Time-resolved two-photon induced anisotropy decay: The rotational diffusion regime

Abstract

Two-photon excitation (TPE) of randomly oriented chromophores in solution generates an anisotropic distribution. In a previous paper [Chem. Phys. 179, 513 (1994)], the polarization dependence of the TPE signal probed by a secondary spectroscopic transition (fluorescence or transient absorption) was determined. In this paper, the time dependence of anisotropic two-photon induced fluorescence or transient absorption signals due to rotational diffusion is treated in spherical tensor formalism. The two-photon signal in general contains isotropic (orientation independent) and anisotropic (orientation dependent) contributions. The latter decay with up to five exponential components. Four time-dependent anisotropy parameters can be defined and measured, allowing additional information, not available in conventional one-photon fluorescence depolarization measurements, to be determined. The special case of one-color TPE is discussed in particular. It is shown that by measurement of the linear and circular anisotropies r 1 (t) and r 2 (t), more than one rotational correlation time can be determined in many cases, providing information on rotational diffusion parameters not readily determined by analogous one-photon methods and leading in some cases to resolution of rotational motion about the principal diffusion axes of the molecule.

Quantitating the Dynamics of NBD Hexanoic Acid in Homogeneous Solution and in Solutions Containing Unilamellar Vesicles

“…The zero-time anisotropies for these two different excitation polarizations are related to the two-photon tensor elements according to eq 4, for systems where S xx , S xy ()S yx ) and S yy are the dominant elements. [21][22][23] Knowing the experimental values of r 1 (0) and r 2 (0), we can determine the relative values of S xx and S xy when S yy is normalized to unity. Because we are concerned with the relative values of the tensor elements and not their absolute magnitudes, normalization of the tensor elements to S yy does not reduce the relevant information content of our measurements.…”

“…3(S xx -S yy ) 2 -(S xx + S yy ) 2 + 12S xy 2 + 6(S xx 2 -S yy 2 ) (S xx + S yy ) 2 + 3(S xx -S yy ) 2 + 12S xy Rotational diffusion will rerandomize the initially anisotropic orientational distribution of the emitting molecules according to eqs 5 [21][22][23] where τ 0 and τ 2 are two different relaxation time constants. The relative contribution of the two time constants is given by the prefactors c i and d i , which are in turn related to the rotational diffusion constant and the two-photon tensor elements, as described in eqs 6-10 [21][22][23] The relative amplitudes of the decay time constants will provide information about the values of the Cartesian components of the rotational diffusion constant.…”

“…In our discussion of two-photon excited fluorescence anisotropy data, we follow the treatment put forth by the Johnson group. [21][22][23] Our goal is to relate the two-photon excited anisotropy decays of NBDHA in selected environments to the Cartesian components of its rotational diffusion constant.…”

“…The relative contribution of the two time constants is given by the prefactors c i and d i , which are in turn related to the rotational diffusion constant and the two-photon tensor elements, as described in eqs 6-10 [21][22][23] The relative amplitudes of the decay time constants will provide information about the values of the Cartesian components of the rotational diffusion constant. The parameters a, b, N, and ∆ are related to the diffusion constant by…”

The polarisation of two-photon excited fluorescence in rotating molecules

“…The theoretical background for the two-photon excited fluorescence (TPEF) has been established by McClain [5,6], Callis [7], and Wan and Johnson [8,9] who discussed the properties of the two-photon absorption tensor in an ensemble of randomly oriented molecules. McClain [5,6] pointed out that linear combinations of the elements of the two-photon absorption tensor and the elements of the fluorescent tensor can be probed experimentally.…”