S. W. MAYER
2160
Vol. 67
A MOLECULAR PARAMETER RELATIOXSHIP BETWEEN SURFACE TENSION AND LIQUID COMPRESSIBILITY BY
s. w.M-4YER
Laboratories Division, Aerospace Corporation, El Segundo, California Received March 4, 1963 Approximate expressions for the surface tension and compressibility derived in ref. 1-3 are used to predict liquid compressibilities from surface tension data, and vice versa. A relabionship between surface tension and liquid compressibility is obtained by multiplying together the expressions for these properties. This relationship is dependent only on the liquid density and on the diameter of the molecular models; the latter parameter is calculated readily from the surface tension or compressibility. The validity of these expressions is tested for several representative types of liquids: hydrocarbons, halogen-containing organic and inorganic nonelectrolytes, polar organics, liquefied gases, liquid metals, and molten salts. The expressions hold well in most cases, except for the liquid metals. I n general, liquids composed of molecules having more nearly spherical intermolecular potentials exhibit the best correlation with the surface tension-compressibility relation. The Calculated molecular model diameters are comparable with molecular diameters determined by other procedures. On the basis of these favorable results, an approach is suggested for using surface tension data to compute those liquid physical properties and thermodynamic values obtainable from an equation of state for liquids.
Introduction
A fairly precise equation of state for the rigid-sphere fluid has been obtained by Reiss, Frisch, and Lebowitz’ by essentially computing the reversible work of creating a spherical cavity in this fluid. This equation of state has been presented2 in the form
p v- - 1 + y + y 2 RT (1 - Y ) ~
u =
where p is the pressure, V is the molar volume, .y is na3N/6V, N is Avogadro’s constant, and a is the rigidsphere diameter of the molecules comprising the pure liquid. The isothermal compressibility, p, then can be expressed as2
Stillinger has shown2 that, when eq. 2 is applied to molten alkali halides, values of the calculated interionic distances are the same order of magnitude as those found for the solid alkali halides from X-ray diffraction data. I n additional studies, the approaches used by Reiss, Frisch, and LeboTvitz’ have been extended to the surface tension of real fluids including nonelectrolyte^^^^ as well as molten salts6 and liquid metals.E I n these studies, the following relationship3 was used for the surface tension, u u=-
]-y + (118Y2 - y)2
IcT 12y 4na2 [1 - y
bility from surface tension data and vice versa. The term pa/2 in eq. 3 is generally negligible3in comparison with the other term on the right-hand side of this equation. Then, the identities nNa2 = 6yV/a and lc = R/N can be used to write the following expression for surface tension
(3)
For real fluids th@molecular parameter a is the hardcore7 diameter of the molecules comprising the fluid. I n the present study, eq. 3 has been combined with eq. 2 in such a way as to provide a relatively simple and convenient relationship for computing liquid compressi(1) H. Reiss, H.L. Frisch, and J. L. Lebowitz, J . Chsm. Phys., 31, 369 (1959). (2) E. Helfand, H.L. Frisch, and J. L. Lebowitr, ibid., 84, 1037 (19bl); F. H. Stillinger, Jr., ibid., 36, 1581 (1961). (3) H. Reiss, H. L. Frisch, E. Helfand, and J. L. Lebowitz. i b d , 84, 119 (1960). (4) 8. W.Mayer, ibid., 88, 1803 (1963). (5) H.Reiss and S. W. Mayer, ibzd., 34, 2001 (1961). (6) 9. W. Mayer, zbid.. 35, 1513 (1961). (7) J. 0.Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” John Wdey and Sons, Inc., New York,N. Y., 1954.
