Biomedical subjects

Daan Frenkel

Publications and source records attributed to Daan Frenkel.

At least 37 records · Page 2Linked to original sources

PubMed2005

Oriented primary crystal nucleation in lamellar diblock copolymer systems.

We report a numerical study of the primary crystal nucleation of diblock copolymers in a lamellar phase. Only one of two polymer blocks is crystallizable; the other is maintained in a glassy state. We find that crystals in this lamellar geometry tend to nucleate with the chain axis perpendicular to the lamellar plane. However, if in the same lamellar structure, we break the junction between the crystallizable and non-crystallizable blocks of the polymers, we find that crystallites tend to align parallel to the lamellar plane. This observation clarifies the molecular origin of the competition between parallel and perpendicular crystallite orientations in real block-copolymer systems.

Journal Article↗

PubMed2004

Speed-up of Monte Carlo simulations by sampling of rejected states.

The Markov chain Monte Carlo method is an important tool to estimate the average properties of systems with a very large number of accessible states. This technique is used extensively in fields ranging from physics to genetics and economics. The rejection of trial configurations is a central ingredient in existing Markov chain Monte Carlo simulations. I argue that the efficiency of Monte Carlo simulations can be enhanced, sometimes dramatically, by properly sampling configurations that are normally rejected. This "waste-recycling" of microstates is useful in sampling schemes in which only one of a large set of trial configurations is accepted. It differs fundamentally from schemes that extract information about the density of macrostates from virtual Monte Carlo moves. As a simple illustration, I show that the method greatly improves the calculation of the order-parameter distribution of a two-dimensional Ising model. This method should enhance the efficiency of parallel Monte Carlo simulations significantly.

Journal Article↗

PubMed2004

Designing specificity of protein-substrate interactions.

One of the key properties of biological molecules is that they can bind strongly to certain substrates yet interact only weakly with the very large number of other molecules that they encounter. Using a simple lattice model, we test several methods to design molecule-substrate binding specificity. We characterize the binding free energy and binding energy as a function of the size of the interacting units. Our simulations indicate that there exists a temperature window where specific binding is possible. Binding sites that have been designed to interact quite strongly with specific substrates are unlikely to bind nonspecifically to other substrates. In other words, the conflict between specific interactions between small numbers of biomolecules and weak, nonspecific interaction with the rest need not be a very serious design constraint.

Amino Acid Sequence↗

PubMed2004

The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics.

The turnover frequency of the catalytic oxidation of CO at RuO2(110) was calculated as a function of temperature and partial pressures using ab initio statistical mechanics. The underlying energetics of the gas-phase molecules, dissociation, adsorption, surface diffusion, surface chemical reactions, and desorption were obtained by all-electron density-functional theory. The resulting CO2 formation rate [in the full (T,p(CO),p(O2)) space], the movies displaying the atomic motion and reactions over times scales from picoseconds to seconds, and the statistical analyses provide insight into the concerted actions ruling heterogeneous catalysis and open thermodynamic systems in general.

Journal Article↗

PubMed2004

Crystal nucleation of colloidal suspensions under shear.

We use Brownian dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.

Biophysical Phenomena↗

PubMed2004

Discrete solution of the electrokinetic equations.

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number.

Journal Article↗

PubMed2004

Phase diagram of the adhesive hard sphere fluid.

The phase behavior of the Baxter adhesive hard sphere fluid has been determined using specialized Monte Carlo simulations. We give a detailed account of the techniques used and present data for the fluid-fluid coexistence curve as well as parametrized fits for the supercritical equation of state and the percolation threshold. These properties are compared with the existing results of Percus-Yevick theory for this system.

Journal Article↗

PubMed2004

Melting of polydisperse hard disks.

The melting of a polydisperse hard-disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation-unbinding mechanism, as an extension of the two-dimensional hard-disk melting problem. We find that while there is pronounced fractionation in polydispersity, the apparent density-polydispersity gap does not increase in width, contrary to 3D polydisperse hard spheres. The point where the Young's modulus is low enough for the dislocation unbinding to occur moves with the apparent melting point, but stays within the density gap, just like for the monodisperse hard-disk system. Additionally, we find that throughout the accessible polydispersity range, the bound dislocation-pair concentration is high enough to affect the dislocation-unbinding melting as predicted by Kosterlitz, Thouless, Halperin, Nelson, and Young.

Journal Article↗

PubMed2004

Large effect of polydispersity on defect concentrations in colloidal crystals.

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.

Journal Article↗

PubMed2004

Cubatic phase for tetrapods.

We investigate the phase behavior of tetrapods, hard nonconvex bodies formed by four rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.

Journal Article↗

PubMed2004

Self-poisoning of crystal nuclei in hard-rod liquids.

