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.     

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

The elastic semi-space consolidation under the normal load on a square area

We investigate the elastic saturated semi-space consolidation under the uniform normal load on a square area. The analytical forms for the fluid pressure and the semi-space surface settlement are found by the solutions to the Dirichlet problem for the Laplace equation and the first boundary-value problem for the heat equation.     

Determination of the accessible volume and the interaction parameter in the adsorption mode of liquid chromatography

The main physical parameters in liquid chromatography of oligomers-the accessible volume and the adsorption interaction parameter-are discussed. It is shown, that in liquid adsorption chromatography (LAC) there is a linear relation between elution volume and the distance of two subsequent peaks of a homologous series. From the intercept of the regression lines in such a plot the accessible volume can be easily determined at any mobile phase in LAC (corresponding to conditions of weak or strong adsorption) without any information about the molar mass of the peaks. From the slope of this dependence the adsorption interaction parameter of a given repeat unit can be obtained. The accurate determination of the accessible volume and the adsorption interaction parameter in the LAC regime is presented for PEG, PPG and fatty alcohols on various reversed phase columns with different pore size in methanol-water or acetone-water mobile phases. The difference between the void volume, the dead volume or hold-up volume (from the solvent peak position) and the accessible volume (obtained by this procedure) is discussed.     

Variational measures related to local systems and the Ward property of \mathcal{P}-adic path bases

Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a -adic path system that defines a differentiation basis which does not possess Ward property.     

Interaction between Wells and a Groundwater Stream

The interaction between a natural contaminated groundwater stream and a flow induced by wells is investigated. When the flow is potential, the boundaries of the regions protected from the contaminated stream are determined for several configurations of their location and all possible flow diagrams. Dimensionless critical well flow rates corresponding to transition from one diagram to another are found.