摘要:

Modified Entrainment Method for Measuring Vapour Pressures and Heterogeneous Equilibrium Constants Part 4.-The Gallium Arsenide/Hydrogen Chloride System BY DAVID BATTAT, MARC M. FAKTOR,':: IAN GARRETT AND RODNEY H. Moss Post Office Research Department, Brook Road, Dollis Hill, London NW2 7DT Received 27th March, 1974 The modified entrainment method described earlier has been used to study the GaAs/HCl system. Above about 900 K, the principal gallium vapour species is the monochloride, for which A 1 f ~ ; ~ ~ = - 63.2 k 3 kJ mol-' and S298 = 247 2 2 J molkL K-I. Below this temperature, another gallium species thought to be GaCI, becomes important. 1. INTRODUCTION The reactions between the Group IIh-VB compounds and the hydrogen halides are widely used in the electronics industry for depositing thin films of these compounds by chemical vapour The reaction of gallium arsenide with hydrogen chloride, the most exploited of these systems so far, has been the subject of various thermodynamic 5-8 and mass spectrometric 9 * l o studies, usually in parallel with crystal growth experiments. Although it is now generally agreed that the dominant reaction is : GaAs(so1id) + HCl(gas) +GaCl(gas) + $As4(gas) + +H,(gas) (1) the enthalpy of formation of gallium monochloride is not accurately known.Further- more, recent investigations of the dissociation of the tetrameric arsenic molecule ''* '' have suggested a value of 227 kJ mol-l for AH,",, for the reaction : As,(gas) +2As,(gas) instead of 280 kJ mol-1 as suggested earlier,13 so that the conventional vapour transport system may contain a significant partial pressure of As, at the usual oper- ating temperature of 1000-1050 K.l 5 to study the gallium arsenide/hydrogen chloride system. This method, in addition to permitting us to calculate thermodynamic parameters for the transport reactions, provides a rapid, definitive, and inexpensive test of chemical vapour transport systems. We used the modified entrainment method described previously EXPERIMENT,AL The apparatus has been described in detail previously.14* l5 Gallium arsenide was nominally undoped material supplied by Mining and Chemical Products, hydrogen was purified by passing through a palladium diffuser, and hydrogen chloride was electronic grade, supplied by Air Products Ltd., with a quoted purity of 99.99 %.The flow of hydrogen chloride was controlled by two stainless steel needle valves in series, using the gas cylinder as an effectively constant pressure source. The hydrogen flow was controlled with a needle valve and smoothed with a simple network of capillaries and ;I ballast tank. 2302 Flow rates were measured with Meterate flow meters.D . BATTAT, M . M . FAKTOR, I . GARRETT AND R . H. MOSS 2303 The hydrogen chloride flow meter was calibrated initially by determining the HCl content of the HC1+H2 gas mixture by titration against aqueous NaOH. The temperature of the bottle was measured with a Pt/Pt-13 % Rh thermocouple, the bead being about 3 mm below the bottle. The rate of weight loss from the sample bottle, ri/, was measured as a function of tem- perature, using two ratios of HCl to H2 in the gas stream : p ~ c l / P ( = ~)=0.083 and 0.051, where PHCl is the partial pressure of HCI and P is the total pressure (PHCi+pH2).3. RESULTS The experimental results of the two runs are given in table 1 . In fig. 1 is plotted in was a function of reciprocal temperature for the two runs. TABLE 1 .-THE EXPERIMENTAL RESULTS 713 763 763 808 808 859 859 904 904 904 950 950 950 0.248 0.419 0.430 0.628 0.646 1.049 0.992 1.916 1.922 1.916 3.588 3.708 3.633 1003 1003 1003 1048 1048 1048 1096 1096 1147 1147 I193 1193 1244 1244 6.295 6.343 6.312 9.696 9.552 9.492 13.080 12.91 5 15.76 15.72 18.07 18.07 19.78 19.46 742 764 788 813 836 840 908 908 1008 1008 1103 1103 1200 0.183 0.246 0.288 0.369 0.47 1 0.477 1.220 1.299 4.507 4.555 9.I80 9.430 13.065 1200 1200 1249 I249 1 I51 1151 865 865 1054 1054 952 952 13.125 13.170 14.205 13.935 1 1.244 1 1.364 0.65 1 0.663 6.480 6.544 2.408 2.400 4. ANALYSIS OF RESULTS Each of the curves in fig. 1 shows three regions : a straight section at low temper- atures, (I), a second straight section at intermediate temperatures, (II), and a curving off at the highest temperatures (111). The two straight sections represent the effect of two transport reactions, one of which is dominant at the low temperatures, and the other at the high temperatures. The curving off in region 111 is a result of the equi- librium constant for the dominant reaction becoming large. We previously derived l4 a general expression for the equilibrium constant in a system with one dominant reaction : where E is the fractional concentration of reactant in the gas stream (pHCI/P in the present experiment) and t is the transport function, defined as : Here I is the length and A the cross-sectional area of the neck of the bottle, M is the molecular weight of the condensed phase, and D is the diffusion coefficient (an average over all the species may be used in an approximate simple treatment. We will use a refined treatment l 6 below).Hence : 5 = RTlW/MPAD.2304 MObIPIED ENTRAINMENT METHOD Thus as Kp becomes large, Wvaries with temperature only inasmuch as D/T varies, i.e. the term in the brackets is close to E. As regards the relative positions of the two curves in fig. 1, we note that the vertical distance between them is constant, within experimental error, over regions I1 and 111, and takes a larger, not quite constant, value over region I. It is possible to explain this observation only if the reaction which is dominant at low temperatures results in a volatile gallium species with a different ratio of gallium to chlorine than that of the gallium species formed by the high temperature reaction.Thus the reason for the change in slope between regions I and I1 cannot be due merely to the dissociation of As, or polymeric gallium chloride (though both these processes may occur as well). Furthermore the sign of the slope in region I indicates that the reaction is endothermic, thus ruling out l7 gallium trichloride as the volatile species in this region. 103 KIT FIG. I.-Plot of experimental data for GaAs/HCl.There are two other gallium chlorides for which some data are available in the literature : GaCI, [ref. (18) and (19)] and Ga(GaC1,) [ref. (20) and (21)]. We there- fore have two possibilities to consider for the reaction in region (I) : GaAs(so1id) + 2HCl(gas) +GaCl,(gas) + $As,(gas) + H,(gas) GaAs(so1id) + 2HCl(gas) +&Ga(GaCl,)(gas) + $As,(gas) + H,(gas). (2) (3) In addition, recent data ficant extent in our experimental temperature range (700-1250 K) : 9 l 2 indicate that the dissociation of As, occurs to a signi- As, +2As2. (4)D. BATTAT, M . M. FAKTOR, I . GARRETT AND R . H . MOSS 2305 We therefore have two schemes of simultaneous reactions to consider, namely : (I), (2) and (4) Or (0, (3) and (4). SCHEME 1 By applying the one-dimensional transport equations ' 4* to the flow in the neck of the bottle, and solving them for the boundary conditions appropriate in this experi- ment,' we obtain a master equation relating the rate of loss of weight @to the equi- librium constants K,, K2 and K4 for reactions (I), (2) and (4) : The derivation of this equation is given in the Appendix, where the quantities K ( i ) and K ( i ) are defined.The quantity 5' is related to the transport function : 5' = E H C ~ / E = WRTI/MPAE DHCI,H2 where DHCI,Hr is the binary diffusion coefficient for HCl in hydrogen (the majority species in our experiment), and y is the second-order correction l6 for multi-component diffusion. The quantities K(Y) and K ( i ) are both functions of K4. - 2.0 I I I I I I I 1 0 .8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 103 KIT FIG. 2.-Scheme 1 for GaAs/HCl : 0, experiment ; -, theory. In solving eqn (3, we have taken the value for K4 given by Murray et aL1I' l 2 Eqn (5) now contains four unknowns, i.e. the enthalpy and entropy changes AHl, AH2, AS1, AS2 for reactions (1) and (2). For any set of values of these four quantities, eqn (5) may be solved, and the expected rate of weight loss calculated as a function of 1-732306 MODIFIED ENTRAINMENT METHOD temperature. best fit to our experimental data. The problem now reduces to finding that set of values which gives the The criterion for the best fit was taken to be that should be a minimum, the summation being over all experimental points. Because of the slight scatter in the experimental data, the minimum of this function is about 4 kJ wide in the AHl and AH2 dimensions, and about 2 J K-' wide in the AS1 and AS2 dimensions.The values thus derived, appropriate to our mean experimental temperature of 950 K, are given in table 2 below. Fig. 2 shows the calculated variation of ri/ with temperature, with our experimental points for comparison. TABLE 2.-sECOND LAW ENTHALPY AND ENTROPY CHANGES FOR REACTION AT OUR MEAN TEMPERATURE OF 950 K (a) scheme 1 ( 6 ) scheme 2 A H , 157+3 kJ 11101k' AH, 159+5 kJ mol-' AS, 134.5+ 1.5 J mol-I K-I ASl 141+4 J mol-' K-' AH2 4 4 1 3 kJ mol-' AH, 67f5 kJ mol-' AS2 35.3+ 1.5 J mo1-' K-' AS3 91 +4 J 17101-I K-I SCHEME 2 The master equation for this case is : where the quantities K{Y1 and K { i ) are explained in the Appendix, and r' has the same meaning as before.We find that this equation does not fit our experimental data nearly as well as does eqn (5). Fig. 3 shows the calculated variation of W with tem- perature, in comparison with our experimental data. The parameter values which result in the best fit are given in table 2. The uncertainties in these values indicate the width of the minimum in the function o2 in the four dimensions. The minimum value of o2 is rather larger than for scheme 1. The values are : scheme 1 , 0.1924 ; scheme 2. 0.9484. While it is possible to obtain a good fit to each of the curves in fig. 1 separately, it is not possible to fit the two experimental curves simultaneously. 5. DISCUSSION While it is obviously possible to obtain values of the entropy and enthalpy changes for transport reactions using the method we have described, the curves in fig.I have a more immediately obvious and valuable message to the preparer of materials. If one wishes to transport a material by chemical vapour transport in a temperature gradient, one can use experimental curves such as those in fig. I to determine the temperature range in which to operate. Thus we can say that below about 900K and above 1200 K very little transport in a temperature gradient can be achieved, while the tem- perature range which will produce the fastest rate of transport is at the upper end of region 11. It is interesting to note that our experiment has confirmed, in a matter of days, the knowledge gained empirically over several years for the gallium arsenidel hydrogen chloride system.As a method for providing a rapid, cheap, and rcvcaliirg test of a transport system, this type of experiment has much to offer. The moreD. BATTAT, M. M. FAKTOR, I . GARRETT AND R. H. MOSS 2307 familiar method,22 of putting the solid to be transported into a sealed capsule with some transporting agent, placing the capsule in a furnace, and awaiting developments (sometimes for several months) is frequently unproductive and uninstructive. 'h c .I - 2 . 0 1 ' I I I I I I 0.8 0.9 1.0 1 . 1 1.2 1.3 1.4 1.5 103 KIT FIG. 3.-Scheme 2 for GaAs/HCl : 0, experiment ; -, theory. From the enthalpy and entropy changes for reactions listed in table 2, we have calculated enthalpies of formation and entropies of the species GaCI, GaCl, and Ga(GaC1,).For the first two, specific heat data have been estimated by Shaulov and Mosin,l* and we have corrected our values to room temperature. Very few data concerning Ga(GaC1,) as a vapour molecule are available in the literature, and we ha.ve been unable to estimate its specific heat or entropy with any confidence. The results are given in table 3 with values from the literature for comparison. The enthalpy of formation of gallium monochloride has been reported as - 67.6 kJ mol-I by Fergusson and Gabor 23 (modified by Day 6), as -84f20 kJ mol-l by Sh.aulov and Mosin using bond energy data, and as -80 kJ mol-1 by Hurle and M ~ l l i n , ~ who fitted computed growth rates and compositions of Group 111-V alloys to experimental data. In their computations, they used Arthur's l 3 value of 266 kJ niol-' for the dissociation enthalpy of As, to 2As2.We have used the value reported recently by h4urray et aZ.l19 l 2 (228_+ 6 kJ mol-I), who employed a much-improved experimental technique. For comparison, we have also used Arthur's value for K4 in eqn (5), and we do indeed obtain an enthalpy of formation of gallium monochloride close to that reported by Hurle and Mullin ( - 75.7 4 kJ mol-I), which we therefore consider to be in error because of the inaccurate dissociation enthalpy of As, used by them.2308 MODIFIED ENTRAINMENT METHOD The entropy of gallium monochloride was reported as 236 J mol-' K-' by Fergus- son and Gabor 23 (modified by Day 6), and as 240 J mol-1 K-l by Hurle and Mullin. Shaulov and Mosin l8 calculated the entropy as 240 J mol-l K-l.Our second law value is acceptably close to these values. We have used the calculated thermodynamic functions of Shaulov and Mosin to correct our data to room temperature. TABLE 3 .-ENTHALPIES OF FORMATION AND ENTROPIES OF GALLIUM CHLORIDES (a) scheme 1 ~- GaCl GaC12 A f f f i w I s ; 9 s / AHf&sl kJ mol-1 J mol-1 K-1 kJ mol-1 S&s/J mol-1 K-1 references - 63.2f 3 247+ 2 - 267f 3 265 3- 2 this work, 2nd Iaw - 67.6 236 23 -84+20 240 - 260f 25 302 18 - 80 240 4 - 270f 10 combination of (19) and (21) estimates (see text) 279, 290+ 10 (6) scheme 2 Ga (GaC14) - G aC1 -6Of5 250f4 -117k5 161+4 this work, 2nd law We are not able to calculate values of Kl and K2 from each of our experimental points individually, so that a third law calculation for enthalpies of formation is not possible in the normal way.The good agreement betwen our second-law entropy and the calculated entropy indicates that our second-law enthalpy is reliable, however. For gallium dichloride, the enthalpy of formation was estimated by Shaulov and Mosin as -260+25 kJ mol-1 using bond energies. The enthalpy of formation of GaCl, liquid 21 is -341 kJ molt1. The vapour pressure over the liquid was meas- ured by Laubengayer and Schirmer, l whose data indicate an enthalpy of evaporation of 70+ 8 kJ mol-l. The enthalpy of formation of GaCl, vapour is thus -27Of 10 kJ mol-l, in good agreement with our second law value. The entropy of GaCl, has been calculated ( s 2 9 8 = 302 J mol-l K-l) by Shaulov and Mosin, assuming a bent molecule with a Cl-Ga-C1 bond angle of 120°, and fundamental frequencies esti- mated by comparison with the chlorides of boron and aluminium.While their calculated value is subject to the errors inevitable in such an estimation, the disagreement with our second law value is disturbing. We have calculated the entropy using the same frequencies, but assuming a linear structure for the molecule. The result [table 2(a)] is closer to our second law experimental value but still 18 J mol-l K-l larger. Comparing GaCl, with linear dichlorides 24 (of Mg, Ca, Si, Ti, Fe, Zr, W, Hg and Pb), on the basis of atomic weight of the metal atom, we estimate a value of 290+ 10 J mol-l K-l for s&8. We discuss the low temperature region below. The enthalpy of formation and entropy of gallium tetrachlorogallate, obtained by scheme 2, are shown in table 3.Note that these values are appropriate to our mean experimental temperature of 960 K. No thermodynamic functions for this vapour molecule appear in the literature, although the solid is well characterised.20 We would expect the structure to be similar to NaA1F4,24 KA1F4,24 and T1A1F4.25 Empirical formulae 1 7 9 26 for entropies of vapour molecules are seriously in error for these complex molecules. Earlier we showed l 4 that for a system with only a single transport reaction, theD. BATTAT, M . M. FAKTOR, I . GARRETT AND R . H . MOSS 2309 rate of weight loss @is proportional to the equilibrium constant Kp so long as Kp is not too large (< 5, say). Thus a plot of In pagainst 1 /T has a slope of - AH/R.In this system we have at least three reactions occurring simultaneously over much of our temperature range, and we note that the straight-line sections in regions I and I1 on fig. 1 have slopes corresponding to roughly 48 and 95 kJ mol-1 K-l respectively. While the slope of region I is near to the enthalpy change of reaction (2), the slope in region I1 is very different from the enthalpy change of reaction (1). This difference is due to the dissociation of As, being significant in region 11, and to the equilibrium constants becoming sufficiently large as to make the rate of transport less temperature sensitive. Michelitsch et aL7 have measured the rate of etching of a gallium arsenide wafer in a HCl + H, gas mixture as a function of temperature, and have obtained an enthalpy of 104 -t 12 kJ mol-I K-l from their plot of logarithm of the rate of weight loss against recip- rocal temperature. This they interpret as being the enthalpy change for reaction (l), an interpretation which this work shows to be erroneous.By working over an extended temperature range, we have been able to study the regions (i.e. regions I and 111) either side of the temperature range investigated by Michelitsch et al., which is the temperature range in which most chemical vapour transport experiments are carried out in this system. The effects which predominate in regions I and I11 have some influence in region 11. Thus the slope of the In ri/ against 1/T plot does not give the enthalpy change for reaction (1) simply. 6. CONCLUSIONS The method described in this paper provides a rapid, cheap, and revealing test of potential chemical vapour transport systems.In addition, it yields thermodynamic data for the transport reactions. In the GaAs/HCl system, at least two volatile gallium species are formed. At high temperature and low chlorine potential, the monochloride predominates. Its enthalpy of formation AHf&,8 is -63+3 kJ mol-l, and its entropy SZg8 is 247$-2 J rri01-~ IS-' (second law results). At low temperature and higher chlorine potential, another gallium species is formed. Our experiment lends tentative support to the dichloride since for this molecule we get a good fit to our experimental data using eqn (3, and our second law enthalpy of formation (AHf;g8 = -267f 3 kJ mol-l), is in good agreement with literature values.The second-law entropy (SZ98 = 265 J mol-' K-l) is unaccountably low in comparison with reasonable estimates. Our value for the enthalpy change for reaction (1) is larger than the values reported previously in the literature. We conclude that this discrepancy is a result of previous workers using a smaller temperature range, and thus being precluded from studying the low and high temperature regions (regions I and 111). The effects which dominate in these regions also influence region 11, the mid-range of temperature, leading to a smaller " apparent " enthalpy change. APPENDIX Here we derive the master equation (5) relating the rate of weight loss @to the equilib- rium constant K1, K2, and K4 for reactions (l), (2) and (4) considered in scheme 1.The master equation (5a) for scheme 2 may be derived in a similar manner, as may the correspond- ing equations for schemes of reactions invoIving GaCl, or (GaCl), vapour species. We will not derive these here, as the method is very similar for all schemes. For a vapour mixture containing one component (hydrogen in our case) in substantial majority, the one-dimensional transport equations for the minority species 14-16 are : Ji = niU- Dl(dni/dx) (Al)2310 MODIFIED ENTRAINMENT METHOD where Ji is the flux (in molar units) of species i, U is the mole-average Stefan velocity,27 ni is the molar concentration of species i, and Di is the binary diffusion coefficient of species i in the majority species. Integration of the transport equations for the minority species yields the solutions : where P is the total pressure Zipi, J is &.Ii, (0) and (1) denote partial pressures in the reaction bottle and at the open end of the neck (i.e.in the furnace gas stream), and ti is the transport function, defined as ti = JRTZ/PDi. (A3) The symbols were defined earlier in the text. Since ti is at most of the order of E the fractional HCl concentration in the gas stream, and consequently small compared with unity, we may express the partial pressures inside the reaction bottle as : The quantities pi(l)/P are known boundary conditions. If there is a single reaction occur- ring,14 the Ji values are related by stoichiometric coefficients and may be related simply to the rate of weight loss. Here we are considering three simultaneous reactions, and the relationships between the Ji values become temperature dependent, and Pi(O)/P = Pi(l)/f'+ J i t i l J .(A41 We define : ,y = JAs2/JAs4 (A51 = JGaCI/JGaC12. (A61 It can now be shown that the partial pressures inside the reaction bottle are given by : where ti is the reduced transport function : ti = WRTZ/AMPD,. Note that if there is a single re.action, ti K ti andJ K W/AM. the relation between J and W depends on quantities such as a and 8. With more than one reaction, We can express a and 6 in terms of the equilibrium constants, and we obtain : whereD . BATTAT, M . M . FAKTOP., I . GARRETT AND R . H . MOSS 2311 and where K l DGaCl 8' = ~ - ___ K2 E DGaCI: which is the value of # at the open end of the neck of the bottle, and 5' = &I/& (A17) which approaches unity as K1 becomes very large, i.e.5' is a measure of the extent of reaction. We now define the parameters : and (A1 8) Note that if reaction (2) did not exist, K1 would be Kc';) (i.e. if O--+ GO). ( I ) did not exist ( b O ) , K2 would be Kc;). tions into the expression for K , : Similarly, if reaction We can now substitute for o! and 8 in eqn (A7)-(A1 l), and substitute the resulting equa- PGaCI(0)JPHr(O) c P * ~ ~ ( O ) I ~ _ _ _ K , = ~ P,Cl(O) Using the parameters Kc';) and Kc;), we obtain the master equation : In our experimental temperature range, the second term on the right of eqn (A21) is not very far from unity. Thus we find, approximately : We have included also the second-order approximation l6 to multicomponent diffusion.This has the effect of multiplying each ti by factors yi which are functions of the binary diffusion coefficients for all pairs of species in the system. To the accuracy of our second- order correction, YCaCl = YGaClz = ?As4 = ]'As2 = +3e2& YHCl = 1 + 10&+4&1. We have used Graham's law 28 to estimate ratios of binary diffusion coefficients. The best fit of eqn (5) to our experimental data is obtained if we take DHC~ (273 K) to be 0.4 cm2 s-I, with a temperature dependence of To.8. This is not in agreement with our previous measure- ment l6 of DHC~ (273 K) of 0.54 cm2 s-' with $ temperature dependence of In view of the uncertainty in the coefficients of E and CHC~ in YHCI, which have been estimated using Graham's law, this discrepancy is not considered to be serious.If we accept that DHCI/YHCI must have such a value as to produce a good fit to our experimental data in region 111, then the uncertainties in DHC~ and YHC~ do not affect our best fit values for AH: and AS;.23 12 MODIFIED ENTRAINMENT METHOD We have considered also the effect of reactions in the gas phase within the neck of the This work bottle. will be reported in a future communication. It can be shown that the master equations ( 5 ) and (5a) remain valid. We thank the Director of Research of the Post Office for permission to publish this paper. I J. R. Knight, D. Effer and P. R. Evans, Solid State Electronics, 1965, 8, 178. H. T. Minden, J. Electrochem. SOC., 1965, 112, 300. J. J. Tietjen, R. E. Enstrom and D. Richman, R.C.A.Rev., 1970, 31, 635 ; Solid State Tech., 1972, 42. J. B. Mullin and D. T. J. Hurle, J. Luminescence, 1973, 7 , 176 ; D. T. J. Hurle, J. B. Mullin, J. Phys. Chem. Solids, Suppl. No. 1, 1967, 241. D. J . Kirwan, J. Electrochem. SOC., 1970, 117, 1572. G. F. Day, Heterojunction Device Concepts, Varian Report No. 324-6Q, Air Force Contract No. AF 33 (615)-1988 (Varian Associates, Palo Alto, California). M. Michelitsch, W. Kappa110 and G. Hellbardt, J. Electrochem. SOC., 1964, 111, 1248. A. Boucher and L. Hollan, J. Electrochem. SOC., 1970, 117, 932. V. S. Ban, J. Electrochem. SOC., 1971, 118, 1473. J. J. Murray, C. Pupp and R. F. Pottie, J. Chem. Phys., 1973, 58, 2569. l o V. S . Ban, J. Electrochem. SOC., 1972, 119, 761. l 2 C. Pupp, J. J. Murray and R. F. Pottie, J. Chem. Thermodynamics, 1974, 6, 123. I 3 J. R. Arthur, J. Phys. Chem. Solids, 1967, 28, 2257. l4 D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday Z, 1974, 70,2267. l5 D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974, 70, 2280. l 6 D. Battat, M. M. Faktor, I. Garrett and R. H. Moss, J.C.S. Faraday I, 1974, 70, 2293. l7 0. Kubaschewski, E. L1. Evans and C. B. Alcock, Metallz~gical Thermochemistry (Pergamon, New York, 4th edn., 1967). Yu. Kh. Shaulov and A. M. Mosin, Zhur.5~. Khim., 1973, 47, 1131. l 9 A. W. Laubengayer and F. B. Schirmer, J. Amer. Chem. SOC., 1940, 62, 1578. 2o J. D. Beck, R. H. Wood and N. N. Greenwood, Inorg. Chem., 1970, 9, 86. 2 1 P. I. Fedorov and G. A. Lovetskaya, Zhur. neorg. Khim., 1968, 13, 3357. 22 see, for example, the references cited in H. Schafer, Chemical Transport Reactions (Academic 2 3 R. R. Fergusson and T. Gabor, J. Electrochem. SOC., 1964, 111, 585. 24 J.A.N.A.F. Thermochemical Tables (U.S. Department of Commerce, Nat. Bur. Stand., Wash- 2 5 D. H. Feather and A. Buchler, J. Phys. Chem., 1973, 77, 1599. 26 W. E. Dasent, Inorganic Energetics (Penguin, London, 1971). 27 D. A. Frank-Kamenetskii, Difusion and Heat Transfer in Chemical Kinetics, trans. J. P. Apple- 28 T. Graham, Phil. Trans, Roy. SOC., 1846, 136, 573. Press, London, 1964). ington, 2nd edn., 1971). ton (Plenum, New York, 1969).

