Capillary condensation of periodic phases in self-assembling systems

Self-assembling systems confined in slit-like pores of a width L are studie d. We focus on phase transitions between uniform and ordered periodic phase s. As shown by previous experimental and theoretical studies, the periodic phases respond elastically to the applied stress when the size lambda of th e unit cell is much larger than the size of molecules. For such phases a si mple modification of the Kelvin equation for the phase coexistence in a sli t is derived. The shift of the phase transition in confinement is given by two terms. The first term is the standard Kelvin equation, and the second o ne depends on the elastic modulus of the periodic phase. The modified Kelvi n equation (MKE) is verified by explicit calculations in a lattice model fo r oil-water-surfactant mixtures. We show that the two terms can be comparab le even for L similar to 10 lambda. While for L >5 lambda the MKE is obeyed very well in our model, for narrow slits we find significant deviations be tween actual transitions and the MKE, associated with an inelastic behavior of the periodic phase for L <5 lambda. We also show that in self-assemblin g systems a phase which in bulk is not stable for any thermodynamical state (except for a line of muliphase points) can become stable in a slit with p articular external surfaces. (C) 2001 American Institute of Physics.