Heterospectral Principal Component Analysis Two-Dimensional Correlation Spectrosocpy as a Robust Method for Determining Surface Adsorption Preference

Abstract

Vibrational sum-frequency spectra encode information on the orientation and population of molecules at surfaces. Although orientation information can be extracted by simultaneously analyzing spectra acquired in two different beam polarization combinations, it is more difficult to isolate information on the surface population of adsorbed species when their orientation also changes. This is critical for the widespread adoption of this technique, as many systems are known to change their adsorbed structure in response to variation of the bulk concentration. Here we demonstrate that reconstructed sum-frequency spectra using the first principal component from a principal component analysis (PCA) markedly diminishes the spectral contributions due to molecular orientation. We show that the reconstructed spectra are excellent candidates for a subsequent surface-bulk heterospectral analysis to reveal the preference for a particular species to be adsorbed from a binary mixture.

Graphical abstract

This is a visual representation of the abstract.

Introduction

Technologies for sensing, promoting biocompatibility, and filtration rely on the selective adsorption of specific molecules from the ambient gas or liquid–solution phase.^1–3 Although a perfect selectivity is not necessary achieved or desired, surfaces are often inherently or intentionally tailored to exhibit a preference for a particular analyte. The mechanism of selectivity is often linked to non-bonded interactions resulting from charge or hydrophobicity.^4–6 Over the last few decades, vibrational sum-frequency generation (SFG) has been developed into a versatile technique for studying surfaces and buried interfaces with remarkably specificity for interfacial species that are distinguished from the bulk on the basis of symmetry.^7–9 Since the generation of light at the sum-frequency is a second-order nonlinear optical effect, it requires a break in the inversion symmetry found in isotropic achiral phases. ¹⁰ However, even though the non-centrosymmetric requirement forms the basis of the sought surface-selectivity, it also results in the measured signals being extremely sensitive to the orientation and conformation of molecules on surfaces. Although this is a bonus overall, as SFG has been proven to be a capable method to extract quantitative surface orientation information,^11–14 it also means that the effects of surface population (i.e. the surface number density) and molecular orientation need to be separated. If the ultimate goal is to comment on the orientation, the most common approach is to perform the analysis based on ratios of signals obtained using two different beam polarization combinations, thereby effectively canceling the effect of the population of molecules. However, the opposite study is more challenging, as there are not many techniques that can restore the linearity of the signal with respect to population from the overall nonlinear variation due to re-orientation of surface-adsorbed species.

We previously described a technique whereby SFG spectra collected under varying concentrations of species in the bulk are analyzed together with bulk infrared (IR) and/or Raman spectra.^15–17 Heterospectral two-dimensional correlation spectroscopic (2D-COS) analysis provides an ideal platform for this comparison.^18–20 Using heterospectral 2D-COS, the relative changes in surface and bulk signals can be used to reveal the surface preference for a particular species. However, in consideration of the above points, this can be true only if all of the SFG signal can be attributed to changes in surface population. In other words, we need to be sure that, at least for the moiety associated with a particular vibrational mode, there are no contributions to the changing SFG signal from reorientation. Fortunately, 2D-COS also provides a sensitive means for this check, as the asynchronous component of the SFG homospectral 2D-COS readily reveals any reorientation.^15,16 Although we have demonstrated that this is a useful analysis procedure, it still leaves a large number of cases where molecules accumulate on the surface and reorient as they become more crowded, and are therefore excluded from surface preference analysis. We therefore have been looking for a way to modify this method so that it is more universally applicable.

It has been recognized that the power of 2D-COS can be extended when combined with chemometric methods such as principal component analysis (PCA).^21–25 PCA is known for its ability to capture the most dominant features in revealing trends across datasets, and is therefore an attractive option for assisting our desire to uncover trends in surface population when the bulk population changes. Here we demonstrate that a reconstructed SFG spectrum using only the first principal component (PC1) obtained from PCA is an ideal candidate for a heterospectral 2D-COS-based procedure that includes bulk IR and/or Raman data. We will first demonstrate this using model spectra whose surface population is known from the simulation parameters. This is also an opportunity to illustrate that the technique works because PC1 is highly correlated to the surface population. We then show that this can be applied to the analysis of surface preference using experimental spectra from a binary mixture of heptane and toluene in contact with a hydrophobic surface, resolving previous ambiguities regarding this system.

