Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Abstract

An end-tethered polymer chain compressed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flowerlike conformation partially escaped from the gap. This phase transition is first order in the thermodynamic limit of infinitely long chains. A rigorous analytical theory is presented for a Gaussian chain in two ensembles: ͑a͒ the H-ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and ͑b͒ the conjugate f-ensemble, in which the external compression force f is the independent parameter. Details about the metastable chain configurations are analyzed by introducing the Landau free energy as a function of the chain stretching order parameter. The binodal and spinodal lines, as well as the barrier heights between the stable and metastable states in the free energy landscape, are presented in both ensembles. In the loop region for the average force with dependence on the distance H ͑i.e., in the H-ensemble͒ a negative compressibility exists, whereas in the f-ensemble the average distance as a function of the force is strictly monotonic. The average fraction of imprisoned segments and the lateral force, taken as functions of the distance H or the average H, respectively, have different behaviors in the two ensembles. These results demonstrate a clear counterexample of a main principle of statistical mechanics, stating that all ensembles are equivalent in the thermodynamic limit. The authors show that the negative compressibility in the escape transition is a purely equilibrium result and analyze in detail the origin of the nonequivalence of the ensembles. It is argued that it should be possible to employ the escape transition and its anomalous behavior in macroscopically homogeneous, but microscopically inhomogeneous, materials.

Modelling negative linear compressibility in tetragonal beam structures

“…The same technique has also proved the presense of NLC in methanol monohydrate (Fortes et al, 2011). Other materials have been shown to have NLC triggered by a pressure induced phase transition, molecular dynamic simulations show that hydrocarbon chains will experience a very pronounced phase change under high hydrostatic loading that leads to the chains suddenly becoming aligned thus causing an expansion on a particular axis (Skvortsov et al, 2007). Paratellurite was shown to exhibit NLC (Skelton et al, 1976) due to a phase transition induced by increased pressure where the symmetry changes from a tetragonal to an orthorhombic structure at 8kbar.…”

Role of temperature in the decohesion of an elastic chain tethered to a substrate by onsite breakable links

“…Although the equivalence of the Gibbs and Helmholtz statistical ensemble has been proved for a large class of systems (namely, single flexible polymer chains without confinement effects and with a continuous pairing interaction potential between neighboring monomers [86][87][88][89][90][91]), interestingly, it cannot be assumed for other structures. Indeed, other classes of problems, e.g., concerning the escape of a polymer confined between two surfaces and the desorption of a polymer initially tethered onto a surface, exhibit an unusual nonequivalence between the defined statistical ensembles [113][114][115][116][117][118]. In particular, in Refs.…”

“…In particular, in Refs. [113,114] an end-tethered polymer chain compressed between two pistons is considered and shows nonequivalence of the ensembles and a phase transition corresponding to the escape from the gap between the pistons. Reference [115] deals with the desorption of a single chain from a substrate without excluded volume interactions: also in this case the equivalence of the ensembles and the emergence of a phase transition are thoroughly discussed.…”

Thermodynamics of small systems with conformational transitions: The case of two-state freely jointed chains with extensible units

“…However, it is noteworthy to mention that some particular cases on non-equivalence between dual canonical ensembles have been recently discussed for confined polymer chains. [90][91][92]…”