Molecular Mean-field Theory Research Articles

Phase transitions of a mixed spin ferrimagnet in high temperatures

In this research paper molecular mean field theory (MMFT) has been investigated based on Gibbs-Bogoliubov free energy function of a ferromagnetic mixed spin-3 and spin-5/2 Blume-Capel model with different magnetic crystal fields. The free energy of the proposed ferrimagnet has been evaluated depending on the trial Hamiltonian operator. Minimizing the free energy, one may induce characteristic features of the longitudinal magnetizations, phase transitions and spin compensation temperatures, in the ranges of low temperatures, respectively. In particular, we study the effect of crystal field domains on the critical phenomena for the proposed model. The sublattice magnetization dependence of freerenergy function has been discussed as well. Our results predict the existence of multiple spin compensation sites in the disordered Blume-Capel Ising system for a simple cubic lattice.

Phase transitions of a mixed spin ferrimagnet in high temperatures

In this research paper molecular mean-field theory (MMFT) has been investigated based on Gibbs-Bogoliubov free energy function of a ferrimagnetics mixed spin-3 and spin-5/2 Blume-Capel model with different magnetic crystal fields. The free energy of the proposed ferrimagnet has been evaluated depending on the trial Hamiltonian operator. Minimizing the free energy, one may induce characteristic features of the longitudinal magnetizations, phase transitions and spin compensation temperatures, in the ranges of low temperatures, respectively. In particular, we study the effect of crystal field domains on the critical phenomena for the proposed model. The sublattice magnetization dependence of free energy function has been discussed as well. Our results predict the existence of multiple spin compensation sites in the disordered Blume-Capel Ising system for a simple cubic lattice.

Ferrimagnetic Characteristics and Spin Compensation Temperatures of a Mixed Spin-3 and Spin-5/2 Blume–Capel Model

We study the molecular mean-field theory (MMFT) based on the Gibbs–Bogolyubov free energy function of a ferrimagnetic with mixed spin-3 and spin-5/2 for various magnetic crystal fields in the Blume–Capel model. We have evaluated the free energy depending on the trial Hamiltonian operator. By minimizing the free energy of the present system, we have obtained the characteristic features of the longitudinal magnetizations, compensation temperatures, and re-entrant behaviors in the ranges of low temperatures. In particular, we study the effect of magnetic anisotropies on the critical phenomena for the proposed model. The sublattice magnetization dependence of the free energy function has been discussed as well. Our results predict the existence of multiple spin compensation points in the disordered Blume–Capel system for a square lattice.

Theoretical analysis of the elastic free energy contributions to polymer brushes in poor solvent: A refined mean-field theory.

We consider polymer brushes in poor solvent that are grafted onto planar substrates and onto the internal and external surfaces of a cylinder using molecular dynamics simulation, self-consistent field (SCF), and mean-field theory. We derive a unified expression for the mean field free energy for the three geometrical classes. While for low grafting densities, the effect of chain elasticity can be neglected in poor solvent conditions, it becomes relevant at higher grafting densities and, in particular, for concave geometries. Based on the analysis of the end monomer distribution, we introduce an analytical term that describes the elasticity as a function of grafting density. The accuracy of the model is validated with molecular dynamics simulations as well as SCF computations and shown to yield precise values for the layer thickness over a wide range of system parameters. We further apply this model to analyze the gating behavior of switchable brushes inside nanochannels.

Thermal conductivity of Fe-Si alloys and thermal stratification in Earth’s core

Light elements in Earth's core play a key role in driving convection and influencing geodynamics, both of which are crucial to the geodynamo. However, the thermal transport properties of iron alloys at high-pressure and -temperature conditions remain uncertain. Here we investigate the transport properties of solid hexagonal close-packed and liquid Fe-Si alloys with 4.3 and 9.0 wt % Si at high pressure and temperature using laser-heated diamond anvil cell experiments and first-principles molecular dynamics and dynamical mean field theory calculations. In contrast to the case of Fe, Si impurity scattering gradually dominates the total scattering in Fe-Si alloys with increasing Si concentration, leading to temperature independence of the resistivity and less electron-electron contribution to the conductivity in Fe-9Si. Our results show a thermal conductivity of ∼100 to 110 W⋅m-1⋅K-1 for liquid Fe-9Si near the topmost outer core. If Earth's core consists of a large amount of silicon (e.g., > 4.3 wt %) with such a high thermal conductivity, a subadiabatic heat flow across the core-mantle boundary is likely, leaving a 400- to 500-km-deep thermally stratified layer below the core-mantle boundary, and challenges proposed thermal convection in Fe-Si liquid outer core.

