- Email: [email protected]
Nuclear resonance in solid hydrocarbons
Physica XVII, no 3-4
Maart-April 1951
NUCLEAR RESONANCE IN SOLID HYDROCARBONS by E. R. ANDREW D e p a r t m e n t of Natural Philosophy, St. Andrews, Scotland
Synopsis An investigation has been made of the variation with temperature of the proton magneti.c resonance absorption line-width of four long chain aliphatic compounds and eight aromatic hydrocarbons. The aliphatic compounds are dimorphous. I n the lower temperature modification it is concluded t h a t the molecules are rigid at 95°K, b u t t h a t an increasing n u m b e r of molecules rotate about their length as the temperature increases; it. seems unlikely t h a t rotational oscillation alone can account for the observed reduction of line-width as the temperature increases. I n the upper temperature modification all the molecules rotate. There was no evidence of molecular rotation in naphthalene up to the melting point. Benzene, however, shows a sharp line-width transitions at a b o u t 110°K. I t is suggested t h a t this is due to t u n n e l l i n g or rotation of the molecules about their hexagonal axes. Since only a small fraction of the n u m b e r of molecules need rotate in order to bring about a reduction in line-width, the hypothesis of molecular rotation in solid benzene is not incompatible with the interpretation by Kastler and F r u h l i n g of the R a m a n spectral lines as due to the rotational oscillation of molecules in the solid. The xylenes, mesitylene, and hexamethylbenzene show internal rotation of the CH 3 groups at all temperatures above 95°K. I n addition, hexamethylbenzene has a line-width transition over the range 1 3 5 - - 2 1 0 ° K , a t t r i b u t e d to tunnelling or rotation of the molecules about their hexagonal axes.
Preliminary results are given of measurements on other organic compounds (durene, pentamethylbeneze and hexaethylbenzene). Solid h y d r o c a r b o n s are f r u i t f u l s u b j e c t s for s t u d y b y n u c l e a r r e s o n a n c e m e t h o d s for s e v e r a l r e a s o n s . I n t h e first p l a c e o n e c a n o b t a i n s t r u c t u r a l i n f o r m a t i o n x). X - r a y d e t e r m i n a t i o n s of t h e c r y s t a l s t r u c t u r e of h y d r o c a r b o n s are u s u a l l y l i m i t e d t o s t a t i n g t h e p o s i t i o n s --
4 0 5 -
406
E . R . ANDREW
of the carbon atoms, and one is then left to gues~ the positions of the hydrogen nuclei. Since the interproton distances govern the local magnetic field, which in turn determines the resonance linewidth, measurements of the linewidth enable one to confirm postulated positions of the protons in the unit cell. Secondly one can detect molecular rotation which occurs in many of these weakly bound solids, since it causes a reduction of the local field and thus of the resonance linewidth 2). Unambiguous evidence of such rotation has hitherto only been obtainable from X-ray or dielectric measurements. X-ray measurements only give such information if each molecule spends most of its time rotating, whereas the nuclear resonance linewidth will be affected even though each molecule spends only a very. small fraction of its time rotating. Dielectric measurements do not suffer from this lack of sensitivity, but they are only applicable to polar molecules, whereas non-polar molecules are more likely to rotate on account of their greater symmetry. Moreover dielectric measurements give no evidence of rotation about axes parallel to the direction of the electric moment vector. From nuclear resonance measurements one can also detect internal rotation of groups, such as methyl groups, within fixed molecules. Thirdly, from a practical standpoint, hydrocarbons are good subjects for s t u d y because the high gyromagnetic ratio of the proton ensures a relatively large signal strength, and because the zero spin of 12C simplifies the interpretation of the results. I will now illustrate these remarks with results obtained from experiments on three types of hydrocarbon. Most of this work was carried out at Harvard University 3), although some preliminary results will also be given of recent measurements made at the University of St. Andrews with Mr. F. A. R u s h w o r t h. The first group of hydrocarbons are the normal paraffins of general formula CnH2~+2. B y X-ray analysis these molecules have been found b y M ti 1 1 e r 4) to consist of a plane zig-zag chain of carbon atoms with the tetrahedral interbond angle of 1091/2°, (Figure 1(a)). It is therefore reasonable to suppose that the carbon-hydrogen bonds are also tetrahedrally distributed as shown, and one m a y suppose the length of the. bond to be that found spectroscopically in simpler molecules such as methane. Figure l(b) shows in plan the parallel packing of the molecules in the unit ce.U. The theoretical second
NUCLEAR RESONANCE IN SOLID HYDROCARBONS
407
t
m o m e n t of the resonance line can now be c o m p u t e d with the aid of V a n V t e c k's formula 5) since for a polycrystalline material a knowledge of all the i n t e r - p r o t o n distances in the crystal lattice is all t h a t is required. F o r n-octacosane (n-C28Hss) and dicetyl (n-C32H~) the calculated values are 27.0 and 26-9 gauss 2 respectively. The exper i m e n t a l values o b t a i n e d b y simple calculation from resonance lines
Fig. l. a) Diagram illustrating the structure of long chain paraffin molecules. b) Diagram illustrating the packing of long chain paraffin molecules in the unit cell. The molecules are shown projected on the base of the unit cell. Open circles represent carbon atoms; solid circles represent hydrogen atoms.
