Quasi-elastic scattering by dilute, ideal, polymer solutions: II. Effects of hydrodynamic interactions

Abstract

Each moving unit of a long, flexible, molecule induces in the surrounding solvent a velocity field vhich reacts on the motion of other segments. This long-range hydrodynamic interaction modifies strongly the dynamical form factor S(qv) at low frequencies co and small scattering vectors q. For neutron scattering (qRc ^ where Rq is the radius of gyration of the polymer), the frequency width A c of S(qu>) at fixed q becomes proportional to q*(for an ideal coil). Also the effect of stretching the molecule becomes more dramatic, since stretching greatly reduces the hydrodynamic interactions, asolvent *

Internal Mechanical Response of a Polymer in Solution

“…Figure 4(a) shows G(τ) and a fit to a stretched exponential of the form G(τ) ∝ exp[−(τ/τ 0 ) β ], with a stretching exponent of β= 0.58 ± 0.02. From de Gennes' models of dynamic light scattering, we expect a stretching exponent of β Rouse =1/2 [16], and β Zimm = 2/3 [17]. The observed value of β indicates that hydrodynamic coupling is important on time scales of 10-500 ms, as predicted by Shusterman et al, although hydrodynamic screening by the walls of the trap may reduce β from its free-solution value.…”

“…[17], but surmised that this effect would be difficult to observe. This effect arises because D depends on the instantaneous conformation: more extended conformations diffuse more slowly than more compact conformations.…”

“…In the last line of the appendix of Ref. [17], Dubois-Violette and de Gennes predicted that in the limit of strong internal hydrodynamic interactions, lim τ→0 C (4) (τ) = 1.7%. Averaging C (4) (τ) for the 100 ms subsequent to the τ = 0 spike, we found C (4) (τ) = 1.4% ± 0.4% (mean ± standard deviation; n = 20 data points), consistent with the prediction of Ref.…”

Neutron spin-echo investigations on the dynamics of polymers

“…For the coherent scattering measuring the pair correlation function this relation is expected to be only asymptotically valid. For the Rouse and the reptation models characteristically different time dependences for the mean square displacements are obtained (de Gennes, , 1971Dubois-Violette & de Gennes, 1967) Rouse (ArZ(t) ) = 2aE(wt/Tz) 1/2 …”

Fine characterization of oligomers and polymers in dilute solution

“…As is well known, OðkÞ reflects the translational motion of the entire polymer chain in the range of hS 2 i 1=2 kt1, while it reflects the internal motions of the chain in the range of hS 2 i 1=2 k\1. For long enough, flexible polymer chains without excluded volume, it was considered on the basis of the Gaussian chain model that the plot of Z 0 OðkÞ=k B Tk 3 against hS 2 i 1=2 k is universal, or the plot, especially its height in an intermediate range of k, is independent of the polymer-solvent system [37][38][39]. On the other hand, it has been shown on the basis of the HW chain model that the above plot may depend on the kind of polymer even for large molecular weight ð' 10 7 Þ [40].…”