Vs. reciprocal temperature

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

Fig. 3.10 Conductivity vs reciprocal temperature circles, Bi4V20n vertical lines separate a, P, y phases triangles, Vi.sCuo.jOh-j crosses Bi4Vi,8To.20n- squares, Bi4Vi,8Nbo.20ii -j-...

Fig. 3.11 Proton conductivity vs reciprocal temperature for several particle hydrates compared with that of 1 M HCl.

Figure 7. Variation of unimolecular dissociation rate constant vs. reciprocal temperature for the proton-bound methoxide ion, ((CH30)2H]. Arrhenius parameters derived...

Fig. 9. Plot of log T, relaxation time vs. reciprocal temperature for the diglycidyl ether of bisphenol-A uncured (A) and cured with methylenedianiline at 54 °C (B), 100 °C (C) and 180 °C (D) (adapted from Refs.53) and16y)...

When several temperature-dependent rate constants have been determined or at least estimated, the adherence of the decay in the system to Arrhenius behavior can be easily determined. If a plot of these rate constants vs. reciprocal temperature (1/7) produces a linear correlation, the system is adhering to the well-studied Arrhenius kinetic model and some prediction of the rate of decay at any temperature can be made. As detailed in Figure 17, Carstensen s adaptation of data, originally described by Tardif (99), demonstrates the pseudo-first-order decay behavior of the decomposition of ascorbic acid in solid dosage forms at temperatures of 50° C, 60°C, and 70°C (100). Further analysis of the data confirmed that the system adhered closely to Arrhenius behavior as the plot of the rate constants with respect to reciprocal temperature (1/7) showed linearity (Fig. 18). Carsten-sen suggests that it is not always necessary to determine the mechanism of decay if some relevant property of the degradation can be explained as a function of time, and therefore logically quantified and rationally predicted. 

Fig. 59. Graph of relative volatility (evaporation) rates vs reciprocal temperature for Ba(dfhd)2, Ba(ofhd)2, Ba(fod)2, Ba(hfac)2, and Ba(ppm)2. (Redrawn from Ref. 213.)...

Fig. 70. Electrical conductivity vs. reciprocal temperature for several metallic oxides. (After Morin (448).)...

The plutonium-uranium ratio in liquid solution was not consistent with that added. There seems little doubt that this discrepancy resulted from the precipitation of two different compounds as the alloy cooled from higher temperatures. Pu2Zn17 decomposes peritectically at 1083° K. to form PuZn8 and liquid (3). Presumably the PuZn8-based three-component form dissolves and reprecipitates on the U2Zn17 matrix near this temperature, as the temperature is lowered. The selected data of P/540 (5) show slightly different slopes for the plots of log solubility vs. reciprocal temperature for Pu-Zn and U-Zn. This variance probably reflects difference in technique by the two groups of experimenters, since it does not show in parallel Pu-Zn and U-Zn experiments by Elliott and coworkers on which that part of P/540 was based. 

In their reply to Furic s criticism, Nagaoka et al. suggested [166] that (i) the 180° rotation model proposed by Furic [162] would have an activation energy much higher than 5 kj mol-1, and (ii) if rotation of the -C02H H02C- unit was the mechanism of proton relaxation, the Tx vs reciprocal temperature curve should be the symmetric curve predicted by classical relaxation theory (i.e. without proton tunnelling effects at low temperature). 

Activation Energy bv Different Measurement Techniques - Table V compares activation energy data obtained by three different experimental methods for three different samples. Corresponding Arrhenius plots are shown in Figures 5 and 6. In both figures the log frequency vs. reciprocal temperature plot for RSA II and DMTA are parallel to each other, giving very close E values. 

An Arrhenius plot of log rate constant vs. reciprocal temperature (Figure 6) indicates an activation energy of 61.9 1.3 kcal/mol for dodecene cracking. This is similar to the activation energies measured for n-paraffin cracking and is somewhat higher than previously measured values for alpha-olefins (6). 

Fig. 11. Plot of the initial rate coefficient (log scale) vs. reciprocal temperature for the oxidation of hydrazine k — — (d[NH3]/d/)([N2H4][02]). Data taken from Bowen and Birely . ...

