Cyperaceae of East Africa - III

Volume: XX

Cyperaceae of East Africa - V

Volume: 2

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

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

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

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

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.

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

Gene Dosage Effects at the Imprinted Gnas Cluster

Genomic imprinting results in parent-of-origin-dependent monoallelic gene expression. Early work showed that distal mouse chromosome 2 is imprinted, as maternal and paternal duplications of the region (with corresponding paternal and maternal deficiencies) give rise to different anomalous phenotypes with early postnatal lethalities. Newborns with maternal duplication (MatDp(dist2)) are long, thin and hypoactive whereas those with paternal duplication (PatDp(dist2)) are chunky, oedematous, and hyperactive. Here we focus on PatDp(dist2). Loss of expression of the maternally expressed Gnas transcript at the Gnas cluster has been thought to account for the PatDp(dist2) phenotype. But PatDp(dist2) also have two expressed doses of the paternally expressed Gnasxl transcript. Through the use of targeted mutations, we have generated PatDp(dist2) mice predicted to have 1 or 2 expressed doses of Gnasxl, and 0, 1 or 2 expressed doses of Gnas. We confirm that oedema is due to lack of expression of imprinted Gnas alone. We show that it is the combination of a double dose of Gnasxl, with no dose of imprinted Gnas, that gives rise to the characteristic hyperactive, chunky, oedematous, lethal PatDp(dist2) phenotype, which is also hypoglycaemic. However PatDp(dist2) mice in which the dosage of the Gnasxl and Gnas is balanced (either 2∶2 or 1∶1) are neither dysmorphic nor hyperactive, have normal glucose levels, and are fully viable. But PatDp(dist2) with biallelic expression of both Gnasxl and Gnas show a marked postnatal growth retardation. Our results show that most of the PatDp(dist2) phenotype is due to overexpression of Gnasxl combined with loss of expression of Gnas, and suggest that Gnasxl and Gnas may act antagonistically in a number of tissues and to cause a wide range of phenotypic effects. It can be concluded that monoallelic expression of both Gnasxl and Gnas is a requirement for normal postnatal growth and development

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