**16** Publications

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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

J Phys Condens Matter 2020 May;32(20):205402

Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Epinal Way, Loughborough, LE11 3TU, United Kingdom.

In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of statistical physics, while the constitutive relations are developed in the framework of the standard phase-field theory, by following the variational formalism and the principles of non-equilibrium thermodynamics. To enhance the numerical practicality of the model, quasi-incompressible hydrodynamic equations are derived, where sound waves are absent (but density change is still possible), and therefore the time scale of solidification is accessible in numerical simulations. The model development is followed by a comprehensive mathematical analysis of the equilibrium and propagating one-dimensional solid-liquid interfaces for different density-phase couplings. It is shown, that the fluid flow decelerates/accelerates the solidification front in case of shrinkage/expansion of the solid compared to the case when no density contrast is present between the phases. Furthermore, such a free energy construction is proposed, in which the shape of the equilibrium planar phase-field interface is independent from the density-phase coupling, and the equilibrium interface represents an exact propagating planar interface solution of the quasi-incompressible hydrodynamic equations. Our results are in agreement with previous theoretical predictions.

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http://dx.doi.org/10.1088/1361-648X/ab670e | DOI Listing |

May 2020

Phys Rev E 2017 May 4;95(5-1):052801. Epub 2017 May 4.

Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)JCOMEL0953-898410.1088/0953-8984/26/5/055001], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

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http://dx.doi.org/10.1103/PhysRevE.95.052801 | DOI Listing |

May 2017

Phys Rev E 2016 Sep 22;94(3-1):033114. Epub 2016 Sep 22.

Department of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway and Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary.

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

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http://dx.doi.org/10.1103/PhysRevE.94.033114 | DOI Listing |

September 2016

Phys Rev E 2016 Jan 25;93(1):013126. Epub 2016 Jan 25.

Department of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway.

In this paper, a generalization of the Cahn-Hilliard theory of binary liquids is presented for multicomponent incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion-type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free-energy functional is presented for an arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and we demonstrate that the energy penalization for multicomponent states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (four-component) systems. Simulations addressing liquid-flow-assisted spinodal decomposition in these systems are also presented.

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http://dx.doi.org/10.1103/PhysRevE.93.013126 | DOI Listing |

January 2016

Phys Chem Chem Phys 2015 Aug;17(31):20259-73

Department of Physics and Technology, University of Bergen, Allégaten 55, 5007 Bergen, Norway.

In this paper the quantitative applicability of van der Sman/van der Graaf type Ginzburg-Landau theories of surfactant assisted phase separation [van der Sman et al., Rheol. Acta, 2006, 46, 3] is studied for real systems displaying high surfactant concentrations at the liquid-liquid interface. The model is applied for the water/heptane/asphaltene system (a model of heavy crude oil), for which recent molecular dynamics (MD) simulations provide microscopic data needed to calibrate the theory. A list of general requirements is set up first, which is then followed by analytical calculations of the equilibrium properties of the system, such as the equilibrium liquid densities, the adsorption isotherm and the interfacial tension. Based on the results of these calculations, the model parameters are then determined numerically, yielding a reasonable reproduction of the MD density profiles. The results of time-dependent simulations addressing the dynamical behaviour of the system will also be presented. It will be shown that the competition between the diffusion and hydrodynamic time scales can lead to the formation of an emulsion. We also address the main difficulties and limitations of the theory regarding quantitative modelling of surfactant assisted liquid phase separation.

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http://dx.doi.org/10.1039/c5cp02357b | DOI Listing |

August 2015

Phys Rev E Stat Nonlin Soft Matter Phys 2015 Mar 9;91(3):032404. Epub 2015 Mar 9.

Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway.

In this paper diffuse interface models of surfactant-assisted liquid-liquid phase separation are addressed. We start from the generalized version of the Ginzburg-Landau free-energy-functional-based model of van der Sman and van der Graaf. First, we analyze the model in the constant surfactant approximation and show the presence of a critical point at which the interfacial tension vanishes. Then we determine the adsorption isotherms and investigate the validity range of previous results. As a key point of the work, we propose a new model of the van der Sman/van der Graaf type designed for avoiding both unwanted unphysical effects and numerical difficulties present in previous models. In order to make the model suitable for describing real systems, we determine the interfacial tension analytically more precisely and analyze it over the entire accessible surfactant load range. Emerging formulas are then validated by calculating the interfacial tension from the numerical solution of the Euler-Lagrange equations. Time-dependent simulations are also performed to illustrate the slowdown of the phase separation near the critical point and to prove that the dynamics of the phase separation is driven by the interfacial tension.

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http://dx.doi.org/10.1103/PhysRevE.91.032404 | DOI Listing |

March 2015

Chem Soc Rev 2014 Apr 8;43(7):2159-73. Epub 2014 Jan 8.

Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary.

Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the crystalline phase appears via heterogeneous nucleation in/on the precursor cluster. Herein, we review recent results by a simple dynamical density functional theory, the phase-field crystal model, for (precursor-mediated) homogeneous and heterogeneous nucleation of nanocrystals. It will be shown that the mismatch between the lattice constants of the nucleating crystal and the substrate plays a decisive role in determining the contact angle and nucleation barrier, which were found to be non-monotonic functions of the lattice mismatch. Time dependent studies are essential as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning.

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http://dx.doi.org/10.1039/c3cs60225g | DOI Listing |

April 2014

J Phys Condens Matter 2014 Feb 12;26(5):055001. Epub 2013 Dec 12.

Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, PO Box 49, H-1525 Budapest, Hungary.

