Bimodal loop-gap resonator

JOURNAL

OF MAGNETIC

RESONANCE

loo,

484-490 ( 1992)

Bimodal Loop-Gap Resonator A. I. TSAPIN* AND JAMES S. HYDE National

Biomedical

ESR

Center,

Medical

College

of Wisconsin,

Milwaukee,

Wisconsin

53226

AND

W. FRONCISZ Department

of Biophysics,

Institute

of Molecular

Biology,

Jagiellonian

University,

Krakow,

Poland

Received January 31, 1992 A bimodal loop-gap resonator for electron-electron double resonance at X band is described. Considerable detail is given on frequency tuning; in one of the geometries described, a total tuning range of 500 MHz in the difference of the resonant frequencies of the two modes was achieved. The hypothesis is made that bimodal loop-gap resonators, because of their relatively low Q values, offer opportunities to arrive at structures that are more practical than bimodal cavities for routine EPR use. Data appear to support this hypothesis. 0 I 992 Academic pns, Inc.

Bimodal microwave cavities were introduced into electron paramagnetic resonance spectroscopy by Teaney et al. ( 1) and have been used by numerous investigators since then. A comprehensive analysis has been presented by Moore (2). These papers, and most of the others that have appeared (3)) have been concerned with cavities where the two modes resonate at the same frequency, permitting detection of induction in analogy to the crossed NMR coils of Bloch et al. ( 4). For induction, various “paddles” are introduced in order to decouple the two modes. The main technical problem lies in management of the decoupling strategy. Electron-electron double resonance, ELDOR, became feasible through development of bimodal cavities where the resonances were at different frequencies (5). In ELDOR, an intense pumping microwave frequency irradiates one transition, and saturation transfer to another transition is monitored with a weak observing microwave frequency. The key idea in the paper by Hyde et al. (5) was to create two resonant modes that in some regions of space did not overlap and in other regions of space were orthogonal. It then became possible to tune the resonant frequency of one mode without affecting the resonant frequency of the other mode. For ELDOR, the main technical problem lies in tuning the frequencies over a wide range. When the modes resonate at widely different frequencies, decoupling is a less serious problem. Loop-gap resonators (LGR) for EPR were introduced by Froncisz and Hyde (6). These lumped circuit devices are characterized by very high filling factor, 7, approaching * On leave from Institute of Chemical Physics, USSR Academy of Sciences, Moscow, Russia. 0022-2364192 $5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form resewed.

484

BIMODAL

LOOP-GAP

RESONATOR

485

unity, a rather low quality factor, QO, and a high value of microwave field, HI, for a given level of incident power. A review has recently appeared ( 7). Hyde et al. (8) used an LGR in a reflection bridge for ELDOR. The loaded Q was 230, corresponding at X band to a separation of 3 dB points of 41 MHz. Both pump and observe frequencies were incident on the resonator. These frequencies could be symmetrically placed about the resonance frequency of the LGR; alternatively, either the pump frequency or the observe frequency could be centered. It was generally preferable to center the pump frequency since it is necessary that the pump power not reach the observe detector crystal. Careful match of the resonator to about 30 dB combined with use of a microwave trap circuit reduced the pump microwave power at the detector crystal by more than 50 dB. The scheme works well, but several compromises are made: (a) the observe frequency is well separated from the resonance frequency of the LGR, thereby reducing the sensitivity, (b) the trap microwave circuit prevents the pump and observing frequencies from being set closer than about 5 MHz, and (c) the power reflected at the observe frequency can be similar in magnitude to the power in the reference arm, which complicates the bridge adjustment. For ELDOR between 14N and 15N spin labels, a separation of 26 MHz is required, and the approach in Ref. (8) worked very well. For ELDOR between adjacent hyperline lines of i4N spin labels, the required separation of 44 MHz was also manageable. However, it was not possible using this equipment to measure saturation transfer between the outermost lines of spin labels, e.g., ml = + 1 to ml = - 1. In this paper we study an alternative ELDOR strategy: the use of a bimodal loopgap resonator. As in the early ELDOR bimodal-cavity resonator, the microwave fields of the two modes do not overlap in some regions of space, but overlap and are orthogonal in the sample-containing region. In addition to ELDOR and to detection of induction signals, bimodal resonators could in principle be useful in a number of other fields of EPR spectroscopy. They are sometimes used in pulse EPR experiments in order to reduce the instrumental deadtime. There is an opportunity to improve the signal-to-noise ratio by 2 ‘/2 by quadrature detection, i.e., detecting both the induced signal and the reflected signal, and combining. We are of the opinion that they could be helpful in multiquantum EPR (9-12). In these experiments, there is a need to isolate intense CW irradiating microwave frequencies from the signal-detection system. Bimodal cavity resonators, despite intensive development, are not widely used primarily because the high Q values make them difficult to tune and decouple. Our working hypothesis is that the loop-gap resonator with its low Q and high filling factor offers the opportunity to arrive at practical bimodal resonator structures for routine EPR use. MICROWAVE

