Glass transition in fullerenes: mode-coupling theory predictions

We report idealized mode-coupling theory results for the glass transition of ensembles of model fullerenes interacting via phenomenological two-body potentials. Transition lines are found for C60, C70 and C96 in the temperature-density plane. We argue that the observed glass-transition behavior is indicative of kinetic arrest that is strongly driven by the inter-particle attraction in addition to excluded-volume repulsion. In this respect, these systems differ from most standard glass-forming liquids. They feature arrest that occurs at lower densities and that is stronger than would be expected for repulsion-dominated hard-sphere-like or Lennard-Jones-like systems. The influence of attraction increases with increasing the number of carbon atoms per molecule. However, unrealistically large fullerenes would be needed to yield behavior reminiscent of recently investigated model colloids with strong short-ranged attraction (glass-glass transitions and logarithmic decay of time-correlation functions).Comment: 10 pages, 5 figure

Sensitivity of arrest in mode-coupling glasses to low-q structure

We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor $S(q)$ at wavevectors around the first sharp diffraction peak $q_0$, we find a strong (and inverted) response to structure at wavevectors \emph{below} this peak: an increase in $S(q_0/2)$ {\em lowers} the degree of arrest over a wide $q$-range. This strong sensitivity to `caged cage' packing effects, on length scales of order 2d, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.Comment: 4 pages, 5 figures. v2: 3 figures replaced; text rewritte

Fluid adsorption near an apex: Covariance between complete and critical wetting

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group (RG) and mean field analysis (MF) shows this covariance is obeyed in 2D, 3D and for long and short ranged forces. This connection should be experimentally accesible and provides a means of checking theoretical predictions for critical wetting.Comment: 4 pages, 1 figure, submitted to Physical Review Letter

Can adding oil control domain formation in binary amphiphile bilayers?

Bilayers formed of two species of amphiphile of different chain lengths may segregate into thinner and thicker domains composed predominantly of the respective species. Using a coarse-grained mean-field model, we investigate how mixing oil with the amphiphiles affects the structure and thickness of the bilayer at and on either side of the boundary between two neighbouring domains. In particular, we find that oil molecules whose chain length is close to that of the shorter amphiphiles segregate to the thicker domain. This smooths the surface of the hydrophobic bilayer core on this side of the boundary, reducing its area and curvature and their associated free-energy penalties. The smoothing effect is weaker for oil molecules that are shorter or longer than this optimum value: short molecules spread evenly through the bilayer, while long molecules swell the thicker domain, increasing the surface area and curvature of the bilayer core in the interfacial region. Our results show that adding an appropriate oil could make the formation of domain boundaries more or less favourable, raising the possibility of controlling the domain size distribution.Comment: 18 pages including 5 figure

Can amphiphile architecture directly control vesicle size?

Bilayer membranes self-assembled from simple amphiphiles in solution always have a planar ground-state shape. This is a consequence of several internal relaxation mechanisms of the membrane and prevents the straightforward control of vesicle size. Here, we show that this principle can be circumvented and that direct size control by molecular design is a realistic possibility. Using coarse-grained calculations, we design tetrablock copolymers that form membranes with a preferred curvature, and demonstrate how to form low-polydispersity vesicles while suppressing micellization.Comment: 4 pages, 4 figures. Version 2: Calculations performed for a fuller range of parameters, accepted for publication in Physical Review Letter

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study

nterfacial structure and correlation functions near a two-dimensional wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant

3D wedge filling and 2D random-bond wetting

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.Comment: 7 pages, 3 figures, accepted for publication in Europhysics Letter

Size selection and stability of thick-walled vesicles

In recent experiments, small, thick-walled vesicles with a preferred size were formed from copolymers where the degree of polymerisation of the hydrophobic block, N_B, was significantly greater than that of the hydrophilic block, N_A. We show that a simple mean-field theory can reproduce several aspects of the behaviour of these vesicles. Firstly, we find a minimum in the free energy of the system of vesicles as a function of their radius, corresponding to a preferred size for the vesicles, when N_B is several times larger than N_A. Furthermore, the vesicle radius diverges as N_B is increased towards a critical value, consistent with the instability of the vesicles with respect to further aggregation seen in the experimental work. Finally, we find that this instability can also be triggered in our model by changing the interaction strength of the copolymers with the solvent

Temperature dependence of micelle shape transitions in copolymer solutions:the role of inter-block incompatibility

The nature of the transition between worm-like and spherical micelles in block copolymer dispersions varies between systems. In some formulations, heating drives a transition from worms to spheres, while in other systems the same transition is induced by cooling. In addition, a sphere-worm interconversion can be accompanied either by an increase or a decrease in the core solvation, even if the direction of the temperature dependence is the same. Here, self-consistent field theory is used to provide a potential explanation of this range of behaviour. Specifically, we show that, within this model, the dependence of the transition on the incompatibility χBS of the solvophobic block B and the solvent S (the parameter most closely related to the temperature) is strongly influenced by the incompatibility χAB between B and the solvophilic block A. When χAB is small (χAB < 0.1), it is found that increasing χBS produces a transition from worm-like micelles to spheres (or, more generally, from less curved to more curved structures). When χAB is above 0.1, increasing χBS drives the system from spheres to worm-like micelles. Whether a transition is observed within a realistic range of χBS is also found to depend on the fraction of solvophilic material in the copolymer. The relevance of our calculations to experiments is discussed, and we suggest that the direction of the temperature dependence may be controlled not only by the solution behaviour of the solvophobic block (upper critical solution temperature-like versus lower critical solution temperature-like) but also by χAB

Hydrogen bonding in acrylamide and its role in the scattering behavior of acrylamide-based block copolymers

Hydrogen bonding plays a role in the microphase separation behavior of many block copolymers, such as those used in lithography, where the stronger interactions due to H-bonding can lead to a smaller period for the self-assembled structures, allowing the production of higher resolution templates. However, current statistical thermodynamic models used in descriptions of microphase separation, such as the Flory-Huggins approach, do not take into account some important properties of hydrogen bonding, such as site specificity and cooperativity. In this combined theoretical and experimental study, a step is taken toward the development of a more complete theory of hydrogen bonding in polymers, using polyacrylamide as a model system. We begin by developing a set of association models to describe hydrogen bonding in amides. Both models with one association constant and two association constants are considered. This theory is used to fit IR spectroscopy data from acrylamide solutions in chloroform, thereby determining the model parameters. These parameters are then employed to calculate the scattering function of the disordered state of a diblock copolymer with one polyacrylamide block and one non-hydrogen-bonding block in the random phase approximation. It is then shown that the expression for the inverse scattering function with hydrogen bonding is the same as that without hydrogen bonding, but with the Flory-Huggins parameter χ replaced by an effective value χeff=χ+δχHB(f), where the hydrogen-bonding contribution δχHB depends on the volume fraction f of the hydrogen-bonding block. We find that models with two constants give better predictions of bond energy in the acrylamide dimer and more realistic asymptotic behavior of the association constants and δχHB in the limit of high temperatures