Background and Methods

Model Spectra

Model IR, Raman, and SFG spectra were created for methanol and glycerol from density functional theory using B3LYP/6-311G(d,p) and a Lorentzian profile with a half-width at full maximum (HWFM) of 10 cm⁻¹. An empirically-determined frequency scaling factor of 0.935 was used, which is lower than the gas-phase value recommended for this basis set, ²⁶ but provides better agreement with experimental results in the condensed phase. To characterize the bulk solution phase, either IR or Raman spectra can be used, but we prefer to construct a hybrid IR $\times$ Raman spectrum for better comparison with surface SFG spectra. The details of the hybrid spectral construction have been described previously. ²⁷ The resulting bulk IR $\times$ Raman spectra are shown in Figure 1a with pure methanol indicated with the solid black line, and pure glycerol with the dashed black line. Intermediate concentrations were modeled representing 9 binary mixtures in step sizes of $x^{\mathrm{b}}=0.1$ where the superscript b indicates that we are referring to the mole fraction in the bulk. Since we know the assignment of all vibrational modes in the model, frequencies corresponding to methanol are marked by solid vertical lines; frequencies pertaining to glycerol are indicated by dashed vertical lines.

Figure 1.

Model spectra for methanol–glycerol mixtures generated for (a) the bulk solution phase using a combination of the IR and Raman response, (b) the surface SFG response, and (c) the SFG response reconstructed from PC1. The pure methanol spectrum is shown with the solid black trace, and its characteristic frequencies are indicated by solid vertical black lines. The pure glycerol spectrum is shown with the dashed black trace, and its features are highlighted with vertical dashed black lines. The mixtures are indicated by colors described in the inset legends. The perturbation proceeds in the direction of increasing bulk methanol mole fraction.

We next construct $\mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}$ spectra corresponding to the SFG response for the pure components and mixtures on the surface. As ${\chi }^{(2)}$ depends on both population (the surface mole fraction $x^{\mathrm{s}}$ and the molecular orientation, we need to specify $\theta$ , the alignment of the molecular long axes with respect to the surface normal. The model spectra appearing in Figure 1b were created by varying the tilt angle in a linear fashion linked to the surface mole fraction

$$\theta (x^{\mathrm{s}})=x^{\mathrm{s}}({\theta }_{\mathrm{end}}-{\theta }_{\mathrm{start}})+{\theta }_{\mathrm{start}}$$

(1)

For both molecules, we assume an upright orientation ( ${\theta }_{\mathrm{start}}=0\circ$ ) for the pure component in contact with the surface. As the surface population changes, the molecules become increasingly tilted, with ${\theta }_{\mathrm{end}}=70\circ$ for methanol and ${\theta }_{\mathrm{end}}=80\circ$ for glycerol. The surface populations were determined according to

$$x^{\mathrm{s}}=\frac{x^{\mathrm{b}}}{K-K{x}^{\mathrm{b}}+x^{\mathrm{b}}}$$

(2)

where $K=4$ was chosen as the value of the equilibrium coefficient.

Experimental Spectra

Full details of the sample preparation and the experimental conditions have been described previously. ¹⁶ In brief, high-performance liquid chromatopgraphy (HPLC) grade heptane and toluene (Fischer Chemicals) were used to prepare mixtures of the two liquids. Bulk Raman spectra were collected using a commercial Raman spectrometer (Renishaw InVia) with 532 nm excitation using a custom liquid cell. Bulk IR absorption spectra were collected using Fourier transform infrared (FT-IR) (Perkin-Elmer Spectrum Two) on the surface of a single-bounce diamond ATR crystal. The hybrid IR $\times$ Raman spectra were created using a procedure that we described previously.^16,27 The resulting spectra, that we hereafter refer to simply as the bulk spectra of the mixtures, are shown in Figure 2a.

