444 research outputs found
Absorption/Expulsion of Oligomers and Linear Macromolecules in a Polymer Brush
The absorption of free linear chains in a polymer brush was studied with
respect to chain size and compatibility with the brush by means of
Monte Carlo (MC) simulations and Density Functional Theory (DFT) /
Self-Consistent Field Theory (SCFT) at both moderate, , and
high, , grafting densities using a bead-spring model.
Different concentrations of the free chains are
examined. Contrary to the case of when all species are almost
completely ejected by the polymer brush irrespective of their length , for
we find that the degree of absorption (absorbed amount)
undergoes a sharp crossover from weak to strong () absorption,
discriminating between oligomers, , and longer chains. For a
moderately dense brush, , the longer species, ,
populate predominantly the deep inner part of the brush whereas in a dense
brush they penetrate into the "fluffy" tail of the dense
brush only. Gyration radius and end-to-end distance of absorbed
chains thereby scale with length as free polymers in the bulk. Using both
MC and DFT/SCFT methods for brushes of different chain length , we demonstrate the existence of unique {\em critical} value of
compatibility . For the energy of free
chains attains the {\em same} value, irrespective of length whereas the
entropy of free chain displays a pronounced minimum. At all density
profiles of absorbing chains with different intersect at the same distance
from the grafting plane. The penetration/expulsion kinetics of free chains into
the polymer brush after an instantaneous change in their compatibility
displays a rather rich behavior. We find three distinct regimes of penetration
kinetics of free chains regarding the length : I (), II (), and III (), in which the time of absorption grows with
at a different rate. During the initial stages of penetration into the
brush one observes a power-law increase of with power
whereby penetration of the free chains into the
brush gets {\em slower} as their concentration rises
Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model
A polymer chain tethered to a surface may be compact or extended, adsorbed or
desorbed, depending on interactions with the surface and the surrounding
solvent. This leads to a rich phase diagram with a variety of transitions. To
investigate these transitions we have performed Monte Carlo simulations of a
bond-fluctuation model with Wang-Landau and umbrella sampling algorithms in a
two-dimensional state space. The simulations' density of states results have
been evaluated for interaction parameters spanning the range from good to poor
solvent conditions and from repulsive to strongly attractive surfaces. In this
work, we describe the simulation method and present results for the overall
phase behavior and for some of the transitions. For adsorption in good solvent,
we compare with Metropolis Monte Carlo data for the same model and find good
agreement between the results. For the collapse transition, which occurs when
the solvent quality changes from good to poor, we consider two situations
corresponding to three-dimensional (hard surface) and two-dimensional (very
attractive surface) chain conformations, respectively. For the hard surface, we
compare tethered chains with free chains and find very similar behavior for
both types of chains. For the very attractive surface, we find the
two-dimensional chain collapse to be a two-step transition with the same
sequence of transitions that is observed for three-dimensional chains: a
coil-globule transition that changes the overall chain size is followed by a
local rearrangement of chain segments.Comment: 17 pages, 12 figures, to appear in J. Chem. Phy
Adsorption transition of a self-avoiding polymer chain onto a rigid rod
The subject of this work is the adsorption transition of a long flexible
self-avoiding polymer chain onto a rigid thin rod. The rod is represented by a
cylinder of radius R with a short-ranged attractive surface potential for the
chain monomers. General scaling results are obtained by using renormalization
group arguments in conjunction with available results for quantum field
theories with curved boundaries [McAvity and Osborn 1993 Nucl. Phys. B 394,
728]. Relevant critical exponents are identified and estimated using geometric
arguments.Comment: 19 pages, 4 figures. To appear in: J. Phys.: Condens. Matter, special
issue dedicated to Lothar Schaefer on the occasion of his 60th birthda
Hard sphere fluids confined between soft repulsive walls: A comparative study using Monte Carlo and density functional methods
Hard-sphere fluids confined between parallel plates a distance apart are
studied for a wide range of packing fractions, including also the onset of
crystallization, applying Monte Carlo simulation techniques and density
functional theory. The walls repel the hard spheres (of diameter ) with
a Weeks-Chandler-Andersen (WCA) potential , with range . We
vary the strength over a wide range and the case of simple hard
walls is also treated for comparison. By the variation of one can
change both the surface excess packing fraction and the wall-fluid
and wall-crystal surface free energies. Several
different methods to extract and from Monte Carlo
(MC) simulations are implemented, and their accuracy and efficiency is
comparatively discussed. The density functional theory (DFT) using Fundamental
Measure functionals is found to be quantitatively accurate over a wide range of
packing fractions; small deviations between DFT and MC near the fluid to
crystal transition need to be studied further. Our results on density profiles
near soft walls could be useful to interpret corresponding experiments with
suitable colloidal dispersions.Comment: 23 pages, 7 ps, eps figure
Free energy of alternating two-component polymer brushes on cylindrical templates
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.Comment: 5 pages, 5 figures, accepted for publication in the Journal of
Chemical Physic
From Capillary Condensation to Interface Localization Transitions in Colloid Polymer Mixtures Confined in Thin Film Geometry
Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer
mixtures confined between two parallel repulsive structureless walls are
presented and analyzed in the light of current theories on capillary
condensation and interface localization transitions. Choosing a polymer to
colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to
