arXiv subjects

M. J. Greenall

Publications and source records attributed to M. J. Greenall.

At least 19 recordsLinked to original sources

arXiv2024

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 solvation of the core, 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 $χ_{BS}$ of the solvophobic block B and the solvent S (the parameter most closely related to the temperature) is strongly influenced by the incompatibility $χ_{AB}$ between B and the solvophilic block A. When $χ_{AB}$ is small ($χ_{AB}\le 0.1$), it is found that increasing $χ_{BS}$ produces a transition from worm-like micelles to spheres (or, more generally, from less curved to more curved structures). When $χ_{AB}$ is above 0.1, increasing $χ_{BS}$ drives the system from spheres to worm-like micelles. Whether a transition is observed within a realistic range of $χ_{BS}$ is also found to depend on the fraction of solvophilic material in the copolymer. The relevance of our calculations to experimental results 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 versus lower critical solution temperature) but also by $χ_{AB}$.

cond-mat.soft↗

arXiv2018

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 $χ_\text{eff}=χ+δχ_\text{HB}\left(f\right)$, where the hydrogen-bonding contribution $δχ_\text{HB}$ 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 $δχ_\text{HB}$ in the limit of high temperatures.

cond-mat.soft↗

arXiv2017

Size selection and stability of thick-walled vesicles

In recent experiments, small, thick-walled vesicles with a narrow size distribution 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. Using a mean-field theory, we 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.

cond-mat.soft↗

arXiv2016

Disk-shaped bicelles in block copolymer/homopolymer blends

Mixtures of micelle-forming and lamella-forming amphiphiles in solution can form disk-shaped bilayers, sometimes referred to as bicelles. Using self-consistent field theory (SCFT), we investigate the structure and stability of these aggregates in a blend of two species of PS-PDMS diblock with PDMS homopolymer at 225C. We find that the center of each disk is mainly composed of lamella-forming diblocks, while its thicker rim is mostly formed of micelle-forming diblocks. However, this segregation is not perfect, and the concentration of micelle formers is of the order of 10% on the flat central surface of the bicelle. We also find that the addition of micelle former to the mixture of lamella former and homopolymer is necessary for disk-like bicelles to be stable. Specifically, the free energy density of the disk has a minimum as a function of the disk radius when both micelle- and lamella-forming diblocks are present, indicating that the bicelles have a preferred, finite radius. However, it decays monotonically when only lamella former is present, indicating that the bicelle structure is always unstable with respect to further aggregation in these systems. Finally, we identify a concentration range where the bicelle is predicted to have a lower free energy density than the simple cylindrical and lamellar aggregates, and so might be thermodynamically stable.

cond-mat.soft↗

arXiv2014

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.

cond-mat.soft↗

arXiv2013

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.

cond-mat.soft↗

arXiv2011

Hydrophobic droplets in amphiphilic bilayers: a coarse-grained mean-field theory study

Hydrophobic molecules such as oils and certain drugs can be encapsulated between the two leaflets of an amphiphilic bilayer in both lipid and polymer systems. We investigate the case where the hydrophobic molecules are incompatible with the amphiphile tails and so form droplets. Using a coarse-grained mean-field model (self-consistent field theory, or SCFT), we find that droplets of a wide range of sizes have the same characteristic lens shape, and explain this result in terms of simple capillarity arguments, consistent with the measured variations of surface concentrations of amphiphile in the bilayer and in the monolayers that cover the droplet. We study the effect of the strength chi_BO of the repulsion between the hydrophobic liquid and the amphiphile tails on the droplet shape, and find a gradual flattening of the droplet as chi_BO is reduced. The droplet remains at least metastable even at very low values of chi_BO. This is in contrast to the behavior as the length of the hydrophobic molecules is varied. Specifically, if these molecules are at least as long as the amphiphile tails, increasing their length further is found to have little effect on the droplet shape, while reducing their length below this value quickly causes the droplet to become unstable.

cond-mat.soft↗

arXiv2011

Controlling the micellar morphology of binary PEO-PCL block copolymers in water-THF through controlled blending

