Thickness measurements hydrodynamic, adsorbed

Experimentally, the form of 4>(z) has been recently established for adsorbed homopolymers and terminally anchored tails by the Bristol group (17,20). Knowing 4>(z) one may then calculate the r.m.s. thickness of the adsorbed layer. Previous measurements of the "thickness" (1-4) have usually involved ellipsometry (flat surfaces) or some hydrodynamic technique (particles). In neither case can the calculated thickness be unambiguously related to 4>(z), although recent theoretical work by Cohen Stuart et al. (21), to be discussed at this meeting, has made an attempt to relate the hydro-dynamic thickness, 6, to < >(z). 

Experimental studies of the adsorption of polyelectrolyte have been reported by several authors Pefferkom, Dejardin, and Varoqui (3) measured the hydrodynamic thickness of an alternating copolymer of maleic acid and ethyl vinyl ether adsorbed on the pore walls in cellulose ester filter as a function of the molecular weight and the concentration of NaCl. Robb et al. (4) studied the adsorption of carboxy methyl cellulose and poly (acrylic acid) onto surfaces of insoluble inorganic salts. However, their studies are limited to the measurements of adsorbance and the fraction of adsorbed segments. 

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. 

Concerning the experimental side of polymer adsorption studies the quantity A was only measurable at the early stage of the study, but in 19SS the thickness of the adsorbed layer became accessible to measurement by a hydrodynamic method and in 1961 the quantity p was first determined by infrared spectroscopy. Ellipsometry came up in 1963, which enabled both the adsorbance and the thickness of the adsorbed layer to be measured simultaneously. 

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 ensuing lowering of (3u/3pH) p has been experimentally observed and Is a measure of the hydrodynamic thickness of the adsorbed layer. Let us call this and for the sake of simplicity interpret it as identical to the shift of a slip plane, originally situated at the outer Helmholtz plane (fig. 4.42). Let us also assume that near the p.z.c. the value of is not much affected by the presence of segments in the Stem layer (in the plateau this approximation is poorer). Then [4.10.1) can be applied again, but d /dyr now follows from (3.5.22). Carrying out the differentiation, one obtains... 

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 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. 

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. 

Hydrodynamic Measurements. Hydrodynamic methods rely on the fact that the flow of solvent past a surface having adsorbed poisoners is different from the flow of solvent past an uncovered surface. The thickness measured in this technique is called the hydrodynamic thickness. The difference in pressure drop between a coated and uncoated capillary under identical flow conditions can be used to estimate hydrodynamic film thickness (16). 

We report here, for the first time, that hydrodynamic forces can dramatically Increase the rate of desorption in polymer systems which are otherwise irreversibly adsorbed under no-flow conditions. Indeed, at high enough shear stresses, complete removal of the polymer is possible. The technique of ellipsometry is well suited for this problem as simultaneous measurements of both film thickness and adsorbance are possible during the flow process. 

The major advantage of protein adsorption studies on high surface area materials is that changes of some extensive properties which accompany the process of adsorption are large enough to be directly measured heat of adsorption through microcalorimetry 141), uptake or release of small ions by a combination of electrokinetic methods and titration 142), thickness of adsorbed layer or an increase of the volume fraction of solid phase by a hydrodynamic method like viscometry 143). Chromatographiclike analysis can also be applied to protein adsorption 144). 

Fig. 15. Hydrodynamic thickness (in nm) vs. M, on a long-log scale, for PEO adsorbing on PS latex from water as measured by Cohen Stuart et al. (1984c). The isolated coil diameter is also shown.

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. 

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