Modeling of Magnetic and Magnetocaloric Properties by the Molecular Mean Field Theory in La0.6Sr0.4Mn0.9V0.1O3 Oxide

Based on the mean-field theory, the magnetic and magnetocaloric behavior of La0.6Sr0.4Mn0.9V0.1O3 manganese oxide has been analyzed. The Bean-Rodbell equation of state presents a second-order magnetic phase transition with a η factor of η = 0.71. Using the experimental data of magnetization M (H, T), the molecular mean-field parameter is found to be λ1 = 2.19 T g emu−1. The Brillouin function makes it possible to determine the total angular moment J, the saturation magnetization MS, and the Lande factor g for La0.6Sr0.4Mn0.9V0.1O3 sample. We simulated the magnetization as a function of the magnetic field and the temperature by applying the mean-field theory, as well as the variation of the magnetic entropy change ΔSM(T). As observed, the simulated results close with experimental data. The magnetic entropy changes for the samples were also estimated by using the mean-field scaling theory, and the results show a difference between the theoretical and experimental values.

Structural Analysis and Theoretical Investigations of the Magnetocaloric Effect for La0.7Ba0.15Ag0.15MnO3 Manganite Prepared Using Sol-Gel Route

Structural analysis, magnetocaloric properties, and theoretical investigations of the magnetocaloric effect were carried out in the crystalline La0.7Ba0.15Ag0.15MnO3 manganite prepared using sol-gel route. The phase purity and structure of this sample were checked by X-ray diffraction technique and Rietveld analysis. From magnetic measurements, the ferromagnetic to paramagnetic (FM-PM) phase transition was observed around TC = 255 K. The maximum change in magnetic entropy (\( \Delta {S}_M^{max} \)) and relative cooling power (RCP) extracted from magnetic measurements were 3.48 J × kg-1 × K-1 and 225 J × kg-1 at an applied magnetic field of 5 T. These magnetocaloric parameters offer to the sample the possible use in the magnetic refrigeration technology. The magnetic entropy simulation by using different theories such as the Weiss molecular mean-field theory and the Landau theory shows good correlation between the theoretical values of −∆SM(T) and the experimental ones estimated from Maxwell relation.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model.

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Study of the Magnetocaloric Effect by Means of Theoretical Models in La0.6Ca0.2Na0.2MnO3 Manganite Compound

In this work, an overview of the Weiss molecular mean-field theory, the Bean–Rodbell model and the Landau theory is presented, providing the theoretical background for simulating the magnetocaloric properties for La0.6Ca0.2Na0.2MnO3 manganite. Results showed that sample exhibits second-order ferromagnetic (FM)–paramagnetic (PM) magnetic phase transition and relatively higher values of magnetic entropy change (−∆SM). In application point of view, this material can be used in magnetic refrigeration technology. The theoretical values of −∆SM determined using each theory agree well with the experimental ones estimated from Maxwell relations. In other part, a good agreement in the spontaneous magnetization values, Mspont(T), estimated from (−∆SM vs. M2) and (H/M vs. M2) data was found. Also, the values of the critical exponent (β) found from both methods are close and check that the mean-field model is adequate to study the MCE in La0.6Ca0.2Na0.2MnO3 sample.

Modeling of magnetic and magnetocaloric properties by the molecular mean field theory in La0.8Ca0.2MnO3 oxides with first and second magnetic phase transition

Abstract Magnetic and magnetocaloric properties of La0.8Ca0.2MnO3 manganese oxides has been analyzed based on the mean-field theory. The Bean-Rodbell equation of state shows a second and first order magnetic phase transition for the sample annealed at 1200 °C (S1) and 800 °C (S2) with a η factor of η = 0.6 and η = 1.4 respectively. Using the experimental data of magnetization M (H,T), the molecular mean-field parameter are found to be λ1 = 0.6564 T g eum−1 and λ1 = 0.8876 T g eum−1 for S1 et S2 respectively. Brillouin function allows us to determine the total angular moment J, the saturation magnetization MS and the Lande factor g for all samples. Knowing all these parameters, and by applying the mean-field theory, we simulated the magnetization as a function of the magnetic field and the temperature, as well as the variation of the magnetic entropy change ΔSM (T). We can see that the simulated results are in good agreement with experimental data.

Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model

The fourth-gradient model for fluids—associated with an extended molecular mean-field theory of capillarity—is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals’ one and other models associated with a second order expansion. The aim of the paper is to prove—with a fourth-gradient internal energy already obtained by the mean field theory—that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations’ systems when an equation of energy associated with high order deformation of a continuum medium is taken into account.

Modelling of particle-laden flow inside nanomaterials.

In this paper, we demonstrate the usage of the Nernst-Planck equation in conjunction with mean-field theory to investigate particle-laden flow inside nanomaterials. Most theoretical studies in molecular encapsulation at the nanoscale do not take into account any macroscopic flow fields that are crucial in squeezing molecules into nanostructures. Here, a multi-scale idea is used to address this issue. The macroscopic transport of gas is described by the Nernst-Planck equation, whereas molecular interactions between gases and between the gas and the host material are described using a combination of molecular dynamics simulation and mean-field theory. In particular, we investigate flow-driven hydrogen storage inside doubly layered graphene sheets and graphene-oxide frameworks (GOFs). At room temperature and with slow velocity fields, we find that a single molecular layer is formed almost instantaneously on the inner surface of the graphene sheets, while molecular ligands between GOFs induce multi-layers. For higher velocities, multi-layers are also formed between graphene. For even larger velocities, the cavity of graphene is filled entirely with hydrogen, whereas for GOFs there exist two voids inside each periodic unit. The flow-driven hydrogen storage inside GOFs with various ligand densities is also investigated.

Molecular Modeling of the Lamellar to Inverse Hexagonal Phase Transition in Dope-Dopc Lipid Systems

In the proper physiological state, myelin sheaths consist of tightly packed lipids and proteins and insulate neurons in both the central and peripheral nervous systems. However, defective myelin sheaths in multiple sclerosis (MS), and other demyelinating diseases, ultimately cause vesiculation of the lipids contained in the sheaths. Increasing the proportion of phosphatidylethanolamine in myelin was shown experimentally to cause structural instabilities due to an abnormal packing structure. The unstable form favors inverted hexagonal phases as a result of lipid headgroup size and geometry, whereas normal myelin composition favors a smooth lamellar phase. Through a molecular mean field theory approach, we produce phase diagrams of lipid systems with varying concentrations of phosphatidylethanolamine and phosphatidylcholine to capture the transitions between inverted hexagonal and lamellar phases. Analyzing structural instabilities in myelin sheaths may provide us with a clearer understanding of multiple sclerosis and other demyelinating diseases.

Reversibility and criticality in amorphous solids.

The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a ‘front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

Nanomotor dynamics in a chemically oscillating medium.

Synthetic nanomotors powered by chemical reactions have potential uses as cargo transport vehicles in both in vivo and in vitro applications. In many situations, motors will have to operate in out-of-equilibrium complex chemically reacting media, which supply fuel to the motors and remove the products they produce. Using molecular simulation and mean-field theory, this paper describes some of the new features that arise when a chemically powered nanomotor, operating through a diffusiophoretic mechanism, moves in an environment that supports an oscillatory chemical reaction network. It is shown how oscillations in the concentrations in chemical species in the environment give rise to oscillatory motor dynamics. More importantly, since the catalytic reactions on the motor that are responsible for its propulsion couple to the bulk phase reaction network, the motor can change its local environment. This process can give rise to distinctive spatiotemporal structures in reaction-diffusion media that occur as a result of active motor motion. Such locally induced nonequilibrium structure will play an important role in applications that involve motor dynamics in complex chemical media.