ISSN:0300-9599    

DOI:10.1039/F19747002302

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Thermodynamics of n-Alkane+Dimethylsiloxane Mixtures Part 1 .-Gas-Liquid Critical Temperatures and Pressures BY ERIC DICKINSON AND IAN A. MCLURE* Department of Chemistry, The University, Sheffield S3 7HF Received 1 5th February, 1974 Gas-liquid critical temperatures T," have been determined for four mixtures : (i) n-hexane+ hexamethyldisiloxane, (ii) n-octane + hexamethyldisiloxane, (iii) n-octane + octamethyltrisiloxane, and (iv) n-octane + 2,2,4,4-tetramethylpentane. Using a statistical model based upon the van der Waals one-fluid approximation, values of T2 for each mixture are related to a parameter t which is proportional to the energy of interaction between the unlike molecular species. Gas-liquid critical pressuresgg are reported for mixtures (i), (ii) and (iii), and the results are discussed in terms of possible deviations from the Lorentz combining rule of collision diameters.The most common and the best known of the limited class of polymers which are liquid at ordinary temperatures are the polysiloxanes or silicones. As a class the silicones are distinguished by low volatility and low heat of vaporization, low melting point and consequently long liquid range, low surface tension, low viscosity and low energy of activation of viscous flow, low density and high compressibility, high thermal conductivity, and high resistance to thermal and photochemical degradation. These properties have led to the extensive technological applications of silicones, notably as shock absorber and heat transfer fluids. At the molecular level the silicones offer the opportunity to study the behaviour of a simple chain-molecule or homologous series in the liquid state over a vastly greater range of molecular weight than is possible for any other homologous series.In the area of the bulk statistical thermodynamics of liquid mixtures of chain molecules there have been relatively few reports in which homologous mixtures of silicones or mixtures of silicones with other substances have been studied apart from the work of Patterson and co-workers and of Young and co- workers. A systematic programme of study of the thermodynamic behaviour of such mixtures has been under way in this laboratory for the past five years, and this paper, the first in a series which will present accounts of the results of the programme, is concerned with mixtures of the type n-alkane + linear dimethylsiloxane.We report here measurements of gas-liquid critical temperatures and pressures for the systems n-hexane + hexamethyldisiloxane, n-octane + hexamethyldisiloxane, and n-octane + octamethyltrisiloxane ; for the mixture n-octane + 2,2,4,4-tetramethylpentane7 we report only the critical temperatures. Previous studies of the critical properties of systems containing dimethylsiloxanes have been limited either to mixtures of two homologues or to mixtures involving the globular molecule octamethylcyclotetra- si loxane. 2, In any analysis of a set of similar mixtures, it is useful to assess the relative in- fluence of the strengths of the unlike molecular interactions upon the thermodynamic properties of mixing. In this paper we use the experimental critical loci to derive quantitative estimates of deviations from the so called " geometric mean rule " of the pairwise intermolecular energies, and to examine the possibility of a breakdown for these systems of the hard-sphere combining rule of the collision diameters, 23132314 THERMODYNAMICS OF MIXTURES EXPERIMENTAL MATERIALS The samples of n-hexane (99.97 mol %)and n-nonane (99.71 rnol %)were Phillips research grade (lot no.1287 and 1378 respectively). The B.D.H. n-heptane was 99.5mol % pure. The n-octane (99.0mol %) was obtained from Newton Maine Company, and the 2,2,4,4- tetramethylpentane was a gift from B.P. Chemicals. After drying with sodium, all hydro- carbon samples were used without further purification.Two samples of hexamethyldi- siloxane were used : the first, taken from a batch prepared for a vapour pressure s t ~ d y , ~ contained less than 0.01 mol % impurity ; the second, prepared by fractional distillation of a Hopkin and Williams MS 200 silicone fluid (0.65 cst), was better than 99.0 mol % pure. The octamethyltrisiloxane and decamethyltetrasiloxane were better than 99.0 rnol % pure as determined by gas-liquid chromatography. APPARATUS AND PROCEDURE The apparatus for measuring the critical temperatures and pressures, shown schematically in fig. 1, was an adaptation of the apparatus used by Young and co-worker~.~ E 8' C B" D JJ FIG. 1,-The critical point apparatus : A, thick-walled glass sample tube (i.d. 1.5 mm) ; B, B', B , glass-to-metal couplings ; C, sight-glass for mercury-oil interface ; D, stainless steel flexible tube ; E, exit to screw press and gauge ; F, stainless steel valve ; G, aluminium heating block (30 cm long, 16 cm diam.) ; H, asbestos jacket ; I, chromel-alumel thermocouple (10 junctions) ; J, light source.A vertical thick-walled Pyrex tube A (approximately 60 cm long and 1.5 mm internal diameter) was sealed at its upper end, and held at its lower end by a glass-to-metal pressure- tight coupling B. The coupling incorporated a self-tightening Neoprene seal ; a similar type had been successfully tested by Ambrose at pressures up to 8 MPa (about 80 atm). A second glass tube C was supported by the couplings B' and B", and was joined to A by a flexible steel connecting tube D.The sample was confined over mercury, and the position of the mercury sample boundary was regulated by means of a screw-press at E. Oil was usedE . DICKINSON AND I . A . MCLURE 2315 as pneumatic fluid, and the oil-mercury interface was visible at some position along the tube C. Pressures wcrc measured with a Budenburg Bourdon-type standard test gauge, calibrated by the makers and accurate to within +_7 kPa. The pressure at the liquid/vapour meniscus was the sum of the barometric pressure, that determined from the gauge, and the hydrostatic heads of mercury, oil, and liquid sample. Except during the filling procedure, the stainless steel diaphragm tap F was open. The oven consisted of a cylindrical lagged aluminium block G (30 cm long and 16 cm diameter), electrically heated and supported by refractory material inside a large asbestos jacket H.The glass tube A was free to move along a vertical axis within a hole drilled down the centre of the aluminium cylinder. The temperature of the block was measured at concentric positions around the sample tube by a ten-junction chromel-alumel thermocouple I, whose output was calibrated from the known critical temperatures of the n-alkanes (n-hexane through n-nonane). The liquid/vapour interface, illuminated by a filtered light source J, was viewed by eye through a small hole in the heating block. The mole fractions of each component in the mixture were determined from the known volumes delivered by a calibrated Agla syringe. Before the tube A was sealed off, the sample was degassed by repeated freezing, pumping and thawing using liquid nitrogen as refrigerant.The critical point was estimated by visually observing the temperature of disappearance of the liquid/vapour meniscus at the centre of the fluid column (approximately 10 cm high). The heating rate at this stage of the experiment was less than 0.02 K min-l. The critical pressures were corrected for the presence of mercury vapour by subtracting the vapour pressure of mercury at that temperature. Certain inhomogeneities in the composition of the sample were expected to follow from the lack of continuous stirring in the critical region. As only a very small amount of 2,2,4,4-tetramethylpentane was available for study, it was decided, for reasons of simplicity of handling, to investigate its mixtures with n-octane in sealed glass tubes (rather than ones having mercury reservoirs at their lower ends).The larger standard deviation in the critical temperature data of the three siloxane-containing systems (see next section) may be at least partially attributable to temperature uncertainties associated with heat conduction down the mercury column. RESULTS The critical temperatures (kO.2 K) and critical pressures (5-20 kPa) of the pure substances are listed in table 1. The critical temperatures T' of decamethyltetra- siloxane and 2,2,4,4-tetramethylpentane are in good agreement with previous deter- minations. ' * The values of T' for hexamethyldisiloxane and octamethyltrisiloxane TABLE 1 .-EXPERIMENTAL CRITICAL CONSTANTS OF PURE SUBSTANCES substance TC/K pr/MPa Vc/cm3 mol-* hexamethyldisiloxane 518.8 1.91 583 octamethyl trisiloxane 565.4 1.46 828 decamethyl tetrasiloxane 599.4 1.19 n-hexane (507.4) 3.04 370 n-octane (568.7) 2.48 492 2,2,4,4-tetramethylpentane 574.4 530 a Used in calibration of thermocouple ; 0 estimated as indicated in text ; C from ref.(8). are slightly lower than those recently reported,l probably due to the presence of small amounts of siloxanes of different inolecular weights ; this explanation is substantiated by the higher value of Tc obtained with the less rigorously purified sample of hexa- methyldisiloxane used in the mixture with n-hexane (see table 2). The critical pressures pc of n-cctane and the siloxanes are in good agreement with the literature2316 THERMODYNAMICS OF MIXTURES TABLE 2.-cRITICAL TEMPERATURES OF MIXTURES system x2 T,,CIK x2 n-hexane( 1) + hexamet hyldisiloxane(2) 0 507.4 0.459 0.079 509.1 0.542 0.125 509.3 0.737 0.283 512.4 0.783 0.298 512.5 0.803 0.368 51 3.4 1 .o n-octane( 1)+ hexamethyIdisiloxane(2) 0 568.7 0.696 0.203 558.3 0.807 0.276 554.5 0.893 0.433 546.9 1 .o 0.550 540.9 n-octane( 1) + oct amet hyl trisiloxane(2) 0 568.7 0.438 0.035 570.6 0.546 0.107 570.4 0.720 0.152 569.0 0.782 0.343 567.9 1 .o n-octane( 1)+ 2,2,4,4-tetramethylpentane(2) 0 568.6 0.610 0.166 569.4 0.756 0.332 570.3 1 .o 0.453 571.0 T , W 515.5 516.6 519.2 519.4 519.8 521.4 534.9 528.6 524.3 518.8 567.3 567.1 566.4 566.0 565.4 571.9 572.9 574.4 va1ues.l.The value of p" measured for n-hexane is appreciably higher than that suggested by Kudchadker et aL8 The experimental critical temperatures 7'; of the mixtures n-hexane + hexamethyl- disiloxane, n-octane + hexamethyldisiloxane, n-octane + octamethyltrisiloxane and n-octane + 2,2,4,4tetramethylpentane are listed in table 2.The results for three of the systems are fitted to an equation of the form where x1 is the mole fraction of the n-alkane. The skewed " residual critical temp- eratures " AT: for the system n-octane + octamethyltrisiloxane require the modified equation The coefficients to and tl and the standard deviation ot are given in table 3. TABLE 3.-LEAST SQUARES PARAMETERS AND STANDARD DEVIATIONS FOR EQN (I), (2) AND (3) mixture [(1)+(2)1 to/K f l / K ut/K po/MPa pl/MPa u,/MPa n-hexane + hexamethyldisiloxane 5.8 2.8 0.25 -0.44 -0.23 0.029 n-octane+ hexamethyldisiloxane -0.1 4.4 0.38 -0.28 -0.03 0.020 n-octane + octamethyltrisiloxane 0.4 -5.9 0.57 -0.31 -0.08 0.016 n-octane + 2,2,4,4-tetramethylpent ane - 0.8 0.5 0.03E .DICKINSON AND J . A . MCLURE 2317 The experimental critical pressures p: of the mixtures n-hexane + hexamethyl- disiloxane, n-octane + hexamethyldisiloxane and n-octane + octamethyltrisiloxane are shown in fig. 2. The coefficients po and p 1 and the standard deviation op, obtained from fitting the data to an equation of the form APk = r?:-XlP; -2P; = XlX2[Po+P1(1-2Xl)l, (3) are recorded in table 3. 261- I 20 18 16 (iii) 1 4 ' . ' " ' ' ' ' ' I x2 FIG. 2.-Gas-liquid critical pressures of (i) n-hexane + hexamethyldisiloxane, (ii) n-octane + hexa- methyldisiloxane and (iii) n-octane + octamethyltrisiloxane. The points show the experimental critical pressures p ; plotted against the mole fraction of siloxane x 2 .The solid curve is the equation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XlP; + x2p;. DISCUSSION The gas-liquid critical temperature of a binary mixture composed of nonpolar molecules with similar characteristic energy and size parameters gives a useful esti- mate of the relative strength of the unlike pairwise interaction energy. The theoretical analysis of the critical locus is described by Rowlinson lo ; it is summarized briefly below. of composition x which is conformal with each of the pure components and with a reference substance 0.t Two intermolecular parameters, fa, and h,, (cc, p = 1 , 2), are defined by the relations It is assumed that there exists an equivalent substance f a b = &ap/&oo and 1laD = o,3PIo20, (4) t An analysis of the p , V, T properties of dimethylsiloxane oligomers at reduced temperatures T/TC in the range 0.5 to 0.8 [ref.(16)] indicates that the series follows a similar corresponding states principle to that of the n-alkanes. Certain small differences outside the experimental error are evident, however, notably in the variation with temperature of the thermal expansion coefficient.2318 THERMODYNAMICS OF MIXTURES where cclB and oOlB are respectively the molecular energy and size constants appropriate to the a-P interaction. The parameters of the equivalent substance,f, and h,, are given by fxh, = x:f 1 1 h 1 1 + 2x Ix’2.fl2 11 1 2 + .4 f 2 2h 2 2 7 ( 5 ) h, = ~ : h , , + 2 x , x , h , ~ + ~ ~ h ~ ~ , (6) and the critical temperature Ti, the critical volume V: and the critical pressure pz are related to the critical properties of the reference substance by the equations T: = f,T& v; = h , G , P i = (f,/h,)p;.(7) (d2G,/d~i),,T = 0, (d3G,/Z~2),,, = 0, (8) The critical point in a binary mixture of mole fraction x2 satisfies the equations for material stability : where G , is the molar Gibbs free energy. If the quotients T:/T,C and Y,i/Y: are assumed to be close to unity, the resulting derivatives (dpx/d V)$,, and (d2px/d Vz)$,x may be expressed as Taylor expansions in (T,: - Tz) and ( V: - V;),’O and for the van der Waals equation of state the difference between the critical temperature of the mixture and that of the equivalent substance is simply given by T; - = x,x,T.mf:/4f,) + (h:/4h,)I2, (9) wheref; and 11; are the derivatives off, and hx with respect to xz.TABLE 4.-vALUES OF < REQUIRED TO FIT GAS-LIQUID CRITICAL TEMPERATURES 5 mixture [ ( I ) -t (2)] X I = 0.5 X I = 0.25 XI = 0.75 n-hexane + hexamethyldisiloxane 0.993 0.995 0.992 n-octane + octamethyl trisiloxane 0.993 0.991 0.996 n-oct ane + 2,2,4,4-t et r amet hylpent ane 0.998 0.998 0.998 n-octane + hexamethyldisiloxane 1.004 1.006 1.002 For the four mixtures of table 2, the parametersf,,, .f22, hll and hZ2 are derived from the critical constants listed in table 1. The critical volumes of n-hexane and n-octane are taken from the literature. The critical volumes of hexamethyldisiloxane and octamethyltrisiloxane are estimated empirically, assuming a critical compressi- bility factor 2“ given by (0.291 -0.08~), where co is Pitzer’s acentric factor.The critical volume of 2,2,4,4-tetramethylpentane is derived from a correlative procedure using the known critical volumes of 2,2,3,3-tetraniethylbutane7 2,2,4-trimethyl- pentane and 2,2,3-trimethylbutane. For the unlike interactions, we use the combining rules Jl2 = <(f;lJ;2)+, (10) (1 1) 1,” - (h4 +h+ )/2 12 - 1 1 2 2 7 where for a given system the parameter 5 is adjusted to fit the experimental eyuimolar gas-liquid critical temperature. The critical temperature data have also been analysed l 2 by solving exactly the set of equations which defines the critical point in a van der Waals r n i ~ t i i r e , ~ ~ i.e.eqn (9, (6) and (8). The derived values of ( differ from those in table 4 by less than 0.001, indicating that the curtailment of the Taylor series expansion is a valid assump- tion for these mixtures. The replacement of the “ repulsive part ” of the van der Waals equation by an equation of state which represents more precisely the properties The deduced values of ( are given in table 4.E . DICKINSON AND I . A . MCLURE 2319 of the hard-sphere fluid l4 also makes little difference to the analysis. For example, using the equation of Carnahan and Starling l 5 together with the van der Waals attractive term,I4 eqn (9) becomes 'The values of 5 obtained from eqn (12) are larger than those listed in table 4 by no more than 0.002. If the theory were exact, the value of 5 obtained from fitting the critical temper- atures at x = 0.5 would be the same as that at other compositions.In fact, we find that 5 varies with mole fraction by an amount slightly greater than the experimental uncertainty, an inconsistency which could reflect a deviation from one or more of the theoretical assumptions (e.g. the concept of conformality or the combining rule for h12Jr). Table 4 shows the changes in the values of 5 required to fit the experimental data at x = 0.25 and x = 0.75. It is clear that each of the four systems studied conforms closely to the geometric mean rule of pairwise interaction energies [i.e. eqn (10) with 5 = 1.01. Since the magnitude of is insensitive to the exact form of the equation of state in the critical region, it appears that the thermodynamic properties of this set of mixtures are not influenced by any large cross-term energy effects.The similarity of behaviour between the system n-octane + 2,2,4,4tetramethylpentane and the three binary sys- tems containing the siloxanes suggests that (in terms of the gas-liquid critical temper- atures of its mixtures) the dimethylsiloxane molecule acts as if it were a highly methyl- ated hydrocarbon. The two n-alkane + dimethylsiloxane mixtures with similar values of 412 = hl1-h2, [system (i), 412 = -0.45; system (iii), 412 = -0.511 lead to the same value for 5, a result which is considerably lower than that for system (ii) (where 412 = -0.17).$ This apparent lowering of 5 with increasing size differ- ence of the components has also been observed in mixtures of octamethylcyclotetra- siloxane with the cycloalkanes.2 In a subsequent paper,4 the derived equimolar 5 value of n-hexane + hexamethyl- disiloxane is used to calculate the thermodynamic excess mixing properties of the system at room temperature.The good agreement between the experimental and t,heoretical excess functions for this mixture gives us some confidence in the meaning- fulness of the 5 values obtained from the critical data. But, until the critical loci of further n-alkane + dimethylsiloxane mixtures have been thoroughly investigated, and any chain length dependent trends analysed, we consider it imprudent to attach any further molecular significance to the slight differences between the 5 values for the systems studied in this work.The critical pressure& of a binary mixture is related to the critical pressurepz of an equivalent substance by the equation lo : TL- Tz = x,x2T~[(0.832 f:/fx)+(0.216 lt'Jhx)I2. (12) A value of 7.2 for the logarithmic slope of the critical isochore of hexamethyldisiloxane has been estimated l6 using a relationship derived froin the theoretical approach of Cook and Rowlinson l 7 : (8 lnp/a In 2"); = w+dC(2w- 3). (14) t The predicted T," does appear, however, to be insensitive to the magnitude of the cross-term size parameter. $ The difference between the pure component critical temperatures is greatest for system (ii), and it has been suggested by one of the referees that the rather larger values of 5 obtained for this system might reflect the inability of the theory to cope adequately with results over an extended temperature range .2320 THERMODYNAMICS OF MIXTURES The parameter 6" denotes corresponding states deviations from the behaviour of a reference substance argon, for which (8 lnp/d In T); is found experimentally to be w = 5.365.1° An optimum value of 6" = 0.24 satisfactorily correlates the reduced vapour pressures near Tc.16 A straightforward linear least squares analysis of the plot of In p against In T in the range 0.9 < T/T" < 1 .O produces a slightly larger value of (8 lnp/a In T ) = 7.5 t O .1 . That we choose to use the estimate derived from the Cook and Rowlinson approach influences in no way the subsequent conclusions. It might have been expected from eqn (1 3) that the critical pressures of the mixtures would show positive deviations from the lines x&+x2&. As fig.2 indicates, however, a small negative deviation is observed for each of the systems studied. We believe that this effect is real, whilst at the same time being fully aware that some uncertainties, resolvable only by more careful experiments, do remain concerning the importance or otherwise of efficient stirring in the determination of critical pressures of mixtures. For n-octane + hexamethyldisiloxane, where the two molecules are similar in size and energy, the van der Waals approximation together with the value of < = 1.004 obtained from the critical temperatures' gives calculated critical pressures which are almost linear in composition (and therefore lie above the experimental results). Theory and experiment can beforced to coincide by invoking a 2 % positive deviation from the Lorentz combining rule of the collision diameters [eqn (1 l)].Whether such a large deviation can be justified is a matter for conjecture. Nonetheless, because of the apparent sensitivity to variations in h I 2 , it is clear that for certain thermodynamic properties of mixtures deviations from the Lorentz combining rule should be given at least as much attention as is routinely directed towards deviations from the Berthelot " geometric mean rule ". E. D. acknowledges the receipt of a S.R.C. Studentship. We thank Dr. C. L. Young for the gift of the high temperature oven, and B.P. Chemicals for the gift of the hydrocarbon. C. L. Young, J.C.S. Furuduy 11, 1972, 68, 580.C. P. Hicks and C. L. Young, Trans. Furuduy SOC., 1971, 67, 1598. C. L. Young, J.C.S. Furuduy 11, 1972, 68, 452. E. Dickinson, I. A. McLure and B. H. Powell, J.C.S. Furuduy I, 1974, 70, 2321. R. J. Powell, F. L. Swinton and C. L. Young, J. Chenz. Thermodynamics, 1970, 2, 105. D. Ambrose, J. Sci. Instr., 1963, 40, 129. D. Ambrose and R. Townsend, Trans. Faruday Soc., 1968, 64, 2622. A. P. Kudchadker, G. H. Alani and B. J. Zwolinski, Chem. Rev., 1968, 68, 659. D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1968,55,43. W. B. Brown, Phil. Trans. A , 1957, 250, 175. lo J. S. Rowlinson, Liquids and Liquid Mixtures (Butterworth, London, 2nd edn., 1969), chap. 9. l2 E. Dickinson, unpublished work. l3 P. H. van Konynenburg, Ph.D. Diss. (UCLA, 1968).I4 R. L. Scott, Physical Chemistry: An Adr,unced Treatise, ed. H. Eyring, D. Henderson and W. Jost (Academic Press, New York, 1972), vol. VIII, chap. 1. N. F. Carnahan and K. E. Starling, J. Chern. Phys., 1969, 51, 635. E. Dickinson, Ph.D. Thesis (Sheffield, 1972). l7 D. Cook and J. S. Rowlinson, Proc. Roy. SOC. A , 1953, 219, 405. Thermodynamics of n-Alkane+Dimethylsiloxane Mixtures Part 1 .-Gas-Liquid Critical Temperatures and Pressures BY ERIC DICKINSON AND IAN A. MCLURE* Department of Chemistry, The University, Sheffield S3 7HF Received 1 5th February, 1974 Gas-liquid critical temperatures T," have been determined for four mixtures : (i) n-hexane+ hexamethyldisiloxane, (ii) n-octane + hexamethyldisiloxane, (iii) n-octane + octamethyltrisiloxane, and (iv) n-octane + 2,2,4,4-tetramethylpentane. Using a statistical model based upon the van der Waals one-fluid approximation, values of T2 for each mixture are related to a parameter t which is proportional to the energy of interaction between the unlike molecular species.Gas-liquid critical pressuresgg are reported for mixtures (i), (ii) and (iii), and the results are discussed in terms of possible deviations from the Lorentz combining rule of collision diameters. The most common and the best known of the limited class of polymers which are liquid at ordinary temperatures are the polysiloxanes or silicones. As a class the silicones are distinguished by low volatility and low heat of vaporization, low melting point and consequently long liquid range, low surface tension, low viscosity and low energy of activation of viscous flow, low density and high compressibility, high thermal conductivity, and high resistance to thermal and photochemical degradation.These properties have led to the extensive technological applications of silicones, notably as shock absorber and heat transfer fluids. At the molecular level the silicones offer the opportunity to study the behaviour of a simple chain-molecule or homologous series in the liquid state over a vastly greater range of molecular weight than is possible for any other homologous series. In the area of the bulk statistical thermodynamics of liquid mixtures of chain molecules there have been relatively few reports in which homologous mixtures of silicones or mixtures of silicones with other substances have been studied apart from the work of Patterson and co-workers and of Young and co- workers.A systematic programme of study of the thermodynamic behaviour of such mixtures has been under way in this laboratory for the past five years, and this paper, the first in a series which will present accounts of the results of the programme, is concerned with mixtures of the type n-alkane + linear dimethylsiloxane. We report here measurements of gas-liquid critical temperatures and pressures for the systems n-hexane + hexamethyldisiloxane, n-octane + hexamethyldisiloxane, and n-octane + octamethyltrisiloxane ; for the mixture n-octane + 2,2,4,4-tetramethylpentane7 we report only the critical temperatures. Previous studies of the critical properties of systems containing dimethylsiloxanes have been limited either to mixtures of two homologues or to mixtures involving the globular molecule octamethylcyclotetra- si loxane.2, In any analysis of a set of similar mixtures, it is useful to assess the relative in- fluence of the strengths of the unlike molecular interactions upon the thermodynamic properties of mixing. In this paper we use the experimental critical loci to derive quantitative estimates of deviations from the so called " geometric mean rule " of the pairwise intermolecular energies, and to examine the possibility of a breakdown for these systems of the hard-sphere combining rule of the collision diameters, 23132314 THERMODYNAMICS OF MIXTURES EXPERIMENTAL MATERIALS The samples of n-hexane (99.97 mol %)and n-nonane (99.71 rnol %)were Phillips research grade (lot no.1287 and 1378 respectively). The B.D.H. n-heptane was 99.5mol % pure. The n-octane (99.0mol %) was obtained from Newton Maine Company, and the 2,2,4,4- tetramethylpentane was a gift from B.P. Chemicals. After drying with sodium, all hydro- carbon samples were used without further purification. Two samples of hexamethyldi- siloxane were used : the first, taken from a batch prepared for a vapour pressure s t ~ d y , ~ contained less than 0.01 mol % impurity ; the second, prepared by fractional distillation of a Hopkin and Williams MS 200 silicone fluid (0.65 cst), was better than 99.0 mol % pure. The octamethyltrisiloxane and decamethyltetrasiloxane were better than 99.0 rnol % pure as determined by gas-liquid chromatography.APPARATUS AND PROCEDURE The apparatus for measuring the critical temperatures and pressures, shown schematically in fig. 1, was an adaptation of the apparatus used by Young and co-worker~.~ E 8' C B" D JJ FIG. 1,-The critical point apparatus : A, thick-walled glass sample tube (i.d. 1.5 mm) ; B, B', B , glass-to-metal couplings ; C, sight-glass for mercury-oil interface ; D, stainless steel flexible tube ; E, exit to screw press and gauge ; F, stainless steel valve ; G, aluminium heating block (30 cm long, 16 cm diam.) ; H, asbestos jacket ; I, chromel-alumel thermocouple (10 junctions) ; J, light source. A vertical thick-walled Pyrex tube A (approximately 60 cm long and 1.5 mm internal diameter) was sealed at its upper end, and held at its lower end by a glass-to-metal pressure- tight coupling B.The coupling incorporated a self-tightening Neoprene seal ; a similar type had been successfully tested by Ambrose at pressures up to 8 MPa (about 80 atm). A second glass tube C was supported by the couplings B' and B", and was joined to A by a flexible steel connecting tube D. The sample was confined over mercury, and the position of the mercury sample boundary was regulated by means of a screw-press at E. Oil was usedE . DICKINSON AND I . A . MCLURE 2315 as pneumatic fluid, and the oil-mercury interface was visible at some position along the tube C. Pressures wcrc measured with a Budenburg Bourdon-type standard test gauge, calibrated by the makers and accurate to within +_7 kPa. The pressure at the liquid/vapour meniscus was the sum of the barometric pressure, that determined from the gauge, and the hydrostatic heads of mercury, oil, and liquid sample. Except during the filling procedure, the stainless steel diaphragm tap F was open.The oven consisted of a cylindrical lagged aluminium block G (30 cm long and 16 cm diameter), electrically heated and supported by refractory material inside a large asbestos jacket H. The glass tube A was free to move along a vertical axis within a hole drilled down the centre of the aluminium cylinder. The temperature of the block was measured at concentric positions around the sample tube by a ten-junction chromel-alumel thermocouple I, whose output was calibrated from the known critical temperatures of the n-alkanes (n-hexane through n-nonane).The liquid/vapour interface, illuminated by a filtered light source J, was viewed by eye through a small hole in the heating block. The mole fractions of each component in the mixture were determined from the known volumes delivered by a calibrated Agla syringe. Before the tube A was sealed off, the sample was degassed by repeated freezing, pumping and thawing using liquid nitrogen as refrigerant. The critical point was estimated by visually observing the temperature of disappearance of the liquid/vapour meniscus at the centre of the fluid column (approximately 10 cm high). The heating rate at this stage of the experiment was less than 0.02 K min-l. The critical pressures were corrected for the presence of mercury vapour by subtracting the vapour pressure of mercury at that temperature.Certain inhomogeneities in the composition of the sample were expected to follow from the lack of continuous stirring in the critical region. As only a very small amount of 2,2,4,4-tetramethylpentane was available for study, it was decided, for reasons of simplicity of handling, to investigate its mixtures with n-octane in sealed glass tubes (rather than ones having mercury reservoirs at their lower ends). The larger standard deviation in the critical temperature data of the three siloxane-containing systems (see next section) may be at least partially attributable to temperature uncertainties associated with heat conduction down the mercury column. RESULTS The critical temperatures (kO.2 K) and critical pressures (5-20 kPa) of the pure substances are listed in table 1.The critical temperatures T' of decamethyltetra- siloxane and 2,2,4,4-tetramethylpentane are in good agreement with previous deter- minations. ' * The values of T' for hexamethyldisiloxane and octamethyltrisiloxane TABLE 1 .-EXPERIMENTAL CRITICAL CONSTANTS OF PURE SUBSTANCES substance TC/K pr/MPa Vc/cm3 mol-* hexamethyldisiloxane 518.8 1.91 583 octamethyl trisiloxane 565.4 1.46 828 decamethyl tetrasiloxane 599.4 1.19 n-hexane (507.4) 3.04 370 n-octane (568.7) 2.48 492 2,2,4,4-tetramethylpentane 574.4 530 a Used in calibration of thermocouple ; 0 estimated as indicated in text ; C from ref. (8). are slightly lower than those recently reported,l probably due to the presence of small amounts of siloxanes of different inolecular weights ; this explanation is substantiated by the higher value of Tc obtained with the less rigorously purified sample of hexa- methyldisiloxane used in the mixture with n-hexane (see table 2).The critical pressures pc of n-cctane and the siloxanes are in good agreement with the literature2316 THERMODYNAMICS OF MIXTURES TABLE 2.-cRITICAL TEMPERATURES OF MIXTURES system x2 T,,CIK x2 n-hexane( 1) + hexamet hyldisiloxane(2) 0 507.4 0.459 0.079 509.1 0.542 0.125 509.3 0.737 0.283 512.4 0.783 0.298 512.5 0.803 0.368 51 3.4 1 .o n-octane( 1)+ hexamethyIdisiloxane(2) 0 568.7 0.696 0.203 558.3 0.807 0.276 554.5 0.893 0.433 546.9 1 .o 0.550 540.9 n-octane( 1) + oct amet hyl trisiloxane(2) 0 568.7 0.438 0.035 570.6 0.546 0.107 570.4 0.720 0.152 569.0 0.782 0.343 567.9 1 .o n-octane( 1)+ 2,2,4,4-tetramethylpentane(2) 0 568.6 0.610 0.166 569.4 0.756 0.332 570.3 1 .o 0.453 571.0 T , W 515.5 516.6 519.2 519.4 519.8 521.4 534.9 528.6 524.3 518.8 567.3 567.1 566.4 566.0 565.4 571.9 572.9 574.4 va1ues.l.The value of p" measured for n-hexane is appreciably higher than that suggested by Kudchadker et aL8 The experimental critical temperatures 7'; of the mixtures n-hexane + hexamethyl- disiloxane, n-octane + hexamethyldisiloxane, n-octane + octamethyltrisiloxane and n-octane + 2,2,4,4tetramethylpentane are listed in table 2. The results for three of the systems are fitted to an equation of the form where x1 is the mole fraction of the n-alkane. The skewed " residual critical temp- eratures " AT: for the system n-octane + octamethyltrisiloxane require the modified equation The coefficients to and tl and the standard deviation ot are given in table 3.TABLE 3.-LEAST SQUARES PARAMETERS AND STANDARD DEVIATIONS FOR EQN (I), (2) AND (3) mixture [(1)+(2)1 to/K f l / K ut/K po/MPa pl/MPa u,/MPa n-hexane + hexamethyldisiloxane 5.8 2.8 0.25 -0.44 -0.23 0.029 n-octane+ hexamethyldisiloxane -0.1 4.4 0.38 -0.28 -0.03 0.020 n-octane + octamethyltrisiloxane 0.4 -5.9 0.57 -0.31 -0.08 0.016 n-octane + 2,2,4,4-tetramethylpent ane - 0.8 0.5 0.03E . DICKINSON AND J . A . MCLURE 2317 The experimental critical pressures p: of the mixtures n-hexane + hexamethyl- disiloxane, n-octane + hexamethyldisiloxane and n-octane + octamethyltrisiloxane are shown in fig. 2. The coefficients po and p 1 and the standard deviation op, obtained from fitting the data to an equation of the form APk = r?:-XlP; -2P; = XlX2[Po+P1(1-2Xl)l, (3) are recorded in table 3.261- I 20 18 16 (iii) 1 4 ' . ' " ' ' ' ' ' I x2 FIG. 2.-Gas-liquid critical pressures of (i) n-hexane + hexamethyldisiloxane, (ii) n-octane + hexa- methyldisiloxane and (iii) n-octane + octamethyltrisiloxane. The points show the experimental critical pressures p ; plotted against the mole fraction of siloxane x 2 . The solid curve is the equation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XlP; + x2p;. DISCUSSION The gas-liquid critical temperature of a binary mixture composed of nonpolar molecules with similar characteristic energy and size parameters gives a useful esti- mate of the relative strength of the unlike pairwise interaction energy.The theoretical analysis of the critical locus is described by Rowlinson lo ; it is summarized briefly below. of composition x which is conformal with each of the pure components and with a reference substance 0.t Two intermolecular parameters, fa, and h,, (cc, p = 1 , 2), are defined by the relations It is assumed that there exists an equivalent substance f a b = &ap/&oo and 1laD = o,3PIo20, (4) t An analysis of the p , V, T properties of dimethylsiloxane oligomers at reduced temperatures T/TC in the range 0.5 to 0.8 [ref. (16)] indicates that the series follows a similar corresponding states principle to that of the n-alkanes. Certain small differences outside the experimental error are evident, however, notably in the variation with temperature of the thermal expansion coefficient.2318 THERMODYNAMICS OF MIXTURES where cclB and oOlB are respectively the molecular energy and size constants appropriate to the a-P interaction. The parameters of the equivalent substance,f, and h,, are given by fxh, = x:f 1 1 h 1 1 + 2x Ix’2.fl2 11 1 2 + .4 f 2 2h 2 2 7 ( 5 ) h, = ~ : h , , + 2 x , x , h , ~ + ~ ~ h ~ ~ , (6) and the critical temperature Ti, the critical volume V: and the critical pressure pz are related to the critical properties of the reference substance by the equations T: = f,T& v; = h , G , P i = (f,/h,)p;.(7) (d2G,/d~i),,T = 0, (d3G,/Z~2),,, = 0, (8) The critical point in a binary mixture of mole fraction x2 satisfies the equations for material stability : where G , is the molar Gibbs free energy.If the quotients T:/T,C and Y,i/Y: are assumed to be close to unity, the resulting derivatives (dpx/d V)$,, and (d2px/d Vz)$,x may be expressed as Taylor expansions in (T,: - Tz) and ( V: - V;),’O and for the van der Waals equation of state the difference between the critical temperature of the mixture and that of the equivalent substance is simply given by T; - = x,x,T.mf:/4f,) + (h:/4h,)I2, (9) wheref; and 11; are the derivatives off, and hx with respect to xz. TABLE 4.-vALUES OF < REQUIRED TO FIT GAS-LIQUID CRITICAL TEMPERATURES 5 mixture [ ( I ) -t (2)] X I = 0.5 X I = 0.25 XI = 0.75 n-hexane + hexamethyldisiloxane 0.993 0.995 0.992 n-octane + octamethyl trisiloxane 0.993 0.991 0.996 n-oct ane + 2,2,4,4-t et r amet hylpent ane 0.998 0.998 0.998 n-octane + hexamethyldisiloxane 1.004 1.006 1.002 For the four mixtures of table 2, the parametersf,,, .f22, hll and hZ2 are derived from the critical constants listed in table 1.The critical volumes of n-hexane and n-octane are taken from the literature. The critical volumes of hexamethyldisiloxane and octamethyltrisiloxane are estimated empirically, assuming a critical compressi- bility factor 2“ given by (0.291 -0.08~), where co is Pitzer’s acentric factor. The critical volume of 2,2,4,4-tetramethylpentane is derived from a correlative procedure using the known critical volumes of 2,2,3,3-tetraniethylbutane7 2,2,4-trimethyl- pentane and 2,2,3-trimethylbutane. For the unlike interactions, we use the combining rules Jl2 = <(f;lJ;2)+, (10) (1 1) 1,” - (h4 +h+ )/2 12 - 1 1 2 2 7 where for a given system the parameter 5 is adjusted to fit the experimental eyuimolar gas-liquid critical temperature.The critical temperature data have also been analysed l 2 by solving exactly the set of equations which defines the critical point in a van der Waals r n i ~ t i i r e , ~ ~ i.e. eqn (9, (6) and (8). The derived values of ( differ from those in table 4 by less than 0.001, indicating that the curtailment of the Taylor series expansion is a valid assump- tion for these mixtures. The replacement of the “ repulsive part ” of the van der Waals equation by an equation of state which represents more precisely the properties The deduced values of ( are given in table 4.E . DICKINSON AND I .A . MCLURE 2319 of the hard-sphere fluid l4 also makes little difference to the analysis. For example, using the equation of Carnahan and Starling l 5 together with the van der Waals attractive term,I4 eqn (9) becomes 'The values of 5 obtained from eqn (12) are larger than those listed in table 4 by no more than 0.002. If the theory were exact, the value of 5 obtained from fitting the critical temper- atures at x = 0.5 would be the same as that at other compositions. In fact, we find that 5 varies with mole fraction by an amount slightly greater than the experimental uncertainty, an inconsistency which could reflect a deviation from one or more of the theoretical assumptions (e.g. the concept of conformality or the combining rule for h12Jr). Table 4 shows the changes in the values of 5 required to fit the experimental data at x = 0.25 and x = 0.75.It is clear that each of the four systems studied conforms closely to the geometric mean rule of pairwise interaction energies [i.e. eqn (10) with 5 = 1.01. Since the magnitude of is insensitive to the exact form of the equation of state in the critical region, it appears that the thermodynamic properties of this set of mixtures are not influenced by any large cross-term energy effects. The similarity of behaviour between the system n-octane + 2,2,4,4tetramethylpentane and the three binary sys- tems containing the siloxanes suggests that (in terms of the gas-liquid critical temper- atures of its mixtures) the dimethylsiloxane molecule acts as if it were a highly methyl- ated hydrocarbon.The two n-alkane + dimethylsiloxane mixtures with similar values of 412 = hl1-h2, [system (i), 412 = -0.45; system (iii), 412 = -0.511 lead to the same value for 5, a result which is considerably lower than that for system (ii) (where 412 = -0.17).$ This apparent lowering of 5 with increasing size differ- ence of the components has also been observed in mixtures of octamethylcyclotetra- siloxane with the cycloalkanes.2 In a subsequent paper,4 the derived equimolar 5 value of n-hexane + hexamethyl- disiloxane is used to calculate the thermodynamic excess mixing properties of the system at room temperature. The good agreement between the experimental and t,heoretical excess functions for this mixture gives us some confidence in the meaning- fulness of the 5 values obtained from the critical data.But, until the critical loci of further n-alkane + dimethylsiloxane mixtures have been thoroughly investigated, and any chain length dependent trends analysed, we consider it imprudent to attach any further molecular significance to the slight differences between the 5 values for the systems studied in this work. The critical pressure& of a binary mixture is related to the critical pressurepz of an equivalent substance by the equation lo : TL- Tz = x,x2T~[(0.832 f:/fx)+(0.216 lt'Jhx)I2. (12) A value of 7.2 for the logarithmic slope of the critical isochore of hexamethyldisiloxane has been estimated l6 using a relationship derived froin the theoretical approach of Cook and Rowlinson l 7 : (8 lnp/a In 2"); = w+dC(2w- 3).(14) t The predicted T," does appear, however, to be insensitive to the magnitude of the cross-term size parameter. $ The difference between the pure component critical temperatures is greatest for system (ii), and it has been suggested by one of the referees that the rather larger values of 5 obtained for this system might reflect the inability of the theory to cope adequately with results over an extended temperature range .2320 THERMODYNAMICS OF MIXTURES The parameter 6" denotes corresponding states deviations from the behaviour of a reference substance argon, for which (8 lnp/d In T); is found experimentally to be w = 5.365.1° An optimum value of 6" = 0.24 satisfactorily correlates the reduced vapour pressures near Tc.16 A straightforward linear least squares analysis of the plot of In p against In T in the range 0.9 < T/T" < 1 .O produces a slightly larger value of (8 lnp/a In T ) = 7.5 t O .1 . That we choose to use the estimate derived from the Cook and Rowlinson approach influences in no way the subsequent conclusions. It might have been expected from eqn (1 3) that the critical pressures of the mixtures would show positive deviations from the lines x&+x2&. As fig. 2 indicates, however, a small negative deviation is observed for each of the systems studied. We believe that this effect is real, whilst at the same time being fully aware that some uncertainties, resolvable only by more careful experiments, do remain concerning the importance or otherwise of efficient stirring in the determination of critical pressures of mixtures. For n-octane + hexamethyldisiloxane, where the two molecules are similar in size and energy, the van der Waals approximation together with the value of < = 1.004 obtained from the critical temperatures' gives calculated critical pressures which are almost linear in composition (and therefore lie above the experimental results). Theory and experiment can beforced to coincide by invoking a 2 % positive deviation from the Lorentz combining rule of the collision diameters [eqn (1 l)]. Whether such a large deviation can be justified is a matter for conjecture. Nonetheless, because of the apparent sensitivity to variations in h I 2 , it is clear that for certain thermodynamic properties of mixtures deviations from the Lorentz combining rule should be given at least as much attention as is routinely directed towards deviations from the Berthelot " geometric mean rule ". E. D. acknowledges the receipt of a S.R.C. Studentship. We thank Dr. C. L. Young for the gift of the high temperature oven, and B.P. Chemicals for the gift of the hydrocarbon. C. L. Young, J.C.S. Furuduy 11, 1972, 68, 580. C. P. Hicks and C. L. Young, Trans. Furuduy SOC., 1971, 67, 1598. C. L. Young, J.C.S. Furuduy 11, 1972, 68, 452. E. Dickinson, I. A. McLure and B. H. Powell, J.C.S. Furuduy I, 1974, 70, 2321. R. J. Powell, F. L. Swinton and C. L. Young, J. Chenz. Thermodynamics, 1970, 2, 105. D. Ambrose, J. Sci. Instr., 1963, 40, 129. D. Ambrose and R. Townsend, Trans. Faruday Soc., 1968, 64, 2622. A. P. Kudchadker, G. H. Alani and B. J. Zwolinski, Chem. Rev., 1968, 68, 659. D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1968,55,43. W. B. Brown, Phil. Trans. A , 1957, 250, 175. lo J. S. Rowlinson, Liquids and Liquid Mixtures (Butterworth, London, 2nd edn., 1969), chap. 9. l2 E. Dickinson, unpublished work. l3 P. H. van Konynenburg, Ph.D. Diss. (UCLA, 1968). I4 R. L. Scott, Physical Chemistry: An Adr,unced Treatise, ed. H. Eyring, D. Henderson and W. Jost (Academic Press, New York, 1972), vol. VIII, chap. 1. N. F. Carnahan and K. E. Starling, J. Chern. Phys., 1969, 51, 635. E. Dickinson, Ph.D. Thesis (Sheffield, 1972). l7 D. Cook and J. S. Rowlinson, Proc. Roy. SOC. A , 1953, 219, 405.

