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Quadrupole relaxation of boron-11 and boron-10 nuclei
JOURNAL
OF MAGNETIC
RESONANCE
3, 411-414 (1970)
QuadrupoleRelaxation of Boron-11 and Boron-10 Nuclei J. W. AKITT Department of Chemistry, University of‘ Newcastle-upon-Tyne, Newcastle-upon-Tyne, NE1 7RlJ, England Received May 11, 1970; accepted July 21, 1970 The often-accepted view that quadrupole relaxation of 1°B is faster than that of IlB is shown to be in error since the effect of the larger 1°B quadrupole moment is more than compensated by its larger nuclear spin. The significance of this for the appearance of the spectra of spin f nuclei coupled to boron is discussed.
The relaxation processes involving the nuclei “B and i”B, and the efiect this relaxation has on the NMR spectra of spin $ nuclei, X, coupled to the boron, are of considerable interest (Z-5). Particular emphasis has been placed recently (2,3) upon the conclusion that as the boron environment is altered so as to decrease the boron relaxation time, Ti (achieved by increasing the electric field gradient at the boron using chemical substitution or by increasing the bulk solution molecular correlation time) the X septet due to X-“B molecules collapses before the X quartet due to X-“B molecules. This conclusion is justified on the grounds that the quadrupole moment of “B (Q = 0.074ex 1O-24 cm’) is greater than that of “B (Q = 0.035e x 10mz4 cm*). (The value quoted for l”B comes from a recent compilation (6) and is lower than that quoted in many NMR Tables.) It is possible to reach a similar conclusion from the consideration that .Z(X-i”B) = 0.335.Z(X-1’B). It has been shown for nuclei with Z = 1 and Z = 3 that the somewhat poorly defined position of intermediate collapse, where the X resonance consists of a broad almost structureless line, is reached when (I, 7) 2nT,J Lz 1. Cl1 This approximation also appears to hold for Z = 3 (5) so that in the case under consideration the value of 27cTiJ will always be smallest for the X-“B molecules, especially if “B relaxation is faster than that of ‘iB. If the above conclusions were correct we would expect that when the resonance of the X-“B molecules was at the intermediate stage of collapse the X-“8 spectrum would be a relatively sharp spike in the centre of the broad X-I’B resonance. An example lineshape is shown in Fig. 1, which was derived graphically from Figs. 2 and 5 of Ref. (5) with 2nT,J NN1 for X-“B species and 27cT,.Z z 0.2 for X-“B species. Such spectral shapes have not been observed in collapsed i9F lines due to certain BF, adducts observed at Newcastle, nor is there any evidence of a central line emerging in Fig. 2 of Ref. (I) or in Fig. 2 of Ref. (3). There is in fact a dearth of published evidence, since broad, structureless lines are not usually considered worth publication. These observations suggest that perhaps X-“B spectral collapse does not occur very much before that of X-“B. 411
412
AKITT
FIG. 1. Estimated lineshape of X resonance if the llB relaxation time were 1.7 times longer than that of 1°B. The scales indicate the position of the X lines for long relaxation times.
It has been shown that the rate of quadrupole relaxation is given by (8)
T;’ = T;’ = -3 p21+3
PI 40 ZZ(21-1) (?)’ ($)li’. For molecules which differ only in that they may contain either l”B or “B, the electric field gradient at the boron nuclei, d2V/dZ2, will be identical for the two isotopes while the rotational correlation time for molecular motion z, will scarcely be altered by the substitution. Equation (2) can thus be simplified to T; ’ 0~ Q'f(I>, PI where the expression involving Z is designated f(Z); values of Z and corresponding values off(Z) are: 9 I 1 3 3 3 z 1.33 0.32 0.2 0.136 o&4 l-(Z) 5 It is immediately apparent that the value of Z is extremely important when comparing the relaxation behaviour of nuclei of different Z, an increase in Z having the opposite effect to an increase in Q. Thus, for example, spin coupling is seen in NbF; (for g3Nb Z = $, Q = 0.2 (6)) (9) while lines due to “Al (Q = 0.149, Z = +) are very much narrower (10) than those due to ‘IGa (Q = 0.146, Z = 2) (II). For the present case substituting values of Q andf(Z) in Eq. [3] we can write CG-‘),,,/(TI-‘),,, = U’AIBIVAOB = 0.635. L41 Thus, as has been observed by Allerhand and Moll (4), the “B has an appreciably longer relaxation time and this will decrease the tendency for the X-“B multiplet to collapse first. Using this value we can determine the relative correlation times (~c>~’ which should produce intermediate spectral collapse for the two isotopes. From Eqs. [Z] and [3] and reintroducing z, we obtain 27cnJ(“B-X) z T; 1 = uj-(I)Q”(r,);;’ where a is a constant. Thus .Z(“B-X) . [Q’fcZ)]‘iB kXd/(4% = .Z(“B-X) [Q2j-(Z)]‘oB’ which takes the value =0.528.
