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Register a new userInterfacial Instability of Charged End-Group Polymer Brushes
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We consider a polymer brush grafted to a surface (acting as an electrode) and bearing a charged group at its free end. Using a second distant electrode, the brush is subject to a constant electric field. Based on a coarse-grained continuum model, we calculate the average brush height and find that the brush can stretch or compress depending on the applied field and charge end-group. We further look at an undulation mode of the flat polymer brush and find that the electrostatic energy scales linearly with the undulation wavenumber, $q$. Competition with surface tension, scaling as $q^2$, tends to stabilize a lateral $q$-mode of the polymer brush with a well-defined wavelength. This wavelength depends on the brush height, surface separation, and several system parameters.
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The organization of nano-particles inside grafted polymer layers is governed by the interplay of polymer-induced entropic interactions and the action of externally applied fields. Earlier work had shown that strong external forces can drive the formation of colloidal structures in polymer brushes. Here we show that external fields are not essential to obtain such colloidal patterns: we report Monte Carlo and Molecular dynamics simulations that demonstrate that ordered structures can be achieved by compressing a `sandwich of two grafted polymer layers, or by squeezing a coated nanotube, with nano-particles in between. We show that the pattern formation can be efficiently controlled by the applied pressure, while the characteristic length--scale, i.e. the typical width of the patterns, is sensitive to the length of the polymers. Based on the results of the simulations, we derive an approximate equation of state for nano-sandwiches.
A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $rho(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $rho_R(2 N_L, z)=rho_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of rings and chains in $z$-direction coincide, too, and increase linearly with $N_L$, the transverse components differ, even with respect to their scaling properties: $R_{gxy}^{(L)} propto N_L^{1/2}$, $R_{gxy}^{(R)} propto N_L^{0.4}$. These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.
We study the changes in the conformations of brushes upon the addition of crosslinks between the chains using the bond fluctuation model. The Flory-Rehner model applied to uni-axially swollen networks predicts a collapse for large degrees of crosslinking $q$ proportional to $q^{-1/3}$ in disagreement with our simulation data. We show that the height reduction of the brushes is driven by monomer fluctuations in direction perpendicular to the grafting plane and not due to network elasticity. We observe that the impact of crosslinking is different for reactions between monomers of the same or on different chains. If the length reduction of the effective chain length due to both types of reactions is accounted for in a function $beta(q)$, the height of the brush can be derived from a Flory approach for the equilibrium brush height leading to $H(q)approx H_{b}beta(q)^{1/3}$, whereby $H_{b}$ denotes the height of the non-crosslinked brush.
We study the adsorption of charged patchy particle models (CPPMs) on a thin film of a like-charged and dense polyelectrolyte (PE) brush (of 50 monomers per chain) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined one-, and two-patched spherical globules, each of the same net charge and (nanometer) size, with mono- and multipole moments comparable to those of small globular proteins. We focus on electrostatic effects on the adsorption far away from the isoelectric point of typical proteins, i.e., where charge regulation plays no role. Despite the same net charge of the brush and globule we observe large binding affinities up to tens of the thermal energy, kT, which are enhanced by decreasing salt concentration and increasing charge of the patch(es). Our analysis of the distance-resolved potentials of mean force together with a phenomenological description of all leading interaction contributions shows that the attraction is strongest at the brush surface, driven by multipolar, Born (self-energy), and counterion-release contributions, dominating locally over the monopolar and steric repulsions.
We use computer simulations to investigate the stability of a two-component polymer brush de-mixing on a curved template into phases of different morphological properties. It has been previously shown via molecular dynamics simulations that immiscible chains having different length and anchored to a cylindrical template will phase separate into striped phases of different widths oriented perpendicularly to the cylindrical axis. We calculate free energy differences for a variety of stripe widths, and extract simple relationships between the sizes of the two polymers, N_1 and N_2, and the free energy dependence on the stripe width. We explain these relationships using simple physical arguments based upon previous theoretical work on the free energy of polymer brushes.
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