ALBERT

Notes: Polymer–metal interfaces are of increasing technological importance in a variety of applications. These interfaces are characterized by specific interactions between functional groups of the organic polymer and the metallic substrate. In order to study the structure of these interfaces at the molecular level, the energetics of the segment–surface interactions must be well characterized. We have used density functional theory to investigate the interactions of poly(methyl methacrylate) (PMMA) oligomers with aluminum surfaces. The aluminum surface is represented by the simple jellium model. The energetics of the interactions between the organic molecules and the aluminum surface are calculated as a function of the orientation with respect to the surface of the organic molecule and various internal degrees of freedom. The computed energy hypersurfaces exhibit a rich structure characterized by several energy minima and barriers. Implications of such an energy hypersurface for the architecture of long chain molecules at the interface are discussed. The energy hypersurfaces also show that the rotational conformational statistics of PMMA interacting with an aluminum surface should be quite different from that of bulk PMMA. The reported energy hypersurfaces have been used to construct an empirical force-field for future molecular simulations of long chains subject to the proper potentials.

Notes: The relaxation dynamics of a polymer chain strongly adsorbed to a solid surface are simulated via a kinetic Ising model that includes chain connectivity constraints (steric hindrance, rotational strain, and configurational entropy). The two polymer architectures examined consist of one or two chemisorbing functional groups per segment. In both architectures, the chemisorbed polymer chain is trapped in nonequilibrium conformational states at low temperatures, but relaxes to equilibrium at higher temperatures with stretched exponential (KWW) relaxation kinetics. The average relaxation time for the two pendant group architecture has a strongly non-Arrhenius temperature dependence that obeys the Vogel–Fulcher law. In contrast, average relaxation times for the one pendant group architecture cannot be described by the Vogel–Fulcher law.

Notes: We develop a model for the adsorption of random heteropolymers onto solid surfaces from solutions that have a finite concentration of polymer. Previous studies that properly average over the quenched sequence distribution have been concerned with isolated chains near surfaces. Our self-consistent-field theory predicts a transition from situations where the surface segment density is enhanced compared with bulk solution concentration to one wherein the surface segment density is depleted. For a specific chemical identity of the random heteropolymer segments and the surface, this adsorption–depletion transition occurs above a threshold value of the strength of the sequence fluctuations. This intriguing finding can be tested directly via neutron scattering experiments (in the reflection mode), and offers opportunities for manipulating interfacial properties. The variation of the excess surface density of segments with polymer concentration in solution near the adsorption–depletion transition is also elucidated. © 1996 American Institute of Physics.

Notes: Motivated by practical issues that pertain to polymer adhesion, we consider the equilibrium behavior of a dilute solution of ideal A–B random block copolymers confined between two solid surfaces. We develop a general theory for the situation wherein the A–A, B–B, and A–B intersegment interactions are different, and furthermore, the A and B segments interact differently with the solid surfaces. Random block copolymers constitute a class of materials wherein a quenched disorder (the sequence distribution) is carried by the fluid whose statistical properties are of interest. In our theory, we perform quenched disorder averages using the replica trick. The nonlocal terms in our action functional are decoupled by introducing a set of random fields. The resulting equations for the propagator are analyzed within the framework of eigenfunction expansions. Since we consider long chains in confined geometries, we invoke the ground state approximation. We also carry out the functional integrals over the random fields using saddle points.Our theory does not treat the segment–surface interactions within a mean field approximation. Our analysis leads to a set of nonlinear self-consistent-field equations. We have solved our general equations numerically for a particular problem. In order to isolate and highlight the effects of dissimilar segment–surface interactions, we consider a case wherein the intersegment interactions are all alike (of the excluded volume type), while the A segments are attracted to the solid surfaces and the B units are repelled. For this specific problem we find that, above a threshold value of the fraction of attractive segments, significant microphase ordering is induced by the surface. This leads to damped oscillations in the composition profile. This onset of significant surface-induced composition fluctuations is accompanied by an "adsorption–desorption transition'' which corresponds to a qualitative change in the shape of the total segment density profile. These and other results are discussed and the experimentally testable consequences of our predictions are elucidated. Our results are in agreement with recent simulation studies. We suggest specific experiments that may shed further light on the physical phenomena revealed by our calculations. © 1994 American Institute of Physics.

