Colloid-Brush Interactions: The Effect of Solvent Quality

Solvent quality affects the interactions between neutral polymer brushes and colloids as manifested in the concentration profiles of the colloidal particles, c(prt)(z), and the corresponding adsorption isotherms. Lowering the solvent quality, and eventual brush collapse, reduce the osmotic pressure at height z within the brush, Pi(z), and with it the associated free energy penalty of inserting a particle into the brush, F-ins(z). Brush collapse thus favors penetration into the brush and adsorption within it, an effect utilized in tissue engineering, chromatography etc. In the self-consistent field theory of brushes, the effect reflects both the amplitude and form of Pi(z). For good, Theta, and poor solvents, denoted by i =g, Theta, and p, the Pi(z) profile is Pi(i)(z) = Pi(i)(0)u(i)(mi) where H-i is the brush height and u(i) = 1 - z(2)/H-i(2). The analysis utilizes the known m(g) = 2, m(Theta) = 3/2 as well as the derived m(p) = 1 together with Pi(p)(0)/Pi(g)(0) similar to H-p/H-g and Pi(Theta)(0)/Pi(g)(0) similar to H-Theta/H-g. F-ins(z) approximate to Pi(i)(z)R-3 incurred by spherical particles of radius R << H-i is significant for R > R-ins(i) similar to Pi(-1/3)(i) (0) where R-ins(i) scales with the grafting density sigma as sigma(-4/9), sigma(-1/2), and sigma(-2/3), respectively. For non-adsorbing particles with R >> R-ins(i) the particles penetrate the brush to a depth of delta(ins)/H-i approximate to (R-ins(i)/R)(ri) with r(i) = 3/2, 2, 3, and delta(ins)(g) > delta(ins)(Theta) > delta(ins)(p). Primary adsorption at the wall due to wall-particle contact attraction energy Ek(B)T is repressed when R > (ERins)-R-1/3(i). Ternary adsorption due to weak monomer-particle attraction is driven by a free energy scaling as similar to phi(z)R-2 and thus stronger in poor solvents when the monomer volume fraction phi(z) is higher. Accordingly, the associated c(prt)(z) is high for particles large enough to accumulate k(B)T or more of attractive monomer-particle contacts but small enough to avoid large F-ins(z).