Absorption/expulsion of oligomers and linear macromolecules in a polymer brush

Heterogeneous binding of polymers on curved nanoparticles

Unraveling protracted polymer binding on curved surfaces of nanoparticles (NPs) is important for the fabrication of multifunctional nanostructures in cutting-edge research disciplines such as directional self-assembly and nanomedicine. By using our newly developed Integral of First-passage Times (IFS), we demonstrate a curvature-dependent heterogeneous binding of polymers on curved NPs, not only in terms of the binding dynamics but also in terms of the final adsorption densities. The highly curved surfaces on NPs can adsorb larger density polymers with binding kinetics that are faster than those on less curved areas, which is consistent with recent experimental observations. In particular, the spherical corners on cubic NPs with a radius of R = 3.0 nm can adsorb polymers at a density 4.1 times higher than those on planar surfaces and 1.7 times higher than those on rod edge surfaces. A unified relationship between adsorption densities and surface curvatures is proposed to collapse all the data onto one master curve. The findings demonstrate a heterogeneous binding of polymers on curved NPs, providing effective guidelines for the rational design of functional nanostructures in different applications.

Predicting protracted binding kinetics of polymers: Integral of first-passage times

Capturing protracted binding kinetics of polymers onto the surface of nanoobjects is crucial for the rational design of multifunctional nanostructures, such as patchy nanoparticles and nanodrug carriers. Recently, we developed a method-integral of first-passage times (IFS)-to successfully predict nonequilibrium, kinetically stable superstructures fabricated by two star polymers. However, whether the protracted binding kinetics predicted by IFS corresponds to the actual polymer adsorption has only been incompletely explored. In this paper, we clarify this issue by using IFS to study polymer adsorption with binding ends onto a planar wall as an example. At low free-energy barriers, the IFS-predicted polymer binding kinetics is consistent with those extracted from direct simulations. At high free-energy barriers, the protracted polymer adsorption predicted by IFS coincides with those measured in experiments. Our findings demonstrate the feasibility of IFS to study long-lived formation kinetics of polymer nanostructures by spanning timescales from picoseconds to macroscopic minutes, which establishes a foundation to use IFS in different applications.

Bulk phase behavior and interfacial properties of binary mixtures of Lennard-Jones chains and solvent: a density functional theory study

A Density Functional Theory study is performed to analyze both bulk and interfacial properties of solvent-polymer binary mixtures. The effects of increasing polymer chain length on the bulk phase diagram morphology and interfacial tension are presented and compared to the prior simulation results. Good agreement between simulation and Density Functional Theory is found, including its ability to reproduce the density inversion phenomenon for highly asymmetric solvent-polymer binary mixtures. The data on the interfacial tensions is used to compute contact angles of the mixture at a planar wall, with particular focus on the wetting transition. The dependence of the wetting temperature on the polymer chain length and the mixture composition is analyzed in detail.

Adsorption on Ligand-Tethered Nanoparticles

We use coarse-grained molecular dynamics simulations to study adsorption on ligand-tethered particles. Nanoparticles with attached flexible and stiff ligands are considered. We discuss how the excess adsorption isotherm, the thickness of the polymer corona, and its morphology depend on the number of ligands, their length, the size of the core, and the interaction parameters. We investigate the adsorption-induced structural transitions of polymer coatings. The behavior of systems involving curved and flat "brushes" is compared.

Nanoparticle diffusion in polymer melts in the presence of weak nanoparticle-monomer attractive interactions: A mode-coupling theory study

Mode-coupling theory is developed and employed to compute the nanoparticle diffusion coefficient in polymer solutions. Theoretical results are compared with molecular dynamics simulation data for a similar model. The theory properly reproduces the simulated effects of the nanoparticle size, mass, and concentration on the nanoparticle diffusion coefficient. Within the mode-coupling theory framework, a microscopic interpretation of the nonmonotonic dependence of the diffusion coefficient on the nanoparticle concentration is given in terms of structural and dynamic effects. Both the size dependence and mass dependence of the diffusion coefficient indicate a pronounced breakdown of the Stokes-Einstein relation for the present model.

Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

Density Functional Theory is employed to study structural properties and interactions between solvent-free polymer-grafted nanoparticles. Both monodisperse and bidisperse polymer brushes with variable chain stiffness are considered. The three major control parameters are the grafting density, the grafted chain length, and its stiffness. The effect of these parameters on the brush-brush overlap and attractive interaction strength is analyzed. The Density Functional Theory results are compared with the available simulation data, and good quantitative agreement is found.

Multiscale Approaches for Confined Ring Polymer Solutions

We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.

