Models of adsorption-induced deformation: ordered materials and beyond.

Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.

Adsorption-induced deformation of mesoporous materials with corrugated cylindrical pores.

Mesoporous materials play an important role both in engineering applications and in fundamental research of confined fluids. Adsorption goes hand in hand with the deformation of the absorbent, which has positive and negative sides. It can cause sample aging or can be used in sensing technology. Here, we report the theoretical study of adsorption-induced deformation of the model mesoporous material with ordered corrugated cylindrical pores. Using the classical density functional theory in the local density approximation, we compared the solvation pressure in corrugated and cylindrical pores for nitrogen at sub- and super-critical temperatures. Our results demonstrate qualitative differences between solvation pressures in the two geometries at sub-critical temperatures. The deviations are attributed to the formation of liquid bridges in corrugated pores. However, at super-critical temperatures, there is no abrupt bridge formation and corrugation does not qualitatively change solvation pressure isotherms. We believe that these results could help in the analysis of an adsorption-induced deformation of the materials with distorted pores.

Nonlocal density functional theory of water taking into account many-body dipole correlations: binodal and surface tension of 'liquid-vapour' interface.

In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard-Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory, dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid-vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the electrostatic interactions at the many-body level is able to describe the liquid-vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid-vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

Effects of Enhanced Flexibility and Pore Size Distribution on Adsorption-Induced Deformation of Mesoporous Materials.

Here, we present a new model of adsorption-induced deformation of mesoporous solids. The model is based on a simplified version of local density functional theory in the framework of solvation free energy. Instead of density, which is treated as constant here, we used film thickness and pore radius as order parameters. This allows us to obtain a self-consistent system of equations describing simultaneously the processes of gas adsorption and adsorbent deformation, as well as conditions for capillary condensation and evaporation. In the limit of infinitely rigid pore walls, when the film becomes several monolayers thick, the model reduces to the well-known Derjaguin-Broekhoff-de Boer theory for pores with cylindrical geometry. We have investigated the effects of enhanced flexibility of the solid as well as the influence of pore size distribution on the adsorption/deformation process. The formulation of the theory allows to determine the average pore size and its width from the desorption branch of the strain isotherm only. The model reproduces the nonmonotonic behavior of the strain isotherm at low relative pressure. Furthermore, we discuss the effect of rigidity of the adsorbent on the pore size distribution, showing qualitatively different results of the adsorption isotherms for rigid and highly flexible materials, in particular, the shift of evaporation pressure to lower values and the absence of a limiting value of the loading at high relative pressure. We also discuss the results of the theory with respect to experimental data obtained from the literature.

Statistical description of co-nonsolvency suppression at high pressures.

We present an application of Flory-type theory of a flexible polymer chain dissolved in a binary mixture of solvents to theoretical description of co-nonsolvency. We show that our theoretical predictions are in good quantitative agreement with the recently published MD simulation results for the conformational behavior of a Lennard-Jones flexible chain in a binary mixture of the Lennard-Jones fluids. We show that our theory is able to describe co-nonsolvency suppression through pressure enhancement to extremely high values recently discovered in experiments and reproduced by full atomistic MD simulations. By analysing the co-solvent concentration in the internal polymer volume at different pressure values, we speculate that this phenomenon is caused by the suppression of the co-solvent preferential solvation of the polymer backbone at the rather high pressure imposed. We show that when the co-solvent-induced coil-globule transition takes place, the entropy and enthalpy contributions to the solvation free energy abruptly decrease, while the solvation free energy remains continuous.

Correction: Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field.

Correction for 'Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field' by A. L. Kolesnikov et al., Soft Matter, 2017, DOI: 10.1039/c7sm00417f.

Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field.

The paper presents a theoretical approach for describing the influence of an electric field on the conformation of an electrically neutral dielectric polymer chain dissolved in a dielectric solvent with an admixture of a target compound. Each monomer and each molecule of the target compound carries positive excess polarizability and the solvent is described as a continuous dielectric medium. The model is based on the Flory-type mean-field theory. We demonstrate non-monotonic dependences of the expansion factor and the concentration of the target compound on the strength of the electric field and molecular polarizability. Namely, the target compound concentration in the internal polymer volume as a function of electric field strength has pronounced maxima if the molecules are polarizable. In addition, the expansion factor of the non-polarizable polymer chain can be controlled by the electric field. The dependences of the expansion factor and target compound concentration on the monomer polarizability exhibit minima and intersection points. The intersection points correspond to the equality of dielectric permittivities in the bulk solution and in the internal polymer volume.

Polymer chain collapse induced by many-body dipole correlations.

We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations.

We present a new simple self-consistent field theory of a polarizable flexible polymer chain under an external constant electric field with account for the many-body electrostatic dipole correlations. We show the effects of electrostatic dipole correlations on the electric-field-induced globule-coil transition. We demonstrate that only when the polymer chain is in the coil conformation, the electrostatic dipole correlations of monomers can be considered as pairwise. However, when the polymer chain is in a collapsed state, the dipole correlations have to be considered at the many-body level.

On the theory of electric double layer with explicit account of a polarizable co-solvent.

