Extreme thermodynamics with polymer gel tori: Harnessing thermodynamic instabilities to induce large-scale deformations

When a swollen, thermoresponsive polymer gel is heated in a solvent bath, it expels solvent and deswells. When this heating is slow, deswelling proceeds homogeneously, as observed in a toroid-shaped gel that changes volume while maintaining its toroidal shape. By contrast, if the gel is heated quickly, an impermeable layer of collapsed polymer forms and traps solvent within the gel, arresting the volume change. The ensuing evolution of the gel then happens at fixed volume, leading to phase separation and the development of inhomogeneous stress that deforms the toroidal shape. We observe that this stress can cause the torus to buckle out of the plane, via a mechanism analogous to the bending of bimetallic strips upon heating. Our results demonstrate that thermodynamic instabilities, i.e., phase transitions, can be used to actuate mechanical deformation in an extreme thermodynamics of materials.

Curvature corrections to the nonlocal interfacial model for short-ranged forces

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.

Defect transitions in nematic liquid-crystal capillary bridges

We use experiment and computational modeling to understand the defect structure and director configuration in a nematic liquid crystal capillary bridge confined between two parallel plates. We find that tuning of the aspect ratio of the bridge drives a transition between a ring defect and a point defect. This transition exhibits hysteresis, due to the metastability of the point-defect structure. In addition, we see that the shape of the capillary-bridge surface determines whether the defect is hyperbolic or radial, with waistlike bridges containing hyperbolic defects and barrel-like bridges containing radial defects.

Beads on a string: structure of bound aggregates of globular particles and long polymer chains

Macroscopic properties of suspensions, such as those composed of globular particles (e.g., colloidal or macromolecular), can be tuned by controlling the equilibrium aggregation of the particles. We examine how aggregation - and, hence, macroscopic properties - can be controlled in a system composed of both globular particles and long, flexible polymer chains that reversibly bind to one another. We base this on a minimal statistical mechanical model of a single aggregate in which the polymer chain is treated either as ideal or self-avoiding, and, in addition, the globular particles are taken to interact with one another via excluded volume repulsion. Furthermore, each of the globular particles is taken to have one single site to which at most one polymer segment may bind. Within the context of this model, we examine the statistics of the equilibrium size of an aggregate and, thence, the structure of dilute and semidilute suspensions of these aggregates. We apply the model to biologically relevant aggregates, specifically those composed of macromolecular proteoglycan globules and long hyaluronan polymer chains. These aggregates are especially relevant to the materials properties of cartilage and the structure-function properties of perineuronal nets in brain tissue, as well as the pericellular coats of mammalian cells.

Emergent tilt order in Dirac polymer liquids

We study a liquid of zigzagging two-dimensional directed polymers with bending rigidity, i.e., polymers whose conformations follow checkerboard paths. In the continuum limit the statistics of such polymers obey the Dirac equation for particles of imaginary mass. We exploit this observation to investigate a liquid of these polymers via a quantum many-fermion analogy. A self-consistent approximation predicts a phase of tilted order, in which the polymers may develop a preference to zig rather than zag. We compute the phase diagram and key response functions for the polymer liquid, and comment on the role played by fluctuations.

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension ϕ, we can determine ϕ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using ϕ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on ϕ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

Dependence of global superconductivity on inter-island coupling in arrays of long SNS junctions

We present measurements of the superconducting transition temperature, Tc, for arrays of mesoscopic Nb islands patterned on Au films, for large island spacings d. We show that Tc ∼ 1/d(2), and explain this dependence in terms of the quasiclassical prediction that the Thouless energy, rather than the superconducting gap, governs the inter-island coupling at large spacings. We also find that the temperature dependence of the critical current, Ic(T), in our arrays is similar to that of single SNS junctions. However, our results deviate from the quasiclassical theory in that Tc is sensitive to island height, because the islands are mesoscopic.

Organization of strongly interacting directed polymer liquids in the presence of stringent constraints

The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in the vicinity of the obstacle, and the associated free-energy cost is found to scale quadratically with the average polymer density. The polymer-polymer interactions are accounted for via a sequence of transformations: from the 3D line liquid to a 2D fluid of Bose particles to a 2D composite fermion fluid and, finally, to a 2D one-component plasma. The results presented here are applicable to a range of systems consisting of noncrossing directed lines.

