Polymers adsorption isotherms

Equation 14 is an approximate, single expression for the polymer adsorption isotherm. At very low concentrations, when G is very... 

Figure 1. Typical polymer adsorption isotherms for n=10 with various values of K. Note the broad plateau regions for the...

To determine which mechanism is operative, it is necessary to obtain information on the extent of adsorption of the polymer (adsorption isotherm), the effect of the adsorbed polymer on the... 

Figure 6.7. A typical high-afflnty polymer adsorption isotherm.

Figure 5.11. A sketch of a typical polymer adsorption isotherm for a polymer in a good solvent adsorbed onto a solid surface, showing the characteristics of a high-affinity isotherm.

Figure 1 A high-affinity polymer adsorption isotherm, which relates the amount of polymer at the particle surface to the amount of polymer in solution (solid line) and a low-affinity Langmuir-...

Polymer adsorption isotherms and residual resistance factors differ between rock types and are given in Sorbie etal. (1982)... 

We have to be aware that for complicated deformable molecules such as polymers, A may depend on 9 As a rule of thumb, we can say that polymer adsorption isotherms are characterized by a very high affinity, represented by a high value of K. The equilibrium concentration is extremely (undetactably) small up to values very close to samration, then it suddenly shoots up very steeply [ 1 ] and c becomes equal to c . This implies that the rate of adsorption drops strongly near saturation, so that the kinetic curve has a sharp break (see Fig. 1). As long as we are not very close to samration we can set equal to zero and rewrite Eq. (10) in a linearized form ... 

Polymers typically exhibit a high-affinity adsorption isotherm as shown in Fig. XI-5 here the adsorbed amount increases very rapidly with bulk concentration and then becomes practically independent of concentration. 

Fig. XI-5. Adsorption isotherm from Ref. 61 for polystyrene on chrome in cyclohexane at the polymer theta condition. The polymer molecular weights x 10 are (-0) 11, (O) 67, (( )) 242, (( )) 762, and (O) 1340. Note that all the isotherms have a high-affinity form except for the two lowest molecular weights.

Adsorption of dispersants at the soHd—Hquid interface from solution is normally measured by changes in the concentration of the dispersant after adsorption has occurred, and plotted as an adsorption isotherm. A classification system of adsorption isotherms has been developed to identify the mechanisms that may be operating, such as monolayer vs multilayer adsorption, and chemisorption vs physical adsorption (8). For moderate to high mol wt polymeric dispersants, the low energy (equiUbrium) configurations of the adsorbed layer are typically about 3—30 nm thick. Normally, the adsorption is monolayer, since the thickness of the first layer significantly reduces attraction for a second layer, unless the polymer is very low mol wt or adsorbs by being nearly immiscible with the solvent. 

Adsorption is determined by the depletion method using a Dohrmann DC 80 carbon analyzer. The mineral is contacted with the polymer solution and agitated with a mechanical tumbler for 24 hours, a time which has been verified to be sufficient for adsorption to be complete (9). A more detailed description of experimental procedures is given elsewhere (10). All the data reported in this study are taken in the plateau region of the adsorption isotherm. 

Fig. 2. Schematics of adsorption isotherms for polymers, where the adsorbed mass r per unit area of the sorbent surface is plotted against the polymer concentration cp in solution. The steep initial slope of the isotherms indicates...

An approximate analysis of polymer adsorption as a set of sequential reactions leads to a simple equation for the adsorption isotherm expressed in terms of three parameters. Comparison of the model with recently published statistical theories reveals remarkable agreement in both the general shape of the isotherms and the predicted effects of molecular weight. The problems of applying such models to experimental data are discussed. 

A major advantage of the simple model described in this paper lies in its potential applicability to the direct evaluation of experimental data. Unfortunately, it is clear from the form of the typical isotherms, especially those for high polymers (large n) that, even with a simple model, this presents considerable difficulty. The problems can be seen clearly by consideration of some typical polymer adsorption data. Experimental isotherms for the adsorption of commercial polymer flocculants on a kaolin clay are shown in Figure 4. These data were obtained, in the usual way, by determination of residual polymer concentrations after equilibration with the solid. In general, such methods are limited at both extremes of the concentration scale. Serious errors arise at low concentration due to loss in precision of the analytical technique and at high concentration because the amount adsorbed is determined by the difference between two large numbers. 

The equilibrium model for the adsorption of polymers at solid-liquid interfaces recently presented by Hogg and Mirville (1) has been evaluated at some length. It has been shown that, for polymers consisting of a reasonably large number of segments, the adsorption isotherms can be closely approximated by an expression of the form ... 

Recent polymer adsorption theories, such as those of Roe (3) and of Scheutjens and Fleer (h) allow the calculation of displacement isotherms, so that we could study the dependency of these isotherms on various parameters by numerical methods. However, all the essential features of displacement can also be demonstrated by means of a simple analytical expression for the critical point, which can be derived in a straightforward way. 

Determination of the segmental adsorption energy. The determina-tion of x ° is also possible. Since x d can be found from Equation 5 if Xsc an the solvency terms are known, we can add xf° and find x ° by Equation 1. The determination of xf° calls for a separate experiment, e.g., an adsorption isotherm of the displacer from solvent, in the absence of polymer. Following such a scheme we used the values of cr obtained from the displacement isotherms of Figure 3 and 4 to determine segmental adsorption energy parameters Xg° for PVP on silica. The required additional information on xdo was obtained from the initial slopes of dis-... 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

Polymer adsorption is important in the flocculation and stabilization of colloidal sols and has been reviewed by Vincent et al. (1) and Tadros (2). Polyvinyl alcohol (PVA) has been used in these studies because of its practical application in textiles, adhesives, and coatings. The adsorption of PVA has been studied on silver iodide by Fleer (3) and Koopal (4), and on polystyrene (PS) latex particles by Garvey (5). The adsorption isotherms reported by these workers extend up to 600 ppm PVA. The adsorption at... 

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

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