arXiv subjects

A. J. Archer

Publications and source records attributed to A. J. Archer.

At least 19 recordsLinked to original sources

arXiv2026

Tuning polymer architecture for quasicrystal self-assembly

Using computer simulations and theory, we investigate the ultrasoft interactions between dendrimers formed of a central polymer connected by stiff linkers to a corona of flexible polymers, forming `pompoms' at the ends of the linkers. We show that the resulting coarse-grained interaction potential between pairs of dendrimers exhibits tunable lengthscale competition based on properties of the core and corona polymers. We present a simple model for this pair potential, which we confirm using accelerated Monte Carlo methods. We then demonstrate the connection between dendrimer structure and mesoscopic phases by presenting parameter choices that result in stable dodecagonal quasicrystals, and show that the size of the region in the phase diagram where quasicrystals are stable can be controlled by tuning details of the polymer architecture alone. These results pave the way for experimental realization of soft matter quasicrystals by identifying what overall molecular architecture leads to their stability.

cond-mat.soft↗

arXiv2025

Interactions between droplets in immiscible liquid suspensions and the influence of surfactants

We develop a general method for determining the effective interaction potential between two or more droplets suspended within a fluid phase. Our approach is based on classical density functional theory. Here, we apply the method to determine the interaction potential between oil droplets suspended in water and also consider the influence of adding a third species, alcohol. This ternary mixture is that found in the ouzo beverage. The ouzo system exhibits spontaneous emulsification when the neat spirit is mixed with water. The oil emulsion that forms has been observed to be surprisingly long-lived. Here we show that the alcohol in the system does indeed play a role in making the droplets more stable, by decreasing the oil-water interfacial tension and therefore also the strength of the attractive interactions between droplets. Within our theory, the surfactant nature of the alcohol can be enhanced without changing the bulk fluid thermodynamics. In fact, our theory can be used to model surfactant mixtures. In this model, the effective interaction between pairs of oil droplets can become repulsive, with a free-energy barrier to droplets merging, thus making them stable.

cond-mat.soft↗

arXiv2025

Timescales for stochastic barrier crossing: inferring the potential from nonequilibrium data

Kramers' rate theory forms a cornerstone for thermally activated barrier crossing. However, its reliance on equilibrium quantities excludes analysis of nonequilibrium dynamics at early times. Most works have thus focused on obtaining rates and transition time and path distributions in equilibrium. Instead, here we consider early-time nonequilibrium dynamics in a model system of a particle with overdamped dynamics hopping over the barrier in a double-well potential, using the Smoluchowski equation (SE) and stochastic path integral (SPI) mapping of the Langevin equation. We identify several key timescales relevant to nonequilibrium dynamics and quantify them using the SE and SPI approaches. The shortest timescale corresponds to equilibration in a well at time $t \ll τ_{\rm B}$, where $τ_{\rm B}$ is the Brownian diffusion time. The second important timescale is when an inflexion point appears in the effective potential constructed from the density at $t \lessapprox τ_{\rm B}$. Shortly after, the existence of a second potential well can be inferred from sufficient sampling of the dynamics. Interestingly, this timescale decreases with increasing barrier height. We find significant deviations from the equilibrium limit unless $t \gg τ_{\rm B}$. We further calculate \red{the} density current at the barrier for bistable and asymmetric potentials and find that it crosses over to that from equilibrium rate theory at a time that does not appear to depend on the barrier height. Our results have important implications for controlling activated processes at finite times and demonstrate the importance of reaching long enough times to faithfully construct potential landscapes from experimental or simulation data.

cond-mat.stat-mech↗

arXiv2024

Dynamics of particle aggregation in dewetting films of complex liquids

We consider the dynamic wetting and dewetting processes of films and droplets of complex liquids on planar surfaces, focusing on the case of colloidal suspensions, where the particle interactions can be sufficiently attractive to cause agglomeration of the colloids within the film. This leads to an interesting array of dynamic behaviours within the liquid and of the liquid-air interface. Incorporating concepts from thermodynamics and using the thin-film approximation, we construct a model consisting of a pair of coupled partial differential equations that represent the evolution of the liquid film and the effective colloidal height profiles. We determine the relevant phase behaviour of the uniform system, including finding associated binodal and spinodal curves, helping to uncover how the emerging behaviour depends on the particle interactions. Performing a linear stability analysis of our system enables us to identify parameter regimes where agglomerates form, which we independently confirm through numerical simulations and continuation of steady states, to construct bifurcation diagrams. We obtain various dynamics such as uniform colloidal profiles in an unstable situation evolving into agglomerates and thus elucidate the interplay between dewetting and particle aggregation in complex liquids on surfaces.

