Hydrodynamic interactions dominant

Since intersegment hydrodynamic interaction dominates the friction coefficient, we ignore the i = j part that leads to the free-draining contribution. If we define the inverse propagator G according to... 

Here, is a dimensionless number termed the adhesion group. Clearly the larger the value of the adhesion group the more dominant is the London attractive force for a fixed gap width and particle location. On the other hand, for smaller values of hydrodynamic interactions dominate. 

The above results are valid only if the time of measurement is longer than the characteristic time for the relaxation of the various Rouse modes of the Zimm chain. The longest relaxation time for a chain with the Zimm dynamics (corresponding to the Rouse mode p = 1), where the hydrodynamic interaction dominates, is called the Zimm time given by... 

Figure 7.4 In dilute solutions, intrachain hydrodynamic interaction dominates (Zimm dynamics). At higher polymer concentrations, chain interpenetration screens the hydrodynamic interaction, resulting in an apparent Rouse dynamics.

In the dynamics of flexible chains, since hydrodynamic interactions dominate over the segmental friction, we may use eqns [67]-[79] to describe their dynamics. For a linear Gaussian chain, since eqn [149] leads to... 

As in the case of the Rouse dynamics (see Sect. 3.1.1), the intermediate incoherent scattering law for dominant hydrodynamic interaction (Zimm model) can be... 

Comparing Eqs. (83), (84) and Eqs. (21), (22) it follows immediately that Rouse and Zimm relaxation result in completely different incoherent quasielastic scattering. These differences are revealed in the line shape of the dynamic structure factor or in the (3-parameter if Eq. (23) is applied, as well as in the structure and Q-dependence of the characteristic frequency. In the case of dominant hydrodynamic interaction, Q(Q) depends on the viscosity of the pure solvent, but on no molecular parameters and varies with the third power of Q, whereas with failing hydrodynamic interaction it is determined by the inverse of the friction per mean square segment length and varies with the fourth power of Q. 

In this group of disperse systems we will focus on particles, which could be solid, liquid or gaseous, dispersed in a liquid medium. The particle size may be a few nanometres up to a few micrometres. Above this size the chemical nature of the particles rapidly becomes unimportant and the hydrodynamic interactions, particle shape and geometry dominate the flow. This is also our starting point for particles within the colloidal domain although we will see that interparticle forces are of great importance. 

In general, the motion of a polymer chain in solution is governed by intermolecular interaction, hydrodynamic interaction, Brownian random force, and external field. The hydrodynamic interaction consists of the intra- and intermolecular ones. The intramolecular hydrodynamic interaction and Brownian force play dominant roles in dilute solution, while the intermolecular interaction and the intermolecular hydrodynamic interaction become important as the concentration increases. 

The intrinsic viscosity of native and denatured soy proteins have been measured (13). These values, which reflect the hydrodynamic properties oT the protein molecules at infinite dilution, are of little interest to us as far as functionality is concerned. What is of interest is the apparent viscosity of concentrated slurries. In these slurries, the intermolecular protein-protein interactions dominate and are primarily responsible for the observed viscosity behavior. 

FIG. 16.9 Logarithmic plots of [G ]R and [G"]R vs. cot, for bead-spring models. (A) Rouse free-draining (negligible hydrodynamic interaction) (B) Zimm non-draining (dominant hydrodynamic interaction). After Ferry, General References, 1980. 

In theta solvents, experimental results confirm the scaling predicted for [rjh in the limit of dominant hydrodynamic interaction. In good solvents, the measured exponent is generally slightly less than the value, 4/5, predicted for dominant hydrodynamic interaction. The scaling law, [jyJo = for a flexible polymer in a theta solvent is often used to... 

Figure 3.13 Linear viscoelastic data (symbols) for polystyrene in two theta solvents, decalin and diocty Iphthalate, compared to the predictions (lines) of the Zimm theory with dominant hydrodynamic interaction, h = oo. The reduced storage and loss moduli and G are defined by = [G ]M/NAksT and G s [G"]M/A /cbT, where the brackets denote intrinsic values extrapolated to zero concentration, [G jj] = limc o(G /c) and [G j ] = limc +o[(G" — cor)s]/c), and c is the mass of polymer per unit volume of solution. The characteristic relaxation time to is given by to = [rj]oMrjs/NAkBT. For frequencies ro

Label Effect. In order to assess at least partially the effect of the label on the chain dynamics, we also performed measurements on dilute solutions of 9,10-dimethyl anthracene. The reorientation time for the free dye in cyclohexane was - 10 psec, 50 times faster than the time scale for motion of the labeled chain in cyclohexane. Hence we conclude that the observed correlation functions are not dominated by the hydrodynamic interaction of the chromophore itself with the solvent, but can be attributed to the polymer chain motions. 

This comparison indicates that the hydrodynamic interaction of the label with the solvent does not dominate the observed dynamics. 

Hess [13] neglected the hydrodynamic interactions among chain beads and treated the global motions of different chains as uncorrelated (this is to assume a small number of chain-chain contacts and thus to focus on the semi-dilute regime). He deduced that polymer self-diffusion consists of both lateral and longitudinal modes of chain motion until the entanglement parameter t/>(c, N) reaches unity, but it is dominated by the latter (i.e., chains move reptatively)... 

The comparatively lowest importance have the hydrodynamic interactions, their role is important at low concentration of the solid phase in the suspension. In the pastes, in which the share of solid phase is substantial, the electrostatic and van der Waals forces are dominating. Moreover, because of the high surface tension of water and the presence of air in the paste, between cement grains the attractive capillary forces appear. They prevail at the grain size from 1 to 0.1 mm. The maximum capillary stress is given by the following Carman formula ... 

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