Design of a Theoretical Model to Identify Specific SSDNA Aptamers for Biosensing Applications

Aptamers are single stranded DNA or RNA oligonucleotides which bind to proteins, small molecules, cells or organs with high affinity and specificity. Aptamers are designed to work in such a way that they only bind to their target proteins/cells, leaving other neighboring and non-targeting proteins/cells intact. This targeting efficiency makes them a promising solution to the problem associated with affinity and specificity of other bioactive agents, reducing harmful side-effects and costs. Target specific Aptamers can be produced by Systematic Enrichment of Ligands by Exponential Amplification, a method usually known as “SELEX Protocol”. However, this SELEX protocol needs a large pool of ssDNA/RNA library containing ∼1014 unique ssDNA/RNA sequences. Selection of only one aptamer for a target takes 15-18 rounds of selection and each round can take 2-3 days, which makes the process very time consuming and costly. In our model, we are trying to identify specific aptamer sequence for a specific target prior to experimental SELEX by a purely theoretical approach. This is done by rigorous theoretical studies on aptamer behavior in different biological environments. A molecular mean field theory is used which takes into account the size, shape, electrical properties and physical configurations of the aptamers along with the size, shape and physical properties of other chemical species associated with a particular biological environment. Coupling between different interactions, acid-base equilibrium and inhomogeneous distribution of different species along with the minimization of strong electrostatic repulsions gives us the most stable structure of aptamers specific to the target. So, this model can be a very efficient tool for designing aptamers to use in wide range of biosensing applications.

Polyelectrolyte brushes in external fields: molecular dynamics simulations and mean-field theory.

A mean-field model is developed to predict the layer-thickness of sparse and salt-free polyelectrolyte brushes, exposed to an external electric field, which attracts the polyelectrolytes to the substrate. In molecular dynamics simulations, it is shown that a fraction of polymers collapses entirely to screen the charge of the substrate. The remaining brushes are then treated as field-free brushes at reduced grafting density. The mean-field model may thus be applied to field-free brushes, both in their osmotic and their weak charge regimes. It yields simple, closed equations for the brush height and for the partition of counterions in- and outside the brushes, and accurately reproduces simulation data of the collapse of the brushes during the crossover between both charge regimes.

Starlike polymer brushes in Θ-solvent

The properties of starlike polymer brushes in Θ-solvent are investigated using molecular dynamics simulations, scaling- and mean-field theory. Deviations of layer thickness and monomer density from predictions of scaling theory are analyzed and explained. Contrary to common believes, we conclude that the Alexander-deGennes scaling theory is not valid for starlike polymer brushes in Θ-solvent, unless the grafting density is extremely low. A comparison with structural and dynamical properties of starlike polymer brushes in good solvent is carried out. Previous studies in good solvent reported about the dual-population structure of these branched polymer brushes, with coexisting phases of stretched and retracted molecules; the same separation emerges in Θ-solvent, though at higher grafting densities. Molecular tension and population fractions are shown to be solvent-dependent, and a reduced dynamical flip-rate between the two populations is observed for the case of the Θ-brush.

Hydrophobic force, a Casimir-like effect due to hydrogen-bond fluctuations

Hydrophobic force, interfacial tension, and transverse density profile in a confined water system are addressed from first principles of statistical mechanics in a lattice model for water. Using the molecular mean field theory technique we deduce explicit expressions for each of the above mentioned phenomena and show that hydrophobic force is a manifestation of a Casimir-like effect due to hydrogen-bond fluctuations in confined water. It is largely influenced by the long range correlations of orientational fluctuations. Furthermore, the temperature dependence of hydrophobic force between large non-polar surfaces is suggested to be different from that between small solutes. The mechanisms contributing to characteristic behavior in each case are identified. In the case of large surfaces, the prevalence of discrete fluctuation modes in the confinement direction and their entropic contribution to the overall free energy dominate the temperature dependence. Mode discretization is also implicated in the variation of interfacial tension with separation distance between confining surfaces and characteristic density profile of the confined fluid. All the computations are parameter free and compare favorably with results of molecular dynamics simulations and experiments.

Phase separation effects and the nematic–isotropic transition in polymer and low molecular weight liquid crystals doped with nanoparticles

Properties of the nematic–isotropic phase transition in polymer and low molecular weight liquid crystals doped with nanoparticles have been studied both experimentally and theoretically in terms of molecular mean-field theory. The variation of the transition temperature and the transition heat with the increasing volume fraction of CdSe quantum dot nanoparticles in copolymer and low molecular weight nematics has been investigated experimentally and the data are interpreted using the results of the molecular theory which accounts for a possibility of phase separation when the system undergoes the nematic–isotropic transition. The theory predicts that the nematic and isotropic phases with different concentrations of nanoparticles may coexist over a broad temperature range, but only if the nanoparticle volume fraction exceeds a certain threshold value which depends on the material parameters. Such unusual phase separation effects are determined by the strong interaction between nanoparticles and mesogenic groups and between nanoparticles themselves.