Figure 2.

(a) Bulk hybrid IR $\times$ Raman spectra obtained for heptane–toluene mixtures. The pure toluene spectrum is indicated in solid black, including some characteristic bands in vertical lines. The pure heptane component is plotted with the dashed black line, and its key vibational modes are indicated by vertical dashed lines. (b) SFG spectra of these mixtures adsorbed onto a hydrophobic fluoropolymer surface. (c) SFG spectra reconstructed from PC1.

For the surface studies, a thin film of Teflon-AF (Chemours, USA) was spin coated from FC-40 (Sigma Aldrich, Canada) onto the surface of a prism. The film side of the prism was pressed against the opening of a custom liquid cell that we have designed for use with our sum-frequency generation (SFG) setup. ²⁸ In the SFG experiments, a 1064 nm picosecond yttrium aluminum garnet (YAG) laser (Ekspla PL2241A) was doubled to create a 532 nm visible beam and an OPA (Eskpla PG501) was used to create tunable mid-infrared light. SFG spectra were processed to determine the imaginary component of the susceptibility (for better linear additivity of the contributions of the two liquids) using a maximum entropy (MEM)-based method described previously,^16,29 resulting in the profiles shown in Figure 2b.

Principal Component Analysis

Even so-called “1D” vibrational spectroscopies (IR, Raman, SFG, etc.) produce high-dimensional data in the sense that an absorption spectrum may have hundreds of data points along the wavenumber axis. Such rich spectral datasets contain valuable chemical information, but the sheer number of variables (wavenumbers) and the overlap of broad spectral peaks make direct interpretation challenging. PCA is a multivariate analysis technique that addresses this challenge by reducing data dimensionality while preserving most of the variance and information in the dataset.^30,31 This approach is often used to simplify complex datasets by transforming them into a new coordinate system that highlights their most significant features. PCA finds a set of new orthogonal axes, called principal components, which successively capture the major patterns in the data. ³² These new axes are linear combinations of the original variables, capturing the most important patterns in the data while discarding noise and redundancy. The first principal component is the line that best fits the data in a least-squares sense (maximizing the variance of projective distances).^33,34 The second component is the next best-fitting line perpendicular to the first, and so on, each capturing as much remaining variance as possible while being orthogonal to earlier components. ³⁵ PCA outputs two key sets of parameters for the dataset: scores and loadings. Each principal component is defined by a loading vector, which contains the coefficients by which the original variables are linearly combined to form that component. The loadings indicate the weight or influence of each original spectral variable (wavenumber) on that PC. While loadings describe the PCs in terms of variables, the scores describe each sample in terms of the PCs. Every sample gets a numerical score for each principal component, computed by projecting the sample’s data onto that PC axis. In summary, scores tell us how much of each principal component each sample contains, whereas loadings tell us what each principal component represents in terms of original variables. In our system the SFG data set $\mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}(\omega ,x)$ is a two-dimensional matrix and can be written as

$$\mathbf{X}=\left[\begin{array}{ccc}\mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_1,x_1)& \cdots & \mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_n,x_1)\\ \mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_1,x_2)& \cdots & \mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_n,x_2)\\ ⋮& \ddots & ⋮\\ \mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_1,x_m)& \cdots & \mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_n,x_m)\end{array}\right]$$

(3)

where $m$ is the number of spectra at different mole fractions, and $n$ is the number of data points along the wavenumber axis. $\mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}({\omega }_n,x_m)$ is therefore the SFG signal of the $m^{}$ th spectrum at wavenumber $n$ . PCA finds orthogonal vectors that capture maximum variance in mean-centered spectra. By using PCA, the SFG spectra can be defined by

$$\begin{array}{rl}\mathbf{X}& =\mathbf{T}{\mathbf{P}}^{\mathsf{T}}+\mathbf{E}\\ & ={\mathbf{X}}^{\mathrm{\prime }}+\mathbf{E}\end{array}$$

