Spin-lattice relaxation of 15N nuclei

CHEMICAL PHYSICS LETTERS

v01@ic 7. number 5

SPIN-LATTICE

RELAXATION

OF

1 Dccembx

15N

NUCLEI

T. SALUVERE and E. LIPPMAA Inslilrrle of Cqbernelics of fhe Estonian Acadeny oJ.Sciences,

‘__

Receivud

2 Oclober

Tallinn,

USSR

1970

The spin-lnttice rclaxltion of I% nuclei in inorganic ions is governed by inter- nnd intramoleculnl dipole-dipole and shift anisotropy intcrnctions at lowzr tcmpcrntures and by the spin-rotation interaction at higher temperatures. The mensured relnxttion rntes lcsd to rcasonablc rnlues for the 15~ spin-rotation coupling constnnt. 1. INTRODUCTION

SmaIl magnetic moment and low natural abundance (0.38%) of I5N nuclei both contribute to the very low intensity of 15~ NMR signals. This has precluded measuremept of all but the isotopically enriched molecules, but new experimental techniques and chemicaI poIarization esperiments [l] make 15N resonance practical. Quantitative evaluation of 15N NMR spectra, particularly the double resonance spectra, requires some knowledge of the I5N relaxation behaviour that has not been studied before. We have studied some representative inorganic 1SN-containing ions where the simple, nearly spherical structure simplifies the interpretation of experimental results. An universa1 frequency-sweep, time sharing double resonance spectrometer, capable of

2. RESULTS AND DISCUSSION Three contributions (dipole-dipole, spin-rotation and shift anisotropy interactions) to the total experimental spin-lattice relaxation time TI(exp) must be considered: 1 Tl(exp)

=

1 1 Tl(dd, I-H +Tt(sr)+-

Tnbk 1 of the samples -----.._. --_-Snmple

Solvent _____.--

____~.

Compound .._~_________-

1

D20 n)

1.0 g

Cn(15N03)2

2

A20

0.8 g

tL1(~%O3)2

b,

1 Tl(d

-.-

____

_--_..--

Is;\: isotope enrichment (‘c) ~___._

0.6 g

93

0.8 g

93 83

3

Di?O

I.0 g

x:n WV03

0.8 g

H20

0.9 g

NL,%o3

0.G g

93

9

II20

0.8 g

NH4 15N03

0.8 g

9s

6

D20

0.9 g

lSND4h’03

0.8 g

96

7

H20

0.9 g

15~~4~03

0.8 g

96

8

DLO

1.0 g

Na16N02

0.6 g

62

0.9 g

Na15X02

0.6 g

82

H20

(1)

-

4

9

\

operation in a wide range of temperatures at two ’ field strengths (14.1 kG and 9.4 kG) and at any frequency between 1.5 and 26 MHz was used [Z]. 15N relaxation times were determined by measuring the exponential recovery of nuclear magnetization after inversion during adiabatic rapid passage. AL1 samples (see table 1) were degassed with pure argon gas and sealed into 14 mm 0-d. (1.3 ml) spherical ampoules.

Composition

-----._-.--___~ Sample number

1970

3) Contnins 99.7% D20. b) Tetrahydratc.

545

-Volume

7, number 5

CHEMICAL

PRYSICS. LETTERS

.-

- 1. Dey2niber

1970

.-

I

1

.

3.0

3.5 -

4 i#/T

Fig.2. Temperature :md field strength dependence of the 1% spin-lattice rclasation time of Cn(1%0:~):! solutions in D;?O (sample 1) and in HgO (sample 2). Tl(sr) arc cnlculated spin-rotntionnl relaxation times for both samples. Tl(dd. II) is :I c:dcul:\tkd dipole-

Fig. 1. Temperature dependence of the 15~ nuclenr Overhauscr el’fect. Sample numbers correspond to those of table 1.

