On Extrapolating a Supercooled Liquid's Excess Entropy, the Vibrational Component, and Reinterpreting the Configurational Entropy Theory

2001 ◽  
Vol 105 (17) ◽  
pp. 3600-3604 ◽  
Author(s):  
G. P. Johari
Keyword(s):  
Excess Entropy ◽  
Configurational Entropy ◽  
Entropy Theory ◽  
Vibrational Component

Applicability of Free Volume Concept to Relaxation Phenomena in the Glass Transition Range

1968 ◽  
Vol 41 (3) ◽  
pp. 555-563
Author(s):  
A. J. Kovacs
Keyword(s):  
Glass Transition ◽  
Free Volume ◽  
Excess Entropy ◽  
Heat Content ◽  
Configurational Entropy ◽  
Wide Distribution ◽  
Dielectric Constants ◽  
Experimental Point ◽  
Transition Range ◽  
Glass Transition Range

Abstract Except for discrepancies mentioned with respect to pressure investigations, which need future clarification, we can conclude in a general way, as follows. As far as only average parameters of macroscopic specimens are considered (complex moduli, or dielectric constants, volume or heat content etc...), the free volume concept can relate variations of molecular mobility to changes of an average free volume in a semiquantitative way. This average free volume can no longer fully characterize the wide variety of molecular motions involved in the kinetics of redistribution of holes in the liquid during recovery experiments. These kinetic processes involve a wide distribution of retardation times, which may be associated with local distribution of holes, or with that of cooperating groups of molecules, or molecular segments. On the other hand, free volume is not necessarily the fundamental molecular parameter which controls rate of configurational changes, characterized by variation of entropy of the liquid. Even if this is the case, most of the above discussion may be applied to any other average excess parameter, as far as the Doolittle equation is formally adopted, in which f/b is expressed in terms of the new parameter, rather than that of free volume. However, since relaxational free volume, as determined from the WLF equation, and independently measured volume changes are often in close agreement, this means that variations of excess entropy, or those of configurational free energy, and changes in volume are closely related. This conclusion is in agreement with that of Eisenberg and Saito, who found that the Gibbs—Dimarzio theory, based on configurational entropy, is practically equivalent with the free-volume approach. Thus, the free volume concept remains still a valuable tool for unifying different kinds of rate processes from both a theoretical and an experimental point of view, especially in the glass transition range.

Experimental temperature–X(H2O)–viscosity relationship for leucogranites and comparison with synthetic silicic liquids

2004 ◽  
Vol 95 (1-2) ◽  
pp. 59-71 ◽  
Author(s):  
Alan Whittington ◽  
Pascal Richet ◽  
Harald Behrens ◽  
François Holtz ◽  
Bruno Scaillet
Keyword(s):  
Configurational Entropy ◽  
Liquid Composition ◽  
Viscosity Data ◽  
Entropy Theory ◽  
Melt Structure ◽  
Naturally Occurring ◽  
Wide Range ◽  
Compositional Variations ◽  
Water Contents ◽  
Magma Viscosity

ABSTRACTViscosities of liquid albite (NaAlSi3O8) and a Himalayan leucogranite were measured near the glass transition at a pressure of one atmosphere for water contents of 0, 2·8 and 3·4 wt.%. Measured viscosities range from 1013·8 Pa. s at 935 K to 109·0 Pa. s at 1119 K for anhydrous granite, and from 1010·2 Pa. s at 760 K to 1012·9 Pa. s at 658 K for granite containing 3·4 wt.% H2O. The leucogranite is the first naturally occurring liquid composition to be investigated over the wide range of T-X(H2O) conditions which may be encountered in both plutonic and volcanic settings. At typical magmatic temperatures of 750°C, the viscosity of the leucogranite is 1011·0 Pa. s for the anhydrous liquid, dropping to 106·5 Pa. s for a water content of 3 wt.% H2O. For the same temperature, the viscosity of liquid NaAlSi3O8 is reduced from 1012·2 to 106·3 Pa. s by the addition of 1·9 wt.% H2O. Combined with published high-temperature viscosity data, these results confirm that water reduces the viscosity of NaAlSi3O8 liquids to a much greater degree than that of natural leucogranitic liquids. Furthermore, the viscosity of NaAlSi3O8 liquid becomes substantially nonArrhenian at water contents as low as 1 wt.% H2O, while that of the leucogranite appears to remain close to Arrhenian to at least 3 wt.% H2O, and viscosity–temperature relationships for hydrous leucogranites must be nearly Arrhenian over a wide range of temperature and viscosity. Therefore, the viscosity of hydrous NaAlSi3O8 liquid does not provide a good model for natural granitic or rhyolitic liquids, especially at lower temperatures and water contents.Qualitatively, the differences can be explained in terms of configurational entropy theory because the addition of water should lead to higher entropies of mixing in simple model compositions than in complex natural compositions. This hypothesis also explains why the water reduces magma viscosity to a larger degree at low temperatures, and is consistent with published viscosity data for hydrous liquid compositions ranging from NaAlSi3O8 and synthetic haplogranites to natural samples. Therefore, predictive models of magma viscosity need to account for compositional variations in more detail than via simple approximations of the degree of polymerisation of the melt structure.

Review of Social Entropy Theory.

1991 ◽  
Vol 36 (4) ◽  
pp. 347-347
Author(s):  
No authorship indicated
Keyword(s):  
Entropy Theory

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

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