Surface coverage polymers

For so-called steric stabilization to be effective, tire polymer needs to be attached to tire particles at a sufficiently high surface coverage and a good solvent for tire polymer needs to be used. Under such conditions, a fairly dense polymer bmsh witli tliickness L will be present around the particles. Wlren two particles approach, such tliat r < d + 2L, tire polymer layers may be compressed from tlieir equilibrium configuration, tluis causing a repulsive interaction. 

Finally, we briefly mention interactions due to adsorbing polymers. Block copolymers, witli one block strongly adsorbing to tire particles, have already been mentioned above. Flere, we focus on homopolymers tliat adsorb moderately strongly to tire particles. If tliis can be done such tliat a high surface coverage is achieved, tire adsorbed polymer layer may again produce a steric stabilization between tire particles. 

At lower surface coverage, however, tire possibility exists that one polymer chain may attach itself to two particles. If tire adsorjDtion is strong enough, tliis results in an aggregation of tire particles, known as bridging flocculation [33,46, and 47],... 

A MC study of adsorption of living polymers [28] at hard walls has been carried out in a grand canonical ensemble for semiflexible o- 0 polymer chains and adsorbing interaction e < 0 at the walls of a box of size C. A number of thermodynamic quantities, such as internal energy (per lattice site) U, bulk density (f), surface coverage (the fraction of the wall that is directly covered with segments) 9, specific heat C = C /[k T ]) U ) — U) ), bulk isothermal compressibility... 

A particularly simple lattice model has been utilized by Harris and Rice [129] and subsequently by Stettin et al. [130] to simulate Langmuir mono-layers at the air/water interface chains on a cubic lattice which are confined to a plane at one end. Haas et al. have used the bond-fluctuation model, a more sophisticated chain model which is common in polymer simulations, to study the same system [131]. Amphiphiles are modeled as short chains of monomers which occupy a cube of eight sites on a cubic lattice and are connected by bonds of variable length [132], At high surface coverage, Haas et al. report various lattice artefacts. They conclude that the study... 

FIGURE 4-17 Preconcentrating surfaces based on covalent binding of the ligand to a polymer backbone. Q = charge A = electrode area T = surface coverage. (Reproduced with permission from reference 52.)... 

Fig. 28—Schematic representation of two extreme polymer conformations at the surface of the solid at low surface coverage S is the cross-sectional diameter of the polymer chain, and R is the radius of gyration of the molecule in the bulk [42].

The limitation of this method is the relatively low quantum yield of radical formation by chain scission for most polymers. It will take high doses at short wavelengths (< 300 nm) to produce enough initiating radicals for a complete surface coverage of grafted... 

For various reasons, cathodic deposition is the most favoured. The main advantages are that complete surface coverage is obtained and also, because the coating-insoluble polymer is an insulator (inhibiting deposition), a uniform coating is achieved. 

Figure 3. The effect of degree of polymerization on surface coverage (fractional site occupancy) at various polymer concentrations. The solid lines represent the present model and the symbols correspond to the theory of Scheutjens and Fleer. The parameter values are the same as in Figure 2.

Adsorption and Desorption. The adsorption of PS was carried out by introducing the polymer solutions into the cell via a hypodermic syringe. The solution concentrations used for adsorption were 700 PPM for PS-20, 1000 PPM for PS-8, and 1200 PPM for PS-4. According to the previous work by Takahashi et al. (12), those concentrations are large enough to obtain saturated surface coverages. The solution was kept in the cell over a period of one day to insure equilibrium. At the end of one day the supernatant solution was displaced by the pure solvent. For studies of flow-enhanced desorption the pump was... 

Experimental support for the suggestion that depleted surface layers result in attractive forces (at T 0) has come from recent experiments (J.K. and Y.A., submitted) where mica surfaces partially covered by polystyrene in cyclopentane above the 0-temper-ature show a clear mutual attraction, which disappears when full surface coverage by the polymer is attained. 

For both the Si02-g-PS and the Si02-g-PDMS systems the surface coverage of the polymer was determined by elemental microanalysis. In the former case this was supplemented by thermo-gravimetric analysis. 

In common with some other authors (18-20), Napper removed excess stabilizer from the dispersion medium so as to give the dispersed particles full surface coverage, leaving negligible amounts of free polymer in solution. As the solvency was worsened, no more polymer could be adsorbed, so that critical flocculation conditions do not necessarily correspond to surface saturation. In the present work, which may refer more closely with some practical applications, the stabilizer is kept at the plateau adsorption level but at the expense of complicating the system by the presence of free polymer. Clarke and Vincent (21) have reported on the effect of free polystyrene on the stability of silica with terminally-attached sytrene chains, but the very considerable differences to our studies make an assessment of the possible role played by unadsorbed polymer unproductive. 

