We investigate a minimal equilibrium polymerization model for the competition between self-assembly on a boundary and in solution that arises when an assembling system is in the presence of an adsorbing interface. Adsorption generally occurs upon cooling, but assembly (equilibrium polymerization) may arise either upon cooling or heating. Both cases are shown to exhibit a coupling between adsorption and self-assembly. When both assembly and adsorption proceed upon cooling, a change in the ratio of the enthalpy of adsorption to the enthalpy of assembly in solution can switch the system between a predominance of self-assembly in solution to assembly on the substrate. If assembly is promoted by heating and adsorption by cooling, as in many self-assembling proteins in aqueous solution, then a self-assembly analog of a closed loop phase boundary is found. In particular, the order parameter for assembly on the surface exhibits a peak as a function of temperature. As demonstrated by illustrative examples, the coupling between surface adsorption and self-assembly provides a powerful means of switching self-assembly processes on and off. Understanding and controlling this switching phenomenon will be useful in designing and directing self-assembly processes on surfaces for applications to nanomanufacturing and in developing treatments for diseases arising from pathological adsorption-induced assembly.
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