J. H. SMITHAND E. L. FACE
2368
An Estimate of the Librational Barrier in the Solid
Perfluosoalkanes from Heat Capacity Data by J. H. Smith Department of Chemistry, Butler University, Ind&znaplis, Indiana
and E. L. Pace Department of Chemistry, Case Western Reserve University, Cleveland, Ohio (Received December 11,2 ~ 6 8 )
Low-temperature heat capacity measurements have been obtained for the compound CF, and have been used in conjunction with analogous data for CzFo and CsF8 to estimate the potential barriers V ohindering the solidstate molecular libration for the perfluoroalkane series. The heat capacity values are duplicated to approximately 1% by determining the sum of lattice and internal contributions to the total heat capacity and by utilizing a relationship between the Debye 8’s of translational movement for the three compounds. The value of VOis assessed from the lattice rotational contribution assuming a harmonic oscillator model for the librating molecule. It is seen that for molecules such as the perfluoroalkanes,which undergo orientationally disordering transitions, the value of VO at the lowest temperatures is a measure of the amount of thermal energy required to eventually cause the solid-solid transition at some higher temperature.
Introduction Low-temperature thermodynamic studies of the first three members of the perfluoroalkane series, CF,,l C~FG , ~CaFs,ahave shown these compounds to comand prise part of a group of molecular solids termed “plastic c r y s t a l ~ ”which ~ undergo solid-solid disordering transition~.~-’The differences in the heat capacity curves and transition anomalies for these compounds as -CF8 groups are progressively added to the CFI molecule are shown in Figure 1. At the lowest temperatures, these globular molecules experience a potential barrier Vo which hinders molecular libration and is a function of the directive character of the intermolecular potential field exerted by the neighboring molecules. At higher temperatures, a hindered oscillatory molecular motion may begin prior to the transition (as, for instance with CF4) if the molecular envelope is spherical or globular in shape. I n this case, the barrier height V ois further lowered with increasing temperature due to the smoothed-out potential fields of librating nearest-neighbor molecules, When lie is sufficiently lowered so that all molecules begin librating, the transition anomaly occurs, at which point rapid molecular axis realignment occurs along with increased libration around the molecular axis. If on the other hand pretransition libration is sterically unfavorable, Le., V ois high due to nonspherical molecular envelopes such as in CzFBand CaFg, the transition must occur as a result of a concerted cooperative molecular movement and no pretransition rise in the heat capacity is observed. It is seen, therefore, that the quantity Voa t low temperature for each member of the perfluoroalkane series should reflect the decreasing symmetry of these plastically crystalline compounds. The Journal of Physical Chemistru
Further, the temperature a t which the orientationally disordering transition eventually occurs should also be dependent on this quantity. The potential barrier Vo may be obtained for these compounds if a harmonic oscillator model is assumed for the librating molecule8 and the empirical curve-fitting procedure employed by LordeJoand extended by Wulff l1 is utilized.
Experimental Section The calorimetric measurements for CFd were carried out in a previously constructed adiabatic calorimeter.12 The gaseous tetrafluoromethane was condensed into the calorimeter through a vacuum system, and heat capacity measurements were taken from solid hydrogen temperatures (approximately 12°K) to the normal boiling point of the substance. l a Analogous calori(1) This work is taken in part from a thesis by J. H. Smith, submitted in partial fulfillment of the requirements for the Ph.D. degree, Western Reserve University, Cleveland, Ohio, Jan 1968. (2) E. L. Pace and J. G. Aston, J . Amer. Chem. SOC,,70, 666 (1948). (3) E. L. Pace and A. C. Plaush, J . Chew. Phys,, 47, 38 (1907). (4) J. Timmermans, J . Chim. Phys., 35, 331 (19381, (5) Gymposium Report on ”Plastic Crystals and Rotation in the Solid State,“ Phys. Chem. Xolida, 18, 1 (1961). (6) E. F. Westrum, Jr., Pure Appl. Chem., 2 , 241 (1961); 8, 187 (1964). (7) L. A. K. Stavely, Ann. Rev. Phys. Chem., 13, 351 (1962). (8) M. Sorai, H. Suga, and S . Seki, Bull. Chem. SOC.Jap., 38, 1126 (1965). (9) R. C. Lord, Jr., J. E. Ahlberg, and D. H. Andrews, J. Chem. Phys., 5, 649 (1937). (10) R. C. Lord, Jr., ibid., 9, 693 (1941). (11) C. A. Wulff, ibid., 39, 1227 (1963). (12) E. L. Pace, L. Pieroe, and K. Dennis, Rev. Sei. Instrum., 26, 20 (1955). (13) Detailed thermal data to be published.