(4)

where $\mathbf{T}\in {\mathbb{R}}^{m\times k}$ is the scores matrix, $\mathbf{P}\in {\mathbb{R}}^{n\times k}$ is the loadings matrix, $k$ is number of principal components ( $\le min(m,n)$ ), and $\mathbf{E}$ is residual matrix related to noise in the data. In this way, ${\mathbf{X}}^{\mathrm{\prime }}$ can be reconstructed from the sum of its principle components using

$${\mathbf{X}}^{\mathrm{\prime }}=\sum _{r\ge 1}^k{\mathbf{T}}_r{\mathbf{P}}_r^{\mathrm{\top }}$$

(5)

As mentioned, scores show how strongly each spectrum expresses a given PC pattern, and loading represents spectral shapes. The PC1 spectra of the model SFG dataset are shown in Figure 1c, and those loadings obtained for the experimental dataset are shown in Figure 1c, and that produced from the experimental data is shown in Figure 2c. The model and experimental PC2 loading spectra shown in Figure S1.

Results and Discussion

Model System

To illustrate the challenge in interpreting the surface preference, we first inspect the homospectral 2D-COS obtained using SFG data. As we have described previously, ¹⁵ the SFG homospectral synchronous map (Figure 3a) does not provide any information useful for surface preference determination. The analysis therefore starts by a careful examination of the asynchronous map. In order to subsequently interpret the heterospectral signals in terms of surface populations, we require that the molecules don’t reorient as their surface population changes. Figure 3b displays many strong homospectral SFG asynchronous cross-peaks, indicating that reorientation of both methanol and glycerol significantly contribute to their SFG response. We have previously described that, if only one molecule (or part of a molecule) reorients, it may still be possible to continue with the population analysis if the other species or a different part of the molecule doesn’t produce homospectral SFG asynchronous modes. ¹⁵ In the present study, however, we have intentionally modeled a situation where both species reorient. A cautious approach would therefore stop at this stage, with no conclusion about the surface preference possible. However, we briefly consider proceeding to look at the heterospectral surface-bulk 2D-COS to explore the possibility that the spectral changes might be dominated by surface populations. Looking at the glycerol peak at (2904, 2951 cm⁻¹) in the heterospectral synchronous (Figure 3c) and asynchronous maps (Figure 3d), the corrected async cross-peak sign is positive, indicating that the decrease in bulk glycerol occurs before the surface glycerol response decreases. This would normally be an indication that the surface prefers glycerol. Since we know that $K=4$ in our simulation, this happens to be correct. However the (2947, 2904 cm⁻¹) cross-peak for glycerol has a sync-corrected negative sign, contradicting our conclusion. This illustrates the danger in ignoring the warning signs of SFG homospectral cross-peaks for both species. We also have an early indication of this issue in the non-monotonic trends of the SFG spectra shown in Figure 1b.

Figure 3.

(a) Synchronous and (b) asynchronous homospectral 2D-COS obtained from the SFG spectra. (c) Synchronous and (d) asynchronous heterospectral 2D-COS constructed using IR $\times$ Raman spectra for the bulk response and SFG spectra for the surface response. Solid and dashed lines indicate characteristic frequencies as identified in Figure 1.

To find a general solution to this problem, we look for a way to separate the effects of population-dependent surface reorientation from the sought surface population changes. Since our perturbation changes the bulk concentrations in a drastic manner ( $x^{\mathrm{b}}=0\text{--}1$ for each species), it is reasonable to suspect that most of the variance in the spectra originates from population changes, and that the effect of reorientation is a perturbation to these changes. We therefore consider the possibility of reconstructing the SFG spectra from their first principal component (PC1). We can see that PC1 SFG spectra in Figure 1c bear a strong resemblance to the original SFG spectra shown in Figure 1b, as expected given that PC1 captures 91% of the total variance. We also notice that the trends in the PC1 spectral intensities are now monotonic, especially in the previously problematic 2904 and 2947 cm⁻¹ bands.

