Evaluation of translational friction coefficients of macroscopic probes in nematic liquid crystals

We present a study of the translational friction coefficients of spherical and ellipsoidal probes in nematic liquid crystalline fluids, based on the numerical treatment of Leslie-Ericksen equations [Q. J. Mech. Appl. Math. 19, 357 (1966); Adv. Liq. Cryst. 4, (1979); Trans. Soc. Rheol. 5, 23 (1961); Adv. Liq. Cryst. 2, 233 (1976)] for incompressible nematic fluids. Simulations of director dynamics in a local environment surrounding the moving probe are presented, and the dependence of translational diffusion on liquid crystal viscoelastic parameters is discussed. The time evolution of the director field is studied in the presence of an orienting magnetic field in two characteristic situations: Directors of motion parallel and perpendicular with respect to the field. In the particular case under investigation, a detailed analysis is given for the case of spherical, prolate, and oblate ellipsoidal probes in rectilinear motion in nematic (4-methoxibenzylidene-4'-n-butylaniline), together with a comparison with other nematogens, namely, 4,4'-dimethoxuazoxy benzene and (4'-n-pentyl-4-cyanobiphenil). A discussion of the general methodology presented in this work is given for the case of colloidal dispersions in nematic liquid crystals, which are considered as model systems of dispersions of particles in host media with anisotropic physical properties.     

Three-coupled-oscillator model for nonlinear optical response of chiral molecules with tripod-like structure

In this paper, we further study on the relation between the first hyperpolarizability and molecular configuration based on the three-coupled-oscillator model proposed by us. The model is suitable for chiral molecules with the tripod-like structure. We numerically simulate the spectra of first hyperpolarizabilities, and investigate the effects of molecular chiral parameters and coupling coefficients on the hyperpolarizabilities. As an example, we show a calculation of the first-hyperpolarizability spectra for NPAN molecules, which accord well with the experimental result obtained by Barzoukas et al. [M. Barzoukas, D. Josse, P. Fremaux, J. Zyss, J. Opt. Soc. Am. B 4 (1987) 977–986].     

A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections

We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C(6) dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C(8) and C(10). The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.     

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.     

Electric conductivities of 1:1 electrolytes in liquid methanol along the liquid-vapor coexistence curve up to the critical temperature. III. Tetraalkylammonium bromides

The molar conductivities of the dilute solutions of the tetraalkylammonium bromides have been measured in methanol along the liquid-vapor coexistence curve up to about 180 degrees C. The limiting molar conductivities and the molar association constants have been obtained from the analysis of the concentration dependence of the conductivity. On the basis of the present data together with the literature ones, the validity of the Hubbard-Onsager (HO) dielectric friction theory [J. Hubbard, J. Chem. Phys. 68, 1649 (1978)] derived from the continuum model has been examined for the translational friction coefficients of the tetraalkylammonium ions in methanol in the density range of 0.8232 g cm(-3) > or =rho > or =0.5984 g cm(-3) and the temperature range of -15 degrees C < or =t < or =180 degrees C. At high densities and low temperatures, the observed friction coefficients of Me(4)N(+) and Et(4)N(+) are remarkably smaller than the prediction of the HO theory (where Me stands for methyl group and Et for ethyl group); this kind of limitation of the HO theory has not been recognized for smaller ions, and can be attributed to the loosening of the solvent structure closely related to the weak charge effect for the large ions. The negative deviation from the HO theory gradually disappears with decreasing density and increasing temperature, and the friction coefficients of Me(4)N(+) and Et(4)N(+) are explained by the HO theory reasonably well at low densities and high temperatures. For Pr(4)N(+) and Bu(4)N(+) (where Pr stands for propyl group and Bu for butyl group), the experimental friction coefficients lay in the validity range of the HO theory in all the conditions studied here; the breakdown of the continuum theory at low densities and high temperatures has not been observed in this work. The density dependences of the molar association constants of the tetraalkylammonium bromides are qualitatively explained by the Fuoss theory based on the continuum model.     

Design and fabrication of gecko-inspired adhesives

Recently, there has been significant interest in developing dry adhesives mimicking the gecko adhesive system, which offers several advantages compared to conventional pressure-sensitive adhesives. Specifically, gecko adhesive pads have anisotropic adhesion properties; the adhesive pads (spatulae) stick strongly when sheared in one direction but are non-adherent when sheared in the opposite direction. This anisotropy property is attributed to the complex topography of the array of fine tilted and curved columnar structures (setae) that bear the spatulae. In this study, we present an easy, scalable method, relying on conventional and unconventional techniques, to incorporate tilt in the fabrication of synthetic polymer-based dry adhesives mimicking the gecko adhesive system, which provides anisotropic adhesion properties. We measured the anisotropic adhesion and friction properties of samples with various tilt angles to test the validity of a nanoscale tape-peeling model of spatular function. Consistent with the peel zone model, samples with lower tilt angles yielded larger adhesion forces. The tribological properties of the synthetic arrays were highly anisotropic, reminiscent of the frictional adhesion behavior of gecko setal arrays. When a 60° tilt sample was actuated in the gripping direction, a static adhesion strength of ~1.4 N/cm(2) and a static friction strength of ~5.4 N/cm(2) were obtained. In contrast, when the dry adhesive was actuated in the releasing direction, we measured an initial repulsive normal force and negligible friction.     

