Incommensurate smectic-Aphase in the general model of frustrated smectic phases

An incommensurate smectic-A phase (${\mathrm{SA}}_i$) made of two collinear independent density modulations at two incommensurate wave vectors is found to be stable in the phenomenological model of frustrated smectic phases of Prost in mean-field theory. The N-${\mathrm{SA}}_1$-${\mathrm{SA}}_d$-${\mathrm{SA}}_2$-${\mathrm{SA}}_i$ phase diagram is computed; its representation in appropriate axis (i.e., temperature, incommensurability) is fully compatible with the experimental topology recently reported in a binary mixture of 4-n-heptyloxyphenyl-4’-cyanobenzoyloxybenzoate (DB7OCN) and 4-octyloxy-4’-cyanobiphenyl (8OCB).