Adsorption-induced co-assembly of hairy and isotropic particles

We use coarse-grained molecular dynamics simulations to study the behavior of polymer-tethered particles immersed in fluids of isotropic particles. Particles modified with weakly anchored, mobile ligands are considered. We discuss how the concentration of fluid particles affects the morphology of an isolated hairy particle. It is shown that hairy particles present different morphologies including typical core-shell, octopus-like and corn-like, depending on fluid-segment interactions and the fluid density. The mechanism of changes in the shape of hairy particles is explained. The reconfiguration of the polymer corona arises from adsorption of fluid particles "on chains". The adsorbed fluid particles form bridges between the chains. This causes the mobile ligands to merge into clusters on the core surface. A part of the core remains empty so the hairy particle becomes a Janus-like object. We also study co-assembly in mixtures of hairy and isotropic particles. Depending on the strength of fluid-segment interactions, hairy particles with fluid particles trapped inside their coronas remain isolated or form mixed clusters of different structures. The aggregation of hairy particles results from the formation of bridges between chains belonging to different cores by fluid particles.

Semiflexible Polymers in the Bulk and Confined by Planar Walls

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager's theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexible polymers with hard walls and the wall-induced nematic order, which can give rise to capillary nematization in thin film geometry. Various earlier theoretical approaches to these problems are briefly mentioned, and an outlook on the status of experiments is given. It is argued that in many cases of interest, it is not possible to describe the scaled densities at the isotropic-nematic transition as functions of the ratio of the contour length and the persistence length alone, but the dependence on the ratio of chain diameter and persistence length also needs to be considered.

A new insight into the isotropic-nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter in comparison with the DFT prediction. It is also found that DFT becomes unreliable for rather flexible polymers in predicting that the transition from the isotropic (I)-phase to the nematic (N)-phase still exists at very high monomer concentrations (which in reality does not occur). However, under conditions when DFT is accurate, it provides reliable predictions also for the width of the I-N two-phase coexistence region, which are difficult to obtain from MD in spite of the use of very large systems (up to 500 000 monomers) by means of graphics processing units (GPU). For short and not very stiff chains, a pre-transitional chain stretching is found in the isotropic phase near the I-N-transition, not predicted by theories. A comparison with theoretical predictions by Khokhlov-Semenov, Odijk, and Chen reveals that the scaled transition densities are not simply functions of L/lp only, as these theories predict, but depend on d/lp (where d is the chain diameter) as well. Chain properties in the nematically ordered phase are compared to those of chains confined in tubes, and the deflection length concept is tested. Eventually, some consequences for the interpretation of experiments are spelled out.

Anomalous Fluctuations of Nematic Order in Solutions of Semiflexible Polymers

The nematic ordering in semiflexible polymers with contour length L exceeding their persistence length ℓ_{p} is described by a confinement of the polymers in a cylinder of radius r_{eff} much larger than the radius r_{ρ} expected from the respective concentration of the solution. Large-scale molecular dynamics simulations combined with density functional theory are used to locate the isotropic-nematic (I-N) transition and to validate this cylindrical confinement. Anomalous fluctuations due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers elucidates the origins of shortcomings in the description of the I-N transition by existing theories.

Molecular Dynamics Simulations of Poly(ethylene oxide) Grafted onto Silica Immersed in Melt of Homopolymers

Tuning of surface properties plays an important role in applications ranging from material engineering to biomedicine/chemistry. The interactions of chains grafted to a solid support and exposed to a matrix of chemically identical chains represent an intriguing issue. In this work, the behavior of poly(ethylene oxide) (PEO) chains grafted irreversibly onto an amorphous silica and immersed in the matrix of free PEO chains of different polymerization degree is studied using molecular dynamics simulations. The density distributions of grafted and free PEO chains, the height of the grafted layer, overlap parameters, and orientation order parameters depend not only on the grafting density but also on the length of free chains which confirm the entropic nature of the interactions between the grafted and free chains. In order to achieve a complete expulsion of the free chains from the grafted layer, a grafting density as high as 3.5 nm(-2) is necessary. Free PEO chains of 9 monomers leave the grafted layer at lower grafting densities than the longer PEO chains of 18 monomers in contrast with the theoretical predictions. The height of the grafted layer evolves with the grafting density in the presence of free chains in qualitative agreement with the theoretical phase diagram.

