Graduation Semester and Year

2015

Language

English

Document Type

Thesis

Degree Name

Master of Engineering in Civil Engineering

Department

Civil Engineering

First Advisor

Bo Yang

Abstract

Many biomolecules, such as DNA, exhibit properties that are dependent on their electrostatic interaction with an electrolytic solution. Both explicit atomistic and implicit continuum models have been developed to solve the electrostatic problem. The implicit models are based on the Poisson-Boltzmann (PB) equation, whose lower computational cost makes them favored for bio-molecular applications, particularly as the molecule size increases. Among the implicit models, a boundary integral equation (BIE) method involving only numerical treatment on a surface in turn is more efficient than domain-based finite element and finite difference methods. This is especially so in the present case where the electric field varies exponentially requiring specially designed adaptive mesh in the domain-based methods. However, the BIE method is only applicable to linearized PB equation whose fundamental solution is available in an analytical form. When coupled with the linear interfacial continuity condition, it is only valid for low-voltage surfaces. In the present work, a nonlinear interfacial continuity condition is introduced by relating the asymptotes of the nonlinear and the linear PB equations at a surface. Equipped with it, the BIE method can be applied to efficiently and accurately solve the PB problems with high voltage surfaces. Its validity and capability are demonstrated with benchmark examples with one and two spherical particles. In particular, the particle solvation energy is calculated. In the case of two particles, the particle interaction energy is also calculated. The effects of the Debye length of the electrolytic solution and the dielectric mismatch between a particle and the electrolytic solution are examined in detail. A comparison of the linear and the nonlinear PB solutions shows their great difference for highly charged particles, not only in magnitude but also sometimes in variation trend with charge magnitude.

Disciplines

Civil and Environmental Engineering | Civil Engineering | Engineering

Comments

Degree granted by The University of Texas at Arlington

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