Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modelled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both, in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite-size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyse its power-law behaviour on approach of the critical point

Track Based Alignment of Composite Detector Structures

An iterative algorithm for track based alignment is presented. The algorithm can be applied to rigid composite detector structures or to individual modules. The iterative process involves track reconstruction and alignment, in which the chi-2 function of the hit residuals of each alignable object is minimized. Six alignment parameters per structure or per module, three for location and three for orientation, can be computed. The method is computationally light and easily parallelizable. The performance of the method is demonstrated with simulated tracks in the CMS pixel detector and tracks reconstructed from experimental data recorded with a test beam setup

Test of the semischematic model for a liquid of linear molecules

We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].Comment: Revtex, 10 pages, 4 figure

Hard sphere fluids in annular wedges: density distributions and depletion potentials

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high solvent packing fractions larger than 0.4, the explicit density functional results show a deep attractive well for the depletion potential at solute contact, possibly indicating demixing in a binary mixture at low solute and high solvent packing fraction.Comment: 39 page

Molecular mode-coupling theory for supercooled liquids: Application to water

We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with ``exact'' results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones.Comment: 22 pages 4 figures Late

Osmotic compression of droplets of hard rods: A computer simulation study

By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and internal structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or "tactoids" that are formed this way are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we are able to estimate the surface anchoring strength and an average of the elastic constants of the hard-rod nematic

Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study

We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.

Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators

Using molecular dynamics computer simulations we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard- Jones interactions. The q-dependence of the static correlators S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are calculated for l=l'. A thorough test of the predictions of mode coupling theory (MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for l=1,..,6. We find a clear signature for the existence of a single temperature T_c, at which the dynamics changes significantly. The first scaling law of MCT, which involves the critical correlator G(t), holds for l>=2, but no critical law is observed. Since this is true for the same exponent parameter lambda as obtained for the TDOF, we obtain a consistent description of both, the TDOF and ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1 can also be seen from the corresponding susceptibilities (chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega) for which omega'_{min} approx 10 omega_{min} . The asymptotic regime, for which the first scaling law holds, shrinks with increasing l. The second scaling law of MCT (time-temperature superposition principle) is reasonably fulfilled for l \ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong C_l^{(s)}(t) F_s(q,t) for all m.Comment: 11 pages of RevTex, 16 figure

Reality conditions for Ashtekar variables as Dirac constraints

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second class constraints.Comment: 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail: [email protected]