Electric Field Guided Self-Assembly of Molecules
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Electric Field Guided Self-Assembly of Molecules Wei Lu and David Salac Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109 ABSTRACT Adsorbate molecules usually carry electric dipole moments, and the magnitude can be engineered by adding polar groups. This paper investigates the dynamic domain pattern formation of multilayer dipolar molecules on a substrate under the guidance of external electric fields. The simulations reveal self-alignment, pattern conformation and the reduction of feature size in multilayer systems. A novel approach of transporting molecules on a substrate surface by reconfigurable molecular vehicles and embedded electrodes is proposed. INTRODUCTION Self-assembly is an effective way to pattern nanoscale structures on a substrate surface. The spontaneous domain pattern formation of adsorbate molecules has attracted widespread interest. For instance, dendrimer molecules on a mica substrate can form nanoscale disk-like domains with regular size and spacing [1]. Adsorbate molecules usually carry electric dipole moments, and the magnitude can be engineered by adding polar groups [2]. These molecules are mobile on a surface [3]. A dipole type of interaction is characterized by a 1/distance3 variation in the energy. Molecular domains coarsen to reduce the domain boundary energy and refine to reduce the electric dipole interaction energy. This competition determines the feature sizes and leads to a wide variety of stable patterns. We have developed a phase-field model capable of describing the dynamic self-assembly behavior of dipolar molecules in a multilayer system. Simulations reveal self-alignment, pattern conformation and the reduction of feature size via a layer-by-layer approach. A novel approach of transporting molecules on a substrate surface by reconfigurable molecular vehicles and embedded electrodes is proposed. MODEL Consider a multi-layer of molecules adsorbed onto a substrate. The first layer contacts the substrate, and the nth layer is the top layer. Each layer has a thickness of hm , with m between 1 and n, and the total thickness of the multilayer system is h f . The space above the top layer can be either air or a dielectric fluid. An array of electrodes is embedded in the substrate at a depth of hs . Each layer comprises two molecular species carrying different dipole moments. For the nth layer, let concentration C n be the fraction of surface sites occupied by one of the two species, and regard it as a time-dependent, spatially continuous function, C n ( x1 , x 2 , t ) .
Assume that all buried layers are immobile so that we only need to consider the energy that contributes to any configurational change of the top layer. The free energy is given by ⎛ ⎞ ⎛p ⎞ 1⎛ p ⎞ 2 (1) G = ∫ ⎜⎜ g (Cn ) + β ∇Cn + ⎜ n ⎟ (∆φn ) s ⎟⎟ dA + ∫ ⎜ n ⎟ (∆φn )e dA . 2 ⎝ hn ⎠ h n ⎝ ⎠ A⎝ A ⎠ The first integral is the ‘self-energy’ of the layer. The g (C n ) term represents the chemical energy. We may lump any interface energy between the nth layer and its immediate underlying layer
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