RELAXATION
OF BORON NUCLEI
413
Thus as z, is increased from some value where coupling is well-defined, e.g., by cooling, (z,)c,odhis reached first so that the multiplet due to X-“B reaches the point of intermediate collapse before that of X-llB. However, the temperature separation between the collapse of the spectra of the two types of molecule will not be large; for instance, for BF, a change of about two times in z, is produced by a temperature change of 30-40” whereas changes of over 80” are required to produce easily observable changes in the “F spectra (I). It therefore does not seem likely that differential collapse of the multiplets would normally be observed. We have attempted to substantiate this conclusion using the fluorine resonance of the BF, ion in aqueous ammonium fluoroborate. The boron-fluorine coupling constant is small in this system so that at our Bruker spectrometer operating frequency of 84.66 MHz the boron isotope shift completely separates the two fluorine resonances which arise from the species “BF, and “BF,. Ch anges in line shape can easily be compared and one is certain that the two species are in identical environments. The cooling range of such solutions is limited and it was decided to decrease the boron relaxation time by adding glycerol to increase rc. J(F-B) is very sensitive to the nature of the solvent (12) and is reduced as the glycerol content of the system increases, this factor also assisting the tendency towards spectral collapse. The resulting spectra
A
4Hz
FIG. 2. 19F spectra of aqueous NH4BF4. (A) Approx. 2M in water; (E) in 19 % V/V glycerol-water; (H) in 47 % V/V glycerol-water; (L) in 59 % V/V glycerol-water. The decrease in intensity throughout the series is due to salt precipitating as the glycerol concentration is increased. The viscosity changes by approximately thirteen times over this range of solvent compositions (13).
414
AKITT
are shown in Fig. 2. The structure is lost first from the “B multiplet, but this is presumably a function also of the spectrometer resolution. The relative widths of the two resonances maintain the same relation until the highest glycerine concentration and only here is it possible to conclude that the l”B multiplet may be narrowing perceptibly faster than is the stronger one due to ’ ‘B . This however is not detectable by eye in this system and the observation of differential collapse would presumably be even more difficult in a system where the resonances overlapped. These conclusions imply also that the assumption made in the past, when calculating the effect of the l”B on the proton spectra of, for example, diborane (14) or decaborane (15), that the H-“B and H-“B spectra show similar degrees of structure, seems to have been correct.
1. 2.
3. 4. 5.
6. 7. 8.
9. 10.
REFERENCES J. BACON, R. J. GILLESPIE, AND J. W. QUAIL, Can. J. Chem. 41, 3063 (1963). B. H. WATANABE, T. TOTANI, M. OHTSURU, AND M. KUBO, Mol. Phys. 14, 367 (1968). G. E. RYSCHKEWITSCH AND W. J. RADEMAKER, J. Mug. Res. 1, 584 (1969). A. ALLERHAND AND R. E. MOLL, J. Mug. Res. 1, 488 (1969). M. SUZUKI AND R. KUBO, Mol. Phys. 7, 201 (1963). C. M. LEDERER, J. M. HOLLANDER, AND I. PERLMAN, “Table of Isotopes,” 6th ed., John Wiley and Sons, New York, 1961. J. A. POPLE, Mol. Phys. 1, 168 (1958). A. ABRAGAM AND R. V. POUND, Phys. Rev. 92,943 (1953). D. W. AKSNES, S. M. HUTCHINSON, AND K. J. PACKER, Mol. Phys. 14, 301 (1968). J. W.
AKITT,
N.
N.
GREENWOOD,
Il. J. W. AKITT, N. N. GREENWOOD, J2. R. J. GILLESPIE, J. S. HARTMAN,
AND G. D. LESTER, J. Chem. Sot. A, 803 (1969). AND A. STORR, J. Chem. Sot. 4410 (1965). AND
M.
PAREKH,
Can. J. C/rem.
46,
1601 (1968), and references
quoted therein. 13. M. L. SHEELY, Ind. Eng. Chem. 24, 1060 (1932). 14. J. N. SHOOLERY, Discuss. Faraday Sot. 19, 215 (1955). 15. R. L. WILLIAMS, N. N. GREENWOOD, AND J. H. MORRIS,
Spectrochim.
