Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains

The influence of long-range correlated surface and decaying near surface disorder with quenched defects is studied. We consider a correlation function for the defects of the form $\frac{e^{-z/\xi}}{r^{a}}$, where $a<d-1$ and $z$ being the coordinate in the direction perpendicular to the surface and $r$ denotes the distance parallel to the surface. We investigate the process of adsorption of long-flexible polymer chains with excluded volume interactions on a "marginal" and attractive wall in the framework of renormalization group field theoretical approach up to first order of perturbation theory in a double ($\epsilon$,$\delta$)- expansion ($\epsilon=4-d$, $\delta=3-a$) for the semi-infinite $|\phi|^4$ $O(m,n)$ model with the above mentioned type of surface and near the surface disorder in the limit $m,n\to 0$. In particular we study two limiting cases. First, we investigate the scenario where the chain's extension it much larger then $\xi$. Second, we consider the case where the chain's extension is of the order of $\xi$. For both cases we obtained series for bulk and the whole set of surface critical exponents, characterizing the process of adsorption of long-flexible polymer chains at the surface. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the volume are studied.Comment: 31 pages, 5 figures, 2 table

Influence of long-range correlated quenched disorder on the adsorption of long flexible polymer chains on a wall

The process of adsorption on a planar wall of long-flexible polymer chains in the medium with quenched long-range correlated disorder is investigated. We focus on the case of correlations between defects or impurities that decay according to the power-low $x^{-a}$ for large distances $x$, where ${\bf x}=({\bf r},z)$. Field theoretical approach in $d=4-\epsilon$ and directly in $d=3$ dimensions up to one-loop order for the semi-infinite $|\phi|^4$ m-vector model (in the limit $m\to 0$) with a planar boundary is used. The whole set of surface critical exponents at the adsorption threshold $T=T_a$, which separates the nonadsorbed region from the adsorbed one is obtained. Moreover, we calculate the crossover critical exponent $\Phi$ and the set of exponents associated with them. We perform calculations in a double $\epsilon=4-d$ and $\delta=4-a$ expansion and also for a fixed dimension $d=3$, up to one-loop order for different values of the correlation parameter $2<a\le 3$. The obtained results indicate that for the systems with long-range correlated quenched disorder the new set of surface critical exponents arises. All the surface critical exponents depend on $a$. Hence, the presence of long-range correlated disorder influences the process of adsorption of long-flexible polymer chains on a wall in a significant way.Comment: 4 figures, 2 table

Polymer chains in confined geometries: Massive field theory approach

The massive field theory approach in fixed space dimensions $d=3$ is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls and for the mixed case of one inert and one repulsive wall. The well known correspondence between the field theoretical $\phi^4$ O(n)-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. Our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains, because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results and with results of Monte Carlo simulations.Comment: 18 pages, 10 figure

Field theoretical analysis of adsorption of polymer chains at surfaces: Critical exponents and Scaling

The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer adsorption problem and the equivalent problem of critical phenomena in the semi-infinite $|\phi|^4$ n-vector model (in the limit $n\to 0$) with a planar boundary. The whole set of surface critical exponents characterizing the process of adsorption of long-flexible polymer chains at the surface is obtained. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the interior are studied on the basis of renormalization group field theoretical approach directly in d=3 dimensions up to two-loop order for the semi-infinite $|\phi|^4$ n-vector model. The obtained field- theoretical results at fixed dimensions d=3 are in good agreement with recent Monte Carlo calculations. Besides, we have performed the scaling analysis of center-adsorbed star polymer chains with $f$ arms of the same length and we have obtained the set of critical exponents for such system at fixed d=3 dimensions up to two-loop order.Comment: 22 pages, 12 figures, 4 table

Conformational Mechanics of Polymer Adsorption Transitions at Attractive Substrates

Conformational phases of a semiflexible off-lattice homopolymer model near an attractive substrate are investigated by means of multicanonical computer simulations. In our polymer-substrate model, nonbonded pairs of monomers as well as monomers and the substrate interact via attractive van der Waals forces. To characterize conformational phases of this hybrid system, we analyze thermal fluctuations of energetic and structural quantities, as well as adequate docking parameters. Introducing a solvent parameter related to the strength of the surface attraction, we construct and discuss the solubility-temperature phase diagram. Apart from the main phases of adsorbed and desorbed conformations, we identify several other phase transitions such as the freezing transition between energy-dominated crystalline low-temperature structures and globular entropy-dominated conformations.Comment: 13 pages, 15 figure

Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions

The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is perfomed using the collective variables (CV) method in the framework of the $\rho^4$ model approximation. The exponentially decreasing function of the distance between the particles situated at the N sites of a simple cubic lattice is used as the interaction potential. Explicit and rigorous analytical expressions for entropy,internal energy, specific heat near the phase transition point as functions of the temperature are obtained. The dependence of the amplitudes of the thermodynamic characteristics of the system for $T>T_c$ and $T<T_c$ on the microscopic parameters of the interaction potential are studied for the cases $n=1,2,3$ and $n\to\infty$. The obtained results provide the basis for accurate analysis of the critical behaviour in three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure

Stress distribution and the fragility of supercooled melts

We formulate a minimal ansatz for local stress distribution in a solid that includes the possibility of strongly anharmonic short-length motions. We discover a broken-symmetry metastable phase that exhibits an aperiodic, frozen-in stress distribution. This aperiodic metastable phase is characterized by many distinct, nearly degenerate configurations. The activated transitions between the configurations are mapped onto the dynamics of a long range classical Heisenberg model with 6-component spins and anisotropic couplings. We argue the metastable phase corresponds to a deeply supercooled non-polymeric, non-metallic liquid, and further establish an order parameter for the glass-to-crystal transition. The spin model itself exhibits a continuous range of behaviors between two limits corresponding to frozen-in shear and uniform compression/dilation respectively. The two regimes are separated by a continuous transition controlled by the anisotropy in the spin-spin interaction, which is directly related to the Poisson ratio $\sigma$ of the material. The latter ratio and the ultra-violet cutoff of the theory determine the liquid configurational entropy. Our results suggest that liquid's fragility depends on the Poisson ratio in a non-monotonic way. The present ansatz provides a microscopic framework for computing the configurational entropy and relaxational spectrum of specific substances.Comment: 11 pages, 5 figures, Final version published in J Phys Chem

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure