Electrostatic Interactions in Self-assembly Systems

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Many phenomena that occur in the nanoscale, such as the self-assembly of charged amphiphiles, the metal extraction for recovering rare earth elements and nuclear waste as well as water purification, are driven by the electrostatic forces. Although current simulation techniques can handle the long-range Coulomb potential efficiently, the inhomogeneity in materials of such systems often gives rise to significant polarization charges that have to be determined by solving the non-trivial Poisson’s equation at each time step of molecular simulation. Thus, dielectric effects are often ignored in previous simulation studies despite their potential importance. Meanwhile, molecules can dynamically change their charges (dissociation state) according to the environment around. Current molecular simulation framework is unable to handle this efficiently. This dissertation presents various techniques that can resolve the simulation challenges in charged systems and applies them to uncover the significance of electrostatic interactions in those systems. ', 'We first present the mathematical formulations for the variational approach that solves the polarization in dielectric heterogeneous systems. We use this method to compute the surface polarization of ion-containing droplets. For water droplets immersed in oil, the interdroplet interaction is attractive, and the surface polarization makes the major contribution. By contrast, for oil droplets in water, the ion-surface induced charge interaction is repulsive and counteracts the attraction between the ions, leading to a small attractive interaction between the droplets. This research improves our understanding of self-assembly in mixed phases such as metal extraction for recovering rare earth elements and nuclear waste as well as water purification. Then we consider asymmetric 2:1 and 3:1 electrolyte bounded by a sinusoidally deformed solid surface. We demonstrate that even when the surface is neutral, the electrolyte acquires a non-uniform ion density profile near the surface. The profile is asymmetric and leads to the effective charging of the surface. We furthermore show that the charge is modulated by the local curvature. The effective charge is opposite to that of the multivalent ion and is negative at concave regions of the surface. The ion distribution could be altered if there are charged molecules at the interface. ', 'Later, we develop the Monte-Carlo method that self-consistently solves the dynamical dissociation state of amphiphile molecules. Together with a theoretical model, we find that electrostatic effects arising from the inhomogeneity of the interfacial medium are responsible for this strong selectivity between two chemically similar lanthanide ions. Our results show that the interface plays an essential role in separating lanthanides during solvent extraction. We also use the Monte-Carlo simulations and pH titration measurements reveal that ionic correlations in the peptide amphiphile (PA) assemblies shift the ionizable amine pK $\\sim$ 8 from pK $\\sim$ 10 in the lysine headgroup. Our studies correlate the molecular charge and the morphology for a pH-responsive PA system and provide insights into the \\AA-scale molecular packing in such assemblies. In another project, we use simplified theoretical models based on the interplay between electrostatic, bending, van-der Waals and surface energies qualitatively reproduce the experimental observations of the increase in bilayer aspect ratio, membrane rolling and the changes in the inter-bilayer spacing as a function of NaCl concentration. We find the narrow ribbon to sheet transition is a first order phase transition. Overall, our studies correlate electrostatic interaction with the morphological changes of the membrane, and provide a means for attaining and controlling the cochleate morphology. In particular, we speculate that the tunable inter-bilayer spacing can be used for controlled encapsulation and release of macromolecules of different sizes for drug-delivery applications.', 'Last, we further extend our studies to the ion dynamics in charged system. Transport of ionic species in heterogeneous polymeric media is highly dependent on the charge distributions and interactions between mobile and immobile groups. Here we perform coarse-grained molecular dynamics simulations to study the ion dynamics in swollen polyelectrolyte gels under external electric fields. A nonlinear response of the ionic conductivity to an applied electric field, for field strengths that are comparable to the ionic coupling strength, is observed. This behavior correlates to a broadening of the ionic distribution around the polymer backbone under an increasing electric field. Also, we find that the weak-field ionic mobility in gels increases with density, which is opposite to the behavior of simple electrolytes. This relates to the mean coupling between charges that decreases in gels, but increases in simple electrolytes, with increasing density. These results provide more insights into the electric response of polyelectrolyte gels to support the development of applications that combine electric and mechanical properties of polyelectrolyte gels for energy storage, sensing, selective transport, and signal transfer.

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  • 10/28/2019
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