ISSN:0300-9599    

DOI:10.1039/F19747002313

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Thermodynamics of n-Alkane+ Dimethylsiloxane Mixtures Part 2.-Vapour Pressures and Enthalpies of Mixing BY ERIC DICKINSON, IAN A. MCLURE" AND BERNARD H. POWELL Department of Chemistry, The University, Sheffield S3 7HF Received 6th March, 1974 The total vapour pressures of mixtures of n-hexane and hexamethyldisiloxane have been measured by a static equilibrium method at 303.15, 309.15 and 315.15 K. At each temperature the derived equimolar excess Gibbs free energy is small and positive. The excess enthalpy at 298.15 K, as determined by direct calorimetry, has a skew-parabolic composition dependence and a positive equi- molar value of 126 5 2 J mol-I . Theoretical excess functions for n-hexane + hexamethyldisiloxane are calculated from a one-fluid van der Waals model in conjunction with an experimental pure liquid reference substance ; they agree well with experiment.We report here measurements of equilibrium vapour pressures and excess enthal- pies for n-hexane + hexamethyldisiloxane, the choice of system being influenced by (i) the well characterized experimental vapour pressures of the pure materials, 1-3 (ii) the favourable volatility of hexamethyldisiloxane in comparison with other siloxanes and (iii) the inference from the volumes of mixing that a maximum positive deviation from ideality occurs at these relative chain lengths. The results are analysed using an estimate of the deviation from the Berthelot geometric mean law derived from gas- liquid critical temperatures measured in this laboratory. EXPERIMENTAL VAPOUR PRESSURE MEASUREMENTS APPARATUS AND PROCEDURE The static vapour pressure apparatus consisted of an absolute mercury manometer with an accompanying vacuum system which was free from any taps which might have come into contact with organic grease or vapour.Details of design were based primarily upon those of McGlashan and Williamson,l Marsh,' and Gaw and Swintom6 The vapour pressures of the mixtures were measured at two temperatures near each round temperature, one about 0.04K above and the other the same amount below. All cathetometer readings were corrected for the thermal expansion of the brass scale, and an allowance was made for the hydrostatic head of vapour. The temperatures, controlled to within fr 0.001 K, were measured with a Rosemount Engineering Company platinum resistance thermometer (VLF 51A), which was calibrated by reference to the triple point of water (273.16 K) and the sodium sulphate decahydrate transition temperature (305.53 K).8 Errors associated with deviations from verticality of the thermostat windows and variations in the surface tension of mercury (arising from changes in vapour pressure and composition) were assumed to be negligible.The ampoule preparation system was similar to that described by M a r ~ h , ~ except that his Teflon tap and lightly greased joints were replaced by mercury cut-offs and mercury sealed joints respectively. Before being sealed into the ampoules, the samples were degassed by repeated distillation in vucuo. Further details of the apparatus and procedure may be found el~ewhere.~ 23212322 THERMODYNAMICS OF MIXTURES MATERIALS Cyclohexane was Phillips research grade (lot no.1261). It was shown to contain less than 0.01 mole per cent impurity by gas-liquid chromatography using a 2 m silicone grease SE 30 column and a hydrogen flame ionization detector. By the same analysis procedure with a 2 m Apiezon L column, the Phillips research grade n-hexane (lot no. 1287) was shown to be better than 99.97mole per cent pure. By fractional distillation of a Hopkin and Williams MS 200 silicone fluid (0.65 cst), hexamethyldisiloxane of purity about 99.5 mole per cent was obtained ; the major impurity was octamethyltrisiloxane. Preparative gas- liquid chromatography of this material (approximately 400 injections through a 5 m silicone rubber column) yielded a 100 cm3 sample of hexamethyldisiloxane containing less than 0.01 mole per cent impurity. Mercury was purified as described by McGlashan and Williamson,l and was distilled in uacuo directly into the reservoir of the manometer.Densities were taken from ref. (10). VAPOUR PRESSURES OF PURE LIQUIDS In order to assess the precision of the pressure measurements and as a check of the accur- acy of the temperature scale, the vapour pressure of cyclohexane was determined over the temperature range 302-316 K. At a given temperature, the pressure was found to be repro- ducible to within +4 Pa. Table 1 compares the values at two temperatures with those given by the API Antoine equation l 1 (a) and the results of Gaw and Swinton (b) : the agreement appears satisfactory.The vapour pressure of pure n-hexane is listed along with the results for the mixtures. The data are in good agreement with the results of previous workers.’’ TABLE 1 .-VAPOUR PRESSURE OF CYCLOHEXANE PlkPa 303.15 16.253 16.228 16.251 313.15 24.654 24.625 24.646 (a) ref. (11); (6) ref. (6). The experimental vapour pressure of hexamethyldisiloxane was found to be slightly larger than that reported by Scott et aL3 The contents of the first ampoule gave a vapour pressure somewhat higher (0.030 kPa at 303 K) than the contents of the ampoule which had been prepared last, and it was therefore presumed that the degassed bulk material contained a small quantity of unidentified volatile impurity. To ensure that this inconsistency was not reflected in the results for the mixtures, the vapour pressure of each siloxane ampoule was measured carefully near each of the round temperatures prior to becoming part of the liquid mixture, and then appropriate corrections were applied to normalize each siloxane vapour pressure with respect to the value of Scott et al.(In practice this means that the vapour pressure of each mixture is adjusted by an amount ~ ~ ( p s , ~ - p ; ) , where p ; is the vapour pressure of the individual siloxane ampoule, and pi,^ is the reference value at the same temperature.) VAPOUR PRESSURES OF MIXTURES Excess Gibbs free energies GE were calculated using a modification of Barker’s proced- ure.12 Mole fractions were corrected for the amount of vapour above the liquid mixture, and an allowance was made for imperfections of the vapour mixture contained in the volume where V’ is the volume of the vapour pressure cell as far as the reference mark (determined by compression of nitrogen), Y” is the volume between the reference mark and the meniscus, and VL is the volume of the liquid mixture. the effect As the molar excess volume isE .DICKINSON, 1. A . MCLURE AND B . fi. POWELL 2323 of pressure on GE is negligible. The excess Gibbs free energy may be fitted to an expression of the form G: = x2(1- ~2)CSO + d 1 - 2x2>1, (2) where x2 is the mole fraction of component 2, and the constants go and g1 are determined by minimizing the total pressure Table 2 lists the molar volumes, V;,, and Vz,2, and second virial coefficients, Bll and BZ2, needed in calculating GZ for n-hexane(l)+ hexamethyldisiloxane(2) at each temperature. Values of Bl were obtained by extrapolating t.he data of McGlashan and Pofter.l4 The values of B22 are much less dependable, being estimated from an empirical relation derived from the molar enthalpy of vaporization and the molar heat capacity.The quantity (6B)12 = B12-~(B11+B22) was set equal to zero. TABLE 2.-PHYSICAL PROPERTIES USED IN BARKER ANALYSIS V.?, , I / V&21 3 0 3 . 1 5 1 3 2 - 1 8 5 4 2 1 6 - 3389 3 0 9 . 1 5 1 3 4 - 1 7 3 6 2 1 s - 3 1 9 2 3 1 5 . 1 5 1 3 5 - 1 6 3 6 220 - 301 1 TI K cnG mol-' Rll/cm3 mol-1 cm3 mol-1 B22/crn3 rnol-1 CALORIMETRIC MEASUREMENTS APPARATUS AND PROCEDURE The glass calorimeter was based upon the design of Larkin and McG1ashan.l' The heater (resistance 300 Q) was made from 0 .1 2 mm Stabilohm resistance wire wound bifilarly around a cylindrical twin-bore ceramic former. Two thermistors [MP 52(STC), 400 Q] in series formed the unknown arm of the Wheatstone bridge, which was powered by an Advance Instruments low-frequency oscillator (JE2). The bridge output was fed through a Brookdeal low-noise amplifier (type 450) and phase-detector (type 4 1 1). Mixing was accomplished by turning the calorimeter through several complete revolutions-for successful rotation through 360" it was necessary to choose a sufficiently narrow capillary tube. To check the potential precision of the apparatus, enthalpies of mixing were determined for the system benzene+ cyclohexane at 298.2 K. The experimental points for several mole fractions were within + 2 J mol-1 of those reported by other workers.16* l7 MATERIALS The hexamethyldisiloxane was obtained by fractional distillation of the appropriate Hopkin and Williams silicone fluid.Its purity was found by gas-liquid chromatography to be better than 99.0 mole per cent. The Fisons Spectrograde n-hexane was fractionally distilled, and a sample was dried over anhydrous calcium chloride. It was found to be better than 99.0 mole per cent pure. Both samples were degassed and stored in mercury- sealed ampoules. RESULTS Experimental vapour pressures of six mixtures of n-hexane + hexamethyldisiloxane at the temperatures 303.15, 309.15 and 31 5.15 K are recorded in table 3. Also shown are the calculated liquid and vapour mole fractions, and the differences between the experimental vapour pressures and those computed from a two parameter Barker analysis : Ap = p(expt.) -p(calc.).(3) Table 4 shows the coefficient go and its standard deviation go obtained from a one parameter analysis, the coefficients go and g1 and their respective standard deviations uc, and o1 obtained from a two parameter analysis, and the standard deviation of the2324 THERMODYNAMICS OF MIXTURES total pressures ap = p(Ap)2/(6-n)]*, where n is the number of coefficients in the fitting equation. The values of GZ listed in table 5 are derived from the one para- meter analysis. The total experimental uncertainty in p due to errors of thermometry, catheto- metry and data analysis is estimated to be +6 Pa. The overall mole fractions, with associated uncertainties arising from weighing errors, buoyancy corrections and the TABLE 3 .-VAPOUR PRESSURES OF MIXTURES OF n-HEXANE+ HEXAMETHYLDISILOXANE (X2 AND )'2 ARE MOLE FRACTIONS OF HEXAMETHYLDISILOXANE IN LIQUID AND VAPOUR) TIK xz 303.15 0 0.1315 0.1483 0.2742 0.4044 0.5505 0.6949 1 .o 309.15 0 0.1330 0.1501 0.2765 0.4071 0.5532 0.6972 1 .o 315.15 0 0.1346 0.1518 0.2791 0.4106 0.5565 0.7002 1 .o YZ 0 0.0436 0.0497 0.1006 0.1655 0.261 2 0.3946 1 .o 0 0.0456 0.0521 0.1054 0.1734 0.2727 0.4092 1 .o 0 0.0480 0.0548 0.1110 0.1823 0.2848 0.4234 1 .o PlWa &/Pa 24.961 22.669 17 22.351 -6 20.160 6 17.866 2 15.252 - 19 12.690 11 7.137 31.860 28.936 32 28.507 - 17 25.747 23 22.818 - 7 19.534 - 32 16.356 21 9.493 40.221 36.526 42 35.998 -8 32.515 27 28.856 -5 24.778 - 59 20.905 39 12.456 TABLE 4.-PARAMETERS OF LEAST SQUARES ANALYSIS OF VAPOUR PRESSURES T1K n goIRT UolRT giIRT UiIRT d P a 303.15 1 0.0390 0.0027 21 303.15 2 0.0332 0.0030 0.0125 0.0050 15 309.15 1 0.0256 0.0029 28 309.15 2 0.0223 0.0046 0.0072 0.0078 29 315.15 1 0.021 1 0.0032 40 315.15 2 0.0226 0.0054 - 0.0033 0.0093 44 TABLE 5.-EXCESS GIBBS FREE ENERGY OF THE EQUIMOLAR MIXTURE n-HEXANE+ HEXAMETHYL- DISILOXANE GE(x = 0.5)/J mol-' TlK expt.calc. 303.2 25 8 309.2 17 6 315.2 14 4E . DICKINSON, I . A . MCLURE A N D B . H. POWELL 2325 condensation of mercury vapour, are considered to be accurate to within 0.04 per cent. Further errors occur in calculating the mass of the vapour phase owing to uncertainties in the second virial coefficient of hexamethyldisiloxane B22 and the cross-term virial coefficient B1 2.The above experimental uncertainties lead to an estimated absolute error in GE of +_5 J mol-l. The experimental excess enthalpies at 298.15 K, with estimated errors of & 3 J rnol-', are recorded in table 6. The data are represented by the equation with a standard deviation of 1.2 J mol-'.* H:/J mol-1 = xl(l -xl)[502.08-66.96(1 -2x1)] (4) TABLE 6.--EXCEsS ENTHALPIES OF THE MIXTURE n-HEXANE( 1) + HEXAMETHYLDISILOXANE(2) AT 298.15 K 0.0339 16 0.5811 129 0.1115 50 0.6588 118 0.1753 65 0.7674 94 0.2583 88 0.8278 79 0.3429 105 0.8391 72 0.4482 124 0.8745 60 Hg/J mol-' XI Hg/J rnol-' X1 DISCUSSION Excess thermodynamic functions of mixing may be calculated from an empirical equation of state such as the van der Waals equation.l* However, as the thermo- dynamic properties of a suitable reference substance are accurately known, we prefer here to choose an experimental equation of state.The smoothed n-alkane reference of Bhattacharyya, Patterson and Somcynsky l9 (described in terms of the con- figurational properties of a simulative n-heptane) is used in conjunction with the one- fluid van der Waals The equimolar excess volume of the mixture, for instance, is calculated from the equation 20* 21 V;(X = 0.5) = $[(el2v,+s,,v,)-g6~2v~~ - el 2 4 1 2( vfb - 3vf) - 34:2 h h -k 6eI 2 v f f + be12s12(6h+ 6) + ts?2%h ++(el 2 Vff + S125/fh)(fll+ f22 - 2) + +(el 2 6 h + s1 2Vhh)(h 1 1 + h2 2 - 2)1, ( 5 ) where the molecular parameters 012, 412, e12 and s12 are defined by the relations (6) in which&@ and hifl are molecular energy and size constants appropriate to the a+ interaction (a, #I = 1,2). The quantities V,, etc., which depend only upon the thermo- dynamic properties of the reference substance, are given at negligible pressure by 31 812 = fll -f22, e12 = 2f12 -f11-f22, 412 = h l l 4 2 2 , s12 = 2h12--hll--h22, Vf = - VmTa,, Vff = VmT[2ap + TCI; + T(a~t,/aT)~], v& = - VmTa,, Vh = v,, v,, = 0, (7) *It came to our attention between the writing and submission of this paper that Armitage, Pollock and Whittingham (Leicester Polytechnic) found a maximum enthalpy of mixing in this system of about 127 J mol-I at ~ ~ ~ 0 .5 5 .2326 THERMODYNAMICS OF MIXTURES where V, is the molar volume and CI, is the isobaric expansivity. The molar excess Gibbs free energy GE is obtained from an expression analogous to eqn (5) containing the quantities Gf, etc., which are given at zero pressure by : Gf = Urn, Gfr= -TC,,,, Gfh = 0, (8) Gh = -XT, Ghh = RT.Here Urn is the molar configurational internal energy and C,,, is the molar configura- tional heat capacity. The excess enthalpy H$ follows directly from the temperature dependence of GZ /T. The molecular parameters fll, f 2 2 , h l l and / 2 2 2 are calculated from the critical constants of the pure substances,22 and the cross-terms.f,, and hI2 are derived from the combining rules : f 1 2 = t ( f 1 1 f 2 2 ) + ; (9) h t 2 = ( h t , + h$2)/2. (10) The calculated excess Gibbs free energies listed in table 5 are obtained using a value of 5 = 0.993 derived froin an analysis of gas-liquid critical data.22 Also predicted are the excess functions HE(309.2 K, x = 0.5) = I12 J molkl and VE(303.2 K, x = 0.5) = - 1.17 cm3 mol-I.At each temperature, the theoretical curve of GE as a function of composition is S-shaped, becoming negative at high mole fractions of hexamethyldisiloxane. In qualitative accord with the 5 value estimated from the critical temperatures,22 the experimental vapour pressures of the mixtures of n-hexane + hexamethyldi- siloxane exhibit only small deviations from ideality. The derived equimolar excess Gibbs free energies and the directly determined equimolar excess enthalpy are in good agreement with those calculated from the van der Waals one-fluid model. It should be noted, however, that the calculated and experimental H z values do not correspond to exactly the same temperature, and that the exact numerical values of all the theor- etical excess functions should not be given too great a significance, as they depend to some degree upon the particular choice of reference ~ubstance.~ The experimental excess volume is 0.05 cm3 mol-1 at x = 0.5, in poor agreement with the predicted value of - 1.17 cm3 mol-'.A part of this discrepancy may be due to a deviation of the parameter hI2 from the value implied by eqn (1 0), since, unlike the free energy, V; is very sensitive to any variation in the cross-term s12. It may be noted that machine calculations for binary mixtures of Lennard-Jones particles suggest 2 3 9 24 that the predictions of V: from the van der Waals one-fluid theory are too large (in a negative sense) for mixtures with components of widely differing molecular size.In attempting to ascertain the relative importance of the two explanations, we suggest that it might be useful in future work to estimate h12 independently from some other property of the mixture, such as the gas-liquid critical volume or the gas-liquid critical pressure. We thank Professor R. L. Scott for the gift of the computer programme used in the E. D. and B. H. P. acknowledge receipt of S.R.C. Student- vapour pressure analysis. ships. M. L. McGlashan and A. G. Williamson, Trans. Faraday Soc., 1961, 57, 588. C. B. Willingham, W. J. Taylor, J. M. Pignocco and F. D. Rossini, J. Res Nat. Bur. Stand., 1945, 35, 219. D. W. Scott, J. F. Messerly, S. S.Todd, G. B. Guthrie, I. A. Hossenlopp, R. T. Moore, A. Osbom, W. T. Berg and J. P McCullough, J. Phys. Ctlem., 1961, 65, 1320.E . D I C K I N S O N , I . A . MCLURE A N D B . H . POWELL 2321 E. Dickinson and I. A. McLure, J.C.S. Faraday I, 1974, 70, 2328. K. N. Marsh, Trans. Faraday SOC., 1968, 64, 883. W. J. Gaw and F. L. Swinton, Train. Faraday SOC., 1968, 64, 637. R. Fernandez-Prini and J. E. Prue, J. Chem. SOC. A , 1967, 1974. E. Dickinson, Ph.D. Thesis (Sheffield, 1972). l o W. G. Brombacker, D. P. Johnson and J. L. Cross, Mercury Barometers and Manometers (Nat. Bur. Stand. Monograph 8, 1960). Selected Values of Properties of Hydrocarbons and Related Compounds, Amer. Petroleum Inst. Res. Project 44. Thermodynamic Research Center (Texas A & M University, CoIlege Station, Texas, 1965), extant.’ C. R. Barber, R. Handley and E. F. G. Herington, Brit. J. Appl. Phys., 1954, 5, 41. l 2 J. A. Barker, Austral. J. Chem., 1953, 6, 207. l 3 D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1963, 55, 43. l 4 M. L. McGlashan and D. J. B. Potter, Proc. Conf. Thermodynamics and Transport Properties of l5 J. A. Larkin and M. L. McGlashan, J. Chem. SOC., 1961, 3425. l 6 R. H. Stokes, K. N. Marsh and R. P. Tomlins, J. Chem. Thermodynamics, 1969, 1, 211. l 8 M. L. McGlashan, Trans. Faraday SOC., 1970, 66, 18. l9 S. N. Bhattacharyya, D. Patterson and T. Somcynsky, Physica, 1964, 30, 1276. 2o T. W. Leland, J. S. Rowlinson and G. A. Sather, Trans. Faraday SOC., 1968, 64, 1447. 21 W. B. Brown, Phil. Trans. A, 1957,250, 175. 2 2 E. Dickinson and I.A. McClure, J.C.S. Faraday I, 1974, 70, 2313. 23 J. V. L. Singer and K. Singer, Mol. Phys., 1970, 19, 279. 24 I. R. McDonald, Mol. Phys., 1972, 24, 391. Fluids (Inst. Mech. Eng., 1958), p. 60. A. E. P. Watson, I. A McLure, J. E. Bennett and G. C. Benson, J. Phys. Chem., 1965,69,2753. Thermodynamics of n-Alkane+ Dimethylsiloxane Mixtures Part 2.-Vapour Pressures and Enthalpies of Mixing BY ERIC DICKINSON, IAN A. MCLURE" AND BERNARD H. POWELL Department of Chemistry, The University, Sheffield S3 7HF Received 6th March, 1974 The total vapour pressures of mixtures of n-hexane and hexamethyldisiloxane have been measured by a static equilibrium method at 303.15, 309.15 and 315.15 K. At each temperature the derived equimolar excess Gibbs free energy is small and positive.The excess enthalpy at 298.15 K, as determined by direct calorimetry, has a skew-parabolic composition dependence and a positive equi- molar value of 126 5 2 J mol-I . Theoretical excess functions for n-hexane + hexamethyldisiloxane are calculated from a one-fluid van der Waals model in conjunction with an experimental pure liquid reference substance ; they agree well with experiment. We report here measurements of equilibrium vapour pressures and excess enthal- pies for n-hexane + hexamethyldisiloxane, the choice of system being influenced by (i) the well characterized experimental vapour pressures of the pure materials, 1-3 (ii) the favourable volatility of hexamethyldisiloxane in comparison with other siloxanes and (iii) the inference from the volumes of mixing that a maximum positive deviation from ideality occurs at these relative chain lengths.The results are analysed using an estimate of the deviation from the Berthelot geometric mean law derived from gas- liquid critical temperatures measured in this laboratory. EXPERIMENTAL VAPOUR PRESSURE MEASUREMENTS APPARATUS AND PROCEDURE The static vapour pressure apparatus consisted of an absolute mercury manometer with an accompanying vacuum system which was free from any taps which might have come into contact with organic grease or vapour. Details of design were based primarily upon those of McGlashan and Williamson,l Marsh,' and Gaw and Swintom6 The vapour pressures of the mixtures were measured at two temperatures near each round temperature, one about 0.04K above and the other the same amount below.All cathetometer readings were corrected for the thermal expansion of the brass scale, and an allowance was made for the hydrostatic head of vapour. The temperatures, controlled to within fr 0.001 K, were measured with a Rosemount Engineering Company platinum resistance thermometer (VLF 51A), which was calibrated by reference to the triple point of water (273.16 K) and the sodium sulphate decahydrate transition temperature (305.53 K).8 Errors associated with deviations from verticality of the thermostat windows and variations in the surface tension of mercury (arising from changes in vapour pressure and composition) were assumed to be negligible. The ampoule preparation system was similar to that described by M a r ~ h , ~ except that his Teflon tap and lightly greased joints were replaced by mercury cut-offs and mercury sealed joints respectively.Before being sealed into the ampoules, the samples were degassed by repeated distillation in vucuo. Further details of the apparatus and procedure may be found el~ewhere.~ 23212322 THERMODYNAMICS OF MIXTURES MATERIALS Cyclohexane was Phillips research grade (lot no. 1261). It was shown to contain less than 0.01 mole per cent impurity by gas-liquid chromatography using a 2 m silicone grease SE 30 column and a hydrogen flame ionization detector. By the same analysis procedure with a 2 m Apiezon L column, the Phillips research grade n-hexane (lot no. 1287) was shown to be better than 99.97mole per cent pure. By fractional distillation of a Hopkin and Williams MS 200 silicone fluid (0.65 cst), hexamethyldisiloxane of purity about 99.5 mole per cent was obtained ; the major impurity was octamethyltrisiloxane. Preparative gas- liquid chromatography of this material (approximately 400 injections through a 5 m silicone rubber column) yielded a 100 cm3 sample of hexamethyldisiloxane containing less than 0.01 mole per cent impurity.Mercury was purified as described by McGlashan and Williamson,l and was distilled in uacuo directly into the reservoir of the manometer. Densities were taken from ref. (10). VAPOUR PRESSURES OF PURE LIQUIDS In order to assess the precision of the pressure measurements and as a check of the accur- acy of the temperature scale, the vapour pressure of cyclohexane was determined over the temperature range 302-316 K.At a given temperature, the pressure was found to be repro- ducible to within +4 Pa. Table 1 compares the values at two temperatures with those given by the API Antoine equation l 1 (a) and the results of Gaw and Swinton (b) : the agreement appears satisfactory. The vapour pressure of pure n-hexane is listed along with the results for the mixtures. The data are in good agreement with the results of previous workers.’’ TABLE 1 .-VAPOUR PRESSURE OF CYCLOHEXANE PlkPa 303.15 16.253 16.228 16.251 313.15 24.654 24.625 24.646 (a) ref. (11); (6) ref. (6). The experimental vapour pressure of hexamethyldisiloxane was found to be slightly larger than that reported by Scott et aL3 The contents of the first ampoule gave a vapour pressure somewhat higher (0.030 kPa at 303 K) than the contents of the ampoule which had been prepared last, and it was therefore presumed that the degassed bulk material contained a small quantity of unidentified volatile impurity.To ensure that this inconsistency was not reflected in the results for the mixtures, the vapour pressure of each siloxane ampoule was measured carefully near each of the round temperatures prior to becoming part of the liquid mixture, and then appropriate corrections were applied to normalize each siloxane vapour pressure with respect to the value of Scott et al. (In practice this means that the vapour pressure of each mixture is adjusted by an amount ~ ~ ( p s , ~ - p ; ) , where p ; is the vapour pressure of the individual siloxane ampoule, and pi,^ is the reference value at the same temperature.) VAPOUR PRESSURES OF MIXTURES Excess Gibbs free energies GE were calculated using a modification of Barker’s proced- ure.12 Mole fractions were corrected for the amount of vapour above the liquid mixture, and an allowance was made for imperfections of the vapour mixture contained in the volume where V’ is the volume of the vapour pressure cell as far as the reference mark (determined by compression of nitrogen), Y” is the volume between the reference mark and the meniscus, and VL is the volume of the liquid mixture. the effect As the molar excess volume isE .DICKINSON, 1. A . MCLURE AND B . fi. POWELL 2323 of pressure on GE is negligible. The excess Gibbs free energy may be fitted to an expression of the form G: = x2(1- ~2)CSO + d 1 - 2x2>1, (2) where x2 is the mole fraction of component 2, and the constants go and g1 are determined by minimizing the total pressure Table 2 lists the molar volumes, V;,, and Vz,2, and second virial coefficients, Bll and BZ2, needed in calculating GZ for n-hexane(l)+ hexamethyldisiloxane(2) at each temperature. Values of Bl were obtained by extrapolating t.he data of McGlashan and Pofter.l4 The values of B22 are much less dependable, being estimated from an empirical relation derived from the molar enthalpy of vaporization and the molar heat capacity.The quantity (6B)12 = B12-~(B11+B22) was set equal to zero. TABLE 2.-PHYSICAL PROPERTIES USED IN BARKER ANALYSIS V.?, , I / V&21 3 0 3 . 1 5 1 3 2 - 1 8 5 4 2 1 6 - 3389 3 0 9 .1 5 1 3 4 - 1 7 3 6 2 1 s - 3 1 9 2 3 1 5 . 1 5 1 3 5 - 1 6 3 6 220 - 301 1 TI K cnG mol-' Rll/cm3 mol-1 cm3 mol-1 B22/crn3 rnol-1 CALORIMETRIC MEASUREMENTS APPARATUS AND PROCEDURE The glass calorimeter was based upon the design of Larkin and McG1ashan.l' The heater (resistance 300 Q) was made from 0 . 1 2 mm Stabilohm resistance wire wound bifilarly around a cylindrical twin-bore ceramic former. Two thermistors [MP 52(STC), 400 Q] in series formed the unknown arm of the Wheatstone bridge, which was powered by an Advance Instruments low-frequency oscillator (JE2). The bridge output was fed through a Brookdeal low-noise amplifier (type 450) and phase-detector (type 4 1 1). Mixing was accomplished by turning the calorimeter through several complete revolutions-for successful rotation through 360" it was necessary to choose a sufficiently narrow capillary tube.To check the potential precision of the apparatus, enthalpies of mixing were determined for the system benzene+ cyclohexane at 298.2 K. The experimental points for several mole fractions were within + 2 J mol-1 of those reported by other workers.16* l7 MATERIALS The hexamethyldisiloxane was obtained by fractional distillation of the appropriate Hopkin and Williams silicone fluid. Its purity was found by gas-liquid chromatography to be better than 99.0 mole per cent. The Fisons Spectrograde n-hexane was fractionally distilled, and a sample was dried over anhydrous calcium chloride. It was found to be better than 99.0 mole per cent pure. Both samples were degassed and stored in mercury- sealed ampoules.RESULTS Experimental vapour pressures of six mixtures of n-hexane + hexamethyldisiloxane at the temperatures 303.15, 309.15 and 31 5.15 K are recorded in table 3. Also shown are the calculated liquid and vapour mole fractions, and the differences between the experimental vapour pressures and those computed from a two parameter Barker analysis : Ap = p(expt.) -p(calc.). (3) Table 4 shows the coefficient go and its standard deviation go obtained from a one parameter analysis, the coefficients go and g1 and their respective standard deviations uc, and o1 obtained from a two parameter analysis, and the standard deviation of the2324 THERMODYNAMICS OF MIXTURES total pressures ap = p(Ap)2/(6-n)]*, where n is the number of coefficients in the fitting equation.The values of GZ listed in table 5 are derived from the one para- meter analysis. The total experimental uncertainty in p due to errors of thermometry, catheto- metry and data analysis is estimated to be +6 Pa. The overall mole fractions, with associated uncertainties arising from weighing errors, buoyancy corrections and the TABLE 3 .-VAPOUR PRESSURES OF MIXTURES OF n-HEXANE+ HEXAMETHYLDISILOXANE (X2 AND )'2 ARE MOLE FRACTIONS OF HEXAMETHYLDISILOXANE IN LIQUID AND VAPOUR) TIK xz 303.15 0 0.1315 0.1483 0.2742 0.4044 0.5505 0.6949 1 .o 309.15 0 0.1330 0.1501 0.2765 0.4071 0.5532 0.6972 1 .o 315.15 0 0.1346 0.1518 0.2791 0.4106 0.5565 0.7002 1 .o YZ 0 0.0436 0.0497 0.1006 0.1655 0.261 2 0.3946 1 .o 0 0.0456 0.0521 0.1054 0.1734 0.2727 0.4092 1 .o 0 0.0480 0.0548 0.1110 0.1823 0.2848 0.4234 1 .o PlWa &/Pa 24.961 22.669 17 22.351 -6 20.160 6 17.866 2 15.252 - 19 12.690 11 7.137 31.860 28.936 32 28.507 - 17 25.747 23 22.818 - 7 19.534 - 32 16.356 21 9.493 40.221 36.526 42 35.998 -8 32.515 27 28.856 -5 24.778 - 59 20.905 39 12.456 TABLE 4.-PARAMETERS OF LEAST SQUARES ANALYSIS OF VAPOUR PRESSURES T1K n goIRT UolRT giIRT UiIRT d P a 303.15 1 0.0390 0.0027 21 303.15 2 0.0332 0.0030 0.0125 0.0050 15 309.15 1 0.0256 0.0029 28 309.15 2 0.0223 0.0046 0.0072 0.0078 29 315.15 1 0.021 1 0.0032 40 315.15 2 0.0226 0.0054 - 0.0033 0.0093 44 TABLE 5.-EXCESS GIBBS FREE ENERGY OF THE EQUIMOLAR MIXTURE n-HEXANE+ HEXAMETHYL- DISILOXANE GE(x = 0.5)/J mol-' TlK expt.calc. 303.2 25 8 309.2 17 6 315.2 14 4E .DICKINSON, I . A . MCLURE A N D B . H. POWELL 2325 condensation of mercury vapour, are considered to be accurate to within 0.04 per cent. Further errors occur in calculating the mass of the vapour phase owing to uncertainties in the second virial coefficient of hexamethyldisiloxane B22 and the cross-term virial coefficient B1 2. The above experimental uncertainties lead to an estimated absolute error in GE of +_5 J mol-l. The experimental excess enthalpies at 298.15 K, with estimated errors of & 3 J rnol-', are recorded in table 6. The data are represented by the equation with a standard deviation of 1.2 J mol-'.* H:/J mol-1 = xl(l -xl)[502.08-66.96(1 -2x1)] (4) TABLE 6.--EXCEsS ENTHALPIES OF THE MIXTURE n-HEXANE( 1) + HEXAMETHYLDISILOXANE(2) AT 298.15 K 0.0339 16 0.5811 129 0.1115 50 0.6588 118 0.1753 65 0.7674 94 0.2583 88 0.8278 79 0.3429 105 0.8391 72 0.4482 124 0.8745 60 Hg/J mol-' XI Hg/J rnol-' X1 DISCUSSION Excess thermodynamic functions of mixing may be calculated from an empirical equation of state such as the van der Waals equation.l* However, as the thermo- dynamic properties of a suitable reference substance are accurately known, we prefer here to choose an experimental equation of state.The smoothed n-alkane reference of Bhattacharyya, Patterson and Somcynsky l9 (described in terms of the con- figurational properties of a simulative n-heptane) is used in conjunction with the one- fluid van der Waals The equimolar excess volume of the mixture, for instance, is calculated from the equation 20* 21 V;(X = 0.5) = $[(el2v,+s,,v,)-g6~2v~~ - el 2 4 1 2( vfb - 3vf) - 34:2 h h -k 6eI 2 v f f + be12s12(6h+ 6) + ts?2%h ++(el 2 Vff + S125/fh)(fll+ f22 - 2) + +(el 2 6 h + s1 2Vhh)(h 1 1 + h2 2 - 2)1, ( 5 ) where the molecular parameters 012, 412, e12 and s12 are defined by the relations (6) in which&@ and hifl are molecular energy and size constants appropriate to the a+ interaction (a, #I = 1,2).The quantities V,, etc., which depend only upon the thermo- dynamic properties of the reference substance, are given at negligible pressure by 31 812 = fll -f22, e12 = 2f12 -f11-f22, 412 = h l l 4 2 2 , s12 = 2h12--hll--h22, Vf = - VmTa,, Vff = VmT[2ap + TCI; + T(a~t,/aT)~], v& = - VmTa,, Vh = v,, v,, = 0, (7) *It came to our attention between the writing and submission of this paper that Armitage, Pollock and Whittingham (Leicester Polytechnic) found a maximum enthalpy of mixing in this system of about 127 J mol-I at ~ ~ ~ 0 .5 5 .2326 THERMODYNAMICS OF MIXTURES where V, is the molar volume and CI, is the isobaric expansivity. The molar excess Gibbs free energy GE is obtained from an expression analogous to eqn (5) containing the quantities Gf, etc., which are given at zero pressure by : Gf = Urn, Gfr= -TC,,,, Gfh = 0, (8) Gh = -XT, Ghh = RT. Here Urn is the molar configurational internal energy and C,,, is the molar configura- tional heat capacity. The excess enthalpy H$ follows directly from the temperature dependence of GZ /T. The molecular parameters fll, f 2 2 , h l l and / 2 2 2 are calculated from the critical constants of the pure substances,22 and the cross-terms.f,, and hI2 are derived from the combining rules : f 1 2 = t ( f 1 1 f 2 2 ) + ; (9) h t 2 = ( h t , + h$2)/2.(10) The calculated excess Gibbs free energies listed in table 5 are obtained using a value of 5 = 0.993 derived froin an analysis of gas-liquid critical data.22 Also predicted are the excess functions HE(309.2 K, x = 0.5) = I12 J molkl and VE(303.2 K, x = 0.5) = - 1.17 cm3 mol-I. At each temperature, the theoretical curve of GE as a function of composition is S-shaped, becoming negative at high mole fractions of hexamethyldisiloxane. In qualitative accord with the 5 value estimated from the critical temperatures,22 the experimental vapour pressures of the mixtures of n-hexane + hexamethyldi- siloxane exhibit only small deviations from ideality.The derived equimolar excess Gibbs free energies and the directly determined equimolar excess enthalpy are in good agreement with those calculated from the van der Waals one-fluid model. It should be noted, however, that the calculated and experimental H z values do not correspond to exactly the same temperature, and that the exact numerical values of all the theor- etical excess functions should not be given too great a significance, as they depend to some degree upon the particular choice of reference ~ubstance.~ The experimental excess volume is 0.05 cm3 mol-1 at x = 0.5, in poor agreement with the predicted value of - 1.17 cm3 mol-'. A part of this discrepancy may be due to a deviation of the parameter hI2 from the value implied by eqn (1 0), since, unlike the free energy, V; is very sensitive to any variation in the cross-term s12.It may be noted that machine calculations for binary mixtures of Lennard-Jones particles suggest 2 3 9 24 that the predictions of V: from the van der Waals one-fluid theory are too large (in a negative sense) for mixtures with components of widely differing molecular size. In attempting to ascertain the relative importance of the two explanations, we suggest that it might be useful in future work to estimate h12 independently from some other property of the mixture, such as the gas-liquid critical volume or the gas-liquid critical pressure. We thank Professor R. L. Scott for the gift of the computer programme used in the E. D. and B. H. P. acknowledge receipt of S.R.C. Student- vapour pressure analysis. ships. M. L. McGlashan and A. G. Williamson, Trans. Faraday Soc., 1961, 57, 588. C. B. Willingham, W. J. Taylor, J. M. Pignocco and F. D. Rossini, J. Res Nat. Bur. Stand., 1945, 35, 219. D. W. Scott, J. F. Messerly, S. S. Todd, G. B. Guthrie, I. A. Hossenlopp, R. T. Moore, A. Osbom, W. T. Berg and J. P McCullough, J. Phys. Ctlem., 1961, 65, 1320.E . D I C K I N S O N , I . A . MCLURE A N D B . H . POWELL 2321 E. Dickinson and I. A. McLure, J.C.S. Faraday I, 1974, 70, 2328. K. N. Marsh, Trans. Faraday SOC., 1968, 64, 883. W. J. Gaw and F. L. Swinton, Train. Faraday SOC., 1968, 64, 637. R. Fernandez-Prini and J. E. Prue, J. Chem. SOC. A , 1967, 1974. E. Dickinson, Ph.D. Thesis (Sheffield, 1972). l o W. G. Brombacker, D. P. Johnson and J. L. Cross, Mercury Barometers and Manometers (Nat. Bur. Stand. Monograph 8, 1960). Selected Values of Properties of Hydrocarbons and Related Compounds, Amer. Petroleum Inst. Res. Project 44. Thermodynamic Research Center (Texas A & M University, CoIlege Station, Texas, 1965), extant. ’ C. R. Barber, R. Handley and E. F. G. Herington, Brit. J. Appl. Phys., 1954, 5, 41. l 2 J. A. Barker, Austral. J. Chem., 1953, 6, 207. l 3 D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1963, 55, 43. l 4 M. L. McGlashan and D. J. B. Potter, Proc. Conf. Thermodynamics and Transport Properties of l5 J. A. Larkin and M. L. McGlashan, J. Chem. SOC., 1961, 3425. l 6 R. H. Stokes, K. N. Marsh and R. P. Tomlins, J. Chem. Thermodynamics, 1969, 1, 211. l 8 M. L. McGlashan, Trans. Faraday SOC., 1970, 66, 18. l9 S. N. Bhattacharyya, D. Patterson and T. Somcynsky, Physica, 1964, 30, 1276. 2o T. W. Leland, J. S. Rowlinson and G. A. Sather, Trans. Faraday SOC., 1968, 64, 1447. 21 W. B. Brown, Phil. Trans. A, 1957,250, 175. 2 2 E. Dickinson and I. A. McClure, J.C.S. Faraday I, 1974, 70, 2313. 23 J. V. L. Singer and K. Singer, Mol. Phys., 1970, 19, 279. 24 I. R. McDonald, Mol. Phys., 1972, 24, 391. Fluids (Inst. Mech. Eng., 1958), p. 60. A. E. P. Watson, I. A McLure, J. E. Bennett and G. C. Benson, J. Phys. Chem., 1965,69,2753.

