Harmonic Light Scattering to Study Supramolecular Assembly Processes
Authors: Verbiest Thierry 
Published: August 2024

Characterization of complex dynamical processes such as supramolecular aggregation, (electro)chemical reactions or phase transitions, requires in-situ measurement techniques to provide insight into morphology changes, symmetry changes, concentration, or phase changes during the process. Currently available techniques are often not sensitive to all these aspects or too slow for in-situ studies. Instead, very fast and sensitive techniques are needed. Recently, we developed a method based on second-and third harmonic scattering that partially satisfies these requirements (1-3).
Second-harmonic scattering is a nonlinear scattering process in which two incident photons of frequency ω are annihilated to create a new photon at the double frequency 2ω. It is a very sensitive tool to study dynamical processes since it is fast, sensitive to the symmetry of the scatterer and extremely sensitive to aggregation.
For molecular scatterers, the intensity of the scattered second-harmonic light I2ω is given by:
I2ω ∼ N<β2> Iω
2

With N the number scatterers, β the first hyperpolarizability, Iω the intensity of the incident light and < > refers to orientational averaging. Information about the point group symmetry of the scatterer can be inferred by analyzing the polarization components of the scattered light. For aggregated or correlated scatterers I2ω is given by:
I2ω ∼ N'<(Mf(β))2> Iω
2

with N’ the number of scatterers, M the number of molecules in each aggregate, and f(β) a combination of molecular hyperpolarizability components. Also in this case, an analysis of the polarization components of the scattered light will yield information about the symmetry of the aggregated scatterers.
Similar formula’s hold for third harmonic scattering where part of the incident light at frequency ω is scattered at the triple frequency 3ω . For molecular scatterers I3ω is given by
I3
ω ∼ N<γ2> Iω
3

and for correlated scatters
I3
ω ∼ N'<(Mf(γ))2> Iω
3

with γ the second hyperpolarizability.
While both techniques may seem similar, there is an important difference: the symmetry selection rules are very different. Second-harmonic scattering is only allowed if the scatterer is non centrosymmetric, while third-harmonic scattering does not have any symmetry constraints. As such, both techniques are highly complementary. The combination of both, referred to as harmonic scattering, has been used as a very versatile method to study in-situ supramolecular aggregation of macrocycles and conjugated polymers with the ability to completely unravel the nucleation and aggregation dynamics.
Now, we have extended this measurement platform to also include multi-photon fluorescence, linear light scattering, UV/Vis absorption and optical rotation. Hence, in total we can monitor 6 observables for any dynamical process in-situ. Several examples will be given on how this methodology can provide new insights in the mechanism and dynamics of supramolecular aggregation processes.
References
1) Moris, M. et al., Harmonic light scattering study reveals structured clusters upon the supramolecular aggregation of regioregular poly(3-alkylthiophene). COMMUNICATIONS CHEMISTRY, 2, Art.No. ARTN 130 (2019).
2) Hattori, S., et al. Vortex-Induced Harmonic Light Scattering of Porphyrin J-Aggregates. JOURNAL OF PHYSICAL CHEMISTRY B, 125 (10), 2690-2695 (2021)
3) Dok, A.R., et al. Nonlinear optical probes of nucleation and crystal growth: recent progress and future prospects. JOURNAL OF MATERIALS CHEMISTRY C, 9 (35), 11553-11568 (2021).