Heat transfer in NMR of conductive samples with radiofrequency decoupling

JOURNAL

OF MAGNETIC

RESONANCE

45490-502

(1981)

Heat Transfer in NMR of Conductive Samples with Radiofrequency Decoupling DOUGLAS Departments

of Pathology

S. MCNAIR

and Medicine, Baylor College of Medicine, Houston, Texas 77030 Received

May

8, 1981; revised

July

Texas

Medical

Center,

6, 1981

Under conditions of thermal and fluid mechanical equilibrium, heat transfer in a vortex-free liquid in an NMR tube spinning at about 30 Hz is evidently dominated by conduction, to first approximation. In contrast, heat transfer between the spinning tube and its stationary surroundings occurs primarily by convection. When high-power rf decoupling is used, lossy samples such as solutions of electrolytes or molecules having large electric dipole moments may exhibit large increases in average temperature as well as substantial radial temperature gradients, because of inductive dielectric heating. Equations for conduction of heat through such samples were applied to the case where chemical shift depends linearly on temperature, and the resulting expressions for the lineshape were fitted to alP spectra of arylphosphine derivatives which were obtained using loo-MHz proton noise decoupling. For samples with ionic conductivity equal to that of 0.05 M aqueous NaCI, radial temperature gradients of 2.1 and 0.3 K were observed in 12- and S-mm glass tubes, respectively, at 9 W radiated rf power and a maximum sample temperature of 302 K, 11 K above the temperature of the thermostatted gas stream entering the NMR probe. Twelve-millimeter coaxial-

cylinder

sample tubes and coaxial inserts machined from polycrystalline

beryllium

oxide have thermal conductivities 250 times that of glass tubes and equilibrate rapidly in the probe. Heating effects and radial temperature gradients in Be0 tubes equipped with coaxial Be0 inserts were too small to measure. However, calculations suggest that the values should be close to 0.03 K for 9 W decoupling and other conditions as used for the conductive samples in glass tubes without inserts.

Accurate measurement and control of sample temperature have long been a problem in NMR spectroscopy. When high-power heteronuclear decoupling is used, interaction between the radiofrequency electric field and the electric dipole moments of molecules and ions in the sample causes the sample to be heated and usually increases the uncertainty of temperature measurement. In cases where the ionic conductivity of the sample is low, heat generation resulting from absorption of rf energy is relatively small, and errors in temperature measurements may be made correspondingly small. Heating effects become large for aqueous solutions of high ionic strength (I -3), and the temperature at various locations in the active volumes of the sample may be far from uniform. Heating effects are of special concern in dynamic NMR studies of rate processes and chemical equilibria. Dipolar relaxation rates and NOES in systems where molecular reorientation is cooperative may also be sensitive to temperature dispersion arising from rf heating. Determinations of rotational correlation times and 490 0022-2364/81/120490-13$02.00/O Copyright 0 1981 by Academic Press, Inc. AU rights of reproduction in any form reserved.

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conformer distribution in biopolymer or liquid-crystalline lipid systems thus require that temperature be highly uniform and time invariant throughout the active volume and that it be accurately known. In the present work, heating effects produced by loo-MHz proton noise decoupling were observed in solutions having specific conductances comparable to those encountered in biological systems. The magnitudes of these effects and the rates of approach to thermal equilibrium were measured and a new method for controlling them proposed. THEORY

An oscillating electric field imposed on an electrolytic solution causes internal generation of heat, resulting from interaction of ions with their counterions and solvent molecules (4). For many solutions, the rate of heat generation 4 per unit volume depends linearly on the specific conductance mSspover a wide range (5). Very little is known about mechanisms of heat transfer inside NMR sample tubes, but observations by Levy et al. (6) and others suggest that rapid spinning impairs transfer of heat by free convection and that conduction may be the predominant mode, both in the axial direction and in the radial direction. Taking this as a first assumption, expressions can be derived which describe the steadystate conduction of heat and the radial temperature profiles in sample tubes represented by (1) solid or (2) hollow cylinders. In both cases, the active volume which gives rise to the NMR signal has a relatively small height, so that thermal end effects along the axis can be made arbitrarily small. Combined with the property of cylindrical symmetry, this allows simplification of the heat conduction model to a problem in only one dimension (infinitely long cylinders), written mathematically as aT(r, f) -----=a at

