Nonequilibrium heat flows through a nanorod sliding across a surface

The temperature-ramped irreversible Langevin equation [A. V. Popov and R. Hernandez, J. Chem. Phys. 134, 244506 (2007)] has been seen to describe the nonequilibrium atomic oscillations of a nanorod dragged across a surface. The nanorod and surface consist of hydroxylated α-Al(2)O(3) layers as was studied earlier by Hase and co-workers [J. Chem. Phys. 122, 094713 (2005)]. The present approach corresponds to the reduced Frenkel-Kontorova-Tomlinson model in which only one element of the vibrational chain representing a surface layer is considered explicitly. The key new concept centers on a separation of the environment into two effective reduced-dimensional baths: an equilibrium bath arising from the thermostated vibrations of the crystal lattice and a nonequilibrium bath arising from driven oscillations at the contact between the nanorod and the surface. The temperature of the latter is defined by the mean energy of a representative atomic oscillator for a given layer. The temporal temperature fluctuations and the dependence of the static part of the temperature on the sliding velocity are close to those found in the MD simulations of Hase and co-workers.     

Self assembly of Janus ellipsoids

We propose a primitive model of Janus ellipsoids that represents particles with an ellipsoidal core and two semisurfaces coded with dissimilar properties, for example, hydrophobicity and hydrophilicity, respectively. We investigate the effects of the aspect ratio on the self-assembly morphology and aggregation processes using Monte Carlo simulations. We also discuss certain differences between our results and those of earlier results for Janus spheres. In particular, we find that the size and structure of the aggregate can be controlled by the aspect ratio.     

Convergence of Newton’s method under Vertgeim conditions: new extensions using restricted convergence domains

We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead of just Hölder conditions, for the first derivative of the operator involved in combination with our new idea of restricted convergence domains. This way, we find a more precise location where the iterates lie, leading to at least as small Hölder constants as in earlier studies. The new convergence conditions are weaker, the error bounds are tighter and the information on the solution at least as precise as before. These advantages are obtained under the same computational cost. Numerical examples show that our results can be used to solve equations where older results cannot.     

Water under temperature gradients: polarization effects and microscopic mechanisms of heat transfer

We report non-equilibrium molecular dynamics simulations (NEMD) of water under temperature gradients using a modified version of the central force model (MCFM). This model is very accurate in predicting the equation of state of water for a wide range of pressures and temperatures. We investigate the polarization response of water to thermal gradients, an effect that has been recently predicted using Non-Equilibrium Thermodynamics (NET) theory and computer simulations, as a function of the thermal gradient strength. We find that the polarization of the liquid varies linearly with the gradient strength, which indicates that the ratio of phenomenological coefficients regulating the coupling between the polarization response and the heat flux is independent of the gradient strength investigated. This notion supports the NET theoretical predictions. The coupling effect leading to the liquid polarization is fairly strong, leading to polarization fields of ~10(3-6) V m(-1) for gradients of ~10(5-8) K m(-1), hence confirming earlier estimates. Finally we employ our NEMD approach to investigate the microscopic mechanism of heat transfer in water. The image emerging from the computation and analysis of the internal energy fluxes is that the transfer of energy is dominated by intermolecular interactions. For the MCFM model, we find that the contribution from hydrogen and oxygen is different, with the hydrogen contribution being larger than that of oxygen.     

Phase behavior of short-range square-well model

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that the fluid-fluid critical point is metastable for both cases, with the case lambda = 1.25 being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma(II)-crystallin.     

Differential geometry based solvation model. III. Quantum formulation

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model.     

Critical dynamics of dimers: implications for the glass transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.     

Gold nanorods as nanoadmicelles: 1-naphthol partitioning into a nanorod-bound surfactant bilayer

As-prepared gold nanorods, stable in aqueous solution, bear a bilayer of the cationic surfactant cetyltrimethylammonium bromide (CTAB). This bilayer provides a approximately 3 nm thick hydrophobic layer that could be used to sequester hydrophobic organic molecules from aqueous solution. We have investigated the uptake of 1-naphthol as a model hydrophobic compound by CTAB-coated gold nanorods using both ultraviolet-visible spectroscopy and gas chromatography with flame ionization detection. We find the adsorption isotherm of 1-naphthol partitioning into the CTAB bilayer on gold nanorods fits the Langmuir model. The maximum number of bound 1-naphthol molecules is 14.6 +/- 2.2 x 10(3) molecules per gold nanorod, with an equilibrium binding constant of 1.97 +/- 0.79 x 10(4) M(-1) at room temperature.     

Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet

We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.     

Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power q of the interparticle distance, and the attractive part varying with an inverse power p. We consider the combinations (12,11) (model I), (12,6) (model II), and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configurational entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configurational entropy, knowledge of the high temperature activation energies in order to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior.     

