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The paramagnetic susceptibility of a free radical
P h y s i c a X V I I I , no ! I
N o v e m b e r 1952
T H E PARAMAGNETIC S U S C E P T I B I L I T Y OF A F R E E RADICAL b y J. VAN D E N H A N D E L Communication no. 291b from the Kamerlingh Onnes Laboratorium, Leiden, Nederland
Synopsis T h e m a g n e t i c s u s c e p t i b i l i t y of t h e free r a d i c a l CI8H21N202 w a s m e a s u r e d b e t w e e n r o o m t e m p e r a t u r e a n d 1.56°K. B e t w e e n 3 0 0 ° K a n d 4 ° K t h e s u s c e p t i b i l i t y c a n be r e p r e s e n t e d b y a C u r i e - W e i s s l a w : X = C / ( T + A ) --Xdi,~, w h e r e A = 1.5. T h e r e s e e m s t o b e s o m e p o s s i b i l i t y of a n t i - f e r r o m a g n e t i c b e h a v i o u r a t t e m p e r a t u r e s b e l o w 1.5°K.
1. Introduction. A few years ago Dr. H o 1 d e n drew our attention to some m e a s u r e m e n t s on resonance absorption in organic free radicals which were carried out at the Bell Telephone Laboratories 1). Some of the material was sent to us so t h a t we could c a r r y out susceptibility m e a s u r e m e n t s to discover w h e t h e r this salt would be suitable for d e m a g n e t i z a t i o n experiments. T h o u g h this p r o v e d not to be the case, it nevertheless seems worthwhile to publish the results of our m e a s u r e m e n t s , especially as since t h e n work on the properties of free radicals has a t t r a c t e d more att e n t i o n 2). 2. Material and method. The m e a s u r e m e n t s were carried out with a c o m p o u n d t h a t was, as s t a t e d above, sent to us b y Dr. H o 1d e n . Its formula is C18H21N202, and H o l d e n , Yager and Merrittz) called it " B e n f i e l d and K e n y o n ' s radical", a f t e r the chemists who m a d e it in 1926 5): K e n y o n and S u gd e n 4). gave some details of it in 1932. In control experiments, melting point t e m p e r a t u r e s between 91.5 and 93°C were found. N e i t h e r before nor during the susceptibility m e a s u r e m e n t s did the t e m p e r a t u r e rise above the ice-point. Afterwards we got the impression t h a t this precaution had been unnecessary, and t h a t room t e m p e r a t u r e s would not have been harmful. ~921--
922
j. VAN DEN HANDEL
The susceptibilities were measured with a magnetic balance that has been in use at this laboratory for m a n y years 5).
3. The results o/ the measurements at higher temperatures are collected in table I and fig. 1. The table gives the values of Z', the susceptibility per gram after correction for diamagnetism, and of its reciprocal, as functions of the temperature T. ]'ABLE I 7' oK 14.18 14.34 14,46 17.54 20.32 20.32 20.32 66.06 70.51 77.77 153.42 169.76 288.1 291.5
10~.Z '
IO-(/Z"
1 0 c . z ' ( T -5 1.5)
78.04 77.65 77.75 65.83 58.23 58.01 57.31 18.63 17.52 15.56
1.281 1.288 1.286 1.519 1.717 1.724 1.745 5.37 5.71 6.43 12.38 13.42
1224 1230 1241 1253 1271 1266 1251 1259 1262 1233 1252 1276 1237
8.08 7.45 4.27
23.42 23.42
4.27
1251 av. 1250
0.25
/
0.20
/
0.10
/
/
T
0.00 0
--T
F i g . 1.
~oo
2O0
1/•' a s a f u n c t i o n
300°K
of T.
The estimated accuracy of the measurements is of the order of 1½%. For the diamagnetic susceptibility the value 0.44 x 10.-6
.THE
PARAMAGNETIC
SUSCEPTIBILITY
OF A FREE
RADICAL
923
was assumed. The values of Z' can be represented by the formula z'(T -t- 1.5) = 1250 × 10-6, corresponding to a magneton number of p ---- 8.57 + 0.06 Weiss magnetons. This shows that this free radical behaves like a paramagnetic substance with a magnetic moment arising from one spin, in agreement with the results published by H o l d e n , K i t t e l , M e r r i t t and Y a g e r X ) . The fact that it is necessary to introduce a correction for the temperature variation indicates, however, that it is not exactly a single-spin magnetic moment, so that at lower temperatures deviations from the CurieWeiss law could be expected.
