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Langmuir 2021 Feb 20;37(4):1399-1409. Epub 2021 Jan 20.

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the initial concentrations of the two species, we observe varying degrees of stratification in the final dried films. Our model predicts the various structures described in the literature previously from experiments and computer simulations, in particular the small-on-top stratified films. Our model also includes the influence of adsorption of particles to the interfaces.

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http://dx.doi.org/10.1021/acs.langmuir.0c02825 | DOI Listing |

February 2021

Nat Commun 2021 Jan 11;12(1):239. Epub 2021 Jan 11.

Departamento de Química Física (Unidad de I+D+i Asociada al CSIC), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, 28040, Spain.

Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.

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http://dx.doi.org/10.1038/s41467-020-20318-6 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7801427 | PMC |

January 2021

J Phys Condens Matter 2021 Mar;33(11):115401

Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9, 48149 Münster, Germany.

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems described by a suitable free energy functional. In particular, this involves the determination of lines of phase coexistence related to first order phase transitions and the continuation of triple points. To illustrate the method we apply it to a binary phase-field-crystal model for the crystallisation of a mixture of two types of particles. The resulting phase diagram is determined for one- and two-dimensional domains. In the former case it is compared to the diagram obtained from a one-mode approximation. The various observed liquid and crystalline phases and their stable and metastable coexistence are discussed as well as the temperature-dependence of the phase diagrams. This includes the (dis)appearance of critical points and triple points. We also relate bifurcation diagrams for finite-size systems to the thermodynamics of phase transitions in the infinite-size limit.

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http://dx.doi.org/10.1088/1361-648X/abce6e | DOI Listing |

March 2021

Phys Rev E 2020 Sep;102(3-1):032210

Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.

Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on the level of macroscopic observables, one has to rely on equation-free methods like stochastic continuation. Here we investigate how to improve stochastic continuation techniques by adaptively choosing the parameters of the algorithm. This allows one to obtain bifurcation diagrams quite accurately, especially near bifurcation points. We introduce lifting techniques which generate microscopic states with a naturally grown structure, which can be crucial for a reliable evaluation of macroscopic quantities. We show how to calculate fixed points of fluctuating functions by employing suitable linear fits. This procedure offers a simple measure of the statistical error. We demonstrate these improvements by applying the approach in analyses of (i) the Ising model in two dimensions, (ii) an active Ising model, and (iii) a stochastic Swift-Hohenberg model. We conclude by discussing the abilities and remaining problems of the technique.

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http://dx.doi.org/10.1103/PhysRevE.102.032210 | DOI Listing |

September 2020

J Colloid Interface Sci 2021 Jan 3;581(Pt B):729-740. Epub 2020 Aug 3.

Department of Materials, Loughborough University, Loughborough, UK.

We harness the self-assembly of aqueous binary latex/silica particle blends during drying to fabricate films segregated by size in the vertical direction. We report for the first time the experimental drying of ternary colloidal dispersions and demonstrate how a ternary film containing additional small latex particles results in improved surface stability and abrasion resistance compared with a binary film. Through atomic force microscopy (AFM) and energy-dispersive X-ray spectroscopy (EDX), we show that the vertical distribution of filler particles and the surface morphologies of the films can be controlled by altering the evaporation rate and silica volume fraction. We report the formation of various silica superstructures at the film surface, which we attribute to a combination of diffusiophoresis and electrostatic interactions between particles. Brownian dynamics simulations of the final stages of solvent evaporation provide further evidence for this formation mechanism. We show how an additional small latex particle population results in an increased abrasion resistance of the film without altering its morphology or hardness. Our work provides a method to produce water-based coatings with enhanced abrasion resistance as well as valuable insights into the mechanisms behind the formation of colloidal superstructures.

