Dresden 2009 – wissenschaftliches Programm

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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 15: POSTERS Dynamics and Diffusion

CPP 15.12: Poster

Dienstag, 24. März 2009, 14:00–16:30, P3

Fourier-series approach for analytical treatment of diffusion in periodic systems (Floquet method) — •Günter Hempel — Martin-Luther-Universität, Institut für Physik, D-06099 Halle, Germany

The data evaluation of diffusion experiments in periodic systems is often performed (i) at numerical way, (ii) at the basis of an approximately exponential behaviour, or (iii) by means of an analytical solution in terms of rather complicated analytical expressions. Here a simplification is proposed: The diffusion equation is expanded in Fourier series with respect to space coordinates (Floquet method) which results in a system of ordinary differential equations. Solving the latter we obtain the time evolution of the Fourier coefficients of the concentration distribution. They decrease exponentially; the higher the order of the Fourier coefficient is the faster is the decay. At this way the concentration-time dependency can be estimated.

Depending on the experiment, the term concentration might be replaced by temperature, magnetization, spin polarization, or others. Moreover, sometimes not this generalized concentration is of interest but its integral, here denoted as intensity. (In the case of concentration as particle density, the intensity will be the total amount of particles in a certain volume.) This procedure was applied to the data evaluation of a nuclear-spin diffusion experiment in lamellae of a lactide macromonomer. The local magnetization density plays the role of the generalized concentration, and the magnetization of a lamellae that of the intensity.