4. The results o/ the measurements at temperatures in the region o/ liquid helium are shown in table II and fig. 2. The accuracy in the helium region is in general of the order of ½%, but occasionally errors of order 1% occur. In table II, a' is the magnetization per gram, after correction for diamagnetism. " F A B L E II T ° K
4.238
"O 1965 3847 5234 6986 7431 7936 8537 9277
uj~" it o" ]
~"
°K
1.830
1.824
1.559 3.405
2.112
1965 3847 6986 7431 7936 8537 9277
1.550 1.554 1.552 1.562
H O
H/'I"
6986 7431 7936 8537 9377 1965 3847 5234 1965 3847 5234 6324 6986 7431 6324 7936 8537 9277
3817 4060 4336 4664 5069 1077 2109 2869 1260 2467 3357 4056 4481 4766 4080 5107 5483 5940
2.370 2.510 2.687 2.894 3.139 0.654 1.304 1.732 0.710 1.314 1.838 2.264 2.503 2.666 2.264 2.880 3.103 3.385
j. VAN DEN HANDEL
924 03S
0.30 02S
0.20
Ol S
0.I0
005
0"
l°
--
H.Fr
tooo
2000
3000
4000
$000
6 0 0 0 ~/otC
Fig. 2. o' as a function of HIT for different temperatures. 4.238 °1< ~7 1.831 °K O 3.405°I£ ~ 1.824°K ~:~ 2.112°I( .~- 1.550 - - 1.562°K.
5. DiScussion o/ the results. One of the striking features of the m e a s u r e m e n t s oll free radicals with cm spectroscopy is the fact t h a t one observes only v e r y n a r r o w absorption lines, m u c h n a r r o w e r t h a n could be explained b y a dipole-dipole interaction alone. For such an interaction would produce a half-width of some 200 O, while in reality a value of a b o u t 18 ~ was found for this salt 2). According to G o r t e r and V a n Vleck6), this narrowing can be u n d e r s t o o d if we assume the existence of an exchange interaction between the magnetic ions. Such an interaction causes a loss of coherence; this leads to a greater absorption of frequencies corresponding to the centre and to the outside of the wings of the absorption lines, but to a smaller absorption for the inner parts of these wings. The net result is a smaller half-intensity-width. In a theoretical paper, V a n V 1 e c k 7) has given more details of this narrowing. If we accept from this narrowing the existence of an exchange interaction, it m a y still be either positive or negative; in other words, it is possible for it to lead either to ferromagnetism or to a n t i - f e r r o m a g n e t i s m (or perhaps even to a m i x t u r e of both). F r o m the occurrence of a negative Curie t e m p e r a t u r e in the CurieWeiss law, we m a y deduce t h a t there is a possibility t h a t the antiferromagnetic case is the relevant one here. According to V a n V 1 e c k, when only exchange interaction between nearest neigh-
THE PARAMAGNETIC S U S C E P T I B I L I T Y OF A F R E E RADICAL
925
bours is important, the transition point between the paramagnetic and anti-ferromagnetic states occurs at a temperature 0 equal to the value of A appearing in the law of Curie-Weiss valid in the paramagnetic region. If this were the case here, only below 1.5°K would there be any possibility of finding anti-ferromagnetism. Down to the lowest temperature used in our measurements (1.56°K), no anti-ferromagnetism was detected, the susceptibility being still on the increase. The only deviation was the decrease in the value of Z' (T + 1.5), as depicted in fig. 3. These values are listed in table III: (z0 is the extrapolated value of Z' = (r'/H for small values of H). 1300
12oo
/
-
~
o
riO0 I000 i~'X~"r÷L5) 0
l
i
i
i
i
5
I0
IE
20
25"K
,T
11302 ~
t
O- t-I
I O0
0
,
" 8,
200
300
F i g . 3. 1 0 6 . z ' ( T + 1.5) as a f u n c t i o n of T f o r t h e region 1.5--20.3°K and 1.5--291.5°K.
