A polarizable continuum model for molecules at diffuse interfaces

In this work we illustrate an extension of the polarizable continuum model to describe solvation effects on molecules at the interface between two fluid phases (liquid/liquid, liquid/vapor). This extension goes beyond the naive picture of the interface as a plane dividing two distinct dielectrics, commonly employed in continuum models. The main feature of the model is the use of a diffuse interface with an electric permittivity depending on the position. This characteristic clearly allows the study of simple interfaces as well as more complex membrane or multilayer structures. Moreover the smooth variation of the permittivity in the diffuse interface, in contrast to the sharp boundary between two regions, overcomes the numerical divergences due to charges placed at the boundary. The implementation of the model relies on the integral equation formalism, which allows one to calculate the reaction field acting on a molecule immersed in a dielectric environment once the proper Green's function is known. In the present case, such a Green's function is obtained numerically, allowing a large flexibility in the choice of the dielectric permittivity profile. The applications have been selected with the aim of illustrating the capabilities of the model; its present limitations are also discussed.     

Liquid crystalline polymers at interfaces

Main chain liquid crystalline polymers (LCPs) at solid-nematic interfaces exhibit a variety of phase transition between distorted and undistorted states. In one case the transition results from the confinement of grafted chains immersed in a nematic solvent and subject to homeotropic anchoring. The general features of the transition are similar for long and for short chains. The detailed physics is different since long chains exhibit Gaussian, entropic elasticity while the elasticity of the short chain is due to their rigidity. As a result it is possible to weakly confine long chains without triggering a distortion while for short chains the nematic distortion occurs simultaneously with the buckling of the rod like LCPs. Related effects are found for uniformly adsorbed LCPs and for free, confined chains. Different scenarios are expected when homogeneous anchoring is imposed.     

Molecular orientations at interfaces by extended polarizable continuum model

This study presents an investigation into orientation of molecular solutes at the interface of liquid water and other media. The calculation of electrostatic free energy of molecular solute is based on an extension of the polarizable continuum model (PCM) to interfacial system. The extended PCM computational scheme is incorporated with the self‐consistent field procedure which is necessary to obtain more accurate electrostatic free energy and charge density distribution. The computation of non‐electrostatic energy for interfacial system is also realized. Applying the numerical procedure to molecular systems, N,N′‐diethyl‐p‐nitroaniline (DEPNA) at air/water interface and p‐nitrophenol (PNP) at cyclohexane/water interface, the average orientational angles are in reasonable agreement with the experimental results. Taking both the electrostatic and the non‐electrostatic energies into account, the analysis on the energy profiles shows that the electrostatic solvation energy is the dominant factor in determining the orientation angle for PNP, whereas for DEPNA, the orientation angle mainly depends on the cavitation energy. This suggests that, in addition to the electrostatic energy, taking the cavitation energy into account may provide a more complete view when we survey the molecular orientation at interface. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Adsorption of polymers at the solution-solid interfaces

Summary Adsorption of ethyl cellulose, so-called rigid polymer, on the glass surface from various solvents having no groups to make the hydrogen bonds with solid surface was carried out. And the solvent dependence was found. The dependence is, however, small as compared with polyvinyl acetate-glass system (1). A main factor to control the solvent dependence is not competitive between solvent and polymer, but the effect of solvent to extension of polymer in solution, that is, segment density per solid surface area in poor solvent is greater than in better solvent. Maximum adsorption is independent of molecular weight of ethyl cellulose used (Mv=2×10⁴6×10⁴). It is expected that ethyl cellulose lies flat on the glass surface considering adsorption energy per segment (₀>5kT).

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Zusammenfassung Adsorptionen von Äthylzellulose als sozusagen steifes Polymeres an Glasoberfläche aus verschiedenen Lösungsmitteln heraus, die keine Gruppen für Wasserstoff bindungen an die Festoberflächen besitzen, wurden ausgeführt. Es ergab sich in der Tat Lösungsmittelabhängigkeit. Diese ist jedoch klein im Vergleich zu der beim System Polyvinylacetat/Glas. Eine Ursache für die Lösungsmittelabhängigkeit ist nicht direkt die unterschiedliche Solvatation zwischen Lösung und Polymer, sondern der Effekt des Lösungsmittels auf die räumliche Aufweitung des Polymers in Lösungen. Letzteres bedeutet nämlich, die Segmentdichte ist in schlechten Lösungsmitteln größer als in guten. Die maximale Adsorption ist unabhängig vom Molekulargewicht im Bereich vonMv=2×10⁴ bis 6×10⁴. Es ist zu erwarten, daß die Äthylzellulosc flach auf der Glasoberfläche aufliegt, wenn man die Adsorptionsenergie pro Segment betrachtet.

