X. Xing

Topological Defects in Spherical Nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.

Symmetries and elasticity of nematic gels.

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Smectic polymer vesicles

Polymer vesicles are stable robust vesicles made from block copolymer amphiphiles. Recent progress in the chemical design of block copolymers opens up the exciting possibility of creating a wide variety of polymer vesicles with varying fine structure, functionality and geometry. Polymer vesicles not only constitute useful systems for drug delivery and micro/nano-reactors but also provide an invaluable arena for exploring the ordering of matter on curved surfaces embedded in three dimensions. By choosing suitable liquid-crystalline polymers for one of the copolymer components, one can create vesicles with smectic stripes. Smectic order on shapes of spherical topology inevitably possesses topological defects (disclinations) that are themselves distinguished regions for potential chemical functionalization and nucleators of vesicle budding. Here we report on glassy striped polymer vesicles formed from amphiphilic block copolymers in which the hydrophobic block is a smectic liquid crystal polymer containing cholesteryl-based mesogens. The vesicles exhibit two-dimensional smectic order and are ellipsoidal in shape with defects, or possible additional budding into isotropic vesicles, at the poles.

Facilitated translocation of polypeptides through a single nanopore.

The transport of polypeptides through nanopores is a key process in biology and medical biotechnology. Despite its critical importance, the underlying kinetics of polypeptide translocation through protein nanopores is not yet comprehensively understood. Here, we present a simple two-barrier, one-well kinetic model for the translocation of short positively charged polypeptides through a single transmembrane protein nanopore that is equipped with negatively charged rings, simply called traps. We demonstrate that the presence of these traps within the interior of the nanopore dramatically alters the free energy landscape for the partitioning of the polypeptide into the nanopore interior, as revealed by significant modifications in the activation free energies required for the transitions of the polypeptide from one state to the other. Our kinetic model permits the calculation of the relative and absolute exit frequencies of the short cationic polypeptides through either opening of the nanopore. Moreover, this approach enabled quantitative assessment of the kinetics of translocation of the polypeptides through a protein nanopore, which is strongly dependent on several factors, including the nature of the translocating polypeptide, the position of the traps, the strength of the polypeptide-attractive trap interactions and the applied transmembrane voltage.

Morphology of nematic and smectic vesicles

Recent experiments on vesicles formed from block copolymers with liquid-crystalline side chains reveal a rich variety of vesicle morphologies. The additional internal order (“structure”) developed by these self-assembled block copolymer vesicles can lead to significantly deformed vesicles as a result of the delicate interplay between two-dimensional ordering and vesicle shape. The inevitable topological defects in structured vesicles of spherical topology also play an essential role in controlling the final vesicle morphology. Here we develop a minimal theoretical model for the morphology of the membrane structure with internal nematic/smectic order. Using both analytic and numerical approaches, we show that the possible low free energy morphologies include nano-size cylindrical micelles (nano-fibers), faceted tetrahedral vesicles, and ellipsoidal vesicles, as well as cylindrical vesicles. The tetrahedral vesicle is a particularly fascinating example of a faceted liquid-crystalline membrane. Faceted liquid vesicles may lead to the design of supramolecular structures with tetrahedral symmetry and new classes of nano-carriers.

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers.

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.

Thermal fluctuations and rubber elasticity.

The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.

Universal elasticity and fluctuations of nematic gels.

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.

Investigation of Semileptonic {ital B} Meson Decays to {ital p} -Wave Charm Mesons