Computation of determinant expansion coefficients within the graphically contracted function method

Most electronic structure methods express the wavefunction as an expansion of N‐electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

The equation of state of isotropic fluids of hard convex bodies from a high-level virial expansion

We have calculated virial coefficients up to seventh order for the isotropic phases of a variety of fluids composed of hard aspherical particles. The models studied were hard spheroids, hard spherocylinders, and truncated hard spheres, and results are obtained for a variety of length-to-width ratios. We compare the predicted virial equations of state with those determined by simulation. We also use our data to calculate the coefficients of the y expansion [B. Barboy and W. M. Gelbart, J. Chem. Phys. 71, 3053 (1979)] and to study its convergence properties. Finally, we use our data to estimate the radius of convergence of the virial series for these aspherical particles. For fairly spherical particles, we estimate the radius of convergence to be similar to that of the density of closest packing. For more anisotropic particles, however, the radius of convergence decreases with increased anisotropy and is considerably less than the close-packed density.     

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.     

A fast algorithm for simulating flow-induced nucleation in polymers

We present a fast computer simulation algorithm for high dimensional barrier crossing simulations. The algorithm is described with reference to the Graham and Olmsted (GO) model of flow-induced nucleation in polymers [R. S. Graham and P. D. Olmsted, Phys. Rev Lett. 103, 115702 (2009)]. Inspired by Chandler's barrier crossing algorithm [D. Chandler, J. Chem. Phys 68, 2959 (1978)], our algorithm simulates only the region around the top of the nucleation barrier, where the system deviates most strongly from equilibrium. When applied to the kinetic Monte Carlo (kMC) routine used in the GO model, our algorithm has two advantages: it requires very little additional coding; and it is simple enough to be applied to any barrier crossing problem that can be written in terms of a kMC simulation. Our fast nucleation algorithm is shown to vastly decrease the computer time required to perform the kMC simulations of high barrier crossing.     

Studies of human hair by friction force microscopy with the hair-model-probe

We employed a cantilever modified with a self-assembled monolayer (SAM) as a “hair-model-probe” for friction force microscopy (FFM) to measure friction acting between hair and hair-like surfaces. The “hair-model-probe” was prepared by forming a SAM of octadecanethiol on a gold-coated cantilever. We investigated frictional properties of human hair at both root and tip, and the dependency on applied load, influence of scanning direction, and local frictional distribution. The friction coefficient of the hair tip was greater than that of the hair root. Load dependency of friction at the hair tip was clearly observed, while friction at the hair root was less dependent on applied load. At the hair root, an anisotropic frictional property was observed: friction force along the long axis of the hair fiber was about 1.5–2 times larger than that along the short axis. Atomic force microscopy (AFM) images showed striations on the cuticle cells that have about 6 nm depth and their long axis oriented in the direction of the hair fiber. The frictional distribution images revealed that the local areas showing strong shear corresponded to striations. Since such distribution of friction was not observed at the hair tip, it is suggested that the anisotropic frictional property at the hair root was caused mainly by the striations. The frictional distribution in regions that excluded the striations also showed the anisotropic frictional property that friction parallel to the long axis of the hair fiber is greater than that along the short axis. This result suggests that the orientation of fatty acid molecules comprising the fat layer (F-layer) may also contribute to the anisotropic frictional property. We have concluded that loss of the F-layer is a dominant cause of strong friction detected at the hair tip, and at the striations of the hair root.     

Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems

We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.     

Effect of friction between particles in the dynamic response of model magnetic structures

A simple particle-level simulation model that takes into account interparticle friction forces is developed to describe the dynamic response of magneto-rheological fluids. The results obtained for single-width particle chains are found to be in good agreement with slender body theory predictions [J. de Vicente, M.T. López-López, J.D.G. Durán, G. Bossis, J. Colloid Interface Sci. 282 (2005) 193]. The addition of side chains to a single-width one results in one order of magnitude increase of storage modulus and relaxation. The double logarithmic plot of storage and loss moduli vs frequency gives a limiting slope of one when including friction forces between particles. Simulation results are found to be in agreement with experimental measurements on an iron/kerosene model MR-fluid.     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Vibrational dependence of the H2-H2 C6 dispersion coefficients

We use the sum-over-states formalism to compute the imaginary-frequency dipole polarizabilities for H2, as a function of the H-H bond length, at the full configuration interaction level of theory using atom-centered d-aug-cc-pVQZ basis sets. From these polarizabilities, we obtain isotropic and anisotropic C6 dispersion coefficients for a pair of H2 molecules as functions of the two molecules' bond lengths.     

On the equilibrium calculation of the friction coefficient for liquid slip against a wall

We demonstrate that the linear response theory of interface friction presented by Bocquet and Barrat [Phys. Rev. E 49, 3079 (1994)] results in a friction coefficient that is not an intrinsic property of the interface and thus does not correspond to the actual interfacial friction coefficient. We point out that this previous derivation includes an unsubstantiated identification of the velocity field in the nonuniform system with the perturbation applied to the equations of the motion. We present an alternative equilibrium theory of the friction associated with the confined fluid and show how this friction is related to the intrinsic interfacial friction.     

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.