Adhesion of dense linear polymer chains containing a small number of randomly distributed sticker groups (phi(X)) to a solid substrate containing receptor groups (phi(Y),) has been analyzed by a single-chain scaling approach, An entanglement sink probability (ESP) model motivated by vector percolation explains the nonmonotonic influences of sticker concentration (phi(X)), receptor concentration (phi(Y)), and their interaction strength (chi) on the adhesion strength G(IC) of the polymer-solid interface. The ESP model quantifies the degree of interdigitation between adsorbed and neighboring chains on the basis of the adsorbed chain domain with an extension of the scaling treatment of do Gennes. Here, the adsorbed chain domain changes thermodynamically with respect to the energy of interaction parameter, r = chiphi(X)phi(Y). This model considers the situation of a blend consisting of a small volume fraction of adhesive molecules as a compatibilizer at the interface, where these molecules promote adhesion by adsorbing to the surface via sticker-receptor interactions. The percolation model scales solely with r = chiphi(X)phi(Y), and this parameter can be related to both the adhesive potential (G(A)) and the cohesive potential (G(C)). G(A) describes adhesive failure between adsorbed chains and the solid surface and linearly behaves as G(A) similar to r = chiphi(X)phi(Y). The cohesive streng-th between adsorbed and neighboring chains corresponds to G(C) similar to r(-0.5similar to -1.0) = (chiphi(X)phi(Y))(-0.5similar to -1.0). When the fracture stresses for cohesive and adhesive failure are equal, the model predicts maximum adhesion strength at an optimal value of r* Thus, for a given chi value, optimal values phi(X)* and phi(Y)* exist for the sticker and (chiphi(X)phi(Y))* receptor groups, above or below which the fracture energy will not be optimized. Alternatively, if the X-Y interaction strength chi increases, then the number of sticker groups required to achieve the optimum strength decreases. Significantly, the optimum strength is not obtained when the surface is completely covered with receptor groups (phi(Y) = 1) but is closer to 30%. For polybutadiene, the optimum value of r* was determined experimentally (Lee, I.; Wool, R. P. J Adhesion 2001, 75, 299), and typically phi(X)* approximate to 1-3%, phi(Y)* approximate to 25-30%.