RESUMO
The self-orientational structure factor as well as the short-time self-orientational diffusion coefficient is computed for colloids composed by nonspherical molecules. To compute the short-time dynamics the hydrodynamic interactions are not taken into account. The hard molecules with at least one symmetry axis considered are: rods, spherocylinders, and tetragonal parallelepipeds. Because both orientational properties in study are written in terms of the second and fourth order parameters, these automatically hold the features of the order parameters. That is, they present a discontinuity for first order transitions, determining in this way the spinodal line. In order to analyze the nematic phase only, we choose the appropriate values for the representative quantities that characterize the molecules. Different formalisms are used to compute the structural properties: de Gennes-Landau approach, Smoluchowski equation and computer simulations. Some of the necessary inputs are taken from literature. Our results show that the self-orientational properties play an important role in the characterization and the localization of axially symmetric phases. While the self-structure decreases throughout the nematics, the short-time self-diffusion does not decrease but rather increases. We study the evolution of the second and fourth order parameters; we find different responses for axial and biaxial nematics, predicting the possibility of a biaxial nematics in tetragonal parallelepiped molecules. By considering the second order in the axial-biaxial phase transition, with the support of the self-orientational structure factor, we are able to propose the density at which this occurs. The short-time dynamics is able to predict a different value in the axial and the biaxial phases. Because the different behavior of the fourth order parameter, the diffusion coefficient is lower for a biaxial phase than for an axial one. Therefore the self-structure factor is able to localize continuous phase transitions involving axially symmetric phases and the short-time self-orientational diffusion is able to distinguish the ordered phase by considering the degree of alignment, that is, axial or biaxial.
RESUMO
An approach to describe a linear multipolar colloid driven by an external field is developed by considering a colloid which in absence of the field is low structured and its coupling potential is axially symmetric. The equilibrium correlation of one component of the orientation tensor, self and collective, is computed up to linear order in density, which can be measured in an appropriate light scattering experiment. The self-correlation is written in terms of the second and fourth order parameters. All the equilibrium quantities are computed up to two-body level. This is done by assuming that the two-body equilibrium density function is given by the Boltzmann distribution, whereas the one-body density function is computed as solution of the equilibrium N-body Smoluchowski equation in the absence of hydrodynamic interactions. These observables, self and collective, as well as the second and fourth order parameters are able to describe when the colloid would evolve to an orientationally ordered phase. Explicit results for the dipole and quadrupole moments are reported. These results predict a different alignment with the external field for each moment. A relationship is provided between second and fourth order parameters, predicting the critical value of the external field in which the colloid goes into an axially symmetric phase.
RESUMO
We have studied the orientational structure of a dipolar hard-spherical colloid on a homogeneous isotropic phase. The results are expressed as a function of the dipolar strength mu and volume fraction phi of dipolar colloids, and the refractive index of the scattering medium, n(s). The study is based on the self-correlation of the orientation density of the dipolar colloids, which is the static orientational structure factor [F(q)], where q is the wave vector. The importance of this quantity is that for very low phi values, it can be probed in a depolarized light scattering experiment. We have found that the structure of the suspension is better observed for high n(s). F(q) presents a different behavior for dilute and dense concentrations, it is also observed that the position of its minimum depends on phi. The response of a dipolar colloid due to its collective orientational behavior is also studied, using as an "ordering parameter" the static orientational structure factor at q=0[F(q=0)]. The study is performed for isochores as a function of mu. We have divided the analysis into five regimes, from very low to very high phi; values, i.e., phi=0.005 24, 0.1, 0.2, 0.35, and 0.45. Our analysis suggests that the dipolar colloid evolves to an orientationally ordered phase when the dipolar strength is increased, for all concentrations except for the lowest value case, phi=0.005 24. When phi=0.1 the dipolar colloid reaches the transition suddenly, whereas for the very low regime, the slope of F(q=0) first increases as if the dipolar colloid would evolve to an orientationally ordered phase; but near the transition the slope is inverted, resulting in a no global orientational order. Thus, our results suggest that in the very low regime a dipolar colloid may have a reentrant transition.
RESUMO
Orientational hydrodynamic functions and short-time, self-orientational and collective orientational diffusion coefficients of dipolar hard-spherical colloids are performed on a homogeneous isotropic phase, as functions of the wave vector q, for various values of the volume fraction and the dipolar strength of the macroparticles. The calculation is based on the dynamic orientational structure factor, which is the time-dependent self-correlation of the orientation density. We assume that the time evolution of the orientation density is given by the Smoluchoswki's equation, taking into account the hydrodynamic interactions as well as the dipolar interaction. The former are considered assuming pairwise additivity. The importance of the dynamic orientational structure factor is that its initial slope can be measured in a depolarized light scattering experiment. The results predict a different behavior for dilute and for dense dipolar colloids. The ordering phenomena are studied via the ordering coefficients, which are the orientational hydrodynamic functions at q=0. The results show that as the dipolar colloid evolves to the instability line, the translational ordering velocity increases while the rotational one reduces. The short-time orientational diffusion coefficients at q=0 are also performed. They predict that near to the instability line, the dipolar colloid diffuses translationally more than rotationally. At very dilute concentration the dipolar colloid presents an unexpected dynamical behavior, which seems to indicate that the colloid could be evolving to a reentrant phase.