Semiflexible polymer brushes and the brush-mushroom crossover

Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (like a free semiflexible chain) exhibits three different scaling regimes, h/a ∝ N for contour length L = Na < lp, a Gaussian regime, h/a ∝ (Llp)(1/2)/a for lp ≪ L ≪ R* ∝ (lp(2)/a), and a regime controlled by excluded volume, h/a ∝ (lp/a)(1/5)N(ν). The semiflexible brush is predicted to scale as h/a ∝ (lpaσg)(1/3)N in the excluded volume regime, and h/a ∝ (lpa(3)σ(2))(1/4)N in the Gaussian regime. Since in the volume taken by a semiflexible mushroom excluded-volume interactions are much weaker in comparison to a flexible mushroom, there occurs an additional regime where semiflexible mushrooms overlap without significant chain stretching. Moreover, since the size of a semiflexible mushroom is much larger than the size of a flexible mushroom with the same N, the crossover from mushroom to brush behavior is predicted to take place at much smaller densities than for fully flexible chains. The numerical results, however, confirm the scaling predictions only qualitatively; for chain lengths that are relevant for experiments, often intermediate effective exponents are observed due to extended crossovers.

Critical adsorption of a single macromolecule in polymer brushes

The adsorption of long flexible macromolecules by polymer brush-coated surfaces is studied by molecular dynamics simulations and by calculations using density functional and self-consistent field theories. The case of repulsive interactions between the substrate surface and the monomers of both the brush polymers and the extra chains that can get absorbed into the brush is considered. Under good solvent conditions, critical absorption can occur, if the interaction between the monomers of the brush polymers and the extra chain is (weakly) attractive. It is shown that it is possible to map out the details of the critical absorption transition, if the chain length and/or the grafting density of the brush polymers are varied. In this way both the strength and the range of the effective adsorption potential of the substrate surface can be controlled. However, it is found that in the general case there is no straightforward mapping of the present problem to the simpler problem of polymer adsorption in a square well potential, in contrast to suggestions in the literature. In particular, it is found that the fraction of monomers of the long free chain that is absorbed in the brush shows a nonmonotonic variation with the grafting density; i.e. from dense brushes free chains are again expelled from their interior. For strong attraction the free chain then gets adsorbed at the brush-solution interface.

Structural and energetic basis for hybridization limits in high-density DNA monolayers

High-density monolayers (HDMs) of single-strand (ss) DNA are important nanoscale platforms for the fabrication of sensors and for mechanistic studies of enzymes on surfaces. Such systems can be used, for example, to monitor gene expression, and for the construction of more complex nanodevices via selective hybridization with the complementary oligos dissolved in solution. In this framework, controlling HDM hybridization is essential to control the final properties. Different studies demonstrate that at the typical density of ≈10(13) molecules per cm(2) no more than ≈30-40% of the HDM ssDNA is successfully hybridized. Until now, however, the origin of the HDM hybridization limit has remained unclear. In this work, molecular dynamics (MD) simulations of HDM systems with variable hybridization reveal that, independently of other experimental parameters, the effective hybridization for a HDM of this density is intrinsically limited by molecular and electrostatic crowding. A detailed structural analysis of the HDM model shows good agreement with our atomic force microscopy (AFM) experiments, and provides further insight into the steric hindrance behaviour and time-resolved surface topography of these nanostructured systems. The explicit relationship proposed between structural crowding and limited HDM hybridization offers a rationale to control the final properties of HDM-based nanodevices.

Morphological control of grafted polymer films via attraction to small nanoparticle inclusions

Control of the morphologies of polymer films and layers by addition of nanosize particles is a novel technique for design of nanomaterials and is also at the core of some important biological processes. In order to facilitate the analysis of experimental data and enable predictive engineering of such systems, solid theoretical understanding is necessary. We study theoretically and computationally the behavior of plane-grafted polymer layers (brushes) in athermal solvent, decorated with small nanoparticle inclusions, using mean field theory and coarse-grained simulations. We show that the morphology of such layers is very sensitive to the interaction between the polymers and the nanoparticles and to the nanoparticle density. In particular, the mean field model shows that for a certain range of parameters, the nanoparticles induce a sharp transition in the layer height, accompanied by a sharp increase in the number of adsorbed nanoparticles. At other parameter values, the layer height depends smoothly on the nanoparticle concentration. Predictions of the theoretical model are verified by Langevin dynamics simulations. The results of the paper are in qualitative agreement with experiments on in vitro models of biological transport and suggest strategies for morphological control of nanocomposite materials.

Sterically stabilized lock and key colloids: a self-consistent field theory study

A self-consistent field theory study of lock and key type interactions between sterically stabilized colloids in polymer solution is performed. Both the key particle and the lock cavity are assumed to have cylindrical shape and their surfaces are uniformly grafted with polymer chains. The lock-key potential of mean force is computed for various model parameters, such as length of free and grafted chains, lock and key size matching, free chain volume fraction, grafting density, and various enthalpic interactions present in the system. The lock-key interaction is found to be highly tunable, which is important in the rapidly developing field of particle self-assembly.