*K
temperature
TABLE III r
°K 4.23 ~ 3.40 ~ 2.11 ~ 1.83 ~ 1.55 o
10 6 . Z'o
106.X'o(T + 1.5)
219. s 250. 4 322. 7 340 360
1258 1228 1166 1133 1101
This deviation must arise from the fact that the approximations contained in the Curie-Weiss law are no longer justified. It is possibly therefore already an indication of an approaching transition-point to the anti-ferromagnetic state. I wish to express m y sincere thanks to Dr. A. N. H o 1 d e n for sending us this free radical, to Prof. C. J. G o r t e r for valuable discussions, and to Mr. J. A. B e u n for his help with the measurements. Received 25-9-52.
926
T H E P A R A M A G N E T I C S U S C E P T I B I L I T Y OF A F R E E R A D I C A L REFERENCES
1) H o l d e n , A.N., Kittel, C., M e r r i t t , F. R., and Y a g e r , ~V.A., Phys. Rev. (2) 75 (1949) 1614 and (2) 77 (1950) 147. 2) H o l d e n , A. N., Y a g e r , W. A., and M e r r i t t , F. R., Chem. Phys. I:! (1951) 1319. 3) B a n f i e l d , F . H . , and K e n y o n , J., J. chem. Soe. 128 (1926) 1612. 4) K e n y o n , J., and S u g d e n , S., J. chem. Soe. 134 (1932) 170. 5) See e.g. G o r t e r , C. J., d e H a a s , W. J., and v a n d e n H a n d e l , J., Commun. Kamerlingh Onnes Lab., Leiden No. 222d; Proc. kon. Akad. A m s t e r d a m '16 [ 1933) 158. 6) G o r t e r , C. J., aud V a n V l e e k , J. H., C o m m u n . Leiden Suppl. No. 97a: Phys. Rev. (2)72'(1947) 1126. 7) V a n V l e c k, J. H., Phys. Rex,. (2) 74 (1948) 1168.
N o v e m b e r 1952
T H E PARAMAGNETIC S U S C E P T I B I L I T Y OF A F R E E RADICAL b y J. VAN D E N H A N D E L Communication no. 291b from the Kamerlingh Onnes Laboratorium, Leiden, Nederland
Synopsis T h e m a g n e t i c s u s c e p t i b i l i t y of t h e free r a d i c a l CI8H21N202 w a s m e a s u r e d b e t w e e n r o o m t e m p e r a t u r e a n d 1.56°K. B e t w e e n 3 0 0 ° K a n d 4 ° K t h e s u s c e p t i b i l i t y c a n be r e p r e s e n t e d b y a C u r i e - W e i s s l a w : X = C / ( T + A ) --Xdi,~, w h e r e A = 1.5. T h e r e s e e m s t o b e s o m e p o s s i b i l i t y of a n t i - f e r r o m a g n e t i c b e h a v i o u r a t t e m p e r a t u r e s b e l o w 1.5°K.
1. Introduction. A few years ago Dr. H o 1 d e n drew our attention to some m e a s u r e m e n t s on resonance absorption in organic free radicals which were carried out at the Bell Telephone Laboratories 1). Some of the material was sent to us so t h a t we could c a r r y out susceptibility m e a s u r e m e n t s to discover w h e t h e r this salt would be suitable for d e m a g n e t i z a t i o n experiments. T h o u g h this p r o v e d not to be the case, it nevertheless seems worthwhile to publish the results of our m e a s u r e m e n t s , especially as since t h e n work on the properties of free radicals has a t t r a c t e d more att e n t i o n 2). 2. Material and method. The m e a s u r e m e n t s were carried out with a c o m p o u n d t h a t was, as s t a t e d above, sent to us b y Dr. H o 1d e n . Its formula is C18H21N202, and H o l d e n , Yager and Merrittz) called it " B e n f i e l d and K e n y o n ' s radical", a f t e r the chemists who m a d e it in 1926 5): K e n y o n and S u gd e n 4). gave some details of it in 1932. In control experiments, melting point t e m p e r a t u r e s between 91.5 and 93°C were found. N e i t h e r before nor during the susceptibility m e a s u r e m e n t s did the t e m p e r a t u r e rise above the ice-point. Afterwards we got the impression t h a t this precaution had been unnecessary, and t h a t room t e m p e r a t u r e s would not have been harmful. ~921--
922
j. VAN DEN HANDEL
The susceptibilities were measured with a magnetic balance that has been in use at this laboratory for m a n y years 5).
