TY - JOUR

T1 - Phase transitions, Kauzmann curves, and inverse melting

AU - Stillinger, Frank H.

AU - Debenedetti, Pablo G.

N1 - Funding Information:
PGD gratefully acknowledges financial support by the US Department of Energy, Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences (Grant DE-FG02-87ER13714).

PY - 2003/9/1

Y1 - 2003/9/1

N2 - Walter Kauzmann's classic 1948 review of liquid supercooling and glass formation drew attention to the temperatures at which (by extrapolation) enthalpies and entropies of liquid and crystal phases would appear to become equal. In the temperature-pressure (T, p) plane, the collection of such 'Kauzmann temperatures' generate characteristic curves. The present study examines the connection of those Kauzmann loci to equilibrium inverse melting phenomena, i.e. cases where isobaric heating causes freezing of the liquid. Such cases are associated with local minima or maxima in the melting curve pm(T), and we point out the possible relevance of melting curve maxima to the thermodynamics of protein folding. Both equal-enthalpy and equal-entropy Kauzmann curves must pass through melting curve extrema. Three thermodynamic identities have been obtained to describe the vicinity of these points; they involve, respectively, the slopes of the two Kauzmann curves, and the second temperature derivative of the melting pressure. The second of these three equations is formally identical to the first Ehrenfest relation for second-order phase transitions, but carries no phase-transition implication. For purposes of specific numerical illustration, the inverse-melting behavior displayed by 3He at low temperature has been analyzed in detail.

AB - Walter Kauzmann's classic 1948 review of liquid supercooling and glass formation drew attention to the temperatures at which (by extrapolation) enthalpies and entropies of liquid and crystal phases would appear to become equal. In the temperature-pressure (T, p) plane, the collection of such 'Kauzmann temperatures' generate characteristic curves. The present study examines the connection of those Kauzmann loci to equilibrium inverse melting phenomena, i.e. cases where isobaric heating causes freezing of the liquid. Such cases are associated with local minima or maxima in the melting curve pm(T), and we point out the possible relevance of melting curve maxima to the thermodynamics of protein folding. Both equal-enthalpy and equal-entropy Kauzmann curves must pass through melting curve extrema. Three thermodynamic identities have been obtained to describe the vicinity of these points; they involve, respectively, the slopes of the two Kauzmann curves, and the second temperature derivative of the melting pressure. The second of these three equations is formally identical to the first Ehrenfest relation for second-order phase transitions, but carries no phase-transition implication. For purposes of specific numerical illustration, the inverse-melting behavior displayed by 3He at low temperature has been analyzed in detail.

KW - Inverse melting

KW - Kauzmann curves

KW - Kauzmann paradox

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U2 - 10.1016/S0301-4622(03)00089-9

DO - 10.1016/S0301-4622(03)00089-9

M3 - Article

C2 - 14499893

AN - SCOPUS:0141560581

SN - 0301-4622

VL - 105

SP - 211

EP - 220

JO - Biophysical Chemistry

JF - Biophysical Chemistry

IS - 2-3

ER -