A Proposed Method to Obtain Surface Specificity with Pump-Probe and 2D Spectroscopies

Abstract

Surfaces and interfaces are ubiquitous in nature. From cell membranes, to photovoltaic thin films, surfaces have important function in both biological and materials systems. Spectroscopic techniques have been developed to probe systems like these, such as sum frequency generation (SFG) spectroscopies. The advantage of SFG spectroscopy, a second-order spectroscopy, is that it can distinguish between signals produced from molecules in the bulk versus on the surface. We propose a polarization scheme for third-order spectroscopy experiments, such as pump-probe and 2D spectroscopy, to select for surface signals and not bulk signals. This proposed polarization condition uses one pulse perpendicular compared to the other three to isolate cross-peaks arising from molecules with polar and uniaxial (i.e., biaxial) order at a surface, while removing the signal from bulk isotropic molecules. In this work, we focus on two of these cases: XXXY and YYYX, which differ by the sign of the cross-peak they create. We compare this technique to SFG spectroscopy and vibrational circular dichroism to provide insight to the behavior of the cross-peak signal. We propose that these singularly cross-polarized schemes provide odd-ordered spectroscopies the surface-specificity typically associated with even-ordered techniques.

Figure 1.

(A) Schematic of the orientation of two coupled oscillators, a and b, depicted as red arrows in XYZ space. ϕ is the XY plane, θ is in the ZX plane, and ψ is twist angle of the oscillators. Z is the direction light is propagating. (B) Examples of surface systems that have biaxial symmetry (top) and an example that does not have biaxial symmetry (bottom).

Figure 2.

Double-sided Feynman diagrams for arbitrary oscillators i and j for both rephasing and nonrephasing pathways that describe the diagonal and cross-peaks in third-order spectroscopy. The diagonal peaks are shown as interactions only with i and can be represented as iiii. The cross-peaks have interactions with both i and j and can be represented as iijj, ijij, and ijji. Note, ijji is a nonrephasing pathway, ijij is a rephasing pathway, and iijj is both.

Figure 3.

Orientational four-point correlation function values for the pathways iiii, jjjj, iijj, ijij, ijji, jjii, jiji, and jiij as a function of θ and ψ for the surface system using two different polarization conditions: XXXX and XXXY.

Figure 4.

Normalized diagonal and cross peak dependences on θ and ψ angles for both bulk and surface systems for two different polarization conditions: XXXX and XXXY.

Figure 5.

Simulated two-dimensional spectra for two coupled oscillators in both bulk and surface systems under four polarization conditions: XXXX, YYYY, XXXY, and YYYX. The angle between the two oscillators is θ_ab = 30°. For the surface system, oscillator a is along the z axis, while b is in the XZ plane, as shown in Figure 1. For the surface two-dimensional spectra, θ = 30° and ψ = 30°.

Figure 6.

Cross-peak pathway dependence on θ_ab for θ = 30° and for ψ = 30° for XXXY and YYYX polarization conditions. iijj, ijij, jiij, and jiji pathways are equivalent for the XXXY and YYYX functions and are plotted in blue. The ijji and jjii pathways is plotted in red.