James S. Hyde,a,* Robert A. Strangeway,a,b Theodore G. Camenisch,a Joseph J. Ratke,a and Wojciech Fronciszc
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在連續波（CW）EPR光譜學中，通常保持微波頻率恒定并通過EPR光譜掃描所施加的磁場。 原則上，可以保持磁場恒定并掃描微波頻率。 然而，由于微波元件，特別是放置樣品的微波諧振器是窄帶的，所以很少這樣做。
In continuous wave (CW) EPR spectroscopy, it is customary to hold the microwave frequency constant and sweep the applied magnetic field through the EPR spectrum. One could, in principle, hold the magnetic field constant and sweep the microwave frequency. However, this is seldom done because the microwave components, and, particularly, the microwave resonator in which the sample is placed, are narrow band. The bandwidth of a matched resonator Δf is given by the expression Δf = fo/Q, where fo is the microwave resonant frequency and Q is the quality factor of the resonator. Thus, the bandwidth can be increased by increasing the resonant frequency and also by decreasing the Q-value. We have developed a W-band (94 GHz) loop-gap resonator (LGR) that has a Q-value of about 100 [1]. Use of this resonator results in a 3 dB bandwidth of about 1 GHz, which makes microwave frequency sweeps feasible. So-called “frequency agile” EPR spectroscopy at W-band is the subject of this paper.
Rapid passage effects in EPR are well known. They arise from the sweep of the nominally static magnetic field through resonance while applying a sinusoidal magnetic field modulation of sufficiently high frequency and amplitude in the presence of sufficiently high incident microwave power. Weger has classified the various types of effects that can be observed [2]. A single sweep of the magnetic field through an EPR spectrum, if sufficiently rapid, can be expected to tilt the magnetizations of all lines in the spectrum such that the magnetization of each line has a component transverse to the applied field in the rotating frame. With the applied magnetic field, static after the completion of the single sweep, these magnetizations can be expected to precess at different rates as free induction decay (FID) occurs in the familiar manner of FT NMR. However, the possibility of developing a robust EPR analog to FT NMR using magnetic field sweep is remote because of the technical difficulty in producing a sufficiently rapid sweep and the complications arising from induced eddy currents in metallic components of the microwave resonator. In this paper, we show results of analogous experiments where the microwave frequency rather than the magnetic field is swept. The gyromagnetic ratio of the free electron, 2.8 MHz/G, can be used to compare field and frequency sweeps. Eddy currents in the sample resonator are avoided and sweeps of frequency can be much more rapid than sweeps of field.
We have previously described replacement of the customary 100 kHz magnetic field modulation by sinusoidal modulation of the microwave frequency [3]. In the present work, the microwave frequency is swept in either a triangular manner or a trapezoidal manner across a substantial portion of the EPR spectrum (see Fig. 1). Rapid sweeps were obtained with the apparatus of Fig. 2, where the output of this circuit is further mixed with a Q-band source to arrive at 94 GHz. Frequency deviations can be as great as 1 GHz at low repetition rates or as great as 40 MHz at a repetition rate of 2 MHz, with various intermediate combinations also allowed. The frequency sweep rates and maximum deviations are addressed in detail in section 1.4.
Frequency-sweep waveforms: (a) Example display of one of the triangular frequency-sweep waveforms used. (b) The trapezoidal waveform used for the data acquisition in Figs. 7 and and8.8. The H0 lines show the position of the EPR line center in ...
V-band source: YIG-tuned oscillator (YTO) translated by a fixed frequency Gunn diode oscillator (Gunn Osc). LPFs isolate the mixer from oscillator harmonics. The BPF passes the upper sideband from the mixer.
The method was applied to nitroxide spin labels in aqueous solution. The spectra are pure absorption in character if the sweep is sufficiently slow, but exhibit wiggles at more rapid sweeps. This class of experiments was previously explored in proton high-resolution NMR spectroscopy at much lower radio frequencies and longer relaxation times, where it was known as “correlation spectroscopy [4].” As technology improved, NMR correlation spectroscopy was replaced by pulse methods followed by Fourier transformation to produce spectra. In EPR, correlation spectroscopy was first reported by Stoner et al.using the so-called “trityl” radical, which has unusually long relaxation times [5]. They used magnetic field sweep across the single-line spectrum. The working hypothesis presented here is that microwave frequency sweep across the spectrum is an optimum experimental approach for many EPR experiments.
The W-band bridge used in the experiments described here is shown in Fig. 3. This bridge was developed at the National Biomedical EPR Center and previously utilized in somewhat modified configurations in sinusoidal microwave frequency modulation (FM) and saturation recovery (SR) experiments [3,6]. The bridge incorporates multiple frequency translations to generate coherent W-band frequencies from a time-locked synthesizer array, but only the arms used in the experiments described here are shown in Fig. 3. The outputs of the two synthesizers—nominally, 2 and 3 GHz—are upconverted by mixing with the output of a 33 GHz Gunn diode oscillator [7] in the Q-band upconversion mixers to produce 35 and 36 GHz. The synthesizers have a common time base and are thermally stabilized so that they are coherent over the length of the experiment. The 35 GHz Q-band output is then upconverted by mixing with the output of a tunable V-band Gunn diode oscillator—nominally, 59 GHz—in the W-band upconversion mixer. The W-band arm output is directed toward the sample resonator through a high-directivity directional coupler (the “resonator coupler”).
Frequency-swept W-band EPR bridge functional schematic. See Fig. 2 for components key. Nominally, the incident irradiation arm synthesizer is set to 2 GHz, and the reference arm synthesizer is set to 3 GHz. 33 GHz is upconverted to 35 GHz and then to ...
The microwave power reflected from the sample resonator in the vicinity of resonance can be determined from the reflection coefficient Γ:
(1)
where β is the coupling factor, Qu is the unloaded quality factor of the sample resonator (with sample; unloaded refers to “loading by the transmission line”), ωo is the resonant frequency, and Δω is the frequency deviation from resonance. In a conventional EPR experiment, Δω is nominally set to zero and maintained by an automatic frequency control (AFC) circuit. In a swept frequency experiment, Δω is swept from some nominal negative value, through resonance, to some nominal positive value. The direct implication is a frequency dependent offset to the baseline of a spectrum. The increase in the reflection coefficient can be appreciable at the extremes of a frequency sweep. For example, if a sample resonator with sample has Qu = 200 and a return loss of 35 dB (|Γ| = 0.0178) at a resonant frequency of 94 GHz, the return loss of the real part of the reflection coefficient at a 20 MHz offset from resonance is 34.1 dB while the return loss of the imaginary part of reflection coefficient is 27.4 dB. Baseline correction is implemented by subtracting the off-EPR resonance signal from the on-EPR resonance signal, as addressed later in this paper.