measured at 95°K are 26.6 and 27-1 gauss 2. This good agreement with t h e o r y confirms the postulated positions of the protons in the molecule. The theoretical Values were calculated on the assumption t h a t the molecules were rigid in the crystal lattice; since the experimental values were the same at 205°K as at 95°K, this assumption is justified.
E. 1~. A N D R E W
408
At higher temperatures however the second moment gradually decreased, as shown in figure 2, until about 6 ° below the melting point, where a transition point occurs; here the line narrowed sharply. M ti 11 e r has shown from his X-ray measurements that above ,
0
i
s~
~
0_
.
2©
n-C~.
o
3O i i
Z W
o
201
Io
n-C~H.
a z
0
0
- - - - -
3~
D_
2c
"'---o------_
,©
n-CleH3e .....
~Io
2~o
2~o
~8o
3oo
3~o
s~
360
TEMPERATURE OK Fig. 2. T h e v a r i a t i o n w i t h temperature of the second moment of the resonance line for three n o r m a l paraffins.
this transition temperature all the molecules rotate about their long axes in the solid state; the sharp decrease in second moment confirms this. There is however quite a considerable decrease in second moment even below the transition temperature. This decrease will be p a r t l y due to rotational oscillation of the molecules, but calculation shows that this form of motion is unlikely to account for the whole effect. It is more likely that a small proportion of the molecules rotate below the transition point, the number increasing with temper ature. The bottom curve in figure 2 illustrates results obtained for the
NUCLEAR RESONANCE IN SOLID HYDROCARBONS
409
shorter paraffin n-octadecane n - C i s H s s , which does not exhibit a transition point. Its behaviour up to the melting point is similar to that of the longer paraffins up to their transition points. A second type of hydrocarbon is benzene. The theoretical second moment was calculated on the assumption that the carbonhydrogen bonds lay symmetrically in the plane of the carbon hexagon, and were of length intermediate, between the known values for - - C - - H and = C - - H 8). The experimental value obtained from measurements at 94°K was consistent with these assumptions and indicated the absence of appreciable molecular motion at that temperature.
B BENZENE ul
i--: o.
6
.1-
bJ
z
2
._1
TEMPERATURE
°K
Fig. 3. The variation with temperature of the resonance linewidth for benzene.
As figure 3 shows, the resonance linewidth in solid benzene narrowed quite sharply over the range 100--120°K, and then remained constant up to the melting point. The second moment above 120°K is quantitatively in agreement with the view that the benzene molecttles rotate about their hexagonal axes: Since benzene exhibits no specific heat anomaly, the commencement of rotation is just the gradual increase with temperature of the proportion of molecules which have sufficient energy to clear the potential barrier hindering rotation. At about 110°K this proportion reaches the necessary value (of order 10-7) required to narrow the resonance line. Although the proportion increases rapidly with temperature, it is probably n o more than a few per cent at the melting point. At any instant the large majority of molecules are thus merely executing rotational
410 /
E.R.