We report a Monte Carlo study of the pathway for crystal nucleation in a fluid of hard, colloidal rods. In the earliest stages of nucleation, a lamellar crystallite forms. Subsequent thickening of this lamella is hampered by the fact that the top and bottom surfaces of this crystallite are preferentially covered by rods that align parallel to the surface. As a consequence, subsequent growth of individual crystals is stunted. Experimental evidence for such stunted crystal growth has recently been reported by Maeda and Maeda in experiments on suspensions of colloidal rods [Phys. Rev. Lett. 90, 018303 (2003)]]. The simulations suggest that, in experiments, the growth of multilayer colloidal crystals can be selectively enhanced by the application of an external aligning field.

Journal Article↗

PubMed2004

Phase behavior and selectivity of DNA-linked nanoparticle assemblies.

We propose a model that can account for the experimentally observed phase behavior of DNA-nanoparticle assemblies [J. Am. Chem. Soc. 125, 1643 (2003)]; Science 289, 1757 (2000)]]. The binding of DNA-coated nanoparticles by dissolved DNA linkers can be described by exploiting an analogy with quantum particles obeying fractional statistics. In accordance with experimental findings, we predict that the phase-separation temperature of the nanocolloids increases with the DNA coverage of the colloidal surface. Upon the addition of salt, the demixing temperature increases logarithmically with the salt concentration. Our analysis suggests an experimental strategy to map microscopic DNA sequences onto the macroscopic phase behavior of the DNA-nanoparticle solutions. Such an approach should enhance the efficiency of methods to detect (single) mutations in specific DNA sequences.

Base Sequence↗

PubMed2004

Quantitative prediction of crystal-nucleation rates for spherical colloids: a computational approach.

This review discusses the recent progress that has been made in the application of computer simulations to study crystal nucleation in colloidal systems. We discuss the concept and the numerical methods that allow for a quantitative prediction of crystal-nucleation rates. The computed nucleation rates are predicted from first principles and can be directly compared with experiments. These techniques have been applied to study crystal nucleation in hard-sphere colloids, polydisperse hard-sphere colloids, weakly charged or slightly soft colloids, and hard-sphere colloids that are confined between two-plane hard walls.

Journal Article↗

PubMed2003

Large difference in the elastic properties of fcc and hcp hard-sphere crystals.

We report a numerical calculation of the elastic constants of the fcc and hcp crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of these elastic constants are very different (up to 20%), even though the free-energy, pressure, and bulk compressibility of the two crystal structures are very nearly equal. As a consequence, a moderate deformation of a hard-sphere crystal may make the hcp phase more stable than the fcc phase. This finding has implications for the design of patterned templates to grow colloidal hcp crystals. We also find that, below close-packing, there is a small, but significant, difference between the distances between hexagonal layers (c/a ratios) of fcc and hcp crystals.

Journal Article↗

PubMed2003

Velocity fluctuations and dispersion in a simple porous medium.

We model a fluid-filled disordered porous medium by a lattice-Boltzmann system with randomly broken links. The broken links exert a friction on the fluid without excluding volume. Such a model closely mimics the idealized picture of a porous medium, which is often used in the theoretical analysis of hydrodynamic dispersion. We find that the Brinkman equation describes both the mean flow characteristics and the spatial decay of velocity fluctuations in the system. However, the temporal decay of the velocity correlations (that a particle experiences as it moves with the fluid), cannot be simply related to the spatial decay. It is this temporal decay that determines the dispersivity. Thus, hydrodynamic dispersion is generally greater than theories based on spatial correlations would imply. This is particularly true at high densities, where such theories considerably underestimate both the magnitude and transient time scale for dispersion. Nonetheless, temporal velocity correlations are still ultimately screened and the hydrodynamic dispersion coefficient converges exponentially. The long-lived transients reported for more realistic systems must therefore be due explicitly to the presence of excluded volume.

Journal Article↗

PubMed2003

Continuous freezing in three dimensions.

We analyze the freezing transition in a system of hard particles with a very long-ranged repulsion. The long-range repulsion makes first-order freezing transitions continuous, but leaves the initial stages of the crystallization unchanged: the crystal phase must still nucleate. The coexistence between bulk phases is replaced by microphase separation.

Journal Article↗

PubMed2003

Competition of percolation and phase separation in a fluid of adhesive hard spheres.

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.

Journal Article↗

PubMed2002

Smectic filaments in colloidal suspensions of rods.

In supersaturated isotropic mixtures of hard rods, smectic filaments have recently been observed. We propose a model for formation and growth of these filaments similar to the Hoffman-Lauritzen model for polymer crystallization. Filament thickness is determined by a compromise between maximizing the amount of smectic phase formed and minimizing the nucleation barrier for adding new segments to the growing filament. We compare our analytical results to kinetic Monte Carlo simulations.

Journal Article↗