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Journal of Physical Chemistry B

Volumn 111, Issue 42, 2007, Pages 12195-12203

Symmetry numbers and statistical factors in self-assembly and multivalency

(4) Ercolani, Gianfranco a Piguet, Claude b Borkovec, Michal b Hamacek, Josef b

a UNIVERSITY OF ROME TOR VERGATA (Italy)

b UNIVERSITY OF GENEVA (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL BONDS; NUMBER THEORY; PROBLEM SOLVING; STATISTICAL METHODS;

GEOMETRICAL FEATURES; MULTIVALENCY; SYMMETRY NUMBERS;

SELF ASSEMBLY;

EID: 35748971816 PISSN: 15206106 EISSN: None Source Type: Journal
DOI: 10.1021/jp0740705 Document Type: Article

Times cited : (102)

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30
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- To avoid circular arguments that justify the direct count method on the basis of the symmetry number method and vice versa, we wish to remark that the statistical factor 4 for the equilibrium in eq 11 can be also obtained by the following reasoning. Let us envisage a stochastic process in which bodi the reactants and products are generated by sequential extraction of a couple of atoms from a large pool of A and B atoms present in equal amounts. The probability of extracting either an A or a B atom is 0.5. The formation of A2 requires two consecutive extractions of A with a total probability of 0.25. Analogously, the formation of B2 requires two consecutive extractions of B with the same total probability of 0.25. The formation of AB can be accomplished either by extracting A and then B or by extracting B and then A; the two ways of forming AB both have a probability of 0.25, so the probability to form AB in two consecutive extractions is 0.5. The statistical equil
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33
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- For concepts and nomenclature regarding prostereoisomerism, see ref 23, Chapter 8.

38
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- b-n+1or the concept of effective molarity and its applications, see refs 4b and 18.
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39
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- ext, = 2.
- ext, = 2.

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