We have studied semileptonic B meson decays with a P-wave charm meson in the final state using 3.29 × 10 BB̄ events collected by the CLEO II detector at the Cornell Electron-positron Storage Ring. We find a value for the exclusive semileptonic product branching fraction: B(B− → D 1`ν̄`)B(D 1 → Dπ) = (0.373 ± 0.085 ± 0.052 ± 0.024)% and an upper limit for B(B− → D 2 `ν̄`)B(D 2 → Dπ) < 0.16% (90% C.L.). These results indicate that at least 20% of the total B− semileptonic rate is unaccounted for by the observed exclusive decays, B− → D`ν̄, B− → D`ν̄, B− → D 1`−ν̄, and B− → D 2 `−ν̄. (Submitted to Physical Review Letters) SLAC-PUB-9836 hep-ex/9708035 Work supported in part by Department of Energy Contract DE-AC03-76SF00515 Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309, USA A. Anastassov, J. E. Duboscq, D. Fujino, K. K. Gan, T. Hart, K. Honscheid, H. Kagan, R. Kass, J. Lee, M. B. Spencer, M. Sung, A. Undrus, R. Wanke, A. Wolf, M. M. Zoeller, B. Nemati, S. J. Richichi, W. R. Ross, P. Skubic, M. Bishai, J. Fast, J. W. Hinson, N. Menon, D. H. Miller, E. I. Shibata, I. P. J. Shipsey, M. Yurko, S. Glenn, S. D. Johnson, Y. Kwon, S. Roberts, E. H. Thorndike, C. P. Jessop, K. Lingel, H. Marsiske, M. L. Perl, V. Savinov, D. Ugolini, R. Wang, X. Zhou, T. E. Coan, V. Fadeyev, I. Korolkov, Y. Maravin, I. Narsky, V. Shelkov, J. Staeck, R. Stroynowski, I. Volobouev, J. Ye, M. Artuso, A. Efimov, M. Goldberg, D. He, S. Kopp, G. C. Moneti, R. Mountain, S. Schuh, T. Skwarnicki, S. Stone, G. Viehhauser, X. Xing, J. Bartelt, S. E. Csorna, V. Jain, K. W. McLean, S. Marka, R. Godang, K. Kinoshita, I. C. Lai, P. Pomianowski, S. Schrenk, G. Bonvicini, D. Cinabro, R. Greene, L. P. Perera, G. J. Zhou, B. Barish, M. Chadha, S. Chan, G. Eigen, J. S. Miller, C. O’Grady, M. Schmidtler, J. Urheim, A. J. Weinstein, F. Würthwein, D. W. Bliss, G. Masek, H. P. Paar, S. Prell, V. Sharma, D. M. Asner, J. Gronberg, T. S. Hill, D. J. Lange, S. Menary, R. J. Morrison, H. N. Nelson, T. K. Nelson, C. Qiao, J. D. Richman, D. Roberts, A. Ryd, M. S. Witherell, R. Balest, B. H. Behrens, W. T. Ford, H. Park, J. Roy, J. G. Smith, J. P. Alexander, C. Bebek, B. E. Berger, K. Berkelman, K. Bloom, D. G. Cassel, H. A. Cho, D. S. Crowcroft, M. Dickson, P. S. Drell, K. M. Ecklund, R. Ehrlich, A. D. Foland, P. Gaidarev, L. Gibbons, B. Gittelman, S. W. Gray, D. L. Hartill, B. K. Heltsley, P. I. Hopman, S. L. Jones, J. Kandaswamy, P. C. Kim, D. L. Kreinick, T. Lee, Y. Liu, N. B. Mistry, C. R. Ng, E. Nordberg, M. Ogg, J. R. Patterson, D. Peterson, D. Riley, A. Soffer, B. Valant-Spaight, C. Ward, M. Athanas, P. Avery, C. D. Jones, M. Lohner, C. Prescott, J. Yelton, J. Zheng, G. Brandenburg, R. A. Briere, A. Ershov, Y. S. Gao, D. Y.-J. Kim, R. Wilson, H. Yamamoto, aPermanent address: Lawrence Livermore National Laboratory, Livermore, CA 94551. bPermanent address: BINP, RU-630090 Novosibirsk, Russia. cPermanent address: Yonsei University, Seoul 120-749, Korea. dPermanent address: Brookhaven National Laboratory, Upton, NY 11973. ePermanent address: University of Texas, Austin TX 78712

Topology of Smectic Order on Compact Substrates

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a torus as well as on a sphere, we find that both systems exhibit many topologically distinct low energy states that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For a smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.