STRUCTURE

Figure 1 illustrates the bimodal resonator. Critical dimensions and performance data are given in Table 1. The two modes are supported by identical two-loop-onegap resonators. Symmetric resonators (i.e., idential loops) as well as asymmetric resonators with the two loops of each mode of different diameter, one being 8.4 times smaller in cross-sectional area than the other, have been constructed. In the asymmetric resonator, the small loops are crossed. It was used in most of our experiments. Consider

486

TSAPIN, HYDE,

AND FRONCISZ Sample Access

7

FIG. 1. Bimodalloop-gap resonator of the “asymmetric type.” See Table 1 for dimensions. The microwave coupling structures are not shown, and only one of the two frequency-tuning assemblies is illustrated. The static magnetic field is perpendicular to the plane that is determined by the two intersecting small loops. Cutout spaces above and below the loops are called “cups” in the text.

a line sample extending through the sample loop of one resonator. Only that portion of the sample that also lies in the sample loop of the other resonator can be considered active. The structure in Fig. 1 was machined into a block of rexolite plastic 2.95 X 1.93 X 1.93 cm using a numerically controlled mill. The gaps were cut by hand using a saw (blade thickness, 0.4 1 mm). It was then silver-plated on all sides to a nominal thickness

TABLE 1 Critical Data-Bimodal

Sample loop diameter (mm) Outer loop diameter (mm) Length of loops (mm) Separation of loop centers (mm) Gap (mm) Cup depth (cm) Cup width (cm) Cup length (cm) Material

Qo

ho (H, in gauss for 1 W incident power) Isolation (dB) Tuning screw diameter (mm) Tuning screw pitch (mm/turn) Tuning range of each mode (MHz)

Resonators Asymmetric

Symmetric

1.6 4.65 10 6 0.25 0.43 1.02 1.42 Silver-plated Rexolite 700 2.5 to 3 >35 8 0.31 50

2.6 2.6 10 6 0.4 0.43 1.02 I .42 Silver-plated Rexolite 1200 > 15-20 8 0.31 250

BIMODAL

LOOP-GAP

RESONATOR

487

of 10 pm. The static magnetic field must be perpendicular to the 1.93 X 1.93 cm faces. Silver plating on these faces was removed in order to facilitate penetration of 100 kHz magnetic field modulation. Rexolite is a microwave dielectric that has been used in this laboratory in many microwave circuits. It does not appear to contain paramagnetic species that could give rise to background contamination. Although the design is intended to keep microwave fields out of the rexolite, we chose to use it as a precaution against signals arising from stray fields that might enter it. Microwave coupling was by loops of nominal diameter, 5 mm, that terminate 0.14 1 in. coaxial semirigid cable. Variable coupling was achieved by mechanical adjustment of the separation of the coupling loop and the resonator loop. This type of coupling has been analyzed in considerable detail (13). The introduction of Ref. ( 14) surveys the various coupling structures that have been used for loop-gap resonators. The coupling loops are at one end of each of the large loops of the LGRs. Structures for tuning the resonant frequency of each mode are introduced at the other end of each large loop. Figure 1 also illustrates the frequency-tuning geometry. It shows a “cup” into which the tuning screw is inserted. An identical cup at the other side contains the coupling loop. The design concept is somewhat intuitive. Rather dispersed lines of flux pass across the space in the cups at the ends of loops from one loop to the other. Introduction of a suitable metallic object into this region can therefore be expected to shift the resonance frequency to a higher frequency. In order to achieve smooth tuning with good frequency resolution, a special tap was purchased to produce 80 threads per inch ( 3 1.4 per centimeter), as indicated in Fig. 1. Insertion of a sample shifts the frequency of one mode with respect to the other. By experience, this shift could partially be compensated by adjusting the dimensions of one of the gaps prior to silver plating. Fine tuning was accomplished by inserting small pieces of dielectric into one of the gaps such that with a sample inserted, the frequency of the sample-containing mode is Aw lower than the frequency of the crossed mode, where Aw is the range of the frequency-tuning device. The separation of the two modes then can be varied continuously over a range of 2Aw. It is noted that no “paddles” or adjustable means for minimizing the coupling between the modes have been used in the work reported here. Modulation coils were constructed for use at 100 kHz in a Varian EPR spectrometer. RESULTS

