2460
NOTES
clear that C* is nearly a constant by virtue of the Gruneisen law, while B* ( T ) is temperature dependent only. Differentiating eq 1 once again, we get
c* =
- (l/vo)(b2p/bv2)T--I(bp/bv)T
Since the Gruneisen parameter formula
y
(2)
is given by the Slater
-
= -(v/2)(bp/bv)T-'(b2p/bv2)T
"3
(3)
from eq 2 and 3 follows
c* = ' / Z ( V / V O )
(7
+
2/8)
-'
Co
=
3/(6yo
=
f(v> + Tdv)
which is similar to the Griineisen-Debye approximation.' Let v = vT at any arbitrary temperature T and p = 0. Neglecting the effect of low pressure on thermal expansion, we may write vT = vo[l ao(T - To)]. Now integrating eq 1 gives
+
p = &(T)Iexp(vT - v)/v~C*- 11 (5) which is the desired form for small temperature rises with UT ~ 0 .
@a>
which may be considered approximately equal to the constant Cowith v ss vo. Thus we may put
C*
P
+ 4)
(2b)
Temperature Measurement in Fluorine Magnetic Resonance Spectroscopy1
From eq 1 and 2 we can solve for B*(T) in the form by Norbert 14uller and Timothy W. Johnson
B * ( T ) = (vo/v)KC* - p =
-p
(b2P/~V2)T-'(~P/~V)Tz
(4)
Department of Chemistry, Purdue University, Lafayette, Indiana 47007 (Received January 24, 1969)
It will be convenient to put B*(To)' = KoCo - 1
Bo
CoKo
(44
in which KO is related to yo by the Griineisen constant yo = crovoKo/c, with specific heat c, and thermal expansivity 010 nearly constant. But eq 4 is not the final form we seek. Since Gruneisen parameter is otherwise given by Y = (v/cu)(bp/Wo
(34
eliminating y from eq 2a and 3a gives ( b p / W t J= (C,/2VOC*) - (W3V)
Differentiating this equation once again, we get d2p/bvbT = 2c,/3v2 but differentiation of eq 1 gives
b2p/bTdv =
- (l/VoC*) [(bp/bT),+ dB*/dT] - (l/voCu)(yc,/v
+ dB*/dT)
From these we obtain dB*/dT = - ( c , ~ / u ) - (2c,voC*/3v2)
- (c,/v) [Y
=
+ (37 + 2) -'I
(4b)
which is nearly a constant for solids obeying the Gruneisen law. Also, eq 4b shows that B*(T) is a decreasing function as pointed in ref 2. From eq 4a and 4b we now get
B*(T) = CoKo
(co/v)[r
+ (37 + 2)-'1(T
- To)
(44
Once the parameters vo, C*, and B*(T) are determined, eq 1 can serve to establish the thermic equation of state for the solid. We find that by the use of eq 1, 2a, and 4c this equation of state is in the form The Journal of Physical Chemistry
The study of high-resolution nmr spectra as a function of temperature is greatly facilitated if sample temperatures can be determined indirectly with an "nmr thermometer.'' Ideally such a thermometer consists of a compound or mixture containing nuclei of the same isotopic species as those under investigation and giving rise to a spectrum consisting of two sharp peaks with a known, strongly temperature-dependent separation. When such a mixture is placed in a capillary within the working sample, both the desired temperature-dependent data and the signals which are used for the temperature determination can be recorded in a single sweep over the spectrum. Several types of hydrogen nmr thermometer are in common US^,^-^ and it was reported6 while this work was in progress that signals from CFC1, and CFzCClz in a mixture which also contained CFC12CFC12 served as a fluorine nmr thermometer between -10 and - 110". Other temperature-dependent fluorine nmr spectra are known6 which could provide a basis for thermometry, but no convenient method has been described for determining temperatures in the range -40 to +loo" using the fluorine spectra of readily available compounds. I n studying the spectra of fluorinated solutes in aqueous solutions we have found (1) Supported by the National Science Foundation through Grant GP-8370 and by the National Institutes of Health through a predoctoral fellowship awarded to T. W. J. (2) .Publication No. 87-202-006 B168, Varian Associates, Palo Alto, Calif. (3) R. Duerst and A. Merbach, Rev. Sei. Instrum., 36, 1896 (1965). (4) F. Conti, (bid., 38, 128 (1967). (5) R. A. Newmark and R. E. Graves, J . Phys. Chem., 72, 4299 (1968). (6) See for example J. Jonas, L. Borowski, and H. 5. Gutowsky, J. Chem. Phys., 47, 2441 (1967).
NOTES it desirable to develop such a procedure, and the results are reported here.
Experimental Section A survey of a number of commercially available7 organofluorine compounds showed that the chemical shift difference between the signals of 1,1,2-trichlorotrifluoro-l-propene, CF&C1=CCI2, and 1,2-difluorotetrachloroethane, CFC12CFC12, is strongly temperature dependent, suggesting that a mixture of these materials would be suitable for thermometry. To allow the CF3CC1=CC12 resonance to be used as the internal lock signal for the Varjan HA-60-IL spectrometer (operated at 56.445 MHz) the mixture should consist predominantly of this component. A solution containing 2% CFC12CFC12by volume was found to be satisfactory. The shift difference is quite insensitive to minor concentration changes for such a mixture, so that no extraordinary precautions are required. The nmr spectrum of CFaCC1=CC12 showed less than 1% of a contaminant which appeared (chemical shift and temperature dependence) to be CFC12CFC12. The CFClzCFClzadded to make the thermometric mixture contained5 a trace of CF2C1CC13,but since it was used at high dilution this should have no significant effect on the measured shifts. Accordingly, both materials were used without further purification. Temperatures were adjusted and controlled with a Varian V-4341/V-6057 variable temperature accessory and measured with a Technique Associates Thermotest 1 using a copper-constantan thermocouple junction. I n preliminary runs the solution was sealed in a 3 X 50 mm thin-walled capillary placed in an nmr tube halffilled with hexane or paraffin oil, the junction being suspended in the tube directly above the capillary. This procedure gave acceptable results below room temperature, but the plot of chemical shift against
246 1 temperature changed slope at higher temperatures in a way suggestive of a vertical temperature gradient in the sample tube. Final results were obtained using an nmr tube provided with a thermocouple well consisting of a 4-mm 0.d. tube drawn into a capillary at the lower end and ring-sealed to the nmr tube at the top. The thermometric solution was enclosed in the annular region between the inner and outer tubes. For each point, the temperature was determined after lowering the thermocouple so that the junction was at the center of the receiver coil, then the spectrum was recorded with the thermocouple removed and immediately afterwards the temperature was remeasured. The two temperatures usually differed by a few tenths of a degree, in no case by more than 0.5', and their average was taken as the best value.
Results The working range of this thermometer is limited at the lower end by the broadening of the signal from CFC12CFC12,which becomes severe below -45', and at the upper end by the danger of explosion attendant on the increasing vapor pressure of the mixture (CF3CC1= CC12 boils at 88.1' and CFC12CFClzat 91'). Data points were obtained a t -35.3 and +92.2' and 15 intermediate temperatures. They showed no systematic deviation from the best straight line, found by least squares to be T = 555.0 - 1.5296 (Hz at 56.445 MHz) or T = 555.0 - 86.306 (ppm), with a root-mean-square deviation of 0.22 Hz or 0.33'. The major cause of the scatter is probably that the temperature and chemical shift could not be measured simultaneously, and the controller2 does not eliminate small temperature fluctuations. (7) Peninsular Chemresearch Inc., Gainewille, Fla.
Volume 73, Number 7 July 1960
