Quantum critical behavior in heavily doped LaFeAsO1−x_{1-x}Hx_x pnictide superconductors analyzed using nuclear magnetic resonance

We studied the quantum critical behavior of the second antiferromagnetic (AF) phase in the heavily electron-doped high-$T_c$ pnictide, LaFeAsO$_{1-x}$H$_x$ by using $^{75}$As and $^{1}$H nuclear-magnetic-resonance (NMR) technique. In the second AF phase, we observed a spatially modulated spin-density-wave-like state up to $x$=0.6 from the NMR spectral lineshape and detected a low-energy excitation gap from the nuclear relaxation time $T_1$ of $^{75}$As. The excitation gap closes at the AF quantum critical point (QCP) at $x \approx 0.49$. The superconducting (SC) phase in a lower-doping regime contacts the second AF phase only at the AF QCP, and both phases are segregated from each other. The absence of AF critical fluctuations and the enhancement of the in-plane electric anisotropy are key factors for the development of superconductivity.Comment: accepted in Phys. Rev.

Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200

A general theory of DNA-mediated and other valence-limited interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure

Orientational order and glassy states in networks of semiflexible polymers

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $\theta\sim 2\pi/M$ leads to long range $M$-fold orientational order, e.g., "hexatic" or "tetratic" for $\theta=60^{\circ}$ or $90^{\circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.Comment: 20 pages, added references, minor changes, final version as published in PR

Elasticity of Stiff Biopolymers

We present a statistical mechanical study of stiff polymers, motivated by experiments on actin filaments and the considerable current interest in polymer networks. We obtain simple, approximate analytical forms for the force-extension relations and compare these with numerical treatments. We note the important role of boundary conditions in determining force-extension relations. The theoretical predictions presented here can be tested against single molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules. Our work is motivated by the buckling of the cytoskeleton of a cell under compression, a phenomenon of interest to biology.Comment: Submitted for publication, five pages, three figure

Structure and dynamics of colloidal depletion gels: coincidence of transitions and heterogeneity

Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20 volume fraction poly(methyl methacyrlate) colloids with the non-adsorbing depletant polystyrene added at a size ratio of depletant to colloid of 0.043. As the strength of the short-range attractive interaction is increased, clusters become increasingly structurally heterogeneous, as characterized by number-density fluctuations, and dynamically immobilized, as characterized by the single-particle mean-squared displacement. The number of free colloids in the suspension also progressively declines. As an immobile cluster to gel transition is traversed, structural heterogeneity abruptly decreases. Simultaneously, the mean single-particle dynamics saturates at a localization length on the order of the short-range attractive potential range. Both immobile cluster and gel regimes show dynamical heterogeneity. Non-Gaussian distributions of single particle displacements reveal enhanced populations of dynamical trajectories localized on two different length scales. Similar dependencies of number density fluctuations, free particle number and dynamical length scales on the order of the range of short-range attraction suggests a collective structural origin of dynamic heterogeneity in colloidal gels.Comment: 14 pages, 10 figure

Static and dynamic properties of large polymer melts in equilibrium

We present a detailed study of the static and dynamic behavior of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [{\it Zhang et al.} ACS Macro Lett. 3, 198 (2014)] we investigate their static and dynamic scaling behavior as predicted by theory. We find that for semiflexible chains in a melt, results of the mean square internal distance, the probability distributions of the end-to-end distance, and the chain structure factor are well described by theoretical predictions for ideal chains. We examine the motion of monomers and chains by molecular dynamics simulations using the ESPResSo++ package. The scaling predictions of the mean squared displacement of inner monomers, center of mass, and relations between them based on the Rouse and the reptation theory are verified, and related characteristic relaxation times are determined. Finally we give evidence that the entanglement length $N_{e,PPA}$ as determined by a primitive path analysis (PPA) predicts a plateau modulus, $G_N^0=\frac{4}{5}(\rho k_BT/N_e)$, consistent with stresses obtained from the Green-Kubo relation. These comprehensively characterized equilibrium structures, which offer a good compromise between flexibility, small $N_e$, computational efficiency, and small deviations from ideality provide ideal starting states for future non-equilibrium studies.Comment: 13 pages, 10 figures, to be published in J. Chem. Phys. (2016

Formation of helical states in wormlike polymer chains

We propose a potential for wormlike polymer chains which can be used to model the low-temperature conformational structures. We successfully reproduced helix ground states up to 6.5 helical loops, using the multicanonical Monte Carlo simulation method. We demonstrate that the coil-helix transition involves four distinct phases: coil(gaslike), collapsed globular(liquidlike), and two helical phases I and II (both solidlike). The helix I phase is characterized by a helical structure with dangling loose ends, and the helix II phase corresponds to a near perfect helix ordering in the entire crystallized chain.Comment: 5 pages, 2 figures, Submitted to PR

The distribution function of a semiflexible polymer and random walks with constraints

In studying the end-to-end distribution function $G(r,N)$ of a worm like chain by using the propagator method we have established that the combinatorial problem of counting the paths contributing to $G(r,N)$ can be mapped onto the problem of random walks with constraints, which is closely related to the representation theory of the Temperley-Lieb algebra. By using this mapping we derive an exact expression of the Fourier-Laplace transform of the distribution function, $G(k,p)$, as a matrix element of an inverse of an infinite rank matrix. Using this result we also derived a recursion relation permitting to compute $G(k,p)$ directly. We present the results of the computation of $G(k,N)$ and its moments. The moments $$ of $$ can be calculated \emph{exactly} by calculating the (1,1) matrix element of $2n$-th power of a truncated matrix of rank $n+1$.Comment: 6 pages, 2 figures, added a referenc