Dynamic Heterogeneity by Higher Moments of a Relaxing Quantity
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R. RICHERT Max-Planck-Institut fir Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany ABSTRACT A relaxation experiment usually acquires a measure for the mean energetic distance of the system from the thermodynamic equilibrium and its temporal evolution. For sufficiently small perturbations necessary to assure linear responses such data is bound to remain undecisive as regards the spatial nature of the relaxation process, heterogeneous or homogeneous. The technique of solvation dynamics near the glass transition can probe the entire distribution of site specific energies and its approach towards equilibrium, so that apart from the mean solvation energy v(t) also higher moments in terms of the inhomogeneous optical linewidth ainh(t) become accessible. While v(t) maps the dielectric relaxation behaviour of the liquid, cinh(t) is found to be sensitive to the spatial nature of the underlying process. Contrasting experiment and simulation leads to the conclusion, that the relaxation time is a site specific quantity, i.e. the heterogeneous nature is found to dominate. INTRODUCTION A common feature of supercooled liquids is their approach 4(t) towards equilibrium in a nonexponential fashion, even if the perturbation is small enough such that the response is linear with respect to the amplitude of the perturbation [ 1,2]. For the ensemble averaged structural relaxation or cc-process temporal patterns which are approximated by the stretched exponential or Kohlrausch-Williams-Watts (KWW) decay function ý(t) =-o.exp[-(t/tww)
] , 0 PE transition is to initiate a dielectric relaxation process of the adjacent liquid towards the equilibrium with respect to the excited state dipole moment 9E [6]. The quantities observed by phosphorescence spectroscopy are the energy differences v(T 1 ) - v(S 0 ). Polarizing the liquid by the electric field created by Aji lowers the energy level of the excited state and increases that of the ground state, such that the emission energy vi(t) of each probe molecule 'i' becomes a function of time whenever orientational polarization is active within the lifetime -cph of the excited state T 1 . The average emission energy v(t) = (vi(t))i reflects the dynamics of the Stokes shift which is quantitatively dictated by the dielectric properties of the solvent regarding both the temporal pattern and the absolute energy values [7,8]. At time t = 0 the emission spectrum is a gaussian profile characterized by its mean v(O) and standard deviation Uinh(0) and in the equilibrium state the spectrum is again of gaussian shape with standard deviation Uinh(OO) = Uinh(0) = U,, but with a red-shifted mean value at v(oo) [8]. The entire Stokes shift is given by Av = v(0) - v(00) and the normalized decay is represented by the so called Stokes shift correlation function C(t) = [v(t) - v(00)] / [v(O) - v(x)]
(3)
.
Detailed solvation data is available for quinoxaline (QX) as a phosphorescent chromophore with a lifetime tph &0.3 s dissolved in the glass-former 2-methyltetrahydrofuran (MTHF) [6-8]. For this example a
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