Figure 2. Typical viscosity results vs. reciprocal temperature for some of the fluxes listed in Table I.

When the nonlinearity of the log viscosity vs. reciprocal temperature data was first observed, tests were made to insure that the curvature was real and not an artifact of the experimental apparatus. Hysteresis curves and constant temperature for extended time tests showed that the nonlinearity was not caused gf zovolatilization alkali or fluoride constituents or from thermal deviations in the furnace setup. It was found that the observed curvature of the data was not an artifact and represented the true physical behavior of the materials. The application of the Kirchoff-Rankine equation... 

Figure 4. Least squares analysis of log (Viscosity) vs. reciprocal temperature. Present study O Shaw ( )A Corey ( 14) . Vertical bars indicate two standard deviations.

Fig. 2. (A) Flash-induced AA in the SDS-fractionated PS-1 core complex (CPI) at 5 K [ with and o without DCIP] (B) Flash-induced AA in TSF-I particles containing dithionite and neutral red at pH 10 and frozen while being illuminated (C) left AA induced by 300-ns, dye laser flashes [710 nm for the blue and green region 590 nm for the red region] insets show individual AA transients at 696 and 480 nm (C) right The difference between the difference spectrum in the left panel and that of P700. (D) Plot of the rate constant vs. reciprocal temperature. Figure source (A) Mathis, Sauer and Remy (1978) Rapidly reversible flash-induced electron transfer on a P-700 chlorophyll-protein complex isolated with SDS. FEBS Lett 88 277 (8) Sauer, Mathis, Acker and van Best (1979) Absorption changes of P-700 reversible in milliseconds at low temperature in Triion-solubilized photosystem I particles. Biochim Biophys Acta 545 469 (C and D) Shuvalov, Dolan and Ke (1979) Spectral and kinetic evidence for two eariy electron acceptors in phoiosystem I. Proc Nat Acad Sci, USA 76 771,773.

Figure 3.5 Plot of second virial coefficient vs. reciprocal temperature (Problem 3.8).

Figure 1. Solubility vs. temperature and log solubility vs. reciprocal temperature plots for MgDS ( ) and CaDS (O). Data from Ref. 10 included...

Figure 3. Dissolution rate at pH 5.8 vs. reciprocal temperature—Fredonia limestone.

Figure 2. Median molecular jump rate (3T )-1 vs. reciprocal temperature for liquid water, water in charcoal pores, and water in zeolite 13-X...

Figure 27. Plot of ln(KEg) -F PAVg/RT vs. reciprocal temperature ror the reaction YAG + OH-apatite + 25/4 quartz = 5/4 grossular + 5/4 anorthite + 3 YPO4 monazite + 1/2 H2O. Solid squares = xenotime-bearing assemblages, open squares = xenotime-absent assemblages. Least squares regression line is fit to all data points. Horizontal error bars represent temperature uncertainty of 30°C. Vertical error bars ate la (In Kgq + PAV/RT), derived from propagation of uncertainties in P ( 1000 bars), T ( 30°C), AVrxn (1%), compositional parameters (0.001 mole fraction YAG, 0.01 mole fraction all others), and /(H2O) ( 7.5 1000 trial Monte Carlo simulation). Labels on graph indicate sample numbers. From Pyle et al. (2001).

George and Karkhanavala 208) have ascribed a value of about 450 C for the transition point in a-UjOg from the break occurring in the electrical conductivity vs. reciprocal temperature curve. Girdhar and Westrum 288) have found a small A-type anomaly of specific heat capacity in UjOg at 210"C. 

Figure 5 Arrhenius plots of the logarithm of the frequency location of the p-peak vs. reciprocal temperature for equilibrated (O) unequilibrated ( ) LEXAN 141. Equilibrated samples were stored in di Na at 30-35°C for 24 hours prior to testing.

Figure 8 Arrhenius plots of the logarithm of the frequency of m ocimum loss vs. reciprocal temperature for the dielectric a-relaxations in GE LEXAN 145 PC ( ), VALOX 315 PBT ( ), a 5 4 PC/PBT blend (4) and a 5 4 PC/PBT blend containing 10% impact mMifier ( [adapted from ref 48]...

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