LIBRATIONAL BARRIER IN
THE
2369
SOLIDPERFLUOROALKANES
34
28 F
26 24
22
20
/
-
/"
/'
-
/
/'
Y
i
2 16 A
\
8 12 9
14
IO
9-06.
8 -
CF4, (PRESENT WORK)
C2 Fs, (REFERENCE 2)
I -
6 -
C3F8, (REFERENCE 3)
4 2 01 0
I
I
I
I
I
I
20
40
60
80
100
120
I 140
I 160
I 180
TEMPERATURE, OK
Figure 1. Molar heat capacity.
metric data were already available for hexafluoroethane2 and perflu~ropropane.~Purity analysis carried out by the method of Rossini14showed less than 0.1% impurity in all cases, and third-law entropy verification was also performed for the case of CFI. The empirical curve-fitting procedures were carried out on an 1107 IBM computer.
Discussion The experimental heat capacity curves can be duplicated to about 1% (except for the lowest temperatures) by summing the various contributions to the experimentally derived quantity C,.l0 The internal contribution to the total heat capacity is calculated from 38-6 i=l
where the first term accounts for the intramolecular vibrations which are represented by the summation of Einstein function8 for an S atom molecule having a vibrational degeneracy G, and the second represents the restricted internal rotation of m groups within the molecule, also given by an Einstein function. Values of C? may therefore be computed a t various temperatures and subtracted from the experimental curve. The remaining contribution to C , is now the volume expansion term and the lattice contribution. The
former is approximated at low temperatures by a Nernst-Lindemann relation'6
c, - c v - 0.0214CP2T Tm
(2)
(where Tm is the melting temperature) and subtracted from the previous result. The remaining curve is now fitted to a sum of Debye and Einstein functions (3)
which represent, respectively, the translational and rotational (librational) degrees of freedom. The trial and error quality of determining Debye and Einstein 0's for this curve-fitting procedure is lessened by utiliaing the relation
(4) (where M is the gram-molecular weight and V is the molar volume) which was first derived by Lindemann'e (14) F. D. Rossini, "Chemical Thermodynamics," John Wiley & Sons, Inc., New York, N. Y., 1950,pp 454-456. (16) W. Nernst and F. A. Lindemann, 2. Elektrochem., 17, 817 (1911). (16) F.A,Lindemann, Phys. Z.,11, 609 (1910). Volume 73, Number 7 July 1969
2370
J. H. SMITHAND E. L. PACE ~
~~~~
Table I : Contributions to the Total Heat Capacity of CFI [in cal/(deg mol)] as a Function of Temperature
Temp, OK
13.0 14.0 15.0 17.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
CY1
Translational heat capacity
0 * 000 0.000 0.000 0.000 0 I000 0.000 0.000 OIO0O 0.000 0.001 0,002
1,520 1.757 1.990 2,432 3.017 3.769 4.295 4.665 4.930 5.124 5,269
Vibrational heat capacity,
CVL
Rotational heat capacity
Torsional heat oapacity
1.977 2.374 2.782 3.606 4.782 6.424 7.652 8.651 9.213 9.707 10 * 082
0 457 0.617 0.792 1,174 1.765 2.655 3 357 3.886 4.283 4.583 4 813
0.000
NernstLi n d e m a n n heat capacity
I
b
0.012 0.020 0,029 0.055 0.115 0.266 0 475 0.728 1.016 1.337 1 683
0.000 0.000 0 * 000 0.000 0.000 0 * 000 0.000 0.000 0.000 0.000
I
+
[aCvL b CY' ]zT
-
a = 0.0181:
0.50
Exptl heat capaoity
Calod heat capacity
