If multidimensional coherent spectroscopy could be extended to seven dimensions (χ(8)), a new feature would emerge: the ability to measure bath coordinates that affect the rate of the observable, but that are not themselves directly observable. These ideas are used to develop a new approach to single-molecule kinetics based on multidimensional correlation functions. Three incoherent dimensions remain that measure rate correlations and rate exchange. A spectral representation makes explicit the parallel to frequency correlation and frequency exchange in 3D coherent spectroscopy (Fig. 1). These methods have been applied to single-molecule dichroism measurements of a BODIPY probe in o-terphenyl near its glass transition (Tg + 1.5 K and Tg + 4.5 K). The observable is probe rotation, which nearly matches the α-relaxation of the host, with mean times of 15 s and 3.0 s, respectively. The dichroism decay is strongly stretched, as is typical near Tg. Two-dimensional results confirm that this nonexponential decay is largely due to rate heterogeneity induced by spatial domains. The existence of such domains is widely accepted, but their properties have been difficult to observe directly. Extending the correlation functions to 3D shows that the domain lifetime is 22 times the α-relaxation time. Thus, α-relaxation is not the final relaxation process that establishes equilibrium in the supercooled liquid. An early relaxation component is attributed to molecules lying in the boundaries between domains.

Single-molecule, multidimensional measurements of rate-domain lifetimes near the glass transition

2019 Fall National Meeting

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