ISSN:0300-9599    

DOI:10.1039/F19747002321

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Thermodynamics of n-Alkane+Dimethylsiloxane Mixtures Part 3.-Excess Volumes B Y ERIC DICKINSON AND IAN A. MCLURE* Department of Chemistry, The University, Sheffield S3 7HF Received 24th April, 1974 Excess volumes have been measured dilatometrically for binary mixtures of six n-alkanes (n- pentane, n-hexane, n-heptane, n-octane, n-decane and n-tetradecane) with four linear dimethyl- siloxanes (dimer, trimer, tetramer and pentamer) at 303.2 K, and for four other mixtures. The sign and magnitude of the excess volumes depend intimately upon the chain lengths of the oligomers. The phenomenological corresponding states theory of Patterson is shown to reproduce qualitatively the experimental chain length dependence. Suggestions for the success of the model are discussed briefly in terms of the properties of the pure components, and the disadvantages of two other ap- proaches-the van der Waals one-fluid model and the Prigogine cell theory-are identified.An application of Brsnsted’s principle of congruence to ternary mixtures is discussed. In previous papers measurements of vapour pressures and gas-liquid critical temperatures for mixtures of the type n-alkane + linear dimethylsiloxane were analysed in terms of the relative strengths of the unlike pairwise interaction energies. We now present the results of measurements of excess volumes of mixing for a large number of these systems and attempt to show that their chain length dependence may be interpreted in terms of a simple corresponding states approach. Linear dimethylsiloxanes are completely miscible with n-alkanes over a broad range of temperature and pressure.In binary mixtures where the components are of very different molecular size, phase separation is observed 2 * 3 above a lower critical solution point (near to the gas-liquid critical temperature of the more volatile component). At low reduced temperatures, however, away from the gas-liquid critical region, there is complete miscibility. Hence, since each dimethylsiloxane oligomer (up to the high polymer) is liquid at ambient temperatures and pressures, the limiting factor in an isothermal study of this type is the shorter liquid range of the n-alkanes. At 303.2 K and 1 atm pressure, we are restricted to paraffins having between 4 and 19 carbon atoms in the chain. Mixtures involving the following constituents are considered here : n-pentane, n-hexane, n-heptane, n-octane, n-decane, n-tetradecane and n-octadecane ; hexamethyldisiloxane (dimer), octamethyltrisiloxane (trimer), decamethyltetrasiloxane (tetramer) and dodecamethylpentasiloxane (pen- tamer).EXPERIMENTAL The excess volumes of mixing were measured using the continuous dilution dilatometer described p r e v i ~ u s l y . ~ Isothermal compressibilities, required to correct the observed volume changes for the effects of variations in the hydrostatic pressure, were taken from the work of Orwoll and Flory and Sadler.6 The dimethylsiloxanes were obtained by fractionally distilling the appropriate Hopkin and Williams MS 200 silicone fluids. All final samples had a purity of better than 99.0 mol % as indicated by gas-liquid chromatography with a 2 m silicone rubber (SE 30) stationary phase, The samples of n-pentane (99.5 mol %), n-hexane (99.0 mol %), n-heptane (99.5 rnol 2328E .DICKINSON A N D I . A . MCLURE 2329 %) and n-decane (99.0 mol %) were obtained from British Drug Houses and were used as received. The Newton Maine n-octane and n-octadecane, and the Phillips n-tetradecane, contained less than 1.0 mol % impurity. RESULTS Excess volumes were determined at 303.2 K over the whole composition range for the mixtures of six n-alkanes (n-pentane, n-hexane, n-heptane, n-octane, n-decane and n-tetradecane) with four linear dimethylsiloxanes (dimer, trimer, tetramer and pentamer). Also investigated were the systems n-heptane + pentamer at 323.2 K, TABLE 1 .-EXCESS VOLUME PARAMETERS A i (IN EQUATION 1) FOR n-ALKANE+ DIMETHYL- SILOXANE MIXTURES AT TEMPERATURE T.bv IS THE STANDARD DEVIATION ; np IS THE NUMBER OF EXPERIMENTAL POINTS. n-alkanes (1) + hexamethyldisiloxane (2) component 1 n-pentane n-hexane n-heptane n-octane n-decane n-tetradecane n-oct adecane component 1 n-pentane n-hexane n- hep tane n- oc tane n-decane n-te tradecane n-tetradecane TI K 303.2 303.2 303.2 303.2 303.2 303.2 303.2 A0 0.128 0.112 - 0.107 - 0.26 I -0.915 - 1.459 - 1.903 A1 - 0.043 0.001 0.005 - 0.009 -0.189 - 0.299 - 0.540 A2 - 0.010 0.049 - 0.025 - 0.023 - 0.020 - 0,033 - 0.224 n-alkanes (1)+ octamethyltrisiloxane (2) T/K 303.2 303.2 303.2 303.2 303.2 303.2 323.2 A0 0.050 0.177 0.03 1 - 0.059 - 0.407 -0.871 - 1.234 A1 - 0.01 6 0.000 - 0.030 - 0.057 - 0.057 -0.204 - 0.103 A2 - 0.020 0.064 - 0.014 0.019 0.027 0.008 0.096 n-alkanes (1)+ decamethyltetrasiloxane (2) component 1 TI K A0 A1 A2 n-pentane 303.2 -0.111 0.020 0.013 n-hept ane 303.2 0.129 0.014 -0.044 n-decane 303.2 -0.150 0.028 -0.044 n-hexane 303.2 0.149 0.049 0.040 n-oct ane 303.2 0.051 0.047 0.031 n-tetradecane 303.2 - 0.535 -0.102 0.002 n-pentane/ n-decane 303.2 0.167 0.018 0.032 =V 0.001 0.002 0.002 0.004 0.003 0.003 0.003 =V 0.002 0.002 0.001 0.002 0.002 0.001 0.004 OV 0.001 0.001 0.002 0.001 0.002 0.001 0.001 n-alkanes (1) + dodecamethylpentasiloxane (2) component 1 TIK A0 A1 A2 0, n-pen t ane 303.2 -0.194 0.026 0.044 0.002 n-hexane 303.2 0.146 0.034 -0.002 0.003 n-hep tane 303.2 0.187 0.031 0.007 0.001 n-hept ane 323.2 0.188 0.056 0.015 0.002 n-octane 303.2 0.136 0.O00 0.082 0.002 n-tetradecane 303.2 - 0.341 - 0.028 0.005 0.002 n-decane 303.2 -0.023 -0.002 0.007 0.001 UP 11 11 10 12 7 13 14 nP 9 11 9 11 8 11 7 nP 11 10 11 10 10 11 9 nP 10 11 6 9 9 10 102330 THERMODYNAMICS OF TI-ALKANE -k DIMETHYLSILOXANE MIXTURES n-tetradecane + triiner at 323.2 K, n-octadecane + diiner at 303.2 K, and n-pentane/ n-decane + tetramer at 303.2 K.The fractional volume changes A V/ V for each mixture were fitted by least squares ’ to an equation of the form -0.4 I I I I I I I I 1 I I I where #2 is the volume fraction of component 2.* Table 1 lists the coefficients Ai, the standard deviation gV and the number of experimental points np. (Molar excess volumes YE, if required, may be calculated using the densities of Orwoll and Flory and Pretty.*) The values of oV fluctuate within the range 0.001 to 0.004%, but it should be noted that since standard deviations derived from dilution dilatometry, especially those from a single run, tend to overestimate the intrinsic precision of the data, the actual accuracy may be slightly less than that implied by table 1.Fig. 1 shows a plot of the fractional volume change AV/V at volume fraction 0.5 against the chain length of the n-alkane component of the mixture. Solid curves are drawn through the sets of points corresponding to a given siloxane. 0.1 1 DISCUSSION Any theory of chain molecule liquid mixtures could be reasonably expected to reproduce the following features of the experimental data : (a) the increasingly negative excess volumes as the relative size differences between the two components become (i) Fractional volume changes and volume fractions are more closely related to the actual experimental quantities than excess volumes per mole and mole fractions.(ii) A plot of the last two variables produces a very skewed curve for many of these mixtures. (iii) Excess volumes and compositions computed on a molar basis are entirely inappropriate for comparing the present results with those for mixtures containing polymeric alkanes or siloxanes, * We express the results in this form for the following reasons.E . DICKINSON AND I . A . MCLURE 233 1 larger ; (6) the small but positive excess volumes with hydrocarbons of intermediate chain length; (c) a distinct "cross-over point" in the individual siloxane curves at around hydrocarbon number n = 6.With these criteria in mind, we discuss in detail the phenomenological corresponding states treatment developed by Patterson, and compare the conclusions with those resulting from two other approaches, the simple van der Waals model and the Prigogine cell theory. CORRESPONDING STATES THEORY OF CHAIN MOLECULE LIQUID MIXTURES According to Prig~gine,~ the configurational thermodynamic properties of an oligomeric liquid are related to the corresponding reduced quantities by reduction parameters which depend only upon the chain length n. With the exclusion of any combinatorial term, the molar Gibbs free energy G,, the molar volume V, and the molar entropy S, are given at temperature T and pressure p by the equations G,(p, T, n) = G(p, T)U*(n), U*(II) = N , g ( n ) ~ ; (2) V,(p, T, i z ) = V(p, T)V*(n), (3) S,,,(p, T, n) = S(p, T)S*(n), S*(n) = IVAc(n)k.(4) V*(n) = NAr(n)a3 : The dimensionless reduced quantities G, Pand are functions of the reduced tem- perature Tand the reduced pressure p . The reduction parameters U*, Y*, and S* are related to an arbitrary spherical reference molecule,' with characteristic energy c and size a, by the effective numbers of segments q(n), r(n) and c(n), which are propor- tional respectively to the molecular surface area, the molecular volume and the number of external degrees of freedom of the chain molecule. The temperature and pressure reduction factors, T* = T/T and p* = p / p , are given by T*(n) = U*(n)/S*(n) = q(n)&/c(n)k, p'k(n) = uyn>/ V*(17) = q(n)&/r(n)a3.( 5 ) (6) In terms of the phenomenological formulation of the corresponding states the molar principle, as introduced by Hijmans volume of the mixture is expressed in the form where (p") and (T) are the reduced pressure and temperature of the mixture, and (V*) is the average volume reduction parameter. For a binary mixture a t negligible pressure, the excess volume is and developed by Patterson,". Vrn(p, T ) = V(<jj>, < T>)< v*>, (7) V: = ( x V: + x v;> P( ( T) j - x VT P( T, ) - x2 V ; V( T2). (8) In eqn (8), ( V * ) has been replaced by a mole fraction average of V$ and V:. (T) is related to TI and 4; by the surface fraction average where XI is the surface fraction of component 1 : (T) = T/(T*) = XITl + XzT*, (9) X I = x,pTV"f(X,pT~T+x,pqV;).(10) Expansion of the reduced volume of each pure component about that of the mixture yields the equation VE = - (~1x2 VT - x ~ X , Vq)AT(d P/d( T)) - (+)(XI X i V t - N ~ X : V;)(AQ2(d2 Pjd( T ) 2 ) - ( & ) ( x ~ X ~ V T - X.~X:VZ)(AT)~(~~ P/d( Q3),2332 THERMODYNAMICS OF n-ALKANE f DIMETHYLSILOXANE MIXTURES where terms of order (AT)" = (TI - T2)" or higher are ignored. gous to eqn (1 1) may be developed for the other excess functions. Expressions analo- REDUCTION PARAMETERS A N D REDUCED EQUATION OF STATE Before employing an explicit expression such as eqn (1 1) to calculate the excess mixing properties of a group of conformal substances, it is necessary first to define a self-consistent set of reduction parameters and a reduced equation of state.In testing the corresponding states principle from methane to polymethylene, Patterson and Bardin l 3 evaluated reduction factors for the n-alkanes. To facilitate comparison with the n-alkane analysis, we use the same procedure here for the linear dimethyl- siloxanes (the details are discussed elsewhere 14). TABLE 2.-RELATIVE VOLUME AND TEMPERATURE REDUCTION PARAMETERS OF THE LINEAR DIMETHYLSILOXANES dimethylsiloxane oligoiner V*/ V* T*/T; dimer 1.259 0.H2 trimer 1.746 0.943 tetramer 2.228 0.992 pentamer 2.723 1.025 The volume and temperature reduction parameters listed in table 2 were derived from the molar volumes and isobaric expansivities of the dimethylsiloxanes.8 Follow- ing Patterson et aZ.,13 n-octane is taken as the arbitrary reference substance (with reduction parameters Vo* and To*).The n-alkane pressure reduction factors are essentially independent of chain length, whereas an analysis of the thermal pressure coefficient data of the dimethylsiloxanes suggests that their relative pressure reduc- tion factors p*/p$ decrease with increasing chain length. l4 However, until this effect is substantiated by measurements of dimethylsiloxane p , V, T properties over a much larger temperature range, it seems reasonable to stay with an average value of p*/p$ = 0.804.-f- The temperature derivatives of the reduced volume are derived from the experi- mental data of the pure components 5 9 6- * through the relations : dV/dT = apVT*, (12) (1 3) d2 V/d T2 = VT*2(du,/dT) + ( I /V)(dV/dT)2, d3V/dT3 = 2T*2(dV/dT)(d~,/dT) +(I /V)(dV/dT)(d2V/dT2)+ VT*3(d2ap/dT2), (14) where ap is the isobaric expansivity.The dimensionless quantity (a,T)-l appropriate to the mixture is taken as the arithmetic mean of the values of (ct,T)-l which each of the pure components would have at a reduced temperature (T} equal to that of the mixture. [The pure component values of (a,T)-l should, of course, be identical for substances obeying the same principle of corresponding states.] The values of CI,, (dcr,/dT) and (d2m,/dT2) are taken from the work of Orwoll and Flory' and Pretty.' COMPARISON OF EXPERIMENT A N D THEORY The theoretical excess volumes, as calculated from eqn (1 1) at 303.2 K, are Fractional volume changes AV/V for the equimolar mixtures illustrated in fig.2. I- The general conclusions are unaffected by small changes in the parameter p * . Since the aim is not to obtain perfect agreement with experiment, the exact values are not very important,E . DICKINSON AND I . A . MCLURE 2333 are plotted against the chain length of the hydrocarbon. As in fig. 1, each curve represents the separate mixing of an individual siloxane with a series of n-alkanes. A comparison of experiment and theory reveals several notable features. The sign and magnitude of the experimental and calculated excess volumes depend intimately upon the relative chain lengths of the components. With regard to the 0.2 0. I 0 - 0.1 -0.2 - 0.3 kh a 2 - 0.4 - 0.5 - 0.6 3 4 5 6 7 8 9 10 I I 12 13 1 4 1 n FIG. 2.-Volume changes of n-alkane + dimethylsiloxane mixtures as predicted by the Patterson phenomenological treatment.The fractional volume change A V/ V at mole fraction 0.5 is plotted against the chain length n of the alkane component of the mixture. Solid curves are drawn through the sets of points corresponding to a given siloxane : 0, dimer ; A, trimer ; 0, tetramer ; V , pentamer. calculated volume changes, the form of the curves arises solely from the relative sizes of the reduction parameters ; it is not the product of some judiciously chosen adjustable parameter. The array of curves in fig. 2 shows good qualitative agreement with the gross features of the experimental data (fig. l), but the calculated excess volumes are generally larger than those observed experimentally.Especially noteworthy is the prediction of a “cross-over region” around IZ = 5 : the experimental lines appear to intersect at n z 6 . Again, however, the magnitude of AV/Vis overestimated, at this point by a factor of about 2+. Clearly, the phenomenological treatment outlined above offers neither a good fit nor a rigorous interpretation of the excess volumes of n-alkanes + linear dimethyl- siloxanes. It does demonstrate, however, that the apparently complex volumetric behaviour of these mixtures is usefully described by a simple application of the principle of corresponding states. Other models, such as the van der Waals approxi- mation,l tend to reproduce badly the excess volumes of these systerns,1’14 especially for those mixtures containing oligomers whose molecular sizes are very different.Although the curves calculated from the van der Waals equation exhibit l4 an apparent periodic dependence upon the chain length, it is one with turning points corresponding to the mixtures in which the sizes of the two different chain molecules approach equality, e.g. the mixtures dimer + n-tetradecane, etc. No positive volume changes are predicted. Neither is there a tendency for the theoretical curves to intersect at a given hydrocarbon number as is observed experimentally. Whilst positive volume changes can be produced from the van der Waals equation by invoking appropriate2334 THERMODYNAMICS OF n - A L K A N E -I- DIMETHYLSILOXANE MIXTURES deviations from the Berthelot combining rule, the artifice does nothing to satisfy any of the other objections.The qualitative success of the Patterson approach may be interpreted graphically. A plot of reduced volume against reduced temperature is invariably concave upwards (see fig. 3), thereby leading to negative volume changes for binary mixtures where y2 (T)! (T)” T I T FIG. 3.-The dependence of the reduced volume of a mixture ?(<?)) ypon the reduced temperature { f>. For the case (f> = <i”>’, A V/ V is negative ; alternatively, if (2‘) = ( T ) ” , A V/V is positive. p:=pZ. Sets of mixtures falling into this category are the binary systems formed from two n-alkanes,I6 two dimethylsiloxanes or two perfluoro-n-alkanes. For these systems the surface fraction XI is approximately equal to the volume or segment fraction $1, and, in fig.3, the reduced volume of the mixture V((F)’) lies almost di- rectly below the reduced volume of the unmixed pure components, r( .fl) + +2 v(.f2), since <T>Z41Tl+$21;. (15) Conversely, for mixtures of conformal substances with different pressure reduction factors, positive volume changes are possible if The inequality (16) is most likely to be satisfied if I TI - 7’1 is small. In comparison with their hydrocarbon analogues, the high reduced temperatures of the dimethyl- siloxanes decrease only slowly with increasing chain length-a feature which has been attributed l 8 to the greater siloxane chain flexibility. Positive excess volumes occur with components having similar reduced temperatures, but in mixtures of dimethylsiloxanes with n-alkanes of extreme chain length (large or small) negative volume changes are expected, and found.If we suppose further, that the individual n-alkane and siloxane molecules are subdivisible into arbitrary identical segments with characteristic parameters E and 0, then, from eqn (6), a siloxane molecule has associated with it a valuz of ( q / r ) larger than that for a n-alkane. This might be interpreted on a molecular basis by postu- lating that, due to shielding by the peripheral methyl groups, a -SiO - siloxane seg- ment makes fewer “extcrnal contacts” than does a --CH2CH2- alkane segment. V( ( T ) ”) = V( x1 TI + x2 T2) > (b 1 V( TJ + 4 2 V( T2). (16)E . DICKINSON A N D I . A . MCLURE 2335 The parameter c has no direct influence on the sign of V i ,but it does, through the ratio (c/q), determine the values of the pure component reduced temperatures. As the chain length dependence of (c/q) is much smaller for the dimethylsiloxanes than for the n-alkanes, much smaller volume changes are expected for binary mixtures of the former, a prediction which is borne out by experiment.6 THE PRIGOGINE AVERAGE POTENTIAL CELL MODEL Prigogine’s average potential approach for chain molecule mixtures involves a model of the liquid state composed of a lattice of cells whose volume varies as a function of the temperature, pressure and composition.Each oligomer interacts with neighbouring “segments” of adjacent oligomers via qz contacts, where z is the co-ordination number of the quasi-lattice. If the two different chain molecules are considered to be composed of equal sized segments interacting identically with segments of adjacent molecules according to a well-defined pair potential (that is, if, in the Prigogine nomenclature, p = 6 = 6 = 0), then the species will differ only in their relative values of the parameters q(n), r(n) and c(n).In testing the applicability of this simplified Prigogine model to the n-alkane+ dimethylsiloxane mixtures, we consider three different but related procedures for generating the chain length dependent parameters. In the first method, r(n) is calculated by arbitrarily designating a segment to be one of the units -CH,, -CH2CH2-- or -SiO-, each of which is thereafter taken to be of the same size. The parameter q(n) is derived from the relation (17) with z = 10, and the values of c(n) are taken from the corresponding states analysis of Simha and H a ~ 1 i k .l ~ The pure n-alkane component of the mixture is used as reference substance. A comparison of the experimental volume changes with those obtained by this procedure reveals that, with the exception of mixtures involving hexamethyldisiloxane and certain of the lower n-alkanes, the excess volumes predicted from structural effects alone are an order of magnitude smaller than those observed experimentally. The relative magnitudes of the predicted volume changes are, however, in fair agreement with experiment. The correct order is obtained at the extremes of hydrocarbon chain length, and a reversal is implied (with the exclusion of the dimer) in the region n-octane to n-decane.The form of the results is insensitive to the exact value of the co-ordination number z. We use, in the second method, values of r(n) and c(n) which are in compliance with the thermodynamic reduction parameters V*(n) and S*(n) defined in eqn (3) and (4). Expressed as linear dependences upon the chain length, these are given by 13.14 q ( 4 = KZ - 2)/zIr(n) + (2/4 rI = (nl+0.84)/2.0, (1 8) r2 = (n, + 0.16)/0.929, (19) ~1 = ( ~ 1 + 6.0)/2.006, (20) c2 = (n, + 2.02y0.873, (21) where the subscripts 1 and 2 refer to the n-alkane and dimethylsiloxane components respectively. The same reference substances as before are employed, and q(n) is again defined by eqn (17) with z = 10. The excess volume for each mixture is pre- dicted to be always small and negative irrespective of the relative chain lengths of the components.This feature is a direct consequence of the similarity in the values taken2336 THERMODYNAMICS OF n-ALKANE + DIMETHYLSILOXANE MIXTURES by the ratios (ql / r , ) and (q2/r2) : that is, it is due to the fact that the parameter p*(n) is nearly the same for both o1igomers.T As stated previously, it might be expected on simple molecular grounds that - --SO- .- siloxane segments would make significantly fewer external contacts (due to shielding by peripheral methyl groups) than -CH2CH2- n-alkane segments. To take some account of this effect in the third method, we restrict each middle siloxane segment to one less contact than its hydrocarbon counterpart by use of the relation and keep all other conditions identical to those of the previous procedure. The results of this manoeuvre are shown in fig.4 : small positive and negative chain length q2 = MZ - 3)/Zi+ (414, (22) 6 a 10 12 14 16 n FIG. 4.-Volume changes calculated from the simplified Prigogine cell theory. The fractional volume change A V/ Y at volume fraction 0.5 is plotted against the chain length n of the alkane com- ponent of the mixture. Solid curves are drawn through the sets of points corresponding to a given siloxane : 0, dimer ; A, trimer ; 0, tetramer ; V, pentamer. dependent volume changes, together with a “cross-over point” (AV/V = 4 x ; nl = 6) in excellent, but almost certainly fortuitous, agreement with experiment. p ; is now significantly greater than p ; ; or, in molecular terms, (q/r), >(q/r)2.The number of external degrees of freedom, 3c, enters the mixing expression through and large differences in molecular flexibility tend to increase ITl - T21 thereby pro- ducing a larger negative VE. Thus it is seen that, if the appropriate values of q(n), ~ ( n ) and c(n) are inserted into the Prigogine cell m0de1,~ predictions similar to those of fig. 2 can be generated. However, the cell theory equations are based upon a quasi-lattice partition fun~tion,~ and many assumptions of questionable validity have to be made in the specification of relative segment sizes and the lattice co-ordination number. This apparently large degree of arbitrariness, as applied to mixtures of dissimilar chain molecules, limits the usefulness of the cell theory in interpreting the thermodynamic behaviour f If c is set equal to unity throughout, the system simplifies to a set of binary mixtures of rigid rods of different lengths.The associated volume change, negative for all values of n1 and n2, arises out of the extra contracts at the end of a chain molecule over those in the middle. So, even for a mixture in which 6 = 0 = 0, the structural factor conceals inherent “ energetic effects ” in the form of the parameter q.E. DICKINSON AND I . A . MCLURE 2337 of this set of systems. However, only very unreasonable choices of q(n), r(n), c(n) and z alter the basic qualitative picture. THE TERNARY MIXTURE n-PENTANE + n-DECANE + DECAMETHYLTETRASILOXANE Brransted’s principle of congruence 2o states that the thermodynamic properties of a mixture of homologues are identical, with the exception of the Gibbs paradoxical term, to those of a molecule of average chain length ii = C xini, 1 where x i is the mole fraction of the species with chain length ni. The principle implies, for instance, that an equimolar mixture of n-pentane + n-decane has the same molar volume as a pseudo-n-alkane of chain length 6 = 7.5.Hence, although n-pentane and n-decane each give a negative equimolar excess volume with deca- methyltetrasiloxane (the values at 303.2 K are -0.042 and -0.099 cm3 mol-l respectively), a mixture with the pseudo-n-alkane of chain length 7.5 should at the same temperature exhibit a positive volume change, in line with any realistic interpola- tion of the n-heptane and n-octane points of fig. 1. The prediction is fulfilled qualitatively with V:(xs = 0.5) = Vnl(x, = 0.5, x5 = 0.25, xlo = 0.25) -x,Vm(xs = 1) -(1 -x,)Vm(x5 = 0.5, xlo = 0.5) equal to (0.098 & 0.007) cm3 mol-l, where x,, xs and xi0 are respectively the mole fractions of decamethyltetrasiloxane, n-pentane and n-decane.The interpolated value from fig. 1 has a positive value of (0.053 & 0.005) cm3 rnol-l, although the excess volume relative to the three unmixed pure components is still, of course, negative. We thank Miss C. W. Green for her preliminary experimental work on this prob- lem. E. D. acknowledges receipt of a S.R.C. Studentship. E. Dickinson, I. A. McLure and B. H. Powell, J.C.S. Faraday I, 1974, 70, 2321. P. I. Freeman and J. S. Rowlinson, Polymer, 1959, 1, 20. D. Patterson, G. Delmas and T. Somcynsky, Polymer, 1967, 8, 503. E. Dickinson, D. C. Hunt and I. A. McLure, J. Chem. Thermodynamics, submitted for publica- tion. R. A. Orwoll and P. J. Flory, J. Amer. Chem. Soc., 1967, 89, 6814. P. A. Sadler, Ph.D. Thesis (Sheffield, 1971). A. J. Pretty and I. A. McLure, unpublished results. I. Prigogine, The Molecular Theory of Solutions (North-Holland Amsterdam, 1957), chap. 16. ’ D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1967, 55, 43. lo J. Hijmans, Physica, 1961, 27, 433. l1 D. Patterson, Rubber Chem. Technol., 1967, 40, 1. l2 D. Patterson and G. Delmas, Disc. Faraday SOC., 1970, 49, 98. l3 D. Patterson and J. M. Bardin, Trans. Faraday SOC., 1970, 66, 321. l4 E. Dickinson, Ph.D. Thesis (Sheffield, 1972), chap. 9. l 5 T. W. Leland, J. S. Rowlinson and G. A. Sather, Trans. Faraday SOC., 1968, 64, 1447. l6 J. S. Rowlinson, Liquids and Liquid Mixtures (Butterworth, London, 2nd edn., 1969), chap. 4. l7 E. E. Erickson, M.S. Dim. (UCLA, 1969). lB D. Patterson, S. N. Bhattacharyya and P. Picker, Trans. Faraday SOC., 1968, 64, 648, l9 R. Simha and A. J. Havlik, J. Amer. Chem. SOC., 1964, 86, 197. 2o J. N. Brsnsted and J. Koefoed, Kgl. Danske Vid. Selsk. (Mat.-Fys. Medd.), 1946, 22, 17. 1- -74

