Thickness of the adsorbed polymer layer

Results indicated that poly(DADMAC) will reduce damage caused by contact of low salinity fluid lost from the cement slurry with swelling clays present in the formation. An increase in poly (DADMAC) molecular weight from 600,000 to 2.6 X 10 daltons resulted in a decreased polymer effectiveness. The test columns were of relatively high permeability so the thickness of the adsorbed polymer layer, predicted to be greater for the higher molecular weight polymer, would have little effect on the observed flow rates. 

The thickness of the adsorbed polymer layer at each dose level was thus estimated from the following sequence of steps ... 

Other dimensionless groups that compare the thickness of the adsorbed polymer layer to the radius of the particle or the radius of gyration of the polymer to the particle radius in polymer/colloid mixtures can also be easily defined. We are mostly concerned with the volume fraction and the Peclet number Pe in our discussions in this chapter. However, the other dimensionless groups may appear in the equations for intrinsic viscosity of dispersions when the dominant effects are electroviscous or sterically induced. 

Polymer adsorption has been reviewed by many authors28-37. An earlier volume of this journal presented an article which dealt with polymer adsorption studies made before 196429. This paper gives a review of subsequent advances in this field of study. In Chap. B, the principal theories are described, confining ourselves to those which are amenable to experimental teste. Chapter C gives a brief survey of typical measuring techniques. In Chap. D, important experimental data on the thickness of the adsorbed polymer layer and the fraction of adsorbed segments are summarized and discussed, along with their comparison with relevant theories. 

As has been depicted in Fig. 1, various conformations are possible for adsorbed polymers, depending on polymer-polymer, polymer-solvent, and polymer-interface interactions and the flexibility of polymers. To determine experimentally the conformation of adsorbed polymers only adsorption isotherm data are insufficient. The average thickness of the adsorbed polymer layer, the segment density distribution in this layer, the fraction of adsorbed segments, and the fraction of surface sites occupied by adsorbed segments must be measured. Recently, several unique techniques have become available to measure these quantities. 

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. 

Ohm26,78-79), among others, called attention to the anomalous viscosity behavior of polymer solutions at very low concentration. Plots of j sp/C against C were found to curve either down or up at such concentrations, and the anomaly was attributed to the adsorption of polymer molecules onto the capillary wall. In order to calculate the thickness of the adsorbed polymer layer, Ohrn used the equation... 

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. 

Our first attempt to apply electro-optics in the investigation of the adsorption of neutral polyacrylamide on kaolinite particles was in 1988 [4,5]. Several electro-optical parameters were used to follow the adsorption of polymer on colloid particles—the amplitude of the electro-optical effect, the critical frequency of relaxation of the low- and high-frequency effects, the electro-optical decay time after the switching off of the electric field. Variations in these parameters with concentration of the added polymer give information on the particle electric polarizability, the thickness of the adsorbed polymer layer, the size of aggregates that appear in the suspension due to flocculation [4-10], etc. 

At point B, the accommodation of additional chains has reached its maximum. The relative crowding of the chains at point B means that the molecules will not be able to attain their true statistical equilibrium conformations instead, a pseudoequilibrium will be attained. In the region between A and B, it is usually found that the thickness of the adsorbed polymer layer increases, since more units of each chain are forced further away from the adsorbent surface (longer loops and tails are formed see Fig. 14.4). 

The thickness of the adsorbed polymer layer may also be calculated from electrophoretic mobility measurements by calculating the zeta-potential at the plane of shear of the particle. This potential corresponds to the potential at the periphery of the adsorbed layer. By also measuring the zeta-potential of the bare particle and assuming a value of 4 A for the Stern layer, use of Eq. 15 allows the calculation of be, the electrokinetic thickness of the adsorbed layer (13). 

A Variable Angle Spectroscopic EUipsometer of the type M200-F (J.A. Woollam Co. Inc., Lincoln, USA) with a spectral range from 245 to 995 nm was used to determine the thickness of the adsorbed polymer layers. Measurements were performed in ambient at three different angles (65, 70, and 75° with respect to the surface normal). For each polymer adlayer, i.e. Sil-PEG (from toluene), Sil-PEG (from acidic aqueous solution), and PLL-g-PEG (from aqueous HEPES buffer), five samples were prepared to obtain statistical data. The measurements were fitted with multilayer models using WVASE32 analysis software. The analysis of optical constants was based on a bulk silicon/ SiOj, layer, fitted in accordance with the Jellison model. After adsorption of the molecules, the adlayer thickness was determined using a Cauchy model A = 1.45, B = 0.01, C = 0). 

Figure 4.31 Schematic illustration of the conformation of an anionic polyelectrolyte on a ceramic surface as a function of pH. (8 is the thickness of the adsorbed polymer layer.) (From Ref. 37.)...

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... 

Dehning a as the particle radius, and 5a as the effective thickness of the adsorbed polymer layer, a linear lit of = 2.1 was found, see Figure 14.26 (90). If the bound chains are assumed to be roughly spherical or perhaps mushroom in shape (see Figure 12.21), then 5a corresponds to the effective diameter of the bound chains. 

The thickness of the adsorbed polymer layer at maximum adsor-bance was found to be proportional to the square root of the molecular weightDiMarzio and McCrackin, from their one-dimensional study of adsorption under conditions of independent adsorption sites, predicted an increase in the extension from the surface that is proportional to the square root of the molecular weight. 

The kinetics of polymer adsorption has also been studied in capillary flow by measiuing the electrokinetic streaming potential [ 0], In this method one measures the Z-potential which can be related to the position of the surface of shear, fi om which the thickness of the adsorbed polymer layer may be inferred. The method is particularly sensitive for detecting tails protruding into the solution. 

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