Entropy of ice phases: Difference between revisions

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{{Stub-water}}
==Ice rules==
==Ice rules==
Or the Bernal-Fowler rules<ref>[J. D. bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]</ref>,
The '''ice rules''', also known as the ''Bernal-Fowler rules''
give us how the hydrogen atoms are distributed in the ices. Each oxygen atom has two hydrogen atoms attached
<ref>[http://dx.doi.org/10.1063/1.1749327 J. D. Bernal and R. H. Fowler "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions", Journal of Chemical Physics '''1''' pp. 515- (1933)]</ref>,
to it at a distance about 1 amstrong, and one hydrogen atom resides on each O-O bond. There are
describe  how the [[hydrogen]] atoms are distributed in the [[ice phases| ices]]. Each [[oxygen]] atom has two hydrogen atoms attached
many ways to distribute the protons such that these rules are satisfied and all are equally probable.
to it, at a distance of approximately  1 ångström, one hydrogen atom resides on each O-O bond. There are
The ice with this random distribution must have null dipole moment.  
many ways to distribute the protons such that these rules are satisfied, and all are equally probable.
For this reason, the residual entropy of ice is correctly predicted. The observed residual entropy
For this reason, the residual [[entropy]] of ice is correctly predicted. The observed residual entropy
was descibed, for the first time, by the statistical model for ice Ih introduced by Pauling
was described for the first time using the statistical model for [[ice Ih]] introduced by Linus Pauling
<ref>[Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society 57 pp. 2680–2684 (1935)]</ref>. Who suggested a random arrangement of protons. By means
<ref>[http://dx.doi.org/10.1021/ja01315a102 Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society '''57''' pp. 2680–2684 (1935)]</ref>.  
of a simple calculation, Pauling showed that the resulting disordered phase requires the addition of
Pauling suggested a random arrangement of protons. By means
a combinatorial entropy -NKB ln 3/2 to the teorical estimate. This finding demostrated that a crystal
of a simple calculation he showed that the resulting disordered phase requires the addition of
phase such as ice Ih could show full disorder at 0 K (against prediction from the third principe).
a combinatorial entropy of <math>-Nk_B \ln (3/2)</math> to the theoretical estimate. This finding demonstrated that a crystal
phase such as ice Ih could show full disorder at 0K, which is in contrast to the  prediction from the [[Third law of thermodynamics |third principle of thermodynamics]].


==References==
==References==
#[http://dx.doi.org/10.1021/ja01315a102 Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society '''57''' pp. 2680–2684 (1935)]
<references/>
#[http://dx.doi.org/10.1063/1.1725363 E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice",  Journal of Chemical Physics '''40''' 1577 (1964)]
'''Related reading'''
#[http://dx.doi.org/10.1063/1.1705058 J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics '''7''' 1484 (1966)]
*[http://dx.doi.org/10.1063/1.1725363 E. A. DiMarzio and F. H. Stillinger, Jr. "Residual Entropy of Ice",  Journal of Chemical Physics '''40''' 1577 (1964)]
#[http://dx.doi.org/10.1063/1.452433    Rachel Howe and R. W. Whitworth "The configurational entropy of partially ordered ice", Journal of Chemical Physics '''86''' pp. 6443-6445 (1987)]
*[http://dx.doi.org/10.1063/1.1705058 J. F. Nagle "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice", Journal of Mathematical Physics '''7''' 1484 (1966)]
#[http://dx.doi.org/10.1063/1.453743    Rachel Howe and R. W. Whitworth "Erratum: The configurational entropy of partially ordered ice <nowiki>[J. Chem. Phys. 86, 6443 (1987)]</nowiki>", Journal of Chemical Physics '''87''' p. 6212 (1987)]
*[http://dx.doi.org/10.1063/1.452433    Rachel Howe and R. W. Whitworth "The configurational entropy of partially ordered ice", Journal of Chemical Physics '''86''' pp. 6443-6445 (1987)]
#[http://dx.doi.org/10.1063/1.1808693      Luis G. MacDowell, Eduardo Sanz, Carlos Vega, and José Luis F. Abascal "Combinatorial entropy and phase diagram of partially ordered ice phases", Journal of Chemical Physics '''121'''  pp. 10145-10158 (2004)]
*[http://dx.doi.org/10.1063/1.453743    Rachel Howe and R. W. Whitworth "Erratum: The configurational entropy of partially ordered ice <nowiki>[J. Chem. Phys. 86, 6443 (1987)]</nowiki>", Journal of Chemical Physics '''87''' p. 6212 (1987)]
#[http://dx.doi.org/10.1063/1.2800002 Bernd A. Berg and Wei Yang "Numerical calculation of the combinatorial entropy of partially ordered ice",  Journal of Chemical Physics '''127''' 224502 (2007)]
*[http://dx.doi.org/10.1063/1.1808693      Luis G. MacDowell, Eduardo Sanz, Carlos Vega, and José Luis F. Abascal "Combinatorial entropy and phase diagram of partially ordered ice phases", Journal of Chemical Physics '''121'''  pp. 10145-10158 (2004)]
*[http://dx.doi.org/10.1063/1.2800002 Bernd A. Berg and Wei Yang "Numerical calculation of the combinatorial entropy of partially ordered ice",  Journal of Chemical Physics '''127''' 224502 (2007)]
*[http://dx.doi.org/10.1063/1.4879061  Jiří Kolafa "Residual entropy of ices and clathrates from Monte Carlo simulation", Journal of Chemical Physics '''140''' 204507 (2014)]
*[http://dx.doi.org/10.1063/1.4882650  Carlos P. Herrero and Rafael Ramírez "Configurational entropy of hydrogen-disordered ice polymorphs", Journal of Chemical Physics '''140''' 234502 (2014)]
 
 
 
[[category: water]]
[[category: water]]

Latest revision as of 13:45, 23 June 2014

Ice rules[edit]

The ice rules, also known as the Bernal-Fowler rules [1], describe how the hydrogen atoms are distributed in the ices. Each oxygen atom has two hydrogen atoms attached to it, at a distance of approximately 1 ångström, one hydrogen atom resides on each O-O bond. There are many ways to distribute the protons such that these rules are satisfied, and all are equally probable. For this reason, the residual entropy of ice is correctly predicted. The observed residual entropy was described for the first time using the statistical model for ice Ih introduced by Linus Pauling [2]. Pauling suggested a random arrangement of protons. By means of a simple calculation he showed that the resulting disordered phase requires the addition of a combinatorial entropy of to the theoretical estimate. This finding demonstrated that a crystal phase such as ice Ih could show full disorder at 0K, which is in contrast to the prediction from the third principle of thermodynamics.

References[edit]

  1. ↑ J. D. Bernal and R. H. Fowler "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions", Journal of Chemical Physics 1 pp. 515- (1933)
  2. ↑ Linus Pauling "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement", Journal of the American Chemical Society 57 pp. 2680–2684 (1935)

Related reading

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