Notes: In this paper, we consider the behavior of random heteropolymers in a quenched disordered medium. We develop a field theory and obtain a mean-field solution that allows for replica symmetry breaking. The presence of an external disorder leads to the formation of compact states; a homopolymeric effect. We compute the phase diagram for two classes of problems. First, we consider the situation wherein the bare heteropolymer prefers like segments to segregate, and second, we examine cases where the bare heteropolymer prefers unlike segments to mix. For the first class of systems, we find a phase diagram characterized by a replica symmetry broken phase that exists below a particular temperature. This temperature grows with the strength of the external disorder. In the second class of situations, the phase diagram is much richer. Here we find two replica symmetry broken phases with different patterns separated by a reentrant phase. The reentrant phase and one of the two replica symmetry broken phases are induced by interactions with the external disorder. The dependence of the location of the phase boundaries on the strength of the external disorder are elucidated. We discuss our results from a physical standpoint, and note the testable experimental consequences of our findings. © 1995 American Institute of Physics.

Notes: Understanding the interfacial organization of heteropolymers near solid surfaces is an issue of fundamental interest that is relevant for many technological and biological applications. In this paper we address several questions pertaining to the surface-induced ordering and the adsorption–desorption phase behavior of a dilute solution of two-letter random heteropolymers interacting with a solid surface. Our analysis is based on a statistical field theoretic formulation of the propagator for the problem of interest. We employ the replica trick to alleviate analytical difficulties which arise when considering averaging over the sequence distribution of the A and the B units. In order to highlight the effects of the surface, we consider the situation wherein the intersegment interactions are of the excluded volume type while the segment–surface interactions of the A and B segments are arbitrarily different. Within the replica symmetric solution, we show that proper coarse-graining of the interaction potentials leads to exact analytical expressions for the self-consistent propagator of the heteropolymer at theta conditions and for the case where excluded volume interactions prevail. One of our interesting findings is that heteropolymers undergo an adsorption–desorption transition in the vicinity of a surface that interacts with the different types of segments in arbitrarily different ways. This is consistent with our previous numerical findings for much more restricted circumstances.We explicitly analyze the influence of the fluctuations in the sequence distribution on the conformational organization of the adsorbed chains and obtain the scaling behavior of properties of interest in the vicinity of the adsorption–desorption threshold with respect to the disorder strength and other polymer interaction parameters. Specifically, invoking the Ehrenfest theorem we find that the adsorption–desorption transition at theta conditions is a second-order phase transition while in the case where excluded volume interaction prevails the transition becomes first order. We also obtain exact analytical expressions for the adsorption–desorption threshold. The threshold exhibits quite an unusual dependence on the strength of the disorder. Finally, we compute the point of onset of repulsive forces between plates that confine a random copolymer solution as a function of chain sequence distribution. We suggest specific experiments employing the surface force apparatus that could directly test our predictions. © 1995 American Institute of Physics.

Notes: We consider the diffusion of ionic species in technologically relevant materials such as zeolites. These materials are characterized by a disordered density distribution of charged sites that couple with the diffusing species. We present a model for ion diffusion in a specific form of charged disorder. This is a primitive model for ion diffusion in charged or acidic zeolites. The theory relies on a path integral representation of the propagator, and a Gaussian field theory for the effects of the disorder. We use the Feynman–Bogoliubov variational method to treat the model, and calculate the diffusion coefficient for ions in a medium characterized by randomly located charges. Numerical solution of our equations, and asymptotic analyses of the same, show that in our theory there is a crossover from diffusive to subdiffusive behavior beyond a threshold value for the average density of the disorder. This threshold coincides with the actual diffusion changing from processes well approximated by Gaussian paths to those involving escapes from deep potential wells and barrier crossings. These results are discussed in the context of recent field-theoretic and renormalization group approaches to the problem of diffusion in random media. Our approach to diffusion in random media appears reasonably general and should be applicable to many technologically relevant problems, and is not compute intensive.