physics.flu-dyn↗

arXiv2023

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid such as water, surrounded by the gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapour phase is the thermodynamic equilibrium state, then of course droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e. on the nature of the particle interactions with the liquid, and of course also on the vapour temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapour, thereby demonstrating droplet stability.

cond-mat.soft↗

arXiv2022

Stochastic transitions: Paths over higher energy barriers can dominate in the early stages

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of reaction rate theory for determining the rates of the transitions apply in the long-time limit. However, at short times, the system can instead choose to pass over higher energy barriers with much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also present an extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. {\bf 128}, 061103 (2008)] to determine the most likely path at both short and long times.

cond-mat.stat-mech↗

arXiv2020

Length-scales in sheared soft matter depend sensitively on molecular interactions

The structure and degree of order in soft matter and other materials is intimately connected to the nature of the interactions between the particles. One important research goal is to find suitable control mechanisms, to enhance or suppress different structures. Using dynamical density functional theory, we investigate the interplay between external shear and the characteristic length-scales in the interparticle correlations of a model system. We show that shear can controllably change the characteristic length-scale from one to another quite distinct value. Moreover, with specific small changes in the form of the particle interactions, the applied shear can either selectively enhance or suppress the different characteristic wavelengths of the system, thus showing how to tune these. Our results suggest that the nonlinear response to flow can be harnessed to design novel actively responsive materials.

cond-mat.soft↗

arXiv2020

Quasicrystal formation in binary soft matter mixtures

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with integral equation theory. Quasicrystal formation requires particle ordering with two characteristic lengthscales in certain particular ratios. How the lengthscales are related to the form of the pair interactions is reasonably well understood for one component systems, but less is known for mixtures. In our model mixture of big and small colloids confined to an interface, the two lengthscales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively. The small-small lengthscale is not significant. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors.

cond-mat.soft↗

arXiv2019

Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals?

For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.

cond-mat.soft↗

arXiv2018

Density functional theory for the crystallization of two-dimensional dipolar colloidal alloys

Two-dimensional mixtures of dipolar colloidal particles with different dipole moments exhibit extremely rich self-assembly behaviour and are relevant to a wide range of experimental systems, including charged and super-paramagnetic colloids at liquid interfaces. However, there is a gap in our understanding of the crystallization of these systems because existing theories such as integral equation theory and lattice sum methods can only be used to study the high temperature fluid phase and the zero-temperature crystal phase, respectively. In this paper we bridge this gap by developing a density functional theory (DFT), valid at intermediate temperatures, in order to study the crystallization of one and two-component dipolar colloidal monolayers. The theory employs a series expansion of the excess Helmholtz free energy functional, truncated at second order in the density, and taking as input highly accurate bulk fluid direct correlation functions from simulation. Although truncating the free energy at second order means that we cannot determine the freezing point accurately, our approach allows us to calculate ab initio both the density profiles of the different species and the symmetry of the final crystal structures. Our DFT predicts hexagonal crystal structures for one-component systems, and a variety of superlattice structures for two-component systems, including those with hexagonal and square symmetry, in excellent agreement with known results for these systems. The theory also provides new insights into the structure of two-component systems in the intermediate temperature regime where the small particles remain molten but the large particles are frozen on a regular lattice.

cond-mat.soft↗

arXiv2018

Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation

We investigate the liquid state structure of the two-dimensional (2D) model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focussing on the radial distribution function $g(r)$ and its asymptotic decay $r\to\infty$. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is $\approx1.932$. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the non-equilibrium growth or decay of small amplitude density fluctuations in a bulk fluid.

cond-mat.soft↗

arXiv2017

Dynamical density functional theory for the evaporation of droplets of nanoparticle suspension

