MODEL FOR LINE TENSION IN 3-PHASE EQUILIBRIUM

We propose a model free-energy functional of two order parameters with which to calculate the interfacial and line tensions in three-phase equilibrium. The Euler-Lagrange equations for the free-energy minimum are solved exactly, yielding the spatial variation of the order parameters analytically. In terms of a parameter b2 in the model the three interfacial tensions, in dimensionless form, are 1/2(1 + b2), 1/2(1 + b2), and 2. When b2 = 3 the three phases play symmetrical roles and the line tension, again in the appropriate units, is calculated to be -6/pi + 2/-square-root-3 = -0.755.... A wetting transition, where the sum of two of the interfacial tensions becomes equal to the third, occurs as b2 --> 1 +. A quantity that approximates the line tension is found to vanish proportionally to the first power of the vanishing contact angle as the wetting transition is approached.