Steric Interactions Polymer Adsorption

As before, we consider the interaction of two flat plates coated by grafted polymeric layers. Once the interaction between the two flat surfaces is known, the Derejaguin approximation and virial expansion can be used to determine the stability of the spherical colloidal dispersion as described previously. 

The physics of the polymer brush (see Fig. 7.5) has been treated in several approximations. In the simplest approach, the polymers are all assumed to terminate on the same surface z = h, while a more accurate description takes into account the distribution of ends in the region between the grafting surface and the top of the brush in a self-consistent manner For simplicity, we consider an intermediate approach where the probability to find a polymer end is proportional to the density, c(z). We consider a polymer in a good 

The free energy per unit area, y, of the brush is thus written  

The Lagrange multiplier, (jl, is fixed so that f c(z)dz = N, where d is the area per chain on the surface. One finds 

The polymers are strongly stretched h N) compared to their extent in solution (where their size scales with the much smaller quantity, although if d a V (i.e., the area per chain is large), the chains are not nearly fully stretched (Le., although h Na, h may be much smaller than Na as indicated by Eq. (7.28) in the limit that d a v). 

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Polymer molecules are often employed to stabilize colloids [1]. In most theoretical treatments of the effect of polymer adsorption [2-5], only the steric force is taken into account, and the steric force and the traditional double-layer force for particles devoid of hairs are assumed to be additive. The steric force is a short-range interaction which acts only when the chains on the surfaces of the two particles interpenetrate [6-8]. However, in addition to this short-range interaction, a hairy surface can also generate another effect, because it can change the dielectric constant in the vicinity of the surface. 

If the grafted polymer is not adsorbed on the second plate, then the grafted polymer provides only steric interaction between the plates. This repulsive steric interaction increases the stability of the colloidal system. To calculate the steric interaction between two plates, the adsorption constant Kads in eq 11 should be taken to be zero in this case. 

If the grafted polymer molecules are also adsorbed on the second plate, then the force between the two plates includes both bridging and steric interactions. In this case, the adsorption contributions to the total free energy must be included among the free-energy contributions. When the polymer is charged, eqs... 

Whatever the mechanism is, particles adhere spontaneously if, at constant temperature and pressure, the Gibbs energy G of the system decreases. The main contributions to the Gibbs energy of particle adhesion A Gad are from electrostatic, hydrophobic and dispersion forces,1 5 and, furthermore, in case of protein adsorption, from rearrangements in the structure of the protein molecule.6 9 When the sorbent surface is not smooth but hairy , additional, mainly steric, interactions come into play.4,10 12 Hairy surfaces are often encountered in nature as a result of adsorbed or grafted natural polymers, such as polysaccharides, that reach out in the surrounding medium with some flexibility. Interaction of particles with such hairy surfaces will be dealt with in section 3. 

The hard sphere interaction energy is an accurate approximation for short-range interactions between particles. This occurs when we have steric stabilization [33,34] due to polymer adsorption and electrostatic stabilization with a thin double layer [35,36] (i.e., high ionic... 

Tiller and O Melia (1993) compared their polymer adsorption statistics calculations with data from laboratory experiments on the interaction of polyacrylic and polyaspartic acid as well as of humic acids with hematite. Their conclusion is that, at low ionic strength, anionic polyelectrolytes affect the coagulation of positively charged particles by altering the net surface charge in a way similar to that of multivalent, monomeric anions. Steric repulsion, at low ionic strength (i.e., in fresh water), plays little or no role in the stabilization of hematite colloids by the organic macromolecules used in their work calcium... 

The colloidal stabilization of aqueous dispersions by polymer surfactants is believed to be a result of the adsorption of the amphiphilic macromolecules on the particle surface. This adsorption results in the formation of mono- or multi-layers of certain structure and thickness which provide sterical and/or electrostatic stabilization effects [1-5], Polymer adsorption from aqueous solution on a particle surface is a result of specific interactions of various active sites on the particle surface with corresponding sites (groups) of the macromolecule. Therefore the adsorption behaviour and the colloidal stabilization may be used as a sensitive approach (tool) to elucidate the effects of the polymers structural differences on their behaviour on the liquid-solid interface [6-9],... 

An analysis presented of the forces contributing to the attraction and repulsion interactions between macromolecules in acrylate latices. The electrostatic repulsion forces, enthalpy and entropy effects, and the attraction forces from the expanded Hamaker equation are analysed. The influence of the structure of copolymers consisting of monomeric units of alkyl acrylate or methacrylate (methyl to n-butyl) and acryhc or methacryhc acid on the physico-chemical properties of the latices and their stabihty were determined. On the basis of experiments and calculations it was established that the stability of latices is decided by two mechanisms. The first (ionic stabilisation) consists in adsorption of anionic emulsifier particles, and the second (ionic-steric stabilisation) involves adsorption of such an emulsifier on an adsorption layer formed by the polymer macromolecules forming the latex. 25 refs. Articles from this journal can be requested for translation by subscribers to the Rapra produced International Polymer Science and Technology. 

Adsorbed on the surface of dispersed particles, polymer chains lessen the attraction energy by steric reasons (the minimum distance to which particles can approach increases) and because they change the efficient Hamaker s constant value. The attraction energy in expressions for Ur dependence on A is the function of not only interaction constants of dispersed phase A, dispersion medium A2 and the phase with the medium A 2, but of Gamaker s constant for adsorption layer 3 too. The effect of polymer adsorption layers on molecular attraction of particles has been described theoret-ically. Below is an expression for Ur, based on the Lifshits macroscopic theory... 

Polymer adsorption may result in bridging attraction or steric repulsion between two particles. The scaling theory of polymer adsorption that accounts for the interactiOTi between the polymer and the surface and for variation of polymer concentration near the surface [53, 54] was used for derivation of the interaction potential between two spherical colloidal particles coated by polymer [55-57] ... 

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