On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)

By estimating the force and torque acting on the cube for the two cases of a uniform flow field and a rotational flow field, we have discussed whether or not there is a coupling between the translational and the rotational motion. From the characteristics of the friction coefficients, we may understand that there is no coupling between the translation motion and the rotational motion in the situation of the Reynolds number being sufficiently smaller than unity. In contrast, in the case of a non-slow flow field with the Reynolds number larger than unity, the coupling characteristics of the motion of a cube is certainly recognised and therefore the interaction with the ambient fluid is characterised by a variety of friction coefficients including friction coefficients that relate the forces acting on the cube to the angular velocities of the rotational motion. Hence, the employment of these translational and rotational diffusion coefficients for a cube enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles in order to analyse the dynamic characteristics of a cubic particle suspension.

Highlights

1. We have considered a flow problem around a cube in order to numerically clarify the characteristics of the translational and rotational friction or diffusion coefficients.

2. In a slow flow field the motion of the cube need only to be characterised by two friction coefficients, i.e. the translational and rotational friction coefficients.

3. In the case of a non-slow flow field, the coupling characteristics between the translational motion and the rotational motion are recognised.

4. Employment of these diffusion coefficients enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles.

     

Quasi-2D Monte Carlo simulations of the regime change in the aggregates of magnetic cubic particles on a material surface

We have investigated the aggregate structure of a suspension composed of magnetic particles with a cubic geometry by means of Monte Carlo simulations. From the viewpoint of application to the technology of surface modification, we have considered a quasi-two-dimensional suspension in thermodynamic equilibrium. As the magnetic interaction strength is increased, the effects of the thermal energy are reduced and the particles tend to aggregate together. These aggregates of cubic particles are not chain-like, but are designated as closely packed clusters. An applied magnetic field tends to enhance the formation of clusters along the field direction but does not significantly regularise the internal structure of the cluster. This is mainly due to the preference of a face-to-face contact configuration for the alignment of particles with cubic geometry. The regime of the internal structure of aggregates has a significant effect on the characteristics of the alignment of the magnetic moments with regard to the external magnetic field direction. Our simulations indicate that larger closely packed clusters are formed with increasing volumetric fraction, whereas the internal structure of the closely packed clusters is not found to be significantly influenced by the change in the volumetric fraction.     

Application of the Brownian dynamics method to a rod-like hematite particle dispersion

We have investigated various problems that arise in applying the Brownian dynamics method to a suspension composed of rod-like hematite particles, which have a magnetic moment normal to the particle axis direction. The accuracy and the deviation of simulation results from theoretical solutions have been discussed by comparison with the theoretical solutions that were obtained by solving the basic equations of the orientational distribution function. The characteristics of the negative viscosity are not observed to be dependent on a time interval unless a sufficiently short time interval is used. The present simulation results can satisfactorily reproduce the qualitative characteristics of the negative magneto-rheological effect that was predicted by the previous theoretical investigation. Good quantitative agreement is obtained in the range of small-applied magnetic fields, but agreement is not significantly good in the large magnetic field region. The deviation of the negative viscosity from the theoretical prediction cannot be improved by using a more accurate numerical algorithm such as moving from Euler to second-order or fourth-order Runge–Kutta. The results of the orientational distribution can well reproduce the characteristic features that the distribution has a gradual shape with low linear-like peak, which is in significant contrast to the sharp single-peak distribution of a ferromagnetic rod-like particle dispersion. The present orientational distributions are in significantly good agreement with those of the theoretical prediction in regard to the position and the height of a peak and the general shape of the overall profile. Good agreement of the present magnetisation curves with the theoretical prediction verifies that the spin rotational Brownian motion is activated at a physically reasonable level in the present simulations.     

Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect

ABSTRACT

We present a simple coarse-grained model with the molecular crowding effect in solvent to investigate the structure and dynamics of protein complexes including association and/or dissociation processes and investigate some physical properties such as the structure and the reaction rate from the viewpoint of the hydrophobic intermolecular interactions of protein complex. In the present coarse-grained model, a function depending upon the density of hydrophobic amino acid residues in a binding area of the complex is introduced, and the function involves the molecular crowding effect for the intermolecular interactions of hydrophobic amino acid residues between proteins. We propose a hydrophobic intermolecular potential energy between proteins by using the density-dependent function. The present coarse-grained model is applied to the complex of cytochrome f and plastocyanin by using the Langevin dynamics simulation to investigate some physical properties such as the complex structure, the electron transfer reaction rate constant from plastocyanin to cytochrome f and so on. We find that for proceeding the electron transfer reaction, the distance between metals in their active sites is necessary within about 18 Å. We discuss some typical complex structures formed in the present simulation in relation to the molecular crowding effect on hydrophobic interactions.     

Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame

An advanced fixed sectional aerosol dynamics model describing the evolution of soot particles under simultaneous nucleation, coagulation, surface growth and oxidation processes is successfully implemented to model soot formation in a two-dimensional laminar axisymmetric coflow methane/air diffusion flame. This fixed sectional model takes into account soot aggregate formation and is able to provide soot aggregate and primary particle size distributions. Soot nucleation, surface growth and oxidation steps are based on the model of Fairweather et al. Soot equations are solved simultaneously to ensure convergence. The numerically calculated flame temperature, species concentrations and soot volume fraction are in good agreement with the experimental data in the literature. The structures of soot aggregates are determined by the nucleation, coagulation, surface growth and oxidation processes. The result of the soot aggregate size distribution function shows that the aggregate number density is dominated by small aggregates while the aggregate mass density is generally dominated by aggregates of intermediate size. Parallel computation with the domain decomposition method is employed to speed up the calculation. Three different domain decomposition schemes are discussed and compared. Using 12 processors, a speed-up of almost 10 is achieved which makes it feasible to model soot formation in laminar coflow diffusion flames with detailed chemistry and detailed aerosol dynamics.