Adsorption of nonionic and anionic polyacrylamides on kaolinite clay is studied together with various flocculation properties (settling rate, sediment volume, supernatant clarity and suspension viscosity) under controlled conditions of pH, ionic strength and agitation. Adsorption and flocculation data obtained simultaneously for selected systems were correlated to obtain information on the dependence of flocculation on the surface coverage. Interestingly, optimum polymer concentration and type vary depending upon the flocculation response that is monitored. This is discussed in terms of the different properties of the floes and the floe network that control different flocculation responses. Flocculation itself is examined as the cumulative result of many subprocesses that can depend differently on system properties. 

In order to generate information on the mechanism of flocculation by polymers it is, however, necessary to correlate flocculation with various system properties, particularly adsorption. Thus, if particle/polymer-polymer/particle contact is the aggregation mechanism, the flocculation responses should be expected to continuously increase with surface coverage. On the other hand, if particle/polymer-particle contact is predominant and if the polymer adsorption is essentially irreversible, maximum flocculation might be expected under submonolayer conditions. In order to determine the nature of this relationship for the present systems, selected flocculation responses are plotted in Figures 8 and 9 as a function of surface coverage for the nonionic and the anionic polymer respectively. The assumptions involved in the computation of the surface coverage are to be noted at this point ... 

Flocculation was correlated with both adsorption density and estimated surface coverage for the nonionic and 33% hydrolyzed polyacrylamides. Maximum settling rate was obtained with the nonionic flocculent at 0.1 and with the hydrolyzed sample at 0.2 surface coverage. Supernatant clarity showed a maximum at a surface coverage of Na-kaolinite by the hydrolyzed polyacrylamide of 0.1. At higher surface coverages (such as 0.5) considered in the past to be optimum for flocculation, complete dispersion was obtained with both the nonionic and the anionic polymer. 

The viscoelastic behavior of concentrated (20% w/w)aqueous polystryene latex dispersions (particle radius 92nm), in the presence of physically adsorbed poly(vinyl alcohol), has been investigated as a function of surface coverage by the polymer using creep measurements. From the creep curves both the instantaneous shear modulus, G0, and residual viscosity, nQ, were calculated. 

The increase in the rheological parameters, ri0> G0 and 1(5 with reduction in surface coverage points towards an increase in particle interaction. This could be the result of either flocculation by polymer "bridging" (which is favourable at coverages <0.5) or as a result of coagulation due to the van der Waals attraction between the "bare" patches on the particles. In the absence of any quantitative relationship between interaction forces and rheology, it is clearly difficult... 

The two major theories of flocculation, the bridging model (1) and the electrostatic patch model (2, 3 ), provide the conceptual framework for the understanding of polymer-aided flocculation, but they do not directly address the kinetics of the process. Smellie and La Mer (4) incorporated the bridging concept into a kinetic model of flocculation. They proposed that the collision efficiency in the flocculation process should be a function of the fractional surface coverage, 0. Using a modified Smoluchowski equation, they wrote for the initial flocculation rate... 

This approach is based on the assumption that polymer adsorption is fast ("instantaneous") compared with flocculation. In other words the surface coverage is taken to be constant during the flocculation process. Equation (1) states that the flocculation rate tends to zero when 0 tends to 0 or 1. The maximum rate occurs at 0 = 0.5, i.e., at 50% surface coverage. 

The flocculation rate dependency on the fractional surface coverage 0 in Equation (1) has been qualitatively confirmed (13, 14), although the maximum rate appears to occur for a surface coverage of less than 50%. The adsorption rate is also a function of 0, and it has been shown (15) for adsorption onto a smooth solid surface that the rate is proportional to the fraction of polymer-free surface area, 1-0. This approach has not... 

Flocculation experiments were also performed with half of the latex pretreated with polymer to ensure complete surface coverage. Coagulation rates were determined using aluminum chloride at pH 3. 

It has been assumed that the total surface area of a floe is proportional to the number of singlets in that floe, a reasonable assumption for small floes and open floe structures. The effective fractional surface coverage, 0k, is not necessarily equal to the fractional surface coverage at equilibrium for a given amount of adsorbed polymer. This will be discussed in some detail below. 

---