Effect of short-range correlation between chain elements on the hydrodynamic radius and the first cumulant in dilute polymer solutions

First and Second Concentration-Dependent Coefficients of Translational Diffusion and Sedimentation for Poly(α-methylstyrene) in a Good Solvent

“…Calculating the hydrodynamic radius, R H , for each sample from the Stokes−Einstein relation R H = k B T /6πη s D 0 ( R H representation of eq 17 is R H = 1.215 × 10 -9 M w 0.561 ) and using the corresponding R G value, which will be reported in the forthcoming paper, we obtain the radius ratio R G / R H = 1.49−1.55 for the PαMS/benzene system, with the value slightly increasing with M w . This value is consistent with those established experimentally for highly swollen flexible chains in good solvents: 1.54 (PαMS/toluene), 1.50 3 or 1.38−1.45 4 (polyisoprene/cyclohexane), 1.41−1.63 (PS/benzene), and 1.35−1.61 (PS/THF, ethylbenzene), but is much smaller than the theoretical value for pseudo-Gaussian swollen chains, 1.860. , Reasons for the differences between experiment and theory were attributed by us 3,35 to the non-Gaussian nature in the swollen chain segment distributions and to the Oseen hydrodynamic interactions in the Kirkwood scheme; the R G / R H value for fully swollen chains was reasonably predicted to be 1.596 with the chain expansion parameters ν = 0.5830, t = 2.398, and l = 2.802. Since Gaussian chains should have t = l = 2, this discussion suggests that R G / R H is affected by a variation in internal friction with chain expansion.…”

“…This value is consistent with those established experimentally for highly swollen flexible chains in good solvents: 1.54 (PRMS/toluene), 5 1.50 3 or 1.38-1.45 4 (polyisoprene/cyclohexane), 1.41-1.63 (PS/ benzene), 1 and 1.35-1.61 (PS/THF, ethylbenzene), 33 but is much smaller than the theoretical value for pseudo-Gaussian swollen chains, 1.860. 34,35 Reasons for the differences between experiment and theory were attributed by us 3,35 to the non-Gaussian nature in the swollen chain segment distributions and to the Oseen 3) data by Selser in benzene at 30 °C. 6 The solid line represents eq 17.…”

Corrections to scaling in the hydrodynamic properties of dilute polymer solutions

“…Other RG studies resulted in ρ ∞ = 1.562 17 (this value was later revised to 1.51, see Ref. 18) and ρ ∞ = 1.62 19 , while a semi-empirical relation based on fitting the distribution function of internal distances to light scattering data yields ρ ∞ = 1.5955 12,18 . A value of ρ ∞ ≈ 1.6 was also found in Brownian Dynamics simulations 13 .…”

“…Furthermore, Schäfer and Baumgärtner 15 performed a detailed RG calculation and predicted in one-loop order for the universal amplitude ratio 19 , while a semi-empirical relation based on fitting the distribution function of internal distances to light scattering data yields ρ ∞ = 1.5955 12,18 . A value of ρ ∞ ≈ 1.6 was also found in Brownian Dynamics simulations 13 .…”