Thermodynamics and stochastic thermodynamics of strongly coupled systems.

We further develop the strong-coupling theory of thermodynamics and stochastic thermodynamics for continuous systems, constructed in the previous work [Phys. Rev. Res. 4, 013015 (2022)2643-156410.1103/PhysRevResearch.4.013015]. A small system strongly interacting with a its environment, the dynamics of the system is assumed to be much slower than that of the bath. The system Hamiltonian is defined to be the Hamiltonian of mean force, whereas the system entropy is defined as the Gibbs-Shannon entropy. Equilibrium ensemble theories and thermodynamic theories are established for the system. Variations of three types of parameters are considered: (i) the system parameter λ which couples to the system and to the interaction, (ii) the bath parameter λ^{'} which couples to the bath only, and (iii) the temperature T=1/ß. The work done to the system consists of three parts, proportional to dλ, dλ^{'}, and dß respectively. The part proportional to dß can be understood as the work done by the bath. As long as λ^{'} and ß are not fixed, the work is not the change of total energy of the joint system. The differences between our strong-coupling equilibrium thermodynamics and the classical thermodynamics are discussed. The thermodynamic theory is promoted to the nonequilibrium level. Both the first and second laws of thermodynamics, as well as fluctuation theorems, are established for nonequilibrium processes. For processes with varying temperatures, fluctuation theorems cannot be expressed in terms of integrated work alone. Regardless of various subtleties, however, the stochastic thermodynamic theory is formulated in terms of system variables only, and dS-ßd[over ¯]Q is the change of total entropy. Thermodynamic quantities of the system are related to those of the joint system, and the equivalence of theories at two levels of coarse-graining is explicitly demonstrated. Finally we show that there are infinite numbers of equivalent strong-coupling theories, each determined by its definition of system Hamiltonian. Our theory is distinguished by its maximal similarity with the weak-coupling theory.

Manipulation of the Topological Ferromagnetic State in a Weyl Semimetal by Spin-Orbit Torque.

Magnetic Weyl semimetals (MWSMs) exhibit unconventional transport phenomena, such as large anomalous Hall (and Nernst) effects, which are absent in spatial inversion asymmetry WSMs. Compared with its nonmagnetic counterpart, the magnetic state of a MWSM provides an alternative way for the modulation of topology. Spin-orbit torque (SOT), as an effective means of electrically controlling the magnetic states of ferromagnets, may be used to manipulate the topological magnetic states of MWSMs. Here we confirm the MWSM state of high-quality Co2MnGa film by systematically investigating the transport measurements and demonstrating that the magnetization and topology of Co2MnGa can be electrically manipulated. The electrical and magnetic optical measurements further reveal that the current-induced SOT switches the topological magnetic state in a 180-degree manner by applying positive/negative current pulses and in a 90-degree manner by alternately applying two orthogonal current pulses. This work opens up more opportunities for spintronic applications based on topological materials.

Alignment destabilizes crystal order in active systems.

We combine numerical and analytical methods to study two-dimensional active crystals formed by permanently linked swimmers and with two distinct alignment interactions. The system admits a stationary phase with quasi-long-range translational order, as well as a moving phase with quasi-long-range active force director and velocity order. The translational order in the moving phase is significantly influenced by alignment interaction. For Vicsek-like alignment, the translational order is short ranged, whereas the bond-orientational order is quasi-long ranged, implying a moving hexatic phase. For elasticity-based alignment, the translational order is quasi-long ranged parallel to the motion and short ranged in the perpendicular direction, whereas the bond orientational order is long ranged. We also generalize these results to higher dimensions.

Gradual Crossover from Subdiffusion to Normal Diffusion: A Many-Body Effect in Protein Surface Water.

Dynamics of hydration water is essential for the function of biomacromolecules. Previous studies have demonstrated that water molecules exhibit subdiffusion on the surface of biomacromolecules; yet the microscopic mechanism remains vague. Here, by performing neutron scattering, molecular dynamics simulations, and analytic modeling on hydrated perdeuterated protein powders, we found water molecules jump randomly between trapping sites on protein surfaces, whose waiting times obey a broad distribution, resulting in subdiffusion. Moreover, the subdiffusive exponent gradually increases with observation time towards normal diffusion due to a many-body volume-exclusion effect.

