July, 1957
DIFFERENTIAL THERMAL ANALYSIS OF
J. R. Pickhardt for construction of much of the equipment, and t o Chemical Engineering Division
INORGANIC
HYDRATES
917
personnel who kindly furnished distilled halogen fluoride.
DIFFERENTIAL THERMAL ANALYSIS OF INORGANIC HYDRATES' BY HANSJ. BORCHARDT AND FARRINQTON DANIELS Contribution from the Department of Chemistry,University of Wisconsin, Madison, Wisconsin Received January 8 , 1967
Differential thermographs are presented for CuS04.5H20,CoC12.6H20,MnCl24Hz0, SrC126H20a?d BaBr~2H20. TWO kinds of anomalous peaks were observed. One originates from the formation and subsequent vaporization of liquid water when a hydrate decomposes. This situation has sometimes led to the erroneous interpretation of data in the literature. The other type of anomalous peak is due to the sudden change in the thermal conductivity of a sample when liquid forms. X-Ray measurements were used to determine the origin of the peaks in the differential thermographs. The X-ray data are given for the compound CUSOI-CUOand new lines are given for SrC12.2H20.
Introduction Differential thermal analysis (DTA) is a useful tool for studying the processes which occur in a material on heating. The difference between the temperature of a sample of powder and that of a standard powder is recorded as the two are heated simultaneously. Endothermic processes such as melting or dehydration are shown by minima or "peaks" in the curve in which temperature differences are plotted against the temperature. Certain conditions, however, may influence the differential thermograph and lead to misinterpretations. Inorganic hydrates, for example, where nonequilibrium conditions exist, may give rise t o extra peaks as will be described. The copper sulfate-hydrate system was studied with DTA by Taylor and Klug.2 These authors obtained a differential thermograph of CuS04. 5H20, for the temperature range 40 to 160') essentially the same as that shown by the solid line in Fig. 1. The product formed at 120' after the double peak was identified as CuS04.3Hz0. Since the transition from CuS04.5Hz0 t o CuSO4.3Hz0 occurred in two stages, as evidenced by the appearance of a double peak, these authors concluded that an intermediate phase existed. Chemical analysis of the product after the first peak of the doublet gave a Cu to HzO ratio of 1:4. Thus Taylor and Klug reported the existence of CuSO4-4Hz0. More recently, Ghosh* reported evidence for this compound as a result of thermogravimetric studies. Its existence is mentioned in several authoritative texts. -6 CuS04.5HzO as well as CoC12-6H20, MnCl2.4Hz0, SrCl2.6H20, BaBr2.2H20 and BaCl2.2H20 were studied in this Laboratory with DTA. The differential thermograph of each of these com(1) Presented in part at the 129th meeting of the American Chemical Society, Dallas, Texas, April, 1956. Further details may be found in a Ph.D. thesis by Hans J. Borchardt, filed in the Library of the University of Wisconsin, June, 1956. (2) T. I. Taylor and H. P. Klug, J . Chem. Phys., 4,601 (1936). (3) B. Chosh, J . Indian Chsm. SOC.,20, 120 (1943). (4) J. E. R i d , "The Phase Rule and Heterogeneous Equilibrium," D. Van Nostrand Co., New York, N. Y., 1951, p. 140. (5) 5. Bowden. "The Phase Rule and Phase Reactions." The Macmillan Co., New York, N. Y., 1938, p. 71. (6) N. V. Sidgwick, "The Chemical Elements and Their Compounds," Oxford Press, 1950, p. 155. (Sidgwick erroneously cites Taylor and Hug' as a reference for CuSOr.2HnO. These authors make no mention of a dihydrate.)
pounds, with the exception of BaCl~2H20,showed one more peak than would be expected on the basis of their commonly known hydrates. An intensive effort to find corroboration for new phases using X-ray techniques led, without exception, to negative results. Further observation made it apparent that when these unexpected peaks occur the hydrate does not go directly to water vapor and the next lower hydrate, but that liquid water is formed. The subsequent vaporization of this water gives rise t o the extra peak. The occurrence of this phenomenon is determined by the phase relationships of the hydrate and the procedure followed in differential thermal analysis.