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology which allows a direct coupling between the free energy functional of the classical density functional theory and the Navier-Stokes equation. In contrast to the Ginzburg-Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the phase-field crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal-liquid interface is in good qualitative agreement with the molecular dynamics simulations.

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http://dx.doi.org/10.1088/0953-8984/26/5/055001 | DOI Listing |

February 2014

Phys Rev Lett 2012 Jan 11;108(2):025502. Epub 2012 Jan 11.

Research Institute for Solid State Physics and Optics, Budapest, Hungary.

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.

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http://dx.doi.org/10.1103/PhysRevLett.108.025502 | DOI Listing |

January 2012

Phys Rev Lett 2011 Oct 20;107(17):175702. Epub 2011 Oct 20.

Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.

Dynamical density-functional simulations reveal structural aspects of crystal nucleation in undercooled liquids: The first appearing solid is amorphous, which promotes the nucleation of bcc crystals but suppresses the appearance of the fcc and hcp phases. These findings are associated with features of the effective interaction potential deduced from the amorphous structure.

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http://dx.doi.org/10.1103/PhysRevLett.107.175702 | DOI Listing |

October 2011

Phys Rev Lett 2011 May 11;106(19):195502. Epub 2011 May 11.

Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.

Using atomic scale time-dependent density functional calculations we confirm that both diffusion-controlled and diffusionless crystallization modes exist in simple 2D systems. We provide theoretical evidence that a faceted to nonfaceted transition is coupled to these crystallization modes, and faceting is governed by the local supersaturation at the fluid-crystalline interface. We also show that competing modes of crystallization have a major influence on mesopattern formation. Irregularly branched and porous structures are emerging at the crossover of the crystallization modes. The proposed branching mechanism differs essentially from dendritic fingering driven by diffusive instability.

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http://dx.doi.org/10.1103/PhysRevLett.106.195502 | DOI Listing |

May 2011

J Phys Condens Matter 2010 Sep 20;22(36):364101. Epub 2010 Aug 20.

Research Institute for Solid State Physics and Optics, PO Box 49, H-1525 Budapest, Hungary.

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, and determine the line free energy in 2D and the height of the nucleation barrier in 2D and 3D for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that, in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from the sphere to specific faceted shapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic; this anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggregation in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simulations. An oscillatory effective pair potential resembling those for model glass formers has been evaluated from structural data of the amorphous phase obtained by instantaneous quenching. Finally, we present results for eutectic solidification in a binary PFC model.

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http://dx.doi.org/10.1088/0953-8984/22/36/364101 | DOI Listing |

September 2010

J Phys Chem B 2009 Apr;113(15):5141-8

Research Institute for Solid State Physics and Optics, H-1525 Budapest, POB 49, Hungary.

The hard-sphere system is the best known fluid that crystallizes: the solid-liquid interfacial free energy, the equations of state, and the height of the nucleation barrier are known accurately, offering a unique possibility for a quantitative validation of nucleation theories. A recent significant downward revision of the interfacial free energy from approximately 0.61kT/sigma(2) to (0.56 +/- 0.02)kT/sigma(2) [Davidchack, R.; Morris, J. R.; Laird, B. B. J. Chem. Phys. 2006, 125, 094710] necessitates a re-evaluation of theoretical approaches to crystal nucleation. This has been carried out for the droplet model of the classical nucleation theory (CNT), the self-consistent classical theory (SCCT), a phenomenological diffuse interface theory (DIT), and single- and two-field variants of the phase field theory that rely on either the usual double-well and interpolation functions (PFT/S1 and PFT/S2, respectively) or on a Ginzburg-Landau expanded free energy that reflects the crystal symmetries (PFT/GL1 and PFT/GL2). We find that the PFT/GL1, PFT/GL2, and DIT models predict fairly accurately the height of the nucleation barrier known from Monte Carlo simulations in the volume fraction range of 0.52 < varphi < 0.54, whereas the CNT, SCCT, PFT/S1, and PFT/S2 models underestimate it significantly.

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http://dx.doi.org/10.1021/jp8097439 | DOI Listing |

April 2009

J Chem Phys 2007 Aug;127(7):074710

Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.

In the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.

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http://dx.doi.org/10.1063/1.2752506 | DOI Listing |

August 2007

J Chem Phys 2007 Aug;127(7):074709

Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.

The phase field theory (PFT) has been applied to predict equilibrium interfacial properties and nucleation barrier in the binary eutectic system Ag-Cu using double well and interpolation functions deduced from a Ginzburg-Landau expansion that considers fcc (face centered cubic) crystal symmetries. The temperature and composition dependent free energies of the liquid and solid phases are taken from CALculation of PHAse Diagrams-type calculations. The model parameters of PFT are fixed so as to recover an interface thickness of approximately 1 nm from molecular dynamics simulations and the interfacial free energies from the experimental dihedral angles available for the pure components. A nontrivial temperature and composition dependence for the equilibrium interfacial free energy is observed. Mapping the possible nucleation pathways, we find that the Ag and Cu rich critical fluctuations compete against each other in the neighborhood of the eutectic composition. The Tolman length is positive and shows a maximum as a function of undercooling. The PFT predictions for the critical undercooling are found to be consistent with experimental results. These results support the view that heterogeneous nucleation took place in the undercooling experiments available at present. We also present calculations using the classical droplet model [classical nucleation theory (CNT)] and a phenomenological diffuse interface theory (DIT). While the predictions of the CNT with a purely entropic interfacial free energy underestimate the critical undercooling, the DIT results appear to be in a reasonable agreement with the PFT predictions.

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http://dx.doi.org/10.1063/1.2752505 | DOI Listing |

August 2007