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ABSTRACT: Molecular building blocks interacting at the nanoscale organize spontaneously into stable monolayers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately controlled, represents a viable route to manufacture practical nanodevices. With this goal in mind, we seek to capture the salient features of the self-assembly process by means of an interaction-site model. The geometry of the building blocks, the symmetry of the underlying substrate, and the strength and range of interactions encode the self-assembly process. By means of Monte Carlo simulations, we have predicted an ample variety of ordering motifs which nicely reproduce the experimental results. Here, we explore in detail the phase behavior of the system in terms of the temperature and the lattice constant of the underlying substrate.
The European Physical Journal E 03/2012; 35(3):1-8. · 1.94 Impact Factor
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ABSTRACT: We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.
Journal of Physics Condensed Matter 06/2011; 23(23):234121. · 2.55 Impact Factor
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ABSTRACT: Self-organized monolayers of highly flexible \Frechet dendrons were deposited
on graphite surfaces by solution casting. Scanning tunneling microscopy (STM)
reveals an unprecedented variety of patterns with up to seven stable
hierarchical ordering motifs serving as a versatile model system. The essential
molecular properties determined by molecular mechanics simulations are
condensed to a coarse grained interaction site model of various chain
configurations. In a Monte Carlo approach with random starting configurations
the experimental pattern diversity can be reproduced in all facets of the local
and global ordering. Based on an energy analysis of the Monte Carlo and
molecular mechanics modeling the thermodynamically most stable pattern is
predicted coinciding with the pattern, which dominates in the STM images after
several hours or upon moderate heating.
02/2011;
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ABSTRACT: Scanning tunneling microscopy (STM) images of self-organized monolayers of Frechet dendrons display a variety of two-dimensional ordering motifs, which are influenced by engineering the molecular interactions. An interaction-site model condenses the essential molecular properties determined by molecular mechanics modeling, which in a Monte Carlo approach successfully predicts the various ordering motifs. This confirms that geometry as well as a few salient weak interaction sites encode these structural motifs.
Nano Letters 02/2010; 10(3):833-7. · 13.20 Impact Factor
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ABSTRACT: We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system's phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall's delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.
The European Physical Journal E 10/2008; 27(1):47-56. · 1.94 Impact Factor
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ABSTRACT: The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including "herringbone" and "Japanese 6 in 1" phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.
Physical Review Letters 09/2005; 95(8):088302. · 7.37 Impact Factor
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ABSTRACT: We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.
Physical Review E 11/2004; 70(4 Pt 2):046101. · 2.26 Impact Factor
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ABSTRACT: We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.
Physical Review Letters 03/2003; 90(8):086601. · 7.37 Impact Factor
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ABSTRACT: We establish that a mode-coupling approximation for the dynamics of
multi-component systems obeying Smoluchowski dynamics preserves a subtle yet
fundamental property: the matrices of partial density correlation functions are
completely monotone, i.e. they can exactly be written as superpositions of
decaying exponentials only. This statement holds, no matter what further
approximations are needed to calculate the theory's coupling parameters. The
long-time limit of these functions fulfills a maximum property, and an
iteration scheme for its numerical determination is given. We also show the
existence of a unique solution to the equations of motion for which power
series both for short times and small frequencies exist, the latter except at
special points where ergodic-to-nonergodic transitions occur. These transitions
are bifurcations that are proven to be of the cuspoid family.
02/2002;
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European Physical Journal - Special Topics, v.189, 141-145 (2010).
