(603f) Two-Dimensional Monte Carlo Simulations of a Polydisperse Colloidal Dispersion Composed of Ferromagnetic Particles
A ferrofluid is classed as a functional fluid because it exhibits attractive functional properties in an applied magnetic field. The ferromagnetic particles in the ferrofluid tend to aggregate to form thick chain-like clusters under the influence of a strong external magnetic field. These clusters give rise to a large resistance in a flow field. Hence, several fluid engineering applications such as mechanical dampers and actuators using this phenomenon are under development. Therefore, the aggregate structures for various conditions have to be clarified in order to develop new functional fluids that can be applied in broad fields of science and technology.
A microscopic simulation approach - powerful technique such as the Monte Carlo (MC) method - can be used to clarify the particle aggregation phenomena. Hence, several molecular simulations using this method have already been conducted on ferromagnetic colloidal dispersions. However, these previous investigations have generally tended to use an idealized dispersion comprising identical spherical particles with the same diameter.
On the other hand, investigations on the polydispersity of aggregate structures are indispensable for clarifying the aggregate structures and magnetic properties of a real ferrofluid. There are several studies on the polydisperse ferromagnetic particle system. However, these studies have primarily investigated the system for a relatively weak magnetic interaction between particles. In other words, they have studied the short chain-like clusters in detail. This is because a particle rarely moves away from a cluster due to a large energy barrier when the particle-particle interactions in the ferromagnetic particle system are very strong. Thus, the conventional Monte Carlo method based on the Metropolis method cannot reproduce aggregate structures of thick chain-like clusters.
If the particle-particle interaction increases, a number of complicated microstructures are expected to be detected. In this study, we introduce a cluster-moving MC method , which is suitable for reproducing physically reasonable aggregate structures for strong particle-particle interactions. This method has a considerably higher rate of convergence in achieving an equilibrium state because the clusters formed during simulations can move as composite single particles.
The objective of the present study is to clarify the aggregate structures of the polydispersed ferromagnetic colloidal dispersion by the cluster-moving MC method. The number of particles N and the area fraction of particles φa are taken as N = 900 and φa = 0.1, respectively. The particle-size distribution is assumed to be Gaussian, and we have considered two different cases of standard deviation, σ = 0.2 and σ = 0.35, with the same average diameter d0 = 1.0. Influences of both the particle-particle and particle-field interactions on the internal structures of the aggregate structures are analyzed in terms of a pair correlation function and a radial distribution function. In addition, the cluster size distribution and angular distribution function have been investigated. The results obtained in this study are summarized as follows:
First, we obtained aggregate structures in the absence of an external magnetic field, and we compared the aggregate structures in a polydisperse system with those in a monodisperse system. In the monodisperse system, open necklace-like clusters are formed and they extend with the increasing strength of the magnetic particle-particle interaction; however, there are few clusters that are larger than those composed of approximately thirty particles. The reason for this characteristic may be interpreted as follows: Single-moving particles have to be combined with short chain-like clusters such that they grow to form long open necklace-like clusters. However, after open necklace-like clusters have grown to a certain degree, the number of single-moving particles significantly decreases such that the cluster size distribution attains equilibrium and does not change.
In the polydisperse system with a small standard deviation in the particle size distribution, σ = 0.2, larger necklace-like clusters are formed and some loop-like clusters can be observed. On the other hand, in a polydisperse system with a larger standard deviation, σ = 0.35, clump-like clusters are formed for a weak magnetic particle-particle interaction. For a stronger magnetic interaction, larger size clusters that exhibit a complicated network structure are formed.
We then investigated the aggregate structures under a strong magnetic field. In this case, chain-like clusters are formed along the magnetic field direction. In the case of a small standard deviation in the particle-size distribution (σ = 0.2), straight chain-like clusters extend along the magnetic field direction with an increase in the particle-particle interaction. This is due to the fact that single-moving particles combine with short chain-like clusters. Moreover, the thick chain-like clusters are formed more quickly in a polydisperse system that has a large standard deviation in particle size (σ = 0.35).
Finally, we consider the aggregate structures for the strong magnetic interactions between particles. The influence of the magnetic field on the aggregate structures in a monodisperse system and both small and large standard deviations in the particle-size distribution are compared.
In the case of the monodisperse system, thin, bent chain-like clusters become straight with an increase in the strength of the magnetic field. In the case of the small standard deviation of σ = 0.2, the branch-like, loop-like and bent chain-like clusters decrease with an increase in the strength of the magnetic field. In the case of a significantly strong magnetic field, particles align strongly along the magnetic field direction and form thick, straight, chain-like clusters. The reason for these characteristics may be interpreted as follows: In the case where the influence of the magnetic field is weak, the particles that aggregate around the large particles tend to form branch-like or clump-like structures rather than straight chain-like clusters. This is because the aggregation is dominated by the influence of the interaction between the particles. The influence of the interaction between the particles decreases relative to the increase in strength of the magnetic field. This leads to the formation of straight chain-like clusters along the magnetic field direction.
In the case of a large standard deviation of σ = 0.35, large clump-like clusters are formed in the initial stages of the chain-like cluster formation during the simulation. This is because there are several large particles with a sufficiently strong particle-particle interaction to form the clump-like clusters. However, as the influence of the magnetic field dominates, the particles align along the magnetic field direction to form straight chain-like clusters. This leads to the formation of the rather thick straight chain-like clusters; however, the number of branch-like and bent structures found in the chain-like clusters decreases.
One of the characteristics of particle aggregation in the polydisperse system is the appearance of various interesting structures such as the clump-like and branch-like structures due to the strong interaction of larger particles. In order to investigate the formation of these structures, we consider a case in which the three particles are in contact with each other. We assume that two particles j have the same fixed diameters dj and the other has a variable diameter di. We then propose two representative configurations of these three particles: linear and triangular, and we investigate the influence of the diameter di of the particle i on the potential energies of the two typical configurations.
The obtained potential energy curves imply that the triangular configuration is more stable than the linear configuration when the particle diameter ratio di / dj is greater than 2.1. This is because the influence of the attractive interaction between particles i and j dominates over the influence of the repulsive interaction between the two identical particles j with an increase in the particle diameter. The formation of the triangular configuration for the polydisperse system enhances the formation of the branch-like or clump-like structures.
 A. Satoh, J. Colloid Interface Sci., 150 (1992) 461.
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