AND

DISCUSSION

A possible criticism of the design presented here is the small filling factor corresponding to the active region where both resonant fields overlap. Consider just one mode. As previously noted, the small loop has 8.4 times less cross-sectional area than the large loop. Since the total flux is the same in both and stored energy varies as H:, it follows that the stored energy in the small loop is 8.4 times that in the large loop. If a sample were to fill the small loop, the filling factor of 7 would be 8.4/9.4 = 0.89. This estimate of 7 neglects stored energy in any magnetic fields that might be in the gap itself and in the region beyond the ends of the loops, which is thought to be a fairly good assumption. This is, of course, a very high value; however, the walls of the sample tube exclude sample volume and reduce it by about 50%. The actual volume of the small loop is 20 mm3. The actual volume of the active region is 2.7 mm3, a ratio of 7.4. If a line sample of diameter about 1 mm extends

488

TSAPIN, HYDE,

AND FRONCISZ

through the resonator, the ratio of sample in the full length of the small loop to sample in the active region is 6.3. The two modes were tuned to the same frequency with such a line sample in place. An EPR signal was observed in reflection and in induction. The ratio of the signal intensities was about 5, in satisfactory overall consistency, noting that the RF fields fall off at the ends of the loops and are a maximum in the center. It was hoped in the design presented here to achieve a high degree of isolation for the following reasons: (a) the microwave coupling loops are well isolated from each other, (b) the tuning mechanisms are in regions of space (i.e., the cups) where microwave fields at only one frequency are expected to be present, and (c) construction using a numerically controlled mill should result in a high degree of mechanical precision. The isolation of the asymmetric bimodal resonator when the resonance frequencies coincide is reliably 35 dB and improves monotonically to 4.5 dB as the resonance frequency difference increased to 100 MHz. Isolation is not notably affected by sample insertion. Tuning of one resonance frequency does not significantly affect the other resonance frequency as determined using a microwave network analyzer to examine the properties of the structure. Isolation of the symmetric bimodal resonators was significantly poorer, being of the order of 15-20 dB when the difference frequency was less than 15 MHz and improving to 25 dB at 60 MHz separation and 30 dB at 100 MHz separation. All isolations were measured with an aqueous sample inserted. A series of special microwave test jigs was made in order to study frequency-tuning properties of the bimodal resonator. With the geometry in Fig. 1, frequency shift as a function of tuning screw position was determined as shown in Fig. 2a. The position labeled “0” corresponds to the tuning screw end flush with the top of the cup. The

-10

-5

0

10

15

TURN: FIG. 2. Frequency-tuning data. (a) Asymmetric resonator with tuning screw over large loop. (b) Asymmetric resonator with tuning screw over small loop. (c) Symmetric resonator. Each turn corresponds to 0.31 mm. The “0” turn position is with the end of the tuning screw flush with the end of the cup.

