Resumen

Using the Smoluchowski equation approach, without hydrodynamic interactions, the spinodal decomposition of linear spherical colloids with anisotropic interaction po¬tential is modeled. By considering only inhomogeneities up to third order in density gradients and the first order in the pair correlation function in density gradient a generalized Fick diffusion equation is derived, where the effective collective diffusion coefficient at long times is obtained up to second order wavevector dependence. Equi¬librium expressions for the osmotic pressure and the so-called Cahn-Hilliard square coefficient are provided in terms of reduced spherical harmonic expansion coefficients for the equilibrium pair correlation and the anisotropic interaction potential. This approach is equivalent to the Cahn-Hilliard theory for decomposition up to leading term in density gradients. This model is also able to study demixing kinetics in linear spherical anisotropic colloids.

With the derived Cahn-Hilliard equation, a zeroth approximation was perfomed. To this approximation, mean spherical approximation (MSA) calculations were per¬formed to study the phase diagram of the dipolar hard sphere fluid. The zeroth approximation involves no preferred orientations in the system, thus restraining the system to very simple interpretations. The zeroth approximations yields a variety of physical results. Physical results are the areas of the phase diagram were both the Cahn-Hilliard coefficient and the osmotic pressure are postive. As the temper¬ature increases the quantity of physical results decrease in a linear trend. Isotherm T = 0.025 was analyzed and multiple unstable thermodynamic states were found.

Palabras clave: Smoluchowski, colloidal dynamics, effective diffusion coefficient.

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Gálvez Vallejo, J. L. 2017. Smoluchowski equation approach for inhomogeneities for linear spherical colloids with anisotropic interaction potentials. Tesis Licenciatura. Química. Departamento de Ciencias Químico Biológicas, Escuela de Ciencias, Universidad de las Américas Puebla. Mayo. Derechos Reservados © 2017.