3. The results o/ the measurements at higher temperatures are collected in table I and fig. 1. The table gives the values of Z', the susceptibility per gram after correction for diamagnetism, and of its reciprocal, as functions of the temperature T. ]'ABLE I 7' oK 14.18 14.34 14,46 17.54 20.32 20.32 20.32 66.06 70.51 77.77 153.42 169.76 288.1 291.5
10~.Z '
IO-(/Z"
1 0 c . z ' ( T -5 1.5)
78.04 77.65 77.75 65.83 58.23 58.01 57.31 18.63 17.52 15.56
1.281 1.288 1.286 1.519 1.717 1.724 1.745 5.37 5.71 6.43 12.38 13.42
1224 1230 1241 1253 1271 1266 1251 1259 1262 1233 1252 1276 1237
8.08 7.45 4.27
23.42 23.42
4.27
1251 av. 1250
0.25
/
0.20
/
0.10
/
/
T
0.00 0
--T
F i g . 1.
~oo
2O0
1/•' a s a f u n c t i o n
300°K
of T.
The estimated accuracy of the measurements is of the order of 1½%. For the diamagnetic susceptibility the value 0.44 x 10.-6
.THE
PARAMAGNETIC
SUSCEPTIBILITY
OF A FREE
RADICAL
923
was assumed. The values of Z' can be represented by the formula z'(T -t- 1.5) = 1250 × 10-6, corresponding to a magneton number of p ---- 8.57 + 0.06 Weiss magnetons. This shows that this free radical behaves like a paramagnetic substance with a magnetic moment arising from one spin, in agreement with the results published by H o l d e n , K i t t e l , M e r r i t t and Y a g e r X ) . The fact that it is necessary to introduce a correction for the temperature variation indicates, however, that it is not exactly a single-spin magnetic moment, so that at lower temperatures deviations from the CurieWeiss law could be expected.
4. The results o/ the measurements at temperatures in the region o/ liquid helium are shown in table II and fig. 2. The accuracy in the helium region is in general of the order of ½%, but occasionally errors of order 1% occur. In table II, a' is the magnetization per gram, after correction for diamagnetism. " F A B L E II T ° K
4.238
"O 1965 3847 5234 6986 7431 7936 8537 9277
uj~" it o" ]
~"
°K
1.830
1.824
1.559 3.405
2.112
1965 3847 6986 7431 7936 8537 9277
1.550 1.554 1.552 1.562
H O
H/'I"
6986 7431 7936 8537 9377 1965 3847 5234 1965 3847 5234 6324 6986 7431 6324 7936 8537 9277
3817 4060 4336 4664 5069 1077 2109 2869 1260 2467 3357 4056 4481 4766 4080 5107 5483 5940
2.370 2.510 2.687 2.894 3.139 0.654 1.304 1.732 0.710 1.314 1.838 2.264 2.503 2.666 2.264 2.880 3.103 3.385
j. VAN DEN HANDEL
924 03S
0.30 02S
0.20
Ol S
0.I0
005
0"
l°
--
H.Fr
tooo
2000
3000
4000
$000
6 0 0 0 ~/otC
Fig. 2. o' as a function of HIT for different temperatures. 4.238 °1< ~7 1.831 °K O 3.405°I£ ~ 1.824°K ~:~ 2.112°I( .~- 1.550 - - 1.562°K.