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.

Frustration and glassiness in spin models with cavity-mediated interactions

We show that the effective spin-spin interaction between three-level atoms confined in a multimode optical cavity is long-ranged and sign changing, like the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in positional randomness can realize spin systems having disordered and frustrated interactions. We argue that, whenever the atoms couple to sufficiently many cavity modes, the cavity-mediated interactions give rise to a spin glass. In addition, we show that the quantum dynamics of cavity-confined spin systems is that of a Bose-Hubbard model with strongly disordered hopping but no on-site disorder; this model exhibits a random-singlet glass phase, absent in conventional optical-lattice realizations. We briefly discuss experimental signatures of the realizable phases.

Weber blockade theory of magnetoresistance oscillations in superconducting strips

Recent experiments on the conductance of thin, narrow superconducting strips have found periodic fluctuations, as a function of the perpendicular magnetic field, with a period corresponding to approximately two flux quanta per strip area [A. Johansson et al., Phys. Rev. Lett. 95, 116805 (2005)]. We argue that the low-energy degrees of freedom responsible for dissipation correspond to vortex motion. Using vortex-charge duality, we show that the superconducting strip behaves as the dual of a quantum dot, with the vortices, magnetic field, and bias current respectively playing the roles of the electrons, gate voltage, and source-drain voltage. In the bias-current versus magnetic-field plane, the strip conductance displays regions of small vortex conductance (i.e., small electrical resistance) that we term "Weber blockade" diamonds, which are dual to Coulomb blockade diamonds in quantum dots.

Anomalously elastic intermediate phase in randomly layered superfluids, superconductors, and planar magnets

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Superconducting nanowires fabricated using molecular templates

The application of single molecules as templates for nanodevices is a promising direction for nanotechnology. We use suspended deoxyribonucleic acid molecules or single-walled carbon nanotubes as templates for fabricating superconducting devices and then study these devices at cryogenic temperatures. Because the resulting nanowires are extremely thin, comparable in diameter to the templating molecule itself, their electronic state is highly susceptible to thermal fluctuations. The most important family of these fluctuations are the collective ones, which take the form of Little's phase slips or ruptures of the many-electron organization. These phase slips break the quantum coherence of the superconducting condensate and render the wire slightly resistive (i.e., not fully superconducting), even at temperatures substantially lower than the critical temperature of the superconducting transition. At low temperatures, for which the thermal fluctuations are weak, we observe the effects of quantum fluctuations, which lead to the phenomenon of macroscopic quantum tunneling. The modern fabrication method of molecular templating, reviewed here, can be readily implemented to synthesize nanowires from other materials, such as normal metals, ferromagnetic alloys, and semiconductors.

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.

Inherent stochasticity of superconductor-resistor switching behavior in nanowires

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

Nematic elastomers: from a microscopic model to macroscopic elasticity theory

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

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.

Magnetic-field enhancement of superconductivity in ultranarrow wires

We study the effect of an applied magnetic field on sub-10-nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and do so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces.

Glassy correlations and microstructures in randomly cross-linked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent cross-links are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerge upon sufficient cross-linking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of cross-linking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellas or random structures with a unique wavelength, can be energetically favorable.

Squeezing superfluid from a stone: coupling superfluidity and elasticity in a supersolid

Starting from the assumption that the normal solid to supersolid (NS-SS) phase transition is continuous, we develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic moduli and thermal expansion coefficients near the transition and, conversely, that inhomogeneous lattice strains can induce local variations of the superfluid transition temperature, leading to a broadened transition.

Cavity approach to the random solid state

The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal motion. This approach is of relevance to a wide class of random solids, including rubbery media (formed via the vulcanization of polymer fluids) and chemical gels (formed by the random covalent bonding of fluids of atoms or small molecules). The cavity approach confirms results that have been obtained previously via replica mean-field theory, doing so in a way that sheds new light on their physical origin.

Quantum Interference Device Made by DNA Templating of Superconducting Nanowires

The application of single molecules as templates for nanodevices is a promising direction for nanotechnology. We used a pair of suspended DNA molecules as templates for superconducting two-nanowire devices. Because the resulting wires are very thin, comparable to the DNA molecules themselves, they are susceptible to thermal fluctuations typical for one-dimensional superconductors and exhibit a nonzero resistance over a broad temperature range. We observed resistance oscillations in these two-nanowire structures that are different from the usual Little-Parks oscillations. Here, we provide a quantitative explanation for the observed quantum interference phenomenon, which takes into account strong phase gradients created in the leads by the applied magnetic field.

