Monte Carlo simulations of the nucleation and growth process of colloidal particles.

We have examined the effect of the total initial monomer concentration and that of the monomer-monomer attraction energy on the nucleation and growth process of colloidal particles using a reversible aggregation model (Shih-Aksay-Kikuchi model) with the Monte Carlo method. We showed that the equilibrium monomer concentration c(e) exhibited a peak with respect to the total initial monomer concentration c(t). Furthermore, the solution may be divided into three regimes with respect to c(t). In the first regime where the initial monomer concentration was low, all monomers remained as individual monomers in the solution and c(e) increased linearly with c(t). In the second regime where small clusters of monomers began to form, c(e) underwent a peak with respect to c(t). In the third regime where large particles form, c(e) slowly decreased with c(t). Moreover, with increasing monomer-monomer attraction energy, the peak in c(e) moved to a lower c(t) and became sharper. The equilibrium monomer concentration surrounding a particle with respect to particle size was shown to agree with the Kelvin equation, indicating that the model can indeed capture the equilibrium solution physics involving colloidal particles. The peak exhibited in c(e) versus c(t) was manifested as a peak in the monomer concentration versus time under conditions where monomers were gradually fed to the solution. The present simulation is a simulation model for illustrating a peaked solute concentration with respect to time first proposed by LaMer and Dinegar. We further showed that the supersaturation peak in the monomer concentration versus time depended on the feeding rate. The peak height increased with an increasing feeding rate.

Vibrations and static responses of asymmetric bimorph disks of piezoelectric ceramics.

In an earlier article, the flexural vibrations in bimorph disks and extensional vibrations in homogeneous disks of piezoelectric ceramics were studied. In the present paper, the coupled flexural and extensional vibrations and static responses in an asymmetric bimorph disk, which is formed by bonding together two piezoelectric ceramic disks of unequal thickness and opposite polarization, are investigated. Governing equations of coupled motions for asymmetric bimorphs are deduced from the recently derived 2-D, first-order equations for piezoelectric crystal plates with thickness-graded material properties. Then, closed form solutions of these equations for circular disks are obtained for free vibrations, piezoelectrically forced vibrations, and responses under static voltage difference. Resonance frequencies, distribution of displacements and surface charges, impedances, and static responses are calculated for asymmetric bimorph disks of various thickness ratios and diameter-to-thickness ratios. Experimental data on resonances and impedances are obtained for asymmetric bimorph disks of PZT-857 for different thickness ratios. Comparisons of predicted and measured results show that the agreements are close.

Piezoelectric ceramic disks with thickness-graded material properties.

A system of two-dimensional, first-order equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties recently was deduced from the three-dimensional equations of linear piezoelectricity. These equations are simplified for the two limiting cases of thickness-graded piezoelectric properties, i.e., the homogeneous plate and bimorph of piezoelectric ceramics. Closed-form solutions are obtained from these reduced equations for the flexural and thickness-shear vibrations and static response of bimorph disks as well as for the extensional and thickness-stretch vibrations of homogeneous disks. Frequency spectra and modes are computed and examined. Resonance frequencies for both homogeneous and bimorph disks of PZT-857 are computed and measured. The comparison of the results shows that the agreement is close.