Experimeqtal DTA Apparatus.-The DTA a 'paratus wa8 a modification of that reported by W'hitetead and Breger' which makes use of radiation shields in place of conventional insulation so that a vacuum can be attained readily. Pt-Pt 10% Rh thermocouples are used in a ceramic sample holder. The sample well was 5/32 inch in diameter and 5/8 inch deep, having a capacity of 0.1 to 0.2 g. With such small samples, the heat effect is very small and hence considerable amplification is necessary. An amplification factor of the order of 2000 was used most frequently. The high amplification in turn required special techniques to assure exact centering of the differential thermocouple in the furnace. To achieve this, a device was incorporated which allowed the position of the furnace to be varied continuously by small increments. Details are given elsewhere' The furnace is wound with nichrome wire. Different gases may be introduced by evacuating the furnace and bleeding in the desired gas. The output from the differential thermocouple is amplified by a Liston-Becker model 14 d.c. breaker amplifier and is then recorded on a Brown recording potentiometer having a scale 0 to 20 millivolts. The rate of temperature rise was programmed on a Brown Potentiometer Pyrometer which also gave a record of the sample temperature. For most work a rate of temperature rise of 10' per minute was used. Commercial C.P. material was used without further purification. The samples for DTA were ground to 100-200 mesh and diluted with an equal weight of calcined alumina. Alumina also served as reference material. Some aspects of the procedure are discussed in greater detail in another paper.8 X-Ray Analysis.-All X-ray work was performed on a North American Philips Type 12045 diffraction instrument using a copper target and nickel filter. For identification purposes a Philips 52057A, 57.3 mm. diameter camera was used. For the patterns reported herein a Philips 52056, 114.59 mm. camera was employed. The patterns were checked on a Norelco diffractometer. For work at ele(7) W. L. Whitehead and I. A. Breger, Science, 111, 279 (1950). (8) H.J. Borchardt. J . Chem. Ed., 83, 103 (1956).
HANSJ. BORCHARDT AND FARRINGTON DANIELS
918
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Vol. 61
only in periods of high relative humidity. The observation was verified by controlling the atmosphere in the furnace. With an initially dry atmosphere, a single peak always occurred. With a furnace atmosphere initially saturated with water vapor, the doublet always appeared. I n order t o determine the origin of the extra peak, samples of CuS04.5Hz0 were partially dehydrated and X-ray diffraction photographs taken. All lines could be assigned to the lines reported in the literature for CuSO4.5Hz0 and CuS04.3HzO. Since the extra peak occurred only at higher vapor pressures, a procedure was followed to give high pressures of water vapor. An intimate mixture containing approximately 55 mole yo CuSO4. 5Hz0 and 45 mole % ' CuS04.3Hz0was sealed in a quartz capi.llary. On the basis of the size of the capillary and the amount of sample taken, no significant quantity of CuSO4.5H20dissociated, when the partial pressure of water vapor in the capillary reached 1 atmosphere. This capillary was maintained a t 90" for several hours in a high temperature X-ray camera. No new lines appeared. It was further heated t o approximately 95" where a blank photograph resulted. Examination of the capillary showed that liquid was present and only a little salt remained. By shifting the position of the capillary a feeble X-ray pattern of the remaining salt was obtained. The pattern corresponded to CuS04-3HzO. I n order to observe portions of the X-ray pattern continually while CuS04.5Hz0 was heated, the previously described sample arrangement on the diffractometer was used. The sample temperature was followed as a function of time a t a constant heating rate. Breaks in the time-temperature curve occurred a t 92.5", 102 and 115". The line of CuSO4.5Hz0 having a Bragg d value of 3.70 was scanned during heating. No significant changes were observed until the sample had been heated a t 92.5" for approximately one minute. At this point the sample shrank and was not available to the X-ray beam. The shrinking and visible wetting of the sample showed clearly that liquid water was forming. Even more convincing was the observation of water vapor steaming from the sample holder for the duration of the 102" break in the heating curve. Since the breaks in the heating curve correspond to the peaks in the differential thermograph, the doublet observed by Taylor and Klug3 and in this investigation is not due to a tetrahydrate, but simply to the processes
+
CUSO~-~H~O + ( S ) CuSOa.BHnO(s) 2H20(1) 2H20(1) +2HzO(g) (from satd. soln.).
