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 $L$ and compatibility $\chi$ with the brush by means of Monte Carlo (MC) simulations and Density Functional Theory (DFT) / Self-Consistent Field Theory (SCFT) at both moderate, $\sigma_g = 0.25$, and high, $\sigma_g = 1.00$, grafting densities using a bead-spring model. Different concentrations of the free chains $0.0625 \le \phi_o \le 0.375$ are examined. Contrary to the case of $\chi = 0$ when all species are almost completely ejected by the polymer brush irrespective of their length $L$, for $\chi < 0$ we find that the degree of absorption (absorbed amount) $\Gamma(L)$ undergoes a sharp crossover from weak to strong ($\approx 100$) absorption, discriminating between oligomers, $1\le L\le 8$, and longer chains. For a moderately dense brush, $\sigma_g = 0.25$, the longer species, $L > 8$, populate predominantly the deep inner part of the brush whereas in a dense brush $\sigma_g = 1.00$ they penetrate into the "fluffy" tail of the dense brush only. Gyration radius $R_g$ and end-to-end distance $R_e$ of absorbed chains thereby scale with length $L$ as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length $32 \le N \le 256$, we demonstrate the existence of unique {\em critical} value of compatibility $\chi = \chi^{c}<0$. For $\chi^{c}(\phi_o)$ the energy of free chains attains the {\em same} value, irrespective of length $L$ whereas the entropy of free chain displays a pronounced minimum. At $\chi^{c}$ all density profiles of absorbing chains with different $L$ 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 $\chi$ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length $L$: I ($1\le L\le 8$), II ($8 \le L \le N$), and III ($L > N$), in which the time of absorption $\tau$ grows with $L$ at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of $\Gamma \propto t^\alpha$ with power $\alpha \propto -\ln \phi_o$ whereby penetration of the free chains into the brush gets {\em slower} as their concentration rises

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.

Structure of Colloid-Polymer Suspensions

We discuss structural correlations in mixtures of free polymer and colloidal particles based on a microscopic, 2-component liquid state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the relevant polymer degree of freedom is the center of mass, for polymers larger than the (nano-) particles conformational rearrangements need to be considered. They have the important consequence that the polymer depletion layer exhibits two widely different length scales, one of the order of the particle radius, the other of the order of the polymer radius or the polymer density screening length in dilute or semidilute concentrations, respectively. Their consequences on phase stability and structural correlations are discussed extensively.Comment: 37 pages, 17 figures; topical feature articl

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Self-Consistent Field study of Polyelectrolyte Brushes

We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve the self-consistent field equations and study the monomer density profile, the distribution of counterions, and the total charge distribution. We study the scaling relations for the brush height and compare them to the prediction of other theories. We find a weak dependence of the brush height on the grafting density.We fit the counterion distribution outside the brush by the Gouy-Chapman solution for a virtual charged wall. We calculate the amount of counterions outside the brush and find that it saturates as the charge of the polyelectrolytes increases

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

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

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]

Experimentally manipulated self-affirmation promotes reduced alcohol consumption in response to narrative information

Background: Health-risk information is increasingly being conveyed through accounts of personal experiences or narrative information. However, whether self-affirmation can enhance the ability of such messages to promote behavior change has yet to be established. Purpose: This study aims to test whether self-affirmation (a) promotes behavior change following exposure to narrative information about the risks of excessive alcohol consumption and (b) boosts message acceptance by increasing narrative engagement. Methods: In an experimental design, female drinkers (N = 142) reported their baseline alcohol consumption and were randomly allocated to condition (Self-Affirmation, Control). All participants next watched an extract of a genuine narrative piece in which the central character discussed her liver disease and its link with her previous alcohol consumption. Then, participants completed measures assessing engagement with the narrative and message acceptance. The primary outcome was alcohol consumption, assessed at 7-day follow-up. Results: Self-affirmed participants reported consuming significantly less alcohol at follow-up compared to baseline (mean 7-day decrease = 5.43 units); there was no change in alcohol consumption for the control group. Immediately post-manipulation, self-affirmed participants (vs. control) showed more message acceptance and reported greater engagement with the information. The impact of self-affirmation on message acceptance was mediated by narrative engagement. Conclusions: Self-affirmation can promote behavior change following exposure to health information, even when presented in narrative form

Improving polymeric microemulsions with block copolymer polydispersity

Recent experiments have demonstrated that block copolymers are capable of stabilizing immiscible homopolymer blends producing bicontinuous microemulsion. The stability of these polymeric alloys requires the copolymer to form flexible, nonattractive monolayers along the homopolymer interfaces. We predict that copolymer polydispersity can substantially and simultaneously improve the monolayers in both of these respects. Furthermore, polydispersity should provide similar improvements in systems, such as colloidal suspensions and polymer/clay composites, that utilize polymer brushes to suppress attractive interactions