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http://dx.doi.org/10.1016/j.jcis.2020.08.001 | DOI Listing |

January 2021

Soft Matter 2020 Apr;16(14):3564-3573

G. W. Gray Centre for Advanced Materials, Department of Physics & Mathematics, University of Hull, Hull HU6 7RX, UK.

Hard-core/soft shell (HCSS) particles have been shown to self-assemble into a remarkably rich variety of structures under compression due to the simple interplay between the hard-core and soft-shoulder length scales in their interactions. Most studies in this area model the soft shell interaction as a square shoulder potential. Although appealing from a theoretical point of view, the potential is physically unrealistic because there is no repulsive force in the soft shell regime, unlike in experimental HCSS systems. To make the model more realistic, here we consider HCSS particles with a range of soft shell potential profiles beyond the standard square shoulder form and study the model using both minimum energy calculations and Monte Carlo simulations. We find that by tuning density and the soft shell profile, HCSS particles in the thin shell regime (i.e., shell to core ratio ) can form a large range of structures, including hexagons, chains, squares, rhomboids and two distinct zig-zag structures. Furthermore, by tuning the density and r1/r0, we find that HCSS particles with experimentally realistic linear ramp soft shoulder repulsions can form honeycombs and quasicrystals with 10-fold and 12-fold symmetry. Our study therefore suggests the exciting possibility of fabricating these exotic 2D structures experimentally through colloidal self-assembly.

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http://dx.doi.org/10.1039/d0sm00092b | DOI Listing |

April 2020

Phys Rev Lett 2020 Feb;124(6):065702

Departamento de Química-Física (Unidad de I+D+i Asociada al CSIC), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.

Understanding the wetting properties of premelting films requires knowledge of the film's equation of state, which is not usually available. Here we calculate the disjoining pressure curve of premelting films and perform a detailed thermodynamic characterization of premelting behavior on ice. Analysis of the density profiles reveals the signature of weak layering phenomena, from one to two and from two to three water molecular layers. However, disjoining pressure curves, which closely follow expectations from a renormalized mean field liquid state theory, show that there are no layering phase transitions in the thermodynamic sense along the sublimation line. Instead, we find that transitions at mean field level are rounded due to capillary wave fluctuations. We see signatures that true first order layering transitions could arise at low temperatures, for pressures between the metastable line of water-vapor coexistence and the sublimation line. The extrapolation of the disjoining pressure curve above water-vapor saturation displays a true first order phase transition from a thin to a thick film consistent with experimental observations.

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http://dx.doi.org/10.1103/PhysRevLett.124.065702 | DOI Listing |

February 2020

Phys Rev E 2019 Aug;100(2-1):022140

School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each. One approximation that is made in standard derivations is to neglect a term of form ∇·[n∇Ln], where n is the scaled density profile and L is a linear operator. We show that this term makes a significant contribution to the stability of the crystal, and that dropping this term from the theory forces another approximation, that of replacing the logarithmic term from the ideal gas contribution to the free energy with its truncated Taylor expansion, to yield a polynomial in n. However, the consequences of doing this are (i) the presence of an additional spinodal in the phase diagram, so the liquid is predicted first to freeze and then to melt again as the density is increased; and (ii) other periodic structures, such as stripes, are erroneously predicted to be thermodynamic equilibrium structures. In general, L consists of a nonlocal convolution involving the pair direct correlation function. A second approximation sometimes made in deriving PFC theory is to replace L with a gradient expansion involving derivatives. We show that this leads to the possibility of the density going to zero, with its logarithm going to -∞ while being balanced by the fourth derivative of the density going to +∞. This subtle singularity leads to solutions failing to exist above a certain value of the average density. We illustrate all of these conclusions with results for a particularly simple model two-dimensional fluid, the generalized exponential model of index 4 (GEM-4), chosen because a DDFT is known to be accurate for this model. The consequences of the subsequent PFC approximations can then be examined. These include the phase diagram being both qualitatively incorrect, in that it has a stripe phase, and quantitatively incorrect (by orders of magnitude) regarding the properties of the crystal phase. Thus, although PFC models are very successful as phenomenological models of crystallization, we find it impossible to derive the PFC as a theory for the (scaled) density distribution when starting from an accurate DDFT, without introducing spurious artifacts. However, we find that making a simple one-mode approximation for the logarithm of the density distribution lnρ(x) rather than for ρ(x) is surprisingly accurate. This approach gives a tantalizing hint that accurate PFC-type theories may instead be derived as theories for the field lnρ(x), rather than for the density profile itself.

