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On the Escape Transition of a Tethered Gaussian Chain; Exact Results in Two Conjugate Ensembles
Author(s) -
Skvortsov Alexander M.,
Klushin Leonid I.,
Leermakers Frans A. M.
Publication year - 2006
Publication title -
macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 1022-1360
DOI - 10.1002/masy.200650509
Subject(s) - thermodynamic limit , chain (unit) , gaussian , statistical mechanics , physics , phase transition , statistical physics , limit (mathematics) , monotonic function , degrees of freedom (physics and chemistry) , canonical ensemble , compressibility , thermodynamics , mathematics , quantum mechanics , mathematical analysis , monte carlo method , statistics
Summary: Upon compression between two pistons an end‐tethered polymer chain undergoes an abrupt transition from a confined coil state to an inhomogeneous flower‐like conformation that is partially escaped from the gap. In the thermodynamic limit the system demonstrates a first‐order phase transition. A rigorous analytical theory of this phenomenon for a Gaussian chain is presented in two ensembles: a) the H ‐ensemble, in which the distance H between pistons plays the role of the control parameter, and b) the conjugate f ‐ensemble in which the external compression force f is the independent parameter. A loop region for 〈 f ( H )〉 with negative compressibility exists in the H ‐ensemble, while in the f ‐ensemble 〈 H ( f )〉 is strictly monotonic. The average lateral forces taken as functions of H (or 〈 H 〉, respectively) have distinctly different behavior in the two ensembles. This result is a clear counterexample of the main principles of statistical mechanics stating that all ensembles are equivalent in the thermodynamic limit. Another theorem states that the thermodynamic potential as a function of volume must be concave everywhere. We demonstrated that the exact free energy in the H ‐ensemble contradicts this statement. Inapplicability of these fundamental theorems to a macromolecule undergoing the escape transition is clearly related to the fact that phase coexistence in the present system is strictly impossible. This is a direct consequence of the tethering and the absence of global translational degrees of freedom of the polymer chain.