@T(r, t) + 1 Wr, f) ar2 r ar

1+4 (t>0;0
[II

CPP

where T is absolute temperature, I is time, r radial coordinate, and a! the thermal diffusivity (equal to k/c,p, k the thermal conductivity of the sample, c, the specific heat capacity at constant pressure, and p the density). Variations in convective heat transfer at the outer surface of the tubes may be neglected in first approximation so that initial and boundary conditions for the solid cylinder of radius R are simply T(r, 0) = T,,; aT(O, t)l&

= 0;

T(R, t) = T,,; T(0, t) f a.

PI

Conditions for a hollow cylinder having inner and outer radii R, and Rlr both surfaces at constant temperature, are the same except T(R,, t) = T(R,, t) = T,

Both problems can be solved analytically yield the relations AT(r)

= T(r, 00) - T,, = q(R’

(t 2 0).

using integral transforms - r2)/4k

(0 < r < R)

r31

(7,8)

and [41

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DOUGLAS

S. MCNAIR

for the solid cylinder and J-C,-)= qr,

m) - ~~ = (qMk)(R:

- r2 - 2RF, In (R,IrN,

R, < r < R,,

= (q/4k)(R:

- r’ - 2R,? In (RJr)),

R, < r < Rz

for the hollow cylinder, ture and

where k and q are independent

[51

of time and tempera-

R” = CR: - R3 [61 n In (RiIR:) ’ If we further assume (1) that the shielding of a particular nucleus is linearly dependent on the ambient temperature and changes at the rate h Hz.K-I, (2) that the corresponding temperature coefficient of the nucleus used for neld/frequency locking is negligible over the range T,, to T(0, to), (3) that H, and H2 rf magnetic fields and the electric fields that accompany them are homogeneous, (4) that corrections for filling factor variations are small, and (5) that sensitivity of NMR detection is independent of the radial coordinate (negligible skin effect; see (3) above), then the NMR absorption-mode spectrum represented by a continuous superposition of infinitely narrow lines 6(v,) may be written 1 G(v)a

AAT

(AAT(0))1'2I o

for the solid cylinder,

(hAT(0) - u~)~'%(u- vo)dvo,

171

where 6 is the Dirac delta and v,(R) = 0.

In the case of Lorentzian lines of nonzero width, the convolution-product for Fourier transforms gives G(v)a

1

theorem

AAT

(AAT(O))"2I o

(hAT(0) - ~~)l’~[l + 4@T;“(v - vo)2]-1duo,

PI

where T$ has its usual meaning. Computations were performed using this expression for various values of Tg and other parameters normalized and dimensionless, resulting in the family of theoretical spectra plotted in Fig. 1. This expression was also used in the least-squares fitting of experimental spectra as discussed below, to obtain estimates of AT(O)in samples contained in glass tubes without inserts. EXPERIMENTAL

NMR Spectroscopy

Phosphorus-31 spectra were obtained in the Fourier transform mode with a Varian XL-loo-15 spectrometer operating at 40.52 MHz. A Nicolet 1080 minicomputer equipped with NTCFT software was used for data acquisition and reduction, and Transform Technology pulse hardware provided lo-psec pulses for all experiments. Quadrature-phase detection was used throughout, with a constant acquisition time of 10.24 set (4 K word and 200-Hz spectral width for observing triphenylphosphine oxide only, offset synthesizer set on-resonance; 32 K word

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3.0

0.8 0.6 0.4 -

3.0

2.0

1.0

0.0

-1.0

-2.c I-

FIG. 1. Theoretical lineshapes for nucleus showing downfield shift with increasing temperature, for values of T; shown. The abscissa is dimensionless normalized frequency, corresponding to normalized values of tube radius, sample thermal conductivity, dielectric loss, and absorbed rf power per unit volume.