+
aRT@ Y> 4V(1 - Y ) ~
(4)
Multiplying eq. 4 by eq. 2 one obtains
pa =
4 2 - 3Y 4(1
+
+
$I8>
(5)
This relationship makes it feasible to compute the compressibility from surface tension and vice versa. Density data are the only additional data needed, and these are generally available for a liquid for which the surface tension or compressibility has been measured. Obviously, i3 and u are related through the molecular parameter a (y is dependent on a ) , but the parameter a can be calculated readily from eq. 2 or eq. 4 in accordance with the availability of experimental results for p or u, respeotively. This computation procedure was used to test the applicability of eq. 5 by examining the agreement between the measured surface tension and the surface tension computed from eq. 5 by using the parameter a which had been calculated from eq. 2 . A parallel test of eq. 5 was made by comparing the measured compressibility with the compressibility computed from eq. 5 by using the parameter a which had been calculated from eq. 4.
Results In Tables I-TI, the results are summarized for computations to test the validity of eq. 5 , the molecular parameter relationship between surface tension and compressibility. In the fifth and sixth columns of each table, the measureds and computed surface tensions are presented for comparison. The surface tension was computed from eq. 5 by using the measured compressibility and as, which is the value of the parameter a calculated from eq. 2. The seventh and eighth columns compare measured compressibility with computed compressibility. The compressibility was computed from (8) Landolt-Bornstein Tabellen, I1 Band, 3. Teil, Springer-Verlag, Berlin, 1956.
RELATIONSHIP BETWEEN SCRFACE TENSION AKD LIQCIDCOWPRESSIBILITY
Oct., 1963
2161
TABLE I COMPtiTED AND MEASURED SURFACE TENSIONS AXD COMPRESSIBILITIES FOR HYDROCARBON LIQUIDS Liquid
Temperature, OK.
a,,
10-8 om.
ap, 10-8 cm.
Surface tension," dynea/cm. Measured Computed
Compressibility, 10-11 cm.z/dyne Measured Computed
Benzene 293.1 5.05 5.02 28.9 28 9.4b 8 27.5 27 10. lb 10 Benzene 303.1 5.02 5.00 25.0 25 11.gb 12 Benzene 323.1 4.94 4.96 Toluene 293.1 5.44 5.42 28.4 27 9 .ob 8 5.41 5.40 27.3 27 9.6b 10 Toluene 303.1 5.36 25.0 26 1l.lb 12 323.1 5.33 Toluene Hexane 293.1 5.57 5.66 18.4 20 15.3' 18 19 16.8' 21 5.63 17.4 Hexane 303.1 5.51 16.3 19 18.3' 25 5.45 5.61 Hexane 313.1 22.3 22 11.8" 12 6.03 273.1 6.04 Heptane 21 13.7G 15 5.98 20.3 Heptane 293.1 5.95 20 14.8' 17 5.96 19.3 303.1 5.90 Heptane 24 10.0" 10 6.36 23.8 Octane 273.1 6.36 23 11.5" 12 6.32 21.7 293.1 6.29 Octane 20.7 22 12.4' 14 6.31 303.1 6.25 Octane 28.6 28 8.4d 8 5.77 293.1 5.79 m-Xylene 27 9.Od 9 5.75 27.4 303.1 5.76 m-Xylene 26 9.6d 10 5.74 26.4 5.73 m-Xylene 313.1 23.7 24 12.3e 12 5.33 Cyclohexane 304.1 5.33 Values for the measured surface tensions throughout the tables were obtained from ref. 8. References for all the following tables are found in these footnotes (ref. b through n). a, was calcukited from the corresponding value of the surface tension in accordance E. B. Fryer, J. C. Hubbard, and D. H. Andrews, J . Am. Chem. Soc., 51,759 (1929). H. E. Eduljee, D. M. Newitt, and with eq. 4. D. Tyrer, ibid., 105, 2534 (1914). e N. M. Philip, Proc. I n d i a n Acad. Sci., 9A, 109 K. E. Weale, J . Chem. Soc., 3086 (1951). R. E. Gibson and 0. H. Loeffler, J . Am. Chem. Soc., 61, 2515 (1939). 1 D. M. Newik and K. E. Weale, J. Chem. Soc., 3092 (1951). R. E. Gibson and 0. H. Loeffler, ibid., 63, 898 (1941). 3' L. Bergmann, "Der UltraA. Weissler, zbid., 71, 1272 (1949). (1939). schall," Fourth E d . , Herzl-Verlag, Zurich, 1954, p. 372 ff. !: A. Van Itterbeek, A. de Bock, and L. Verhaegen, Physica, 15, 624 D. Harrison and E. A. Moelwyn-Hughes, Proc. Roy. Soc. (London), A239, 0. J. Kleppa, J . Chem. Phys., 18, 1331 (1950). (1949). 230 (1957). (I
TABLE I1 HALOGEN-CONTAINING COMPOUNDS Liquid
Temperature,
OK.