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http://dx.doi.org/10.1103/PhysRevE.100.022140 | DOI Listing |

August 2019

J Phys Condens Matter 2019 Aug 12;31(31):315102. Epub 2019 Apr 12.

Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, United Kingdom.

We calculate density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes et al (2015 J. Chem. Phys. 142 074702) to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness h of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as h is varied and thereby determine the binding potential as a function of h. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.

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http://dx.doi.org/10.1088/1361-648X/ab18e8 | DOI Listing |

August 2019

Phys Rev E 2018 Aug;98(2-1):022407

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

We present a theoretical framework based on an extension of dynamical density-functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumors. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell-pair interactions, different cell types, phenotypes, and cell birth and death processes (including cell division), to provide a biophysically consistent description of processes bridging across the scales, including describing the tissue structure down to the level of the individual cells. Analysis of the model is presented for single-species and two-species cases, the latter aimed at describing competition between tumor and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumor growth behavior, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell-pair-interaction parameters.

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http://dx.doi.org/10.1103/PhysRevE.98.022407 | DOI Listing |

August 2018

Sci Technol Adv Mater 2018 9;19(1):203-211. Epub 2018 Mar 9.

Centre of Biological Engineering, Wolfson School, Loughborough University, Loughorough, UK.

Bacterial cellulose (BC) has interesting properties including high crystallinity, tensile strength, degree of polymerisation, water holding capacity (98%) and an overall attractive 3D nanofibrillar structure. The mechanical and electrochemical properties can be tailored upon incomplete BC dehydration. Under different water contents (100, 80 and 50%), the rheology and electrochemistry of BC were evaluated, showing a progressive stiffening and increasing resistance with lower capacitance after partial dehydration. BC water loss was mathematically modelled for predicting its water content and for understanding the structural changes of post-dried BC. The dehydration of the samples was determined via water evaporation at 37 °C for different diameters and thicknesses. The gradual water evaporation observed was well-described by the model proposed ( up to 0.99). The mathematical model for BC water loss may allow the optimisation of these properties for an intended application and may be extendable for other conditions and purposes.

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http://dx.doi.org/10.1080/14686996.2018.1430981 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5917443 | PMC |

March 2018

J Chem Phys 2017 Jul;147(3):034501

H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom.

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

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http://dx.doi.org/10.1063/1.4993175 | DOI Listing |

July 2017

J Chem Phys 2017 Jul;147(2):024701

Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential g(h) which is an excess free energy per unit area that depends on the liquid film height h. Given a microscopic theory for the liquid, to determine g(h), one must calculate the free energy for liquid films of any given value of h, i.e., one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of h, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate g(h) and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We also show that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.

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http://dx.doi.org/10.1063/1.4990702 | DOI Listing |

July 2017

J Chem Phys 2017 Mar;146(12):124703

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

Using classical density functional theory(DFT), we calculate the density profile ρ(𝐫) and local compressibility χ(𝐫) of a simple liquidsolvent in which a pair of blocks with (microscopic) rectangular cross section are immersed. We consider blocks that are solvophobic, solvophilic and also ones that have both solvophobic and solvophilic patches. Large values of χ(𝐫) correspond to regions in space where the liquid density is fluctuating most strongly. We seek to elucidate how enhanced density fluctuations correlate with the solvent mediated force between the blocks, as the distance between the blocks and the chemical potential of the liquid reservoir vary. For sufficiently solvophobic blocks, at small block separations and small deviations from bulk gas-liquid coexistence, we observe a strongly attractive (near constant) force, stemming from capillary evaporation to form a low density gas-like intrusion between the blocks. The accompanying χ(𝐫) exhibits a structure which reflects the incipient gas-liquid interfaces that develop. We argue that our model system provides a means to understanding the basic physics of solvent mediated interactions between nanostructures, and between objects such as proteins in water that possess hydrophobic and hydrophilic patches.

