Hydrodynamic thickness of adsorbed polymer layers

Several methods may be applied to determine the hydrodynamic thickness of adsorbed polymer layers, of which viscosity, sedimentation coefficient (using an ultracentrifuge) and dynamic light scattering measurements are the most convenient. A less accurate method is from zeta potential measurements. These techniques are based on hydrodynamic techniques and these are discussed below. 

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. 

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.

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). 

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. 

Garvey et al.85) made a similar sedimentation study on poly(vinyl alcohol) adsorbed on polystyrene latex particles. Adsorbance of the polymer was also measured. Both the thickness of the adsorbed layer and the adsorbance increased linearly with the square root of the molecular weight. The volume occupied by a polymer molecule in the adsorbed layer was approximately equal to that of the effective hydrodynamic sphere in bulk solution. However, the measured values of LH were greater than the hydrodynamic diameters of the polymer coils in solution. Thus, it may be concluded that adsorbed poly(vinyl alcohol) assumes a conformation elongated in the direction normal to the surface. 

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. 

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. 

When two particles each with a radius R and containing an adsorbed polymer layer with a hydrodynamic thickness 5j, approach each other to a surface-surface separation distance h that is smaller than 25, the polymer layers interact with each other, resulting in two main situations [12] (i) the polymer chains may overlap with each other and/or (ii) the polymer layer may undergo some compression. In both cases, there will be an increase in the local segment density of the polymer chains in the interaction region. However, the real situation is perhaps in between the above two cases - that is, the polymer chains may undergo 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. 

Several methods may be used to determine the adsorbed layer thickness, 8. Most of the methods depend on measuring the hydrodynamic radius of the particles with and without the adsorbed polymer layer. For example, one may measure the relative viscosity, of a dispersion with an adsorbed polymer layer. Assuming that the particles behave as hard spheres (when 8 is small compared with the particle radius R) of noninteracting units (low volume fraction of the disperse phase), can be related to the effective volume fraction, [Pg.355]

By carrying out the measurements in the presence and absence of polymer layers, one can obtain 8. In the presence of an adsorbed polymer layer, the hydrodynamic radius is the sum of the core radius and the adsorbed layer thickness, whereas in the absence of the polymer layer, 7 is simply the core radius. Again, as with the viscosity technique, this method cannot be directly applied to emulsions, which are polydisperse and with a radius that is large for significant Brownian motion. 

The second most common parameter used to characterize the polymer layer is its thickness. The layer thickness is the principal factor in defining the effectiveness of the polymer as a steric stabilizer. The thickness of the adsorbed layer is usually defined as the distance of the plane of shear from the particle surface. This distance is generally referred to as the hydrodynamic thickness, 8, and is obtained from several different techniques such as measurement of the diffusion coefficient, sedimentation coefficient, or electrophoretic mobility of the particles with and without the presence of the adsorbed polymer layer. 

Colloidal suspensions can be classified as soft sphere systems because the repulsive intoactions occur at some characteristic distance from the particle surface. For electrostatic and stoic stabilization, this distance is the Debye length (1/ K) and the thickness of the adsorbed polymer layer, respectively. For stoically stabilized suspensions, the adsorbed polymer layer leads to an increase in the hydrodynamic radius of the particle. When the adsorbed layer is densely packed, the principles described above for hard sphere systems are applicable, provided that the volume fraction of particles/is replaced by an effective volume fraction /gy given by... 

Measuring electrokinetic potentials before and after polymer adsorption, that is, the Stern potential of the bare quartz surface ij/i and C potential, which reflect a shift in the position of slipping plane, it becomes in principle possible to assess the hydrodynamic thickness 5 of an adsorbed polymer layer. Assuming that presence of polymer does not change significantly the exponential distribution of local potential values il/(x) in the electrical double layer, the hydrodynamic thickness may be calculated from the Gouy equation... 

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