as,
10-8 om.
Carbon tetrachloridle 293.1 5.18 5.16 26.8 303.1 5.14 5.14 25.5 Carbon tetrachloride 24.2 5.11 Carbon tetrachloride 313.1 5.10 Chloroformi 283 1 4.82 4.80 28.6 Chloroform 293.1 4.78 4.78 27.2 4.76 Chloroform 303.1 4.74 25.9 Ethyl bromide 293.1 4.55 24.0 4.55 Ethyl iodidle 293.1 4.84 28.8 4.81 Ethylene dichloride 293.1 4.84 4.81 32.2 Tetrachloroethane 298.1 5.56 34.9 5.54 Chlorobenzene 293.1 5.46 5.40 33.3 Chlorobenzene 303.1 5.43 5.38 32.1 Chlorobenzene 323.1 5.37 5.36 29.8 Bromobenzene 298.1 5.58 35.6 5.51 Sulfuryl chloride 336.1 4.75 4.75 25.5 Germanium tetrachloride 22.4 303.1 5.43 5.45 Phosphorus trichloride 303.1 4.96 4.93 27.8 Phosphorun tribroinide 303.1 5.46 5.30 44.7 Phosphorus oxychloride 303.1 5.16 5.09 30.9 Arsenic trichloride 303.1 5.12 5.04 37.8 Antimony pentachloride 303.1 5.91 5.90 30.0 References for the measured compressibility data are cited in the footnotes to Table I. I
a
a& 10-0 om.
Surface tension, dynes/cm. Measured Computed
eq. 5 by using the measured surface tension8 and a,, which is the value of the parameter a calculated from cq. 4. None of the measured isothermal coinpressibilities in Tables 1-17 was obtained by high-pressure volume change methods since those measurements do not provide p a t atmiospherjc pressure. Instead, the results of sound-velocity methodsQ were used throughout the (9) E. B. Fryer, J. C. Hubbard, and D. H. Andrews. J . Am. Chem. S O C . ~ 61, 759 (1929).
26 26 24 28 27 27 24 28 31 34 31 30 29 33 26 22 27 35 28 34 30
--Compressibility,"--10-11 cm.a/dyne Measured Computed
10.3b 11.2b 12.26 9 .2b 9 .gb 10.8' 12 .gd 9 .gd 8 .Od 6.2' 7 .4b 7.gb 8.gb 6.7' 12.6h 12 .gh 10 .4h 6.0h 9 .3h 6.7h 7.5h
10 11 12 9 10 11 13 9 7 6 6 7 9 6 13 13 10 4 8 6 7
tables. All the hydrocarbon liquids for which measurements of the isothermal compressibility could be found are listed in Table I. I n Table I1 are presented all the halogen-containing organic and inorganic nonelectrolytes for which data could be found. Table I11 summarizes measured and computed cs and p for alcohols and other organic liquids. Results are presented in Table I V for cryogenic and liquefied gases. I n Table V the results, which are relatively poor, are given for liquid metals near their melting points and for water over a
2162
Vol. 67 TABLE I11 LIQUIDSCOMPOSED OF POLAR ORQANIC MOLECULES Liquid
a
Temperature, OK.
ac, 10-8 om.
ap, 10-8 cm.