These findings are consistent with the classical vapor pressure-temperature diagram of the CuSO4hydrate system (Fig. 2). On heating CuSO45Hz0 above its dissociation temperature, trihydrate and water vapor form. This water vapor does not diffuse away from the sample at an appreciable rate. The resulting increase in the local partial pressure of water as the temperature is raised would be given by the dotted line if the system were in equilibrium. In DTA the temperature is probably somewhat higher than indicated since relatively large rates of temperature rise are
July, 1957
DIFFERENTIAL THERMAL ANALYSISOF
employed. When the partial pressure of water vapor becomes somewhat greater than 568 mm., the vapor pressure a t the quadruple point (A),9 the remaining CuSO4-5Hz0becomes unstable with respect to the trihydrate and saturated solution. This transition gives rise to the first large peak in the differential thermograph (Fig. 1) and the first break in the heating curve. On further heating, the vapor pressure of the saturated solution increases until it reaches atmospheric pressure, a t which point (B) water boils off and the second peak appears, these two peaks comprising the doublet. The next two peaks in Fig. 1 result from the transition of trihydrate t o mono (130”), and monohydrate t o anhydrous salt (250”), respectively, a t a vapor pressure equal to atmospheric pressure. The failure of a double peak (occasioned by the production of liquid water) to appear when the initial gas is dry, is attributed to the fact that the partial pressure of water vapor in the tube never gets as high as the vapor pressure of the saturated solution and all of the CuS04.5Hz0 is dissociated before a pressure of 568 mm. is reached. The other evidence for CuS04.4Hz0 is Taylor and Klug’s3 chemical analysis and Ghosh’s4 thermogravimetric work. With regard t o the former, one can only conclude that their sample may have consisted of a fortuitous mixture of CuS04.3Hz0 and adhering solution. Ghosh relied quite heavily on sudden deflections of a simplified thermobalance. His method indicated the presence of CuS04.4 l/z HzO and CU504.4 1/3 HzO as well as CuS04.4Hz0, neither of which have been observed in any other studies. Other Hydrates.-The occurrence of extra peaks in the differential thermal analysis of hydrates due to formation of saturated solution is not uncommon. Figure 3 shows the differential thermographs of five other hydrates. The processes giving rise to the peaks are summarized in Table 11. Confirmatory X-ray analyses were performed to show when new phases were present and when they were not. In the course of this work two distinct new lines were found in partially dehydrated SrClz.6Hz0. These were traced to SrC12.2Hz0, being the first two lines exhibited by this compound and occurring at Bragg d values of 5.64 and 4.55. They are the second and third most intense lines, having relative intensities of 79 and 90, respectively. The X-ray data are given in Table 111. The lines are consistent with the structure of SrC12.2H20 reported by Jensen, lo corresponding to reflections from the 200 and 011 planes, respectively. The necessary requirements for the appearance of a liquid phase in the differential thermal analysis of a hydrate are (1) that the hydrate system contains a quadruple point where hydrate, next lower hydrate, saturated solution and water vapor are in equilibrium; (2) that this quadruple point occurs a t a water vapor pressure which is less than atmospheric pressure; (3) that the rate of dissociation of the hydrate be rapid (if the sample tem-
.
.
(9) E. M. Collins and A. W. C. Menaies, THIS JOURNAL, 40, 379 (1938). (10) K. Jenaen, Denskr Videnslc. Selsk. Mat. F g s . Medd., SO (No.5 ) , 22 (1942).
INORGlNIC
919
HYDRATES
Fig. 2.-Vapor pressure-temperature diagram of the CuS04-hydrate system. The areas 5, 3 and 1 represent the stable regions of the penta-, the tri- and the monohydrate.
I
I
I
0
50
IO0 150 TEMPERATURE ‘C.
