The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamic
s and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density rho the expected power-law scaling for the interaction energy between different chains e_intersimrho^(21/8), the total pressure Psimrho^3 and the dimensionless compressibility gT=lim(q->0)(S(q)sim1/rho^2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size xi(rho) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wavevector q. We comment briefly on finite persistence length effects.
Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain sub
chain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.
Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform w
ith only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one such technique, which was recently implemented at FSU in the form of a C++ program called SEQCSim, which we releasing publicly. We also discuss the potential benefits of this simulation in quantum computing research and education, and outline some possible directions for further progress.
Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) sim N^{1/d}$ with $N$ being the chain length. Using molecular dynamics simulations we show that the irregular shapes of these chai
ns are characterized by a perimeter length $L(N) sim R(N)^{dpm}$ of fractal dimension $dpm = d-Theta_2 =5/4$ with $Theta_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arc-lengths $s$ down to a few monomers. The Kratky representation of the intramolecular form factor $F(q)$ reveals a strong non-monotonous behavior with $q^2F(q) sim 1/(qN^{1/d})^{Theta_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($s F(q) sim L(s)$) the form factor may allow to test our predictions in real experiments.
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood fr
om simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers) to no excluded volume (`phantom chains). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.
Presenting theoretical arguments and numerical results we 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 $u(s) approx s/rho R^3(s) approx ce/sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, $ce approx 1/rho be^3$ the ``swelling coefficient, $be$ 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 $be$ and the swelling coefficient $ce$ of asymptotically long chains. At striking variance to the short-range decay suggested by Florys 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 considered briefly.
