T H E
J O U R N A L
O F
PHYSICAL CHEMISTRY Registered in U . S. Patent Ofice @ Copyright, 1964, by the American Chemical Society
VOLUME 68, XUNBER 9 SEPTEJIBER 15, 1964
Statistical ‘I’hermodynamicsof the Polyphenyls.
I.
Molar Volumes and
Compressibilities of Biphenyl and m-, 0-, and p-Terphenyl Solid and Liquid’
by Jack Opdycke, James P. Dawson, Ronald K. Clark, Melvyn Dutton, James J. Ewing, and Hartland H. Schmidt Department of Chemistry, University of California, Riverside, California
(Receked M a y 6 , 2,964)
The molar volumes aiid isothermal coiiipressibilities of biphenyl and of 0-, m-, and pterphenyl have been measured in the solid and liquid ranges from room teiiiperature up to 350, 450, 400, aiid 400°, respectively, aiid up to 170 atm. pressure. Individual liquid isotheriiis are fitted by a yuadr.atic expression in the pressure to within the precision liniits of the volume nieasurenieiits which range from f10-5 to =!= 10 I.jmole probable error. Coefficients of the isotherm expressions are expanded in a power series in temperature to provide a single empirical expression for the volume of each compound over the whole liquid range. Representative values of the molar volumes (1. /mole) a t zero pressure are: biphenyl, 0.13153 (s, 30’) and 0.15573 (1, 75’); o-terpheiiyl, 0.19775 (s, 30’) and 0.22180 (1, 75’); m-terphenyl, 0.19234 (s, 30’) aiid 0.22279 (1, 100’); p-terphenyl, 0.18836 (s, 30°) arid 0.24298 (1, 225’). The results are compared with the predictions of the Tait equation for the compressibility of liquids and the function T V 2 ( d P / b T ) ,= a is compared for the coiupounds. The Tait equation “ConstaIlt” C is roughly independent of temperature within the first 100’ above the melting point but increases somewhat a t higher teinperatures. The fuliction a is found to increase with pressure over niost of the temperature range and has a total niaxiniuiii variation of 20% for any one compound over the liquid range investigated.
Introduction This investigation of the thermodynamic properties of the polyphenyls and the applicability of various statistical thermodynamic niodels to the Correlation of these properties was begun not only because of the interest in the coinpounds themselves for their remark-.
able temperature and radiation stability compared to niost organic molecules, but also because comparisons ( I ) This work was supported in part by contract A T ( I I - ~ ) - ~ ~ , Project No. 79 under the USAEC Division of Reactor Development and was presented a t the 146th National AIeeting of the American ChernicRl Society, Denver, C O ~ O . , January 19-24, 1964.
2385
2386
J. OPDYCKE, J. DAWSON, R. CLARK,M. DUTTOS,J. EWING, AND H. SCHMIDT
of properties within the series seemed likely to provide especially interesting examples for tests of theories of structural and intermolecular interaction effects of polymers and their solutions. In addition to the advantages for theory testing shared with the alkane series, e.g., the availability of a fairly complete set of pure isomers aniong the lower members of the series and stability of the fluid phase over a fairly wide range of temperatures for these shorter polymers, the polyphenyls have the additional advantage of greater internal rigidity and conformational simplicity which make the effects upon the therniodynaniic properties of restricted segment motions within the molecule niore pronounced. Furthermore, as will be shown in the second paper of the series, the intermolecular potential function parameters for segments of the polyphenyls as derived from current theories of polymer structural effects seem to follow quite a regular pattern within the series with the effective linear dimension of the segments falling within about 4% of that of benzene. Application of polymer theories can thus follow calculations from models much niore satisfactorily than in the case of alkanes where the ethylene group is about the size of methane and end effects are a p p r e ~ i a b l e . ~Also, , ~ more properties of the pure polymer are accessible to measurement, the liquid and vapor ranges being included, than is the case for high polymers.