200
250
Fig. 3.-DifTerential thermographs of several hydrated salts. The second peak in each of the top four thermographs is a “false” peak due to vaporization of water.
perature has attained a value greater than the boiling point of saturated solution before appreciable local vapor pressures are established, no liquid can form) ; and (4)the water vapor which is evolved must be confined t o the immediate vicinity of the sample. Conditions (3) and (4) require that an intermediate rate of temperature rise be employed if a liquid phase is to be observed. With very rapid heating rates the system is too far from equilibrium and condition (3) will not be met. Very low rates of temperature rise mill allow time for the water vapor to diffuse away from the sample. The temperatures and pressures a t the quadruple point for the hydrates are summarized in Table IV. All samples comply with the requirement that the pressure a t the quadruple point must be below atmospheric. BaClz.2H20 is the only material studied where condensation failed to take’ place, as indicated by the absence of an extra peak in the DTA curve. The relatively small difference between the vapor pressure of BaC12.2Hz0 a t the quadruple point and atmospheric pressure requires close adherence to equilibrium conditions if the formation of liquid is to be observed. This condition, obviously, was not met.
920
HANSJ. BORCHARDT AND FARRINGTON DA4NIELS
Vol. 61
TABLE I1 PROCESSES WHICHGIVERISE TO THE PEAKSI N FIG.3 Hydrate
Peak No. and temp.'
Prooess
CoClz.6Hz0
l(49') 2 (99")b 3 (137') 4 (175') l(55') 2 ( 1 02')b 3 (135') 4 (210') SrCll .6H20 l(66') 2 (122')b 3 (132') 4 (183') BaBrz 2H20 l(Il0') 2 (118°)b 3 (209') BaClz .2Hz0 l(125') 2 (200') These temperatures bear an uncertainty of about &5".
+ + + + + + + + + +
CoClz.6HzO(s) -* CoC1~.2HzO(s) 4Hz0(1) 4Hz0( 1) 4 4Hz0( 9) CoClz*2HzO(s)4 CoClz*HzO(s) HzO(g) CoClz.HzO(s) -* CoClz(s) HzO(g) MnClz-4HzO(s)-* MnCl2.2H20(s) 2H20(1) 2Hz0(1) 4 2HzO(g) MnCl~.2H20(s)-+ MnClz.HzO(s) HZO(g) MnClz HzO( s) -* MnCL( s) HzO(g) SrCl~.6HzO(s) SrClZ.2HzO(s) 4H~0(1) 4Hz0(1) -* 4HzO(g) SrC1~.2HzO(s)+ SrClz.HZO(s) HzO(g) SrClZ.HzO(s) SrClz(s) BaBr 2Hz0( s) BaBrz H20(s) HzO(1) HzO(1) -* HzO(g) BaBrz .HzO(8 ) -* BaBs(s) HzO(g) BaClz.2HZO(s) -* BaClz.HzO(s) HzO(g) BaClz. H20(s) BaC12(s) HzO(g) Water boiling from mturated solution.
--
-
-
+ + +
b
TABLE I11 X-RAYDATAFOR SRCLs'2HzO Line no.
2'
3
41
5
6
7
4.55 90
3.98 47
3.28
3.20 100
2.88 24
2.80 45
1"
d
5.64 79
I/Io Line no.
d I/Io Line no.
10
11
12
13
14
15
16
2.65 34
2.61 24
2.54 32
2.48 34
2.44 15
2.27 24
2.26 32
21
22
24
25
19
20
23
8
2.71 27 17
2.19 11
9
2.66 71 18
2.14 3
26
d 2.115 2.103 2.025 1.985 1.886 1.857 1.927 1.973 Ill0 27 40 29 8 31 19 15 5 These lines are not reported in the A.S.T.M. index. b Line 4 appears as a separate line in the photograph but did not resolve completely from line 5 in the Geiger counter diffractometer trace a t a chart speed of 1/4'/minute using 1' slits. Hence, its relative intensity is not reported. It is a very weak line.
TABLE IV TEMPERATURE AND PRESSURE AT QUADRUPLE POINTFOR HYDRATES Hydrate
CoClz.6HzO MnC1z.4Hz0 SrClv6HzO BaBrv2HzO BaClr2HzO
TW.
52.4 58.1 61.6 107.9 101.9
P , mm.
Ref.
