Two-dimensional structure in a generic model of triangular proteins and protein trimers

Motivated by the diversity and complexity of two-dimensional crystals formed by triangular proteins and protein trimers, we have investigated the structures and phase behavior of hard-disk trimers. In order to mimic specific binding interactions, each trimer possesses on `attractive' disk which can interact with similar disks on other trimers via an attractive square-well potential. At low density and low temperature, the fluid phase mainly consists of tetramers, pentamers, or hexamers. Hexamers provide the structural motif for a high-density, low-temperature periodic solid phase, but we also identify a metastable periodic structure based on a tetramer motif. At high density there is a transition between orientationally ordered and disordered solid phases. The connections between simulated structures and those of 2D protein crystals -- as seen in electron microscopy -- are briefly discussed.Comment: 7 pages, 6 figure

Structure, dynamics, and thermodynamics of ferrofluids

A survey of recent work on the structure, dynamics, and thermodynamics of ferrofluids is given. The emphasis is on new theoretical descriptions and computer simulations of simple models of colloidal ferromagnetic nanoparticles, but some favourable comparisons with experiments are shown to justify the choices of models. The survey summarises combined theoretical and computational studies of field-induced microstructure in ferrofluids, magnetisation curves, static and dynamic initial magnetic susceptibilities, thermodynamic properties, and sedimentation profiles. © 2018, Springer International Publishing AG

Modied mean-field theory of one-dimensional spin models with anisotropy and long-range dipolar interactions

The effects of interactions and anisotropy on the magnetic properties of linear chains of superparamagnetic nanoparticles are studied theoretically by mapping the problem onto spin models. With zero anisotropy, the magnetic dipole moments are free to rotate, and the system resembles a classical ferromagnetic Heisenberg model with long-range dipolar interactions. With strong anisotropy, they are constrained to align with the chain, and the system resembles the classical ferromagnetic Ising model with long-range interactions. Using a modified mean-field theory, expressions for the magnetization curve and initial magnetic susceptibility are derived from the response of a single particle subject to an effective field arising from the applied field and the interactions with the other particles. Various approximations for the effective field are tested against results from Monte Carlo simulations. It is shown that, for physically relevant interaction strengths, reliable theoretical predictions for both the zero-anisotropy and strong-anisotropy cases can be derived in a simple closed form. © P.J. CAMP, A.O. IVANOV, 2020.Ministry of Science and Higher Education of the Russian FederationThe authors are honored to contribute to this special issue celebrating Professor Leonid Bulavin’s 75th birthday. The authors’ collaboration began after they met at the 2005 Physics of Liquid Matter: Modern Problems conference in Kyiv, organized by Professor Bulavin. P.J.C. thanks the Ural Federal University for supporting collaborative visits between Edinburgh and Ekaterinburg. The research was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (theme “Magnet” and Contract No. 02.A03.21.006)

Transient cavities and the excess chemical potentials of hard-spheroid solutes in dipolar hard sphere solvents

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of hard-spheroid solutes with aspect ratios $x$ in the range $1/5 \leq x \leq 5$, and with volumes between one and twenty times that of a solvent molecule, are presented. It is shown that for a given molecular volume and solvent dipole moment (or temperature) a spherical solute has the lowest excess chemical potential and hence the highest solubility, while a prolate solute with aspect ratio $x$ should be more soluble than an oblate solute with aspect ratio $1/x$. For a given solute molecule, the excess chemical potential increases with increasing temperature; this same trend is observed in the case of hydrophobic solvation. To help interpret the simulation results, comparison is made with a scaled-particle theory that requires prior knowledge of a solute-solvent interfacial tension and the pure-solvent equation of state, which parameters are obtained from simulation results for spherical solutes. The theory shows excellent agreement with simulation results over the whole range of solute elongations considered.Comment: 10 pages, 10 figure

Effects of interactions on magnetization relaxation dynamics in ferrofluids

The dynamics of magnetization relaxation in ferrofluids are studied with statistical-mechanical theory and Brownian dynamics simulations. The particle dipole moments are initially perfectly aligned, and the magnetization is equal to its saturation value. The magnetization is then allowed to decay under zero-field conditions toward its equilibrium value of zero. The time dependence is predicted by solving the Fokker-Planck equation for the one-particle orientational distribution function. Interactions between particles are included by introducing an effective magnetic field acting on a given particle and arising from all of the other particles. Two different approximations are proposed and tested against simulations: a first-order modified mean-field theory and a modified Weiss model. The theory predicts that the short-time decay is characterized by the Brownian rotation time τB, independent of the interaction strength. At times much longer than τB, the asymptotic decay time is predicted to grow with increasing interaction strength. These predictions are borne out by the simulations. The modified Weiss model gives the best agreement with simulation, and its range of validity is limited to moderate, but realistic, values of the dipolar coupling constant. © 2020 American Physical Society.A.O.I. gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Contract No. 02.A03.21.006, Ural Mathematical Center Project No. 075-02-2020-1537/1)

Effects of interactions, structure formation, and polydispersity on the dynamic magnetic susceptibility and magnetic relaxation of ferrofluids

Linear response theory relates the decay of equilibrium magnetisation fluctuations in a ferrofluid to the frequency-dependent response of the magnetisation to a weak ac external magnetic field. The characteristic relaxation times are strongly affected by interactions between the constituent particles. Similarly, the relaxation of an initially magnetised system towards equilibrium in zero field occurs on a range of timescales depending on the structure of the initial state, and the interactions between the particles. In this work, ferrofluids are modelled as colloidal suspensions of spherical particles carrying point dipole moments, and undergoing Brownian motion. Recent theoretical and simulation work on the relaxation and linear response of these model ferrofluids is reviewed, and the effects of interactions, structure formation, and polydispersity on the characteristic time scales are outlined. It is shown that: (i) in monodisperse ferrofluids, the timescale characterising the collective response to weak fields increases with increasing interaction strength and/or concentration; (ii) in monodisperse ferrofluids, the initial, short-time decay is independent of interaction strength, but the asymptotic relaxation time is the same as that characterising the collective response to weak fields; (iii) in the strong-interaction regime, the formation of self-assembled chains and rings introduces additional timescales that vary by orders of magnitude; and (iv) in polydisperse ferrofluids, the instantaneous magnetic relaxation time of each fraction varies in a complex way due to the role of interactions. © 2022 The AuthorsMinistry of Education and Science of the Russian Federation, Minobrnauka; Ural Federal University, UrFUA.O.I. gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University project within the Priority 2030 Program)

Theory of the dynamic magnetic susceptibility of ferrofluids

The dynamic magnetic response of a ferrofluid to a weak ac magnetic field is studied using statistical mechanical theory and Brownian dynamics simulations, taking account of dipole-dipole interactions between the constituent ferromagnetic colloidal particles, and the presence of a range of particle sizes. The effects of interactions and polydispersity on the frequency dispersion are shown to be substantial: the amplitude of the response can be about twice that of a noninteracting system; the frequency for peak power loss can be reduced by about one half; and polydispersity effects can even change the qualitative appearance of the susceptibility spectrum. © 2018 American Physical Society