Density functional theory of simple polymers in a slit pore. II. The role of compressibility and field type

Density functional theory of equilibrium random copolymers: application to surface adsorption of aggregating peptides

We generalize a recently developed polymer density functional theory (PDFT) for polydisperse polymer fluids to the case of equilibrium random copolymers. We show that the generalization of the PDFT to these systems allows us to obtain a remarkable simplification compared to the monodispersed polymers. The theory is used to treat a model for protein aggregation into linear filaments in the presence of surfaces. Here we show that, for attractive surfaces, there is evidence of significant enhancement of protein aggregation. This behaviour is a consequence of a surface phase transition, which has been shown to occur with ideal equilibrium polymers in the presence of sufficiently attractive surfaces. For excluding monomers, this transition is suppressed, though an echo of the underlying ideal transition is present in the sudden change in the excess adsorption.

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G (D)(r,r', N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r'. The expression for G(r,r', s) is found to be the sum of the commonly accepted Dirichlet result G (D)(r,r', N) = G (0)(r,r', N) - G (0)(r,r'', N) , where r'' is the mirror image of r', and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/[Formula: see text]is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.

Density-functional theory for polymer fluids with molecular weight polydispersity

We develop a density-functional theory for polydisperse polymer fluids satisfying the Schulz-Flory distribution. The resulting equations are remarkably simple and quickly solved, the computational effort scaling with the polydispersity index, rather than the average molecular weight. Equilibrium, or "living", polymers enter naturally as very polydisperse samples. We illustrate the importance of polydispersity on colloid stability by investigating interactions between adsorbing and nonadsorbing surfaces. Significant free energy barriers are present in monodisperse samples, but these diminish as the degree of polydispersity increases.

Hybrid Density Functional Theory for Homopolymer Mixtures Confined in a Selective Nanoslit

By integrating polymer density function theory (DFT) and single-chain molecular simulation, a hybrid DFT is developed for homopolymer mixtures confined in a selective nanoslit. Two weighting functions are adopted separately in the polymer DFT for repulsive and attractive contributions to the excess free energy functional. The theoretical results agree well with simulation data for the density profiles, configurations (tail, loop and train), adsorption amounts, layer thicknesses, and partition coefficients. The polymer-slit interaction is found to have a large effect on the density profiles and partition coefficients but is found to have a small effect on the average sizes and percentages of the configurations. Nearly half of the polymer segments form tails, and the other half form trains. In addition, bridges are observed to form for sufficiently long polymer chains. As the length difference between two polymers increases, the effect of chain connectivity becomes increasingly important.

Effect of attractions on the structure of polymer solutions confined between surfaces: A density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.

Polymer density functional theory approach based on scaling second-order direct correlation function

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

Comparison of density functional theory and simulation of fluid bilayers

We compare results of classical density functional theory (DFT) to molecular dynamics (MD) simulations of coarse-grained models of lipids in solvent. We find that the DFT captures the liquid structure of coarse-grained lipids both near surfaces and in bilayers adequately. In contrast we find that the MD simulations do not predict ordering in bilayers as is observed in low temperature DFT calculations. The mechanical properties of the fluid DFT bilayers are qualitatively similar to those of the MD bilayers; in particular the shapes of the lateral stress profiles are similar. Values of the area compressibility modulus are in reasonable agreement with previous work on coarse-grained lipids.

Density functional theory approach for coarse-grained lipid bilayers

Lipid bilayers are important inhomogeneous fluid systems that mediate the environment of cells and the interaction of cells with their environment. A variety of approaches have been taken to model the lipid molecules in bilayers, from all atom molecular dynamics to rigid body liquid crystals. In this paper we discuss the application of a density functional theory approach that treats the lipid molecules at the coarse-grained level of a freely jointed chain. This approach allows for compressibility effects, and can therefore be used to study not only the long range structure in lipid bilayers, but also the nanoscale structure induced in the bilayer when the lipids crystallize or when an inclusion (e.g., an embedded protein) is present. This paper presents a detailed analysis of fluid bilayers and lamellae predicted by the theory. In particular we locate solutions with zero surface tension. We calculate the phase diagram for all possible phases with planar symmetry, including uniform macrophases. Surprisingly, we find a first-order phase transition from the lamellar phase to an isolated bilayer phase on lowering the temperature. This transition appears to be driven by solvent packing effects. A further lowering of the temperature leads to a set of highly ordered bilayers.

Density Functional Theory of Realistic Models of Polyethylene Liquids in Slit Pores: Comparison with Monte Carlo Simulations†

Density functional theory is applied to study properties of fully detailed, realistic models of polyethylene liquids near surfaces and compared to results from Monte Carlo simulations. When the direct correlation functions from polymer reference interaction site model (PRISM) theory are used as input, the theory somewhat underpredicts the density oscillations near the surface. However, good agreement with simulation is obtained with empirical scaling of the PRISM-predicted direct correlation functions. Effects of attractive interactions are treated using the random-phase approximation. The results of theoretical predictions for the attractive system are also in reasonable agreement with simulation results. In general, the theory performs best when the wall-polymer interaction strength is comparable to polymer-polymer interactions.

Structure of inhomogeneous polymer solutions: A density functional approach

The structure of polymer solutions confined between surfaces is studied using a density functional theory where the polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system, calculated through the Verlet-modified type bridge function. The uniform bulk fluid direct correlation function required as input has been calculated from the reference interaction site model integral equation theory using the Percus-Yevick closure relation. The calculated results on the density profiles of the polymer as well as the solvent are shown to compare well with computer simulation results.

Comparison of random-walk density functional theory to simulation for bead-spring homopolymer melts

Density profiles for a homopolymer melt near a surface are calculated using a random-walk polymeric density functional theory, and compared to results from molecular dynamics simulations. All interactions are of a Lennard-Jones form, for both monomer-monomer interactions and surface-monomer interactions, rather than the hard core interactions which have been most investigated in the literature. For repulsive systems, the theory somewhat overpredicts the density oscillations near a surface. Nevertheless, near quantitative agreement with simulation can be obtained with an empirical scaling of the direct correlation function. Use of the random phase approximation to treat attractive interactions between polymer chains gives reasonable agreement with simulation of dense liquids near neutral and attractive surfaces.

Single homopolymers in the relative density representation

A single symmetric homopolymer is studied in the grand ensemble of its monomeric units. For an arbitrary external field but next neighbor interactions alone, such a system is represented as a functional of the local density to local fugacity ratio, conjugate to the fugacity, with the excess grand potential as thermodynamic generating function. A sample case in a spherical enclosure is solved, where a complementary exclusion from a spherical volume requires an extension to a grand ensemble of polymers. A preliminary extension is also made in mean field form to non-neighbor interactions, as well as to nonsymmetric interactions.

Polymer depletion interaction between two parallel repulsive walls

The depletion interaction between two parallel repulsive walls confining a dilute solution of long and flexible polymer chains is studied by field-theoretic methods. Special attention is paid to self-avoidance between chain monomers relevant for polymers in a good solvent. Our direct approach avoids the mapping of the actual polymer chains on effective hard or soft spheres. We compare our results with recent Monte Carlo simulations [A. Milchev and K. Binder, Eur. Phys. J. B 3, 477 (1998)] and with experimental results for the depletion interaction between a spherical colloidal particle and a planar wall in a dilute solution of nonionic polymers [D. Rudhardt, C. Bechinger, and P. Leiderer, Phys. Rev. Lett. 81, 1330 (1998)].