and 1600-Hz spectral width otherwise; digital resolution 0.098 Hz) and no delay. No exponential broadening or apodization were used. Nitrogen pressure and flow to the turbine were adjusted to give spinning rates of 25 to 28 Hz for each of the sample tubes used. Proton noise-decoupling power at 100 MHz was varied between 4 and 9 W with an uncertainty of about 0.5 W. A Bird Engineering Model 43 directional wattmeter was used for measurements of forward and reflected power. Measurements of H2 field strength by the method of Pachler (9) showed full decoupling in the range 4 to 9 W. Serial experiments on each sample tube were performed at each value of decoupler power, and at least 12 hr was allowed for probe equilibration after a change in decoupler power. The Varian V4412 probe employs a crossed-coil design with a Faraday shield. Each sample was shaken with Chelex 100 (Bio-Rad) resin and degassed by bubbling with dry argon for 2 min immediately prior to being sealed in the NMR tube. Temperature

Measurement

and Control

Temperature of the cooled nitrogen supplied to the Varian variable temperature controller was approximately 282 K, and the flow rate measured at the temperature controller rotameter (300 K) was 1000 liter. hr-‘. The settings of the temperature controller and the nitrogen flow remained constant during all of the work described. Gas delivered to the probe was regulated at 291 K. Temperatures of the nitrogen and of samples in glass tubes in the probe were measured with a Yellow Springs Instrument Series-400 thermistor and a Technical Hardware Corporation TM-401 digital bridge. For each tube type, between-run reproduci-

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bility was determined by measuring the chemical shift difference between (C,H,),P and (C,H,),PO (10). Calibrated against thermistor readings for temperatures between 291 and 333 K, the chemical shift difference for the solutions studied was characterized by a temperature coefficient of approximately - 1.3 Hz- K-l at 40.52 MHz, consistent with the value previously reported in toluene solutions. The tempco A for the triphenylphosphine oxide resonance was 0.9 Hz. K-’ in the downfield direction. Lineshape fitting to calculate the positions of the two peaks gave between-run deviations of less than +-0.1 Hz during the period 2 to 12 hr after introducing the sample into the probe, corresponding to temperature drift of 20.1 K or less. Materials

Dimethyl sulfoxide-d, (99.5 atom%) was obtained from Aldrich Chemical Company. LiBr and LiCl were analytical grade (J. T. Baker and Alfa Ventron). Saturated solutions of LiBr or LiCl in DMSO-d, were dried with 3-A molecular sieves (Fisher) and diluted with dry DMSO-d, to give a specific conductance of 5.55 x 10m3 fi-l.crn-l at 298 K, measured with a Radiometer CDM3 bridge equipped with a 0.316-cm CDC314 cell and calibrated using KCl. Triphenylphosphine and triphenylphosphine oxide were from Tridom-Fluka and were purissimum and practicum grades, respectively. Glass 12-mm flat-bottom tubes and the 5-mm coaxial cell were Wilmad types 5 14A-7PP and WGS- 12BL. The glass 12-mm tube was fitted with a glass antivortexing plug. Polycrystalline 98%-dense beryllium oxide parts were fabricated by Accuratus Corporation, Washington, N. J. Numerical

Analysis

A CDC 7600-based CYBER 174 machine was used for all lineshape calculations, except as noted. Simpson’s rule was applied in numerical approximations of integrals. Experimental spectra were analyzed using a IO-point (0.5 Hz per point) least-squares fit to the theoretical lineshape previously described. The first point for the triphenylphosphine oxide lines was taken 2.00 Hz downfield from the peak, the peak itself being assigned to the fifth point at 0.00 Hz. A 700-line FORTRAN implementation of a modified Gauss-Newton procedure originally developed by Powell (II) for two parameters (X,, a dimensionless coefficient; Xp, the total shift dispersion in hertz, equal to hAT(0)) was used. The routine incorporates an iterative matrix inversion scheme to optimize the two parameters, which are initially set to arbitrary values. The procedure also incorporates a steepest-descent algorithm with all derivatives approximated by finite differences. Convergence of the routine was found to be somewhat sensitive to the accuracy of the initial values of the parameters, because of the nonlinear nature of the equations. RESULTS

Rate

of Thermal

AND

DISCUSSION

Equilibration

Insertion of a conducting sample into an NMR probe may affect heat transfer in the probe in several ways. For a cylindrical tube of radius RI which rotates