Surface tension, dynes/om. Measured Computed
Methanol 283.1 3.36 3.50 23.4 Methanol 303.1 3.28 3.46 21.7 Ethanol 273.1 4.06 4.17 24.3 Ethanol 293.1 4.00 4.13 23.0 1-Propanol 301.1 4.50 4.63 23.1 2-Propanol 303.1 4.43 4.64 20.6 Butanol 302.4 4.96 5.13 23.9 Cyclohexanol 304.9 5.49 5.51 32.2 Glycol 293.1 4.44 4.45 47.7 Glycol 353.1 4.29 4.35 42.3 Ether 283.1 5.00 5.08 18.2 Ether 293.1 4.93 5.04 17.0 Ether 303.1 4.87 5.01 15.9 Acetic acid 293.1 4.08 4.14 27.7 Acetic acid 303.1 4.06 4.14 26.8 Acetic anhydride 303.1 5.24 5.18 31.2 Ethyl acetate 293.1 5.16 5.17 24.3 Acetone 293.1 4.47 4.51 23.3 Acetone 313.1 4.37 4.44 20.9 Acetophenone 303.1 5.95 5.84 39.2 Aniline 293.1 5.39 5.34 42.9 Aniline 323,l 5.32 5.30 39.4 Aniline 363.1 5.22 5.25 34.3 Nitrobenzene 293.1 5.70 5.60 43.9 Xtrobenxene 313.1 5.66 5.57 41.4 Carbon disulfide 293.1 4.33 4.27 32.4 Carbon disulfide 323.1 4.21 4.19 27.8 References for the measured compressibility data are cited in the footnotes t o Table I.
27 27 28 27 27 26 29 33 48 46 20 19 18 30 30 29 24 24 23 33 40 38 36 38 37 30 27
Measured
10-11 om.2/dyne Computed
11.5b 13.0b 9.9b 11.2b 10 .Be 11.26 8.5O 6.6" 3.7; 4.7; 16.6b 18.4b 20.8b 9.1d 9.P 8 .ge 11.3" 12 .8b 15 .Bb 6.1e 4.sd 5 .3d 6.7d 4.gd 5 .5d 9.2b 11.Sb
15 19 13 15 15 18 13 7 4 6 20 23 27 11
12 8 11 14 18 4 4 5 8 4
5 8 11
TABLE IV COMPUTED AND MEASCRED SURFACE TESSIONS AXD COYPRESSIBILITIES OF NOSMETALLIC ELEMEXTS Liquid
a
Temperature, OK.
a,, 10-8 om.
ap, 10-8 em.
Surface tension, dynes/cm. Measured Computed
Oxygen 89.5 3.24 3.23 13.6 Oxygen 63.1 3.48 3.33 20.3 Kitrogen 77.1 3.41 3.41 8.9 Kitrogen 76.1 3.41 3.38 9.1 Kitrogen 3.50 70.1 3.41 10.5 Chlorine 293.1 3.50 3.61 18 .O Bromine 293.1 4.20 4.13 41.5 Argon 87.1 3.15 3.19 11.o 3.18 3.20 11.5 Argon 84.1 References for the measured compressibility data are cited in the footnotes to Table I.
range of temperatures. Finally, a comparison of measured and computed u and p is made for representative molten salts in Table VI.
Discussion It can be seen in Table I that the agreement between measured and computed surface tensions and compressibilities was particularly good for the cyclic hydrocarbons : benzene, toluene, m-xylene, and cyclohexane. The agreement for the aliphatic hydrocarbons, heptane and octane, was quite good, but that for hexane was not as good as for the other hydrocarbons. The intermolecular potential fields of the molecular models u ~ e d lin. ~ obtaining eq. 2 and 3 were spherically symmetrical. Consequently, it is not unexpected that liquids composed of molecules which deviate markedly from spherical symmetry , such as the long-chain aliphatics, would conform less well to eq. 5 . Of course, it is possible to speculate that rotational averaging in the liquid can improve the approximation to spherical intermolecular potentials so as to lead to better agreement with eq. 5 than otherwise would be anticipated.
