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Register a new userFree energy of alternating two-component polymer brushes on cylindrical templates
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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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Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $sigma$ are varied over a wide range and the crossover from ``mushroom to ``brush behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $sigma$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enough $N$ and $sigma$ (and small enough pore diameters) the opposite behavior occurs, i.e. the brush is compressed by confinement. These findings are used to discuss the corresponding theories on polymer brushes at concave substrates.
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.
Molecular Dynamics (MD) simulations are presented for a coarse-grained bead-spring model of ring polymer brushes under compression. Flexible polymer brushes are always disordered during compression, whereas semiflexible brushes tend to be ordered under sufficiently strong compression. Besides, the polymer monomer density of semiflexible polymer brush is very high near the polymer brush surface, inducing a peak value of free energy near the polymer brush surface. Therefore, by compressing nanoparticles (NPs) in semiflexible ring brush system, NPs tend to exhibit a closely packed single layer structure between the brush surface and the impenetrable wall, which provide a new access of designing responsive applications.
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 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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