Colloid-Brush Interactions: The Effect of Solvent Quality

• Published in: Macromolecules 2011-05, Vol.44 (9), p.3622-3638
• Main Authors: Halperin, A, Kröger, M, Zhulina, E. B
• Format: Article
• Language: English
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/ma200068d

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, Π(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 Π(z). For good, Θ, and poor solvents, denoted by i = g, Θ, and p, the Π(z) profile is Π i (z) = Π i (0)u i m i 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 Θ = 3/2 as well as the derived m p = 1 together with Π p (0)/Π g (0) ∼ H p /H g and ΠΘ(0)/Π g (0) ∼ H Θ/H g . F ins(z) ≈ Π i (z)R 3 incurred by spherical particles of radius R ≪ H i is significant for R > R ins(i) ∼ Π i −1/3(0) where R ins(i) scales with the grafting density σ as σ−4/9, σ−1/2, and σ−2/3, respectively. For non-adsorbing particles with R ≫ R ins(i) the particles penetrate the brush to a depth of δins/H i ≈ (R ins(i)/R) r i with r i = 3/2, 2, 3, and δins(g) > δins(Θ) > δins(p). Primary adsorption at the wall due to wall-particle contact attraction energy Ek B T is repressed when R > E 1/3 R ins(i). Ternary adsorption due to weak monomer-particle attraction is driven by a free energy scaling as ∼ϕ(z)R 2 and thus stronger in poor solvents when the monomer volume fraction ϕ(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).