Hydrodynamic thickness adsorbed polymers

Dhinojwala A and Granick S 1997 Surface forces In the tapping mode solvent permeability and hydrodynamic thickness of adsorbed polymer brushes Macromoiecuies 30 1079-85... 

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

In this paper we present results for a series of PEO fractions physically adsorbed on per-deutero polystyrene latex (PSL) in the plateau region of the adsorption isotherm. Hydro-dynamic and adsorption measurements have also been made on this system. Using a porous layer theory developed recently by Cohen Stuart (10) we have calculated the hydrodynamic thickness of these adsorbed polymers directly from the experimental density profiles. The results are then compared with model calculations based on density profiles obtained from the Scheutjens and Fleer (SF) layer model of polymer adsorption (11). 

Segment density profiles and hydrodynamic thickness measurements have been made for polyethylene oxides adsorbed on polystyrene latex. Comparison with theoretical models shows that the hydro-dynamic thickness is determined by polymer segments (tails) at the extremity of the distribution. It is also concluded that the sensitivity of the s.a.n.s. experiment precludes the measurement of segments in this region and that the experimental segment density profiles are essentially dominated by loops and trains. 

The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

Measurements of hydrodynamic thickness LH have been performed by many investigators and, in most cases, the measured LH were almost twice the radii of gyration of polymer coils in bulk solution. It is desirable to clarify the theoretical relationship between LH and the root-mean-square thickness of the adsorbed polymer layer. Some progress in this direction has been made recently. 

The high precision of the disk centrifuge allowed the comparison of sedimentation velocities of colloidal particles with and without an adsorbed polymer layer, from which the hydrodynamic thickness of the adsorbed layer could be calculated (4). Here the disk centrifuge, giving complete size distributions, made the use of monodisperse samples unnecessary. 

Hydration and conformation of protective polymers generally depend on the thermodynamic parameters. The thickness of an adsorbed layer of polymer has been studied using latex as the substrate. An apparent hydrodynamic thickness... 

Figure 4.42. Determination of the hydrodynamic thickness of adsorbed charge-free polymer layers from the slope of the mobility curve near the Isoelectric point.

Various methods have been proposed to measure the thickness of an adsorbed polymer layer. Depending on the method, a different property of the layer is determined. For example, hydrodynamic and electroklnetlc techniques probe the extension of the tails and give a thickness which may exceed considerably the average thickness as obtained from ellipsometry or from the reflected or scattered intensity of visible light, of X-rays, or of neutron radiation. In this section we can touch upon Just a few aspects of the various techniques. 

The method of capillary Jlow measures the increase in resistance for solvent flow through a capillary (or a porous plug) due to an adsorbed polymer layer. This increase can be translated into a smaller effective capillary (or pore) radius through the Hagen-Polseuille law (1.6.4.18). The hydrodynamic radius d is supposed to be given by the difference between the "covered" and the "bare" radius. In such experiments the observed hydrodynamic thickness sometimes turns out to be flow-rate dependent. In such cases an extrapolation to zero flow rate needs to be carried out. 

One would perhaps expect that the hydrod3mamlc and electrokinetic methods measure the same thickness. This is in general not true, however. Contributions to the electrokinetic flux are located exclusively in the electrical double layer (i.e., up to distance of order x ) where the hydrodynamic flux is strongly Impeded by the adsorbed polymer. Also, since the extension of the electrical double layer is variable with the location d of the electrokinetic slip... 

The distribution of segments in loops and tails, p(z), which extend in several layers from the surface. p(z) is usually diflBcult to obtain experimentally, although recently the application of small-angle neutron scattering has been used to obtain such information. An alternative and useful parameter for assessing steric stabilisation is the hydrodynamic thickness, Sf, (the thickness of the adsorbed or grafted polymer layer plus any contribution from the hydration layer). Several methods can be applied to measure 5, as will be discussed below. 

Figure 6.9 shows the adsorption isotherms for PEO with different molecular weights on PS (at room temperature). It can be seen that the amount adsorbed (in mg m" ) is increased in line with increases in the polymer molecular weight [37]. Figure 6.10 shows the variation in hydrodynamic thickness i5(, with molecular weight M. 5), shows a linear increase with log M, and increases with n, the number of segments in the chain, according to ... 

Polymers are also essential for the stabilisation of nonaqueous dispersions, since in this case electrostatic stabilisation is not possible (due to the low dielectric constant of the medium). In order to understand the role of nonionic surfactants and polymers in dispersion stability, it is essential to consider the adsorption and conformation of the surfactant and macromolecule at the solid/liquid interface (this point was discussed in detail in Chapters 5 and 6). With nonionic surfactants of the alcohol ethoxylate-type (which may be represented as A-B stmctures), the hydrophobic chain B (the alkyl group) becomes adsorbed onto the hydrophobic particle or droplet surface so as to leave the strongly hydrated poly(ethylene oxide) (PEO) chain A dangling in solution The latter provides not only the steric repulsion but also a hydrodynamic thickness 5 that is determined by the number of ethylene oxide (EO) units present. The polymeric surfactants used for steric stabilisation are mostly of the A-B-A type, with the hydrophobic B chain [e.g., poly (propylene oxide)] forming the anchor as a result of its being strongly adsorbed onto the hydrophobic particle or oil droplet The A chains consist of hydrophilic components (e.g., EO groups), and these provide the effective steric repulsion. 

When two particles, each with a radius R and containing an adsorbed surfactant or polymer layer with a hydrodynamic thickness 5, approach each other to a surface-surface separation distance h that is smaller than 25, the surfactant or polymer layers interact with each other, with two main outcomes [1] (i) the surfactant or polymer chains may overlap with each other or (ii) the surfactant or polymer layer may undergo some compression. In both cases, there will be an increase in the local segment density of the surfactant or polymer chains in the interaction region this is shown schematically in Figure 8.1. The real-hfe situation perhaps lies between the above two cases, however, with the surfactant or polymer chains undergoing some interpenetration and some compression. 

Adsorption of a polymer necessarily implies a change in the conformation the most common description is the loop-train-tail model (Jenkel and Rum-bach 1951) shown schematically in figure 5.10. The trains are made up of segments in direct contact with the surface, whereas loops have no direct contact with the surface but are in close proximity. Tails are non-adsorbed chain ends. Although tail segments may constitute a small proportion of all segments, they determine the hydrodynamic layer thickness of the adsorbed polymer. Many other properties of adsorbed polymers are determined by the total segment concentration profile as a function of the distance from the surface. 

The Dynamic Light Scattering (DLS) technique was used to measure radii of the PS latex spheres with and without adsorbed polymer brushes. We could then deduce the polymer brush hydrodynamic layer thickness by taking the difference of the radii. DLS measures the intensity autocorrelation as a function of delay time, which gives information on the diffusion constant of particles in a dilute solution. The translational diffusion coefficient, D, is related to the solution temperature T, particle radius r, and solvent viscosity ri by the Stokes-Einstein relation ... 

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