ESM Method and Laplace Transform of Klafter-Blumen Equation for DET Analysis in Polymer Blend Like Materials
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ESN 14ETHOD AND LAPLACE TRANSFORM OF KLAFTER-BLUKEN EQUATION FOR DET AHALYSIS IN POLYKER BLEND LIKE NATERIALS. ONDER PEKCAN, Istanbul Technical University, Physics Department. Maslak, Istanbul, Turkey. ABSTRACT Fluorescence decay curves from particles composed of poly(vinyl acetate) (PVAc) and naphthalene (N) labelled poly (2-ethylhexyl methacrylate) (PEHMA) were analyzed for Direct Energy Transfer (DET) from N to anthracene by the exponential series method(ESM). An averaged apparent dimension of d=2.0 were observed. The Laplace transformed Klafter-Blumen(KB) equation for the lifetime distribution was used to interpret these dimensions. Additional fluorescence experiments were carried out on Polymer films composed of the same material above. Exposure of the films to a pentane solution of 9-anthrylmethyl pivalete (AMP) transferred the AMP molecules exclusively to the PEHMA phase of the material. ESM analysis together with transformed KB equation showed that PEHMA thread has a unique dimension of 1.3 in PVAc matrix of this polymer film. INTRODUCTION DET method together with the single photon counting technique is routinely applied to study many heterogeneous systems. Using fluorescence decays with DET the distribution of probe molecules embedded in fractal lattice [1] or in restricted has been characterized. Special attention was geometries [2] paid, to porous glass [3], silica [4] and polymer membranes [5]. In our previous work we reported that local structure of interpenetrating network like morphology can be characterized with DET method in polymer membranes [7] and in latex particles [6]. In these systems one might expect a distribution of donor lifetimes. ESM has been used to recover fluorescence lifetime distributions from both simulated and experimental decay data [8-12]. This method is based on a recover of the coefficients of an exponential series with a fixed lifetime. In fact, the from lifetimes recovery of distributions of fluorescence data are closely related to inversion of fluorescence decay Laplace transforms. In other words the fluorescence decay law can transform of a known distribution function be given by Laplace [11-12]. Recently we reported that ESM analysis can be used to determine dimensionality of rubbery network in a glassy polymer particle [13]. More general form of F6rster decay law [14] is known as KB equation [15-16] which was derived to explain donor fluorescence decay in fractal object in the presence of acceptors. KB Eq has been used to study effective dimensionality in restricted geometries [17-20]. In this paper the Laplace transform of KB equation was derived. The obtained distribution function was compared with the experimentally recovered lifetime distributions which were obtained from polymer particles and films. ESM was used to of lifetimes from an underlying distribution recover experimentally obtained donor fluorescence decays. Mlat. Res. Soc. Symp. Proc. Vol. 290. @1993 Materials Research Society
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EXPONENTIAL SERIES METHOD (ESM) In some cases the physical process under
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