ISSN:0300-9599    

DOI:10.1039/F19747002328

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Explosive Oxidation of Hydrogen Sulphide : Self-heating, Chain-branching and Chain-thermal Contributions to Spontaneous Ignition BY PETER GRAY AND MALCOLM E. SHERRINGTON*T School of Chemistry, The University, Leeds LS2 9JT Received 7th March, 1974 The spontaneously explosive oxidation of hydrogen sulphide in a 290 cm3 vessel has been in- vestigated over a temperature range 280-360°C and between pressures of 10 and 120 mmHg. Con- ditions for ignition have been mapped on ap,Tdiagram. Very fine thermocouples (25 pm Pt-Pt/Rh) have been used to detect and measure self-heating, and special emphasis has been laid on the direct measurement of the size and form of the temperature against time histories for different initial con- ditions or locations on the ignition diagram. The effects of reactant proportions and of added diluents (with different thermal conductivities) on the second and third ignition limits have also been studied. Although the reaction exhibits many features traditionally associated with purely branched chain explosions, the direct temperature measurements have revealed extensive self-heating under very varied conditions of pressure and temperature. Boundaries may be drawn on the ignition diagram that separate the regions where a combined chain-thermal mechanism is responsible for explosions (I) from those which may be considered as purely thermal (11) or isothermal branched chain (111) in nature.The measured temperature against time histories provide novel experimental support for the unified theoretical treatment of chain and thermal explosions of Gray and Yang.Critical tempera- ture rises are smaller than would be expected on a purely thermal basis, and induction times are longer. In the chain-thermal region, the rate of self-heating immediately prior to ignition is not always rapid ; indeed, temperature excesses may be relatively steady or even decreasing when spon- taneous explosion takes place. We should expect similar behaviour in the hydrogen-oxygen reaction. Explosions in gaseous systems commonly arise either from branched radical-chain reactions that accelerate most isothermally, or from self-heating accompanying highly exothermic reaction. Recent studies of the explosive decomposition of chlorine dioxide have demonstrated that it is of the former type, ignitions occurring with little or no change in the temperature of the reacting gas.In contrast, the decompositions of diethyl peroxide and methyl nitrate,3 and the oxidations of hydrazine and mono- methylhydrazine all involve substantial self-heating both under non-explosive conditions and prior to explosion. The onset of ignition in these reaction^^-^ is thermally controlled, and their course is in excellent agreement with the predictions '-' of thermal explosion theory. Of course, not all gas-phase ignitions can be attributed to purely branched chain or purely thermal processes; attempts to separate the two may be misguided if in such cases the progress of the reaction is not dominated by either mechanism alone, but instead is the result of both chain and thermal effects.An important unification of thermal and branched-chain explosion theory was made by Gray and Yang.' They applied their ideas to the hydrogen + oxygen reaction and especially to the oscillatory reactions and other complexities found in the oxidation of hydrocarbons. Recent experimental investigation^'^-^^ have established the occurrence of significant t present address : Esso Research Centre, Abingdon, Berks. OX13 6AE. 2338P. GRAY AND M. E . SHERRINCTON 2339 temperature changes in hydrocarbon oxidations, and have shown that the complex behaviour observed cannot be interpreted in purely branched chain or purely thermal terms. It is the purpose of the present study to discover the extent to which self-heating contributes to the onset of explosive behaviour in the gas-phase oxidation of hydrogen sulphide, and to examine quantitatively the chain-thermal regime of the reaction.In many ways, the oxidation of hydrogen sulphide closely resembles that of hydrogen, and the more convenient conditions of temperature and pressure required for ignition make it particularly suitable for experimental investigation. Many of the features of the oxidation of hydrogen sulphide are also to be seen in the oxidations of am- monia ’ and carbon disulphide,16 so that information obtained in its investigation may assist in interpreting other reactions. Early work on hydrogen sulphide was primarily concerned with the location of explosion limits on a pressure against temperature diagram. The existence of what was taken to be a simple lower bound was established by several worker^,'^-^^ until Yakovlev and Shantarovich20 found another explosion region at yet lower pressurss.‘Their work 2o demonstrated the existence of three explosion limits over a range of temperature, and they mapped the “explosion peninsula” situated between the first and second limits. More recently, Marsden investigated the reaction mass- spectrometrically in the neighbourhood of the third limit. He concluded that S 2 0 was the most likely important branching intermediate, and except during explosion he found no evidence for diatomic SO. He also detected the formation of hydrogen prior to ignition. Gray and Yang’s unified theory * predicts qualitative differences in the develop- rnent of temperature rises between cases where both thermal and radical effects are important, and cases where reaction is thermally controlled.Principally, the maxi- mum temperature excesses compatible with stability are less when chain branching occurs than those expected from purely thermal theory, and the temperature evolution prior to ignition can show more varied forms. In a purely thermal explosion, the reactant temperature rises moderately at first, inflects, and then proceeds at an increasingly rapid rate, culminating in explosion. By contrast, a chain-thermal ignition may be preceded by a relatively steady, or even by a decreasing reactant temperature which persists until the discontinuous increase in temperature accom- panying explosion itself. Accordingly, in this work, temperatures and pressures are measured for the stoichionietric mixture 2 H2S + 3 O2 both near to the ignition limits and under other conditions.Interest is directed in particular to the nature, magnitude, and duration of explosive and non-explosive temperature against time histories. Attention is also paid to the effects of inert diluents on the explosion limits and to the variation of these limits with the reactant proportions, these results providing useful additional evidence in assessing the degree to which self-heating and radical processes combine to con- tribute to ignitions in this reaction. EXPERIMENTAL MATE R I A 1, S All gases were taken from cylinders. Hydrogen sulphide (Matheson Co.) was frozen under liquid nitrogen and degassed before use by trap-to-trap vacuum distillation.Oxygen, nitrogen and carbon dioxide (B.O.C. Ltd.) were dried by trapping water at -79°C. Helium, neon, argon, krypton (B.O.C. Ltd.) and hexafluoroethane (Matheson Co.) were used without further purification.2340 CHAIN-THERMAL IGNITION I N HzS COMBUSTION APPARATUS The reaction vessel was a Pyrex sphere (radius 41 mm, volume 0.29 dm3) heated in an electric furnace and thermostatted to better than 0.5"C. Measurements of reactant temperatures at the vessel centre during reaction were made by a very fine thermocouple constructed by butt welding 25 pm diameter platinum and platinum/l3 % rhodium wires (Johnson Matthey) to produce a junction less than 50 pm in size. The junction and supports were coated with silica to minimize catalytic effects. The thermocouple entered the vessel from above, along the vessel's vertical diameter, with its " hot "junction at the vessel centre ; the cold junction was kept at 0°C.Pressure measurements were made by a sensitive pressure transducer (Langham-Thompson UP 2), readings being accurate to & 1 Torr. Signals from the thermocouple and transducer were amplified and displayed on a storage oscilloscope (Tetronix 564 B). Temperature changes could be reproduced to better than _+ 1°C. The reaction vessel was connected to a conventional glass vacuum line by means of an electro- magnetic valve. Gas-pressure measurements in the vacuum line could be made either with a glass spiral gauge, or by means of a wide-bore mercury manometer. The spiral gauge was used where the gas pressure was less than 20 Torr ; otherwise, the mercury manometer was used and read with a cathetometer.PROCEDURE Gas mixtures of the required compositions were made up manometrically and allowed sufficient time (greater than 30 min) to mix completely. These mixtures were subsequently admitted to the evacuated vessel through the electromagnetic valve normally opened for 0.1 s ; opening the valve initiated measurements of temperature against time and pressure against time histories, which could be displayed simultaneously on the storage oscilloscope. Critical pressure limits for ignition at a particular vessel temperature were determined as the mean of the closest subcritical and supercritical reactant pressures that could be observed. The dependence of the critical ignition limit on vessel temperature, on the variation of the composition of the reactant mixture, and on the extent of dilution with inert gases was investigated.In general, the different ignition limits were sufficiently separate from each other for there to be no confusion over which particular limit was being determined. Difficulties were encountered only in the immediate vicinity of the " lobes " i.e. where dpldt-, GO. Subcritical temperature against time histories were followed for over 100 pairs of values of initial temperature and pressure in the non-explosive region of the ignition diagram, the maximum temperatures achieved always being recorded. Under supercritical conditions, interest centres both on the maximum temperatures achieved before ignition and on the qualitative form of the temperature against time histories for different initial conditions (p, T ) around the ignition boundary.RESULTS IGNITION I N STOICHIOMETRIC MIXTURES The most striking feature of the gas phase reaction in a stoichiometric mixture of hydrogen sulphide and oxygen is the existence, under certain conditions of vessel temperature, of multiple critical pressure limits separating explosive from non- explosive behaviour. As in the hydrogen + oxygen reaction there is first a low pressure limit p 1 above which the reaction is accelerated to explosion by degenerate branched radical chain processes alone. At higher pressures, a second limit p 2 is reached beyond which ignitions cease. This limit increases with increase in ambient tempera- ture. I t eventually merges with a third limit p 3 at the root of the explosion peninsula.The dependence of critical total pressures on ambient temperature for the stoichio- metric mixture, 2 H,S + 3 02, are shown in fig. 1. The points a, b, c, d indicated in this figure correspond to four characteristically different modes of behaviour.100 80 60 4 8 b 4 --.. 40 2 0 0 F+G. 1 .-Dependence of critical ignition pressure on vessel temperature for stoichiometric mixture 2H2S + 3 O2 ; induction periods (seconds) indicated by broken arrows. O L 0 I EXPLOSIONS 10 NON -EXPLOSIVE R EACTl ON EXPOSIONS I I I 20 30 40 50 60 %HzS FIG. 2.-Composition-dependence of second ( p z ) and third ( p 3 ) ignition limits for mixtures of hydro- gen sulphide and oxygen at 340°C.2342 CHAIN-THERMAL IGNITION IN H2S COMBUSTION All explosions are characterized by rapid (almost discontinuous) changes in both temperature and pressure, and at all but the very low pressures, explosions are accompanied by a visible flash.The light is generally easily observable, being pink in colour above the third limit but becoming both feebler and bluer as the ignition boundary is traversed, until near the first limit (less than 5 Torr) it is too feeble to be detected. The lengths of the periods vary with the initial conditions of pressure and temperature or position on the ignition diagram. Where self heating accompanies ignition, induction periods are generally short (1-3 s), while under isothermal conditions they are often very long (frequently in excess of 1-2 min), the length of the induction period increasing continuously along the ignition boundary from a to d.Typical values corresponding to marginally explosive conditions are indicated on fig. 1 . For pressures and tem- peratures near to the merging of the second and third limits (between b and c), induction periods are intermediate between the two extremes, ranging from 8-10 to around 20-30 s. All ignitions are preceded by induction periods. IGNITION LIMITS FOR NON-STOICHIOMETRIC MIXTURES The behaviour of the reactant mixture is dependent on its composition as well as on pressure and temperature, and to display it adequately, a three-dimensional ignition diagram is necessary. An extensive study was not attempted but fig. 2 shows the variation of the critical explosion pressure with mole percentage H2S along the second and third limits for an ambient temperature of 340°C.At the second limit, the critical pressure p 2 rises linearly with decreasing H2S content, explosion becoming progressively easier for increasingly lean mixtures. Similarly, explosion also becomes easier with decreasing H,S content along the third limit, p 3 falling rapidly at first but varying more slowly where the two limits p 2 and p 3 merge (ca. 23% H2S). Thus, at 340°C for mixtures containing marginally less than 23 % H2S, ignitions are observed over the entire pressure range. One aspect of the merging of the second and third limits is that, at a vessel temperature of 340°C and a reactant pressure 36 Torr, this composition represents the tip at which p 2 and p 3 coalesce.The behaviour of the third limit with respect to reactant composition in the oxidation of hydrogen sulphide contrasts markedly with the simpler behaviour found in the oxidation of methylhydrazine, where the critical ignition pressure passes through a minimum value situated between the stoichiometric and equimolar com- positions, and rises rapidly for mixtures much leaner than stoichiometric. In the oxidation of hydrogen sulphide however, the limitp, does not pass through a minimum value but continues to decrease past the stoichiometric composition (40 % H2S), right up to the point at which it merges with the second limit and explosion becomes inevitable. IGNITIONS IN DILUTED MIXTURES The effects of dilution by inert gas on the critical ignition pressures have been investigated at the third and second limits.(i) In the first type of experiment carried out, mixtures of hydrogen sulphide, oxygen and diluent in the ratio 2 :3 :3 were used, the third explosion limit being determined at different ambient temperatures. Three diluents were used, helium, neon and krypton, and the results are expressed in fig. 3 as a plot of the critical partial pressure of the reactants required for ignition, p(H,S) + p ( 0 2 ) against ambient temperature. Helium and neon increase the critical explosion pressure at the lowerP . GRAY A N D M . E. SHERRINGTON 2343 ambient temperatures (i.e. make explosion more difficult) but their effect diminishes with increase in temperature, and dilution with neon has very little effect near the merging of the second and third limits (around point b).Krypton lowers the critical explosion pressure, making explosion easier, and the lowering is marked all along the limit. Ta/"C FIG. 3.--Effect of dilution on critical partial pressure, p(H2S)+p(02), at the third limit for mixtures 2 H2S + 3 O2 + 3 diluent at various vessel temperatures. (0, helium, A, neon ; 9, krypton). I I I I I 1 I 0 10 20 30 40 50 60 70 % diluent FIG. 4.-Effect of dilution on critical partial pressure, p(H2S)+p(Oz), of second limit p z in mixtures 2 H2S+3 O2 +diluent. Ambient temperature 340°C. 0, helium ; A, argon ; 0, nitrogen ; 0, carbon dioxide ; x , hexafluoroethane.2344 CHAIN-THERMAL IGNITION I N H2S COMBUSTION (ii) In the second type of experiment, the dependence on dilution of the critical partial pressure for ignition p(H,S) +p(O,) was examined at the second limit for a constant ambient temperature of 340°C.Fig. 4 shows the effect of five diluents, helium, argon, nitrogen, carbon dioxide and hexafluoroethane. In all cases the explosive region contracts and explosion is made harder ; the second limit is lowered by dilution, the extent of the depression being approximately linear with degree of dilution. Helium and argon depress the limit least; carbon dioxide and hexa- fluoroethane depress it the most. EXTENT OF SELF-HEATING UNDER SUBCRITICAL CONDITIONS Over a hundred temperature against time histories have been recorded in the non- explosive region. Although both the magnitude and duration of the temperature histories vary widely under different initial conditions of temperature and pressure, certain basic features are common to them all.The thermocouple always registers a brief (ca. 0.1 s) initial cooling as the cold reactant mixture enters the hot vessel. The temperature then rises above that of the vessel and passes through a maximum value before returning to ambient as the reactants are consumed and the reaction is completed. 100 80 40 20 0 1 1 - 300 ,/ 320 34 0 360 TaI0C FIG. 5 .-Self heating accompanying oxidation of hydrogen sulphide. Stoichiometric mixture 2 H2S + 3 O2 Contour lines for temperature rises of 0, 10, 20, 30,40°C. L corresponds to predicted ignition limit from purely thermal theory. At the lower vessel temperatures (around 300°C) and near the third limit, the maximum temperature excess is high (over 40"C), but the reactants maintain this value only momentarily.Further along the limit, at higher vessel temperatures and lower pressures, the maximum self-heating observed just below the third limit de- creases, falling to values between 20 and 30°C near point b. Under these conditions the maximum excess is maintained by the system for several seconds. The degree of self-heating for different initial conditions is displayed in fig. 5 by contour lines corresponding to quasi-stationary temperature rises of AT = 10, 20, 30 and 40°C.P . GRAY AND M . E. SHERRINGTON 2345 The dotted contour line AT = 0 separates the isothermal and non-isothermal regimes. Clearly, both the isothermal and non-isothermal regimes are quite extensive. Self- heating is still observed around point c (see fig.1) under conditions normally described as near the second limit and where, classically, ignitions might have been ascribed to branched chain processes alone. At lower ambient temperatures (300-32OoC), departures from isothermal behaviour are readily observed under conditions well below the third limit ; marked temperature rises are still found for initial pressures of only one half the appropriate critical values. Farkas reported l9 the existence of temperature rises preceding ignition, i.e. above the third limit, but not in sub-critical systems. The inability of Thompson l7 to detect any self-heating in the non-explosive regime and his report of not more than 1 degree rise even after partial ignitions are probably to be attributed to his use of unsuitable temperature measuring equipment. Non-explosive Explosive 0 Ta = 296°C Pc = 83 torr 4 (a) (b) ? Ta = 343°C 5 Pc = 51 torr (4 u iz Ta = 352°C Pc = 34 torr (4 u Ta = 325°C 5 Pc = 12torr t L I I l L 155 ""t 501 t FIG.6.-Non-explosive and explosive temperature against time histories at the four points a, by c, d indicated on ignition diagram in fig. 1 (a and b are located on the third limit ; c and d on the second). SUPERCRITICAL AND SUBCRITICAL TEMPERATURE AGAINST TIME HISTORIES Supercritical mixtures show temperature against time histories prior to ignition initially similar in appearance and magnitude to those observed in corresponding subcritical cases. When ignitions occurred, whether above the third limit or between the first and second limits, they were all marked by a sudden discontinuous jump in temperature.Fig. 6 shows four pairs of temperature against time histories cor- responding respectively to pairs of points marginally above and below a, b, c and d Curves 6(a) are for low ambient temperatures and for high reactant pressure up around the third limit. The evolution of both the non-explosive and explosive of fig. 1.2346 CHAIN-THERMAL IGNITION I N H2S COMBUSTION temperature histories closely resembles purely thermally controlled behaviour. 2 , 5 The maximum stable temperature excess (ca. 45°C) is high, and the development of temperature just before explosion, accelerating the reaction to ignition is rapid. Curves 6(d) are for conditions situated at the lower part of the second limit.No temperature excess at all is observed in the non-explosive reaction, nor is there any rise in temperature prior to ignition in the explosive case. The temperature against time traces closely resemble the behaviour reported for the chlorine dioxide decomposi- tion and are typical of purely isothermal chain branching processes. Initial conditions correspond to points on fig. 1, situated close to the region where the second and third limits merge : b is on the upper portion, corresponding to the lowest part of the third limit and c on the lower portion, corresponding to the highest part of the second limit. At b, the reaction attains a steady temperature excess which in the explosive case is increasing only slowly right up to the moment of ignition.The magnitude of the maximum temperature excess attainable (ca. 2SOC) is smaller by some 3040% than would be predicted on a purely thermal basis. On the temperature record 6(c), the temperature excess is smaller still, the maximum value being only about 12°C; in the explosive case, the temperature has actually passed its maximum and is falling when explosion occurs. The temperature traces represented by curves 6(b) and 6(c) correspond to behaviour which cannot be satisfactorily explained on either a purely thermal or a purely chain basis; both mechanisms are contributing in varying degree to these ignitions. Curves 6(b) and 6(c) are quite different. DISCUSSION Previous work on the oxidation of hydrogen sulphide has concentrated on the explosion and the identification of intermediates responsible for chain-branching.The present experiments are in reasonable quantitative accord with earlier work 7-21 so far as the location of explosion limits, the variation of induction periods, and the effects of composition and diluents are concerned ; some specific comparisons are referred to below. The principal aim of the present study, however, is the evaluation of the relative contributions of physical and chemical processes to ignition. By the direct detection and measurement of temperature changes accompanying reaction we are able to define the conditions in which thermal factors or chain-branching factors can alone account for the observed behaviour, and to map the conditions in which neither mechanism is completely dominant but where both compete for control of stability of the reaction.The findings are important not only for this oxidation but for the kinetically related hydrogen + oxygen system. THE ISOTHERMAL REGION Beneath the zero self-heating contour line (AT = 0) of fig. 5, reaction is truly isothermal. This contour bounds a region that contains the entire first ignition limit, the ignition peninsula and most of the second limit. Throughout this region, iso- thermal branched chain reactions make the important contribution, and thermal effects play an insignificant role. This is also confirmed by the qualitative form of the temperature histories preceding ignitions [fig. 6(d) where ignition occurs without any previous self heating.] It is only near the uppermost part of the second limit, where the second and third limits merge, that any significant degree of self-heating is observed, and even there the limiting temperature excesses are small, typically only a few degrees centigrade.The effects of dilution at the second limit further support the conclusion that thermal factors have little to do with ignitions in this region.P . GRAY AND M. E. SHERRINGTON 2347 Ignition is made harder in all cases, the explosive domain contracting and the critical pressure being lowered in proportion to the amount of diluent added. The simple monatomic gases helium and argon have least effect on the limit, and the polyatomic gases carbon dioxide and hexafluoroethane have the greatest. These differences are to be interpreted 23 in terms of the different “third body’’ efficiency of the diluents.Any change in this efficiency in turn induces corresponding changes in the rate of homogeneous chain termination of the radical reactions. The addition of any inert gas increases termination, and polyatomic molecules, being more efficient as third bodies than monatomic molecules, have the greater relative effect on the lowering of the ignition limit, as is found here. Work by Davies and Walsh 24 confirms these results ; they report that the efficien- cies of diluents in lowering the second limit diminish in the order CO, > N, > He > Ar, and that the efficiencies decrease slightly as the temperature rises, but are relatively insensitive to reactant proportions. An estimate for the activation energy of chain-branching can be got from the temperature- dependence of the second limit RT2(d lnp,/dT) if this originates in varying com- petition between a chain branching reaction with activation energy Eb and a termina- tion process without activation energy (as may be assumed for the hydrogen + oxygen ignition diagram).Here, E2 is 122 kJ mol-’, significantly greater than the value of Yakovlev and Shantarovich.20 Under no circumstances is the limit raised. Detailed knowledge of the elementary reactions involved is still lacking. THE THIRD LIMIT AND THE EXTENT OF THERMAL CONTRIBUTIONS In contrast to the behaviour observed near the first and second explosion limits, reaction along the third limit is far from isothermal, and strong self-heating persists for conditions well removed from the limit itself.In view of the marked degree of self-heating, it is illuminating to contrast the measured critical ignition pressures with predictions derived from the theory 6*7 appropriate to purely thermal explosions. Simple conductive theory predicts that, along a thermal ignition limit, the dimension- less heat release rate 6 is a constant and that a graph of ln(p,,/T ;) against 1 /Ta should be a straight line of gradient E/2R, where pcr is the critical total ignition pressure at ambient temperature T,, and E is the effective activation energy of an isothermal reaction with second order pressure-dependence overall. Fig. 7 shows how the conditions at the third limit for the ignition of 2 H,S + 3 0, obey this relation for the higher pressures and lower temperatures, and how the limit deviates from linearity as the temperature increases and the critical pressure falls.The deviation of the limit from thermal prediction is discernible at temperatures above 310°C. This deviation may be thought to reflect the extent to which chain processes become progressively more important as the temperature rises and the third limit approaches the explosion peninsula. From the linear portion of the graph in fig. 7 we derive a value for the activa- tion energy E3 of 98+5 kJ mol-l. Earlier workers 1 7 v 1 * reported values of 80 to 84 kJ mol-l for E3, but the discrepancy is not significant because they forced their lines through points corresponding to the root of the peninsula where chain-branching contributions are present.The broken line L on figure 5 corresponds to the straight line portion of fig. 7. At and above L, ignitions can be interpreted on a purely thermal basis; beneath it, ignition is increasingly influenced by branched chain reactions. These influences are reflected in (i) the response to variations in reactant proportions (ii) the influence of dilution by inert gases.2348 CHAIN-THERMAL IGNITION I N H2S COMBUSTION The effects of reactant composition on the ignition pressure have been described for an ambient temperature of 340°C. based on purely thermal factors 6*7 would suggest that on passing from hydrogen sulphide-rich to hydrogen sulphide-lean mixtures the critical ignition pressure should fall to a minimum value and then begin to rise again.Observed behaviour is significantly different from this. The ignition pressure ( p 3 ) is seen to decrease past stoichiometric (40% H2S) to the point where it merges with the second limit ( p 2 ) and explosion becomes inevitable. This behaviour in lean mixtures reflects the changing nature of the limit ; as the hydrogen sulphide content decreases so the chain influence becomes pro- gressively more marked until, at the composition (ca. 23 %) conditions that correspond to the root of the peninsula, the second and third limits meet. Simple considerations 0.6 n 2 4 --.- W CI 0.4 0.2 1 .o 0.8 - - - - - - - NON-LINEARITY DUE TO THE SECOND LIMIT I .66 1.70 I .74 I .7a lo3 KITa In (pc/T,2) on 1 ITa is linear on purely thermal theory.) FIG. 7.-Predicted and observed temperature dependence of third ignition limit.(Dependence of The effects of dilution on the critical ignition pressures also reflect the changing nature. The three diluents were chosen because of their widely different thermal conductivities. According to a stationary state treatment,7 the effect of diluents on purely thermal explosion is to make the explosion easier or more difficult according to whether the overall conductivity A of the gaseous mixture is lowered or raised : pCrccA. As expected, helium and neon, with high thermal conductivity, make ex- plosion harder at the lower temperatures and higher pressures, but further along the ignition limit where thermal influences are less their effect is quite small. Krypton lowers the limit over a wider range, possibly because it makes thermal explosion easier {lowers p 3 ) and terminates branched chains effectively (lowers p z ) .P .GRAY AND M. E . SHERRINGTON 2349 THE CHAIN-THERMAL REGIME The boundaries of the isothermal region and of the pure thermal ignition have been discussed above. Between them lies the region where both chain-branching and thermal contributions are important, and whose description and interpretation require the framework of unified treatment. Certain interactions, indirectly observed, between chain and thermal processes have been touched on already; two further features of ignition deserve emphasis here; both are derived from direct temperature measurements. The first is the reduction in the stably attainable temperature rise ATcr accompanying exothermic oxidation along the ther- mal limit ; the second is the qualitative difference in temperature against time histories preceding ignition nearer to the isothermal limit.(i) According to simple stationary conductive t h e ~ r y , ~ maximum stable tempera- ture excesses in a spherical vessel of about 1.61 RT;/E are allowed ; the excess expected rises to about 1.85 RT,2/E when consumption of reactants 25 is considered. Accepting the value of the activation energy derived from the linear portion of the plot in fig. 7, this corresponds to predicted critical temperature rises of about 45 to 50°C at T, = 3OO0C, in good agreement with the maximum stable rises experimentally observed near to point a. On simple theory, the critical excesses should increase monotonically (as T,2) with increase in ambient temperature around the ignition boundary.Fig. 5 indicates that the converse occurs : temperature excesses never reach such values ; at T, = 340°C, near point b, the highest sub-critical excess so far observed is only 28”C, around half that suggested on thermal grounds. The dis- crepancy increases around the boundary; near point c only a 12°C excess can be realized. Both are readily located. (ii) Temperatures also vary differently with time from the lively accelerations that are a prelude to purely thermal explosions : instead they may rise only sluggishly, be relatively steady or even decrease, as is the case near point c. on the unification of thermal and chain-branching theories of explosions, Gray and Yang outline qualitatively the results which have here been observed quantitatively in the oxidation of hydrogen sulphide.In the chain-thermal region of the reaction we are, by definition, concerned with the regime in which the two different mechanisms compete for control, and in many ways the combined effects reflect the compromise. Maximum stable temperature rises are predicted 26 and found to be markedly below their purely thermal counterparts, and the entire temperature development is slower paced. In particular, induction times are much longer than in purely thermal explosion, being typically of the order of 10-30 s, though these values are significantly shorter than the induction periods observed in the purely isothermal regime. The temperature excesses immediately preceding ignition are often surprisingly steady and the temperature “jumps” occur suddenly with little or no additional self-heating. Indeed, in the region where the second and third limits merge the reactant temperature is falling when ignition occurs.The contribution to the explosion under such conditions by branched chain radical processes is clearly very great. Similar behaviour might be expected near the second limit in the hydrogen + oxygen reaction but although falling temperatures before ignition have been reported 2 2 they appear to be the artificial consequence of the conventional “withdrawal” technique used to locate the limit : reactant temperatures fall by adiabatic expansion. In their original paper A re-investigation of this system would be timely.We are grateful to S.R.C. for the award of a studentship to M.E.S.2350 CHAIN-THERMAL IGNITION I N H2S COMBUSTION P. Gray and J. K. K. Ip, Combustion and Flame, 1972, 18, 361. D. H. Fine, P. Gray and R. MacKinven, Proc. Roy. SOC. A , 1970, 316, 223, 241 and 255; P. Gray, D. T. Jones and R. MacKinven, Proc. Roy. SOC. A , 1971,325, 175. H. Goodman, P. Gray and D. T. Jones, Combustion and Flame, 1972, 19, 157. P. Gray and E. B. O'Neill, Trans. Faraday ,Yoc., 1972, 68, 564. P. Gray and M. E. Sherrington, J.C.S. Faraday Z, 1974, 70, 740. N. N. Semenov, Chemical Kinetics and Chain Reactions (Oxford U. P., Oxford, 1st edn., 1935). D. A. Frank-Kamenetskii, Diflusion and Heat Exchange in Chemical Kinetics (Plenum, New York, 2nd edn., 1969). B. F. Gray and C. H.Yang, J. Phys. Chem., 1965, 69, 2747. B. F. Gray and C. H. Yang, 11th Symp. (Znt.) Combustion (Combustion lnst., Pittsburgh, 1967), p. 1099. l o C . H. Yang and B. F. Gray, J. Phys. Clrern., 1969, 73, 3395. B. F. Gray and C. H. Yang, Trans. Farnday SOC., 1969, 65, 1553, 1614. j 2 J. H. Knox and R. G. W. Norrish, Trans. Fauaday SOC., 1954, 50, 928. l 3 R. Hughes and R. F. Simmons, Combustion atid Flame, 1970, 14, 103. l4 J. F. Griffiths, P. Gray and P. G . Felton, 14fh Synzp. ( h t . ) Combustion (Combustion lnst., l5 J. N. Bradley, Trans. Fauaday Snc., 1967, 63, 2945, l6 A. L. Myerson and F. R. Taylor, J. Anzer. Clzem. Soc., 1953, 75, 4345. l 7 H. A. Taylor and E. M. Livingston, J. Chem. Plzys., 1931, 35, 2676. l 9 L. Farkas, 2. Elektrochem., 1931, 37, 670. 2o B.Yakovlev and P. Shantarovich, Acta Physicochim. U.S.S.K., 1937, 6, 71. 2 1 D. G. H. Marsden, Canad. J. Chem., 1963, 41, 2607. 22 J. A. Barnard and A. G. Platts, Combustion Sci. Tech., 1972, 6, 133. 23 W. Jost, Low Temperature Oxidation (Gordon and Breach, New York, 1965). *' D. A. Davies and A. D. Walsh, 14th Symp. ( h t . ) Combustion (Combustion Inst., Pittsburgh, 25 B. J. Tyler and T. A. B. Wesley, 11th Symp. (Int.) Cornbustion (Combustion Inst., Pittsburgh, 26B. F. Gray, Trans. Fmadzy SDC., 1969, 65, 2133. Pittsburgh, 1972), p. 453. H. W. Thompson and N. Kelland, J. Chenz. Soc., 1931, 1809. 