Acta.
21, 1579 (1965).
OF MAGNETIC
RESONANCE
3, 411-414 (1970)
QuadrupoleRelaxation of Boron-11 and Boron-10 Nuclei J. W. AKITT Department of Chemistry, University of‘ Newcastle-upon-Tyne, Newcastle-upon-Tyne, NE1 7RlJ, England Received May 11, 1970; accepted July 21, 1970 The often-accepted view that quadrupole relaxation of 1°B is faster than that of IlB is shown to be in error since the effect of the larger 1°B quadrupole moment is more than compensated by its larger nuclear spin. The significance of this for the appearance of the spectra of spin f nuclei coupled to boron is discussed.
The relaxation processes involving the nuclei “B and i”B, and the efiect this relaxation has on the NMR spectra of spin $ nuclei, X, coupled to the boron, are of considerable interest (Z-5). Particular emphasis has been placed recently (2,3) upon the conclusion that as the boron environment is altered so as to decrease the boron relaxation time, Ti (achieved by increasing the electric field gradient at the boron using chemical substitution or by increasing the bulk solution molecular correlation time) the X septet due to X-“B molecules collapses before the X quartet due to X-“B molecules. This conclusion is justified on the grounds that the quadrupole moment of “B (Q = 0.074ex 1O-24 cm’) is greater than that of “B (Q = 0.035e x 10mz4 cm*). (The value quoted for l”B comes from a recent compilation (6) and is lower than that quoted in many NMR Tables.) It is possible to reach a similar conclusion from the consideration that .Z(X-i”B) = 0.335.Z(X-1’B). It has been shown for nuclei with Z = 1 and Z = 3 that the somewhat poorly defined position of intermediate collapse, where the X resonance consists of a broad almost structureless line, is reached when (I, 7) 2nT,J Lz 1. Cl1 This approximation also appears to hold for Z = 3 (5) so that in the case under consideration the value of 27cTiJ will always be smallest for the X-“B molecules, especially if “B relaxation is faster than that of ‘iB. If the above conclusions were correct we would expect that when the resonance of the X-“B molecules was at the intermediate stage of collapse the X-“8 spectrum would be a relatively sharp spike in the centre of the broad X-I’B resonance. An example lineshape is shown in Fig. 1, which was derived graphically from Figs. 2 and 5 of Ref. (5) with 2nT,J NN1 for X-“B species and 27cT,.Z z 0.2 for X-“B species. Such spectral shapes have not been observed in collapsed i9F lines due to certain BF, adducts observed at Newcastle, nor is there any evidence of a central line emerging in Fig. 2 of Ref. (I) or in Fig. 2 of Ref. (3). There is in fact a dearth of published evidence, since broad, structureless lines are not usually considered worth publication. These observations suggest that perhaps X-“B spectral collapse does not occur very much before that of X-“B. 411
412
AKITT
FIG. 1. Estimated lineshape of X resonance if the llB relaxation time were 1.7 times longer than that of 1°B. The scales indicate the position of the X lines for long relaxation times.
It has been shown that the rate of quadrupole relaxation is given by (8)
T;’ = T;’ = -3 p21+3
PI 40 ZZ(21-1) (?)’ ($)li’. For molecules which differ only in that they may contain either l”B or “B, the electric field gradient at the boron nuclei, d2V/dZ2, will be identical for the two isotopes while the rotational correlation time for molecular motion z, will scarcely be altered by the substitution. Equation (2) can thus be simplified to T; ’ 0~ Q'f(I>, PI where the expression involving Z is designated f(Z); values of Z and corresponding values off(Z) are: 9 I 1 3 3 3 z 1.33 0.32 0.2 0.136 o&4 l-(Z) 5 It is immediately apparent that the value of Z is extremely important when comparing the relaxation behaviour of nuclei of different Z, an increase in Z having the opposite effect to an increase in Q. Thus, for example, spin coupling is seen in NbF; (for g3Nb Z = $, Q = 0.2 (6)) (9) while lines due to “Al (Q = 0.149, Z = +) are very much narrower (10) than those due to ‘IGa (Q = 0.146, Z = 2) (II). For the present case substituting values of Q andf(Z) in Eq. [3] we can write CG-‘),,,/(TI-‘),,, = U’AIBIVAOB = 0.635. L41 Thus, as has been observed by Allerhand and Moll (4), the “B has an appreciably longer relaxation time and this will decrease the tendency for the X-“B multiplet to collapse first. Using this value we can determine the relative correlation times (~c>~’ which should produce intermediate spectral collapse for the two isotopes. From Eqs. [Z] and [3] and reintroducing z, we obtain 27cnJ(“B-X) z T; 1 = uj-(I)Q”(r,);;’ where a is a constant. Thus .Z(“B-X) . [Q’fcZ)]‘iB kXd/(4% = .Z(“B-X) [Q2j-(Z)]‘oB’ which takes the value =0.528.
