References and Notes(1) Rare Earth Metal Containing Polymers,8.

An early theme in probability was calculating the fair ante for various games of chance. Nicolas Bernoulli introduced a seemingly innocent game, first published in 1713, that yielded a paradoxical result. The result has become known as the St. Petersburg paradox, because of an analysis written later by Daniel Bernoulli in the Commentary of the St. Petersburg Academy.

f,~exp(_izu_[ul~)du with 0 2 since it may, for some values of z, become negative. The use of the expression exp -[t/T] ~ as a relaxation function for dynamical processes in materials was first proposed by Kohlrausch (1866). Its reciprocal plays an important role in creep phenomenon (l~ and its Fourier transform appears in investigations of response of materials to periodic driving forces (electrical and mechanical).Closed form expressions exist for (1) for few values of a other than a = 2. When a = 1 one has the Cauchy distribution Ql(z) = (1/~r)(1 + z 2) (4) Q2/3(z ) = ( 3 )l/2z-lexp( -~7z-2)W1/2,,/6 ( 2@z2 )The value of Q~ (0)

The relative permittivity and dielectric strength have been determined for a bisphenol A polycarbonate (BPA-PC), in which a cyanoethyl group has been substituted for one of the geminal dimethyl groups. The new material (CN-PC) has a glass transition temperature that is 19 K higher than that for BPA-PC. In addition, the dielectric strength of CN-PC, 405 V/μm, is somewhat smaller than that for BPA-PC, 620 V/μm. The relative permittivity was determined from 10 to 10 5 Hz over a wide temperature range and at pressures up to 0.25 GPa. While the real part of the relative permittivity at 10 3 Hz and room temperature for BPA-PC is about 3, that for CN-PC is found to be greater than 4. Correspondingly, the γ relaxation region in CN-PC is very strong. For the γ relaxation, a strong increase in peak height as temperature increases and a strong decrease in peak height as pressure increases are observed. A relaxation is found at temperatures higher than the γ relaxation. This process is labeled as the β relaxation because it appears to be related to the β relaxation in BPA-PC in that the strength and position depend on the history of the material. The effects of pressure on the γ relaxation for both CN-PC and BPA-PC are quite large and similar to those previously seen for the γ relaxation in a fluorinated tetraaryl bisphenol A polycarbonate (DiF p-TABPA-PC). In fact, the activation volume is found to be approximately the same for all three BPA-PC-based materials despite wide variations in both peak position and peak height. Finally, computer studies of the model compounds, 4,4′-diphenylpentanenitrile and diphenyl carbonate, were carried out. Both provide insight into the nature of the γ relaxation with the latter yielding an activation volume in approximate agreement with the experimental values.

REPORT DOCUMENTATION PAGE FUNDING NUMBERSGrant number: N00014D1AF00002'PR Number: 01PR02263-00 PERFORMING ORGANIZATION NAME(S) ANO ADORESS(ES)United States Naval Academy Physics Department Annapolis, MD 21402. PERFORMING ORGANIZATION REPORT NUMBER 29 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)Office of SUPPLEMENTARY NOTES Prepared for publication in Physical Review Letters 12». DISTRIBUTION/AVAILABILITY STATEMENTReproduction in whole or in part is permitted for any purpose of the United States Government. This document has been approved for public release and sale, its distribution is unlimited. 12b. DISTRIBUTION CODE ABSTRACT [Maximum 200 wordjjA model, based on defect diffusion, is developed that describes temperature and pressure dependence of dielectric relaxation, ionic conductivity and viscosity of glass-forming liquids near the glass transition temperature. The resultant expressions for ionic conductivity are compared with experimental results for the polymer electrolytes poly(ethylene glycol) (PEG) and polypropylene glycol) (PPG) containing LiCF 3 S0 3 . Those for dielectric relaxation are compared with experimental results for polypropylene oxide) (PPO) and poly(vinyl acetate). The theoretical viscosity law is compared to experiments on propylene carbonate (PC). SUBJECT TERMSIonic Conductivity, Dielectric Relaxation, Viscosity, High Pressure, Theory, Experiment. The theoretical viscosity law is compared to experiments on propylene carbonate (PC).