We now use these PC1 SFG spectra in place of the raw SFG spectra for our 2D-COS analysis. The similarity in the SFG homospectral synchronous response (comparing Figures 3a and 4a) is reassuring, as we don’t want to perturb the spectral lineshape significantly. The first striking observation is the absence of any SFG asynchronous peaks in Figure 4b. Although this appears to be a success, we need to be careful before reaching any conclusions about the degree to which we have removed reorientation effects, as it is known that any homospectral correlation between principal components (PC $n$ -PC $n$ ) cannot result in asynchronous signals. ²² This is due to the effect of the Noda–Hilbert operator $\mathbf{N}$ when combined with the same principal components. This can be seen when using Eq. (5) to create the asynchronous map

$$\begin{array}{rl}\mathrm{\Psi }({\omega }_1,{\omega }_2)& =\frac{1}{m-1}\mathbf{X}({\omega }_1{)}^{\mathrm{\top }}\mathbf{N}\mathbf{X}({\omega }_2)\\ & =\frac{1}{m-1}\sum _{r,s}{\mathbf{p}}_r({\omega }_1)[{\mathbf{t}}_r^{\mathrm{\top }}N{\mathbf{t}}_s]{\mathbf{p}}_s({\omega }_2{)}^{\mathrm{\top }}.\end{array}$$

(6)

When using only a single principal component, Eq. 6 becomes

$$\mathrm{\Psi }(\omega ,\omega )=\frac{1}{m-1}{\mathbf{p}}_i({\mathbf{t}}_i^{\mathrm{\top }}N{\mathbf{t}}_i){\mathbf{p}}_i^{\mathrm{\top }}=\mathbf{0}.$$

(7)

As the Noda–Hilbert transformation matrix $\mathbf{N}$ is skew-symmetric, the term ${\mathbf{t}}_i^{\mathrm{\top }}N{\mathbf{t}}_i$ equals zero for any value of $i$ .^22,36 Therefore, there is no peak in the asynchronous homospectral map when using only PC1.

Figure 4.

(a) Synchronous and (b) asynchronous homospectral 2D-COS obtained from SFG spectra reconstructed using PC1 only. (c) Synchronous and (d) asynchronous heterospectral 2D-COS constructed using IR  $\times$  Raman spectra for the bulk response and PC1 SFG spectra for the surface response. Solid and dashed lines indicate characteristic frequencies as identified in Figure 1.

We therefore examine the result of our action based on the correlation of the original and PC1 SFG spectra with the surface populations. Initially, the SFG dataset consisted of a matrix of size $9\times 500$ , corresponding to nine surface mole fractions and 500 wavenumber points. To quantify how much of the total variance in the raw SFG spectra can be explained by population (surface mole fraction) change alone, the spectra were first mean-centered at each wavenumber to obtain dynamic spectra $\mathbf{W}$ , which removes absolute intensity offsets. The surface mole fraction vector was similarly mean-centered to create $\mathbf{x}$ , representing deviations from the average composition. A linear least-squares model was then used to project the dynamic spectral variations onto the surface mole fraction. This was accomplished by forming the outer product of the mean-centered spectra with the mean centered mole fractions, yielding a population-favored reconstructed dataset

$$\mathbf{y}=\frac{\mathrm{cov}(\mathbf{x},\mathbf{W})}{\Vert \mathbf{x}{\Vert }^2}$$

(8)

The 500-element vector $\mathbf{y}$ is essentially the slope of the original mean-centered spectral intensity at each wavenumber with respect to mole fraction. This reconstruction represents the spectral changes that would be expected if population were the only varying parameter. Here, the denominator $\Vert \mathbf{x}{\Vert }^2$ represents the variance of the surface mole fraction vector. Dividing the covariance by this variance serves as a necessary normalization step that converts the raw correlation into a linear regression coefficient (or slope). This ensures that $\mathbf{y}$ carries the correct physical units of spectral intensity change per unit of mole fraction, rather than an arbitrary unscaled magnitude. If there was no surface reorientation, these relationships would be linear at each mole fraction. We now need a way to create spectra that reflect these slopes as a function of the mean centered surface mole fractions $\mathbf{x}$ ; this is accomplished from the outer product

$$\mathbf{Z}=\mathbf{x}\otimes \mathbf{y}$$

(9)

that results in a $9\times 500$ matrix. Finally, we can compare $\mathbf{z}$ with the $9\times 500$ element dataset consisting of our dynamic (mean-centered) SFG spectra, $\mathbf{W}$ using Pearson’s correlation coefficient, that we determine to be 0.86. In other words, there is an 86% correlation between the SFG spectra, and the surface populations. Note that this is one of the utilities of having a model data set since, in the case of real experimental data, the surface mole fractions are unknown.

