer and Zimm (1984). The determination of MWs of a solute in dilute solution depends on the ideal, Raoult s Law term (which diminishes as the reciprocal of the MW), but to eliminate the non-ideal terms which can be substantial for polymers and which are independent of MW, one has to go to ever lower concentrations, and eventually one runs out of measurement accuracy . The methods which were introduced in the 1940s and 1950s are analysed in Chapter 11 of Morawetz s book. 

Stockmayer, W.H. and Zimm, B.H. (1984) When polymer science looked easy, Annu. Rev. Phys. Chem. 35, 1. 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

The crystallographic radius assigned to the ion Fc+++ is comparable with that assigned to the scandium ion Sc+++. The ions K, Ca+t, and Sc+++ have the same number of electrons, and the same closed electronic shells as the argon atom. In aqueous solution there will be electrostatic forces of attraction between Ca++ and Cl, and between 8c+ t+ and Cl- but the quantum-mechanical forces between these ions will be forces of repulsion only. Between Fe+++ and Cl-, on the other hand, there may be quantum-mechanical forces of attraction. In view of the rather intense electrostatic attraction between Fe+++ and a negative ion, a 1 E. Rabinowitch and W. H. Stockmayer, J. Am. Chern. Soc., 64, 341 (1942). 

Kurata, M. and Stockmayer, W. H. Intrinsic Viscosities and Unperturbed Dimensions of Long Chain Molecules. Vol. 3, pp. 196—312. 

The sedimentation coefficient for wormlike chains was first worked out by Hearst and Stockmayer [123], later improved by Yamakawa and Fujii [124] to give this expression for s ... 

The branching ratio for geometric dimensions (g,) was defined by Zimm and Stockmayer as... 

---