In this study the relaxation rate due to dipoledipole interaction with protons was separated through the use of nuclear Overhauser effect in double resonance spectra. If all proton-signals are saturated, then

P=- 1

TI(dd. H)

2YlSN IQ -I* 1 ---=TI( exp) rlH 16

K Ti(exp)

’

(2)

where K represents the share of both inter- and intramolecular dipole-dipole interactions with protons re!ative to the total relaxation rate. Since y15N :0. the 15N signal reverses sign (1, 4 0) in double resonance spectra if K :,- 2y15N/ylH. There is a net gain in the (negative) slgnal amplitude in double resonance spectra as compared with single resonance only if K > 4Y15N;3’1H_ This is possible for -NH,, groups or at low temperatures when the relaxation rate l/Tl(dd. H) is dominant. These relationships are presented in fig. 1 that incidentally provides a good example of the little investigated heteronuclear intermolecular Overhauger effect. It is immediately apparent that the intermolecular dipole-dipole interaction is significant at low temperatures only, and at higher temperatures the relaxation rate due to the spin-rotation interaction l;TI(sr) [3,4] is predominant. particularly in heavy water solutions (see figs. 2 and 3). The slight difference in Tl(sr) relaxation times in Ca(N03)2 solutions (fig.2) is due to different sample viscosities. as

Tl(Sr. D):TI(sr, 546

H) = ~~~~~~~~~~

.

dipole relnxntion time.for the second sample and T,(u) a calculated shift nnisdtropy relaxation time for the first sample where dipole-dipoie interaction is negligible.

The spin-rotation interaction is particularly strong in nitrite ions-and in sample 8.dominates at all temperatures (fig.3). The dipole-dipole interaction with deuterons l:TI(dd,D) is negligible in all cases, as is also the interaction with protons in 99.7% D20. In the magnetically dilute solution of Ca(N03)2 in D20 both the dipole-dipole and spin-rotation relaxation times are very long and the otherwise elusive shift anisotropy relaxation rate 1; Tl(a) becomes measurable (fig. 2). The relaxation time due to this interaction was separated through measurements at two field strengths (at 6.08 MHz and at 4.05 MHz). so that at 6.08 MHz TI(a) =

@Al2 iW”,)2 Ti(exp) VI;)2

T;(exp)

T;‘(exp) - Ti(eXp)

’

(3)

The shift anisotropy relaxation rime at - 30°C and 6.08 MHz equals Tl(a) = 175 gee. Together with the correlation time 7c = ;q +-- 1.2 x lo-16 set (found from the 14N linewidth) it leads to the very reasonable value Acr = 3OP ppm for the anisotropy of I5N chemical shift in the NO; ion. This value is comparable with the 14N chemical-shift anisotropy 40 = 360 f 73 ppm in methyl isocyanide [20]. As all this analysis is correct_ only insofar as the extreme narrowtig condition is satisfied, it was checkkd with a Ca(14NO3)2 solution of identical composition at - 300, where the 14N_line-

CHEMICAL I’HSSICS LETTERS

1 Decemhcr 1970

IOL. 3.0

-

35

40

-.-

lO+T

pig.3. Temperature dcpcndenccs of the 1% spin-lattice rclasnlion times of.XnN03 and SaXOz solutions in DgO and 1120. Sam&numbers correspond to those of table 1. TI (dd. H) nre calculntcd dipole-dipolc relwntion

the modulus of the spin-rotation

times for solulions in H$.

1’

width was 300 Hz, giving together with e2q(3 > 0.5 MHz [ 51 wo~c < 9 x 10m3 *=. 1. It is interesting to note that only for the 19F nucleus in CHFC12 has the contribution of shift-anisotropy interaction to the relaxation time been proven by direct experiment [6]. It is absent in P406 and benzotrifluoride at room temperature 17.81. The possible interference terms between the dipole-dipole and shift anisotropy interactions that may lead to a non-exponential signal recovery [91 after a rapid passage inversion were absent in all our experiments, including those with Ca(N03)2 + D20. In the ammonium ion (sample 7 in fig. 4) the dipole-dipole interaction predominates in the whole temperature range, but in the deuterated compound (sample 6) TI(expJ = 270 set at 97OC and again the spin-rotation interaction is the most important relaxation mechanism. The interand intramolecular contributions could not be separated for I5NHi because of rapid proton exchange. Chemical exchange phenomena also precluded the study of I5NDi relaxation al lower temperatures. 3. 15N SPIN-ROTATION CONSTANTS