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http://dx.doi.org/10.1063/1.4978352 | DOI Listing |

March 2017

Phys Rev E 2017 Feb 6;95(2-1):023104. Epub 2017 Feb 6.

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.

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http://dx.doi.org/10.1103/PhysRevE.95.023104 | DOI Listing |

February 2017

J Chem Phys 2017 Feb;146(6):064705

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

For a film of liquid on a solid surface, the binding potential g(h) gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure Π=-∂g/∂h. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of g(h). Here, the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures g(h) decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.

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http://dx.doi.org/10.1063/1.4974832 | DOI Listing |

February 2017

J Phys Condens Matter 2016 06 26;28(24):244017. Epub 2016 Apr 26.

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK.

The surface freezing and surface melting transitions that are exhibited by a model two-dimensional soft matter system are studied. The behaviour when confined within a wedge is also considered. The system consists of particles interacting via a soft purely repulsive pair potential. Density functional theory (DFT) is used to calculate density profiles and thermodynamic quantities. The external potential due to the confining walls is modelled via a hard wall with an additional repulsive Yukawa potential. The surface phase behaviour depends on the range and strength of this repulsion: when the repulsion is weak, the wall promotes freezing at the surface of the wall. The thickness of this frozen layer grows logarithmically as the bulk liquid-solid phase coexistence is approached. Our mean-field DFT predicts that this crystalline layer at the wall must be nucleated (i.e. there is a free energy barrier) and its formation is necessarily a first-order transition, referred to as 'prefreezing', by analogy with the prewetting transition. However, in contrast to the latter, prefreezing cannot terminate in a critical point, since the phase transition involves a change in symmetry. If the wall-fluid interaction is sufficiently long ranged and the repulsion is strong enough, surface melting can occur instead. Then the interface between the wall and the bulk crystalline solid is wetted by the liquid phase as the chemical potential is decreased towards the value at liquid-solid coexistence. It is observed that the finite thickness fluid film at the wall has a broken translational symmetry due to its proximity to the bulk crystal, and so the nucleation of the wetting film can be either first order or continuous. Our mean-field theory predicts that for certain wall potentials there is a premelting critical point analogous to the surface critical point for the prewetting transition. When the fluid is confined within a linear wedge, this can strongly promote freezing when the opening angle of the wedge is commensurate with the crystal lattice.

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http://dx.doi.org/10.1088/0953-8984/28/24/244017 | DOI Listing |

June 2016

J Chem Phys 2015 Dec;143(24):244904

Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom.

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase diagram using Monte Carlo computer simulations and also with density functional theory (DFT). The DFT predictions for the structures formed are in good agreement with the results from the simulations, which occur in the portion of the phase diagram where the theory predicts the uniform fluid to be linearly unstable. However, the mean-field DFT does not correctly describe the transitions between the different morphologies, which the simulations show to be analogous to micelle formation. We determine how the heat capacity varies as the model parameters are changed. There are peaks in the heat capacity at state points where the morphology changes occur. We also map the lattice model onto a continuum DFT that facilitates a simplification of the stability analysis of the uniform fluid.

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http://dx.doi.org/10.1063/1.4937941 | DOI Listing |

December 2015

J Chem Phys 2015 Feb;142(7):074702

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

The contribution to the free energy for a film of liquid of thickness h on a solid surface due to the interactions between the solid-liquid and liquid-gas interfaces is given by the binding potential, g(h). The precise form of g(h) determines whether or not the liquid wets the surface. Note that differentiating g(h) gives the Derjaguin or disjoining pressure. We develop a microscopic density functional theory (DFT) based method for calculating g(h), allowing us to relate the form of g(h) to the nature of the molecular interactions in the system. We present results based on using a simple lattice gas model, to demonstrate the procedure. In order to describe the static and dynamic behaviour of non-uniform liquid films and drops on surfaces, a mesoscopic free energy based on g(h) is often used. We calculate such equilibrium film height profiles and also directly calculate using DFT the corresponding density profiles for liquid drops on surfaces. Comparing quantities such as the contact angle and also the shape of the drops, we find good agreement between the two methods. We also study in detail the effect on g(h) of truncating the range of the dispersion forces, both those between the fluid molecules and those between the fluid and wall. We find that truncating can have a significant effect on g(h) and the associated wetting behaviour of the fluid.

