Bond-bond Correlation Research Articles

Exploring conformations of comb-like polymers with varying grafting density in dilute solutions.

Comb-like polymers have shown potential as advanced materials for a diverse palette of applications due to the tunability of their polymer architecture. To date, however, it still remains a challenge to understand how the conformational properties of these polymers arise from the interplay of their architectural parameters. In this work, extensive simulations were performed using dissipative particle dynamics to investigate the effect of grafting density, backbone length, and sidechain length on the conformations of comb-like polymers immersed in a good solvent. To quantify the effect of these architectural parameters on polymer conformations, we computed the asphericity, radius of gyration, and backbone and sidechain end-to-end distances. Bond-bond correlation functions and effective Kuhn lengths were computed to quantify the topological stiffness induced by sidechain-sidechain interactions. Simulation results reveal that the effective Kuhn length increases as grafting density and sidechain length increase, in agreement with previous experimental and theoretical studies. This increase in stiffness results in comb-like polymers adopting extended conformations as grafting density and sidechain length increase. Simulation results regarding the radius of gyration of comb-like polymers as a function of grafting density are compared with scaling theory predictions based on a free energy proposed by Morozova and Lodge [ACS Macro Lett. 6, 1274-1279 (2017)] and scaling arguments by Tang et al. [Macromolecules 55, 8668-8675 (2022)].

Valence bond fluctuations in the Kitaev spin model

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and their entanglement properties. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogues. We also show how these valence bond fluctuations can locate quantum phase transitions between the three gapped and the gapless Majorana semi-metal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the 111 direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions towards the three gapped phases. The linear scaling behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Neel magnetic state.

Explaining the stock-stock, bond-bond and stock-bond correlation across countries

This paper examines the behaviour of the same asset-cross country and cross-asset same country correlations for stocks and bond for four (Germany, Japan, UK, USA) major economies. Using the realised volatility methodology to construct time-varying correlations, the results reveal that rising same asset correlations occur when cross-asset correlations fall. While there is evidence of segmentation of Japanese assets within international markets. We seek to explain the movement in correlations and note that the variables that exhibit a positive predictive relation for the stock-bond correlation, exhibit a negative predictive relation for the stock-stock and bond-bond correlations and that this is linked to economic conditions. Within this, four variables (inflation, stock returns, consumer sentiment and purchasing managers index) exhibit consistent significance across the regressions. Using these variables, we construct a correlation indicator variable that is used to construct a switching portfolio. This constructed portfolio constructed outperforms buy-and-hold alternatives.

Explaining the stock-stock, bond-bond and stock-bond correlation across countries

Explaining the stock-stock, bond-bond and stock-bond correlation across countries

How a local active force modifies the structural properties of polymers.

We study the dynamics of a polymer, described as a variant of a Rouse chain, driven by an active terminal monomer (head). The local active force induces a transition from a globule-like to an elongated state, as revealed by the study of the end-to-end distance, the variance of which is analytically predicted under suitable approximations. The change in the relaxation times of the Rouse-modes produced by the local self-propulsion is consistent with the transition from globule to elongated conformations. Moreover, also the bond-bond spatial correlation for the chain head are affected by the self-propulsion and a gradient of over-stretched bonds along the chain is observed. We compare our numerical results both with the phenomenological stiff-polymer theory and several analytical predictions in the Rouse-chain approximation.

Spin liquid phase of theS=12J1−J2Heisenberg model on the triangular lattice

We study the $S=1/2$ Heisenberg model on the triangular lattice with nearest neighbor interaction $J_1$ and next nearest neighbor interaction $J_2$ with the density matrix renormalization group. We are able to study long open cylinders with widths up to 9 lattice spacings. At an intermediate $J_2$ region $0.06 \lesssim J_2/J_1 \lesssim 0.17$, we find evidence for a spin liquid (SL) state with short range spin-spin, bond-bond and chiral correlation lengths, bordered by a classical $120^\circ$ N\'eel ordered state at small $J_2$ and by a two sub-lattice collinear magnetically ordered state at larger $J_2$. Focusing on $J_2/J_1 = 0.1$, we find a number of signatures of a gapped SL phase: two quasi-degenerate ground states on even cylinders, with an energy gap that decreases exponentially with the cylinder width; a dimerization effect on odd cylinders; and large spin triplet and singlet bulk gaps.

Lattice Monte Carlo simulations of polymer melts.

We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction 0.5. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor Sc(q) [minimum in the Kratky-plot] found by Wittmer et al. [EPL 77, 56003 (2007)] for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.

Polymerlike statistical characterization of two-dimensional granular chains

Statistical behaviors of packing collections of granular chains in a two-dimensional container have been investigated experimentally. On compaction from their own gravity, the longer chains pack into a structure with lower packing density due to the prevalence of backbone loops. The packing of chains can be considered as the jamming of the granular system. The structure factor of packing chains shows scaling behavior g(q)∼q(-2) in good agreement with dense polymer solutions. In addition, we compute various probability distributions of distances and estimate three crucial contact exponents, finding that the scaling behavior from granular chains is in accord with the theoretical expectation of polymers. Finally, an orientational anticorrelation of granular chains is observed by bond-bond correlation function, which agrees with the results in the two-dimensional model of compact polymers.