1973), p. 475. 1967), p. 1115. Explosive Oxidation of Hydrogen Sulphide : Self-heating, Chain-branching and Chain-thermal Contributions to Spontaneous Ignition BY PETER GRAY AND MALCOLM E.SHERRINGTON*T School of Chemistry, The University, Leeds LS2 9JT Received 7th March, 1974 The spontaneously explosive oxidation of hydrogen sulphide in a 290 cm3 vessel has been in- vestigated over a temperature range 280-360°C and between pressures of 10 and 120 mmHg. Con- ditions for ignition have been mapped on ap,Tdiagram. Very fine thermocouples (25 pm Pt-Pt/Rh) have been used to detect and measure self-heating, and special emphasis has been laid on the direct measurement of the size and form of the temperature against time histories for different initial con- ditions or locations on the ignition diagram. The effects of reactant proportions and of added diluents (with different thermal conductivities) on the second and third ignition limits have also been studied.Although the reaction exhibits many features traditionally associated with purely branched chain explosions, the direct temperature measurements have revealed extensive self-heating under very varied conditions of pressure and temperature. Boundaries may be drawn on the ignition diagram that separate the regions where a combined chain-thermal mechanism is responsible for explosions (I) from those which may be considered as purely thermal (11) or isothermal branched chain (111) in nature. The measured temperature against time histories provide novel experimental support for the unified theoretical treatment of chain and thermal explosions of Gray and Yang. Critical tempera- ture rises are smaller than would be expected on a purely thermal basis, and induction times are longer.In the chain-thermal region, the rate of self-heating immediately prior to ignition is not always rapid ; indeed, temperature excesses may be relatively steady or even decreasing when spon- taneous explosion takes place. We should expect similar behaviour in the hydrogen-oxygen reaction. Explosions in gaseous systems commonly arise either from branched radical-chain reactions that accelerate most isothermally, or from self-heating accompanying highly exothermic reaction. Recent studies of the explosive decomposition of chlorine dioxide have demonstrated that it is of the former type, ignitions occurring with little or no change in the temperature of the reacting gas. In contrast, the decompositions of diethyl peroxide and methyl nitrate,3 and the oxidations of hydrazine and mono- methylhydrazine all involve substantial self-heating both under non-explosive conditions and prior to explosion.The onset of ignition in these reaction^^-^ is thermally controlled, and their course is in excellent agreement with the predictions '-' of thermal explosion theory. Of course, not all gas-phase ignitions can be attributed to purely branched chain or purely thermal processes; attempts to separate the two may be misguided if in such cases the progress of the reaction is not dominated by either mechanism alone, but instead is the result of both chain and thermal effects. An important unification of thermal and branched-chain explosion theory was made by Gray and Yang.' They applied their ideas to the hydrogen + oxygen reaction and especially to the oscillatory reactions and other complexities found in the oxidation of hydrocarbons.Recent experimental investigation^'^-^^ have established the occurrence of significant t present address : Esso Research Centre, Abingdon, Berks. OX13 6AE. 2338P. GRAY AND M. E . SHERRINCTON 2339 temperature changes in hydrocarbon oxidations, and have shown that the complex behaviour observed cannot be interpreted in purely branched chain or purely thermal terms. It is the purpose of the present study to discover the extent to which self-heating contributes to the onset of explosive behaviour in the gas-phase oxidation of hydrogen sulphide, and to examine quantitatively the chain-thermal regime of the reaction. In many ways, the oxidation of hydrogen sulphide closely resembles that of hydrogen, and the more convenient conditions of temperature and pressure required for ignition make it particularly suitable for experimental investigation.Many of the features of the oxidation of hydrogen sulphide are also to be seen in the oxidations of am- monia ’ and carbon disulphide,16 so that information obtained in its investigation may assist in interpreting other reactions. Early work on hydrogen sulphide was primarily concerned with the location of explosion limits on a pressure against temperature diagram. The existence of what was taken to be a simple lower bound was established by several worker^,'^-^^ until Yakovlev and Shantarovich20 found another explosion region at yet lower pressurss.‘Their work 2o demonstrated the existence of three explosion limits over a range of temperature, and they mapped the “explosion peninsula” situated between the first and second limits. More recently, Marsden investigated the reaction mass- spectrometrically in the neighbourhood of the third limit. He concluded that S 2 0 was the most likely important branching intermediate, and except during explosion he found no evidence for diatomic SO. He also detected the formation of hydrogen prior to ignition. Gray and Yang’s unified theory * predicts qualitative differences in the develop- rnent of temperature rises between cases where both thermal and radical effects are important, and cases where reaction is thermally controlled. Principally, the maxi- mum temperature excesses compatible with stability are less when chain branching occurs than those expected from purely thermal theory, and the temperature evolution prior to ignition can show more varied forms. In a purely thermal explosion, the reactant temperature rises moderately at first, inflects, and then proceeds at an increasingly rapid rate, culminating in explosion.By contrast, a chain-thermal ignition may be preceded by a relatively steady, or even by a decreasing reactant temperature which persists until the discontinuous increase in temperature accom- panying explosion itself. Accordingly, in this work, temperatures and pressures are measured for the stoichionietric mixture 2 H2S + 3 O2 both near to the ignition limits and under other conditions. Interest is directed in particular to the nature, magnitude, and duration of explosive and non-explosive temperature against time histories.Attention is also paid to the effects of inert diluents on the explosion limits and to the variation of these limits with the reactant proportions, these results providing useful additional evidence in assessing the degree to which self-heating and radical processes combine to con- tribute to ignitions in this reaction. EXPERIMENTAL MATE R I A 1, S All gases were taken from cylinders. Hydrogen sulphide (Matheson Co.) was frozen under liquid nitrogen and degassed before use by trap-to-trap vacuum distillation. Oxygen, nitrogen and carbon dioxide (B.O.C. Ltd.) were dried by trapping water at -79°C. Helium, neon, argon, krypton (B.O.C.Ltd.) and hexafluoroethane (Matheson Co.) were used without further purification.2340 CHAIN-THERMAL IGNITION I N HzS COMBUSTION APPARATUS The reaction vessel was a Pyrex sphere (radius 41 mm, volume 0.29 dm3) heated in an electric furnace and thermostatted to better than 0.5"C. Measurements of reactant temperatures at the vessel centre during reaction were made by a very fine thermocouple constructed by butt welding 25 pm diameter platinum and platinum/l3 % rhodium wires (Johnson Matthey) to produce a junction less than 50 pm in size. The junction and supports were coated with silica to minimize catalytic effects. The thermocouple entered the vessel from above, along the vessel's vertical diameter, with its " hot "junction at the vessel centre ; the cold junction was kept at 0°C.Pressure measurements were made by a sensitive pressure transducer (Langham-Thompson UP 2), readings being accurate to & 1 Torr. Signals from the thermocouple and transducer were amplified and displayed on a storage oscilloscope (Tetronix 564 B). Temperature changes could be reproduced to better than _+ 1°C. The reaction vessel was connected to a conventional glass vacuum line by means of an electro- magnetic valve. Gas-pressure measurements in the vacuum line could be made either with a glass spiral gauge, or by means of a wide-bore mercury manometer. The spiral gauge was used where the gas pressure was less than 20 Torr ; otherwise, the mercury manometer was used and read with a cathetometer. PROCEDURE Gas mixtures of the required compositions were made up manometrically and allowed sufficient time (greater than 30 min) to mix completely.These mixtures were subsequently admitted to the evacuated vessel through the electromagnetic valve normally opened for 0.1 s ; opening the valve initiated measurements of temperature against time and pressure against time histories, which could be displayed simultaneously on the storage oscilloscope. Critical pressure limits for ignition at a particular vessel temperature were determined as the mean of the closest subcritical and supercritical reactant pressures that could be observed. The dependence of the critical ignition limit on vessel temperature, on the variation of the composition of the reactant mixture, and on the extent of dilution with inert gases was investigated.In general, the different ignition limits were sufficiently separate from each other for there to be no confusion over which particular limit was being determined. Difficulties were encountered only in the immediate vicinity of the " lobes " i.e. where dpldt-, GO. Subcritical temperature against time histories were followed for over 100 pairs of values of initial temperature and pressure in the non-explosive region of the ignition diagram, the maximum temperatures achieved always being recorded. Under supercritical conditions, interest centres both on the maximum temperatures achieved before ignition and on the qualitative form of the temperature against time histories for different initial conditions (p, T ) around the ignition boundary. RESULTS IGNITION I N STOICHIOMETRIC MIXTURES The most striking feature of the gas phase reaction in a stoichiometric mixture of hydrogen sulphide and oxygen is the existence, under certain conditions of vessel temperature, of multiple critical pressure limits separating explosive from non- explosive behaviour.As in the hydrogen + oxygen reaction there is first a low pressure limit p 1 above which the reaction is accelerated to explosion by degenerate branched radical chain processes alone. At higher pressures, a second limit p 2 is reached beyond which ignitions cease. This limit increases with increase in ambient tempera- ture. I t eventually merges with a third limit p 3 at the root of the explosion peninsula. The dependence of critical total pressures on ambient temperature for the stoichio- metric mixture, 2 H,S + 3 02, are shown in fig.1. The points a, b, c, d indicated in this figure correspond to four characteristically different modes of behaviour.100 80 60 4 8 b 4 --.. 40 2 0 0 F+G. 1 .-Dependence of critical ignition pressure on vessel temperature for stoichiometric mixture 2H2S + 3 O2 ; induction periods (seconds) indicated by broken arrows. O L 0 I EXPLOSIONS 10 NON -EXPLOSIVE R EACTl ON EXPOSIONS I I I 20 30 40 50 60 %HzS FIG. 2.-Composition-dependence of second ( p z ) and third ( p 3 ) ignition limits for mixtures of hydro- gen sulphide and oxygen at 340°C.2342 CHAIN-THERMAL IGNITION IN H2S COMBUSTION All explosions are characterized by rapid (almost discontinuous) changes in both temperature and pressure, and at all but the very low pressures, explosions are accompanied by a visible flash.The light is generally easily observable, being pink in colour above the third limit but becoming both feebler and bluer as the ignition boundary is traversed, until near the first limit (less than 5 Torr) it is too feeble to be detected. The lengths of the periods vary with the initial conditions of pressure and temperature or position on the ignition diagram. Where self heating accompanies ignition, induction periods are generally short (1-3 s), while under isothermal conditions they are often very long (frequently in excess of 1-2 min), the length of the induction period increasing continuously along the ignition boundary from a to d. Typical values corresponding to marginally explosive conditions are indicated on fig.1 . For pressures and tem- peratures near to the merging of the second and third limits (between b and c), induction periods are intermediate between the two extremes, ranging from 8-10 to around 20-30 s. All ignitions are preceded by induction periods. IGNITION LIMITS FOR NON-STOICHIOMETRIC MIXTURES The behaviour of the reactant mixture is dependent on its composition as well as on pressure and temperature, and to display it adequately, a three-dimensional ignition diagram is necessary. An extensive study was not attempted but fig. 2 shows the variation of the critical explosion pressure with mole percentage H2S along the second and third limits for an ambient temperature of 340°C. At the second limit, the critical pressure p 2 rises linearly with decreasing H2S content, explosion becoming progressively easier for increasingly lean mixtures.Similarly, explosion also becomes easier with decreasing H,S content along the third limit, p 3 falling rapidly at first but varying more slowly where the two limits p 2 and p 3 merge (ca. 23% H2S). Thus, at 340°C for mixtures containing marginally less than 23 % H2S, ignitions are observed over the entire pressure range. One aspect of the merging of the second and third limits is that, at a vessel temperature of 340°C and a reactant pressure 36 Torr, this composition represents the tip at which p 2 and p 3 coalesce. The behaviour of the third limit with respect to reactant composition in the oxidation of hydrogen sulphide contrasts markedly with the simpler behaviour found in the oxidation of methylhydrazine, where the critical ignition pressure passes through a minimum value situated between the stoichiometric and equimolar com- positions, and rises rapidly for mixtures much leaner than stoichiometric. In the oxidation of hydrogen sulphide however, the limitp, does not pass through a minimum value but continues to decrease past the stoichiometric composition (40 % H2S), right up to the point at which it merges with the second limit and explosion becomes inevitable.IGNITIONS IN DILUTED MIXTURES The effects of dilution by inert gas on the critical ignition pressures have been investigated at the third and second limits. (i) In the first type of experiment carried out, mixtures of hydrogen sulphide, oxygen and diluent in the ratio 2 :3 :3 were used, the third explosion limit being determined at different ambient temperatures.Three diluents were used, helium, neon and krypton, and the results are expressed in fig. 3 as a plot of the critical partial pressure of the reactants required for ignition, p(H,S) + p ( 0 2 ) against ambient temperature. Helium and neon increase the critical explosion pressure at the lowerP . GRAY A N D M . E. SHERRINGTON 2343 ambient temperatures (i.e. make explosion more difficult) but their effect diminishes with increase in temperature, and dilution with neon has very little effect near the merging of the second and third limits (around point b). Krypton lowers the critical explosion pressure, making explosion easier, and the lowering is marked all along the limit.Ta/"C FIG. 3.--Effect of dilution on critical partial pressure, p(H2S)+p(02), at the third limit for mixtures 2 H2S + 3 O2 + 3 diluent at various vessel temperatures. (0, helium, A, neon ; 9, krypton). I I I I I 1 I 0 10 20 30 40 50 60 70 % diluent FIG. 4.-Effect of dilution on critical partial pressure, p(H2S)+p(Oz), of second limit p z in mixtures 2 H2S+3 O2 +diluent. Ambient temperature 340°C. 0, helium ; A, argon ; 0, nitrogen ; 0, carbon dioxide ; x , hexafluoroethane.2344 CHAIN-THERMAL IGNITION I N H2S COMBUSTION (ii) In the second type of experiment, the dependence on dilution of the critical partial pressure for ignition p(H,S) +p(O,) was examined at the second limit for a constant ambient temperature of 340°C.Fig. 4 shows the effect of five diluents, helium, argon, nitrogen, carbon dioxide and hexafluoroethane. In all cases the explosive region contracts and explosion is made harder ; the second limit is lowered by dilution, the extent of the depression being approximately linear with degree of dilution. Helium and argon depress the limit least; carbon dioxide and hexa- fluoroethane depress it the most. EXTENT OF SELF-HEATING UNDER SUBCRITICAL CONDITIONS Over a hundred temperature against time histories have been recorded in the non- explosive region. Although both the magnitude and duration of the temperature histories vary widely under different initial conditions of temperature and pressure, certain basic features are common to them all. The thermocouple always registers a brief (ca.0.1 s) initial cooling as the cold reactant mixture enters the hot vessel. The temperature then rises above that of the vessel and passes through a maximum value before returning to ambient as the reactants are consumed and the reaction is completed. 100 80 40 20 0 1 1 - 300 ,/ 320 34 0 360 TaI0C FIG. 5 .-Self heating accompanying oxidation of hydrogen sulphide. Stoichiometric mixture 2 H2S + 3 O2 Contour lines for temperature rises of 0, 10, 20, 30,40°C. L corresponds to predicted ignition limit from purely thermal theory. At the lower vessel temperatures (around 300°C) and near the third limit, the maximum temperature excess is high (over 40"C), but the reactants maintain this value only momentarily. Further along the limit, at higher vessel temperatures and lower pressures, the maximum self-heating observed just below the third limit de- creases, falling to values between 20 and 30°C near point b.Under these conditions the maximum excess is maintained by the system for several seconds. The degree of self-heating for different initial conditions is displayed in fig. 5 by contour lines corresponding to quasi-stationary temperature rises of AT = 10, 20, 30 and 40°C.P . GRAY AND M . E. SHERRINGTON 2345 The dotted contour line AT = 0 separates the isothermal and non-isothermal regimes. Clearly, both the isothermal and non-isothermal regimes are quite extensive. Self- heating is still observed around point c (see fig. 1) under conditions normally described as near the second limit and where, classically, ignitions might have been ascribed to branched chain processes alone.At lower ambient temperatures (300-32OoC), departures from isothermal behaviour are readily observed under conditions well below the third limit ; marked temperature rises are still found for initial pressures of only one half the appropriate critical values. Farkas reported l9 the existence of temperature rises preceding ignition, i.e. above the third limit, but not in sub-critical systems. The inability of Thompson l7 to detect any self-heating in the non-explosive regime and his report of not more than 1 degree rise even after partial ignitions are probably to be attributed to his use of unsuitable temperature measuring equipment. Non-explosive Explosive 0 Ta = 296°C Pc = 83 torr 4 (a) (b) ? Ta = 343°C 5 Pc = 51 torr (4 u iz Ta = 352°C Pc = 34 torr (4 u Ta = 325°C 5 Pc = 12torr t L I I l L 155 ""t 501 t FIG.6.-Non-explosive and explosive temperature against time histories at the four points a, by c, d indicated on ignition diagram in fig. 1 (a and b are located on the third limit ; c and d on the second). SUPERCRITICAL AND SUBCRITICAL TEMPERATURE AGAINST TIME HISTORIES Supercritical mixtures show temperature against time histories prior to ignition initially similar in appearance and magnitude to those observed in corresponding subcritical cases. When ignitions occurred, whether above the third limit or between the first and second limits, they were all marked by a sudden discontinuous jump in temperature. Fig. 6 shows four pairs of temperature against time histories cor- responding respectively to pairs of points marginally above and below a, b, c and d Curves 6(a) are for low ambient temperatures and for high reactant pressure up around the third limit.The evolution of both the non-explosive and explosive of fig. 1.2346 CHAIN-THERMAL IGNITION I N H2S COMBUSTION temperature histories closely resembles purely thermally controlled behaviour. 2 , 5 The maximum stable temperature excess (ca. 45°C) is high, and the development of temperature just before explosion, accelerating the reaction to ignition is rapid. Curves 6(d) are for conditions situated at the lower part of the second limit. No temperature excess at all is observed in the non-explosive reaction, nor is there any rise in temperature prior to ignition in the explosive case.The temperature against time traces closely resemble the behaviour reported for the chlorine dioxide decomposi- tion and are typical of purely isothermal chain branching processes. Initial conditions correspond to points on fig. 1, situated close to the region where the second and third limits merge : b is on the upper portion, corresponding to the lowest part of the third limit and c on the lower portion, corresponding to the highest part of the second limit. At b, the reaction attains a steady temperature excess which in the explosive case is increasing only slowly right up to the moment of ignition. The magnitude of the maximum temperature excess attainable (ca. 2SOC) is smaller by some 3040% than would be predicted on a purely thermal basis.On the temperature record 6(c), the temperature excess is smaller still, the maximum value being only about 12°C; in the explosive case, the temperature has actually passed its maximum and is falling when explosion occurs. The temperature traces represented by curves 6(b) and 6(c) correspond to behaviour which cannot be satisfactorily explained on either a purely thermal or a purely chain basis; both mechanisms are contributing in varying degree to these ignitions. Curves 6(b) and 6(c) are quite different. DISCUSSION Previous work on the oxidation of hydrogen sulphide has concentrated on the explosion and the identification of intermediates responsible for chain-branching. The present experiments are in reasonable quantitative accord with earlier work 7-21 so far as the location of explosion limits, the variation of induction periods, and the effects of composition and diluents are concerned ; some specific comparisons are referred to below.The principal aim of the present study, however, is the evaluation of the relative contributions of physical and chemical processes to ignition. By the direct detection and measurement of temperature changes accompanying reaction we are able to define the conditions in which thermal factors or chain-branching factors can alone account for the observed behaviour, and to map the conditions in which neither mechanism is completely dominant but where both compete for control of stability of the reaction. The findings are important not only for this oxidation but for the kinetically related hydrogen + oxygen system.THE ISOTHERMAL REGION Beneath the zero self-heating contour line (AT = 0) of fig. 5, reaction is truly isothermal. This contour bounds a region that contains the entire first ignition limit, the ignition peninsula and most of the second limit. Throughout this region, iso- thermal branched chain reactions make the important contribution, and thermal effects play an insignificant role. This is also confirmed by the qualitative form of the temperature histories preceding ignitions [fig. 6(d) where ignition occurs without any previous self heating.] It is only near the uppermost part of the second limit, where the second and third limits merge, that any significant degree of self-heating is observed, and even there the limiting temperature excesses are small, typically only a few degrees centigrade.The effects of dilution at the second limit further support the conclusion that thermal factors have little to do with ignitions in this region.P . GRAY AND M. E. SHERRINGTON 2347 Ignition is made harder in all cases, the explosive domain contracting and the critical pressure being lowered in proportion to the amount of diluent added. The simple monatomic gases helium and argon have least effect on the limit, and the polyatomic gases carbon dioxide and hexafluoroethane have the greatest. These differences are to be interpreted 23 in terms of the different “third body’’ efficiency of the diluents. Any change in this efficiency in turn induces corresponding changes in the rate of homogeneous chain termination of the radical reactions.The addition of any inert gas increases termination, and polyatomic molecules, being more efficient as third bodies than monatomic molecules, have the greater relative effect on the lowering of the ignition limit, as is found here. Work by Davies and Walsh 24 confirms these results ; they report that the efficien- cies of diluents in lowering the second limit diminish in the order CO, > N, > He > Ar, and that the efficiencies decrease slightly as the temperature rises, but are relatively insensitive to reactant proportions. An estimate for the activation energy of chain-branching can be got from the temperature- dependence of the second limit RT2(d lnp,/dT) if this originates in varying com- petition between a chain branching reaction with activation energy Eb and a termina- tion process without activation energy (as may be assumed for the hydrogen + oxygen ignition diagram).Here, E2 is 122 kJ mol-’, significantly greater than the value of Yakovlev and Shantarovich.20 Under no circumstances is the limit raised. Detailed knowledge of the elementary reactions involved is still lacking. THE THIRD LIMIT AND THE EXTENT OF THERMAL CONTRIBUTIONS In contrast to the behaviour observed near the first and second explosion limits, reaction along the third limit is far from isothermal, and strong self-heating persists for conditions well removed from the limit itself. In view of the marked degree of self-heating, it is illuminating to contrast the measured critical ignition pressures with predictions derived from the theory 6*7 appropriate to purely thermal explosions.Simple conductive theory predicts that, along a thermal ignition limit, the dimension- less heat release rate 6 is a constant and that a graph of ln(p,,/T ;) against 1 /Ta should be a straight line of gradient E/2R, where pcr is the critical total ignition pressure at ambient temperature T,, and E is the effective activation energy of an isothermal reaction with second order pressure-dependence overall. Fig. 7 shows how the conditions at the third limit for the ignition of 2 H,S + 3 0, obey this relation for the higher pressures and lower temperatures, and how the limit deviates from linearity as the temperature increases and the critical pressure falls.The deviation of the limit from thermal prediction is discernible at temperatures above 310°C. This deviation may be thought to reflect the extent to which chain processes become progressively more important as the temperature rises and the third limit approaches the explosion peninsula. From the linear portion of the graph in fig. 7 we derive a value for the activa- tion energy E3 of 98+5 kJ mol-l. Earlier workers 1 7 v 1 * reported values of 80 to 84 kJ mol-l for E3, but the discrepancy is not significant because they forced their lines through points corresponding to the root of the peninsula where chain-branching contributions are present. The broken line L on figure 5 corresponds to the straight line portion of fig. 7. At and above L, ignitions can be interpreted on a purely thermal basis; beneath it, ignition is increasingly influenced by branched chain reactions.These influences are reflected in (i) the response to variations in reactant proportions (ii) the influence of dilution by inert gases.2348 CHAIN-THERMAL IGNITION I N H2S COMBUSTION The effects of reactant composition on the ignition pressure have been described for an ambient temperature of 340°C. based on purely thermal factors 6*7 would suggest that on passing from hydrogen sulphide-rich to hydrogen sulphide-lean mixtures the critical ignition pressure should fall to a minimum value and then begin to rise again. Observed behaviour is significantly different from this. The ignition pressure ( p 3 ) is seen to decrease past stoichiometric (40% H2S) to the point where it merges with the second limit ( p 2 ) and explosion becomes inevitable.This behaviour in lean mixtures reflects the changing nature of the limit ; as the hydrogen sulphide content decreases so the chain influence becomes pro- gressively more marked until, at the composition (ca. 23 %) conditions that correspond to the root of the peninsula, the second and third limits meet. Simple considerations 0.6 n 2 4 --.- W CI 0.4 0.2 1 .o 0.8 - - - - - - - NON-LINEARITY DUE TO THE SECOND LIMIT I .66 1.70 I .74 I .7a lo3 KITa In (pc/T,2) on 1 ITa is linear on purely thermal theory.) FIG. 7.-Predicted and observed temperature dependence of third ignition limit. (Dependence of The effects of dilution on the critical ignition pressures also reflect the changing nature. The three diluents were chosen because of their widely different thermal conductivities.According to a stationary state treatment,7 the effect of diluents on purely thermal explosion is to make the explosion easier or more difficult according to whether the overall conductivity A of the gaseous mixture is lowered or raised : pCrccA. As expected, helium and neon, with high thermal conductivity, make ex- plosion harder at the lower temperatures and higher pressures, but further along the ignition limit where thermal influences are less their effect is quite small. Krypton lowers the limit over a wider range, possibly because it makes thermal explosion easier {lowers p 3 ) and terminates branched chains effectively (lowers p z ) .P .GRAY AND M. E . SHERRINGTON 2349 THE CHAIN-THERMAL REGIME The boundaries of the isothermal region and of the pure thermal ignition have been discussed above. Between them lies the region where both chain-branching and thermal contributions are important, and whose description and interpretation require the framework of unified treatment. Certain interactions, indirectly observed, between chain and thermal processes have been touched on already; two further features of ignition deserve emphasis here; both are derived from direct temperature measurements. The first is the reduction in the stably attainable temperature rise ATcr accompanying exothermic oxidation along the ther- mal limit ; the second is the qualitative difference in temperature against time histories preceding ignition nearer to the isothermal limit.(i) According to simple stationary conductive t h e ~ r y , ~ maximum stable tempera- ture excesses in a spherical vessel of about 1.61 RT;/E are allowed ; the excess expected rises to about 1.85 RT,2/E when consumption of reactants 25 is considered. Accepting the value of the activation energy derived from the linear portion of the plot in fig. 7, this corresponds to predicted critical temperature rises of about 45 to 50°C at T, = 3OO0C, in good agreement with the maximum stable rises experimentally observed near to point a. On simple theory, the critical excesses should increase monotonically (as T,2) with increase in ambient temperature around the ignition boundary. Fig. 5 indicates that the converse occurs : temperature excesses never reach such values ; at T, = 340°C, near point b, the highest sub-critical excess so far observed is only 28”C, around half that suggested on thermal grounds.The dis- crepancy increases around the boundary; near point c only a 12°C excess can be realized. Both are readily located. (ii) Temperatures also vary differently with time from the lively accelerations that are a prelude to purely thermal explosions : instead they may rise only sluggishly, be relatively steady or even decrease, as is the case near point c. on the unification of thermal and chain-branching theories of explosions, Gray and Yang outline qualitatively the results which have here been observed quantitatively in the oxidation of hydrogen sulphide. In the chain-thermal region of the reaction we are, by definition, concerned with the regime in which the two different mechanisms compete for control, and in many ways the combined effects reflect the compromise.Maximum stable temperature rises are predicted 26 and found to be markedly below their purely thermal counterparts, and the entire temperature development is slower paced. In particular, induction times are much longer than in purely thermal explosion, being typically of the order of 10-30 s, though these values are significantly shorter than the induction periods observed in the purely isothermal regime. The temperature excesses immediately preceding ignition are often surprisingly steady and the temperature “jumps” occur suddenly with little or no additional self-heating. Indeed, in the region where the second and third limits merge the reactant temperature is falling when ignition occurs. The contribution to the explosion under such conditions by branched chain radical processes is clearly very great. Similar behaviour might be expected near the second limit in the hydrogen + oxygen reaction but although falling temperatures before ignition have been reported 2 2 they appear to be the artificial consequence of the conventional “withdrawal” technique used to locate the limit : reactant temperatures fall by adiabatic expansion. In their original paper A re-investigation of this system would be timely. We are grateful to S.R.C. for the award of a studentship to M.E.S.2350 CHAIN-THERMAL IGNITION I N H2S COMBUSTION P. Gray and J. K. K. Ip, Combustion and Flame, 1972, 18, 361. D. H. Fine, P. Gray and R. MacKinven, Proc. Roy. SOC. A , 1970, 316, 223, 241 and 255; P. Gray, D. T. Jones and R. MacKinven, Proc. Roy. SOC. A , 1971,325, 175. H. Goodman, P. Gray and D. T. Jones, Combustion and Flame, 1972, 19, 157. P. Gray and E. B. O'Neill, Trans. Faraday ,Yoc., 1972, 68, 564. P. Gray and M. E. Sherrington, J.C.S. Faraday Z, 1974, 70, 740. N. N. Semenov, Chemical Kinetics and Chain Reactions (Oxford U. P., Oxford, 1st edn., 1935). D. A. Frank-Kamenetskii, Diflusion and Heat Exchange in Chemical Kinetics (Plenum, New York, 2nd edn., 1969). B. F. Gray and C. H. Yang, J. Phys. Chem., 1965, 69, 2747. B. F. Gray and C. H. Yang, 11th Symp. (Znt.) Combustion (Combustion lnst., Pittsburgh, 1967), p. 1099. l o C . H. Yang and B. F. Gray, J. Phys. Clrern., 1969, 73, 3395. B. F. Gray and C. H. Yang, Trans. Farnday SOC., 1969, 65, 1553, 1614. j 2 J. H. Knox and R. G. W. Norrish, Trans. Fauaday SOC., 1954, 50, 928. l 3 R. Hughes and R. F. Simmons, Combustion atid Flame, 1970, 14, 103. l4 J. F. Griffiths, P. Gray and P. G . Felton, 14fh Synzp. ( h t . ) Combustion (Combustion lnst., l5 J. N. Bradley, Trans. Fauaday Snc., 1967, 63, 2945, l6 A. L. Myerson and F. R. Taylor, J. Anzer. Clzem. Soc., 1953, 75, 4345. l 7 H. A. Taylor and E. M. Livingston, J. Chem. Plzys., 1931, 35, 2676. l 9 L. Farkas, 2. Elektrochem., 1931, 37, 670. 2o B. Yakovlev and P. Shantarovich, Acta Physicochim. U.S.S.K., 1937, 6, 71. 2 1 D. G. H. Marsden, Canad. J. Chem., 1963, 41, 2607. 22 J. A. Barnard and A. G. Platts, Combustion Sci. Tech., 1972, 6, 133. 23 W. Jost, Low Temperature Oxidation (Gordon and Breach, New York, 1965). *' D. A. Davies and A. D. Walsh, 14th Symp. ( h t . ) Combustion (Combustion Inst., Pittsburgh, 25 B. J. Tyler and T. A. B. Wesley, 11th Symp. (Int.) Cornbustion (Combustion Inst., Pittsburgh, 26B. F. Gray, Trans. Fmadzy SDC., 1969, 65, 2133. Pittsburgh, 1972), p. 453. H. W. Thompson and N. Kelland, J. Chenz. Soc., 1931, 1809. 1973), p. 475. 1967), p. 1115.