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With 5 figures and 4 tables     

Analytical theory of ideal polydisperse polymers at interfaces

We use a recently developed continuum theory to present an exact treatment of the interfacial properties of ideal polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. We apply our theory to a number of cases, including, non-adsorbing and adsorbing surfaces, as well as telechelic chains.     

Theory of electron localization at dielectric-metal interfaces: a continuum model

Localization of electrons at dielectric-metal interfaces is studied in the framework of a continuum model. The layer of thickness L, with a negative electron affinity, is characterized by the static dielectric constant epsilons and by the optical dielectric constant epsiloninfinity. It is found that the electron localization along the plane of the interface occurs if the layer thickness exceeds a critical value Lc. In the case of a high polar layer, the electron energy of the localized ground state shows a nonmonotonic dependence on the layer thickness. A strong correlation between low-lying excitations and the spread of the localized state has been established. The magnitude of the correlation parameter is close to the analogous correlation for the solvated electron in the bulk. The localization dynamics is discussed in terms of relaxation along a polarization coordinate, which is directly connected to the polarization energy of the layer.     

A study of dilational rheological properties of polymers at interfaces

Viscoelastic properties of two polymers, partially hydrolyzed polyacrylamide and partially hydrolyzed modified polyacrylamide, widely used in chemical flooding in the petroleum industry, were investigated at three interfaces, water-air, water-dodecane, and water-crude oil, by means of a dilational method provided by I.T. Concept, France, at 85 degrees C. Polymer solutions were prepared in brine with 10,000 mg/l sodium chloride and 2000 mg/l calcium chloride. It has been shown that the viscoelastic modulus increases with the increment of polymer concentration in the range of 0-1500 mg/l at the water-air interface. Each polymer shows different viscoelatic behavior at different interfaces. Generally speaking, values of the viscoelastic modulus (E), the real part (E'), and the imaginary part (E") at the crude oil-water interface for each polymer are lower than at the air-water or water-dodecane interface. The two polymers display different interfacial properties at the same interface. Polymer No. 2 gives more viscous interfaces than polymer No. 1. All the information obtained from this paper will be helpful in understanding the interfacial rheology of ultra-high-molecular-weight polymer solutions.     

Developments of the spin labelling study of polymers at interfaces

The spin labelling method has been used in a large variety of situations, in the broad field of polymers at solid interfaces. The relevance of the method is confirmed on linear neutral chains of poly (ethylene oxide) (PEO) in well defined situations and compared with the simple theoretical calculations of a mean field theory or some scaling arguments. Both theories have their own strengths and weaknesses. Then the fact, that polymers at solid liquid interfaces are three components systems, is considered and successively the effect of varying the polymer architecture, the solid surface and the solvent is studied. In all these cases specific results are obtained by Electron Paramagnetic Resonance (EPR) showing the usefulness and the versatility of the method.     

Behavior of polymers at surfaces and interfaces as observed in simulated systems

Cooperative motion algorithm (CMA) is used to simulate polymer chains in three types of dense systems reflecting special cases of polymer behavior at surfaces and interfaces: polymer brushes with variable grafting density in the range 0–1, both in a neutral solvent and in a polymer melt, layers of end-functionalized polymers between parallel end-adsorbing walls, and copolymers of various distributions of comonomer units (random, block and gradient copolymers) at interfaces with noncompatible polymers.     

Multicanonical procedure for continuum peptide models

The multicanonical (Muca) Monte Carlo method enables simulating a system over a wide range of temperatures and thus has become an efficient tool for studying spin glasses, first‐order phase transitions, the helix–coil transition of polypeptides, and protein folding. However, implementation of the method requires calculating the multicanonical weights by an iterative procedure that is not straightforward and is a stumbling block for newcomers. A recursive procedure that takes into account the statistical errors of all previous iterations and thus enables an automatic calculation of the weights without the need for human intervention after each iteration has been proposed. This procedure, which has already been tested successfully for lattice systems, is extended here to continuum models of peptides and proteins. The method is examined in detail and tested for models of the pentapeptide Leu‐enkephalin (Tyr‐Gly‐Gly‐Phe‐Leu) described by the potential energy function ECEPP. Because of the great interest in the structural mapping of the low‐energy region of biomolecules, the energy of structures selected from the Muca trajectory is minimized. The extent of conformational coverage provided by the method is examined and found to be very satisfactory. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1251–1261, 2000     

Polydisperse telechelic polymers at interfaces: analytic results and density functional theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

Evolution of the elastic modulus at the interfaces of amorphous glassy polymers

The method of shear deformation of adhesive compounds based on high-molecular-mass glassy polymers is used for the pioneering analysis of changes in the elastic modulus as a function of contact time and temperature at the symmetric and asymmetric polymer-polymer interfaces. The kinetics of changes in the elastic modulus and strength of adhesive joints during shearing at a contact temperature below the actual glass-transition temperature of the polymer bulk is analyzed. The elastic modulus can be generally described in terms of the classical principle of the temperature-time analogy with respect to the conditions of the formation of adhesive joints. Molecular and thermoactivation mechanisms of the evolution of adhesive viscoelastic and strength characteristics are discussed.     