In the case of the SFG spectra reconstructed using the first principal component (PC1), applying the same procedure shows that the slopes at each wavenumber, $\mathbf{y}$ , are already available as the PC1 loading values. This simplifies the analysis for PC1. We compute the outer product of the PC1 loadings ( ${\mathbf{P}}_1$ ) and the mean-centered mole fraction ( $\mathbf{x}$ ), and then evaluate the Pearson correlation between this resulting matrix ( $9\times 500$ ) and the mean-centered PC1-reconstructed spectra, obtaining a correlation coefficient of 0.93. This result demonstrates that the PC1-reconstructed SFG spectra are more strongly correlated with surface population changes than the original spectra.

Now using the heterospectral surface(PC1)-bulk correlation synchronous signs in Figure 4c to interpret the signs of the asynchronous cross-peaks observed in Figure 4d, we see that the (2947, 2904 cm⁻¹) peak has become positive. In fact, all modes in the asynchronous map now have the correct signs, consistent with our knowledge ( $K=4$ ) that the surface prefers glycerol. Note that the synchronous and asynchronous maps have the exact same shape here, as these are constructed from model data. This occurs as there is now primarily a population change that results in a variation of both the surface and bulk spectral features. ¹⁷

Experimental Demonstration

We now provide a demonstration using experimental data that we previously collected for binary mixtures of heptane and toluene that are co-adsorbing on a hydrophobic fluropolymer surface. We have previously shown that the homospectral SFG asynchronous spectrum showed cross-peaks for both heptane and toluene, technically eliminating the possibility of further analysis to obtain the surface preference if we were to adhere to the rules strictly. However we noted that the evidence of heptane reorientation was weak, so we decided to continue with the analysis of the heterospectral 2D-COS shown in Figure 5. Observing the negative heptane (2858 cm⁻¹ CH ${}_2$ symmetric stretch, 2875 cm⁻¹ CH ${}_3$ symmetric stretch) cross-peak in Figure 5b and the corresponding positive sign of this peak in Figure 5a, one would conclude that the surface has a toluene preference. However, when we look at a different combination of heptane peaks, selecting the (2875 cm⁻¹ CH ${}_3$ symmetric stretch, 2932 cm⁻¹ CH ${}_2$ asymmetric stretch) the asynchronous and synchronous peaks are both positive, leading to the contradictory conclusion that the surface prefers heptane. Since the isotherm was nearly along the surface-bulk diagonal, we reconciled this discrepancy by concluding that the fluoropolymer surface did not have a strong preference for either molecule. Now, we are able to revisit this data and explanation using our proposed surface(PC1)-bulk technique. We first noticed that, although the original SFG spectra (Figure 2b) show some non-monotonic trends, especially at the heptane 2858 and 2932 cm⁻¹ wavembers, the PC1 loading SFG spectra (Figure 2c) are monotonic everywhere, including these regions. Those PC1 SFG spectra are now used to perform the heterospectral correlation shown in Figure 5c (sync) and Figure 5d (async). Homospectral 2D-COS maps are provided in the Supporting Information. Note that, although the synchronous maps (Figure 5a and c) are similar, some signs have changed in the asynchronous maps. In particular, the heptane (2858, 2875 cm⁻¹) peak has changed sign in the async map only, while the (2858, 2932 cm⁻¹) cross-peak signs remain the same. Moreover, we can now interpret any frequency combination (corresponding to the same or different modes from the same molecule) and we arrive at a consistent interpretation of a slight heptane preference, which is now also consistent with our previous estimation of the adsorption isotherm. ¹⁶

Figure 5.