Experimental The apparatus used for the compressibility measurements was very similar to one described by Beattie.5 Volume measurements were taken from a calibrated screw reading on a mercury conipressor thermostated a t 30’. The protractor on the screw could be read to 0.001 turns with an over-all precision of 0.0006 cc. as determined by repeatedly calibrating the screw for nonlinearity using weights of displaced mercury ejected over a volume range of about 210 cc. Volume changes were transmitted by means of high pressure capillary lines to the sample which was contained in a Pyrex liner surrounded by mercury within a vanadium steel bomb. Pressure measurements were made with a Ruska dead weight oil pressure gauge connected to the mercury system through a capillary in a steel riser block. The gauge was readable under most of the experimental conditions to within the 0.05 atm. required by the precision of the volume measurement at the highest liquid compressibilities, and the absolute accuracy of the gauge was certified by the manufacturer to better than this. Reproducible positioning of the oil-mercury interface was assured by means of an insulated needle in the riser block conThe Journal of Physical Chemistry
tacting the mercury surface and carrying a 1000-c.p.s. signal with less than 1 r.m.s, v. applied to the open circuit. The contact point was established at about 1OG-ohm impedance using a rectifier and an electronic d.c. null detector. This detection system seemed to depend much less upon history of the interface and needle wetting properties than did simpler high current d.c. devices. Two thermostats were employed for the bomb, an oil bath for the range 30-75’ and an oven for temperature up to 4z w
-J
>-
z
I a K w 1.8
W
I
0.9 & m
I-
IO0
200
300 TEMPERATURE (“C)
400
Figure 1. van der W a d ’ s “constant” T V ’ 2 ( 0 P / d T ) v= a for liquid biphenyl and the terphenyls.
c ( t ) values. The standard deviations of c ( t ) for individual isotherms, even after they have been smoothed by the cross plot, range froni about 25y0 ,at the lowest temperatures to about 5% at the highest temperatures. Thus, the direct use of the constants in Table I will lead to widely fluctuating values of B(t) and C. A set of smooth values of 0.4343C which are consistent with an equation of the formof (1)and with the limits of error O F the coefficients of that equation are given in Table [V. It is obvious that these experiments to 170 atm. are not a very sensitive test of the Tait equation. The value of 0.43436 = 0.0937 obtained for benzene, chloro-, bromo-, and nitrobenzene, and aniline by Gibson and LoefflerI4 for the range 2501250 bars and 25-85’ is seen to agree nearly within the estimated probable error in our values with that constant for biphenyl and the terphenyls in the range from somewhat above the nielting point to about 150’ (biphenyl and o- and m-terphenyl) or 100’ (p-terphenyl) above the nielting point. At higher temperatures there is a significant rise in the value of C necessary i,o correlate eq. 1 with eq. 2. The most satisfactory fit between these two equations is obtained by using a 0.4343C value starting a t about 0.07 at the melting points and rising with positive curvature with t . Values
of B (t) in ( 2 ) may be calculated from these C values using (1) to calculate b ( t ) , which is known to much better
precision than c ( t ) , and then applying (4) to calculate B(t). These values of B(t) range from 1000 atm. a t the lowest temperatures to 360 =t 12 atni. at 400’. The truncation of the expansion represented by (3) and (4)is thus justified within experimental error. Table IV : A Set of Smoothed Values of 0.4343C Consistent with an Equation of the Form of ( 1 ) and the Tait Equation ( 2 ) Temp., OC.
Biphenyl
75 100 125 150 175 200 225 250 275 300 325 350 375 400
0.06 0.06
0.09
0.131 0.166
m-Terphenyl
o-Terphenyl
0.07 0.07 0.07 0.07 0.07 0.07 0.071 0.082 0.095 0.107 0.117 0.125 0.133
0.06 0.08 0.08 0.08 0.08 0.08 0.09 0,104 0,119 0.133 0.141 0.146 0.153 0.165
p-Terphenyl
*
0.07 0.071 0.079 0.091 0.103 0.112 0.120 0.127
0.03 0.02 0.02 0.01 0.01 0.01 0.01 0,009 0,008 0,007 0,005 0,005 0,005 0.005
Volume 68, Sumber 9
Septembw, 1964
J. OPDYCKE, J. DAWSON, R. CLARK, 31. DUTTON, J. EWING, AND H. SCHMIDT
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One thermodynamic function which has been found to be nearly constant over wide ranges of temperature and pressure for liquids is the function
a
=
T(bP/dT),V2
=
[(dE/dV),
+PIP
(5)
It can readily be shown12that a constant value of this function for a given liquid is predicted, for spherical molecules of pairwise additive potential energy, from the assumption that the radial distribution function does not depend upon volume or temperature. The result is then a van der Waals
The Journal of Physical Chemistry
expression for the internal energy of the liquid with energy inversely proportional to the volume. Figure 1 shows the variations of a with temperature and volume. The maximum variations for a given compound are about 20% over the range while the probable error is about 2%. I n the following paper a more detailed discussion will be given of the application of the simplifying assumption of inverse proportionality between the volume and the intermolecular segment interaction energy. There we will make allowance for restricted motions of the segments in a free volume theory.