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about its axis and is enclosed in a stationary, coaxial cylindrical cavity of radius Rz, the flow of gas in the annular gap may be characterized as predominantly laminar, turbulent, or vortex. The flow type is determined by the Reynolds number of gas flow in the axial direction, by the Taylor number for flow at a particular angular rate of shear, and by the log-mean gap ratio, equal to In (R,/R,) (12). In turn, convective heat transfer in rotating systems is sensitive to changes in the Reynolds and Taylor numbers (I.?-15), as well as changes in the Nusselt number, a parameter whose value is linearly related to the heat transfer coefficient of each of the surfaces. Unfortunately, no heat transfer data are available for this or for any closely related system. For the geometry, dimensions, angular velocities, and temperatures found in the Varian 12-mm NMR probe with 1000 liter.hr-’ of gas flowing through it, the Nusselt number may have a temperature coefficient of perhaps 0.21%.K-’ (calculated assuming fully developed, laminar flow; see (16)), and the Reynolds and Taylor numbers are expected to change about 0.39%. K-l, in first approximation. Noteworthy in this connection, differences between the temperature of the gas stream and the temperature in the center of proton-decoupled conductive samples ranging up to several tens of degrees Kelvin have been reported by Led and Peterson (I ). With the decoupler turned off, gas and sample temperatures were not detectably different. In this work, temperature increases of 11 and 0 K were observed for the 12-mm glass tube at 9 and 0 W radiated power, respectively, measured with thermistors positioned in the entering gas stream and at the center of the active region of the sample under steady-state conditions. Radiofrequency heating of a sample not only alters the spatial distribution of heat generation in the probe but also affects the rates of convective transfer at tube and probe surfaces. In principle, any nucleus having a nonzero chemical shift temperature coefficient can be used to examine thermal equilibration without perturbing the sample temperature. However, most practical chemical shift thermometers have accuracies not better than 1 K (17-22). One exception is the phosphine 31Pthermometer developed by Dickert and Hellmann (10). For diamagnetic samples of stable composition in well-sealed tubes, the linewidths are determined mainly by Zf, inhomogeneity and temperature dispersion, and accuracy and precision somewhat better than 0.4 K can be routinely achieved. Better still is the 5gCo(CN)3-, thermometer recently proposed by Levy and co-workers (6), which appears to afford precision on the order of 0. I K. The haloalkane 13C thermometers developed by Vidrine and Peterson (21) are also sufficiently sensitive for observing the effects of rf heating but have the disadvantage that the coefficient of the chemical shift is nonlinear in temperature. The uncertainty in the measurements therefore exhibits undesirable temperature dependence. Tradeoffs involving sensitivity, S/N ratio, and spectral resolution impose an upper limit on the rate at which temperature information can be obtained by chemical shift thermometry. In practice, suitable data could not be acquired fast enough from the phosphine system to permit detailed modeling of the kinetics of thermal equilibration of the sample. Qualitatively, it was observed that electrolytefree samples in glass tubes showed triphenylphosphine-triphenylphosphine

496

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S. MCNAIR

oxide chemical shift differences that were stable to within instrumental and digital resolution approximately 30 min after insertion into the probe, while conductive samples in glass exhibited detectable drift for up to 200 min, depending on the rf power radiated by the decoupler. Steady-State

Radial Temperature

Profile

Effects of rf heating on the mean, steady-state sample temperature are widely recognized. Recently, temperature gradients caused by inductive dielectric heating of conductive samples have also received attention (I, 6), but in general the magnitude of the gradients has not been accurately known. Thermocouple or thermistor thermometry is ill suited to studying temperature gradients in NMR tubes, for it is subject to a variety of systematic errors (23,24) including thermal leakage through the sensor leads, rf inductive heating of the sensor itself, and viscous heating and mixing of the rotating liquid sample. Previous use (1) of nonperturbing chemical shift thermometry employed a nonconducting carbon tetrachloride-acetone thermometer solution and a conducting aqueous solution in a double-wall coaxial tube system. Temperature and thermal resistance discontinuities are small for such a system if the partition separating the two liquid phases is thin and has a thermal conductivity similar to that of the liquids (k4300 K) = 6.1 x 10e3 W.cm-‘*K-l; k ,,,,(300 K) = 1.1 x lo-’ W*crn-.‘*K-’ (25)). Results obtained by comparing two experiments-first with the lossy liquid in the annulus between the two tubes and then with the lossy liquid in the inner tubeseriously underestimate the difference between the axial and peripheral temperatures in homogeneous conductive samples which, unlike the three-phase aqueousglass-organic system, show uniform dielectric loss. Boundary conditions and heat TABLE RADIAL

