Quantitative analysis of orientational order in the molecular monolayer by surface second harmonic generation

We have developed a systematic approach to quantitatively determine the orientational order of molecular monolayer based on surface second harmonic generation (SHG) measurement. Traditionally, the experimentally obtainable orientational parameter $D=〈cos θ〉/〈cos3 θ〉$ has been used to determine the averaged orientational angle θ with SHG. Also, it has been widely accepted that without the help from other techniques, SHG was insufficient for determination of both the orientational angle $θ0$ and its distribution Δθ. Here, we derived an explicit and general functional form, $R(θ)=|〈cos θ〉−c * 〈cos3 θ〉|2,$ which is orientationally dependent and is proportional to the SH intensity measured from the molecular monolayer. We further showed that $R(θ)$ contains the full information of the orientational order of the molecular monolayer, and the orientational parameter $D$ represents only a special case of $R(θ).$ Through orientationally sensitive $R(θ)$ and $D,$ both the orientational angle and its distribution could be uniquely and accurately determined from the SHG-only measurements in chosen polarization configurations. Using this approach, we were able to accurately determine both the orientational angle and its distribution in the Langmuir monolayer of a liquid crystal molecule $4′$-n-octyl-4-cyanobiphenyl (8CB) at the air/water interface. With such information, we were not only able to show that the phase transition of 8CB from the gas–liquid coexistence region to liquid region is accompanied with a continuous orientational angular distribution narrowing process, but also for the first time we were able to accurately determine a less than $3°$ tilt angle change of the 8CB chromophore in the whole liquid phase region of the 8CB monolayer. This quantitative approach to orientational analysis of molecular monolayer or multilayer is general for both SHG and sum frequency generation, and should lead the way to more quantitative understanding of the orientational order of molecular films per se.