Title :

Helmholtz and Gibbs ensembles, thermodynamic limit and bistability in polymer lattice models

Author(s) :

Giordano, Stefano [Auteur correspondant]
Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN]
Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 [IEMN]

Journal title :

Continuum Mechanics and Thermodynamics

Pages :

459-483

Publisher :

Springer Verlag

Publication date :

2018-05

ISSN :

0935-1175

English keyword(s) :

Polymer lattice models
Polymer stretching
Isotensional and isometric ensembles
Ensemble equivalence
Lattice Green functions

HAL domain(s) :

Science non linéaire [physics]
Physique [physics]
Physique [physics]/Matière Condensée [cond-mat]
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]

English abstract : [en]

Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching ...
Show more >Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics has not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force-extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force-extension response, whereas the isometric condition causes a sawtooth-like force-extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Institut d'Électronique, de Microélectronique et de Nanotechnologie (IEMN) - UMR 8520

Source :

Harvested from HAL