Scaling theory for end-functionalized polymers confined between two surfaces: Predictions for fabricating polymer/clay nanocomposites

Using scaling theory, we investigate the equilibrium behavior of a melt of functionalized chains, nonfunctionalized polymers, and two infinite, planar surfaces, which model clay sheets. The functionalized chains contain two end groups (one at each chain end) that are highly attracted to the surfaces. We calculate the free energy of the system as a function of the separation between the surfaces for various values of the following parameters: the end-group adsorption energy, the length and volume fraction of the end-functionalized chains, and the interaction energy between the different chains. For polymers confined between the surfaces, we also determine the fraction of loops, tails, bridges, and free chains within this gap. Finally, we isolate conditions for the formation of “exfoliated,” “intercalated,” and immiscible polymer/clay mixtures.

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