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On the contrary, a sufficiently large additive of co-solvent shifts the saturation potential to lower surface potentials. We obtain that an increase in the co-solvent polarizability makes the electrostatic potential profile longer-ranged. However, increase in the co-solvent concentration in the bulk leads to non-monotonic behavior of the electrostatic potential profile. An increase in the co-solvent concentration in the bulk at its sufficiently small values makes the electrostatic potential profile longer-ranged. Oppositely, when the co-solvent concentration in the bulk exceeds some threshold value, its further increase leads to decrease in electrostatic potential at all distances from the electrode.

Communication: Polarizable polymer chain under external electric field in a dilute polymer solution.

We study the conformational behavior of polarizable polymer chain under an external homogeneous electric field within the Flory type self-consistent field theory. We consider the influence of electric field on the polymer coil as well as on the polymer globule. We show that when the polymer chain conformation is a coil, application of external electric field leads to its additional swelling. However, when the polymer conformation is a globule, a sufficiently strong field can induce a globule-coil transition. We show that such "field-induced" globule-coil transition at the sufficiently small monomer polarizabilities goes quite smoothly. On the contrary, when the monomer polarizability exceeds a certain threshold value, the globule-coil transition occurs as a dramatic expansion in the regime of first-order phase transition. The developed theoretical model can be applied to predicting polymer globule density change under external electric field in order to provide more efficient processes of polymer functionalization, such as sorption, dyeing, and chemical modification.

A new equation of state of a flexible-chain polyelectrolyte solution: Phase equilibria and osmotic pressure in the salt-free case.

We develop a first-principle equation of state of salt-free polyelectrolyte solution in the limit of infinitely long flexible polymer chains in the framework of a field-theoretical formalism beyond the linear Debye-Hueckel theory and predict a liquid-liquid phase separation induced by a strong correlation attraction. As a reference system, we choose a set of two subsystems-charged macromolecules immersed in a structureless oppositely charged background created by counterions (polymer one component plasma) and counterions immersed in oppositely charged background created by polymer chains (hard-core one component plasma). We calculate the excess free energy of polymer one component plasma in the framework of modified random phase approximation, whereas a contribution of charge densities' fluctuations of neutralizing backgrounds we evaluate at the level of Gaussian approximation. We show that our theory is in a very good agreement with the results of Monte Carlo and MD simulations for critical parameters of liquid-liquid phase separation and osmotic pressure in a wide range of monomer concentration above the critical point, respectively.

The local phase transitions of the solvent in the neighborhood of a solvophobic polymer at high pressures.

We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the solution as a function of the radius of gyration and the average solvent number density within the gyration volume. The resulting system of coupled equations is solved varying the polymer-solvent repulsion strength at high solvent pressure in the bulk. We show that the coil-globule (globule-coil) transition occurs accompanied by a local solvent evaporation (condensation) within the gyration volume.

A statistical theory of cosolvent-induced coil-globule transitions in dilute polymer solution.

We present a statistical model of a dilute polymer solution in good solvent in the presence of low-molecular weight cosolvent. We investigate the conformational changes of the polymer induced by a change of the cosolvent concentration and the type of interaction between the cosolvent and the polymer. We describe the polymer in solution by the Edwards model, where the partition function of the polymer chain with a fixed radius of gyration is described in the framework of the mean-field approximation. The contributions of polymer-cosolvent and the cosolvent-cosolvent interactions in the total free energy are treated also within the mean-field approximation. For convenience we separate the system volume on two parts: the volume occupied by the polymer chain expressed through its gyration volume and the bulk solution. Considering the equilibrium between the two subvolumes we obtain the total free energy of the solution as a function of radius of gyration and the cosolvent concentration within gyration volume. After minimization of the total free energy with respect to its arguments we obtain a system of coupled equations with respect to the radius of gyration of the polymer chain and the cosolvent concentration within the gyration volume. Varying the interaction strength between polymer and cosolvent we show that the polymer collapse occurs in two cases--either when the interaction between polymer and cosolvent is repulsive or when the interaction is attractive. The reported effects could be relevant for different disciplines where conformational transitions of macromolecules in the presence of a cosolvent are of interest, in particular in biology, chemistry, and material science.

[The ultrasonic diagnosis of acute thrombophlebitis of the vena saphena magna]. / Ul'trazvukovaia diagnostika ostrogo tromboflebita bol'shoi podkozhnoi veny bedra.

A total of 321 patients with suspected acute thrombophlebitis were examined. There were 92 men (30%) and 229 women (70%). For control 15 patients without lower limb vein abnormalities and 19 ones with uncomplicated varicose disease were examined. Ultrasonic examinations using Ultramark-8 (Medata, Sweden) device were carried out in all the patients. Of the 313 cases (in 8 patients the diagnosis of acute thrombophlebitis was not confirmed by ultrasonic examination) ultrasonography results were erroneous in only 6 cases when assessing the proximal borderline of the great subcutaneous femoral vein thrombosis. Hence, the accuracy of duplex scanning in assessment of the proximal border of thrombosis in acute thrombophlebitis was 98.6% in our study. Ultrasonic angio-scanning in patients with superficial thrombophlebitis give reliable and valuable information about the presence, type, and extension of the pathologic process. This helps to optimally solve the therapeutic policy problems and adequately plan surgical intervention.