2.003 2.424 2,845 3.683 4.899 6,677 8,137 9.327 10,310 11.150 11.870
1.994 2.392 2 807 3.678 4.932 6,702 8.227 9.389 10,325 11,101 11.77
0.017 0.026 0.038 0.072 0.150 0.338 0 575 0.838 1.112 1.394 1 686
I
I
I
I
I
Table 11: Contributions to the Total Heat Capacity of CzFo [in cal/(deg mol)] as a Function of Temperature
Temp, OK
Vibrational heat capacity
Translational heat capaoity
12.0 15.0 20.0 25.0 30.0 35.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
0 000 0.000 0.000 0 I002 0.014 0.044 0.103 0,326 0.678 1.135 1.670 2.262 2.895
1 562 2.318 3.343 4,050 4.528 4,855 5.087 6,379 5.548 5.654 5,724 5.773 5.808
I
I
CVL
Rotational heat capacity
1.914 3.169 5.190 6.789 7.962 8.808 9.427 10.234 10.713 11.017 11.220 11.363 11.467
0.352 0.851 1.847 2.739 3.434 3.953 4.340 4.855 5.165 5.363 5.496 5.590 5.659
CVI
Torsional heat capacity
NernstLindemann heat capacity
0,032 0.108 0.331 0.596 0.850 1.082 1.304 1.756 2.257 2 * 812 3.414 4.054 4.722
0.032 0.108 0.331 0.594 0.836 1.038 1,201 1.431 1.579 1,677 1.744 1.792 1.827
0.006 0.020 0,077 0.166 0.283 0.428 0.598 0.974 1.402 1,942 2.580 3.334 4.365
[aCvL
+
bf7~'l*T a = 0.0080;
b = 0.012
0.003 0.011 0,041 0.094 0. I 6 4 0,244 0.332 0.530 0.763 1.040 1.364 1.752 2.202 ~~
Exptl heat capacity
Calcd heat capacity
2.070 3.285 5 590 7.323 8,740 9.945 11,000 12.550 13.750 14.980 16.145 17.310 18.790
1.949 3 288 5,562 7.479 8.976 10.134 11.063 12.520 13.733 14.869 15.998 17.169 18.391
I
I
~~
Table 111: Contributions to the Total Heat Capacity of C3Fs [in cal/(deg mol)] as a Function of Temperature
Temp, OK
30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0
70,O 75.0 80.0 85.0 90.0 95.0
Vibrational heat capacity
Translational heat capacity
0,089 0.195 0.353 0.563 0.824 1,133 1.487 1.880 2 307 2.763 3,241 3.738 4.248 4.768
5.154 5.352 5.487 5.582 5.561 5.703 5,744 5.775 5,800 5.821 5.837 5.851 5.863 5.873
I
NernstCYL
7 942 I
8.728 9.324 9 778 10,128 10,403 10,622 10.798 10,941 11.060 11.158 11.240 11.311 11.371 I
Rotational heat capacity
2 788 3.376 3.837 4.196 4.477 4.700 4.878 5.023 5 I141 5.239 5,321 5.389 5.448 5.498 I
CVI
2.471 2.910 3.314 3.709 4.110 4.528 4.967 5.428 5.011 6.412 6.928 7.455 7.993 8.536
and discussed by Lennard-Jones." If it is assumed, reasonably, that the proportionality constant is the Of Same for the perfluoroalkanesl the required OD and BE are computed by trial and error, and the The Journal of Physical Chemistry
Torsional heat capacity
1Lindemann
2 382 2.715 2.961 3,146 3.286 3.395 3.480 3.548 3,004 3.649 3.687 3.718 3,745 3.768
0 587 0.865 1.182 1.548 1.952 2.408 2,909 3.477 4 I149 4.910 5.763 6.746 7.924 9.272
I
heat capacity I
[aCvL
+
bCyl]zT a
b
0.0108;
- 0,0084
E
0,341 0.493 0.660 0.842 1.035 1.244 1.468 1.710 1.973 2.252 2,554 2.878 3.225 3.594
Exptl heat capacity
10,710 12.040 13.160 14,200 15.130 16,020 16,860 17.710 18,640 19.590 20.550 21.570 22.720 23,920
Calcd
heat capacity
10 754 12.131 13.30 14,329 15.273 16,175 17.057 17.93 18.83 19.72 20.64 21.53 22.63 23.50 I
Debye 9's calculated in this manner may then be compared to those calculated with the above relation. (17) J. E. Lennard-Jones and A. F. Devonshire, Proc. Roy. SOC. (London), ~ 1 7 0 480 , (1939).