14 15 9 9 10 20 38 12 12
C ~ m p r e s s i b i l i t y .10 ~ -11 cm.z/dyne Measured Computed
18.2' 11.o' 32 .4k 31.9' 27.9' 20. l j 6.3j 22.4' 21 .oi
17 8 32 30 22 25 5 25 22
It is apparent in Table I, and in the other tables, that the per cent deviation between a, and up is less at each temperature than the deviation between the measured and calculated u and p. This trend stems from the fact that u and p depend largely on the value of y, which is proportional to a3. Thus, the fractional differences between a, and a~ are magnified in computing u and p. Also, the (1 - y)4 factor in eq. 2 helps make p more sensitive than u to deviations in the parameter a. Equations 2 and 3 were developed on the basis of rigid-sphere and hard-core molecular models which, it was realized,l -6 could only approximate the behavior of actual molecules. They were not intended for accurate (e.g., within 10%) predictions of surface tensions and compressibilities from molecular parameters. ACcordingly, the number of significant figures for computed u and p in these tables was intentionally limited although, in some cases, compensating deviations from spherical models and from the work estimated1m3 to form a spherical cavity in the liquid result in agreement within 10%. In Table I1 it can be seen that eq. 5 is usually quite
Oct., 1963
RELATIONSHIP BETWEEN SURFACE TENSIOX AND LIQUIDCOMPRESSIBILITY
2 163
TABLE V LIQUIDMETALSAND WATER Liquid
Temperature, OK.
a,,
10-8 om.
ap, 10-8 om.
Surface tension,O dynes/om. Measured Computed
Compressibility,a 10 -12 om.S/dyne Measured Computed
2.4' 0.6 Zinc 693 2.72 2.52 795 386 3.2' 1 594 3.06 2.87 560 292 Cadmium 3.8" 0.6 313 3.23 3.01 470 193 Mercury 4.4" 1 442 210 3.18 2.97 433 Mercury 2.4' 0.3 2.79 735 250 303 3.01 Gallium 3.2' 2 429 3.20 3.10 350 243 Indium 4.lZ 1 3.17 410 242 575 3.34 Thallium 21' 4 2.77 2.44 206 91 37 I. Sodium" 40' 16 88 56 3.32 3.04 337 Potassium" 2.4' 0.4 2.33 2.14 735 280 303 Gallium" 3.2' 2 350 271 2.44 2.37 429 Indium" 4.1' 2 410 271 2.53 2.40 575 Thallium" 3.5l 2 2.46 455 298 600 2.59 Lead" 4.3l 2 395 253 2 -65 2.51 544 Bismuth" 3.1' 1 2.38 526 297 2.54 505 Tin" 48d 21 2.71 74 49 283.1 2.93 Water 45d 25 2.72 71 52 303.1 2.88 Water 44d 29 68 55 2.83 2.71 323.1 Water 46 36 2.69 63 56 353.1 2.76 Water 4tId 43 59 56 2.71 2.67 373.1 Water Jn these cases, the computations were a References for the measured compressibility data are cited in the footnotes to Table I. R. N. Lyon, Ed., "Liquid-Metals Handbook," (NAVEbased on an ionic-salt model for liquid metals,einstead of a monatomic model. XOS P-733 (Rev), 1952, pp. 40-56.
TABLE VI MOLTENSALTS Liquid
Temperature, OK.
5s, 10-8 om.
a@,10-8 am.
