Hydrodynamic screening

Though the idea of hydrodynamic screening is easy to understand, the actual formulation nee te somewhat elaborate method. In the following, we shall explain the method using the crudest approximation. The reader who is interested in a complete form of the formulation is advised to see the original papers. 

---

Altenberger, AR TirreU, M Dahler, JS, Hydrodynamic Screening and Particle Dynamics in Porous Media, SemidUute Polymer Solutions and Polymer Gels, Journal of Chemical Physics 84,5122, 1986. 

Fig. 65. Concentration dependence of the hydrodynamic screening length (c). The solid line represents the result of the simultaneous fit, the dashed line in correlation length (c) related to the transition from single to many chain behavior. (Reprinted with permission from [40]. Copyright 1984 American Chemical Society, Washington)...

The Dependencies of Radius of Gyration Rg, Static Correlation Length Hydrodynamic Screening Length Viscosity r, Self-Translational Diffusion Coefficient D, Cooperative Diffusion Coefficient Dc, Coupled Diffusion Coefficient Df, and Electrophoretic Mobility p on c and N for Various Regimes of Polyelectrolyte and Salt Concentrations... 

In view of the dependence of l on c as given in Table I, the hydrodynamic screening length has the following concentration dependence... 

In dilute solutions, Dc = D. In the Rouse regime, Dc depends on both static and hydrodynamic screening lengths and... 

Then we address the dynamics of diblock copolymer melts. There we discuss the single chain dynamics, the collective dynamics as well as the dynamics of the interfaces in microphase separated systems. The next degree of complication is reached when we discuss the dynamic of gels (Chap. 6.3) and that of polymer aggregates like micelles or polymers with complex architecture such as stars and dendrimers. Chapter 6.5 addresses the first measurements on a rubbery electrolyte. Some new results on polymer solutions are discussed in Chap. 6.6 with particular emphasis on theta solvents and hydrodynamic screening. Chapter 6.7 finally addresses experiments that have been performed on biological macromolecules. 

For semidilute suspensions of long rods, Batchelor (1971) developed a theory of hydrodynamic screening, from which he estimated... 

The preceding conclusions may be suitably checked upon comparison with PDMS. We send the interested reader to ref. 15 for the choice of the parameters. Unlike the case of PS, a molten polymer sample was also considered, in which case the hydrodynamic interaction was assumed to vanish [i.e., v(q) = 1] because of the hydrodynamic screening exerted by the polymer chains. In view of the apparently low energy barriers to the rotation around SUO chain bonds, we assumed the internal viscosity to be absent, that is. To = O Incidentally, we remark the difference from the case of polystyrene where, in addition to the intrinsic rotation barrier around C-C bonds adjoining tetrahedral-coordinated atoms ( 3 kcal/mol), the side phenyl rings contribute significantly to the rotational hindrance. In Figure 13 the characteristic times ti/2 [13/4 for the melts [115]] are plotted versus Q. 

The hydrodynamic screening length in semidilute solutions is expected to be proportional to the static correlation length ... 

The hydrodynamic screening length can neither be much larger nor... 

Unfortunately, there is no accurate theoretical estimate of the strength of hydrodynamic interaction or the extent of hydrodynamic screening of polydisperse branched polymers. Hydrodynamic screening usually correlates well with excluded volume screening. As was demonstrated... 

Calculate the stress relaxation modulus G(t), valid for all times longer than the relaxation time of a monomer, for a monodisperse three-dimensional melt of unentangled flexible fractal polymers that have fractal dimension V <1. Assume complete hydrodynamic screening. Hint Keep the fractal dimension general and make sure your result coincides with the Rouse model for V — 2. 

Dtinweg B. Molecular dynamics algorithms and hydrodynamic screening. J. Chem. Phys. 1993 99 6977. 

When diffusion coefficients for BSA were measured in dextran solutions by holographic interferometry, the BSA diffusion coefficient decreased by less than a factor of 2 as dextran concentration was increased from 0 to 0.08 g/mL [54] the diffusion coefficient was not a function of dextran molecular weight (the range tested was 9,300 to 2 x 10 ). The BSA diffusion coefficient was described very well by using Brinkman s equation to estimate the influence of hydrodynamic screening due to dextran molecules in the solution. The dextran fibers were assumed to have a radius of 1 nm the hydraulic permeability, k, of the dextran solution was estimated from the semi-empirical relationship ... 

This approach—which uses Brinkman s equation, with an appropriate correlation to permit estimation of the hydraulic permeability from the structural characteristics of the medium—provides a straightforward method for estimating the influence of hydrodynamic screening in polymer solutions predicted diffusion coefficients for probes of 3.4 and 10 nm in dextran solutions (Pf = 1 nm) are shown in Figure 4.9. This approach should be valid for cases in which probe diffusion is much more rapid than the movement of fibers in the network, although it appears to work well for BSA diffusion in dextran solutions, even though the dextran molecules diffuse as quickly as the BSA probes [54]. 

As their solutions approach the 6 state, Haas and co-workers (25, 26, 49) observe a more sharply critical transition with a shorter apparent relaxation time, which they ascribe to the Zimm relaxation time in the limit of hydrodynamic screening. Figure 19 shows the flow resistance as a function of Reynolds number for a range of concentrations. They identify the condition... 

Increasing polymer concentration affects chain scission in several ways, as it increases the bulk viscoelasticity, the stress transmission efficiency, tq, and the hydrodynamic screening. The hydrodynamic screening means the hydrodynamic interactions become negligible between chain segments whose spatial distance apart is larger than a certain value (termed hydrodynamic screen length). In both... 

In concentrated solutions, with the increase of the polymer concentration, the screen effect of hydrodynamic interactions is enhanced due to the interpenetration of polymer chains. We can assume that the hydrodynamic screening length is close to the screening length of volume exclusion of monomers as given by... 

On the other hand if we neglect the hydrodynamic screening entirely, is given by the same formula as eqn (8.122)... 

---