Intramolecular Vibrational Energy Relaxation of CO₂ in Cross-Linked Poly(ethylene glycol) Diacrylate-Based Ion Gels

Abstract

Ultrafast two-dimensional infrared spectroscopy (2D-IR) and Fourier transform infrared spectroscopy (FTIR) were used to measure carbon dioxide (CO2) in 1-ethyl-3-methylimidazolium bis­(trifluoromethylsulfonyl)­imide ([emim]­[Tf2N]), cross-linked low-molecular-weight poly­(ethylene glycol) diacrylate (PEGDA), and an ion gel composed of a 50 vol % blend of the two. The center frequency of the antisymmetric stretch, ν3, of CO2 shifts monotonically to lower wavenumbers with increasing polymer content, with the largest line width in the ion gel (6 cm–1). Increasing polymer content slows both spectral diffusion and vibrational energy relaxation (VER) rates. An unexpected excited-state absorbance peak appears in the 2D-IR of cross-linked PEGDA due to VER from the antisymmetric stretch into the bending mode, ν2. Thirty-two response functions are necessary to describe the observed features in the 2D-IR spectra. Nonlinear least-squares fitting extracts both spectral diffusion and VER rates. In the ion gel, CO2 exhibits spectral diffusion dynamics that lie between that of the pure compounds. The kinetics of VER reflect both fast excitation and de-excitation of the bending mode, similar to the ionic liquid (IL), and slow overall vibrational population relaxation, similar to the cross-linked polymer. The IL-like and polymer-like dynamics suggest that the CO2 resides at the interface of the two components in the ion gel.

Least-Squares Fitting of Multidimensional Spectra to Kubo Line-Shape Models

“…This manuscript provides a comprehensive study of how fitting generalized Kubo line shapes to multidimensional spectra compares to the CLS method in terms of the accuracy, precision, and reliability of the resulting parameters. While Garrett-Roe and co-workers have shown several examples of model fitting 2D IR waiting-time series using the function in MATLAB, ,,, a comparison of accuracy between model fitting and the CLS method by fitting to simulated spectra, where true values of parameters are known, has been missing. We find that our model fitting routine improves precision over the CLS method by 8–15× on average for Kubo time constants and 8–50× for Kubo amplitudes and homogeneous dephasing, which is due, in part, to a novel figure of merit used in our fitting algorithm that we refer to as the scale invariant gradient norm (SIGN).…”

Least-Squares Fitting of Multidimensional Spectra to Kubo Lineshape Models

“…This manuscript provides a comprehensive study of how fitting generalized Kubo lineshapes to multidimensional spectra compares to the CLS method in terms of the accuracy, precision and reliability of the resulting parameters. While Garret-Roe and coworkers have shown several examples of model fitting 2D IR waiting-time series using the fmincon function in MATLAB, [17][18][19][20] a comparison of accuracy between model fitting and the CLS method by fitting to simulated spectra, where true values of parameters are known, has been missing. We find our model fitting routine improves precision over the CLS method by 8× to 15× on average for Kubo time constants and 8× to 50× for Kubo amplitudes and homogeneous dephasing, which is due in part to a novel figure of merit used in our fitting algorithm that we refer to as the scale invariant gradient norm (SIGN).…”

Generation of High-Lying Vibrational States in Carbon Dioxide through Coherent Ladder Climbing

“…By fitting the resonance frequencies using eq 2, we obtain the anharmonicity of χ e = 0.52% and the corresponding anharmonic shift of 2χ e ω 0 = 24.6 cm −1 , which is consistent with those reported in the previous studies. 36,[38][39][40]45,49 From these results, we can conclude that the CO 2 molecules are vibrationally excited up to the v 3 = 8 state. Note that the small peaks observed between the |0, v 3 ⟩ → |0, v 3 + 1⟩ transitions can originate from the ladder transitions of the hot-band (|1,…”