Amin Yousefi

The structure of molecules at surfaces and buried interfaces can be probed by second-order nonlinear optical techniques that derive their response from environments with broken centrosymmetry, thereby simultaneously enhancing the signal from the molecules of interest and suppressing the responses of the adjacent bulk phases. However, even though these methods are surface-sensitive, extracting orientation information has often relied on significant assumptions about the shape of the orientation distribution and the underlying molecular electronic structure. Here, we illustrate that the measurement of the relative magnitude and the phase of tensor elements that govern the vibrational sum frequency response can be used to construct a ratio of order parameters ⟨P3⟩/⟨P1⟩. This structural parameter does not require knowledge of the hyperpolarizability or even the hyperpolarizability ratio, thereby dramatically increasing the accuracy of its determination. We then show how this parameter can be used to comment on the most probable distribution of tilt angles. This is demonstrated for para-cyanophenol at three different interfaces.

When a molecule or sub-molecular entity is ordered on a surface in a manner that can be described by a tilt- and azimuthal-angle distribution, the projection of the molecular hyperpolarizability into the laboratory frame can be described using spherical harmonics. We illustrate that this lends itself to the construction of ten achiral order parameters associated with vibrational sum-frequency generation. We describe how these order parameters can be extracted from spectral data, first ignoring and then including the dispersion of the local electric fields. We then use these order parameters to determine the most probable orientation distribution without any assumptions about the surface alignment and in the absence of any other type of experimental data. This constitutes a flexible framework for describing a wide array of surface orientation distributions.

Accurate calibration curves are essential for quantitative analysis but are often neglected due to their time, cost, and labour demands. Traditional calibration involves measuring solutions of known concentrations to construct a calibration curve relating analyte concentration to instrument response. While these relationships rarely follow simple closed-form equations, linear approximations are commonly used for simplicity, often being fitted with too few data points for high-accuracy calibration. Continuous calibration was previously developed to address these challenges by continuously infusing a concentrated calibrant solution into a clean matrix solution while monitoring the response in real time. This approach significantly reduces time and labour while generating extensive data, improving calibration precision and accuracy. Despite its advantages, method limitations and technical complexities have hindered widespread adoption. Here, continuous calibration is expanded and simplified with modern accessible equipment, open-source code, and a user-friendly web tool which streamline data processing, generating smoothed and equation-fitted calibration curves complete with quality-of-fit and dynamic range estimates. This method was applied to a broad range of systems and analytical techniques, including external, standard addition, and internal standardization calibrations, and mass spectrometry, and infrared and ultraviolet–visible spectroscopies, with the latter yielding molar absorption coefficients from a single experiment. By reducing time and effort while enhancing precision, these advancements have the potential to improve experimental quality and efficiency across numerous fields.

Order parameters provide a useful qualitative and quantitative description of the distribution of molecules in ordered materials as they are independent of the shape of the orientation distribution. For samples that exhibit uniaxial ordering with no twist preference, extracting ⟨P2⟩ from polarized IR absorption data is common and obtaining ⟨P2⟩ and ⟨P4⟩ from Raman data has also been well-described. However, such an approach is not routine in the analysis of surface sum-frequency generation (SFG) spectra. We first provide a description whereby elements of the second-order susceptibility can be expressed in terms of the order parameters ⟨P1⟩ and ⟨P3⟩. We then illustrate how experimental data would be used to extract those parameters and how a most probable orientation distribution function could be determined by subsequently maximizing the information entropy. Finally, features of this distribution function are explored.