Statistical theory of the compensating effect when anchoring with two orthogonal photoaligned polymers

In this paper we extend a statistical microscopic analysis to the anchoring properties of polymer films obtained by two concomitant or subsequent polymerization processes along two different directions. We can thus explain the recently observed compensating effect of two orthogonal polymerization processes. An expression for the anchoring energy has been evaluated from the extra Helmholtz free energy within an interface layer where the interactions shift from polymer-nematic interactions to nematic-nematic interactions, as in bulk. The result includes the angular dependence on the two photoaligning directions. A procedure of getting controlled anchoring strength in situ is suggested.