Analysis of the radial and longitudinal effects of a planar sample in a single TE102 rectangular electron paramagnetic resonance (EPR) cavity

The response of the cavity to the rotation of a concentrically positioned planar sample of variable width, w (element of) (left angle bracket) 1 mm, 10 mm (right angle bracket) , around the common cavity-sample x-axis in a Bruker single TE102 rectangular cavity (radial effect) has been analysed. The observed dependence of the EPR signal intensity, Ipp, on the rotation angle has a general ovaloid shape with an eccentricity, (epsilon) , which varies linearly with the width, w, of the sample, (epsilon) = 0.0246 + 0.0311 × w, correlation, R = 0.996, for samples with a width greater than 2 mm but shows a positive deviation from linearity for the 1 and 2 mm samples. The dependence of the Ipp value on the planar sample width, w, is non-linear for all polar-angle values investigated. These experimental observations are in a very good agreement with theoretical calculations in which the response is modelled using the Cassinian curves modified for planar sample geometry. Similar trends of the angular Ipp dependence were observed for any position of the planar sample as the centre was moved along the vertical x-axis of the cavity. In the longitudinal Ipp dependence for a planar sample whose length, L = 30 mm, is greater than that of the cavity, then (i) for the case where the whole cavity length is occupied by the sample a constant value for the Ipp (a plateau) is observed and (ii) for sample movement in and out of this plateau region the dependence varies according to the left and right halves of a modified "sine-squared" function. The variation in the signal amplitude along the cavity x-axis (longitudinal effect) can be calculated theoretically using a "sine-squared" curve, modified for an "over full-length cavity" planar sample. In general, the response of the cavity to a planar sample situated at any position on the common sample cavity x-axis can be represented as a product of a modified Cassinian curve and a modified "sine-squared" curve. The non-linear radial effect may give rise to serious sources of systematic error in quantitative EPR spectroscopy with planar sample geometry and shows that accurate and precise positioning of the sample in the microwave cavity is essential.