ANDREW
oscillations; the observation by K a s t I e r and F r u h 1 i n g 7) of the R a m a n lines due to such oscillations is therefore quite compatible with the molecular rotation postulated to explain the nuclear resonance results. The third group of hydrocarbons are the polymethylbenzenes. At the lowest temperature of measurement, 95°K, the experimental value of the second moment was about 9.8 gauss 2 for all three xylenes and for mesitylene. The calculated value, assuming a rigid structure, was however more than double this value for all four compounds. Since the molecules axe all of different shape and symmetry, the most obvious explanation of the low second moment value common to all four is to assume there is internal rotation or tunnelling of the CH 3 groups about the direction of the C--C sidebonds. Calculation shows t h a t such motion does in fact lead to values of the second moment in good agreement with those observed. Internal rotation of the CH 3 groups is also indicated by preliminary measurements on durene (1.2.4.5 tetramethylbenzene) and pentamethylbenzene at 291°K. The most symmetrical member of this group, hexamethylbenzene, also shows this internal motion at temperatures above 95°K. In addition there is a further narrowing of the resonance line over the temperature range 135--210°K which indicates the onset of further motion. The second moment above 210°K is quantitatively consistent with the view t h a t there is hindered rotation of the molecules as a whole about their hexagonal axes. Such motion is in accord with dielectric evidence of molecular rotation in all the polar hexasubstit u t e d methylchlorobenzenes at temperatures down to 200--280 ° below their melting points s). In hexaethylbenzene it seems probable that there is internal rotation of the six methyl groups, but that the molecules do not rotate about an axis normal to the benzene ring. Since the carbon skeleton is presumably no longer planar as in hexamethylbenzene the potential barrier against rotation should in fact be higher. Received 23-%50.
NUCLEAR
RESONANCE
IN S O L I D H Y D R O C ~ A R B O N S
411
REFERENCES
I) G u t o w s k y , H.S., K i s t i a k o w s k y , G. B., P a k e , G. E. and P u r cell, E.M.,J. chem. Phys. 17(1949) 972. 2) G u t o w s k y , H.S. and P a k e , G.E., J. chem. Phys. 18(1950)162. 3) A n d r e w , E. R., J. chem. Phys. "18 (1950) 607. 4) M fill e r, A., Proc. roy. Soc. A I 2 @ (1928) 437; 127 (1930) 4|7; 138 (1932) 514. 5) V a n V l e c k , J.H., Phys. Rev. 74 (1948) I168. 6) H e r z b e r g, G., "Infrared and R a m a n Spectra of Polyatomic Molecules", D. Van Nostrand Co. Inc., N e w York (1945) 440. 7) K a s t l e r , A. and F r u h l i n g , A.,C.R. Acad. Sci. Paris, 218(1944) 998. 8) W h i t e , A. H., B i g g s , B.S. and M o r g a n , S. O., J. Am. chem. Soc. 62 0940) 16.
Maart-April 1951
NUCLEAR RESONANCE IN SOLID HYDROCARBONS by E. R. ANDREW D e p a r t m e n t of Natural Philosophy, St. Andrews, Scotland
Synopsis An investigation has been made of the variation with temperature of the proton magneti.c resonance absorption line-width of four long chain aliphatic compounds and eight aromatic hydrocarbons. The aliphatic compounds are dimorphous. I n the lower temperature modification it is concluded t h a t the molecules are rigid at 95°K, b u t t h a t an increasing n u m b e r of molecules rotate about their length as the temperature increases; it. seems unlikely t h a t rotational oscillation alone can account for the observed reduction of line-width as the temperature increases. I n the upper temperature modification all the molecules rotate. There was no evidence of molecular rotation in naphthalene up to the melting point. Benzene, however, shows a sharp line-width transitions at a b o u t 110°K. I t is suggested t h a t this is due to t u n n e l l i n g or rotation of the molecules about their hexagonal axes. Since only a small fraction of the n u m b e r of molecules need rotate in order to bring about a reduction in line-width, the hypothesis of molecular rotation in solid benzene is not incompatible with the interpretation by Kastler and F r u h l i n g of the R a m a n spectral lines as due to the rotational oscillation of molecules in the solid. The xylenes, mesitylene, and hexamethylbenzene show internal rotation of the CH 3 groups at all temperatures above 95°K. I n addition, hexamethylbenzene has a line-width transition over the range 1 3 5 - - 2 1 0 ° K , a t t r i b u t e d to tunnelling or rotation of the molecules about their hexagonal axes.
