Measurement of Single Molecule Cross-Correlation Functions Using Electric Field Induced Birefringence

A method is derived for the measurement of the single molecule cross-correlation function ⟨v( t ) ω T (0)⟩ in the laboratory frame of reference. This consists of measuring the angular velocity a.c.f.'s in the x and z directions of the laboratory frame after inducing birefringence in the molecular liquid with an electric field E in the z axis. The cross-correlation function is then a convolution of the two angular velocity a.c.f.'s and the Fourier transform of the c.c.f. is, approximately, a ratio of the far infra-red spectra in the x and z axes. The time dependence of ⟨v( t ) ω T (0)⟩ is analysed using computer simulation and simplified analytical theory for different electric field strengths E . (Here v is the molecular centre of mass linear velocity and ω the molecular velocity).