Surface tension,a dynes/om. Measured Computed
Compressibilty," 10 -12 om.z/dyne Measured Computed
NaCl 1073 2.46 2.47 116 119 29 NaCl 114:3 2.40 2.43 110 114 32 117 3 2.37 2.41 107 112 34 NaCl 1273 2.27 2.33 98 105 40 NaCl NaBr 1048 2.56 2.64 98 108 32 107 34 NaBr 1073 2.55 2.63 96 NaBr 1103 2.52 2.60 94 103 36 NaBr 1173 2.47 2.58 90 102 39 NaI 983 2.87 2.91 88 93 37 NaI 973 2.83 2.88 84 90 40 NaI lO4:3 2.74 2.83 78 87 45 NaI 1073 2.70 2.81. 75 86 47 KI 973 3.08 3.09 78 78 50 KI 1033 3.00 3.04 72 75 56 KI 1073 2.94 3.00 69 74 60 KI 111 3 2.88 2.97 66 72 65 ' J. O'M. Bockris, "Modern Aspects of Electrochemistry," Vol. 2, Butterworths Publications, London, 1959, pp. 196, 198.
successful in predicting compressibility from surface tension data, and vice versa, for inorganic chlorides in addition to organic halides. The good agreement between a, and ap in Tables I and I1 suggests that a useful equation of state is given for some classes of liquids by eq. 1 with a , and y computed from surface tension data and eq. 4. This equation for liquids could then be used to provide new relationships for other physical propekties and thermodynamic values which can be obtained from the equation of state ( e . g . , thermal expansivity, the difference between heat capacity a t constant pressure and beat capacity a t constant volume). The liquids listed in Table I11 do not usually show as good agreement bet14 een measured and computed surface tensions and cornpressibilities as do the liquids in Tables I and 11. This trend could be ascribed to the polar nature of the alcohol and oxy-organic molecules in Table I11 since eq. 2 and 3 would be expected to hold best for nonpolar molecule^.^ The extent of agreement prevalent in Table I [I is, however, sufficient to suggest
30 34 37 45 39 41 43 48 41 45 55 59 51 60 67 75
that the value of the surface tension could be used to calculate a useful value of the compressibility of an organic liquid for which no compressibility data were available. Because of the relationship of the surface tension to the parachor, and of the empirical additive dependence of the parachor on molecular composition, it is conceivable that such liquid physical properties and thermodynamic values as those mentioned in the previous paragraph might be roughly estimated on the basis of the molecular structure of organic compounds for which no surface tension measurements were available. However, surface tension measurements usually can be made readily for organic liquids. Most of the elements in Table I V also exhibit reasonably good agreement between observed and predicted u and /3 and between a, and as. The molecular diameter parameter, a,, in the gas phase for several of the molecules in Tables I-IV has been calculated' for the Lennard-Jones 6-12 intermolecular potential function from gas viscosity data. ag exceeds a, by the following
2164
D. M. SPEROS AND R. L. WOODHOUSE
fractions of ai1 Angstrom: benzene, 0.22; hexane, 0.34; cyclohexane, 0.76; carbon tetrachloride, 0.70; chloroform, 0.61; methanol, 0.23; ethanol, 0.40; carbon disulfide, 0.11; nitrogen, 0.18; chlorine, 0.62; bromine, 0.07; argon, 0.24. These are the differences for the lowest T at which a, was calculated. Since a, and up are dependent upon temperature, whereas ag is not, a, or up could be arbitrarily made equal to a, for several liquids simply by choosing the appropriate temperature for the computation of a, or ag. For many liquids (e.g., benzene, Table I), a, is larger than ag at one temperature, but as the temperature is raised the difference vanishes and then up begins to exceed a,. I n a separate report the hypothesis mill be presented (with supporting data and calculations) that the dependence of a,u, and p on T arises from the change in the required diameter of the spherical in the liquid model used for eq. 2 and 3. I n any event, as the agreement in these tables indicates, eq. 5 can be applicable without postulating a hypothesis for the dependence of the parameter a on T . I n Table V, the results for the liquid metals can be seen to be poor relative to the results discussed previously. Inasmuch as the structure of liquid metals would not be expected to correspond well to the molecular (or ionic) structure of fluids implicit in the parameter a of eq. 1-5, it might be anticipated that the liquid metal results 71-ould not be good. Kevertheless, ionic-salt and atomic models for liquid metals were found6 to be consistent with eq. 3 for surface tensions. It might be hypothesized, therefore, that it is eq. 2 in particular which is not follolved well by liquid metals and that compressibility is affected more strongly than surface tension by the electronic aspects of liquid metal structure. The agreement found for water (Table V) becomes good only at the highest temperature examined. The compressibility of mater is considered to be anomalous
