Self-assembly mechanism in colloids: perspectives from Statistical Physics

Motivated by recent experimental findings in chemical synthesis of colloidal particles, we draw an analogy between self-assembly processes occurring in biological systems (e.g. protein folding) and a new exciting possibility in the field of material science. We consider a self-assembly process whose elementary building blocks are decorated patchy colloids of various types, that spontaneously drive the system toward a unique and predetermined targeted macroscopic structure. To this aim, we discuss a simple theoretical model -- the Kern-Frenkel model -- describing a fluid of colloidal spherical particles with a pre-defined number and distribution of solvophobic and solvophilic regions on their surface. The solvophobic and solvophilic regions are described via a short-range square-well and a hard-sphere potentials, respectively. Integral equation and perturbation theories are presented to discuss structural and thermodynamical properties, with particular emphasis on the computation of the fluid-fluid (or gas-liquid) transition in the temperature-density plane. The model allows the description of both one and two attractive caps, as a function of the fraction of covered attractive surface, thus interpolating between a square-well and a hard-sphere fluid, upon changing the coverage. By comparison with Monte Carlo simulations, we assess the pros and the cons of both integral equation and perturbation theories in the present context of patchy colloids, where the computational effort for numerical simulations is rather demanding.Comment: 14 pages, 7 figures, Special issue for the SigmaPhi2011 conferenc

Tests of redshift-space distortions models in configuration space for the analysis of the BOSS final data release

Citation: White, M., Reid, B., Chuang, C. H., Tinker, J. L., McBride, C. K., Prada, F., & Samushia, L. (2015). Tests of redshift-space distortions models in configuration space for the analysis of the BOSS final data release. Monthly Notices of the Royal Astronomical Society, 447(1), 234-245. doi:10.1093/mnras/stu2460Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. In preparation for analysis of redshift-space distortions from the Baryon Oscillation Spectroscopic Survey (BOSS) final data release, we compare a number of analytic and phenomenological models, specified in configuration space, to mock catalogues derived in different ways from several N-body simulations. The galaxies in each mock catalogue have properties similar to those of the higher redshift galaxies measured by BOSS but differ in the details of how small-scale velocities and halo occupancy are determined. We find that all of the analytic models fit the simulations over a limited range of scales while failing at small scales. We discuss which models are most robust and on which scales they return reliable estimates of the rate of growth of structure: we find that models based on some form of resummation can fit our N-body data for BOSS-like galaxies above 30 h(-1) Mpc well enough to return unbiased parameter estimates

Spin-dependent correlation in two-dimensional electron liquids at arbitrary degeneracy and spin-polarization: CHNC approach

We apply the classical mapping technique developed recently by Dharma-wardana and Perrot for a study of the uniform two-dimensional electron system at arbitrary degeneracy and spin-polarization. Pair distribution functions, structure factors, the Helmhotz free energy, and the compressibility are calculated for a wide range of parameters. It is shown that at low temperatures T/ T_F <0.1, T_F being the Fermi temperature, our results almost reduce to those of zero-temperature analyses. In the region T/ T_F >= 1, the finite temperature effects become considerable at high densities for all spin-polarizations. We find that, in our approximation without bridge functions, the finite temperature electron system in two dimensions remains to be paramagnetic fluid until the Wigner crystallization density. Our results are compared with those of three-dimensional system and indicated are the similarities in temperature, spin-polarization, and density dependencies of many physical properties.Comment: 8 pages, 9 figure

A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids

Approximate scattering functions for polydisperse ionic colloidal fluids are obtained by a corresponding states approach. This assumes that all pair correlation functions $g_{\alpha \beta}(r)$ of a polydisperse fluid are conformal to those of an appropriate monodisperse binary fluid (reference system) and can be generated from them by scaling transformations. The correspondence law extends to ionic fluids a {\it scaling approximation} (SA) successfully proposed for nonionic colloids in a recent paper. For the primitive model of charged hard spheres in a continuum solvent, the partial structure factors of the monodisperse binary reference system are evaluated by solving the Orstein-Zernike (OZ) integral equations coupled with an approximate closure. The SA is first tested within the mean spherical approximation (MSA) closure, which allows analytical solutions. The results are found in good overall agreement with exact MSA predictions up to relevant polidispersity. The SA is shown to be an improvement over the ``decoupling approximation'' extended to the ionic case. The simplicity of the SA scheme allows its application also when the OZ equations can be solved only numerically. An example is then given by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach, its possible use in the analysis of experimental scattering data and other related points are also briefly addressed.Comment: 29 pages, 7 postscript figures (included), Latex 3.0, uses aps.sty, to appear in Phys. Rev. E (1999

