Non-DLVO, steric and fluctuation forces

Protrusion Forces III▶ The protrusion force between two amphiphilic surfacesLateral dimension σExtending a distance z i into the solutionΓ protrusion sites per unit area,by potential distribution theorem (Eq. 4.9)The interaction free energyW ( D)= −ΓkTln{ ∫ dz2∫D D−Z2 2−αp D / kTexp[ −αp(z1+ z2)/kT]dz1}= −ΓkTln{( kT / αp)[1 − (1 + Dαp/ kT)e0 0]}Protrusion pressureP−αD / kT2p−D/ λ( ΓαpD/ kT ) eΓαp( D / λ)eD)= −∂W/ ∂D==(14.11)−αpD/ kT−Dλ[1 − (1 + α / ) ] [1 (1 D / λ)e ]pDkT e − +λ < D < 10 λ P(D) = 2.7 Г α pe -D/ λ (λ ≈ kT/α p) (14.12)(/D < λP( D → 0) = 2ΓkT/ D(14.13)