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http://dx.doi.org/10.1063/1.4907732 | DOI Listing |

February 2015

Phys Rev E Stat Nonlin Soft Matter Phys 2014 Mar 31;89(3):032144. Epub 2014 Mar 31.

Department of Mathematical Science, Loughborough University, Loughborough LE11 3TU, United Kingdom.

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process, in which particles diffuse from one cluster to the other while the cluster centers remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move toward each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use dynamical density functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal-sized clusters. As long as the particle hard-core diameter is nonzero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a crossover in the dominance of the two different coarsening modes, which depends on the strength of the attraction between particles, the cluster sizes, and the separation distance between clusters.

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http://dx.doi.org/10.1103/PhysRevE.89.032144 | DOI Listing |

March 2014

J Chem Phys 2013 Oct;139(14):144901

E. Hála Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals of ASCR, 16502 Prague 6, Czech Republic and Department of Physical Chemistry, Institute of Chemical Technology, Prague, 166 28 Praha 6, Czech Republic.

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

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http://dx.doi.org/10.1063/1.4823768 | DOI Listing |

October 2013

Phys Rev E Stat Nonlin Soft Matter Phys 2013 Apr 15;87(4):042915. Epub 2013 Apr 15.

Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom.

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.

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http://dx.doi.org/10.1103/PhysRevE.87.042915 | DOI Listing |

April 2013

Phys Rev E Stat Nonlin Soft Matter Phys 2011 Jun 6;83(6 Pt 1):061401. Epub 2011 Jun 6.

Department of Mathematics, University of Cape Town, Rondebosch, South Africa.

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

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http://dx.doi.org/10.1103/PhysRevE.83.061401 | DOI Listing |

June 2011

Phys Rev Lett 2011 Feb 16;106(7):077801. Epub 2011 Feb 16.

Department of Mathematical Sciences, Loughborough University, Leicestershire, United Kingdom.

We describe the formation of deposition patterns that are observed in many different experiments where a three-phase contact line of a volatile nanoparticle suspension or polymer solution recedes. A dynamical model based on a long-wave approximation predicts the deposition of irregular and regular line patterns due to self-organized pinning-depinning cycles corresponding to a stick-slip motion of the contact line. We analyze how the line pattern properties depend on the evaporation rate and solute concentration.

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http://dx.doi.org/10.1103/PhysRevLett.106.077801 | DOI Listing |

February 2011

J Chem Phys 2010 Dec;133(22):224505

H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

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http://dx.doi.org/10.1063/1.3511719 | DOI Listing |

December 2010

Phys Rev E Stat Nonlin Soft Matter Phys 2009 Aug 28;80(2 Pt 1):021409. Epub 2009 Aug 28.

Max-Planck-Institut für Metallforschung, Heisenbergstr. 3, 70569 Stuttgart, Germany.

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, while the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density-functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion channels is believed to be due to this effect.

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http://dx.doi.org/10.1103/PhysRevE.80.021409 | DOI Listing |

August 2009

J Chem Phys 2009 Sep;131(12):124704

H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.