Sample

TEMPERATURE GRADIENTS INDUCED BY CONTINUOUS NOISE DECOUPLING IN A CONDUCTIVE SOLUTIONS

lOO-MHz

tube

o.d. (mm) 1.2 5.0h 5.0” 12.0 12.0 12.0 12.0

1

Material Glass Glass Glass Glass Glass BeO, BeO,

with insert no insert

Decoupler, radiated power ov 9 4 9 4 9 9 9

Gradient Linewidth (H-8

T WI

0.3 0.4 0.6 1.8 2.4 2.4 2.6

0” 0.3, 2.0, w 2.2,

+

2 SD(K) 0.1, 0.1, 0.2,

cl Experimental conditions: (1) specific conductance: 5.55 x 10m3 fl-‘.cm-’ (-0.5 M LiBr, 0.1 M (&H,),P and 0.1 M (&H,),PO in DMSO-d,) at 298 K; (2) radiated lOO-MHz noise decoupling: (Forward-Reflected) kO.5 W; (3) gas temperature control fixed, set to deliver 1000 liter.hr-’ at 291 K to probe. b Wilmad-type WGS-12BL coaxial inner cell enclosed in 12-mm glass tube, type 514A-7PP. c Precision limited by H, inhomogeneity-related line broadening, arising from tube imperfections.

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A B FIG. 2. 31P spectra of 0.1 M triphenylphosphine oxide in dimethyl sulfoxide-d,. LiBr, 0.5 M. Temperature at the vertical axis of glass sample tube was 302 K, for lOOO-liter. hr-’ gas flow at 291 K. Radiated decoupling power was 9 W. Plot width: 15 Hz. (A) 12-mm glass tube, 640 scans, (B) 1.2-mm glass tube, 3600 scans.

flow as a function of the radial coordinate for each of these systems are different, making such comparisons invalid. In most of the present work, a single-phase system was used to ensure that dielectric properties and chemical composition were as homogeneous as possible. Two exceptions are noted below. First, for numerical analysis of temperature-broadened 31Plineshapes, estimates of the intrinsic linewidth v~,~in the absence of broadening were required. For this purpose, a three-phase system was used which consisted of a glass capillary (1.2mm o.d.) pulled from a borosilicate Pasteur-type pipet and filled with dimethyl sulfoxide-d, approximately 0.5 A4 in LiBr and 0.1 M each in triphenylphosphine and triphenylphosphine oxide. The capillary was centered in a 12-mm glass tube which contained 0.5 M solution of LiBr in DMSO-d6 identical to that in the capillary except for lacking phosphines. Three slP spectra were obtained using 9 W of radiated proton noise decoupling, and the triphenylphosphine oxide line in each was least-squared fitted (NTCFT) to a Lorentzian function. The effective transverse relaxation time so determined was 0.9 set, with a 99% confidence interval of kO.1 set for each (Table 1). Second, a three-phase 12- to 5-mm coaxial system using the same solutions was employed in attempts to check the reliability of the heat conduction model, by changing the radial dimension of the active volume. Chemical shift dispersion, presumably temperature related, of (C6H,),P0 in the inner 5-mm cell gave lines that were consistently 0.3 Hz wider than those observed in the 1.2-mm capillary at 9-W decoupling, corresponding to a calculated temperature difference of 0.3 * 0.1 K from the inner surface of the 5-mm cell to its axis (Table 1). The symmetrical, Lorentzian shape of the lines was preserved (Fig. 2), as expected for the relatively small T,*. Linewidths observed with the decoupler off were equal to those for the 1.2-mm capillary.