Preliminary results are given of measurements on other organic compounds (durene, pentamethylbeneze and hexaethylbenzene). Solid h y d r o c a r b o n s are f r u i t f u l s u b j e c t s for s t u d y b y n u c l e a r r e s o n a n c e m e t h o d s for s e v e r a l r e a s o n s . I n t h e first p l a c e o n e c a n o b t a i n s t r u c t u r a l i n f o r m a t i o n x). X - r a y d e t e r m i n a t i o n s of t h e c r y s t a l s t r u c t u r e of h y d r o c a r b o n s are u s u a l l y l i m i t e d t o s t a t i n g t h e p o s i t i o n s --
4 0 5 -
406
E . R . ANDREW
of the carbon atoms, and one is then left to gues~ the positions of the hydrogen nuclei. Since the interproton distances govern the local magnetic field, which in turn determines the resonance linewidth, measurements of the linewidth enable one to confirm postulated positions of the protons in the unit cell. Secondly one can detect molecular rotation which occurs in many of these weakly bound solids, since it causes a reduction of the local field and thus of the resonance linewidth 2). Unambiguous evidence of such rotation has hitherto only been obtainable from X-ray or dielectric measurements. X-ray measurements only give such information if each molecule spends most of its time rotating, whereas the nuclear resonance linewidth will be affected even though each molecule spends only a very. small fraction of its time rotating. Dielectric measurements do not suffer from this lack of sensitivity, but they are only applicable to polar molecules, whereas non-polar molecules are more likely to rotate on account of their greater symmetry. Moreover dielectric measurements give no evidence of rotation about axes parallel to the direction of the electric moment vector. From nuclear resonance measurements one can also detect internal rotation of groups, such as methyl groups, within fixed molecules. Thirdly, from a practical standpoint, hydrocarbons are good subjects for s t u d y because the high gyromagnetic ratio of the proton ensures a relatively large signal strength, and because the zero spin of 12C simplifies the interpretation of the results. I will now illustrate these remarks with results obtained from experiments on three types of hydrocarbon. Most of this work was carried out at Harvard University 3), although some preliminary results will also be given of recent measurements made at the University of St. Andrews with Mr. F. A. R u s h w o r t h. The first group of hydrocarbons are the normal paraffins of general formula CnH2~+2. B y X-ray analysis these molecules have been found b y M ti 1 1 e r 4) to consist of a plane zig-zag chain of carbon atoms with the tetrahedral interbond angle of 1091/2°, (Figure 1(a)). It is therefore reasonable to suppose that the carbon-hydrogen bonds are also tetrahedrally distributed as shown, and one m a y suppose the length of the. bond to be that found spectroscopically in simpler molecules such as methane. Figure l(b) shows in plan the parallel packing of the molecules in the unit ce.U. The theoretical second
NUCLEAR RESONANCE IN SOLID HYDROCARBONS
407
t
m o m e n t of the resonance line can now be c o m p u t e d with the aid of V a n V t e c k's formula 5) since for a polycrystalline material a knowledge of all the i n t e r - p r o t o n distances in the crystal lattice is all t h a t is required. F o r n-octacosane (n-C28Hss) and dicetyl (n-C32H~) the calculated values are 27.0 and 26-9 gauss 2 respectively. The exper i m e n t a l values o b t a i n e d b y simple calculation from resonance lines
Fig. l. a) Diagram illustrating the structure of long chain paraffin molecules. b) Diagram illustrating the packing of long chain paraffin molecules in the unit cell. The molecules are shown projected on the base of the unit cell. Open circles represent carbon atoms; solid circles represent hydrogen atoms.
measured at 95°K are 26.6 and 27-1 gauss 2. This good agreement with t h e o r y confirms the postulated positions of the protons in the molecule. The theoretical Values were calculated on the assumption t h a t the molecules were rigid in the crystal lattice; since the experimental values were the same at 205°K as at 95°K, this assumption is justified.
E. 1~. A N D R E W
408
At higher temperatures however the second moment gradually decreased, as shown in figure 2, until about 6 ° below the melting point, where a transition point occurs; here the line narrowed sharply. M ti 11 e r has shown from his X-ray measurements that above ,
0
i
s~
~
0_
.
2©
n-C~.
o
3O i i
Z W
o
201
Io
n-C~H.
a z
0
0
- - - - -
3~
D_
2c
"'---o------_
,©
n-CleH3e .....
