arXiv subjects

Xiangjun Xing

Publications and source records attributed to Xiangjun Xing.

At least 55 records · Page 3Linked to original sources

arXiv2012

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 layers in electrolyte solutions with divalent counter-ions 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 (ICDF) and 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 the zeta potential, and thus the structure of electric double layers.

cond-mat.soft↗

arXiv2012

Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.

cond-mat.soft↗

arXiv2012

Phenomenological Theory of Isotropic-Genesis Nematic Elastomers

We consider the impact of the elastomer network on the structure and fluctuations in the isotropic-genesis nematic elastomer, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field, which reflects the memory of the nematic order present at cross-linking, and also encodes local anisotropy due to localized polymers. Thus, we predict a regime of short-ranged oscillatory spatial correlations (both thermal and glassy) in the nematic alignment trapped into the network.

cond-mat.soft↗

arXiv2011

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 supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers.

cond-mat.soft↗

arXiv2011

From Over-charging to Like-charge Attraction in the Weak Coupling Regime

Despite decades of intensive studies, the effective interactions between strongly charged colloids still remain elusive. Here we show that a strongly charged surface with a layer of condensed counter- ions behaves effectively as a conductor, due to the mobile nature of the condensed ions. An external source charge in its vicinity is therefore attracted towards the surface, due to the image charge effect. This mechanism leads to correlational energies for counter-ions condensed on two distinct surfaces, as well as for free ions in the bulk. Generalizing Debye-Huckel theory and image charge methods, we analytically calculate these correlation energies for the two-plates problem, at the iso-electric point, where condensed counterions precisely balance the bare surface charges. At this point, the effective interaction between two plates is always attractive at small separation and repulsive at large separation.

cond-mat.soft↗

arXiv2011

Polydomain structure and its origins in isotropic-genesis nematic elastomers

We address the physics of nematic liquid crystalline elastomers randomly crosslinked in the isotropic state. To do this, we construct a phenomenological effective replica Hamiltonian in terms of two order-parameter fields: one for the vulcanization, the other for nematic alignment. Using a Gaussian variational approach, we analyze both thermal and quenched fluctuations of the local nematic order, and find that, even for low temperatures, the macroscopically isotropic polydomain state is stabilized by the network heterogeneity. For sufficiently strong disorder and low enough temperature, our theory predicts unusual, short-range oscillatory structure in (i.e., anti-alignment of) the local nematic order. The present approach, which naturally takes into account the compliant, thermally fluctuating and heterogeneous features of elastomeric networks, can also be applied to other types of randomly crosslinked solids.

cond-mat.soft↗

arXiv2010

Biaxial Deformations of Rubber: Entanglements or Elastic Fluctuations?

The classical theory of rubber elasticity fails in the regime of large deformation. The un- derlying physical mechanism has been under debate for long time. In this work, we test the recently proposed mechanism of thermal elastic fluctuations by Xing, Goldbart and Radzi- hovsky1 against the biaxial stress-strain data of three distinct polymer networks with very different network structures, synthesized by Urayama2 and Kawabata3 respectively. We find that both the two parameters version and the one-parameter version of the XGR theory provide satisfactory description of the elasticity in whole deformation range. For comparison, we also fit the same sets of data using the slip-link model by Edwards and Vilgis with four parameters. The fitting qualities of two theories are found to be comparable.

cond-mat.soft↗

arXiv2010

The Poisson-Boltzmann Theory for The Two-Plates Problem: Some Exact Results

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric elecrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

physics.class-ph↗

arXiv2010

The Poisson-Boltzmann Theory for Two Parallel Uniformly Charged Plates

We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we derive the functional relation between the surface charge density, the plate separation, and the pressure between plates. For the one plate problem, we obtain exact expressions for the electrostatic potential and for the renormalized surface charge density, both in symmetric and in asymmetric electrolytes. For the two plate problems, we obtain new exact asymptotic results in various regimes.

physics.class-ph↗

arXiv2010

Soft random solids and their heterogeneous elasticity

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their \emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lamé-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.

cond-mat.dis-nn↗

arXiv2009

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.

cond-mat.soft↗

arXiv2009

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.

cond-mat.soft↗

arXiv2008

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 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 torus as well as on 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 smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.

cond-mat.soft↗

arXiv2008

Topological Defects in Spherical Nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S^2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S^2. 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 rather than at the vertices of a regular tetrahedron. This arises from the high elastic anisotropy of the system in which splay (K_1) is far softer than bending (K_3). We also introduce and study a lattice nematic model on S^2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We establish the existence of a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_1/K_3 -> 0. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.

cond-mat.soft↗

arXiv2008

Vacancy diffusion in the triangular lattice dimer model

We study vacancy diffusion on the classical triangular lattice dimer model, sub ject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16 \pm 0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous:

cond-mat.stat-mech↗

arXiv2008

Isotropic-Cholesteric Transition of a Weakly Chiral Elastomer Cylinder

When a chiral isotropic elastomer is brought to low temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nemato-elastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much smaller than the system size, this problem has been studied by Pelcotivs and Meyer, as well as by Warner. In this work, we study the isotropic-cholesteric transition in the weak chirality limit, where the pitch is comparable or much larger than system size. We compare two possible solutions: a helical state as well as a double twist state. We find that the double twist state very efficiently minimizes both the elastic free energy and the chiral nematic free energy. On the other hand, the pitch of the helical state is strongly affected by the nemato-elastic coupling. As a result this state is not efficient in minimizing the chiral nematic free energy.

cond-mat.soft↗

arXiv2007

Nonlinear Elasticity, Fluctuations and Heterogeneity of Nematic Elastomers

Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These {\em solid} liquid crystal amalgams, quite similarly to their (conventional, fluid) liquid crystal counterparts, can spontaneously partially break translational and/or orientational symmetries, accompanied by novel soft Goldstone modes. As a consequence, these materials can exhibit unconventional elasticity characterized by symmetry-enforced vanishing of some elastic moduli. Thus, a proper description of such solids requires an essential modification of the classical elasticity theory. In this work, we develop a {\em rotationally invariant}, {\em nonlinear} theory of elasticity for the nematic phase of ideal liquid crystal elastomers. We show that it is characterized by soft modes, corresponding to a combination of long wavelength shear deformations of the solid network and rotations of the nematic director field. We study thermal fluctuations of these soft modes in the presence of network heterogeneities and show that they lead to a large variety of anomalous elastic properties, such as singular length-scale dependent shear elastic moduli, a divergent elastic constant for splay distortion of the nematic director, long-scale incompressibility, universal Poisson ratios and a nonlinear stress-strain relation fo arbitrary small strains. These long-scale elastic properties are {\em universal}, controlled by a nontrivial zero-temperature fixed point and constitute a qualitative breakdown of the classical elasticity theory in nematic elastomers. Thus, nematic elastomers realize a stable ``critical phase'', characterized by universal power-law correlations, akin to a critical point of a continuous phase transition, but extending over an entire phase.

cond-mat.soft↗

arXiv2007

A Semigroup Theory of Rate Independent Hysteresis

We explore a macroscopic, algebraic approach to rate independent hysteresis using semigroup theory. A macroscopic description of metastable states relevant to rate independent hysteresis is introduced using field history. The semigroup structure of the history space is identified. Using semigroup theory and related mathematical techniques, the general relation between return point memory (RPM) and partial order is discovered. For hysteresis system with RPM, a variational principle is identified. The erasing properties of field histories are also characterized. The connection between this semigroup approach and other models are also discussed.

cond-mat.dis-nn↗