Time‐Resolved Optical Spectroscopy with Multiple Population Dimensions: A General Method for Resolving Dynamic Heterogeneity

Abstract

The discovery of the spin echo by Hahn in 1950 [1] set the stage for the development of a multitude of "coherence" spectroscopies. The expansion, elaboration and application of coherence methods [2] continues to this day in NMR, [3] electronic, [4,5] infrared [6][7][8] and Raman [9][10][11] spectroscopy. The key feature in the original spin echo-and in all subsequent coherence spectroscopies as well-is a comparison of the evolution of a coherence over two different time periods. Herein we show that a parallel, but analogous, set of spectroscopies can be based on comparing the evolution of a population over different time periods. We refer to these spectroscopies as Multiple Population Period Transient Spectroscopies (MUPPETS). In their simplest form, coherence echoes separate homogeneous and inhomogeneous sources of line broadening. Analogous MUP-PETS experiments are a general method for separating homogeneous and heterogeneous sources of nonexponential kinetics. A novel six-beam generalization of heterodyne-detected transient-grating spectroscopy [12,13] is performed to validate the theoretical predictions.In general, any nonexponential relaxation can be attributed to one of two types of mechanism: differences in the rates of different molecules within the sample (dynamic heterogeneity) or a time varying rate for each individual molecule (dynamic homogeneity). Figure 1 illustrates this distinction in the context of electronic relaxation in a four-level optical system. The lefthand side of Figure 1 represents a mixture of two molecules, a and b, that have the same transition frequency, but that have different electronic relaxation rates, k a and k b . A standard, onedimensional (1D) ground-state recovery experiment on the mixture yields a nonexponential decay that is due to the heterogeneity of the rates. (We consider a multiexponential decay to be nonexponential.) Although we will use a permanent heterogeneity in this paper to demonstrate the principles of MUP-PETS, often the structures or local environments that produce different relaxation rates are short-lived and cannot be distinguished by standard methods.The right-hand side of Figure 1 represents a system whose electronic relaxation rate is affected by a conformational coordinate q. As a result of the evolution of q, every molecule experiences an identical nonexponential decay. This mechanism is an example of homogeneous dynamics. In general, sequences of intermediate states, dynamics triggered by excitation and hierarchical kinetics [14] are all capable of creating homogeneous nonexponential decays.The issue of homogeneous versus heterogeneous dynamics becomes important any time nonexponential kinetics are observed, and it plays a role in many diverse areas of chemistry and physics. It has been most deeply discussed in the context of supercooled liquids. The fragmentation of the liquid into mesoscopic domains with varying local viscosity has been observed very close to the glass transition.[15] Computer simulations suggest that this heterogeneity originat...

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