~Io
2~o
2~o
~8o
3oo
3~o
s~
360
TEMPERATURE OK Fig. 2. T h e v a r i a t i o n w i t h temperature of the second moment of the resonance line for three n o r m a l paraffins.
this transition temperature all the molecules rotate about their long axes in the solid state; the sharp decrease in second moment confirms this. There is however quite a considerable decrease in second moment even below the transition temperature. This decrease will be p a r t l y due to rotational oscillation of the molecules, but calculation shows that this form of motion is unlikely to account for the whole effect. It is more likely that a small proportion of the molecules rotate below the transition point, the number increasing with temper ature. The bottom curve in figure 2 illustrates results obtained for the
NUCLEAR RESONANCE IN SOLID HYDROCARBONS
409
shorter paraffin n-octadecane n - C i s H s s , which does not exhibit a transition point. Its behaviour up to the melting point is similar to that of the longer paraffins up to their transition points. A second type of hydrocarbon is benzene. The theoretical second moment was calculated on the assumption that the carbonhydrogen bonds lay symmetrically in the plane of the carbon hexagon, and were of length intermediate, between the known values for - - C - - H and = C - - H 8). The experimental value obtained from measurements at 94°K was consistent with these assumptions and indicated the absence of appreciable molecular motion at that temperature.
B BENZENE ul
i--: o.
6
.1-
bJ
z
2
._1
TEMPERATURE
°K
Fig. 3. The variation with temperature of the resonance linewidth for benzene.
As figure 3 shows, the resonance linewidth in solid benzene narrowed quite sharply over the range 100--120°K, and then remained constant up to the melting point. The second moment above 120°K is quantitatively in agreement with the view that the benzene molecttles rotate about their hexagonal axes: Since benzene exhibits no specific heat anomaly, the commencement of rotation is just the gradual increase with temperature of the proportion of molecules which have sufficient energy to clear the potential barrier hindering rotation. At about 110°K this proportion reaches the necessary value (of order 10-7) required to narrow the resonance line. Although the proportion increases rapidly with temperature, it is probably n o more than a few per cent at the melting point. At any instant the large majority of molecules are thus merely executing rotational
410 /
E.R.
ANDREW
oscillations; the observation by K a s t I e r and F r u h 1 i n g 7) of the R a m a n lines due to such oscillations is therefore quite compatible with the molecular rotation postulated to explain the nuclear resonance results. The third group of hydrocarbons are the polymethylbenzenes. At the lowest temperature of measurement, 95°K, the experimental value of the second moment was about 9.8 gauss 2 for all three xylenes and for mesitylene. The calculated value, assuming a rigid structure, was however more than double this value for all four compounds. Since the molecules axe all of different shape and symmetry, the most obvious explanation of the low second moment value common to all four is to assume there is internal rotation or tunnelling of the CH 3 groups about the direction of the C--C sidebonds. Calculation shows t h a t such motion does in fact lead to values of the second moment in good agreement with those observed. Internal rotation of the CH 3 groups is also indicated by preliminary measurements on durene (1.2.4.5 tetramethylbenzene) and pentamethylbenzene at 291°K. The most symmetrical member of this group, hexamethylbenzene, also shows this internal motion at temperatures above 95°K. In addition there is a further narrowing of the resonance line over the temperature range 135--210°K which indicates the onset of further motion. The second moment above 210°K is quantitatively consistent with the view t h a t there is hindered rotation of the molecules as a whole about their hexagonal axes. Such motion is in accord with dielectric evidence of molecular rotation in all the polar hexasubstit u t e d methylchlorobenzenes at temperatures down to 200--280 ° below their melting points s). In hexaethylbenzene it seems probable that there is internal rotation of the six methyl groups, but that the molecules do not rotate about an axis normal to the benzene ring. Since the carbon skeleton is presumably no longer planar as in hexamethylbenzene the potential barrier against rotation should in fact be higher. Received 23-%50.
NUCLEAR
RESONANCE
IN S O L I D H Y D R O C ~ A R B O N S
411
REFERENCES
I) G u t o w s k y , H.S., K i s t i a k o w s k y , G. B., P a k e , G. E. and P u r cell, E.M.,J. chem. Phys. 17(1949) 972. 2) G u t o w s k y , H.S. and P a k e , G.E., J. chem. Phys. 18(1950)162. 3) A n d r e w , E. R., J. chem. Phys. "18 (1950) 607. 4) M fill e r, A., Proc. roy. Soc. A I 2 @ (1928) 437; 127 (1930) 4|7; 138 (1932) 514. 5) V a n V l e c k , J.H., Phys. Rev. 74 (1948) I168. 6) H e r z b e r g, G., "Infrared and R a m a n Spectra of Polyatomic Molecules", D. Van Nostrand Co. Inc., N e w York (1945) 440. 7) K a s t l e r , A. and F r u h l i n g , A.,C.R. Acad. Sci. Paris, 218(1944) 998. 8) W h i t e , A. H., B i g g s , B.S. and M o r g a n , S. O., J. Am. chem. Soc. 62 0940) 16.