Effects of polymer polydispersity on the phase behaviour of colloid-polymer mixtures

We study the equilibrium behaviour of a mixture of monodisperse hard sphere colloids and polydisperse non-adsorbing polymers at their $\theta$-point, using the Asakura-Oosawa model treated within the free-volume approximation. Our focus is the experimentally relevant scenario where the distribution of polymer chain lengths across the system is fixed. Phase diagrams are calculated using the moment free energy method, and we show that the mean polymer size $\xi_{\rm c}$ at which gas-liquid phase separation first occurs decreases with increasing polymer polydispersity $\delta$. Correspondingly, at fixed mean polymer size, polydispersity favours gas-liquid coexistence but delays the onset of fluid-solid separation. On the other hand, we find that systems with different $\delta$ but the same {\em mass-averaged} polymer chain length have nearly polydispersity-independent phase diagrams. We conclude with a comparison to previous calculations for a semi-grandcanonical scenario, where the polymer chemical potentials are imposed, which predicted that fluid-solid coexistence was over gas-liquid in some areas of the phase diagram. Our results show that this somewhat counter-intuitive result arose because the actual polymer size distribution in the system is shifted to smaller sizes relative to the polymer reservoir distribution.Comment: Changes in v2: sketch in Figure 1 corrected, other figures improved; added references to experimental work and discussion of mapping from polymer chain length to effective radiu

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.

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

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

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

RCT of web-based personalized normative feedback for college drinking prevention: Are typical student norms good enough?

Objectives: Personalized normative feedback (PNF) interventions are generally effective at correcting normative misperceptions and reducing risky alcohol consumption among college students. However, research has yet to establish what level of reference group specificity is most efficacious in delivering PNF. This study compared the efficacy of a web-based PNF intervention employing eight increasingly-specific reference groups against a Web-BASICS intervention and a repeated-assessment control in reducing risky drinking and associated consequences. Method: Participants were 1663 heavy drinking Caucasian and Asian undergraduates at two universities. The referent for web-based PNF was either the typical same-campus student, or a same-campus student at one (either gender, race, or Greek-affiliation), or a combination of two (e.g., gender and race), or all three levels of specificity (i.e., gender, race, and Greek-affiliation). Hypotheses were tested using quasi-Poisson generalized linear models fit by generalized estimating equations. Results: The PNF intervention participants showed modest reductions in all four outcomes (average total drinks, peak drinking, drinking days, and drinking consequences) compared to control participants. No significant differences in drinking outcomes were found between the PNF group as a whole and the Web-BASICS group. Among the eight PNF conditions, participants receiving typical student PNF demonstrated greater reductions in all four outcomes compared to those receiving PNF for more specific reference groups. Perceived drinking norms and discrepancies between individual behavior and actual norms mediated the efficacy of the intervention. Conclusions: Findings suggest a web-based PNF intervention using the typical student referent offers a parsimonious approach to reducing problematic alcohol use outcomes among college students

RCT of Web-based Personalized Normative Feedback for College Drinking Prevention: Are Typical Student Norms Good Enough?

Objectives Personalized normative feedback (PNF) interventions are generally effective at correcting normative misperceptions and reducing risky alcohol consumption among college students. However, research has yet to establish what level of reference group specificity is most efficacious in delivering PNF. This study compared the efficacy of a web-based PNF intervention employing eight increasingly-specific reference groups against a Web-BASICS intervention and a repeated-assessment control in reducing risky drinking and associated consequences. Method Participants were 1663 heavy drinking Caucasian and Asian undergraduates at two universities. The referent for web-based PNF was either the typical same-campus student, or a same-campus student at one (either gender, race, or Greek-affiliation), or a combination of two (e.g., gender and race), or all three levels of specificity (i.e., gender, race, and Greek-affiliation). Hypotheses were tested using quasi-Poisson generalized linear models fit by generalized estimating equations. Results The PNF intervention participants showed modest reductions in all four outcomes (average total drinks, peak drinking, drinking days, and drinking consequences) compared to control participants. No significant differences in drinking outcomes were found between the PNF group as a whole and the Web-BASICS group. Among the eight PNF conditions, participants receiving typical student PNF demonstrated greater reductions in all four outcomes compared to those receiving PNF for more specific reference groups. Perceived drinking norms and discrepancies between individual behavior and actual norms mediated the efficacy of the intervention. Conclusions Findings suggest a web-based PNF intervention using the typical student referent offers a parsimonious approach to reducing problematic alcohol use outcomes among college students

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