48.5 63.2 89.7 664 684
12 9 9 9
11
Fig. 4.-Differential thermograph of NaNOa showing a small peak at about 275' due to a second-order transition, and a large eak at 310' due to fusion. The solid line is obtained wit[ a temperature rise of 15' per minute. The dotted exothermic eak appears when the temperature is raised a t the rate o?30° per minute. It is due to increased thermal conductivity caused by fusion.
the other hydrates when high heating rates (> 15"/min.) are used. A similar phenomenon is observed when fusion occurs except that the peak is in the exothermic direction as shown schematically by the dotted line in Fig. 4. These peaks are explained as follows: The formation of liquid in the sample holder is accompanied by a sudden change in the thermal conductivity of the material, inasmuch as it becomes a continuous medium, hence a much better heat transfer agent. This increased heat conductance causes a small surge of heat to the thermocouple junction as the thermal gradient in the sample diminishes. This gives rise to an exothermic peak. I n the case of the hydrates, the occurrence of this exothermic peak, while an over-all endothermic reaction is taking place, makes it ap-
Small Initial Peaks.-A small initial endothermic peak is observed with CuSOa.5Hz0as well as with
(11) "International Critiod Tables," Vol. 111, McGrsw-Hill Book Co., New York, N. Y.,1928, p. 361. (12) A. von Benrath, Z cmorg. olloem. Chsrn.. 247, 147 (1941).
I
ZOO
I
I
I
250 300 TEMPERATURE,
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350
July, 1957
POTENTIAL FUNCTION MODELOF HYDROGEN BONDS
pear as if two endothermic peaks are occurring. This explanation is consistent with the observation that the small peak occurred in the pattern of CuS0g5Hz0 in Fig. 1 only when the doublet appeared, that is, only when liquid formed in the sample and only at high rates of temperature rise.18 Since the sample wells in this work are very small, thermal gradients are reduced to a minimum. In order t o establish an appreciable gradient high heat(13) Taylor and Klug* observed several small peaks prior to dehydration which they attributed to second-order transitions in CUSO~SHIO. These were observed at sensitivities much higher than those used in the present work and are apparently not the same as the anomalous peak described above.
921
ing rates are necessary. The results of this investigation emphasize precautions which are necessary in the interpretations of some differential thermal analysis measurements. Acknowledgments.-The X-ray work was conducted with the helpful advice of Professor Sturges Bailey of the Department of Geology, University of Wisconsin. The authors are grateful for the support of this research by the Atomic Energy Commission Contract AT(l1-1)-178 and by a grant for fundamental research by the E. I. du Pont de Nemours Company, Inc.
POTENTIAL FUNCTION MODEL OF HYDROGEN BONDS. I1 BY RUDOLPH SCHROEDER' AND ELLIS R. LIPPINCOTT Contribution from the Department of Chemistry, University of Maryland, College Park, Md. Received January 96, 1967
A one-dimensional model for hydrogen bonding based on a potential function and previously applied to 0-H--0 systems has been extended and applied to N-H--0, N-H---N, 0-H---N, N-H---Cl and 0-H--Cl hydrogen bond systems. The model can be used to describe bent as well as linear bonds. One important feature is that only one empirically evaluated parameter is necessary to describe hydrogen bond properties. This parameter is a constant and the same as that used for 0-H---0 systems. For a given X-H---Y hydrogen bond the X-H bonded distance, X-H stretching frequency, X-H-Y hydrogen bond energy, and X---Y force constant can be predicted as a function of the X---Y distance obtained from X-ray diffraction studies. The X-H distance and bonded frequency are referred to an unbonded X-H reference distance and reference frequency which for ease of calculation are fixed for a given type X-H bond. Additional flexibility can be introduced in the model by choosing reference X-H distances and frequencies based on suitable reference compounds. For bent bonds an additional parameter is used which is the angle which the normal X-H direction makes with the X--Y axis. Calculations from the proposed model agree reasonably well with observed data, but a wider range of experimental data 18 needed to check the predictions.
