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A M Skvortsov

Publications and source records attributed to A M Skvortsov.

17 recordsLinked to original sources
PubMed2007

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

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: (a) the H-ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and (b) 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-ensemble) 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.

Biopolymers↗
PubMed2004

Partition function, metastability, and kinetics of the escape transition for an ideal chain.

An end-tethered polymer chain squeezed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation partially escaped from the gap. We present a rigorous analytical theory for the equilibrium and kinetic aspects of this phenomenon for a Gaussian chain. Applying the analogy with the problem of the adsorption of an ideal chain constrained by one of its ends, we obtain a closed analytical expression for the exact partition function. Various equilibrium thermodynamic characteristics (the fraction of imprisoned segments, the average compression, and lateral forces) are calculated as a function of the piston separation. The force versus separation curve is studied in two complementary statistical ensembles, the constant force and the constant confinement width ones. The differences in these force curves are significant in the transition region for large systems, but disappear for small systems. The effects of metastability are analyzed by introducing the Landau free energy as a function of the chain stretching, which serves as the order parameter. The phase diagram showing the binodal and two spinodal lines is presented. We obtain the barrier heights between the stable and metastable states in the free energy landscape. The mean first passage time, i.e., the lifetime of the metastable coil and flower states, is estimated on the basis of the Fokker-Planck formalism. Equilibrium analytical theory for a Gaussian chain is complemented by numerical calculations for a lattice freely jointed chain model.

Journal Article↗
PubMed2002

Exactly solvable model with stable and metastable states for a polymer chain near an adsorbing surface.

We report on the conformational properties and transitions of an ideal polymer chain near a solid surface. The chain is tethered with one of its ends at distance z(0) from an adsorbing surface. The surface is characterized by an adsorption parameter c. The exact expression for the partition function is available. We obtained the distribution of complex zeros of this function. The comparison with the Yang-Lee theory allows the characterization of the phase transitions. A first-order conformational transition from a coil to a (adsorbed) flower conformation occurs at c(*)=6z(0)/N. The flower is composed of a strongly stretched stem and a pancake that collects the remaining adsorbed segments. The degree of stretching of the coil or of the stem serves as an order parameter which parametrizes the analytical expressions of the Landau free energy. The phase diagram with one binodal and two spinodal lines is presented. The height of the barriers between metastable and stable states is obtained and the lifetime of metastable states is estimated. A two-state ansatz is used to develop scaling arguments to account for the effects of excluded volume.

Journal Article↗
PubMedDate not supplied

[Helix-globule transitions of polypeptides selectively reacting with the interface].

An analytical theory of helix-coil transitions for polypeptides in a solution near a flat and homogeneous interface is given. The following cases were considered: a) only the helical parts are absorbtively active; b) only the coiled sections of the chain are active in adsorption. It has been shown that the binding of the polymer chain to the surface is a result of a phase transition of a second order, moreover in case a) the presence of a secondary structure abruptly increases the ability of the macromolecules to bind to the interface. This largely increases the stability of the helical structure of the chain and leads to a practically complete spiralization of the macromolecule. The profile of the conformational transitions was strictly asymmetrical which is typical for the phase transitions. In case b) the process of binding resembles the adsorbtion of the Gaussian coils. In this case the rate of spiralization of the chain decreases in the course of binding and the degradation of the secondary structure is significant even if the helical state in volume is stable. The profile of the transition remains qualitatively similar to the helix-coil transition in volume but is displaced to the region of larger equilibrium constants.

Models, Chemical↗
PubMedDate not supplied

[Studies on the coil-globule transition by the Monte-Carlo method].

The results of a dynamical Monte-Carlo study on the coil-globule and globule-coil transitions are presented. Self-avoiding chains of lengths N = 32 and 64 are investigated. The kinetic model included two- and three-bonds flips. The relaxation of the chain was induced by the abrupt change of the interaction between the monomers. The time evolution of the radius of gyration and the number of intramolecular contacts was obtained. It is established that the transition to the compact state occurs due to the contacts between the monomers close to each other along the chain. The results obtained are compared with the predictions of analytical theories.

Biopolymers↗
PubMedDate not supplied

[Conformational transitions in adsorbed macromolecules with secondary structure].

An analytical theory is presented taking into account the effects of the flat adsorbing surface on the equilibrium properties of the long single-stranded macromolecule possessing a secondary structure. Change of the secondary structure is described in terms of Zimm--Bragg theory; adsorbtion properties are calculated for the lattice model without taking into account the 3-dimensional interactions. It is shown that the presence of the adsorbing surface sharpens helix-coil transition, displacing it towards the lower constants of equilibrium (s). A relation of the critical energy of adsorbtion (--epsilonkappa) on s is obtained at different values of the cooperativity factor sigma. This relationship represents a phase diagram of the system. Various sections of this phase diagram corresponding to different dependence of s and --epsilon on the external factors are considered. It is shown that the process of adsorbtion may occur in different manners: either cooperatively or by the phase transition of type II with jumps in one or in three points.

Kinetics↗