Vol. 67
because its temperature dependence exhibits a minimum near 323’K. The improved agreement with eq. 5 above this temperature could possibly be attributed to some continuing change (e,g., depolymerization) rvhich allows the intermolecular interaction potential better to approximate spherical symmetry. The typical molten alkali halides for which results are summarized in Table VI illustrate a further use to which eq. 5 can be put. Experimental techniques used in the measurement of the velocity of sound in molten alkali halides involve a corrosion problemlowhich could possibly vitiate the compressibility results. Uncertainty as to the reliability of the results could exist, therefore, particularly in the absence of other compressibility data for molten salts. Hon-ever, the correlation between observed and computed u and fl in Table T’I supports the validity of the sound velocity measurements of Bockris and Richards.lo Similarly, the good correlatioii with eq. 5 found for the inorganic chlorides in the second half of Table I1 supports the validity of the sound velocity techniques used for these inorganic liquids. The computed values of a, and up in Table VI are consistent with the measured11 interatomic distances for these halides in the gas phase. I n a previous papert5it was pointed out that the interatomic distances for the gas molecules were the best data available for the hardcore diameter parameter a. The observed interatomic distances, in units of 10-8 cm., for the gas are: NaC1, 2.36; NaBr, 2.50; NaI, 2.71; KI, 3.05. Examination of Table VI shows that a temperature could be selected, for each of the salts, a t which a, or up in the liquid would equal the observed interatomic distances in the gas. (10) J. O’M. Bockris and N. E. Richards, Proc. Rou SOC.(London). A241 44 (1957). (11) A. Honig, M. Mandel, M. L. Stitch, and C. H. Townes, Phw. Rev., 96, 629 (1954).
REALIZATION OF QUANTITATIVE DIFFERENTIAL THERMAL ANALYSIS. I HEATS AND RATES OF SOLID-LIQUID TRANSITIONS BY D. R4. SPEROS AND R. L. WOODHOUSE Lanap Research Laboratory, General Electric Company, Nela Park, Cleveland, Ohio Received March 8, 1963 A direct method for accurate quantitative differential thermal analysis has been developed. The method involves addition or withdrawal of electrical energy from a sample structure in such a manner as to maintain a constant differential temperature between sample and reference thermocouples. The theoretical conditions under which this electrical energy is equal to the true energy of the process are determined. The results of the theoretical analysis a r e applied to the development of a working model. The instrument is used to redetermine the heats of fusion of Sn, iYaiTO,, Pb, Al, and Ag. The application of this procedure to the study of process kinetics is demonstrated. The rates of fusion of the above substances are examined.
I. Introduction Ever since its inception by LeChatelier in 1887,’ the inethod of differential thermal analysis (d.t.a.)Z has been used extensively for the qualitative study of processes involving changes ( A H ) in heat content. The method is simple in principle: a sample substance and a thermally inert reference substance are heated (1) H. LeChatelier, B~LZZ.SOC. franc. mineral., 10, 204 (1887). ( 2 ) W. J. Smothers and Y . Chiang, “Differential Thermal Analysis,” Chemical Publ. Co., New York, N. Y . , 1968.
a t a given rate by an external furnace. The junctions of a differential therniocouple are embedded in or near the sample and inert substances. The electromotive forces developed by these junctions are amplified and continuously compared by displaying on a recorder. Exothermic or endothermic changes that occur in the sample as the furnace temperature is raised are therefore recorded as deviations from a base line and appear as peaks on one side of it or the other. So by means of this method the following information is obtained:
