The role of water in the electrophoretic mobility of hydrophobic objects

Document Type
Doctoral Thesis
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Issue Year
Milicevic, Zoran

The discovery of hydrophobicity is credited to Hermann Boerhave who in the 18th century studied the efficiency of water to dissolve various compounds. Nowadays the significance of hydrophobicity is well recognized as the effect plays an important role in a myriad of phenomena ranging from the folding and activity of peptides and proteins, the process of self assembly of phospholipid membranes and by this, the design and production of meta-materials, to name just a few. In order to understand the hydrophobic effect a lot of attention was devoted to the study of water ordering around hydrophobic objects and now it is widely accepted that, around smaller objects, water forms cages to maintain the network of hydrogen bonds. It is also well established that the hydrophobicity of an interface, droplet or a particle can be modulated by an external electric field. However, the effects of the electric field on water structure around a hydrophobic object are not understood to a satisfactory level.

The application of a homogeneous electric field drives the migration of a charged particle in a process called electrophoresis. Remarkably, it is experimentally well known that uncharged particles like hydrophobic objects also exhibit electrophoretic mobility. However, this mobility is not satisfactorily understood. The recent application of molecular dynamics simulations has only intensified the scientific discussion about the real nature of the electrophoretic mobility of hydrophobic objects as the obtained results were often contradictory and led to numerous ad hoc hypotheses.

The focus of the thesis is to elucidate the controversies surrounding the research of the electrophoresis of hydrophobic objects through the application of molecular dynamics simulations. In order to achieve this a bottom-up approach is applied and a minimal system that is expected to exhibit electrophoretic mobility is designed. This minimal system consists of smooth spherical particle interacting with water molecules only through a simple Lennard-Jones potential, and thereby the particle will be referred to as the Lennard-Jones particle. To gain deeper understanding of our minimal system, prior to looking at its behavior in the presence of an external electric field, we meticulously examine it in the absence of the electric field. Moreover, a judicious study of both the static and dynamic response of pure water at various electric field strengths is performed.

Despite a heavily increasing number of electrochemical applications, the effect of the external electric field on the dynamic properties of bulk water, like shear viscosity, has not yet been investigated. The shear viscosity is studied here by exploiting the merits of the Green-Kubo formalism in the range of the electric field strengths where the non-linear effects are still negligible. To estimate the value of the shear viscosity in the electric field an alternative approach using the Kohlrausch fit is constructed. It is found that the field decreases the component of the shear viscosity perpendicular to itself and increases the components which are parallel. Importantly, the field induces an additional slow relaxation process only in the parallel direction, prolonging by almost tenfold the overall relaxation process with respect to the perpendicular direction. Furthermore, the apparent water shear viscosity increases slightly with the field strength. To provide an explanation for the observed behavior of the shear viscosity a detailed structural analysis of water is performed, including the two-dimensional pair distribution functions between water molecules that take into account the axial symmetry imposed by the electric fields.

Estimation of the transport coefficients of colloids in liquids is still a challenging task for computer simulations. Apart from technical difficulties, the limits of the validity of the Stokes-Einstein relation have not yet been fully established. To shed light on these issues the calculation of the diffusion and the friction coefficients of the designed nanometer-sized Lennard-Jones particle in water at zero electric field is undertaken. A protocol for defining the hydrodynamic radius of the particle is suggested. It is demonstrated that both the diffusion and the friction coefficient, and hence the water shear viscosity, can be calculated independently with a high quantitative mutual agreement. This is used to indirectly demonstrate the validity of the Stokes-Einstein relation in this regime. Various approaches are investigated and an analysis of simulation conditions required for accurate predictions of transport coefficients, with a particular emphasis on the mass of the spherical particle, as well as the size of the system, is presented.

A number of recent molecular dynamics studies performed at nonzero electric fields have shown a tremendous sensitivity of the migration rate of a hydrophobic solute to the treatment of the long range part of the van der Waals interactions. While the origin of this sensitivity was never explained, the mobility is currently regarded as an artifact of an improper simulation setup. These controversial findings are tested here on the system consisting of the Lennard-Jones particle in water. It is observed that a unidirectional field-induced mobility of the hydrophobic object occurs only when the forces are simply truncated. From the careful analysis of the 100 ns long simulations it is found that, only in the specific case of truncated forces, a non-zero van der Waals force acts, on average, on the Lennard-Jones particle. Using the Stokes law it is demonstrated that this force yields quantitative agreement with the field-induced mobility found within this setup. In contrast, when the treatment of forces is continuous, no net force is observed. In this manner, a simple explanation for the previously controversial reports is given.

However, when the simulations are prolonged toward a microsecond scale a unidirectional mobility of the Lennard-Jones particle is also observed for continuous treatments of the van der Waals forces, even though there is no net force acting on the particle. To resolve this, the water structure is analyzed by means of the total solute-solvent correlation function, which includes the orientational degrees of freedom of the solvent. To evaluate the extent of the symmetry loss, the total solute-solvent correlation function is reconstructed in two-dimensions, accounting for the axial symmetry. It is found that the electric field evokes on an average asymmetric distribution of the water molecules around the Lennard-Jones particle. This acts as a steady state density gradient, inducing a phoretic motion of the hydrophobic object towards the region of higher concentration of water. The phoretic and Brownian motion can be distinguished in the mean square displacement of the particle only at times larger than 15 ns. The data is interpreted on a basis of the Derjaguin theory for diffusiophoresis, which predicts the driving velocity of a colloidal particle as a function of the concentration gradient and the solute-solvent interaction potential. An exceptional agreement between this theoretically predicted driving velocity and the simulation results is obtained.

In summary, in this thesis are presented the results from extensive state-of-art molecular dynamics simulations which demonstrate the ability of the approach to retrieve, with quantitative agreement, the transport properties of both water and colloidal particles. More importantly, a plausible mechanism for the electrophoretic mobility of hydrophobic objects is suggested.

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