High-precision estimate of the hydrodynamic radius for self-avoiding walks

Abstract

The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to N=2^{25}≈34×10^{6} monomers, we find that the ratio takes the value R_{G}/R_{H}=1.5803940(45), which is several orders of magnitude more accurate than the previous state of the art. This is facilitated by a sampling scheme which is quite general and which allows for the efficient estimation of averages of a large class of observables. The competing corrections to scaling for the hydrodynamic radius are clearly discernible. We also find improved estimates for other universal properties that measure the chain dimension. In particular, a method of analysis which eliminates the leading correction to scaling results in a highly accurate estimate for the Flory exponent of ν=0.58759700(40).

Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

“…The DE of the NPRG equations has proved to be an approximation scheme which is versatile and capable of [75], MC [76,77], Length doubling method series [78], and 6-loop, d = 3 perturbative RG values [2], and −expansion at order 5 [2] and order 6 [48] are also given for comparison. Results for most precise experiment are also included (polystyrene benzene dilute solutions [74].…”

Single polymer dynamics for molecular rheology

“…In addition to static measures of average polymer size such as R E and R g , the hydrodynamic radius R H is an additional measure of coil dimensions that can be determined by dynamic light scattering experiments [40,47,49,50]. As previously discussed, R H and R g exhibit different power-law scaling relations in the limit of high molecular weight, essentially because these different physical quantities represent distinct averages (over different moments) of fluctuating variables such as local distances between monomers along a polymer chain.…”

“…In brief, Sunthar and Prakash [47] used an Edwards continuum model [51] to show that differences in the crossovers between the swelling of the hydrodynamic radius α H and radius of gyration α g arise due to dynamic correlations to the diffusivity. These differences are important because dynamic correlations are ignored when determining hydrodynamic radius using the Kirkwood expression for hydrodynamic radius [47,50]:…”

Universal dynamics of dilute and semidilute solutions of flexible linear polymers

“…Several computational studies have validated the predictions of universal static properties in perfectly good solvents made by scaling and renormalisation group theories, by using Monte Carlo simulations, with polymer chains represented as self avoiding walks on lattices [26][27][28]. A recent extremely fast implementation by Clisby [29] of Monte Carlo trial moves in the pivot algorithm, has led to the following predictions for three dimensional SAWs, which are probably the most accurate currently available in the literature [30]: ν = 0.58759700 (40), and (R E /R G ) 2 = 6.253531 (10).…”