J. E. Anderson

Mathematical analysis of factors influencing the skin thickness of asymmetric reverse osmosis membranes

The formation of the dense surface skin of asymmetric reverse osmosis membranes is analyzed in terms of a composite process involving solvent diffusion and polymer relaxation. The analysis indicates that films with minimum skin thickness result from (i) rapid polymer relaxation; (ii) strongly concentration‐dependent solvent diffusion coefficients. The numerical results are discussed in terms of experimental variables. It indicates great difficulty in producing asymmetric films with extremely thin surface skins. The implications of this finding are discussed. Experimental NMR self‐diffusion studies of acetone in cellulose acetate are reported.

Rotational Relaxation and Chemical Exchange

This article couples chemical exchange to rotational relaxation in liquids. We found that the relative rates of exchange and molecular rotation have a profound effect on relaxation behavior. Systems exchanging more slowly than the rate of molecular rotation can be distinguished from systems experiencing faster exchange. This leads to a novel class of experiments using molecular rotation as a frequency standard for the exchange process. Since rotational correlation times are typically 10−10–10−12 sec. these experiments provide sensitivity on a time scale not easily achieved by other techniques. Analysis of these experiments is presented. Studies of NMR spin–lattice relaxation in iodine charge‐transfer complexes substantiate this analysis.

Model Calculations of Cooperative Motions in Chain Molecules

This article describes model calculations of the so‐called “perpendicular mode” of dielectric relaxation in chain molecules. Particular emphasis is given to cooperative interactions between adjacent chain elements. An extension of Glaubers model for the time‐dependent statistics of the Ising chain is used for the purpose. A closed‐form expression is given for the dielectric relaxation of an isolated dipolar element in an infinite ring. The influence of chain length and variable mobility along the chain upon dielectric relaxation is also described.

Molecular Association and Molecular Rotation in Liquids

This article concerns the effect of molecular association on the rotary motions of molecules in the liquid state. It is found that two different types of association can be distinguished: (1) In some instances, association involves the formation of polymolecular aggregates, or complexes, that move as a unit. (2) Alternatively, association may involve only correlations in the positions of different molecules, and it may have little effect on molecular motion. The difference between these two cases is analyzed. NMR spin–lattice relaxation studies of various chloroform systems are offered to illustrate these effects. Some of the experimental results suggest that molecular rotation takes place by large‐angle jumps rather than by small diffusive steps against a viscous force.

Molecular Motion and Spatial Order in Liquids: The Aniline/Cyclohexane System

This work probes the relationship between molecular motion and spatial order in binary solutions. We deal with the aniline–cyclohexane system, in which the components are completely miscible above a critical solution temperature, Tc, of 29.5°C and separate into aniline‐rich and cyclohexane‐rich layers at lower temperatures. Previous light‐scattering measurements indicate spatially ordered regions with dimensions of roughly 50 A some 10° above Tc; the size of these regions increases to 1000–2000 A at 0.1° above Tc. Spatial correlations between the positions of the aniline and cyclohexane molecules were examined through studies of: (1) the PMR solvent shift; (2) the intermolecular contribution to spin–lattice relaxation. The results indicate a statistical preference for aniline–aniline and cyclohexane–cyclohexane neighbors rather than aniline–cyclohexane pairings. The self‐diffusion coefficients of both aniline and cyclohexane were determined by pulsed NMR methods over a wide range of temperature and concen...

Angular Velocity Correlation Functions and High‐Frequency Dielectric Relaxation

The angular velocity correlation function can be studied through measurements of dielectric relaxation and far‐infrared absorption. Relations between these quantities are described in this article, and the data of Davies, Pardoe, Chamberlain, and Gebbie are analyzed. Velocity correlation times are obtained for molecules in four simple liquids. Hubbard has obtained a theoretical expression linking the velocity correlation time, the orientation correlation time, and the molecular moment of inertia. This expression is experimentally verified for molecules in nonviscous liquids. Certain paradoxical predictions are found when this expression is applied to viscous liquids and solids. This article considers stochastic models for relaxation, in which the probability of molecular reorientation is modulated by fluctuations in the intermolecular environment. These stochastic models lead to orientation and velocity correlation functions that are consistent with experimental observations.

Nuclear Relaxation in the Benzene–PMMA System

The nuclear relaxation of benzene protons in the benzene–polymethylmethacrylate (PMMA) system has been examined at concentrations up to 35 wt% PMMA. Systems prepared from isotactic and syndiotactic PMMA were studied. The polymer samples ranged in molecular weight between 4 × 104 and 2thinsp;× 106. The concentration dependence of the benzene spin–lattice relaxation time is independent of the mw and tacticity of PMMA and decreases with increasing polymer concentration. The benzene spin–lattice relaxation of samples containing 4 × 104 mw PMMA was resolved into dipolar contributions from: (1) intermolecular pairs of protons; (2) intermolecular pairs of benzene protons; (3) intermolecular benzene–polymer proton pairs. Selective deuterium substitution was used to separate these effects. T2, the benzene spin–spin relaxation time, showed sensitivity to the molecular weight and stereoregularity of the polymer. In contrast to the behavior found in nonpolymeric solutions, (T2 / T1) ratios much greater than unity wer...

Nuclear magnetic relaxation in polymer solutions

Nuclear magnetic relaxation helps in unfolding the pattern of molecular motion in polymer solutions. Information on both solvent and polymer motions can be obtained by appropriate experiments. Examples are given using T1 and T2 measurements on polyethylene oxide, polydimethylsiloxane, polyisobutylene and other systems. Several general features appear in nuclear relaxation of the polymer molecules. T1 is insensitive to the molecular weight of the polymer and to the concentration of the solution up to about 20 % concentration. T1 depends on solvent viscosity though the variation appears to be less pronounced than that predicted by Bloembergen-Purcell-Pound theory. T2, on the other hand, is a function of polymer concentration, and drops rapidly with concentration at high molecular weights. This is in accord with what is known about entanglements in polymer solutions. T1 and T2 are not changed by replacing hydrogen-containing solvents with deuterated substitutes. The rate of solvent motion is too rapid to be effective in nuclear relaxation of the polymer. T 1 and T2 measurements on the solvent in polymer solutions can be analyzed in detail by selective replacement of hydrogen by deuterium. This has been done in the poly(methylmethacrylate)+ benzene system. An apparent anomaly of solvent T2 in solutions of high molecular weight polymer is explained in terms of a fluctuating chemical shift.

Neutron‐scattering studies of bulk polyethylene at intermediate Q values

We report SANS studies of bulk polyethylene (PE) samples crystallized from the melt at different rates. All samples contained both protonated and deuterated PE. Substantial isotopic concentration fluctuations are present in slow‐cooled samples. This is seen as large differences in the low‐angle (low‐Q) SANS. At larger Q values, the SANS data from both materials is approximately identical. We interpret this in terms of an exponential radial correlation function for composition fluctuation whose correlation length is comparable to lamellar dimensions. Numerical calculations show that concentration fluctuations have minimal effect in the intermediate Q region.