Depletion zones and crystallography on pinched spheres.

Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In this work, we investigate the two-dimensional packing structures of charged particles confined on a pinched sphere. By continuously pinching the sphere, we observe cleavage of elongated scars into pleats, proliferation of disclinations, and subsequently, emergence of a depletion zone at the negatively curved waist that is completely void of particles. We systematically study the geometrics and energetics of the depletion zone, and reveal its physical origin as a finite size effect, due to the interplay between Coulomb repulsion and concave geometry of the pinched sphere. These results further our understanding of crystallography on curved surfaces, and have implications in design and manipulation of charged, deformable interfaces in various applications.

Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

Correlation potential of a test ion near a strongly charged plate.

We analytically calculate the correlation potential of a test ion near a strongly charged plate inside a dilute m:-n electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate Δz is much larger than a Gouy-Chapman length, the plate surface will behave effectively as an infinitely charged surface, and the dielectric constant of the plate effectively plays no role. (2) If Δz is larger than a Gouy-Chapman length but shorter than a Debye length, the correlation potential can be interpreted in terms of an image charge that is three times larger than the source charge. This behavior is independent of the valences of the ions. (3) The Green's function vanishes inside the plate if the surface charge density is infinitely large; hence the electrostatic potential is constant there. In this respect, a strongly charged plate behaves like a conductor plate. (4) If Δz is smaller than a Gouy-Chapman length, the correlation potential is dominated by the conventional image charge due to the dielectric discontinuity at the interface. (5) If Δz is larger than a Debye length, the leading order behavior of the correlation potential will depend on the valences of the ions in the electrolyte. Furthermore, inside an asymmetric electrolyte, the correlation potential is singly screened, i.e., it undergoes exponential decay with a decay width equal to the Debye length.

How do spin waves pass through a bend?

Spin-wave devices hold great promise to be used in future information processing. Manipulation of spin-wave propagation inside the submicrometer waveguides is at the core of promoting the practical application of these devices. Just as in today's silicon-based chips, bending of the building blocks cannot be avoided in real spin-wave circuits. Here, we examine spin-wave transport in bended magnonic waveguides at the submicron scale using micromagnetic simulations. It is seen that the impact of the bend is relevant to the frequency of the passing spin wave. At the lowest frequencies, the spin wave continuously follows the waveguide in the propagation process. At the higher frequencies, however the bend acts as a mode converter for the passing spin wave, causing zigzag-like propagation path formed in the waveguide behind the bend. Additionally, we demonstrate a logic-NOT gate based on such a waveguide, which could be combined to perform logic-NAND operation.

Phenomenological theory of isotropic-genesis nematic elastomers.

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, 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 that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment.

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.

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.

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 electrolyte, 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.

Biaxial deformations of rubber: a comparison between entanglement theory and elastic fluctuation theory.

The classical theory of rubber elasticity fails in the regime of large deformation. The underlying physical mechanism has been under debate for a long time. In this work, we test the recently proposed mechanism of thermal elastic fluctuations by Xing, Goldbart, and Radzihovsky (XGR) against the biaxial stress-strain data of three distinct polymer networks with very different network structures, synthesized by Urayama and Kawabata, respectively. We find that both the two-parameter version and the one-parameter version of the XGR theory provide a 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.

Poisson-Boltzmann theory for two parallel uniformly charged plates.

We solve the nonlinear Poisson-Boltzmann equation for two parallel and like-charged plates both inside a symmetric electrolyte, 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.

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.

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 structure of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their elastic properties. Vulcanization theory studies semimicroscopic 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.

Vacancy diffusion in the triangular-lattice dimer model.

We study vacancy diffusion on the classical triangular-lattice dimer model, subject 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 treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16+/-0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: x over 2 proportional variant tbeta, with beta=0.46+/-0.06 . We also find that the same exponent beta governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a "swap-tunneling" mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

Isotropic-cholesteric transition of a weakly chiral elastomer cylinder.

When a chiral isotropic elastomer is brought to the low-temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nematoelastic 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 Pelcovits 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 to 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 nematoelastic coupling. As a result, this state is not efficient in minimizing the chiral nematic free energy.

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.

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.