103/T

INTERACTION

According to Hubbard [3], for spherical molecu!es the spin-rotational contribution l/‘Tl(sr) to the total rate l,/Tl(exp) can be expressed through

Tl(sr)

coupIing tenso

= $ kTEm2, c27Sr

;Ic:

.

where the spin-rotation correlation time ;sr follows from the approximate relation: TC isr = I ‘6kT ,

(5)

where I is the moment of inertia of the molecule and ic the dipolar correlation time. However. (5) is correct only if Tsr Yc as is usual in liquids. and the numerical factor may actually be smaller. For spherical molecules yc = rq [lOI and the correlation time of quadrupole relaxation ; can be determined from the linewidth AY in IjN spectra of unlabelled compounds. as in this case T2 = T1 and ‘h = (2,3;)

(c~~Q)-~Av

_

(6)

The values of iq can be considered to be equal in both compounds_ 14N quadrupolar interaction constants in single crystal? are 0.7 MHz for NOi [5.11] and 5.6 MHz for NO2 [121. The difference between these constants in crystals and in solution and the influence of temperature do not usually exceed 10%. The experimental and calculated data relevant to the calculation of the spin-rotation coupling constant i: are given in table 2. The calculated values of 7; are comparable to those determined by other methods. for example 22.0 kHz in N2 [13]. The value for 3lP. 19.5 kHz in P406 is likewise of similar magnitude [ii. The relationship between the spin-rotation in-

547

teraction and nuclear magnetic shielding [14-161, using the calculated values QNO-) = 1450 x 10m6 _and al,(NOi) = 2453 x 10-6 s 171 leads to c(NOg) = 9.3 kHz and E(NOi) = 23 kHz. These .calculated values are in fair agreement with the experimental ones, but this must be largely accidental, as the calculated shieldings (and their difference) do not agree with the experimental ones. The experimental shift difference equals 238 ppm. but the value calculated from the spinrotation coupling constants in table 2 amounts to 1750 ppm.. The most probable reasons for this discrepancy are the molecular moment of inertia that,may be larger because the polar ions rotate together with some water molecules +d a smaller numerical factor in (5). In the case of 19F nuclei the fit between chemical shifi difference of F2 and CgH5CF3 and the Tl(sr) values is good [la], but the values of 7sr found.from Tl(sr) and Tl(dd) through (5) may disagree [19].

[3] ti_S_Hubhard. Phys.IZcv. 131 (1963, lIZi_ [4] D. Ii. Green-and J. G. Po~les. Proc. Phys. Sot. (London).85 (1965) 87. [a] B. A. Whitehouse.’ J. D.&y and D. J. Royer. J.

iMagnetic

[6]

(1969)

Res.1

(19661 64. [7J D. J. Mowthorpe (1968)

J.Chem.

Php.44

.&Iol. Phys.

15

’

S.1 Chan. J. Magnetic Rcs. 2 (1970) l?O_ [S] >.S.‘Blichirskit l?y?: Letters 24A (1967) 608. [lo] W. T: Huntress. J_ Chcm_ Phy& 48 (1968) 3624. [ll] M.&urdji nnd L.Guib5. Compt.Rend.Acnd.Sci.

(Paris)

260 (1965)

[12] R.-A. Marinti.

-.

1131:

T. Oja.‘$nd’.P. J. Bray,

A27 (1968) 263. [13] M. R. Baker, C..H.Andcrson

[14] [15] [IS] [i?]

Phys. Letters

and N. F. Ramsey.

Phvs. l-+x. 133’ (1964) A1633. -. S.‘F‘! Ramsey, Phys. Rev:76 (iSSO) 699.’ W.tt. Flygare. J.Chcm.P+s:41.(1964) 793. 6. Devereli, Mul. 1~hys.M (1970) 319. D.N..Hend&kson and P. XKuzne~of.Theoret.. Chim.Acta 15 (1969) 57.. R. H. Faulk ind M; Eisner. J. Chem. Phys.44

- ->(1966)

2926.

...

l~.Rughein& 39 (1963) 532.

&XI I’.,S. &&rd. :

1191 J.

[I] E. Lippmaa. T. Pehk and T.Snluvere. to ije

-_I

snd A. d. Chzipman,

429.

-181_ T. E. Burke: nnd

[18]

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