Introduction A- large number of investigators have presented calculations of hydrogen bond properties based on a wide variety of electrostatic and quantum mechanical Criteria for the formation of hy(1) Portion of a dissertation presented as partial fulfillment of the requirement for the degree of Doctor of Philosophy in Chemistry s t the University of Maryland. (2) (a) R. H. Gillette, et al., J . A m . Chem. Soc., 68, 1135 (1936); (b) M. M. Davies, Trans. Faraday SOC.,36, 339 (1940). (3) N. G. Coggeahall, J . Chem. Phys., 18, 978 (1950). (4) C. A. Coulson, "Valence," Oxford Press, 1952,pp. 207-21 1. (5) C. A. Coulson and V. Danielsson, Arkiv Fysik, 8, 239 (1955). (6) J. Lennard-Jones and J. A. Pople, PTOC.Roy. SOC.(London). A202, 166, 323 (1950);Aa06, 151 (1951). (7) M. I. Batuev, Izvest. Akad. Nauk, SSSR, 14, 429 (1950). (8) B. I. Stepanov, Zhurn. fi.2. Khim., 19, 507 (1945); 20, 407 (1946). (9) M.A. Kovner and V. A. Chuenkov, Izvcst. Akad. Nauk, SSSR., 14,435 (1950). (10) N. D.Sokolov, ZhuT. Eksptl, i.Teoret. Fiz., 23, 392 (1952). (11) M.A. Kovner and V. N. Kapshta1,Izvsst. Akad. Nauk, 8er. Fir. S S S R , 17, 561 (1953). (12) W. G. Schneider, J . Chsm. Phys., 23, 26 (1955). (13) K. Nukasawa, J. Tanaka and 9. Nagakura, J . Phys. Soc. Japan, 8,792 (1953). (14) H.Tsubomura, Bull. Chem. SOC.Japan, 87, 445 (1954). (15) C.E. Nordman and W. N . Lipscomb, J . Chem. Phys., 19, 1422 (1951); 21, 2077 (1953). (16) K. Kaku, Kumamofo J . Sci. Ser. A , Math. Phye. Chem., 1, 55 (1954). (17) A. N. Baker, J . Chem. Phys., 2 2 , 1625 (1954). (18) L. P.Kuhn, J . Am. Chem. SOC.,74,2492(1952);76,4323 (1954). JOURNAL, 69, 1129 (1955). (19) G. Barrow, THIS (20) A. R.Ubbelohde and K. J. Gallagher, Acta CrysZ., 8, 71 (1955). (21) I. Oshida, Y. Ooshika and R. Miyasaka. J . Phys. Soo., Japan, 10, 849 (1955). (22) H. Tsubomura, J . Chsm. Phys., 24,927 (1956). (23) HB.H.Gunthard. private communication.
drogen bonds have been presented which are based on experimental evidence as well as these mode l ~ . ~ However, ~ * ~ ~it is generally recognized that at present there is no adequate theory of hydrogen bond formation.26~27 In a previous paper the authors presented a one-dimensional model of 0-H-0 hydrogen bonds based on a potential function from which a number of properties, such as increase in 0-H bond length, OH frequency shift, 0-H---0 bond energy and 0---0 force constants could be successfully predicted or correlated as B function of the 0---0 distance.28 We have extended this model to linear and bent hydrogen bonds of the type X-H---Y and are presenting here the results N-H---C1 for the 0-H--N, N-H--N, N-H-0, and 0-H---Cl hydrogen bond systems. Model Based on a Potential Function By arguments similar to those given in paper 12* the potential function V
= Do[l
- exp(-nAr2/2r)]
(1)
and the one-dimensional model shown in Fig. 1 can be used to obtain a potential function for X-H---Y bonds
v
=
v, + v2 + vs + v,
(2)'
(24) W. S. Fyfe, J . Chem. Phya., 91,2 (1953). (25) C. G.Cannon, Mikrochimica Acta, 555 (1955). (26) D. N. Shigorin and N. S. Dokunikhin, Zhur. fiz. Khim. USSR., as, 1958 (1955). (27) N. D.Sokolov, Uspekhi $r.Nauk, 57, 204 (1955). (28) E. R. Lippincott and R. Schroeder, J . C h m . Phyr., 28, 1090 (1955).