LIBRATIONAL BARRIER IN
THE
SOLIDPERFLUOROALKANES
2371
Table IV: Data Required for the Computation of Debye 6’s of Translational Motion Barrier to internal rotation, cal/mol
Density, g/cm8
Ismallest moment of inertial
domr
89. 56d
1.48 X 10-gc
4350”
3.066 X 10-a8@
173.1”
3610’
5.157 X
125.5b
1.62 (liquid)e 1.96 (solid) 1,70 1.85 (solid) 2.01 (liquid)b
a See ref 2. * See ref 3. E. Gelles and K. S. Pitzer, J . Amer. Chem. Soc., 75, 5259 (1953). See ref 1. 0. Ruff and 0. Bretschneider, 2. Anorg. Allg. Chem., 210, 173 (1933). Normal frequency assignments for CgFs and CaFs were obtained from ref 2 and 3, A. C. Plaush, “The Thermodynamic respectively, and for CFI from P. N. Schata and D. F. Hornig, J . Chem. Phys., 21,1516 (1953). Properties of Perfluoropropane from 14°K to its Normal Boiling Point,” unpublished Ph.D. thesis, Western Reserve University, Sept 1963.
’
Table V : Debye e’s, Einstein e’s, Librational Barrier Values, and Transition Temperature for the Perfluoroalkane Series en.
CF4 CzFe CaFs
” See ref
1.
trial and error, O K f3’K
OD8 calod, OK
79.6 72.5 52.0 See ref 2.
- C,
cal/mol
78.9 74.0 50.1
81.0 79.3 94.0
5,420 f 400 1 0 , 7 6 0 f 830 9,150 rt 600
3
O K
76.23’ 103.98b 99. 37c
See ref 3.
=
+ bC,I)2T
(5)
where a and 6 are empirical constants. The entire procedure is then repeated until the experimental heat capacity is duplicated. The Einstein 0 for the lattice rotational motion may be given, in the harmonic oscillator approximation, as
eE =
Transition temp,
&3OK
Once OD and eE have been derived for the low-temperature range, the volume expansion term is reevaluated usinglo
C,
vo
OE. &3OK
4.463n(Vo)’/8 [ 1 0 4 0 ~ s m a l l e s moment t of inertia
] 1/2
(6)
The reduced moment of inertia, usually seen in this equation,18 is replaced by the smallest moment of inertia of the molecule. The latter quantity is more descriptive of the rotation of the entire rigid molecule in the lattice cavity, rather than the relative motion encountered in internal molecular rotation. We have considered n to be given by the number of potential maxima experienced by the rigid molecule as it makes a rull revolution around its axis of libration (taken to be the axis of the least moment of inertia for C2F6 and C3F8, and the C3 axis for CFJ. The quantity n for CF, and C2F6 is therefore the number of times the molecule duplicates its original spatial orientation of minimum potential energy as it revolves 360” around the libration axis. This is seen t o occur three times for
CF4 and three times for C2F6. The intermolecular potential interactions of the C3F8 molecule can be considered to be of two types. First, the two sets of three fluorine atoms a t the end of the molecule imply a value of n of three, Le., a potential vs. angle of rotation diagram having three minima occurring 120” apart. Superimposed on this diagram, however, is a potential function having minima occurring every 180°, corresponding to the interactions of the set of fluorine atoms on the middle carbon atom. A total of five maxima and therefore a value of n equal to 5 are distinguishable on such a diagram as the C3F8molecule makes a complete revolution around its axis of least moment of inertia,
Results The results of the curve-fitting analysis are given in Tables I to I11 and the data required for its computation are given in Table IV. Table V gives, first, the values of the Debye 0 corresponding to the translational lattice motion which are calculated by both the trial and error method and by use of eq 4 in the form
(7) Since the molar volume of CaF8 was available only in (18) G. J. Janz, “Estimation of Thermodynamic Properties of Organic Compounds,” Academic Press, Ino., New York, N. Y . , 1958, p 27.