Scaling of entropic shear rigidity

The scaling of shear modulus near the gelation-vulcanization transition is explored heuristically and analytically. It is found that in a dense melt the effective chains of the infinite cluster have sizes that scale sublinearly with their contour length. Consequently, each chain contributes k(B)T to the rigidity, which leads to a shear-modulus exponent dnu. In contrast, in phantom elastic networks the scaling is linear in the contour length, yielding an exponent identical to that of the random resistor network conductivity, as predicted by de Gennes. For nondense systems, the exponent should cross over to dnu when the percolation correlation length is much larger than the density-fluctuation length.

h/e Magnetic Flux Modulation of the Energy Gap in Nanotube Quantum Dots

We report experiments on quantum dot single-electron-tunneling (SET) transistors made from short multiwall nanotubes and threaded by magnetic flux. Such systems allow us to probe the electronic energy spectrum of the nanotube and its dependence on the magnetic field. Evidence is provided for the interconversion between gapped (semiconducting) and ungapped (metallic) states. Our tubes exhibit h/e-period magnetic flux dependence, in agreement with simple tight-binding calculations.

Connecting the vulcanization transition to percolation

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wavelength behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it is shown that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with the liquid and critical states.

Semimicroscopic theory of elasticity near the vulcanization transition

Randomly cross-linked macromolecules undergo a liquid to amorphous-solid phase transition at a critical cross-link concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this paper, a semimicroscopic statistical mechanical theory of the elastic properties of the amorphous solid state is developed. This theory takes into account both quenched disorder and thermal fluctuations, and allows for the direct computation of the free energy change of the sample due to a given macroscopic shear strain. This leads to an unambiguous determination of the static shear modulus. At the level of mean field theory, it is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

Renormalization-group approach to the vulcanization transition

The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-field percolation theory (i.e., random graph theory). This minimal model accounts for both the thermal motion of the constituents and the quenched random constraints imposed on their motion by the cross-links, as well as particle-particle repulsion which suppresses density fluctuations and plays a pivotal role in determining the symmetry structure (and hence properties) of the model. A correlation function involving fluctuations of the amorphous solid order parameter, the behavior of which signals the vulcanization transition, is examined, its physical meaning is elucidated, and the associated susceptibility is constructed and analyzed. A Ginzburg criterion for the width (in cross-link density) of the critical region is derived and is found to be consistent with a prediction due to de Gennes. Inter alia, this criterion indicates that the upper critical dimension for the vulcanization transition is 6. Certain universal critical exponents characterizing the vulcanization transition are computed, to lowest nontrivial order, within the framework of an expansion around the upper critical dimension. This expansion shows that the connection between vulcanization and percolation extends beyond mean-field theory, surviving the incorporation of fluctuations in the sense that pairs of physically analogous quantities (one percolation related and one vulcanization related) are found to be governed by identical critical exponents, at least to first order in the departure from the upper critical dimension (and presumably beyond). The relationship between the present approach to vulcanized matter and other approaches, such as those based on gelation-percolation ideas, is explored in the light of this connection. To conclude, some expectations for how the vulcanization transition is realized in two dimensions, developed with H. E. Castillo, are discussed.

Magnetotransport in manganites and the role of quantal phases: theory and experiment

While low-temperature Hall resisitivity rhoxy of La2/3(Ca,Pb)1/3MnO3 single crystals can be separated into ordinary (OHE) and anomalous (AHE) contributions, no such decomposition is possible near the Curie temperature Tc. Rather, the rhoxy data collapse to a single function of the reduced magnetization m=M/Msat, with an extremum at approximately 0.4 m. A new mechanism for the AHE in the inelastic hopping regime is identified that reproduces the scaling curve. An extension of Holstein's model for the hopping OHE, the mechanism arises from the combined effects of the double-exchange-induced quantal phase in triads of Mn ions and spin-orbit interactions.

Early stages of homopolymer collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this paper, a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the straight theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages, the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages scale as N0, N(1/5), and N(6/5), respectively, where N is the degree of polymerization of the chain.