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DOUGLAS

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Clearly, lineshape analysis cannot reliably determine whether the broadening is attributable to temperature gradients unless the lines are significantly distorted. For this reason, the calculations reported for the gradient in the 5-mm cell should be a reasonably accurate estimate of the gradient in a free-spinning 5-mm tube under similar conditions, for the gradient AZ(O) does not depend strongly on the filling factor or on the rates of heat generation and conduction in the region R, < r < R2.

In contrast to the spectral symmetry observed for the 5-mm cell, the singlephase 12-mm glass system gave characteristic, distorted lines (Fig. 2) up to 2.5 Hz wide. Distortion was sufficiently pronounced to permit moderately precise calculations of the radial temperature gradient (Table 1). The value for a sample having a specific conductance of 5.55 x lo-” R-‘.cm-’ and receiving 9-W proton decoupling at 100 MHz was 2.1 + 0.2 K (99% confidence limits). Gradients of this size would be unacceptable in many of the settings where NMR is a favored or, occasionally, the only applicable technique. One of several effective methods of minimizing the radial temperature gradient is to reduce the cross section of the active volume. For cylindrical geometry, an active volume with a tolerable temperature gradient could be achieved, for example, by using a 1.2-mm capillary tube (solid cylinder). Alternatively, it is possible to obtain improved sensitivity for any given temperature gradient by using a thin annular active volume (hollow cylinder; cf. Eqs. [4] to [S]). In addition, there is a small advantage in arranging for the inner and outer surfaces of the annulus to have very nearly identical temperatures (26). This can be accomplished (Fig. 3) by maximizing the thermal conductivities of the

plastic

connector

beryllium

FIG. 3. Beryllium oxide sample tube and coaxial type was limited by H, inhomogeneity arising from

oxide

plug

insert. Spectral resolution achieved imperfect symmetry and camber.

with

proto-

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FIG. 4. 3LP spectra of 0.1 M triphenylphosphine oxide tube. LiBr, 0.5 M. Average temperature 291 K. Plot width: I5 Hz. Radiated decoupling insert, 3600 scans.

IN NMR

499

Oxide

oxide in dimethyl sulfoxide-d, in 12-mm beryllium in the sample was identical to that of the gas stream, power: 9 W (A) Without insert, 640 scans, (B) with

cylindrical plug and the coaxial tube which surrounds it and by minimizing the thermal resistance between the plug and the inner surface of the tube. Beryllium oxide is a material that is ideally suited to this purpose. With a conductivity of 2.72 W.cm-l.K-’ (Ref. (25, Vol. 2, p. 137)), it is a low-loss dielectric whose thermophysical properties are outranked only by those of diamond and are comparable to those of metallic copper (kc-(300 K) = 3.98 W *cm-‘.K-‘). Heatsink grease (k(309 K) = 6.99 x lo-” W.cm-l.K-’ (27) was used to establish thermal contact at each end of the plug. A Be0 tube enhances the rate of thermal equilibration slightly, compared to a Be0 plug in a glass tube. It may also afford a smaller temperature variation in the axial direction at a modest decrement in filling factor (thicker walls). No attempt was made to measure the axial temperature variation. Representative spectra obtained with the annular Be0 cell are shown in Fig. 4. Lineshapes for 9- and 4-W noise-decoupled spectra were indistinguishable, within experimental uncertainty. The finish on the inner surface of the tube was approximately 32 pin. arithmetic average, and tolerances for concentricity and local straightness (camber) were 50.003 in. for the prototype. The linebroadening apparent in Fig. 4 is consistent with an origin in H,, inhomogeneities associated with tube imperfections of these magnitudes (28). The broadening is similar to that for glass tubes of comparable precision, suggesting that resolution might be considerably improved if some of the imperfections were eradicated. The Be0 assembly equilibrated in the probe within about 30 min, and the average temperature of the sample measured using the 31P thermometer was not detectably different from the temperature of the gas stream. The relatively large linewidth impaired estimation of the radial gradient by lineshape analysis. However, if the heat conduction models for the solid and hollow cylinders are valid and if the 2.1 K gradient calculated for the 12-mm glass tube is accurate, then the temperature variation in the annular space formed by the Be0 insert and tube ought not to be larger than about 0.03 K at 9 W radiated rf power. Other calculations based on the models and assumptions previously described indicate that a