Volume 73, Number 7 July 1060
2372
MICHAEL L. HAIRAND WILLIAM HERTL
the liquid state, the ratio of Debye 0's for this compound was calculated using liquid volumes for CF4 and CzFs also. The second method lends added validity to the first as seen from the variance (at most, 2') between the two methods. The values of OE, calculated as the complement of the OD (best fit), for lattice rotational movement are given in column 3 and values of V ocalculated from eq 6 are given in column 4. The transition temperatures of the three compounds are given in the last column. The quantity Vo is a measure, a t the lowest temperatures, of the restrictive potential which hinders the molecule's free rotation in its lattice cavity. As previously explained, at higher temperatures when plastically crystalline behavior commences, these values of V o may not remain constant as for example in the case of CF,. The low-temperature values, however, are a measure of the relative ease with which the particular
molecule may begin, a t some higher temperature, a libration sufficient in magnitude to cause an anomaly in the observed heat capacity. As can be seen, the CgFe molecule experiences the highest potential barrier and will require the greater amount of thermal energy needed to cause the transition anomaly. The transition for the CJ?s molecule occurs slightly below that of the CzFB molecule because Vo is smaller, and finally the CF, molecule, having the lowest value of the restrictive potential, has also the lowest temperature of transition and exhibits a pretransition rise in the heat capacity,
Acknowledgments. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research with Grant No. 1976-A5. The authors are also indebted to Dr. A. Plaush for the computer program used for the curve-fitting analysis.
Reactions of Chlorosilanes with Silica Surfaces
by Michael L. Hair and William Hertl Research & Development Laboratories, Corning Glass Works, Corning, New York 14880 (Received December 17,1068)
Reaction curves have been obtained spectroscopically for the reactions of (CH&SiCl, (CH&SiC12,(CH3)SiC13, and Sicla with the free hydroxyl groups on silica. Kinetic analysis of these curves shows that the monofunctional chlorosilane follows 1.0-order kinetics with respect to the number of surface bonding sites; the multifunctional silanes all follow 1.5 =k 0.2-order kinetics with respect to the number of surface bonding sites. The 1.5 overall reaction order is attributed to the presence of about 50% single OH groups on the surface and 50% geminal OH groups. The four chlorosilanes have an experimental activation energy of 22 & 2 kcal. A fast initial reaction, to the extent of 10-15%, takes place and is believed to be due in part to direct replacement of OH by C1. The validity of the kinetic analysis and confirmation of the replacement of OH by C1 reaction are shown by chlorine analyses of the treated silica. In the temperature range studied (200-400°) the reaction rates are independent of the pressure of chlorosilane. From high resolution spectra it is postulated that a band at 3747 cm-l is due to single OH groups, and that bands at 3751 and 3743 cm-l are due to geminal OH groups. The kiiietics of the chlorosilane reactions are compared and contrasted to the analogous methoxysilane reactions with silica.
Introduction The reactions between chlorosilanes and the surface of silica have been studied and investigated by many workers, primarily because of the utility of these reagents as coupling agents in polymer chemistry and surface deactivating agents in chromatography. Reaction with both freely vibrating and with adjacent Hbonded surface hydroxyl groups has been proposed,'P2 although spectroscopic evidence obtained in evacuated, water-free systems suggests that, a t temperatures below 500°, reaction is with the freely vibrating hydroxyl The Journal of Physical Chemistry
group only. Recent studies by Peris and Armistead and Hockey4indicate that the reaction of a silicon tetrachloride, trichloromethylsilane, or dimethyl dichlorosilane molecule with silica surfaces involves more than one silanol group, despite the fact that these OH (1) V. Ya. Davydov, A. V. Kiselev, and L. T. Zhuravlev, Trans. Faraday SOC.,60, 2254 (1964). (2) L. R. Snyder and J. W. Ward, J. Phys. Chem., 70, 3941 (1966). (3) J. B. Peri, ibid., 70, 2937 (1966). (4) C. G. Armistead and J. A. Hockey, Trans. Faraday Soc., 63, 2549 (1967).
