Divergence Of Heat Capacity Research Articles

The gas–liquid phase-transition singularities in the framework of the liquid-state integral equation formalism

The singularities of various liquid-state integral equations derived from the Ornstein-Zernike relation and its temperature derivatives, have been investigated in the liquid-vapor transition region. As a general feature, it has been found that the existence of a nonsolution curve on the vapor side of the phase diagram, on which both the direct and the total correlation functions become complex-with a finite isothermal compressibility-also corresponds to the locus of points where the constant-volume heat capacity diverges, in consonance with a divergence of the temperature derivative of the correlation functions. In contrast, on the liquid side of the phase diagram one finds that a true spinodal (a curve of diverging isothermal compressibilities) is reproduced by the Percus-Yevick and Martynov-Sarkisov integral equations, but now this curve corresponds to states with finite heat capacity. On the other hand, the hypernetted chain approximation exhibits a nonsolution curve with finite compressibilities and heat capacities in which, as temperature is lowered, the former tends to diverge.

Stability limits for a liquid of Einstein glasses

The thermal properties of a model liquid are expressed in terms of the properties of the glasses that it samples. Each glass is modeled as an Einstein solid with enthalpy H0 at absolute zero and an Einstein temperature that decreases linearly with H0. The number of glasses with enthalpy H0 is represented by a Gaussian distribution. The range over which the liquid exists is bounded below by a Kauzmann temperature, where it has the same entropy as an individual glass, and bounded above by a heat capacity divergence.

Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. I. A thermodynamics analogy.

In a recent paper the authors developed a stochastic model for the response of the cerebral cortex to a general anesthetic agent. The model predicted that there would be an anesthetic-induced phase change at the point of transition into unconsciousness, manifested as a divergence in the electroencephalogram spectral power, and a change in spectral energy distribution from being relatively broadband in the conscious state to being strongly biased towards much lower frequencies in the unconscious state. Both predictions have been verified in recent clinical measurements. In the present paper we extend the model by calculating the equilibrium distribution function for the cortex, allowing us to establish a correspondence between the cortical phase transition and the more familiar thermodynamic phase transitions. This correspondence is achieved by first identifying a cortical free energy function, then by postulating that there exists an inverse relationship between an anesthetic effect and a quantity we define as cortical excitability, which plays a role analogous to temperature in thermodynamic phase transitions. We follow standard thermodynamic theory to compute a cortical entropy and a cortical "heat capacity," and we investigate how these will vary with anesthetic concentration. The significant result is the prediction that the entropy will decrease discontinuously at the moment of induction into unconsciousness, concomitant with a release of "latent heat" which should manifest as a divergence in the analogous heat capacity. There is clear clinical evidence of heat capacity divergence in historical anesthetic-effect measurements performed in 1977 by Stullken et al. [Anesthesiology 46, 28 (1977)]. The discontinuous step change in cortical entropy suggests that the cortical phase transition is analogous to a first-order thermodynamic transition in which the comatose-quiescent state is strongly ordered, while the active cortical state is relatively disordered.

Vibrational melting and its possible relevance to amorphous silicon

The conventional melting of “simple” substances involves configurational excitation from multi-dimensional potential energy basins surrounding crystalline structures to those surrounding amorphous structures. Vibrational anharmonicity changes relatively little in extent across such transitions. Motivated by observations of a sharp melting point for solid amorphous silicon well below that of the crystal, another possibility is proposed. This requires cooperative softening of vibrational modes with increasing mean amplitude. An exactly solvable model for this type of strong anharmonicity demonstrates that it can produce a first-order “intrabasin melting”, or a critical point with a symmetric heat capacity divergence.

Calorimetric investigations of second order ferroelectric transitions

Calorimetric studies employing small temperature intervals were made of the second order ferroelectric transitions in triglycine sulfate and Rochelle salt. No evidence of a heat capacity divergence was observed in Rochelle salt. No strong heat capacity divergence was observed in triglycine sulfate, an observation which may be attributed to the quality of the crystals available for study. In triglycine sulfate it was demonstrated that crystal quality can affect the heat capacity measured in the immediate vicinity of the transition.