Deconvolution of sinusoidal rapid EPR scans

Abstract

In rapid scan EPR the magnetic field is scanned through the signal in a time that is short relative to electron spin relaxation times. Previously it was shown that the slow-scan lineshape could be recovered from triangular rapid scans by Fourier deconvolution. In this paper a general Fourier deconvolution method is described and demonstrated to recover the slow-scan lineshape from sinusoidal rapid scans. Since an analytical expression for the Fourier transform of the driving function for a sinusoidal scan was not readily apparent, a numerical method was developed to do the deconvolution. The slow scan EPR lineshapes recovered from rapid triangular and sinusoidal scans are in excellent agreement for lithium phthalocyanine, a trityl radical, and the nitroxyl radical, tempone. The availability of a method to deconvolute sinusoidal rapid scans makes it possible to scan faster than is feasible for triangular scans because of hardware limitations on triangular scans.

Fig. 1

(a) The modified magnetic field scan profile (blue dashed line) is compared with the experimental sinusoidal scan (red curve). The insert shows the transition from sinusoidal to linear scan in detail. (b) Absolute value of the Fourier transforms of the driving functions for the sinusoidal (red) |D(B)| and modified field scan profiles (dashed blue) |D’(B)|. The insert shows that |D’(B)| coincides with |D(B)| between about −4.25 and 4.25 G, but does not exhibit oscillatory behavior. To emphasize the correspondence between the y-axis of (a) and the x-axis of (b), both axes are labeled in gauss.

Fig. 2

Composite magnetic field profile for rapid scans of LiPc, consisting of two cycles of triangular scan followed by two cycles of sinusoidal scan. The transition between the triangular and sinusoidal scans is marked with a circle.

Fig. 3

Central 10% of rapid scan (a) absorption and (b) dispersion signals for LiPc measured with up-field triangular, trace 1, or sinusoidal, trace 2, scans. For each scan, the x axis is relative to the beginning of the half cycle. Since the signal was not exactly centered in the scan, resonance occurs at slightly different times in the scans.

Fig. 4

Segments of the slow scan absorption spectra of LiPc obtained by deconvolution of the triangular (blue solid) and sinusoidal (small green circles) scans shown in Fig. 3.

Fig. 5

EPR spectra of trityl-CD₃ obtained by deconvolution of sinusoidal (upper, green line) or triangular (lower, blue dashed line) rapid scans. 85% of the full scan width is displayed.

Fig. 6

EPR spectra of aqueous tempone-d₁₆. a) Down-field half cycle of the sinusoidal rapid scan. b) Comparison of the sum of spectra obtained by deconvolution of up-field and down-field signals (trace 1, green) with CW spectrum (trace 2, blue dashed line), and the difference between traces 1 and 2 (trace 3, red).