RELAXATION
OF BORON NUCLEI
413
Thus as z, is increased from some value where coupling is well-defined, e.g., by cooling, (z,)c,odhis reached first so that the multiplet due to X-“B reaches the point of intermediate collapse before that of X-llB. However, the temperature separation between the collapse of the spectra of the two types of molecule will not be large; for instance, for BF, a change of about two times in z, is produced by a temperature change of 30-40” whereas changes of over 80” are required to produce easily observable changes in the “F spectra (I). It therefore does not seem likely that differential collapse of the multiplets would normally be observed. We have attempted to substantiate this conclusion using the fluorine resonance of the BF, ion in aqueous ammonium fluoroborate. The boron-fluorine coupling constant is small in this system so that at our Bruker spectrometer operating frequency of 84.66 MHz the boron isotope shift completely separates the two fluorine resonances which arise from the species “BF, and “BF,. Ch anges in line shape can easily be compared and one is certain that the two species are in identical environments. The cooling range of such solutions is limited and it was decided to decrease the boron relaxation time by adding glycerol to increase rc. J(F-B) is very sensitive to the nature of the solvent (12) and is reduced as the glycerol content of the system increases, this factor also assisting the tendency towards spectral collapse. The resulting spectra
A
4Hz
FIG. 2. 19F spectra of aqueous NH4BF4. (A) Approx. 2M in water; (E) in 19 % V/V glycerol-water; (H) in 47 % V/V glycerol-water; (L) in 59 % V/V glycerol-water. The decrease in intensity throughout the series is due to salt precipitating as the glycerol concentration is increased. The viscosity changes by approximately thirteen times over this range of solvent compositions (13).
414
AKITT
are shown in Fig. 2. The structure is lost first from the “B multiplet, but this is presumably a function also of the spectrometer resolution. The relative widths of the two resonances maintain the same relation until the highest glycerine concentration and only here is it possible to conclude that the l”B multiplet may be narrowing perceptibly faster than is the stronger one due to ’ ‘B . This however is not detectable by eye in this system and the observation of differential collapse would presumably be even more difficult in a system where the resonances overlapped. These conclusions imply also that the assumption made in the past, when calculating the effect of the l”B on the proton spectra of, for example, diborane (14) or decaborane (15), that the H-“B and H-“B spectra show similar degrees of structure, seems to have been correct.
1. 2.
3. 4. 5.
6. 7. 8.
9. 10.
REFERENCES J. BACON, R. J. GILLESPIE, AND J. W. QUAIL, Can. J. Chem. 41, 3063 (1963). B. H. WATANABE, T. TOTANI, M. OHTSURU, AND M. KUBO, Mol. Phys. 14, 367 (1968). G. E. RYSCHKEWITSCH AND W. J. RADEMAKER, J. Mug. Res. 1, 584 (1969). A. ALLERHAND AND R. E. MOLL, J. Mug. Res. 1, 488 (1969). M. SUZUKI AND R. KUBO, Mol. Phys. 7, 201 (1963). C. M. LEDERER, J. M. HOLLANDER, AND I. PERLMAN, “Table of Isotopes,” 6th ed., John Wiley and Sons, New York, 1961. J. A. POPLE, Mol. Phys. 1, 168 (1958). A. ABRAGAM AND R. V. POUND, Phys. Rev. 92,943 (1953). D. W. AKSNES, S. M. HUTCHINSON, AND K. J. PACKER, Mol. Phys. 14, 301 (1968). J. W.
AKITT,
N.
N.
GREENWOOD,
Il. J. W. AKITT, N. N. GREENWOOD, J2. R. J. GILLESPIE, J. S. HARTMAN,
AND G. D. LESTER, J. Chem. Sot. A, 803 (1969). AND A. STORR, J. Chem. Sot. 4410 (1965). AND
M.
PAREKH,
Can. J. C/rem.
46,
1601 (1968), and references
quoted therein. 13. M. L. SHEELY, Ind. Eng. Chem. 24, 1060 (1932). 14. J. N. SHOOLERY, Discuss. Faraday Sot. 19, 215 (1955). 15. R. L. WILLIAMS, N. N. GREENWOOD, AND J. H. MORRIS,
Spectrochim.
Acta.
21, 1579 (1965).