ISSN:0300-9599    

DOI:10.1039/F19747002338

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Inelastic Light Scattering from the Free Surfaces of Viscoelastic Polymer Solutions BY INGEMAR LUNDSTROM* AND DOUGLAS MCQUEEN Organic Electron Physics Group, Chalmers University of Technology, Goteborg, Sweden Received 17th April, 1974 The power spectral density of light scattered inelastically from the free surface of viscoelastic polymer solutions is derived, The theoretical results for stiff rod polymers are compared with previously reported light scattering data on cellulose solutions, and the agreement between theory and experiment is good. Recently we used inelastic laser light scattering to study thermally excited capillary waves on the free surface of water and of solutions of sodium carboxymethylcellulose in water.l The experimental results were not in agreement with the hydrodynamic theory of capillary wave motion on homogeneous viscous media.We proposed that a surface zone of viscosity about 4 CP could explain our data. Since then it has been realized that underestimation of the instrumental bandwidth was one of the causes of this misinterpretation of our results. Better estimates of the bandwidths were made using mercury as the scattering fluid,2 and Langevin has further discussed the prob- lem.3 No surface zone appears to be necessary to describe the results. We now explain the unexpectedly low damping of the capillary waves on the viscous cellulose solutions (which is observed even without correction for the instrumental bandwidth) on the basis of a theory of viscoelasticity of the cellulose solutions. If the cellulose molecules are regarded essentially as stiff rods a little more than 2000A long a rotational diffusion coefficient for these rods can be computed by well known methods, the result being that the theoretical relaxation time is of the order of This means that for angular frequencies below about lo4 s-1 the viscosity is essentially equal to its static value, while well above this frequency it is reduced to about one fourth that amount.The frequencies, co, of the capillary waves studied are of the order lo5 s-I, some- what above the inverse relaxation time of the cellulose rods. Thus, by comparing the detected spectra with the theoretical spectra derived on the basis of this model, an experimental relaxation time can be deduced. We find that it is about 1-3 x s, in satisfactory agreement with the theoretical estimate.Due to the extremely low amplitude of the thermally excited capillary waves, the rate of shear is small, while the practical frequency range is about 1-50 kHz. This means that the light scattering method may be a valuable tool for investigating the viscoelastic properties of polymer solutions. s. THEORY Experimentally, He-Ne laser light is shone on the liquid surface, and some of it is scattered due to the thermally excited capillary waves. The capillary waves act as moving diffraction gratings, the wave vector determining the scattering angle and their 23512352 INELASTIC LIGHT SCATTERING speed and damping determining the Doppler shift. using optical mixing spectroscopy. elsewhere. ' 9 2 g displacement, 5, of the liquid surface.Bouchiat and Me~nier.~ Their result can be written in the form The Doppler shift is measured Detailed descriptions of the apparatus are given Theoretically, it is necessary to calculate the power spectral density of the vertical This has been done for a simple liquid by with = = p/2tlq2, Y = w/4t12q (2) and where a = -ico and Im denotes " imaginary part of ". k is Boltzmann's constant, T the temperature, q the wavenumber (2n/L), m the circular frequency (rad s-l), p the density, y the viscosity, CT the surface tension and i = ,/- 1. When the viscosity is low, the waves propagate and the spectra are approximately Lorentzian with centre frequency coo N" Jaq3/p and halfwidth at halfheight rz2yq2/p. When the viscosity is high, however, above about yc = Jop/q, the waves are over- damped and the spectra are centred around zero frequency and have a halfwidth In our previously reported experiments,l yc was about 40 CP (OX 70 dyn cm-I, qx500 cm-l).However, even for viscosities of the bulk liquid as high as 150 CP the capillary waves propagated. This is due to the viscoelastic properties of the cellulose solutions, as will now be shown. Ferry gives a comprehensive review of molecular theories of viscoelasticity .' As the simplest possible model for the cellulose molecules we choose Kirkwood-Auer rods, that is we regard the cellulose molecules as stiff rods with a length given by the degree of polymerization quoted by the manufacturer (Hercules Incorporated, Wilmington, Delaware, obtained through Hercules Kemiska AB, Hisings Backa, Sweden).In this model the complex viscosity at low concentration can be written r x 0q/2y. with WSL3 z = 18kT ln(L/b) (4) ys is the solvent viscosity, c the solute concentration, [y~] the zero frequency intrinsic viscosity, L the length of the rods and b the length of a monomer section. For the cellulose sample previously studied by us the viscosity average length, L, was some- what greater than 2000A. s. Since z is essentially proportional to L3, a distribution in molecular weights raises the average value of z somewhat. The meaning of eqn (3) is that in order to take into account the effects of visco- elasticity, y* should be substituted for q in the hydrodynamic equations. No other changes are necessary. Thus the power spectral density of light scattered by the sur- face of the cellulose solution is given by eqn (1) with q* from eqn (3) substituted for y.Fig. l(a) shows the effect of this substitution when the zero frequency viscosity is 37 cP, q = 530 cm-l and CT = 70 dyn cm-I (wo = 1.03 x lo5 rad s-l). The effect of varying the relaxation time z is dramatic : for cooz 4 1, the spectra are overdamped This means that z should be of the order ofI . LUNDSTROM AND D. MCQUEEN 2353 as in a simple fluid, while for ooz $= 1, the effective viscosity is reduced by a factor of 4 and the waves propagate. Fig. l(b) shows an example of the detected spectrum for the same values of zero frequency viscosity, surface tension, and wavenumber. It is seen that the best fit of the theoretical spectra occurs for z about 1-3 x 1 0-4 s.Furthermore when cuoz NN 10-30, 10-1 Y .- (b) g 5 $ 4 .r( 4 v 2 . - 3 3 I - ' I0 2 0 3040 5 0 6 0 70 8 0 9 0 I00 I iOl20 I30 I40 i50 w x /rad s-l ::: as in this case, the reduction in the effective viscosity by about a factor 4 means that the waves should propagate for viscosities up to about four times the critical viscosity for a simple fluid. This is in good agreement with our esperimental results : for q = 1 SO CP the waves propagate, but for q = 230 CP they are overdamped. DISCUSSION AND CONCLUSIONS The above viscoelasticity theory is much more satisfactory for interpreting our data on sodium carboxymethylcellulose in water than was the surface zone theory. The model chosen for the cellulose molecules may be too simple.Probably there exists a distribution of relaxation times due to a distribution in the length of the molecules. A single relaxation time z theoretically estimated at about s gives a good fit to the data, however. Clearly, many simultaneous relaxation times can be treated in a similar way. Flexible polymers typically exhibit a spectrum of relaxation2354 INELASTIC LIGHT SCATTERING times. In order to study relaxation times by inelastic light scattering, these relaxation times must be greater than about s in practice. It should be pointed out that variations in our experimental spectra are most noticeable in the low frequency part. Further, it is essential that the low frequency signal not be confused with possible electronic noise in the apparatus itself. We thank Mr.Vijay Singhal for his help. The work was partly supported by grants from Wilhelm och Martina Lundgrens Vetenskapsfond and from the Swedish Natural Science Research Council. N. Hammarlund, L. Ilver, I. Lundstrom and D. McQueen, J.C.S. Furaduy Z, 1973, 69, 1023. D. McQueen, J. Phys. D: Appl. Phys., 1973, 6, 2273. D. Langevin, J.C.S. Faruduy I, 1974, 70, 95. D. McQueen and I. Lundstrom, J.C.S. Faruday Z, 1973, 69, 694. M. A. Bouchiat and J. Meunier, J. Phys., 1971, 32, 561. J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York, 1970), chap. 9. Inelastic Light Scattering from the Free Surfaces of Viscoelastic Polymer Solutions BY INGEMAR LUNDSTROM* AND DOUGLAS MCQUEEN Organic Electron Physics Group, Chalmers University of Technology, Goteborg, Sweden Received 17th April, 1974 The power spectral density of light scattered inelastically from the free surface of viscoelastic polymer solutions is derived, The theoretical results for stiff rod polymers are compared with previously reported light scattering data on cellulose solutions, and the agreement between theory and experiment is good.Recently we used inelastic laser light scattering to study thermally excited capillary waves on the free surface of water and of solutions of sodium carboxymethylcellulose in water.l The experimental results were not in agreement with the hydrodynamic theory of capillary wave motion on homogeneous viscous media. We proposed that a surface zone of viscosity about 4 CP could explain our data. Since then it has been realized that underestimation of the instrumental bandwidth was one of the causes of this misinterpretation of our results.Better estimates of the bandwidths were made using mercury as the scattering fluid,2 and Langevin has further discussed the prob- lem.3 No surface zone appears to be necessary to describe the results. We now explain the unexpectedly low damping of the capillary waves on the viscous cellulose solutions (which is observed even without correction for the instrumental bandwidth) on the basis of a theory of viscoelasticity of the cellulose solutions. If the cellulose molecules are regarded essentially as stiff rods a little more than 2000A long a rotational diffusion coefficient for these rods can be computed by well known methods, the result being that the theoretical relaxation time is of the order of This means that for angular frequencies below about lo4 s-1 the viscosity is essentially equal to its static value, while well above this frequency it is reduced to about one fourth that amount.The frequencies, co, of the capillary waves studied are of the order lo5 s-I, some- what above the inverse relaxation time of the cellulose rods. Thus, by comparing the detected spectra with the theoretical spectra derived on the basis of this model, an experimental relaxation time can be deduced. We find that it is about 1-3 x s, in satisfactory agreement with the theoretical estimate. Due to the extremely low amplitude of the thermally excited capillary waves, the rate of shear is small, while the practical frequency range is about 1-50 kHz.This means that the light scattering method may be a valuable tool for investigating the viscoelastic properties of polymer solutions. s. THEORY Experimentally, He-Ne laser light is shone on the liquid surface, and some of it is scattered due to the thermally excited capillary waves. The capillary waves act as moving diffraction gratings, the wave vector determining the scattering angle and their 23512352 INELASTIC LIGHT SCATTERING speed and damping determining the Doppler shift. using optical mixing spectroscopy. elsewhere. ' 9 2 g displacement, 5, of the liquid surface. Bouchiat and Me~nier.~ Their result can be written in the form The Doppler shift is measured Detailed descriptions of the apparatus are given Theoretically, it is necessary to calculate the power spectral density of the vertical This has been done for a simple liquid by with = = p/2tlq2, Y = w/4t12q (2) and where a = -ico and Im denotes " imaginary part of ".k is Boltzmann's constant, T the temperature, q the wavenumber (2n/L), m the circular frequency (rad s-l), p the density, y the viscosity, CT the surface tension and i = ,/- 1. When the viscosity is low, the waves propagate and the spectra are approximately Lorentzian with centre frequency coo N" Jaq3/p and halfwidth at halfheight rz2yq2/p. When the viscosity is high, however, above about yc = Jop/q, the waves are over- damped and the spectra are centred around zero frequency and have a halfwidth In our previously reported experiments,l yc was about 40 CP (OX 70 dyn cm-I, qx500 cm-l).However, even for viscosities of the bulk liquid as high as 150 CP the capillary waves propagated. This is due to the viscoelastic properties of the cellulose solutions, as will now be shown. Ferry gives a comprehensive review of molecular theories of viscoelasticity .' As the simplest possible model for the cellulose molecules we choose Kirkwood-Auer rods, that is we regard the cellulose molecules as stiff rods with a length given by the degree of polymerization quoted by the manufacturer (Hercules Incorporated, Wilmington, Delaware, obtained through Hercules Kemiska AB, Hisings Backa, Sweden). In this model the complex viscosity at low concentration can be written r x 0q/2y. with WSL3 z = 18kT ln(L/b) (4) ys is the solvent viscosity, c the solute concentration, [y~] the zero frequency intrinsic viscosity, L the length of the rods and b the length of a monomer section.For the cellulose sample previously studied by us the viscosity average length, L, was some- what greater than 2000A. s. Since z is essentially proportional to L3, a distribution in molecular weights raises the average value of z somewhat. The meaning of eqn (3) is that in order to take into account the effects of visco- elasticity, y* should be substituted for q in the hydrodynamic equations. No other changes are necessary. Thus the power spectral density of light scattered by the sur- face of the cellulose solution is given by eqn (1) with q* from eqn (3) substituted for y. Fig. l(a) shows the effect of this substitution when the zero frequency viscosity is 37 cP, q = 530 cm-l and CT = 70 dyn cm-I (wo = 1.03 x lo5 rad s-l).The effect of varying the relaxation time z is dramatic : for cooz 4 1, the spectra are overdamped This means that z should be of the order ofI . LUNDSTROM AND D. MCQUEEN 2353 as in a simple fluid, while for ooz $= 1, the effective viscosity is reduced by a factor of 4 and the waves propagate. Fig. l(b) shows an example of the detected spectrum for the same values of zero frequency viscosity, surface tension, and wavenumber. It is seen that the best fit of the theoretical spectra occurs for z about 1-3 x 1 0-4 s. Furthermore when cuoz NN 10-30, 10-1 Y .- (b) g 5 $ 4 .r( 4 v 2 . - 3 3 I - ' I0 2 0 3040 5 0 6 0 70 8 0 9 0 I00 I iOl20 I30 I40 i50 w x /rad s-l ::: as in this case, the reduction in the effective viscosity by about a factor 4 means that the waves should propagate for viscosities up to about four times the critical viscosity for a simple fluid.This is in good agreement with our esperimental results : for q = 1 SO CP the waves propagate, but for q = 230 CP they are overdamped. DISCUSSION AND CONCLUSIONS The above viscoelasticity theory is much more satisfactory for interpreting our data on sodium carboxymethylcellulose in water than was the surface zone theory. The model chosen for the cellulose molecules may be too simple. Probably there exists a distribution of relaxation times due to a distribution in the length of the molecules. A single relaxation time z theoretically estimated at about s gives a good fit to the data, however. Clearly, many simultaneous relaxation times can be treated in a similar way. Flexible polymers typically exhibit a spectrum of relaxation2354 INELASTIC LIGHT SCATTERING times. In order to study relaxation times by inelastic light scattering, these relaxation times must be greater than about s in practice. It should be pointed out that variations in our experimental spectra are most noticeable in the low frequency part. Further, it is essential that the low frequency signal not be confused with possible electronic noise in the apparatus itself. We thank Mr. Vijay Singhal for his help. The work was partly supported by grants from Wilhelm och Martina Lundgrens Vetenskapsfond and from the Swedish Natural Science Research Council. N. Hammarlund, L. Ilver, I. Lundstrom and D. McQueen, J.C.S. Furaduy Z, 1973, 69, 1023. D. McQueen, J. Phys. D: Appl. Phys., 1973, 6, 2273. D. Langevin, J.C.S. Faruduy I, 1974, 70, 95. D. McQueen and I. Lundstrom, J.C.S. Faruday Z, 1973, 69, 694. M. A. Bouchiat and J. Meunier, J. Phys., 1971, 32, 561. J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York, 1970), chap. 9.

ISSN:0300-9599    

DOI:10.1039/F19747002351

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Dissolution Rates of Ionic Solids Part 2.-Calcium Bis(dihydrogen phosphate) Monohydrate + Anhydrite (Calcium Sulphate) BY ALLAN F. M. BARTON*? AND STEPHEN R. MCCONNEL~ Chemistry Department, Victoria University of Wellington, New Zealand Received 17th April, 1974 The dissolution rate of commercial superphosphate fertiliser was studied at 25, 35 and 45°C using a rotating disc of the solid material. The kinetics were followed by means of a calcium ion-selective electrode and spectrophotometric analyses. The initial process was observed to consist predominately of calcium bis(dihydrogen phosphate) monohydrate dissolution and was transport controlled with an apparent activation energy of 13 3 kJ mol-'. Thereafter diffusion of dissolved monocalcium bis(dihydrogen phosphate) monohydrate through a porous layer of increasing thickness determined the rate of dissolution.This work was carried out as a continuation of an earlier study on dissolution rates of ionic so1ids.l Superphosphate is the world's most important phosphate fertiliser and typically contains 10 % phosphorus as calcium bis(dihydrogen phos- phate) monohydrate, Ca(H,PO,),-H,O and 10 % sulphur as orthorhoinbic anhydrite, CaSO,. Although the literature dealing with the dissolution of superphosphate in soils is considerable, very little work has been reported on systems restricted to superphosphate and aqueous solutions. gently stirred water over a mono- layer of superphosphate granules at 24.5"C and analysed the solution for phosphate and sulphate. They found that the phosphate component dissolved at a rate approxi- mately twenty times faster than that for sulphate.However, the hydrodynamic conditions in such a system are complex and poorly known. In experiments with superphosphate and soil many workers 4-6 have reported that the solution moving away from the fertiliser granule contains much more phosphate than sulphate. This was attributed to the greater solubility of the phosphate inono- hydrate (1 8 g dm-3) compared to anhydrite (2.75 g dm-3) in water. However, dissolution processes in soils are complicated by such factors as reactions between solute and soil particles, variable contact between fertiliser and soil solution and in some cases, leaching. The purpose of this work was to determine, in the absence of soil, the rate and nature of dissolution of superphosphate of known surface area and under known hydrodynamic conditions.Experiments have shown that a rotating disc of dissolving material is the preferred method for investigating dissolution rates 9-11 since Levich l2 has solved the corres- ponding equation of convective diffusion giving the velocity distribution throughout the liquid. From Levich's theory it follows that a transport controlled dissolution t present address : School of Mathematical and Physical Sciences, Murdoch University, Perth, Western Australia. Shawcross and White 23552356 DISSOLUTION RATE OF SUPERPHOSPHATE rate is proportional to CO~,’ where cu is the disc rotation velocity, whereas a chemically controlled rate is independent of rotation speed. Suitable discs of superphosphate were therefore made and rotated in water at various speeds and temperatures and the resulting solutions analysed.EXPERIMENTAL PELLETISATION OF SUPERPHOSPHATE A sample of commercial granulated superphosphate manufactured in a New Zealand fertiliser works from a mixture a Nauru Island and Christmas Island rock phosphate (apatite) was used. Analysis gave the major components as Ca, 24.9 ; P, 10.65 ; S, 9.95 ; Al, 0.4 and Fe, 0.3 %. The X-ray diffraction spectrum of a powdered sample indicated only two sets of detectable peaks, these being identified as belonging to calcium bis(dihydrogen phosphate) monohydrate and orthorhombic anhydrous calcium sulphate (anhydrite). The complex aluminium and iron phosphates were present in small amounts, as can be seen from the elemental analysis figures while the other compounds likely to be present, namely unreacted apatite and dicalcium phosphate, can be assumed to be less than 2-3 % each since they were undetected by the X-ray diffractometer.Since superphosphate is manufactured only in powdered or granular form a method of preparing massive samples suitable for use as rotating discs had to be found. The common practice of pressing powder directly into pellets was unsatisfactory as the pellets crumbled when placed in water. In the granulation process of superphosphate a small amount of water is added to the powder and it is rotated to ball up the material into small hard When the powder was pressed damp (free water = 2 % by weight), with a pressure of 160 MPa the resulting dried pellets were very hard and did not crumble when placed in water.The X-ray diffrac- tion pattern of a ground pellet prepared in this way showed that the composition had not changed, This conclusion might be expected since anhydrite shows a negligible tendency to rehydrate and calcium bis(dihydrogen phosphate) monohydrate decomposes only if it is neutralised in some way.16 The density of this pelletised superphosphate was similar to that of the granular form.4 ROTATING DISC DESIGN The rotating disc apparatus used in this study was similar to that described previously except for the shape of the disc-holder. Following the recommendations of Riddiford and Azim and Riddiford l 8 a flared disc-holder, broad at the bottom and narrow at the top, was constructed from stainless steel and fibre-glass. The holder had an overall diameter of 4.50 cm at the base and 1.16 cm at the top.The underside contained an inset of 2.00 cm diameter and 0.20 cm depth to accommodate the superphosphate pellet. The edge of the pellet was coated with a thin layer of Apiezon H grease and the holder pressed down over it. The holder was then rotated at high speed and the pellet ground flush with the underside using successive grades of grinding paper. In this way a smooth disc of superphosphate having an unbroken edge and one face only exposed to the solution was prepared. The disc was placed in the reaction vessel satisfying the recommendations of Gregory and Riddiford l9 to avoid impedance of the fluid flow in the vessel. A Metrohm Herisau pH-stat consisting of pH-meter E510, Implusomat E473, Dosimat and recorder was used to maintain the solution pH constant at 6.50.ANALYSES The extent of dissolution of the two main components of superphosphate can be deter- mined by measurement of three concentrations : calcium, phosphate and sulphate ions. The calcium ion concentration in the solution was continuously monitored as previously described, using a calcium liquid ion-exchange membrane electrode. The phosphate and sulphate concentrations were determined as follows.2oA . F . M. BARTON A N D S . R . MCCONNEL 2357 The phosphate ion present was complexed with a mixed " vanadomolybdate " [deca- molybdodivanadophosphate(3-)] reagent and the optical density, measured at 420 nm, compared with a calibration plot.The sulphate was precipitated as barium sulphate, under strictly controlled conditions, and the optical density of the turbid suspension measured at 430 nm compared with a calibra- tion plot. The accuracy of the sulphate analysis was improved by using Atlas Tween 80 as a surface agent and by making allowance for interference by the phosphate. RESULTS RATE DATA The calcium concentration against time plots at 25°C for 71, 123,200,330, 550 and 700 rev. min-' are given in fig. 1. In all cases there was an initial linear region of 6-8 min followed by a region of decreasing slope. 10 20 30 40 tlmin FIG. 1.-Plots of calcium concentration against time at 25°C at various rotation speeds (rev. min-') : - -, 71 ; A, 123 ; -y 200; H, 330; - * -y 550; A, 700.Experimental runs were also carried out at 35 and 45°C at 123 rev. min-I and the initial linear plots of calcium concentration against time are shown in fig. 2. The phosphate and sulphate ion concentrations of these solutions were determined at various times and are plotted in fig. 3. Rotation speeds of 71 and 700 rev. min-' were used at a pH of 5.50 but in both cases the calcium, phosphate and sulphate concentration against time plots were identical to those obtained with a pH of 6.50. TREATMENT OF RATE DATA Fig. 3 shows that over the observed period of 40 min the dissolution of anhydrite is so slow that the dissolution rate of superphosphate is effectively that of the phosphate monohydrate. The initial dissolution rate is shown by fig. 1 to be dependent upon2358 DISSOLUTION RATE OF SUPERPHOSPHATE the rotation speed.If these initial values of the observed rate, dcldt, are plotted against d, as in fig. 4, then a straight line is obtained. This indicates that the initial dissolution rate is transport controlled. FIG. 2.-Plots of tlmin calcium concentration against time at 123 rev. min-l at various temperatures : - -, 25°C; 0, 35°C; - -, 45°C. 30 40 t/min FIG. 3.---Plots of phosphate and sulphate concentrations against time at 123 rev. min-' at various temperatures : phosphate; A, 25°C ; I, 35°C ; 0, 45°C : sulphate, 0, 25T, 35"C, 45°C. Values of dc/dt were evaluated for calcium at 25, 35 and 45°C from fig. 2 and used to plot log(dc/dt) against reciprocal absolute temperature to determine an apparent activation energy.21 The value obtained of 13k3 kJ mol-I is within the range nor- mally associated with transport control in aqueous solutions.22 The dissolution ofA .F . M . BARTON A N D S . R . MCCONNEL 2359 calcium bis(dihydrogen phosphate) monohydrate in phosphoric acid has been reported 2 3 to be transport controlled over the pH range 4 to 0.48. 60 55 3 I ," 50- I T3 E - - - 0 45- E m I 2 40- 3 T3 --.- ---- 4 35-: b 30 T - i I I I I I I d l r a d t s-3 FIG. 4.-Variation of dissolution rate of superphosphate with rotation speed at 25°C. 2 4 6 8 10 DISCUSSION VARIATION IN RATE The initial dissolution rate of superphosphate appeared to be controlled by the rate at which the solute moved away from the disc surface. However, after 6-8 min the rate of dissolution decreased indicating that some other factor was influencing the dissolution process.This variation in the observed rate, dcldt, with time can be attributed to four possible causes l 3 : (a) where the bulk concentration c, becomes comparable to the saturation concentration c, at the interface, i.e. change from pseudo zero to first order kinetics ; (b) where the reverse reaction, that is recrystallisation and deposition, becomes important ; (c) where a change in the exposed surface area of the dissolving solid occurs; ( d ) where the diffusion of reactants either way through an insoluble layer at the surface is slow compared to other processes. Both (a) and (b) can be assumed to be unimportant since the reported solubility of the phosphate monohydrate ' is 7.2 x mol dm-3 and the maximum concentration achieved in this work was 6 x mol dm-3, so that less than 1 % of the total reaction was studied.Further evidence to support the assumption that (b) is not influencing the rate was gained by rotating a new disc in a solution obtained from a previous experimental run, that is a solution in which the initial solute concentration was not zero. The resulting calcium concentration against time plot 21 had a shape similar to that obtained by the previous run where the initial solute concentration was zero. This observation indicates that the factor causing the variation in rate was associated with the pellet itself and not the solution in which it was dissolving. The marked increase in dissolution rate when a disc which had been dissolving for 40 min was replaced with a new disc in the same solution could be explained if varia- tion in the exposed surface area of the phosphate monohydrate was a rate influencing factor.However, at all the rotation speeds used, after the observed period of 40 min, the rate had decreased to approximately 10 % of its initial value, a change in magnitude2360 DISSOLUTION RATE OF SUPERPHOSPHATE unlikely to be caused by surface area variation. Therefore (c) was assumed un- important and attention was directed to the possibility that ( d ) was influencing the rate of the dissolution process. Since the phosphate monohydrate has a lower density than anhydrite more rapid molar removal of the former means that it must be removed from within the pellet. This removal of the phosphate monohydrate from within superphosphate has been reported by Williams and others 24 to occur in soil, the fertiliser granule ultimately becoming a porous structure of calcium sulphate.It was therefore proposed that for a rotating disc of superphosphate, the pores or cavities opened up by the loss of calcium bis(dihydrogen phosphate) monohydrate are of dimensions such that the solution contained in them is stationary with respect to the disc. Diffusion of solute through these pores to the disc surface controls the dissolu- tion rate since the chemical steps are fast. This means that as dissolution proceeds the rate will become independent of the rotation speed and will decrease. EVIDENCE FOR FORMATION OF POROUS LAYER If the above proposal is correct then the dissolution kinetics should obey the parabolic law derived by Mott and Gurney 2 5 to describe diffusion processes in ionic crystals.Plots of both the square of the calcium concentration against time and the square of the phosphate concentration against time gave linear graphs 21 showing that the parabolic law was obeyed over the 40 min period observed. Formation of a leached porous layer has been suggested for the parabolic kinetics found for dissolu- tion of some magnesium silicates in acid solutions.26 Examination of the disc surface after rotation for 40 min at all speeds showed it to be not only rougher in texture but also softer and lighter in colour. In cross section the pellet displayed a distinct band extending inwards from the exposed surface, the thickness of this band increasing with the length of time that the disc was exposed to the solution.This layer was porous to solution but the remainder of the pellet was not. Viewed under a low-powered microscope the surface of the disc was covered with pores or holes which were entirely absent from the original undissolved pellet. The maximum diameter of these pores, at the surface; was approximately 5 x cm but the location and size of the pores appeared random. X-ray diffraction patterns of this layer showed a marked decrease in the intensity of the peaks associated with calcium bis(dihydrogen phosphate) monohydrate and also indicated that the calcium sulphate was still present as anhydrite. Samples of superphosphate, outer porous layer and inner undissolved pellet were dissolved completely by boiling in acid, and analysed for phosphate and sulphate as before.These analyses confirmed that the outer layer had been depleted of calcium bis(dihydrogen phosphate) monohydrate as the phosphate content in this portion of the pellet was less than 30 % of that originally present. COMPARISON WITH THEORETICAL TRANSPORT CONTROLLED RATE Since the initial dissolution of superphosphate is controlled by transport away from the outer surface of the rotating disc it is possible to calculate the theoretical rate from the Levich l 2 equation and compare this with the observed rate. The diffusion coefficients for calcium phosphates do not appear to have been reported but as dilute aqueous electrolyte solutions have diffusion coefficients of magnitude cm2 s-l 27 this value was used for D in the following calculations.A .F . M. BARTON AND S . R . MCCONNEL 236 1 The kinematic viscosity v changes very little with concentration 17 so that the value for pure water at 25°C of 8.9 x cm2 s-l was used. From the Levich theory l 2 the theoretical rate constant k?'' is given by where w is the disc rotation speed in rads-l. Substituting for co = 7.4rad s-l (71 rev. min-l) and using the values for D and v given then k?'' = I .2 x lop3 crn S-'. The uncertainty in arises solely from the assumption of the value of D and may be as high as 50 %. The observed rate constant kOTbbS is related to the observed rate dc/dt by the equation where Y is the volume of solution (350 cm3), A is the surface area of calcium bis(di- hydrogen phosphate) monohydrate (estimated as 1.5 cm2 f 10 % by comparison of densities of the phosphate monohydrate and anhydrite), c, is the concentration at the interface (7.2 x mol dm-3) and c, is the bulk concentration, with the approxi- mation that c, = 0.The observed initial value of dc/dt at LU = 7.4 rad s-l was (0.31 k0.02) x Substitution and calculation gives krtPs = (1.0f 0.1) x cm s-l. The good agreement in terms of order of magnitude between the observed and the theoretical rate constants provides further evidence that convective diffusion, that is transport, is controlling the dissolution of superphosphate under the experimental conditions. mol dm-3 s-l. A. F. M. Barton and N. M. Wilde, Trans. Faraday SOC., 1971,67, 3590. L. B. Nelson, Ada Agronomy, 1965, 17, 1.E. E. Shawcross and M. S. White, Annual Rep. New Zealand Fertiliser Manufacturers' Research Association, 1971-72, 28. C. H. Williams, Austral. J. Soil Res., 1971, 9, 83. W. L. Lindsay and H. F. Stephenson, Proc. Soil Sci. SOC. Amer., 1959, 23, 12. L. A. G. Aylmore, M. Karim and J. P. Quirk, Austral. J. Soil Res., 1971, 9, 21. ' Handbook of Chemistry and Physics (The Chemical Rubber Co., Ohio, Slst edn., 1970). E. Bock, Canad. J. Chem., 1961,39, 1746. A. R. Burkin, The Chemistry of Hydrometallurgical Processes (Spon, London, 1966). lo D. P. Gregory and A. C. Riddiford, J. Electrochem. Soc., 1970,107, 950. D. D. Macdonald and G. A. Wright, Canad. J. Chem., 1970,48,2847. V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, New Jersey, 1962).l 3 L. L: Bircumshaw and A. C. Riddiford, Quart. Rev., 1952, 6, 157. l4 R. L. Demmerle and W. J. Sackett, Znd. Eng. Chem., 1949, 41, 1306. l 5 S. J. Gregg and E. G. J. Willing, J. Chem. SOC., 1951, 2916. l 6 W, Stollenwerk, Z. Pflanzenernaher. Dungung u. Bodenk., 1931,21A, 321 ; Chem. Abs., 25,5493. l7 A. C. Riddiford, Adv. Electrochem. Electrochem. Eng., 1966, 4, 47. S. Azim and A. C. Riddiford, Anal. Chem., 1962, 34, 1023. l9 D. P. Gregory and A. C. Riddiford, J. Chem. Soc., 1956, 3756. '* J. Rogers (New Zealand Fertiliser Manufacturers' Research Association), personal communi- 21 S. R. McConnel, MSc. Thesis (Victoria University of Wellington, 1973). 22 S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New 2 3 E.0. Huffman, W. E. Cate, M. E. Deming and K. L. Elmore, J. Agric. Food Chem., 1957,5,266. 24 E. H. Brown, W. E. Brown and J. R. Lehr, Proc. Soil Sci. SOC. Amer., 1959, 23, 3. 2 5 N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford, 2nd edn., 1948). 26 R. W. Luce, R. W. Bartlett and G. A. Parks, Geochim. Cosmochim. Acta, 1972, 36, 35. 27 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn., cation. York, 1941). 1959). Dissolution Rates of Ionic Solids Part 2.-Calcium Bis(dihydrogen phosphate) Monohydrate + Anhydrite (Calcium Sulphate) BY ALLAN F. M. BARTON*? AND STEPHEN R. MCCONNEL~ Chemistry Department, Victoria University of Wellington, New Zealand Received 17th April, 1974 The dissolution rate of commercial superphosphate fertiliser was studied at 25, 35 and 45°C using a rotating disc of the solid material.The kinetics were followed by means of a calcium ion-selective electrode and spectrophotometric analyses. The initial process was observed to consist predominately of calcium bis(dihydrogen phosphate) monohydrate dissolution and was transport controlled with an apparent activation energy of 13 3 kJ mol-'. Thereafter diffusion of dissolved monocalcium bis(dihydrogen phosphate) monohydrate through a porous layer of increasing thickness determined the rate of dissolution. This work was carried out as a continuation of an earlier study on dissolution rates of ionic so1ids.l Superphosphate is the world's most important phosphate fertiliser and typically contains 10 % phosphorus as calcium bis(dihydrogen phos- phate) monohydrate, Ca(H,PO,),-H,O and 10 % sulphur as orthorhoinbic anhydrite, CaSO,.Although the literature dealing with the dissolution of superphosphate in soils is considerable, very little work has been reported on systems restricted to superphosphate and aqueous solutions. gently stirred water over a mono- layer of superphosphate granules at 24.5"C and analysed the solution for phosphate and sulphate. They found that the phosphate component dissolved at a rate approxi- mately twenty times faster than that for sulphate. However, the hydrodynamic conditions in such a system are complex and poorly known. In experiments with superphosphate and soil many workers 4-6 have reported that the solution moving away from the fertiliser granule contains much more phosphate than sulphate.This was attributed to the greater solubility of the phosphate inono- hydrate (1 8 g dm-3) compared to anhydrite (2.75 g dm-3) in water. However, dissolution processes in soils are complicated by such factors as reactions between solute and soil particles, variable contact between fertiliser and soil solution and in some cases, leaching. The purpose of this work was to determine, in the absence of soil, the rate and nature of dissolution of superphosphate of known surface area and under known hydrodynamic conditions. Experiments have shown that a rotating disc of dissolving material is the preferred method for investigating dissolution rates 9-11 since Levich l2 has solved the corres- ponding equation of convective diffusion giving the velocity distribution throughout the liquid. From Levich's theory it follows that a transport controlled dissolution t present address : School of Mathematical and Physical Sciences, Murdoch University, Perth, Western Australia.Shawcross and White 23552356 DISSOLUTION RATE OF SUPERPHOSPHATE rate is proportional to CO~,’ where cu is the disc rotation velocity, whereas a chemically controlled rate is independent of rotation speed. Suitable discs of superphosphate were therefore made and rotated in water at various speeds and temperatures and the resulting solutions analysed. EXPERIMENTAL PELLETISATION OF SUPERPHOSPHATE A sample of commercial granulated superphosphate manufactured in a New Zealand fertiliser works from a mixture a Nauru Island and Christmas Island rock phosphate (apatite) was used.Analysis gave the major components as Ca, 24.9 ; P, 10.65 ; S, 9.95 ; Al, 0.4 and Fe, 0.3 %. The X-ray diffraction spectrum of a powdered sample indicated only two sets of detectable peaks, these being identified as belonging to calcium bis(dihydrogen phosphate) monohydrate and orthorhombic anhydrous calcium sulphate (anhydrite). The complex aluminium and iron phosphates were present in small amounts, as can be seen from the elemental analysis figures while the other compounds likely to be present, namely unreacted apatite and dicalcium phosphate, can be assumed to be less than 2-3 % each since they were undetected by the X-ray diffractometer. Since superphosphate is manufactured only in powdered or granular form a method of preparing massive samples suitable for use as rotating discs had to be found.The common practice of pressing powder directly into pellets was unsatisfactory as the pellets crumbled when placed in water. In the granulation process of superphosphate a small amount of water is added to the powder and it is rotated to ball up the material into small hard When the powder was pressed damp (free water = 2 % by weight), with a pressure of 160 MPa the resulting dried pellets were very hard and did not crumble when placed in water. The X-ray diffrac- tion pattern of a ground pellet prepared in this way showed that the composition had not changed, This conclusion might be expected since anhydrite shows a negligible tendency to rehydrate and calcium bis(dihydrogen phosphate) monohydrate decomposes only if it is neutralised in some way.16 The density of this pelletised superphosphate was similar to that of the granular form.4 ROTATING DISC DESIGN The rotating disc apparatus used in this study was similar to that described previously except for the shape of the disc-holder. Following the recommendations of Riddiford and Azim and Riddiford l 8 a flared disc-holder, broad at the bottom and narrow at the top, was constructed from stainless steel and fibre-glass.The holder had an overall diameter of 4.50 cm at the base and 1.16 cm at the top. The underside contained an inset of 2.00 cm diameter and 0.20 cm depth to accommodate the superphosphate pellet. The edge of the pellet was coated with a thin layer of Apiezon H grease and the holder pressed down over it.The holder was then rotated at high speed and the pellet ground flush with the underside using successive grades of grinding paper. In this way a smooth disc of superphosphate having an unbroken edge and one face only exposed to the solution was prepared. The disc was placed in the reaction vessel satisfying the recommendations of Gregory and Riddiford l9 to avoid impedance of the fluid flow in the vessel. A Metrohm Herisau pH-stat consisting of pH-meter E510, Implusomat E473, Dosimat and recorder was used to maintain the solution pH constant at 6.50. ANALYSES The extent of dissolution of the two main components of superphosphate can be deter- mined by measurement of three concentrations : calcium, phosphate and sulphate ions.The calcium ion concentration in the solution was continuously monitored as previously described, using a calcium liquid ion-exchange membrane electrode. The phosphate and sulphate concentrations were determined as follows.2oA . F . M. BARTON A N D S . R . MCCONNEL 2357 The phosphate ion present was complexed with a mixed " vanadomolybdate " [deca- molybdodivanadophosphate(3-)] reagent and the optical density, measured at 420 nm, compared with a calibration plot. The sulphate was precipitated as barium sulphate, under strictly controlled conditions, and the optical density of the turbid suspension measured at 430 nm compared with a calibra- tion plot. The accuracy of the sulphate analysis was improved by using Atlas Tween 80 as a surface agent and by making allowance for interference by the phosphate.RESULTS RATE DATA The calcium concentration against time plots at 25°C for 71, 123,200,330, 550 and 700 rev. min-' are given in fig. 1. In all cases there was an initial linear region of 6-8 min followed by a region of decreasing slope. 10 20 30 40 tlmin FIG. 1.-Plots of calcium concentration against time at 25°C at various rotation speeds (rev. min-') : - -, 71 ; A, 123 ; -y 200; H, 330; - * -y 550; A, 700. Experimental runs were also carried out at 35 and 45°C at 123 rev. min-I and the initial linear plots of calcium concentration against time are shown in fig. 2. The phosphate and sulphate ion concentrations of these solutions were determined at various times and are plotted in fig.3. Rotation speeds of 71 and 700 rev. min-' were used at a pH of 5.50 but in both cases the calcium, phosphate and sulphate concentration against time plots were identical to those obtained with a pH of 6.50. TREATMENT OF RATE DATA Fig. 3 shows that over the observed period of 40 min the dissolution of anhydrite is so slow that the dissolution rate of superphosphate is effectively that of the phosphate monohydrate. The initial dissolution rate is shown by fig. 1 to be dependent upon2358 DISSOLUTION RATE OF SUPERPHOSPHATE the rotation speed. If these initial values of the observed rate, dcldt, are plotted against d, as in fig. 4, then a straight line is obtained. This indicates that the initial dissolution rate is transport controlled. FIG. 2.-Plots of tlmin calcium concentration against time at 123 rev.min-l at various temperatures : - -, 25°C; 0, 35°C; - -, 45°C. 30 40 t/min FIG. 3.---Plots of phosphate and sulphate concentrations against time at 123 rev. min-' at various temperatures : phosphate; A, 25°C ; I, 35°C ; 0, 45°C : sulphate, 0, 25T, 35"C, 45°C. Values of dc/dt were evaluated for calcium at 25, 35 and 45°C from fig. 2 and used to plot log(dc/dt) against reciprocal absolute temperature to determine an apparent activation energy.21 The value obtained of 13k3 kJ mol-I is within the range nor- mally associated with transport control in aqueous solutions.22 The dissolution ofA . F . M . BARTON A N D S . R . MCCONNEL 2359 calcium bis(dihydrogen phosphate) monohydrate in phosphoric acid has been reported 2 3 to be transport controlled over the pH range 4 to 0.48.60 55 3 I ," 50- I T3 E - - - 0 45- E m I 2 40- 3 T3 --.- ---- 4 35-: b 30 T - i I I I I I I d l r a d t s-3 FIG. 4.-Variation of dissolution rate of superphosphate with rotation speed at 25°C. 2 4 6 8 10 DISCUSSION VARIATION IN RATE The initial dissolution rate of superphosphate appeared to be controlled by the rate at which the solute moved away from the disc surface. However, after 6-8 min the rate of dissolution decreased indicating that some other factor was influencing the dissolution process. This variation in the observed rate, dcldt, with time can be attributed to four possible causes l 3 : (a) where the bulk concentration c, becomes comparable to the saturation concentration c, at the interface, i.e.change from pseudo zero to first order kinetics ; (b) where the reverse reaction, that is recrystallisation and deposition, becomes important ; (c) where a change in the exposed surface area of the dissolving solid occurs; ( d ) where the diffusion of reactants either way through an insoluble layer at the surface is slow compared to other processes. Both (a) and (b) can be assumed to be unimportant since the reported solubility of the phosphate monohydrate ' is 7.2 x mol dm-3 and the maximum concentration achieved in this work was 6 x mol dm-3, so that less than 1 % of the total reaction was studied. Further evidence to support the assumption that (b) is not influencing the rate was gained by rotating a new disc in a solution obtained from a previous experimental run, that is a solution in which the initial solute concentration was not zero.The resulting calcium concentration against time plot 21 had a shape similar to that obtained by the previous run where the initial solute concentration was zero. This observation indicates that the factor causing the variation in rate was associated with the pellet itself and not the solution in which it was dissolving. The marked increase in dissolution rate when a disc which had been dissolving for 40 min was replaced with a new disc in the same solution could be explained if varia- tion in the exposed surface area of the phosphate monohydrate was a rate influencing factor. However, at all the rotation speeds used, after the observed period of 40 min, the rate had decreased to approximately 10 % of its initial value, a change in magnitude2360 DISSOLUTION RATE OF SUPERPHOSPHATE unlikely to be caused by surface area variation.Therefore (c) was assumed un- important and attention was directed to the possibility that ( d ) was influencing the rate of the dissolution process. Since the phosphate monohydrate has a lower density than anhydrite more rapid molar removal of the former means that it must be removed from within the pellet. This removal of the phosphate monohydrate from within superphosphate has been reported by Williams and others 24 to occur in soil, the fertiliser granule ultimately becoming a porous structure of calcium sulphate. It was therefore proposed that for a rotating disc of superphosphate, the pores or cavities opened up by the loss of calcium bis(dihydrogen phosphate) monohydrate are of dimensions such that the solution contained in them is stationary with respect to the disc. Diffusion of solute through these pores to the disc surface controls the dissolu- tion rate since the chemical steps are fast.This means that as dissolution proceeds the rate will become independent of the rotation speed and will decrease. EVIDENCE FOR FORMATION OF POROUS LAYER If the above proposal is correct then the dissolution kinetics should obey the parabolic law derived by Mott and Gurney 2 5 to describe diffusion processes in ionic crystals. Plots of both the square of the calcium concentration against time and the square of the phosphate concentration against time gave linear graphs 21 showing that the parabolic law was obeyed over the 40 min period observed.Formation of a leached porous layer has been suggested for the parabolic kinetics found for dissolu- tion of some magnesium silicates in acid solutions.26 Examination of the disc surface after rotation for 40 min at all speeds showed it to be not only rougher in texture but also softer and lighter in colour. In cross section the pellet displayed a distinct band extending inwards from the exposed surface, the thickness of this band increasing with the length of time that the disc was exposed to the solution. This layer was porous to solution but the remainder of the pellet was not. Viewed under a low-powered microscope the surface of the disc was covered with pores or holes which were entirely absent from the original undissolved pellet.The maximum diameter of these pores, at the surface; was approximately 5 x cm but the location and size of the pores appeared random. X-ray diffraction patterns of this layer showed a marked decrease in the intensity of the peaks associated with calcium bis(dihydrogen phosphate) monohydrate and also indicated that the calcium sulphate was still present as anhydrite. Samples of superphosphate, outer porous layer and inner undissolved pellet were dissolved completely by boiling in acid, and analysed for phosphate and sulphate as before. These analyses confirmed that the outer layer had been depleted of calcium bis(dihydrogen phosphate) monohydrate as the phosphate content in this portion of the pellet was less than 30 % of that originally present.COMPARISON WITH THEORETICAL TRANSPORT CONTROLLED RATE Since the initial dissolution of superphosphate is controlled by transport away from the outer surface of the rotating disc it is possible to calculate the theoretical rate from the Levich l 2 equation and compare this with the observed rate. The diffusion coefficients for calcium phosphates do not appear to have been reported but as dilute aqueous electrolyte solutions have diffusion coefficients of magnitude cm2 s-l 27 this value was used for D in the following calculations.A . F . M. BARTON AND S . R . MCCONNEL 236 1 The kinematic viscosity v changes very little with concentration 17 so that the value for pure water at 25°C of 8.9 x cm2 s-l was used.From the Levich theory l 2 the theoretical rate constant k?'' is given by where w is the disc rotation speed in rads-l. Substituting for co = 7.4rad s-l (71 rev. min-l) and using the values for D and v given then k?'' = I .2 x lop3 crn S-'. The uncertainty in arises solely from the assumption of the value of D and may be as high as 50 %. The observed rate constant kOTbbS is related to the observed rate dc/dt by the equation where Y is the volume of solution (350 cm3), A is the surface area of calcium bis(di- hydrogen phosphate) monohydrate (estimated as 1.5 cm2 f 10 % by comparison of densities of the phosphate monohydrate and anhydrite), c, is the concentration at the interface (7.2 x mol dm-3) and c, is the bulk concentration, with the approxi- mation that c, = 0.The observed initial value of dc/dt at LU = 7.4 rad s-l was (0.31 k0.02) x Substitution and calculation gives krtPs = (1.0f 0.1) x cm s-l. The good agreement in terms of order of magnitude between the observed and the theoretical rate constants provides further evidence that convective diffusion, that is transport, is controlling the dissolution of superphosphate under the experimental conditions. mol dm-3 s-l. A. F. M. Barton and N. M. Wilde, Trans. Faraday SOC., 1971,67, 3590. L. B. Nelson, Ada Agronomy, 1965, 17, 1. E. E. Shawcross and M. S. White, Annual Rep. New Zealand Fertiliser Manufacturers' Research Association, 1971-72, 28. C. H. Williams, Austral. J. Soil Res., 1971, 9, 83. W. L. Lindsay and H. F. Stephenson, Proc. Soil Sci. SOC. Amer., 1959, 23, 12. L. A. G. Aylmore, M. Karim and J. P. Quirk, Austral. J. Soil Res., 1971, 9, 21. ' Handbook of Chemistry and Physics (The Chemical Rubber Co., Ohio, Slst edn., 1970). E. Bock, Canad. J. Chem., 1961,39, 1746. A. R. Burkin, The Chemistry of Hydrometallurgical Processes (Spon, London, 1966). lo D. P. Gregory and A. C. Riddiford, J. Electrochem. Soc., 1970,107, 950. D. D. Macdonald and G. A. Wright, Canad. J. Chem., 1970,48,2847. V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, New Jersey, 1962). l 3 L. L: Bircumshaw and A. C. Riddiford, Quart. Rev., 1952, 6, 157. l4 R. L. Demmerle and W. J. Sackett, Znd. Eng. Chem., 1949, 41, 1306. l 5 S. J. Gregg and E. G. J. Willing, J. Chem. SOC., 1951, 2916. l 6 W, Stollenwerk, Z. Pflanzenernaher. Dungung u. Bodenk., 1931,21A, 321 ; Chem. Abs., 25,5493. l7 A. C. Riddiford, Adv. Electrochem. Electrochem. Eng., 1966, 4, 47. S. Azim and A. C. Riddiford, Anal. Chem., 1962, 34, 1023. l9 D. P. Gregory and A. C. Riddiford, J. Chem. Soc., 1956, 3756. '* J. Rogers (New Zealand Fertiliser Manufacturers' Research Association), personal communi- 21 S. R. McConnel, MSc. Thesis (Victoria University of Wellington, 1973). 22 S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New 2 3 E. 0. Huffman, W. E. Cate, M. E. Deming and K. L. Elmore, J. Agric. Food Chem., 1957,5,266. 24 E. H. Brown, W. E. Brown and J. R. Lehr, Proc. Soil Sci. SOC. Amer., 1959, 23, 3. 2 5 N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford, 2nd edn., 1948). 26 R. W. Luce, R. W. Bartlett and G. A. Parks, Geochim. Cosmochim. Acta, 1972, 36, 35. 27 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn., cation. York, 1941). 1959).