D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used;
phase transitions are analyzed via finite size scaling, as in previous work on
bulk systems and under confinement between identical types of walls. Unlike the
latter work, inequivalent walls are used here: while the left wall has a
hard-core repulsion for both polymers and colloids, at the right wall an
additional square-well repulsion of variable strength acting only on the
colloids is present. We study how the phase separation into colloid-rich and
colloid-poor phases occurring already in the bulk is modified by such a
confinement. When the asymmetry of the wall-colloid interaction increases, the
character of the transition smoothly changes from capillary condensation-type
to interface localization-type. The critical behavior of these transitions is
discussed, as well as the colloid and polymer density profiles across the film
in the various phases, and the correlation of interfacial fluctuations in the
direction parallel to the confining walls. The experimental observability of
these phenomena also is briefly discussed.Comment: 36 pages, 15 figure
Surface Grafting of Poly(L-glutamates). 3. Block Copolymerization
This paper describes for the first time the synthesis of surface-grafted AB-block copolypeptides, consisting of poly(γ-benzyl L-glutamate) (PBLG) as the A-block and poly(γ-methyl L-glutamate) (PMLG) as the B-block. Immobilized primary amine groups of (γ-aminopropyl)triethoxysilane (APS) on silicon wafers initiated the ring-opening polymerization of N-carboxyanhydrides of glutamic acid esters (NCAs). After removal of the BLG-NCA monomer solution after a certain reaction time, the amine end groups of the formed PBLG blocks acted as initiators for the second monomers. This method provides the possibility of making layered structures of surface-grafted block copolymers with tuned properties. Ellipsometry and small-angle X-ray reflection (SAXR) measurements revealed the thickness of the polypeptide layers ranging from 45-100 Å of the first block to 140-270 Å for the total block copolypeptides. The chemical composition of the blocks was determined by X-ray photoelectron spectroscopy (XPS). In addition, Fourier transform infrared transmission spectroscopy (FT-IR) revealed that the polypeptide main chains of both blocks consisted of pure R-helices. The average orientation of the helices ranging from 22-42° with respect to the substrate within the first block to 31-35° in the second block could be derived with FT-IR as well.
Determining the Effective Density and Stabilizer Layer Thickness of Sterically Stabilized Nanoparticles.
A series of model sterically stabilized diblock copolymer nanoparticles has been designed to aid the development of analytical protocols in order to determine two key parameters: the effective particle density and the steric stabilizer layer thickness. The former parameter is essential for high resolution particle size analysis based on analytical (ultra)centrifugation techniques (e.g., disk centrifuge photosedimentometry, DCP), whereas the latter parameter is of fundamental importance in determining the effectiveness of steric stabilization as a colloid stability mechanism. The diblock copolymer nanoparticles were prepared via polymerization-induced self-assembly (PISA) using RAFT aqueous emulsion polymerization: this approach affords relatively narrow particle size distributions and enables the mean particle diameter and the stabilizer layer thickness to be adjusted independently via systematic variation of the mean degree of polymerization of the hydrophobic and hydrophilic blocks, respectively. The hydrophobic core-forming block was poly(2,2,2-trifluoroethyl methacrylate) [PTFEMA], which was selected for its relatively high density. The hydrophilic stabilizer block was poly(glycerol monomethacrylate) [PGMA], which is a well-known non-ionic polymer that remains water-soluble over a wide range of temperatures. Four series of PGMA x -PTFEMA y nanoparticles were prepared (x = 28, 43, 63, and 98, y = 100-1400) and characterized via transmission electron microscopy (TEM), dynamic light scattering (DLS), and small-angle X-ray scattering (SAXS). It was found that the degree of polymerization of both the PGMA stabilizer and core-forming PTFEMA had a strong influence on the mean particle diameter, which ranged from 20 to 250 nm. Furthermore, SAXS was used to determine radii of gyration of 1.46 to 2.69 nm for the solvated PGMA stabilizer blocks. Thus, the mean effective density of these sterically stabilized particles was calculated and determined to lie between 1.19 g cm(-3) for the smaller particles and 1.41 g cm(-3) for the larger particles; these values are significantly lower than the solid-state density of PTFEMA (1.47 g cm(-3)). Since analytical centrifugation requires the density difference between the particles and the aqueous phase, determining the effective particle density is clearly vital for obtaining reliable particle size distributions. Furthermore, selected DCP data were recalculated by taking into account the inherent density distribution superimposed on the particle size distribution. Consequently, the true particle size distributions were found to be somewhat narrower than those calculated using an erroneous single density value, with smaller particles being particularly sensitive to this artifact
Phase behavior of a system of particles with core collapse
The pressure-temperature phase diagram of a one-component system, with
particles interacting through a spherically symmetric pair potential in two
dimensions is studied. The interaction consists of a hard core plus an
additional repulsion at low energies. It is shown that at zero temperature,
instead of the expected isostructural transition due to core collapse occurring
when increasing pressure, the system passes through a series of ground states
that are not triangular lattices. In particular, and depending on parameters,
structures with squares, chains, hexagons and even quasicrystalline ground
states are found. At finite temperatures the solid-fluid coexistence line
presents a zone with negative slope (which implies melting with decreasing in
volume) and the fluid phase has a temperature of maximum density, similar to
that in water.Comment: 11 pages, 15 figures included. To appear in PRE. Some figures in low
quality format. Better ones available upon request from [email protected]
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