BIMODAL

LOOP-GAP

RESONATOR

489

fact that some shift was observed as the tuning screw recedes into the plate at the top of the cup suggests that a greater cup depth might increase the tuning range. The decrease observed when the tuning screw is very close to the loop arises, we believe, from interaction with the electric fields in the gap. If the tuning screw axis is shifted such that there is increased overlap with the gap, this decrease in frequency shift becomes greater. This observation suggests that an alternative frequency-tuning structure might be designed that is intended to interact with the microwave electric fields near the gap. Figure 2b is a measurement of frequency tuning when the tuning screw is directly centered over the small (i.e., sample-containing) loop of the asymmetric resonator. The smooth variation over a range of 250 MHz is notable. Of course, this would interfere with sample insertion, but it seemed likely to us that the tuning range would not change significantly if a sample access hole were drilled down the axis of the tuning screw of a diameter equal to that of the small loop of the resonator. This was verified experimentally. Figure 2c is a similar measurement on the symmetric resonator, again indicating a very wide tuning range. With tuning screws on both outer loops of the symmetric resonator, a total tuning range of 500 MHz is achievable. We studied isolation and Q as a function of tuning screw position. Up to about 12 turns, changes of Q were not significant, but some degradation was observed when the end of the tuning screw was very close to the loop. Frequency-swept ELDOR methodology is described in Ref. (15). The advantages are significant, but the technical complications of sweeping a microwave frequency with simultaneous tracking of the resonance frequency of a resonator are formidable. All ELDOR experiments carried out in this laboratory in recent years have used fieldswept ELDOR techniques where the two frequencies are preset and the static magnetic field is swept. The behavior seen in Fig. 2 is sufficiently encouraging that it would appear practical to develop a bimodal LGR structure for frequency-swept ELDOR. Biological applications of ELDOR have recently been reviewed ( 16). A complication in ELDOR experiments on spin labels is that there are two competing saturationtransfer ELDOR mechanisms: Heisenberg exchange and nitrogen nuclear spin-lattice relaxation. The first is intermolecular, and the second is intramolecular, which permits their separation by changing the concentration. Alternatively, separation can be based on the observation that Heisenberg exchange is independent of Am,, and nitrogen relaxation is dependent. Thus by performing ELDOR between the ml = + 1 and ml = - 1 lines of an 14N-containing spin label, and also between ml = fl and m, = 0, separation becomes possible. Our principal motivation in developing the bimodal ELDOR resonator was to be able to carry out experiments between the high- and lowfield lines as an additional control on our experiments. In work in progress using the bimodal resonator, reciprocal ELDOR reductions extrapolated to infinite power, R ;’ [see Ref. (5)] have been measured on various spin labels. Six experiments are possible: ml = + 1 ti mI = 0, ml = + 1 % m, = - 1, and ml = - 1 5 ml = 0. The data are generally consistent with the assumption that the electron spin-lattice relaxation rates for each hyperfme line are the same, and that Heisenberg exchange is in the strong-exchange limit. There are small inconsistencies possibly associated with breakdowns in the assumptions and additionally complicated

490

TSAPIN,

HYDE,

AND

FRONCISZ

by dipole-dipole intermolecular contributions to electron spin-lattice relaxation. It is our judgement that the capability to measure the six ELDOR signals using the bimodal resonator will be of significant value in refining ELDOR methodology. ACKNOWLEDGMENTS The work was supported by Grams GM22923 and RR01008 from the National thank Mr. Juan Luglio for making some of the microwave measurements.

Institutes

of Health.

We

REFERENCES

1. D. T. TEANEY, 2. 3. 4. 5. 6. 7. 8. 9. IO. II. 12. 13. 14. IS. 16.

AND A. M. PORTIS, Rev. Sci. Instrum. 32, 72 1 ( 196 1). W. S. MOORE, Rev. Sci. Instrum. 44, 158 (1973). C. P. POOLE, JR., “Electron Spin Resonance,” Wiley-Interscience, New York, 1983. F. BLOCH, W. W. HANSEN, AND M. PACKARD, Phys. Rev. 70,474 ( 1946). J. S. HYDE, J. C. W. CHIEN, AND J. H. FREED, J. Chem. Phys. 48,42 11 ( 1968 ). W. FRONC~SZ AND J. S. HYDE, J. Magn. Reson. 47, 5 15 ( 1982). J. S. HYDE AND W. FRONCISZ, in “Advanced EPR: Applications in Biology and Biochemistry” (A. J. Hoff, Ed.), p. 277, Elsevier, Amsterdam, 1989. J. S. HYDE, J.-J. YIN, W. FRONCISZ, AND J. B. FEIX, J. Magn. Reson. 63, 142 (1985). J. S. HYDE, P. B. SCZANIECKI, AND W. FRONCISZ, J. Chem. Sot. Faraday Trans. I 85,390l ( 1989). P. B. SCZANIECKI, J. S. HYDE, AND W. FRONCISZ, J. Chem. Phys. 93, 3891 ( 1990). P. B. S~ZANIECKI, J. S. HYDE, AND W. FRONCISZ, J. Chem. Phys. 94, 5907 ( 1991). H. S. MCHAOURAB, T. C. CHRISTIDIS, W. FRONCISZ, P. B. S~ZANIECKI, AND J. S. HYDE, J. Magn. Reson. 92,429 ( 199 I ) W. FRONCISZ, A. JESMANOWICZ, AND J. S. HYDE, J. Magn. Reson. 66, 135 ( 1986). T. OLES, J. S. HYDE, AND W. FRONCISZ, Rev. Sci. Znstrum. 60, 389 ( 1989). J. S. HYDE, R. C. SNEED, AND G. H. RIST, J. Chem. Phys. 51, 1404 (1969). J. S. HYDE AND J. B. FEIX, “Spin Labeling, III, Theory and Applications” (L. J. Berliner and J. Reuben, Eds.), p. 305, Plenum, New York, 1989. M. P. KLEIN,