Biotin-streptavidin-induced aggregation of gold nanorods: tuning rod-rod orientation

We report herein biotin-streptavidin-mediated aggregation studies of long gold nanorods. We have previously demonstrated end-to-end linkages of gold nanorods driven by the biotin-streptavidin interaction (Caswell et al. J. Am. Chem. Soc. 2003, 125, 13914). In that report, the specific binding of biotin disulfide to the gold nanorod edges was achieved due to the preferred binding of thiol molecules to the Au[111] surface (gold nanorod ends) as opposed to the gold nanorod side faces. This led to the end-end linkage of gold nanorods upon subsequent addition of streptavidin. In this report we demonstrate a simple procedure to biotinylate the entire gold nanorod surface and subsequently form a 3-D assembly by addition of streptavidin. Gold nanorods were synthesized by the three-step seeding protocol documented in our previous articles. The surface of gold nanorods was further modified by a layer of a weak polyelectrolyte, poly(acrylic acid), PAA. A biotin molecule which has an amine group at one end (biotin-PEO-amine) was anchored to the carboxylic acid group of the polyelectrolyte using the well-known carbodiimide chemistry. This process biotinylates the entire gold nanorod surface. Addition of streptavidin further leads to aggregation of gold nanorods. A closer look at the aggregates reveals a preferential side-to-side assembly of gold nanorods. The gold nanorods were characterized at each stage by UV-vis spectroscopy, light scattering, and transmission electron microscopy (TEM) measurements.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

An equation of state for electrolyte solutions by a combination of low-density expansion of non-primitive mean spherical approximation and statistical associating fluid theory

A two-parameter equation of state (EOS) for electrolyte solutions is developed. The equation is in terms of Helmholtz free energy and incorporated with our previous results of the low-density expansion of non-primitive mean spherical approximation (MSA). The concentration dependent dielectric constant is thus inherently included in the model. The statistical associating fluid theory (SAFT) is introduced to represent the association interactions, including the solvent–solvent and ion–solvent. The EOS is tested for 15 aqueous alkali halide solutions at ambient condition. The equation can represent simultaneously the mean ionic activity coefficients, the osmotic coefficients and densities in a good accuracy up to saturated concentration. The comparisons with EOSs published earlier in the literature are carried out. The limitations of the model are also discussed.     

Bound states of a charged particle in the field of an electric quadrupole in two dimensions

The Schrödinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy and find that the particle can be bound by a quadrupole of any magnitude. This result is remarkably different from the one for a charged particle in the field of a nonrelativistic electric dipole in three dimensions where a minimum value of the dipole strength is necessary for capture. Present results differ from those obtained earlier by other author.     

Secant-like methods for solving nonlinear models with applications to chemistry

We present a local as well a semilocal convergence analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new conditions are more flexible than in earlier studies. This way we expand the applicability of these methods, since the new convergence conditions are weaker. Moreover, these advantages are obtained under the same conditions as in earlier studies. Numerical examples are also provided in this study, where our results compare favorably to earlier ones.     

Poisson-Boltzmann description of the electrical double layer including ion size effects

The electrical double layer is examined using a generalized Poisson-Boltzmann equation that takes into account the finite ion size by modeling the aqueous electrolyte solution as a suspension of polarizable insulating spheres in water. We find that this model greatly amplifies the steric effects predicted by the usual modified Poisson-Boltzmann equation, which imposes only a restriction on the ability of ions to approach one another. This amplification should allow for an interpretation of the experimental results using reasonable effective ionic radii (close to their well-known hydrated values).     

Parametrization strategy for the MolFESD concept: quantitative surface representation of local hydrophobicity

We derive a new model for the established concept of the molecular free energy surface density (MolFESD) yielding a more rigorous representation of local surface contributions to the overall hydrophobicity of a molecule. The model parametrization makes efficient use of both local and global information about solvation thermodynamics, as formulated earlier for the problem of predicting free energies of hydration. The free energy of transfer is separated into an interaction contribution and a term related to the cavity formation. Interaction and cavity components are obtained from the statistical three-dimensional (3D) free energy density and a linear combination of surface and volume terms, respectively. An appropriate molecular interaction field generated by the program Grid is used as an approximate representation of the interaction part of the 3D free energy density. We further compress the 3D density by means of a linear combination of localized surface functions allowing for the derivation of local hydrophobic contributions in the form of a free energy surface density. For a set of 400 compounds our model yields significant correlation (R(2) = 0.95, sigma = 0.57) between experimental and calculated log P values. The final model is applied to establish a correlation between partial free energies of transfer for a series of sucrose derivatives and their relative sweetness, as studied earlier in the group of the authors. We find considerable improvement regarding the rms error of the regression thus validating the presented approach.     

Investigation of the effects of the local environment on the surface-enhanced Raman spectra of striped gold/silver nanorod arrays

The effects of the local environment on surface-enhanced Raman scattering (SERS) spectra utilizing gold, silver, and gold/silver striped nanorod array substrates was investigated. The arrays were fabricated using an electrochemical metal deposition into an anodic aluminum oxide template. The analyte chosen for this study was p-nitroso-N,N-dimethylaniline (p-NDMA), which has an electronic structure that is highly sensitive to its surrounding environment. Changes in the peak positions and peak ratios were used to probe the influence of water and the striping pattern on the SERS signal of p-NDMA. We present the results of the fabrication and characterization of the nanorod array substrates, as well as SERS spectra of p-NDMA in both polar and nonpolar environments and SERS spectra on a variety of striped nanorod arrays. The Raman data suggests that the p-NDMA molecule exists in a more polarized state when bound to the gold as compared to the silver rods. We have attempted to use these differences to determine whether the SERS signal predominantly arises from the tips of the rods or from the interior of the array.