Second-order susceptibility tensor of a monolayer at the liquid–air interface: SHG spectroscopy by compression

The complete expression for the macroscopic second-order susceptibility (SOS) tensor χ(2) for a monolayer with C∞ symmetry at the air–liquid interface is derived as functions of the molecular SOS tensor α(2) and the orientational order parameters. The chiral (non-chiral) terms of χ(2) are distinguished by their association with even (odd) order parameters, by which a second-harmonic generation (SHG) circular-dichroism effect can be better understood. An SHG experiment of a 4-cyano-4′-5-alkyl-biphenyl monolayer on an air–water interface by monolayer compression is also discussed.