Phases in Strongly Coupled Electronic Bilayer Liquids

The strongly correlated liquid state of a bilayer of charged particles has been studied via the HNC calculation of the two-body functions. We report the first time emergence of a series of structural phases, identified through the behavior of the two-body functions.Comment: 5 pages, RevTEX 3.0, 4 ps figures; Submitted to Phys. Rev. Let

Negative electrostatic contribution to the bending rigidity of charged membranes and polyelectrolytes screened by multivalent counterions

Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the other so that thermodynamic properties of SCL contribute to the bending rigidity. Thermodynamic properties of SCL are similar to those of Wigner crystal and are anomalous in the sense that the pressure, compressibility and screening radius of SCL are negative. This brings about substantial negative correction to the bending rigidity. For the case of DNA this effect qualitatively agrees with experiment.Comment: 8 pages, 2 figure

Universal Rights and Wrongs

This paper argues for the important role of customers as a source of competitive advantage and firm growth, an issue which has been largely neglected in the resource-based view of the firm. It conceptualizes Penrose’s (1959) notion of an ‘inside track’ and illustrates how in-depth knowledge about established customers combines with joint problem-solving activities and the rapid assimilation of new and previously unexploited skills and resources. It is suggested that the inside track represents a distinct and perhaps underestimated way of generating rents and securing long-term growth. This also implies that the sources of sustainable competitive advantage in important respects can be sought in idiosyncratic interfirm relationships rather than within the firm itself

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies

Citation: Gil-Marin, H., Percival, W. J., Brownstein, J. R., Chuang, C. H., Grieb, J. N., Ho, S., . . . Zhao, G. B. (2016). The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies. Monthly Notices of the Royal Astronomical Society, 460(4), 4188-4209. doi:10.1093/mnras/stw1096We measure and analyse the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) relative to the line of sight (LOS), for LOWZ and CMASS galaxy samples drawn from the final Data Release 12. The LOWZ sample contains 361 762 galaxies with an effective redshift of z(lowz) = 0.32, and the CMASS sample 777 202 galaxies with an effective redshift of z(cmass) = 0.57. From the power spectrum monopole and quadrupole moments around the LOS, we measure the growth of structure parameter f times the amplitude of dark matter density fluctuations sigma 8 by modelling the redshift-space distortion signal. When the geometrical Alcock-Paczynski effect is also constrained from the same data, we find joint constraints on f sigma(8), the product of the Hubble constant and the comoving sound horizon at the baryondrag epoch H(z) r(s)(z(d)), and the angular distance parameter divided by the sound horizon DA(z)/r(s)(zd). We find f(z(lowz)) sigma(8)(z(lowz)) = 0.394 +/- 0.062, D-A(zlowz)/r(s)(z(d)) = 6.35 +/- 0.19, H(z(lowz)) r(s)(z(d)) = (11.41 +/- 0.56) 103 km s(-1) for the LOWZ sample, and f( z(cmass)) sigma 8(z(cmass)) = 0.444 +/- 0.038, D-A(z(cmass))/r(s)(z(d)) = 9.42 +/- 0.15, H(z(cmass)) r(s)(z(d)) = (13.92 +/- 0.44) 103 km s-1 for the CMASS sample. We find general agreement with previous BOSS DR11 measurements. Assuming the Hubble parameter and angular distance parameter are fixed at fiducial +/- cold dark matter values, we find f( zlowz) sigma(8)( z(lowz))= 0.485 +/- 0.044 and f(z(cmass)) sigma(8)(z(cmass))= 0.436 +/- 0.022 for the LOWZ and CMASS samples, respectively

Influence of solvent granularity on the effective interaction between charged colloidal suspensions

We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard sphere solvent. Apart from molecular oscillating forces for nearly touching colloids which arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerably reduced as compared to the prediction based on the primitive model. When these forces are repulsive, the long-distance behaviour can be described by an effective Yukawa pair potential with a solvent-renormalized charge. As a function of colloidal volume fraction and added salt concentration, this solvent-renormalized charge behaves qualitatively similar to that obtained via the Poisson-Boltzmann cell model but there are quantitative differences. For divalent counterions and nano-sized colloids, on the other hand, the hydration may lead to overscreened colloids with mutual attraction while the primitive model yields repulsive forces. All these new effects can be accounted for through a solvent-averaged primitive model (SPM) which is obtained from the full model by integrating out the solvent degrees of freedom. The SPM was used to access larger colloidal particles without simulating the solvent explicitly.Comment: 14 pages, 16 craphic

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling (FSS) technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent $\alpha$. The appearance of such new corrections to scaling is a general feature of systems with constraints.Comment: 12 pages, 2 figures; submitted to Phys. Rev. Let