5. DiScussion o/ the results. One of the striking features of the m e a s u r e m e n t s oll free radicals with cm spectroscopy is the fact t h a t one observes only v e r y n a r r o w absorption lines, m u c h n a r r o w e r t h a n could be explained b y a dipole-dipole interaction alone. For such an interaction would produce a half-width of some 200 O, while in reality a value of a b o u t 18 ~ was found for this salt 2). According to G o r t e r and V a n Vleck6), this narrowing can be u n d e r s t o o d if we assume the existence of an exchange interaction between the magnetic ions. Such an interaction causes a loss of coherence; this leads to a greater absorption of frequencies corresponding to the centre and to the outside of the wings of the absorption lines, but to a smaller absorption for the inner parts of these wings. The net result is a smaller half-intensity-width. In a theoretical paper, V a n V 1 e c k 7) has given more details of this narrowing. If we accept from this narrowing the existence of an exchange interaction, it m a y still be either positive or negative; in other words, it is possible for it to lead either to ferromagnetism or to a n t i - f e r r o m a g n e t i s m (or perhaps even to a m i x t u r e of both). F r o m the occurrence of a negative Curie t e m p e r a t u r e in the CurieWeiss law, we m a y deduce t h a t there is a possibility t h a t the antiferromagnetic case is the relevant one here. According to V a n V 1 e c k, when only exchange interaction between nearest neigh-
THE PARAMAGNETIC S U S C E P T I B I L I T Y OF A F R E E RADICAL
925
bours is important, the transition point between the paramagnetic and anti-ferromagnetic states occurs at a temperature 0 equal to the value of A appearing in the law of Curie-Weiss valid in the paramagnetic region. If this were the case here, only below 1.5°K would there be any possibility of finding anti-ferromagnetism. Down to the lowest temperature used in our measurements (1.56°K), no anti-ferromagnetism was detected, the susceptibility being still on the increase. The only deviation was the decrease in the value of Z' (T + 1.5), as depicted in fig. 3. These values are listed in table III: (z0 is the extrapolated value of Z' = (r'/H for small values of H). 1300
12oo
/
-
~
o
riO0 I000 i~'X~"r÷L5) 0
l
i
i
i
i
5
I0
IE
20
25"K
,T
11302 ~
t
O- t-I
I O0
0
,
" 8,
200
300
F i g . 3. 1 0 6 . z ' ( T + 1.5) as a f u n c t i o n of T f o r t h e region 1.5--20.3°K and 1.5--291.5°K.
*K
temperature
TABLE III r
°K 4.23 ~ 3.40 ~ 2.11 ~ 1.83 ~ 1.55 o
10 6 . Z'o
106.X'o(T + 1.5)
219. s 250. 4 322. 7 340 360
1258 1228 1166 1133 1101
This deviation must arise from the fact that the approximations contained in the Curie-Weiss law are no longer justified. It is possibly therefore already an indication of an approaching transition-point to the anti-ferromagnetic state. I wish to express m y sincere thanks to Dr. A. N. H o 1 d e n for sending us this free radical, to Prof. C. J. G o r t e r for valuable discussions, and to Mr. J. A. B e u n for his help with the measurements. Received 25-9-52.
926
T H E P A R A M A G N E T I C S U S C E P T I B I L I T Y OF A F R E E R A D I C A L REFERENCES
1) H o l d e n , A.N., Kittel, C., M e r r i t t , F. R., and Y a g e r , ~V.A., Phys. Rev. (2) 75 (1949) 1614 and (2) 77 (1950) 147. 2) H o l d e n , A. N., Y a g e r , W. A., and M e r r i t t , F. R., Chem. Phys. I:! (1951) 1319. 3) B a n f i e l d , F . H . , and K e n y o n , J., J. chem. Soe. 128 (1926) 1612. 4) K e n y o n , J., and S u g d e n , S., J. chem. Soe. 134 (1932) 170. 5) See e.g. G o r t e r , C. J., d e H a a s , W. J., and v a n d e n H a n d e l , J., Commun. Kamerlingh Onnes Lab., Leiden No. 222d; Proc. kon. Akad. A m s t e r d a m '16 [ 1933) 158. 6) G o r t e r , C. J., aud V a n V l e e k , J. H., C o m m u n . Leiden Suppl. No. 97a: Phys. Rev. (2)72'(1947) 1126. 7) V a n V l e c k, J. H., Phys. Rex,. (2) 74 (1948) 1168.