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

cond-mat.soft↗

arXiv2017

Spatially Localized Quasicrystals

We investigate quasicrystal-forming soft matter using a two-scale phase field crystal model. At state points near thermodynamic coexistence between bulk quasicrystals and the liquid phase, we find multiple metastable spatially localized quasicrystals embedded in a background of liquid. In three dimensions we obtain spatially localized icosahedral quasicrystals. In two dimensions, we compute several families of spatially localized quasicrystals with dodecagonal structure and investigate their properties as a function of the system parameters. In both cases the localized quasicrystals are metastable, and so correspond to energetically locally favored structures. The presence of such structures is expected to crucially affect the dynamics of the crystallization process.

nlin.PS↗

arXiv2017

Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

We present a Monte Carlo (MC) grid-based model for the drying of drops of a nanoparticle suspension upon a heterogeneous surface. The model consists of a generalised lattice-gas in which the interaction parameters in the Hamiltonian can be varied to model different properties of the materials involved. We show how to choose correctly the interactions, to minimise the effects of the underlying grid so that hemispherical droplets form. We also include the effects of surface roughness to examine the effects of contact-line pinning on the dynamics. When there is a `lid' above the system, which prevents evaporation, equilibrium drops form on the surface, which we use to determine the contact angle and how it varies as the parameters of the model are changed. This enables us to relate the interaction parameters to the materials used in applications. The model has also been applied to drying on heterogeneous surfaces, in particular to the case where the suspension is deposited on a surface consisting of a pair of hydrophilic conducting metal surfaces that are either side of a band of hydrophobic insulating polymer. This situation occurs when using inkjet printing to manufacture electrical connections between the metallic parts of the surface. The process is not always without problems, since the liquid can dewet from the hydrophobic part of the surface, breaking the bridge before the drying process is complete. The MC model reproduces the observed dewetting, allowing the parameters to be varied so that the conditions for the best connection can be established. We show that if the hydrophobic portion of the surface is located at a step below the height of the neighbouring metal, the chance of dewetting of the liquid during the drying process is significantly reduced.

cond-mat.soft↗

arXiv2016

Three-dimensional Phase Field Quasicrystals

We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for 3D soft matter quasicrystal formation.

nlin.PS↗

arXiv2015

Soft-core particles freezing to form a quasicrystal and a crystal-liquid phase

Systems of soft-core particles interacting via a two-scale potential are studied. The potential is responsible for peaks in the structure factor of the liquid state at two different but comparable length scales, and a similar bimodal structure is evident in the dispersion relation. Dynamical density functional theory in two dimensions is used to identify two novel states of this system, the crystal-liquid state, in which the majority of the particles are located on lattice sites but a minority remains free and so behaves like a liquid, and a 12-fold quasicrystalline state. Both are present even for deeply quenched liquids and are found in a regime in which the liquid is unstable with respect to modulations on the smaller scale only. As a result the system initially evolves towards a small scale crystal state; this state is not a minimum of the free energy, however, and so the system subsequently attempts to reorganize to generate the lower energy larger scale crystals. This dynamical process generates a disordered state with quasicrystalline domains, and takes place even when this large scale is linearly stable, i.e., it is a nonlinear process. With controlled initial conditions a perfect quasicrystal can form. The results are corroborated using Brownian dynamics simulations.

cond-mat.soft↗

arXiv2015

Generation of defects and disorder from deeply quenching a liquid to form a solid

We show how deeply quenching a liquid to temperatures where it is linearly unstable and the crystal is the equilibrium phase often produces crystalline structures with defects and disorder. As the solid phase advances into the liquid phase, the modulations in the density distribution created behind the advancing solidification front do not necessarily have a wavelength that is the same as the equilibrium crystal lattice spacing. This is because in a deep enough quench the front propagation is governed by linear processes, but the crystal lattice spacing is determined by nonlinear terms. The wavelength mismatch can result in significant disorder behind the front that may or may not persist in the latter stage dynamics. We support these observations by presenting results from dynamical density functional theory calculations for simple one- and two-component two-dimensional systems of soft core particles.

cond-mat.soft↗

arXiv2014

Solidification in soft-core fluids: disordered solids from fast solidification fronts

Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. For the one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.

cond-mat.soft↗