cording to some recent theories of the osmotic second virial coefficient in the limit of large excluded volumes, i.e., for high molecular weight polymer molecules in thermodynamically "good" solvents, the ratio A2M%,/(Rl,)'/* should attain an essentially constant value. Qualitatively the constancy of this ratio is an expression of the expectation that the interactions of polymer molecule pairs in such media resemble collisions of spheres whose volumes are proportional to (7?2W)V2. If, then, the volumes of the equivalent hydrodynamic spheres observed viscometrically are also proportional to (i?2w)'/' the ratio AtMw/[rj] should be another constant. _The ratio is plotted against log Mw in the center graph of Fig. 7 for the ten polyvinylacetate fractions in methyl ethyl ketone. Over this molecular weight range the ratio is a constant equal to 4.4 X 1024.A plot of A-iM^I [77] against log M-w for the samesystem in the lower graph of Fig. 7 reveals a remarkably constant value, 1.39, for this ratio over the molecular weight range 246,000 to 3,460,000.Here again data of Howard19 have been used to extend the observations to lower molecular weight polymer fractions.It may therefore be stated empirically that the thermodynamic interaction of a pair of high molecular weight polyvinylacetate molecules in methyl ethyl ketone is similar to the collision of spheres having effective volumes proportional to (A!2W) This observation, coupled with the validity-of the equivalent hydrodynamic sphere treatment of limiting viscosity numbers, yields an empirical relation among the quantities AMw and [17]. It has been found40 that this relation is valid for several polymers in thermodynamically good solvents, and similar magnitudes for the ratio A2MW/ [77 ] are observed.

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This study explains why subjects with anterior cruciate ligament tears gain partial control of pathologic anteroposterior laxity with the use of a brace but may continue to experience abnormal translations during activity.

SynopsisEquilibrium acid concentrations, [Ae], were determined in butylene adipate and caprolactone polyesters, of low molecular weight, and in thermoplastic polyurethane elastomers based on these polyesters. Values of [Ae] of the polyesters a t 85°C were 0.7,1.3, and 3-4 X mol/g a t relativehumidities (RH) of 25%,50%, and 93%, respectively.[Ae] of the thermoplastic elastomers a t 85°Cwere about 3 and 7 X lop4 mol/g at 10% and 25% RH, respectively. Values of [Ae] were not very dependent on temperature at constant RH. Equilibrated thermoplastic elastomers had low molecular weights and poor physical properties. Consequently, equilibration does not set a practical limit on hydrolytic degradation, even a t low RH. Equations were developed that described the variation in acid content with time. Rate constants for hydrolysis and esterification increased as RH decreased. Reesterification in the elastomers in the absence of water is too slow to be a useful method of decreasing hydrolytic damage.

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Polystyrene was sulfonated with sulfur trioxide–triethyl phosphate complexes in dichloroethane, the object being to prepare polystyrene sulfonates substantially free of sulfone links between polymer chains. Variations in the sulfone content with reaction conditions were conveniently followed by exclusion chromatography, the sulfone peak appearing at about twice the molecular weight of the main peak. The desired products were obtained from polystyrenes with molecular weights between 1.1 × 105 and 8.7 × 105 by using (at −20 to +25°C) a 5:1 excess of a 1.5:1 complex, the last at a concentration of 0.5M. Completely soluble polystyrene sulfonate was also obtained from polystyrene of molecular weight 2.05 × 106. Requirements for the successful use of the 1.5:1 complex include careful purification of the dichloroethane and, if 2 g or more polystyrene is to be sulfonated, formation of the complex at −20°C. A method is given for measuring the sulfonating capability of the reagent before adding the polymer.