Lifshitz points in blends of AB and BC diblock copolymers

We consider micro- and macro-phase separation in blends of AB and BC flexible diblock copolymers. We show that, depending on architecture, a number of phase diagram topologies are possible. Microphase separation or macrophase separation can occur, and there are a variety of possible Lifshitz points. Because of the rich parameter space, Lifshitz points of multiple order are possible. We demonstrate Lifshitz points of first and second order, and argue that, in principle, up to 5th-order Lifshitz points are possible

Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density $\rho$ and the distance between the walls $L_y$, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a change in $L_y$ leads to many reentrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of inter-layer spacing with $L_y$. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material recovers completely and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy

Micro- vs. macro-phase separation in binary blends of poly(styrene)-poly(isoprene) and poly(isoprene)-poly(ethylene oxide) diblock copolymers

In this paper we present an experimentally determined phase diagram of binary blends of the diblock copolymers poly(styrene)-poly(isoprene) and poly(isoprene)-poly(ethylene oxide). At high temperatures, the blends form an isotropic mixture. Upon lowering the temperature, the blend macro-phase separates before micro-phase separation occurs. The observed phase diagram is compared to theoretical predictions based on experimental parameters. In the low-temperature phase the crystallisation of the poly(ethylene oxide) block influences the spacing of the ordered phase

Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model

The equilibrium phase behavior of microphase-forming substances and models is notoriously difficult to obtain because of the extended metastability of the modulated phases. We develop a simulation method based on thermodynamic integration that avoids this problem and with which we obtain the phase diagram of the canonical three-dimensional axial next-nearest-neighbor Ising model. The equilibrium devil's staircase, magnetization, and susceptibility are obtained. The critical exponents confirm the XY nature of the disorder-modulated phase transition beyond the Lifshitz point. The results identify the limitations of various approximation schemes used to analyze this basic microphase-forming model.Comment: 4 pages, 3 figure

A numerical renormalization group study of laser induced freezing

We study the phenomenon of laser induced freezing, within a numerical renormalization scheme which allows explicit comparison with a recent defect mediated melting theory. Precise values for the `bare' dislocation fugacities and elastic moduli of the 2-d hard disk system are obtained from a constrained Monte Carlo simulation sampling only configurations {\em without} dislocations. These are used as inputs to appropriate renormalization flow equations to obtain the equilibrium phase diagram which shows excellent agreement with earlier simulation results. We show that the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results.Comment: Minor Corrections; Combined version of Europhys. Lett. 67 (2004) p. 814 and Europhys. Lett. 68 (2004) p. 16

Star-Like Micelles with Star-Like Interactions: A quantitative Evaluation of Structure Factor and Phase Diagram

PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.Comment: 5 pages, 4 figures, PRL in pres

Modelling exposure heterogeneity and density dependence in onchocerciasis using a novel individual-based transmission model, EPIONCHO-IBM: implications for elimination and data needs

Background Density dependence in helminth establishment and heterogeneity in exposure to infection are known to drive resilience to interventions based on mass drug administration (MDA). However, the interaction between these processes is poorly understood. We developed a novel individual-based model for onchocerciasis transmission, EPIONCHO-IBM, which accounts for both processes. We fit the model to pre-intervention epidemiological data and explore parasite dynamics during MDA with ivermectin. Methodology/Principal findings Density dependence and heterogeneity in exposure to blackfly (vector) bites were estimated by fitting the model to matched pre-intervention microfilarial prevalence, microfilarial intensity and vector biting rate data from savannah areas of Cameroon and Côte d’Ivoire/Burkina Faso using Latin hypercube sampling. Transmission dynamics during 25 years of annual and biannual ivermectin MDA were investigated. Density dependence in parasite establishment within humans was estimated for different levels of (fixed) exposure heterogeneity to understand how parametric uncertainty may influence treatment dynamics. Stronger overdispersion in exposure to blackfly bites results in the estimation of stronger density-dependent parasite establishment within humans, consequently increasing resilience to MDA. For all levels of exposure heterogeneity tested, the model predicts a departure from the functional forms for density dependence assumed in the deterministic version of the model. Conclusions/Significance This is the first, stochastic model of onchocerciasis, that accounts for and estimates density-dependent parasite establishment in humans alongside exposure heterogeneity. Capturing the interaction between these processes is fundamental to our understanding of resilience to MDA interventions. Given that uncertainty in these processes results in very different treatment dynamics, collecting data on exposure heterogeneity would be essential for improving model predictions during MDA. We discuss possible ways in which such data may be collected as well as the importance of better understanding the effects of immunological responses on establishing parasites prior to and during ivermectin treatment

Direct test of defect mediated laser induced melting theory for two dimensional solids

We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results, (b) there is excellent quantitative agreement between our results and earlier conventional Monte Carlo simulations for the hard disk system and (c) while the qualitative form of the phase diagram is reproduced for systems with soft potentials there is some quantitative discrepancy which we explain.Comment: 11 pages, 14 figures, submitted to Phys. Rev.

Tuning thermal properties and microphase separation in aliphatic polyester ABA copolymers

Four alkyl substituted β-lactones were investigated as monomers in ring opening polymerisation to produce a family of poly(3-hydroxyalkanoate)s. Homopolymers were synthesised using a robust aluminium salen catalyst, resulting in polymers with low dispersity (Đ < 1.1) and predictable molecular weights. ABA triblock copolymers were prepared using poly(L-lactic acid) as the A block and the afore- mentioned poly(3-hydroxyalkanoate) as the B block via a sequential addition method. Characterisation of these copolymers determined they were well controlled with low dispersities and predictable molecular weight. DSC analysis determined copolymers prepared from β-butyrolactone or β-valerolactone yielded polymers with tunable and predictable thermal properties. Copolymers prepared from β-heptanolactone yielded a microphase separated material as indicated by SAXS, with two distinct Tgs. The polymers could be readily cast into flexible films and their improved tensile properties were explored

Structural Uncertainty in Onchocerciasis Transmission Models Influences the Estimation of Elimination Thresholds and Selection of Age Groups for Seromonitoring

Background. The World Health Organization recommends monitoring Ov16 serologyin children aged <10 years for stopping mass ivermectin administration. Transmission models can help to identify the most informative age groups for serological monitoring and investigate the discriminatory power of serology-based elimination thresholds.Model predictions will depend on assumed age-exposure patterns and transmission efficiency at low infection levels. Methods. The individual-based transmission model, EPIONCHO-IBM, was used toassess: i) the most informative age groups for serological monitoring using receiveroperator characteristic curves for different elimination thresholds under various age-dependent exposure assumptions, including those of ONCHOSIM (another widely-used model), and ii) the influence of within-human density-dependent parasite establishment (included in EPIONCHO-IBM but not in ONCHOSIM) on positive predictive values for different serological thresholds.Results. When assuming EPIONCHO-IBM exposure patterns, under-10s are themost informative age group for seromonitoring; when assuming ONCHOSIM’s exposure patterns, 5–15-year olds are the most informative (as published elsewhere).Omitting density-dependent parasite establishment results in more lenientseroprevalence thresholds, even for higher baseline infection prevalence and shorter treatment durations.Conclusions. Selecting appropriate seromonitoring age groups depends critically onage-dependent exposure patterns. The role of density dependence on elimination thresholds largely explains differing EPIONCHO-IBM and ONCHOSIM elimination predictions