Distance Dependence of Angular Correlations in Dense Polymer Solutions

Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance $r$ between the bonds by comparing quantitative predictions of perturbation calculations with numerical data obtained by Monte Carlo simulation of the bond-fluctuation model. We consider both monodisperse systems and grand-canonical (Flory-distributed) equilibrium polymers. Density effects are discussed as well as finite chain length corrections. The intrachain bond-bond correlation function $P(r)$ is shown to decay as $P(r) \sim 1/r^3$ for $\xi \ll r \ll \r^*$ with $\xi$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty epsilon. This is done to vary systematically the dimensionless compressibility g of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various static properties at constant overall monomer density. The compressibility is obtained directly from the low-wave vector limit of the static structure factor. We consider, e.g., the intrachain bond-bond correlation function P(s) of two bonds separated by s monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed (s<<g) the chains are swollen according to the classical Fixman expansion where, e.g., P(s) approximately g(-1)s(-1/2). More importantly, the polymers behave on larger distances (s>>g) like swollen chains of incompressible blobs with P(s) approximately g(0)s(-3/2).

Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped $A$ phase with Abelian anyon excitations to a gapless $B$ phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\ensuremath{\xi}=2\text{ }{\text{sinh}}^{\ensuremath{-}1}[\sqrt{2{J}_{z}\ensuremath{-}1}/(1\ensuremath{-}{J}_{z})]$, which diverges around the critical point ${J}_{z}={(1/2)}^{+}$.

Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) approximately s/rho R3(s) approximately c(e)/sqrt[s] when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c(e) approximately 1/rho b(e)3 the "swelling coefficient," b(e) the effective bond length, and rho the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b(e) and the swelling coefficient c(e) of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s(3/2). Effects of finite chain length are briefly considered.

Single chain structure in thin polymer films: corrections to Flory’s and Silberberg’shypotheses

Conformational properties of polymer melts confined between two hard structurelesswalls are investigated by Monte Carlo simulation of the bond fluctuationmodel. Parallel and perpendicular components of chain extension, bond–bondcorrelation function and structure factor are computed and compared withrecent theoretical approaches attempting to go beyond Flory’s and Silberberg’shypotheses. We demonstrate that for ultrathin films where the thickness,H, is smaller than the excluded volume screening length (blob size),ξ, the chain size parallel to the walls diverges logarithmically,R2/2N≈b2+clog(N) with c∼1/H. The corresponding bond–bond correlation function decreases like a power law,C(s) = d/sω with s being the curvilinear distance between bonds andω = 1. Upon increasingthe film thickness, H, we find—in contrast to Flory’s hypothesis—the bulk exponentω = 3/2 and, more importantly,a decreasing d(H) that gives direct evidence for an enhanced self-interaction of chain segments reflectedat the walls. Systematic deviations from the Kratky plateau as a function ofH are found for the single chain form factor parallel to the walls in agreement with thenon-monotonic behaviour predicted by theory. This structure in the Kratky plateau might giverise to an erroneous estimation of the chain extension from scattering experiments. For largeH the deviations are linear with the wavevector,q, but are very weak. In contrast, for ultrathin films,H<ξ, very strong corrections (albeit logarithmic inq) are found suggesting a possible experimental verification of our results.

Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density rho via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P1(s) approximately s(-omega) with omega=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) approximately g(-omega(0))(s/g)(-omega) with omega(0)=2-2nu=0.824 (nu=0.588 being Flory's exponent) is set by the number of monomers g(rho) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.

A Density Matrix Renormalization Group Study of Polyacene

We study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian using the Symmetrized Density Matrix Renormalization Group (SDMRG) technique. We find a crossover between the two-photon state and the lowest dipole allowed excited state as the system size is increased from tetracene to pentacene. The spin-gap is the smallest gap. We also study the equilibrium geome tries in the ground and excited states from bond orders and bond-bond correlation functions. We find that the Peierls instability in the ground state of polyacene is conditional both from energetics and structure factors computed froth correlation functions.

The 2D frustrated Ising model in the presence of annealing and an anisotropic defect distribution

The authors discuss the anisotropic frustrated Ising model on a square lattice in the presence of annealing. The host lattice has bonds of strength+J. Defects of strength -J are introduced with concentrations c1 along the horizontal (x) direction and c2 along the vertical (y) direction. The annealed model is considered. It is found that for certain ranges of anisotropy and of defect concentration there exists both a high- and a low-temperature paramagnetic phase. A study of bond-bond correlation functions provides an explanation of the low-temperature phase in terms of highly ordered clusters separated from each other by domain walls of negligible energy. The behaviour is very different from the isotopic case.