We study both experimentally and theoretically the self-assembly of binary block copolymers in dilute solution, where self-assembly is triggered by changing the solvent from the common good solvent THF to the selective solvent water, and where the two species on their own in water form vesicles and spherical micelles respectively. We find that in water the inter-micellar exchange of these block copolymers is very slow so that the self-assembled structures are in local but not global equilibrium (i.e., they are non-ergodic). This opens up the possibility of controlling micelle morphology both thermodynamically and kinetically. Specifically, when the two species are first dissolved in THF before mixing and self-assembly (`premixing') by dilution with water, the morphology is found to depend on the mixing ratio of the two species, going gradually from vesicles via `bulbed' rods, rings, Y-junctions and finally to spherical micelles as we increase the proportion of the sphere-formers. On the other hand, if the two species are first partially self-assembled (by partial exchange of the solvent with water) before mixing and further self-assembly (`intermediate mixing'), novel metastable structures, including nanoscopic pouches, emerge. These experimental results are corroborated by self-consistent field theory calculations (SCFT) which reproduce the sequence of morphologies seen in the pre-mixing experiments. SCFT also reveals a clear coupling between polymer composition and aggregate curvature, with regions of positive and negative curvature being stabilized by an enrichment and depletion of sphere formers respectively. Our study demonstrates that both thermodynamic and kinetic blending of block copolymers are effective design parameters to control the resulting structures and allow us to access a much richer range of nano-morphologies than is possible with monomodal block copolymer solutions.

cond-mat.soft↗

arXiv2011

Simple and complex micelles in amphiphilic mixtures: a coarse-grained mean-field study

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. In this paper, we focus on small, spherically-symmetric aggregates in a solution of sphere-forming amphiphile mixed with a smaller amount of lamella-forming amphiphile. Using a coarse-grained mean-field model (self-consistent field theory, or SCFT), we scan the parameter space of this system and find a range of morphologies as the interaction strength, architecture and mixing ratio of the amphiphiles are varied. When the two species are quite similar in architecture, or when only a small amount of lamella-former is added, we find simple spherical micelles with cores formed from a mixture of the hydrophobic blocks of the two amphiphiles. For more strongly mismatched amphiphiles and higher lamella-former concentrations, we instead find small vesicles and more complex micelles. In these latter structures, the lamella-forming species is encapsulated by the sphere-forming one. For certain interaction strengths and lamella-former architectures, the amount of lamella-forming copolymer encapsulated may be large, and the implications of this for the solubilization of hydrophobic chemicals are considered. The mechanisms behind the formation of the above structures are discussed, with a particular emphasis on the sorting of amphiphiles according to their preferred curvature.

cond-mat.soft↗

arXiv2011

Controlling the self-assembly of binary copolymer mixtures in solution through molecular architecture

We present a combined experimental and theoretical study on the role of copolymer architecture in the self-assembly of binary PEO-PCL mixtures in water-THF, and show that altering the chain geometry and composition of the copolymers can control the form of the self-assembled structures and lead to the formation of novel aggregates. First, using transmission electron microscopy and turbidity measurements, we study a mixture of sphere-forming and lamella-forming PEO-PCL copolymers, and show that increasing the molecular weight of the lamella-former at a constant ratio of its hydrophilic and hydrophobic components leads to the formation of highly-curved structures even at low sphere-former concentrations. This result is explained using a simple argument based on the effective volumes of the two sections of the diblock and is reproduced in a coarse-grained mean-field model: self-consistent field theory (SCFT). Using further SCFT calculations, we study the distribution of the two copolymer species within the individual aggregates and discuss how this affects the self-assembled structures. We also investigate a binary mixture of lamella-formers of different molecular weights, and find that this system forms vesicles with a wall thickness intermediate to those of the vesicles formed by the two copolymers individually. This result is also reproduced using SCFT. Finally, a mixture of sphere-former and a copolymer with a large hydrophobic block is shown to form a range of structures, including novel elongated vesicles.

cond-mat.soft↗

arXiv2011

Bilayers in amphiphilic mixtures connected by threadlike micelles: a self-consistent field theory study

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. A specific example of this is seen in solutions of lipid mixtures where the two species form lamellar structures and spherical micelles respectively. Here, vesicles connected by thread-like micelles can form in a narrow concentration range of the sphere-forming lipid. We present a self-consistent field theory (SCFT) study of these structures. Firstly, we show that the addition of sphere-forming lipid to a solution of lamella-former can lower the free energy of cylindrical, thread-like micelles and hence encourage their formation. Next, we demonstrate the coupling between composition and curvature; specifically, that increasing the concentration of sphere-former in a system of two bilayers connected by a thread leads to a transfer of amphiphile to the thread. We further show that the two species are segregated within the structure, with the concentration of sphere-former being significantly higher in the thread. Finally, the addition of larger amounts of sphere-former is found to destabilize the junctions linking the bilayers to the cylindrical micelle, leading to a breakdown of the connected structures. The degree of segregation of the amphiphiles and the amount of sphere-former required to destabilize the junctions is shown to be sensitive to the length of the hydrophilic block of the sphere-forming amphiphiles.