Heterospectral correlation showing the (a) synchronous and (b) asynchronous maps constructed from experimental data for the heptane-toluene mixtures, using the original SFG spectra. (c) Synchronous and (d) asynchornous heterospectral correlation with the SFG data reconstructed from PC1 alone.

These examples illustrate although SFG spectra reconstructed from PC1 still have some residual traces of re-orientation contributing to the response, the PC1 spectra are now dominated by surface population changes, to the point where they make excellent candidate for a heterospectral 2D-COS analysis with bulk IR and/or Raman data. Furthermore, the fact that the homospectral PC1 SFG synchronous maps look practically identical to the raw SFG homospectral synchronous maps is a good indication that this method has not significantly altered the surface population with respect to the bulk concentration perturbation. This brings up an interesting possibility for future investigation, to determine whether such heterospectral PCA-2D-COS can offer a more quantitative description of the adsorption behavior, in a manner that is connected to the equilibrium constants and adsorption isotherm.

To summarize our proposed procedure, the overall workflow involves

Preparing solutions of the (in this case two) components with varying bulk concentrations.

Collecting IR and/or Raman spectra for each concentration in the series. In the event that both IR and Raman data are available, hybrid IR-Raman spectra can be created as described previously.

Collecting SFG spectra when each of the solutions are placed in contact with the surface of interest. Ideally, phase resolved SFG measurements are performed to determine $\mathbb{I}\mathrm{m}\{{\chi }^{(2)}\}$ from the raw $|{\chi }^{(2)}{|}^2$ data. Alternatively, a fitting or MEM-based method can be used for this.

Performing SFG homospectral correlation to investigate the extent of surface reorientation based on the presence of asynchronous cross-peaks. If both species are found to reorient, PCA is performed on the SFG dataset to obtain scores, which describe how each spectrum changes along each principal component, and loadings, which describe the characteristic spectral patterns associated with each component. The explained variance is then used to determine which principal components carry the dominant spectral changes.

Reconstructing the SFG dataset using PC1 only to adjust spectral contributions associated with reorientation (captured in higher PCs). Optionally reconstruct PC2 to visualize orientation-dominated contributions and identify spectral regions most affected by reorientation.

Constructing heterospectral 2D-COS maps using the original bulk spectra (IR and/or Raman) and the PC1-reconstructed SFG spectra. Interpret the heterospectral cross-peak (or suitable diagonal peak) signs to infer whether the surface composition changes in the same direction as (or opposite to) bulk composition, allowing determination of surface adsorption preference.

Conclusion

Heterospectral 2D-COS provides a convenient and simple method of determining the preferential absorbance of components from a mixture. However, the analysis previously required knowledge that species were not reorienting when the surface population changed. This could be verified by confirming the absence of cross-peaks in the homospectral asynchronous correlation of SFG data. However, that procedure left little recourse in situations where surface reorientation did occur. We have demonstrated that this situation can be remedied by using the first principal component of the SFG spectra in the surface–bulk heterospectral correlation. Our model result demonstrated that this works because the PC1 spectrum was strongly correlated to the surface populations. We then applied this method to experimental data of heptane–toluene mixtures in contact with a hydrophobic surface, and were able to unambiguously determine the slight adsorption preference of heptane. This technique resolved previous challenges in understanding this data due to complex reorientation behavior of both species. These illustrations demonstrate that the PCA-2D-COS method has the potential to be applied to a wide range of surface adsorption phenomena.

Supplemental Material

sj-pdf-1-asp-10.1177_00037028261433545 - Supplemental material for Heterospectral Principal Component Analysis Two-Dimensional Correlation Spectrosocpy as a Robust Method for Determining Surface Adsorption Preference

Supplemental material, sj-pdf-1-asp-10.1177_00037028261433545 for Heterospectral Principal Component Analysis Two-Dimensional Correlation Spectrosocpy as a Robust Method for Determining Surface Adsorption Preference by Mahsa Torkamanasadi and Dennis K. Hore in Applied Spectroscopy