We determine the solvent mediated contribution to the effective potentials for model colloidal or nanoparticles dispersed in a binary solvent that exhibits fluid-fluid phase separation. The interactions between the solvent particles are taken to be purely repulsive point Yukawa pair potentials. Using a simple density functional theory we calculate the density profiles of both solvent species in the presence of the "colloids," which are treated as external potentials, and determine the solvent mediated (SM) potentials. Specifically, we calculate SM potentials between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface, and (iii) a colloid and a planar wall with an adsorbed wetting film. We consider three different types of colloidal particles: Colloid A that prefers the bulk solvent phase rich in species 2, colloid C that prefers the solvent phase rich in species 1, and "neutral" colloid B that has no strong preference for either phase, i.e., the free energies to insert the colloid into either of the coexisting bulk phases are almost equal. When a colloid that has a preference for one of the two solvent phases is inserted into the disfavored phase at state points close to coexistence a thick adsorbed "wetting" film of the preferred phase may form around the colloids. The presence of the adsorbed film has a profound influence on the form of the SM potentials. In case (i) reducing the separation between the two colloids of type A leads to a bridging transition whereby the two adsorbed films connect abruptly and form a single fluid bridge. The SM potential is strongly attractive in the bridged configuration. A similar phenomenon occurs in case (iii) whereby the thick adsorbed film on colloid A and that at the planar wall, which prefers the same phase as colloid A, connect as the separation between the colloid and the wall is reduced. In both cases the bridging transition is accompanied, in this mean-field treatment, by a discontinuity of the SM force. On the other hand, for the same wall, and a colloid of type C, the SM potential is strongly repulsive at small separations. For case (ii), inserting a single colloidal particle near the planar fluid-fluid interface of the solvent, the density profiles of the solvent show that the interface distortion depends strongly on the nature of the colloid-solvent interactions. When the interface disconnects from the colloid there is, once again, a discontinuity in the SM force.

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http://dx.doi.org/10.1063/1.3212888 | DOI Listing |

September 2009

J Chem Phys 2008 Dec;129(21):214709

H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler-Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e., we observe a thick film of fluid rich in species 2 adsorbed at the hard wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (prewetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the prewetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters.

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http://dx.doi.org/10.1063/1.3027515 | DOI Listing |

December 2008

Phys Rev E Stat Nonlin Soft Matter Phys 2008 Sep 8;78(3 Pt 1):031402. Epub 2008 Sep 8.

Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom.

Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems with isotropic pair potentials between the particles, due to the fact that the pair interaction between the colloids has competing attraction and repulsion over different length scales. Here we present a simple density functional theory for a model of such a two-dimensional fluid. The theory predicts a bulk phase diagram exhibiting cluster, stripe, and bubble modulated phases, in addition to homogeneous fluid phases. Comparing with simulation results for this model from the literature, we find that the theory is qualitatively reliable. The model allows for a detailed investigation of the structure of the fluid and we are able to obtain simple approximate expressions for the static structure factor and for the length scale characterizing the modulations in the microphase separated phases. We also investigate the behavior of the system under confinement between two parallel hard walls. We find that the confined fluid phase behavior can be rather complex.

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http://dx.doi.org/10.1103/PhysRevE.78.031402 | DOI Listing |

September 2008

Phys Rev E Stat Nonlin Soft Matter Phys 2007 Sep 4;76(3 Pt 1):031501. Epub 2007 Sep 4.

Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.

Fluids in which the interparticle potential has a hard core, is attractive at moderate separations, and repulsive at large separations are known to exhibit unusual phase behavior, including stable inhomogeneous phases. Here we report a joint simulation and theoretical study of such a fluid, focusing on the relationship between the liquid-vapor transition line and any new phases. The phase diagram is studied as a function of the amplitude of the attraction for a certain fixed amplitude of the long ranged repulsion. We find that the effect of the repulsion is to substitute the liquid-vapor critical point and a portion of the associated liquid-vapor transition line, by two first-order transitions. One of these transitions separates the vapor from a fluid of spherical liquidlike clusters; the other separates the liquid from a fluid of spherical voids. At low temperature, the two transition lines intersect one another and a vapor-liquid transition line at a triple point. While most integral equation theories are unable to describe the new phase transitions, the Percus-Yevick approximation does succeed in capturing the vapor-cluster transition, as well as aspects of the structure of the cluster fluid, in reasonable agreement with the simulation results.

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http://dx.doi.org/10.1103/PhysRevE.76.031501 | DOI Listing |

September 2007