Article

# Shape and stability of two-dimensional lipid domains with dipole-dipole interactions.

Department of Physical Electronics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan.

The Journal of Chemical Physics (Impact Factor: 3.12). 01/2007; 125(22):224701. DOI: 10.1063/1.2402160 Source: PubMed

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**ABSTRACT:**Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are coupled to generalized Navier-Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation.Bulletin of Mathematical Biology 02/2010; 72(6):1562-622. · 2.02 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Phase transition of ferroelectric Langmuir monolayers composed of poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) copolymer with various VDF ratios, was investigated. The thermodynamic, dielectric, and structural properties of these two-dimensional ferroelectric systems were analyzed by coupling surface pressure-area isotherms, Maxwell displacement currents (MDCs), and Brewster angle microscopy (BAM) images. A low-temperature phase transition, specific for the ferroelectric monolayer, was found out with an order-disorder phase transition. The phase transition temperature was dependent on the composition ratio of the copolymer, and the Gibbs free energy reached maximum at this temperature. A negative MDC peak representing dipole moment oriented to the subphase was observed during monolayer compression and disappeared above the order-disorder transition. Interestingly, the BAM images showed decrease of domain size with increase of temperature. These results were well explained based on the order-disorder transition. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3212945]The Journal of Chemical Physics 01/2009; 131(10). · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The formation of chiral nanopatterns on low-dimensional ionic assemblies via electrostatic interactions01/2009;

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