cond-mat.soft↗

arXiv2009

Micelle formation in block copolymer/homopolymer blends: comparison of self-consistent field theory with experiment and scaling theory

We present a self-consistent field theory (SCFT) study of spherical micelle formation in a blend of poly(styrene-butadiene) diblocks and homopolystyrene. The micelle core radii, corona thicknesses and critical micelle concentrations are calculated as functions of the polymer molecular weights and the composition of the diblocks. Our results are compared with an earlier scaling theory and with X-ray scattering data. The agreement between self-consistent field theory and experiment for the micelle structure is sometimes quantitative and is generally more successful than scaling theory. For copolymers with relatively light core blocks, SCFT predictions for the critical micelle concentration improve over those of scaling theories by an order of magnitude. In the case of heavier core blocks, SCFT predicts the critical micelle concentration less well due to inaccuracies in the modelling of the bulk chemical potential. Overall, we find that SCFT gives a very good description of spherical micelle formation and hence demonstrate that a mean-field, equilibrium approach is valid for these systems.

cond-mat.soft↗

arXiv2009

Micelle shape transitions in block copolymer/homopolymer blends: comparison of self-consistent field theory with experiment

Diblock copolymers blended with homopolymer may self-assemble into spherical, cylindrical or lamellar aggregates. Transitions between these structures may be driven by varying the homopolymer molecular weight or the molecular weight or composition of the diblock. Using self-consistent field theory (SCFT), we reproduce these effects. Our results are compared with X-ray scattering and transmission electron microscopy measurements by Kinning, Winey and Thomas and good agreement is found, although the tendency to form cylindrical and lamellar structures is sometimes overestimated due to our neglect of edge effects due to the finite size of these aggregates. Our results demonstrate that self-consistent field theory can provide detailed information on the self-assembly of isolated block copolymer aggregates.

cond-mat.stat-mech↗

arXiv2007

Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition

We study a schematic mode-coupling model in which the ideal glass transition is cut off by a decay of the quadratic coupling constant in the memory function. (Such a decay, on a time scale tau_I, has been suggested as the likely consequence of activated processes.) If this decay is complete, so that only a linear coupling remains at late times, then the alpha relaxation shows a temporal crossover from a relaxation typical of the unmodified schematic model to a final strongly slower-than-exponential relaxation. This crossover, which differs somewhat in form from previous schematic models of the cut-off glass transition, resembles light-scattering experiments on colloidal systems, and can exhibit a `slower-than-alpha' relaxation feature hinted at there. We also consider what happens when a similar but incomplete decay occurs, so that a significant level of quadratic coupling remains for t>>tau_I. In this case the correlator acquires a third, weaker relaxation mode at intermediate times. This empirically resembles the beta process seen in many molecular glass formers. It disappears when the initial as well as the final quadratic coupling lies on the liquid side of the glass transition, but remains present even when the final coupling is only just inside the liquid (so that the alpha relaxation time is finite, but too long to measure). Our results are suggestive of how, in a cut-off glass, the underlying `ideal' glass transition predicted by mode-coupling theory can remain detectable through qualitative features in dynamics.

cond-mat.stat-mech↗

arXiv2006

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).

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.soft↗

arXiv2004

Three-dimensional wedge filling in ordered and disordered systems

We investigate interfacial structural and fluctuation effects occurring at continuous filling transitions in 3D wedge geometries. We show that fluctuation-induced wedge covariance relations that have been reported recently for 2D filling and wetting have mean-field or classical analogues that apply to higher-dimensional systems. Classical wedge covariance emerges from analysis of filling in shallow wedges based on a simple interfacial Hamiltonian model and is supported by detailed numerical investigations of filling within a more microscopic Landau-like density functional theory. For sufficiently short-ranged forces mean-field predictions for the filling critical exponents and covariance are destroyed by pseudo-one-dimensional interfacial fluctuations. In this filling fluctuation regime we argue that the critical exponents describing the divergence of lengthscales are related to values of the interfacial wandering exponent $ζ(d)$ defined for planar interfaces in (bulk) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems, recovering the known results for pure (thermal disorder) systems and predicting universal critical exponents for the case of random-bond disorder. Finally we revisit the transfer matrix theory of three-dimensional filling based on an effective interfacial Hamiltonian model and discuss the interplay between breather, tilt and torsional interfacial fluctuations.

cond-mat.stat-mech↗

arXiv2003

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

Interfacial structure and correlation functions near a two-dimensional (2D) 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.

cond-mat.stat-mech↗