Anomalous temperature dependence

Figure 3.8 Anomalous temperature dependence of relative dielectric constant of ferroelectric crystals at the transition temperature (Curie point).

Thus, the model predicts that thermal fluctuations in the tilt and curvature change the way that the tubule radius scales with chiral elastic constant— instead of r oc (THp) 1, the scaling has an anomalous, temperature-dependent exponent. This anomalous exponent might be detectable in the scaling of tubule radius as a function of enantiomeric excess in a mixture of enantiomers or as a function of chiral fraction in a chiral-achiral mixture. 

The second method of detecting tunnelling relies on the fact that the primary hydrogen KIE shows an anomalous temperature dependence when significant tunnelling takes place. In the absence of tunnelling, the temperature dependence of the rate constant should follow the Arrhenius equation (42)... 

This extraordinary study shows with great clarity how far we now are from a reliable understanding of either the linkage between protein flexibility and tunneling in the most general sense, or the physical models that underlie anomalous temperature dependences of isotope effects. 

Frontas ev (59) observed an anomalous temperature dependence in the thermal conductivity of water around 30°-40°C. (Figure 2). (In this illustration the data points are those given by Frontasev, but I believe the curve shown gives a reasonable fit to the experimental data.) He stated specifically that an anomaly existed near 30°-40°C. and that it implies a fundamental modification in water structure in this temperature range. 

We now consider briefly a few examples of the evidence for structural transitions as reflected by anomalous temperature dependencies in some properties of aqueous solutions. 

Water properties near solid interfaces frequently reveal anomalous temperature dependencies. Thus, the zeta-potential for water flowing over a cellulose surface changes in an anomalous, abrupt manner near... 

Kundu B, PratibhaR, MadhusudanaNV (2007) Anomalous temperature dependence of elastic constants in the nematic phase of binary mixtures made of rodlike and bent-core molecules. Phys Rev Lett 99 247802-1-4... 

In the crystal of tin dimethyldichloride, studied by Prager et al. [1986], the observation of coupled rotation is also due to close packing of the methyl groups. In this case, the values V3/B and g 2 are 27.0 and 16.8, respectively. NMR spectra of 2,5-dimethylpyrazine and durene manifest coupled rotations [Takeda and Chihara, 1983]. Sridharan et al. [1985] studied NMR spectra of Ge(CH3)4 and showed that the rotor-rotor interactions in this species result in anomalous temperature dependence... 

Jahn-Teller Effect in the Excited State Anomalous Temperature Dependence of the Zero-Phonon Line... 

Abstract. Two forms of CoO have been prepared from spec, pure Co metal and CoC03 and the magnetic susceptibility of CoO(I) and CoO(II) examined over a temperature range300-700 deg. K. The magnetic data of CoO(II) have shown an anomalous temperature dependence of that in this temperature range CoO(II) passes into CoO(I). This result is in conformity with Mossbauer spectra. Furthermore, D.T.A and temperature dependence of magnetic susceptibility of CoO(II) arises from a first order phase transition. 

Also the results for the Hall coefficients in Fig. 4 reproduce very well the experimental behavior [29,30], The anomalous temperature dependence of the nH is due to the growing role of in its determination with increasing T, being dominantly determined by at T = 0. 

Woutersen S, Emmerichs U, Nienhuys HK, Bakker HJ. Anomalous temperature dependence of vibrational lifetimes in water and ice. Phys Rev Lett 1998 81 1106-1109. 

In the context of the present discussion, it is worth noting that virtually all the experimental systems that exhibit such "anomalous temperature-dependent transfer coefficients are multistep inner-sphere processes, such as proton and oxygen reduction in aqueous media [84]. It is therefore extremely difficult to extract the theoretically relevant "true transfer coefficient for the electron-transfer step, ocet [eqn. (6)], from the observed value [eqn. (2)] besides a knowledge of the reaction mechanism, this requires information on the potential-dependent work terms for the precursor and successor state [eqn. (7b)]. Therefore the observed behavior may be accountable partly in terms of work terms that have large potential-dependent entropic components. Examinations of temperature-dependent transfer coefficients for one-electron outer-sphere reactions are unfortunately quite limited. However, most systems examined (transition-metal redox couples [2c], some post-transition metal reductions [85], and nitrobenzene reduction in non-aqueous media [86]) yield essentially temperature-independent transfer coefficients, and hence potential-independent AS orr values, within the uncertainty of the double-layer corrections. 

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