Monte Carlo methods for polymer chains in two - dimensional geometries (polymers at surfaces and interfaces)

Coarse-grained models of polymers at interfaces can be defined such that their treatment by Monte Carlo simulation is most convenient and efficient for the problem at hand. This simulation strategy is briefly illustrated with three examples: (1) The orientational ordering of rigid rod-like polymers grafted to a surface, where “table methods” can be used, applying a fine discretization of the angles describing rod orientation. (2) Surface enrichment of one species in a polymer blend is treated by a semi-grand-canonical technique. (3) The number of configurations and structure of a star polymer attached with its center to a wall is studied by a “growth technique” generalizing simple sampling methods.     

Physically intuitive continuum mechanics model for quartz crystal microbalance: Viscoelasticity of rubbery polymers at MHz frequencies

Employing a quartz crystal microbalance (QCM) as a MHz-viscoelastic sensor requires extracting information from higher harmonics beyond the Sauerbrey limit, which can be problematic for rubbery polymer films that are highly dissipative because of the onset of anharmonic side bands and film resonance. Data analysis for QCM can frequently obscure the underlying physics or involve approximations that tend to break down at higher harmonics. In this study, modern computational tools are leveraged to solve a continuum physics model for the QCM's acoustic shear wave propagation through a polymer film with zero approximations, retaining the physical intuition of how the experimental signal connects to the shear modulus of the material. The resulting set of three coupled equations are solved numerically to fit experimental data for the resonance frequency Δf_n and dissipation ΔΓ_n shifts as a function of harmonic number n, over an extended harmonic range approaching film resonance. This allows the frequency-dependent modulus of polymer films at MHz frequencies, modeled as linear on a log–log scale, to be determined for rubbery polybutadiene (PB) and polydimethylsiloxane (PDMS) films, showing excellent agreement with time–temperature shifted rheometry data from the literature.     

Relationship between macroscopic and microscopic models of surfactant adsorption dynamics at fluid interfaces

In a companion preceding paper, we presented an experimental investigation into the adsorption dynamics of a diblock copolymer surfactant to a polymer/polymer interface and found them to be well-described by a microscopic model of diffusion in a potential generated using self-consistent field theory. We compare the predictions of the microscopic approach with a macroscopic (adsorption-diffusion) model and demonstrate the equivalence of the two models when the free-energy well underlying surfactant adsorption is flanked by barriers that are significantly larger than thermal energy (kT). However, when the energy barriers are nonexistent, as is the case for the experimental system of interest, a finite interfacial width must be introduced into the classical model to obtain physically meaningful results (i.e., nonnegative desorption rates). Surprisingly, we find that the predictions of the macroscopic finite interfacial width model with no adjustable parameters are in excellent agreement with experimental data presented in the companion paper even though the latter was obtained with molecular resolution. This agreement provides insight into aspects of the free-energy landscape that determine surfactant transport.     

Tight binding models for non ideal semiconductor interfaces

The electronic structure of the (100) Ge-GaAs is studied for a non ideal model which assumes a stoichiometrically disordered interface. By using an ETB model with a 1 s 3p basis, which suffices to describe reasonably the valence bands, and by employing a method of calculation based on the Surface Green Function Matching formalism a fairly simple calculation can be set up which explains adequately the experimentally established semiconductor nature of this interface.     

Freezing single molecule dynamics on interfaces and in polymers

Heterogeneous line broadening and spectral diffusion of the fluorescence emission spectra of perylene diimide molecules have been investigated by means of time dependent single molecule spectroscopy. The influence of temperature and environment has been studied and reveals strong correlation to spectral diffusion processes. We followed the freezing of the molecular mobility of quasi free molecules on the surface upon temperature lowering and by embedding into a poly(methyl methacrylate) (PMMA) polymer. Thereby changes of optical transition energies as a result of both intramolecular changes of conformation and external induced dynamics by the surrounding polymer matrix could be observed. Simulations of spectral fluctuations within a two-level system (TLS) model showed good agreement with the experimental findings.