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cylindrical active volume 1.4 mm in diameter would be necessary to obtain a gradient equal to that in the l.O-mm-wide, 8.4-mm-o.d. annulus of our Be0 prototypes. Neglecting differences involving other contributions to instrumental sensitivity, the number of nuclei in the annular active volume is 14 times that for a 1.4-mm cylindrical one, a theoretical advantage of about 23 dB. In general, other means of establishing a comparably small gradient are inferior to Be0 annuli or glass capillaries. For example, thermal mixing of a sample by forced convection produced by stirring devices is unacceptable for certain biological samples which are sensitive to fluid mechanical shearing forces. Moreover, forced macroscopic mass flux inside a sample tube is not easily controlled or reproduced and is not sufficiently isotropic within the active volume to permit reliable relaxation and Overhauser measurements (29,3(J), even for fully developed turbulent flow. Undesirable phase, amplitude, and lineshape changes also occur with mass flux between regions of different static and rf field strength and homogeneity. Regarding forced convection in the gas outside the tube, it should be emphasized that efforts to enhance convective or conductive heat transfer between a sample tube and its surroundings may help to increase the rate of thermal equilibration and to reduce the difference between the temperature at the center of the sample and that of the entering gas stream, but they may also increase radial temperature variation in the sample. The merits of using a large gas flowrate as recommended by Led and Peterson (I ) are therefore in doubt when the radial temperature variation-and not simply the average temperature increaseis important. CONCLUSION

In recent years, a variety of procedures for minimizing temperature uncertainties in NMR spectroscopy have been advocated. Restricting the power spectrum of Hz field to only those regions of the frequency domain actually needed for decoupling a given sample, using the minimum decoupling field that provides acceptable multiplet collapse and narrowing, reducing the magnitude of H2 outside the active volume, and adding delays to reduce the duty cycle are useful but not always satisfactory. Where high ionic conductivity cannot be avoided, the use of high-current, low-inductance decoupler coils (31), together with a Faraday screen (32), can substantially diminish the rfelectric field intensity. To these wellknown strategies may now be added the judicious use of Be0 sample tube designs. An annular sample cavity, consisting of a step-ground coaxial Be0 plug made to fit inside either a Be0 or glass tube, should afford spectral resolution in proportion to the precision of its construction, as well as excellent sensitivity and S/N compared to a glass capillary for any given value of the radial temperature gradient. The small mean-free pathlength is the feature mainly responsible for the small radial temperature gradients (26,33,34). That is, a single-phase system in a Be0 tube without a coaxial Be0 insert exhibits radial gradients (Table 1) not less than and perhaps exceeding those of a glass system of equal cross section, because of enhanced conduction and convection at the outer surface. Similarly, a Be0 in-

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sert in a glass tube gives temperature gradients not significantly different from the all-Be0 system. Other arrangements which afford small mean-free paths, such as packed beds, can achieve even smaller gradients (33,34) in cases where spectral resolution may be sacrificed. In summary, there is little advantage to using coaxial Be0 inserts when studying samples whose dielectric loss is small. Nor is it necessary, for example, in dynamic proton NMR, when high-power heteronuclear decoupling is not used. However, the relative simplicity of dynamic spectra of nuclei other than proton, the comparatively greater chemical shift range of the other nuclei, and several other factors (35) that contribute to the importance of high-power-decoupled dynamic NMR of nuclei other than proton favor the use of beryllia in a wide range of applications involving conductive samples. The material should prove especially useful in biochemical studies and in work at superconducting fields. Once it is machined and polished to its final form, equipment made of Be0 is chemically and mechanically stable, to a degree that no particular precautions are required for its safe use by laboratory personnel. ACKNOWLEDGMENTS This work was supported in part by institutional gratefully acknowledges additional support from M. Gotto, and Malcolm H. McGavran.

funds from Baylor College Professors Joel D. Morrisett,

of Medicine. The author Jack L. Titus, Antonio

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