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

Adsorption of Externally Stretched Two-Dimensional Flexible and Semi-flexible Polymers near an Attractive Wall

We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction smaller than the non-sequential nearest neighbor attraction, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for greater than, the fraction of monomers at the wall undergoes a first order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte-Carlo simulations.Comment: 15 pages, 6 figure

Hard colloidal rods near a soft wall: wetting, drying, and symmetry breaking

Within an Onsager-like density functional theory we explore the thermodynamic and structural properties of an isotropic and nematic fluid of hard needle-like colloids in contact with a hard substrate coated with a soft short-ranged attractive or repulsive layer. As a function of the range and the strength of the soft interactions we find wetting and drying transitions, a pre-drying line, and a symmetry-breaking transition from uniaxial to biaxial in the wetting and drying film.Comment: 7 pages, 2 figure

Particle Monte Carlo simulation of string-like colloidal assembly in 2 dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. Interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in 2 dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.Comment: 11 pages, 14 figure

Monte-Carlo simulation of string-like colloidal assembly

We study structural phase transition of polymer-grafted colloidal particles by Monte Carlo simulations on hard spherical particles. The interaction potential, which has a weak repulsive step outside the hard core, was validated with use of the self-consistent field calculations. With this potential, canonical Monte Carlo simulations have been carried out in two and three dimensions using the Metropolis algorithm. At low temperature and high density, we find that the particles start to self-assemble and finally align in strings. By analyzing the cluster size distribution and string length distribution, we construct a phase diagram and find that this string-like assembly is related to the percolation phenomena. The average string length diverges in the region where the melting transition line and the percolation transition line cross, which is similar to Ising spin systems where the percolation transition line and the order-disorder line meet on the critical point.Comment: 7 pages, 6 figures, Accepted for Europhysics Letter

Polymer Brushes in Cylindrical Pores: Simulation versus Scaling Theory

The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density \sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with \sigma, is developed and tested by Molecular Dynamics simulations of a bead-spring model.Comment: 35 pages, 38 figure

Conformations, Transverse Fluctuations and Crossover Dynamics of a Semi-Flexible Chain in Two Dimensions

We present a unified scaling description for the dynamics of monomers of a semiflexible chain under good solvent condition in the free draining limit. We consider both the cases where the contour length $L$ is comparable to the persistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures the early time monomer dynamics of a stiff chain characterized by $t^{3/4}$ dependence for the mean square displacement(MSD) of the monomers, but predicts a first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim \ell_p^3$, and a second crossover to the purely diffusive dynamics for the entire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of this scaling description by studying monomer dynamics of dilute solution of semi-flexible chains under good solvent conditions obtained from our Brownian dynamics (BD) simulation studies for a large choice of chain lengths with number of monomers per chain N = 16 - 2048 and persistence length $\ell_p = 1 - 500$ Lennard-Jones (LJ) units. These BD simulation results further confirm the absence of Gaussian regime for a 2d swollen chain from the slope of the plot of $\langle R_N^2 \rangle/2L \ell_p \sim L/\ell_p$ which around $L/\ell_p \sim 1$ changes suddenly from $\left(L/\ell_p \right) \rightarrow \left(L/\ell_p \right)^{0.5}$, also manifested in the power law decay for the bond autocorrelation function disproving the validity of the WLC in 2d. We further observe that the normalized transverse fluctuations of the semiflexible chains for different stiffness $\sqrt{\langle l_{\bot}^2\rangle}/L$ as a function of renormalized contour length $L/\ell_p$ collapse on the same master plot and exhibits power law scaling $\sqrt{\langle l_{\bot}^2\rangle}/L \sim (L/\ell_p)^\eta$ at extreme limits, where $\eta = 0.5$ for extremely stiff chains ($L/\ell_p \gg 1$), and $\eta = -0.25$ for fully flexible chains.Comment: 14 pages, 18 figure

Effect of Adsorbing and Nonadsorbing Polymer on the Interaction Between Colloidal Particles

In this paper it is described how a recent theoretical model can be applied to a system of two colloidal particles in the presence of adsorbing and nonadsorbing polymer. It turns out that in the case of adsorption the most suitable boundary condition is restricted equilibrium, in which a constant amount of polymer is in local equilibrium inside the gap between two particles. At a low polymer dose the formation of bridges gives rise to bridging flocculation, at higher amounts of polymer steric stabilization occurs due to the mutual repulsion of two extended polymer layers. If the polymer does not adsorb on the particles, full equilibrium applies in which the chemical potentials of solvent and polymer in the gap are the same as in the equilibrium bulk solution, The depletion of polymer near the surface may lead to depletion flocculation in not too concentrated polymer solutions. In very concentrated systems the thickness of the depletion zone is relatively small, and the attraction between the particles becomes too weak to overcome the particle entropy, Then the system is restabilized

Irreversibility and Polymer Adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) ~ f^{-4/5}, in rather close agreement with strong physisorption experiments [H. M. Schneider et al, Langmuir v.12, p.994 (1996)].Comment: 4 pages, submitted to Phys. Rev. Let