ISSN:0300-9599    

DOI:10.1039/F19747002355

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Ion Exchange in Mordenite BY RICHARD M. BARRER" AND JACEK KLINOWSKI Physical Chemistry Laboratories, Chemistry Department, Imperial College, London SW7 2AY Received 9th May, 1974 Ion-exchange isotherms have been measured for synthetic mordenite involving the cation pairs Na+ +Cs+, NH: +K+, NH; +Na+, NH: +Li+, 2NH: +Ca2+, 2NH: S r 2 + and 2NH: +Ba2+. In a11 cases except those involving Ca2+ and Sr2+ reversible exchange was effected. The values of the thermodynamic equilibrium constant, Ka, and the standard free energy of exchange, AGe, were calculated for the reversible pairs. For additional combinations of the reversible ionic pairs, Ka and A G e were obtained using the triangle rule. The thermodynamic affinity sequence is Cs+ > K+ > NH; > Na+ > Ba2+ > Li+. The thermodynamic affinity sequence among monovalent alkali metal ions established in this work for mordenite was found to be repeated for other zeolites, provided exchanges which do not go to completion are normalised by considering the equilibrium only in terms of the exchangeable fraction of the ions.Despite the interest in synthetic mordenite, its ready availability and its siliceous, acid-stable nature there have been few measurements of cation exchange in this mineral,'-9 and of these studies only one (using a natural mordenite) presented any isotherm^.^ Measurements were therefore made of exchange isotherms in mordenite involving alkali and alkaline-earth metal cations and the NH: cation. The dimensions of the orthorhombic unit cell of mordenite are lo a = 18.13 A, b = 20.49 and c = 7.52 A, and the idealised unit cell content is Na8[A18Si40096]* 24H20.The main channels in the structure are parallel with (001) and have free dimensions of about 6.7 x 7.0 A. They are lined on both sides by side pockets having entrances of -3.9 A free diameter and are directed along (010). The pockets lining adjacent channels are displaced by $c with respect to each other. A pocket in one channel is linked to each of two pockets belonging to an adjacent channel by shared, distorted, 8-ring windows of free dimension -2.8 A. A sodium ion located in each of these $-rings accounts for half the exchangeable cations in the zeolite. EXPERIMENTAL Synthetic sodium mordenite (sodium Zeolon) was supplied by the Norton Co. The crystals were washed several times with distilled water and were stored over saturated calcium nitrate (relative humidity -56 %).Analysis by standard procedures gave the unit cell composition Thus the ratio Si02/A1203 was 10.53. ment with concentrated NH4CI. The unit cell composition of the product was Na7. 5 6fA17. 6 7si40. 3 6FeO. 0 2 7 0 9 61 *23*6H20* NH4-mordenite was prepared in quantity from some of the Na-form by prolonged treat- (NH4)7.4 6[A17. 67si40.3 6FeO. 0 2 7 0 9 61-l 9-5H20. Either the Na- or the NH,-form, as appropriate, was then used to determine the exchange isotherms of Na++Cs+, NH1; +K+, NH t +Na+, NH 1; $Li+, 2NH +Ca2+, 2NH 1; +Sr2+ and 2NHz+Ba2+. Equilibria were normally measured at 25°C with constant solution 2362R. M . BARRER AND J . KLINOWSKI 2363 concentrations of 0.05 equiv.dm-". Weighed amounts of the homoionic zeolite were equilibrated in 60 cm3 polypropylene bottles with solutions containing known proportions of the competing ions. For each point the bottles were rotated for 10 days for uni-univalent exchanges and 21 days for uni-divalent exchanges. The equilibrium compositions of the supernatant solutions were determined for the metal ions by atomic absorption or emission spectrophotometry and the NHZ by the Kjeldahl method. This was also used to find the NHZ content of the crystals. ANALYSIS OF ISOTHERMS The exchange reaction for ions A Z ~ + and B z ~ + is ZA and ZB are the valencies of the ions of A and B and the subscripts s and c refer to solution and crystalline zeolite respectively. The modified selectivity (or Kielland) quotient is then given by where A , and B, are the equivalent cation fractions of A and B in the zeolite, rnt and rn: are the molalities of A and B in solution and YA and YB are the activity coefficients of ions A and B in the mixed solution, Their ratio, r, was evaluated from the formula (AX) ZA(ZB + Zx)/Zx (BX) ZB(ZA + Zx)/Zx = yiA/y? = [YBX 1 ICYAX 1 (3) using the values of the mean activity coefficients of salts AX and BX in the mixed solution, y(Z5) and y(&, evaluated by the method introduced by Glueckauf.l 1 In eqn (3) Z, is the valence of the common anion X. The plots of log& against A, were then fitted by an appropriate polynomial in A,, using a least squares method. The activity coefficients, f, of individual cations and the thermodynamic equilibrium constant, K,, were then obtained by integration using the expressions : log fp = 0.4343(2, - ZA)B, - B, log K, + (4) log K , = 0.4343(Z,-ZA)+ log K , dA,.s: Linear, quadratic and cubic equations of the form logK, = C*+C1A,+C,A,2+. . . (7) where Co, C1 and C2 are coefficients, were each used to fit the experimental curves. The error of fit in each case is reflected in an R-factor already defined.13 The polynomial giving the lowest R was chosen, Although a higher order polynomial will fit a given number of points better than a lower order one, it does not follow that R is lower for the higher order polynomial because the order of the polynomial is one of the factors influencing R. The best fit equations were quadratic or cubic.TRIANGLE RULE I N GENERAL FORM From the values of K, determined as above [eqn (6)j values of K, may be derived for exchange equilibria additional to those actually measured. Let K:9A, KtPC and K:*A denote the thermodynamic equilibrium constants and AGgA, AGEc and AGgA the corresponding standard free energies per equivalent of reaction for reaction (1) and for the respective reactions Z,CF + + Z,BfB + + Z , BFB + + Z,C,Zc +2364 ION EXCHANGE IN MORDENITE and ZCAfA+ 4- z,c,Zc+ + z,cfc+ 4- ZCA:A+. Then per equivalent of reaction (l), (8) and (9) give AGgA = AGgA-AGgc where with similar relations for AGEA and AG&. Thus from eqn (10) and (11) one obtains (12) K ~ , A = (K~,A)ZC/ZBI(K~,C)ZA!ZB as the general form of the triangle rule. If Ka for any two of the equilibria in eqn (l), (8) and (9) has been measured then the third can be evaluated from eqn (12).RESULTS AND DISCUSSION The experimental isotherms are shown in fig. 1 and 2, and were analysed according to the procedures outlined above. 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 equivalent fraction of entering ion in crystal FIG. 1 .-Ion-exchange isotherms in mordenite. (a) Na+ +NH; ; (b) NH; +Li+ ; (c) NHf +K+ ; (a) Na++Cs+. In all isotherms open circles denote forward isotherm points and filled circles denote reverse isotherm points, all at 25°C and total solution concentration 0.05 equiv. dm-3. In (d) the iso- therm obtained for a natural mordenite is shown as the dashed line. EQUILIBRIUM CONSTANTS AND STANDARD FREE ENERGIES OF EXCHANGE The values of K, and AGe are given in table 1.The experimentally measured equilibria in the table are marked with asterisks. The thermodynamic affinity sequence is Csf > K+ > NHB > Na+ > Ba2+ > Lif.R . M. BARRER A N D J . KLINOWSKI 2365 equivalent fraction of entering ion in crystal FIG. 2.-Ion-exchange isotherms in mordenite. (a) 2NHi +Ca2+ ; (6) 2NHi +Sr2+ ; (c) 2NH: + Ba2+. Open circles denote forward isotherm points and the filled circle in (c) denotes a reverse isotherm point at 25°C and total solution concentration 0.05 equiv. dm-3. In addition in (a) A refers to exchange at 80°C and total solution concentration 0.05 equiv. dm-3, Cl refers to exchange at 80°C and total solution concentration 0.5 equiv. dm-3. TABLE 1 .-THERMODYNAMIC EQUILIBRIUM CONSTANTS AND STANDARD FREE ENERGIES FOR EXCHANGES AT 25°C exchan ye K, AG*/kJ equiv.-' Na++ Cs+ 27.2* Na++K+ 7.28 Na+-+NHz 4.56* 2Na+--+Ba2+ 0.334 Na++Li+ 0.0539 Kf-+ Cs+ 3.74 K+-+NHi 0.627* K++ Li+ 0.007 40 2K+-+Ba2+ 0.006 29 Li++ Csf 505 2Li+--+Ba2+ 1 1 5 Li+-+NHi 84.8* NHi+Cs+ 5.97 2NHi-+Ba2+ 0.01 60" -8.19* - 3.76* 4.21 7.24 -4.92 3.27 1.1 6* 12.2 6.28 - 4.43 5.12* 2Cs+-+Ba2+ 0.000 440 9.58 * Ka and A G e measured experimentally.Other values are derived from the triangle rule. AFFINITY SEQUENCES I N ZEOLITES As the results in table 2 demonstrate, the thermodynamic affinity sequence among monovalent alkali metal ions established in this work for mordenite is repeated for some other zeolites, provided exchanges which do not go to completion are normal- ised l4 by considering the equilibrium only in terms of the fraction of the ions which is exchangeable. The larger alkali metal ions always show the greatest affinity and the smallest (Li) always shows the least affinity for the exchanger.There are a few irregularities in the table, but the trend is very clear. The zeolites considered are all so open that ion sieve effects of the kind that have been reported for analcite 2 5 or sodalite 26 are absent. The regularity of the results does not conform with the diverse2366 ION EXChANGB I N MORbENITE affinity sequences which Eisenman’s theory predicts,27 but does conform to the rule that smaller, more energetically solvated cations concentrate preferentially over larger, less energetically solvated ions in the aqueous solution, while within zeolite crystals of diverse structures the opposite is the case.TABLE 2.-THERMODYNAMIC AFFINITY SEQUENCES IN SOME ZEOLITES zeolite reference sequence mordeni te pliillipsite Na-P Na-X Na-X Na-Y zeolite A cha bazi te zeolite K-GI hectori te* this work 15 16 17 18 18, 19 20 21,22 23 24 Cs > K > Na > Li Cs > K > Rb > Na > Li Cs, Rb, K > Na > Li Rb > Cs > K > Na > Li Cs > Rb > Na > K > Li Cs > Rb 3 K > Na > Li Cs > Na > Rb > K > Li Cs > K > Rb > Na > Li Cs > K > Na > Li Cs > Rb > K > Na * For the clay mineral hectorite a mass action rather than the thermodynamic selectivity is given, based on shapes of forward isotherms only. Those exchanges in table 2 which do not go to completion have in some instances already been normalised by the various authors.Those for Na-X in ref. (1 8) have been normalised by us for the experimental exchange limits for Na+-+Rb+ of 65 % and for Na+-+Cs+ of 72 %. In ref. (18) the exchange limit for Na-X had been assumed for both Rb and Cs to be 82 %. Normalisation in ref. (20) was made for exchange limits Na++Rb+ of 76 % and for Na+--+Cs+ of 63 %. Originally these experimental ex- change limits had been disregarded when calculating K, and AG*, and as a result the affinity sequence in ref. (20) was Na > K > Rb > Li > Cs. Thus the regularity of the affinity sequences appears only after normalisation. Homoionic Ca-, Sr- and Ba-mordenites were not prepared. The largest equiva- lent cation fractions actually reached were 0.60, 0.62 and 0.84 for Ca2+, Sr2+ and Ba2+ respectively (compared with 0.72, 0.49 and 0.73 reported earlier ’).At least in part this behaviour is thought to be associated with the strong hydration of alkaline-earth metal ions, which makes it difficult for such ions to enter the side pockets in mordenite (see Introduction). This difficulty of access cannot be explained in terms of the radii of the anhydrous cations because Cs+, a much larger cation, readily replaces sodium [(fig. 1 (d)]. Because of uncertainty over the limiting extents of exchange [fig. 2(a) and (b)] the equilibria 2NH: +Ca2+ and 2NHi +Sr2+ were not submitted to thermodyn- amic analysis. However, for 2NHi +Ba2+ the form of the isotherm clearly suggests that full exchange could be effected [fig.2(c)] and this exchange was analysed accord- ingly. The exchange 2NHi +Ca2+ was also studied using more concentrated solutions. It was found that the selectivity at 80°C decreased when the concentration of the electrolyte was raised from 0.05 to 0.5 equiv. dm-3 [fig. 2(a)]. This behaviour agrees qualitatively with an earlier study 28 and with the quantitative treatment 29 showing how the selectivity for the ion of higher valence increases with dilution of the aqueous solution. However, this increase is less than expected, which is a further indication that the low-concentration isotherm has not reached equilibrium. Also, for a given electrolyte concentration the isotherm for exchange of NH; by Ca2+ was, as found in earlier equilibrium studies on various zeolites,26 little changed when the temperature was altered from 25 to 80°C. Other notable features are the very low selectivity forR .M. BARRER AND J. KLINOWSKI 2367 Li+[fig. 1(6)] and the extremely good selectivity for Cs+ [fig. l(d)]. The selectivity based on the mass action quotient for Na-i-+Cs+ is greater in the synthetic mordenite than is that recorded by Rao and Rees for the natural mineral from Nova Scotia [fig. Wl. R. M. Barrer, J. Chem. SOC., 1948, 2158. L. L. Ames Jr., Amer. Mineral., 1961, 46, 11 20. H. Takahashi and Y . Nishimura, Seisan-Kenkyu, 1968, 20,466. D. B. Hawkins, Materials Res. Bull., 1967, 2, 1021. G. Lenzi and A. Pozzuoli, Rend. Accad. Sci. Fis. Mat. Naples, 1969, 36, 235. V. A. Chumakov, V. I. Gorshkov, A.M. Tolmachev and V. A. Fedorov, Vestnik Moskov Uniu., 1969, 24, 22. N. F. Erinolenko, L. N. Malashevich, S. A. Levina and A. A. Prokopovich, Vestsi Akad. Nawk Belarus. S.S.R., Ser. Khim. Navuk, 1968, 5 , 18. L. V. C. Rees and A. Rao, Trans. Faraday SOC., 1966, 62, 2103. A. Rao and L. V. C . Rees, Trans. Faraday SOC., 1966, 62,2505. l o W. M. Meier, 2. Krist., 1961, 115, 439. E. Glueckauf, Nature, 1949, 163,414. l2 G. L. Gaines and H. C . Thomas, J. Chem. Phys., 1953, 21(4), 714. l 3 B. M. Munday, Ph.D. Thesis (University of London, 1967). l4 R. M. Barrer, J. Klinowski and H. S . Sherry, J.C.S. Faraday II, 1973, 69, 1669. l 5 R. M. Barrer and B. M. Munday, J. Chern. SOC. A, 1971, 2904. l 6 R. M. Barrer and B. M. Munday, J. Chem. SOC. A, 1971, 2909. l7 R. M. Barrer, L.V. C. Rees and M. Shamsuzzoha, J. Inorg. Nuclear Chem., 1966, 28, 629. l 9 R. M. Barrer, J. A. Davies and L. V. C. Rees, J. Inorg. Nuclear Chem., 1968, 30, 3333. 2o R. M. Barrer, L. V. C . Rees and D. J. Ward, Proc. Roy. SOC. A, 1963, 273, 180. 21 R. M. Barrer and D. C. Sammon, J. Chem. Soc., 1955, 2838. 2 2 R. M. Barrer, J. A. Davies and L. V. C. Rees, J . Inorg. Nuclear Cheni., 1969, 31, 219. 2 3 R. M. Barrer and J. Klinowski, J.C.S. Faraday 1, 1972, 68, 1956. 24 R. M. Barrer and D. L. Jones, J. Chem. SOC. A, 1971, 503. 2 5 R. M. Barrer and D. C. Sammon. J. C12ein. Suc., 1956, 675. 26 R. M. Barrer and J. D. Falconer, Proc. Roy. Sor. A, 1956. 235, 227. ’’ G. Eisenman, Biuphys. J., 1962, 2(2) Suppl., 259. ’’ H. C. Subba Rao and M. M. David, A.I. Cheni. Eng.J., 1957, 3, 187. 29 R. M. Barrsr and J. Klinowski, J.C.S. Faraday I, 1974, 70, 2080. H. S. Sherry, J. Phys. Chem., 1966,70, 1158. Ion Exchange in Mordenite BY RICHARD M. BARRER" AND JACEK KLINOWSKI Physical Chemistry Laboratories, Chemistry Department, Imperial College, London SW7 2AY Received 9th May, 1974 Ion-exchange isotherms have been measured for synthetic mordenite involving the cation pairs Na+ +Cs+, NH: +K+, NH; +Na+, NH: +Li+, 2NH: +Ca2+, 2NH: S r 2 + and 2NH: +Ba2+. In a11 cases except those involving Ca2+ and Sr2+ reversible exchange was effected. The values of the thermodynamic equilibrium constant, Ka, and the standard free energy of exchange, AGe, were calculated for the reversible pairs. For additional combinations of the reversible ionic pairs, Ka and A G e were obtained using the triangle rule.The thermodynamic affinity sequence is Cs+ > K+ > NH; > Na+ > Ba2+ > Li+. The thermodynamic affinity sequence among monovalent alkali metal ions established in this work for mordenite was found to be repeated for other zeolites, provided exchanges which do not go to completion are normalised by considering the equilibrium only in terms of the exchangeable fraction of the ions. Despite the interest in synthetic mordenite, its ready availability and its siliceous, acid-stable nature there have been few measurements of cation exchange in this mineral,'-9 and of these studies only one (using a natural mordenite) presented any isotherm^.^ Measurements were therefore made of exchange isotherms in mordenite involving alkali and alkaline-earth metal cations and the NH: cation.The dimensions of the orthorhombic unit cell of mordenite are lo a = 18.13 A, b = 20.49 and c = 7.52 A, and the idealised unit cell content is Na8[A18Si40096]* 24H20. The main channels in the structure are parallel with (001) and have free dimensions of about 6.7 x 7.0 A. They are lined on both sides by side pockets having entrances of -3.9 A free diameter and are directed along (010). The pockets lining adjacent channels are displaced by $c with respect to each other. A pocket in one channel is linked to each of two pockets belonging to an adjacent channel by shared, distorted, 8-ring windows of free dimension -2.8 A. A sodium ion located in each of these $-rings accounts for half the exchangeable cations in the zeolite.EXPERIMENTAL Synthetic sodium mordenite (sodium Zeolon) was supplied by the Norton Co. The crystals were washed several times with distilled water and were stored over saturated calcium nitrate (relative humidity -56 %). Analysis by standard procedures gave the unit cell composition Thus the ratio Si02/A1203 was 10.53. ment with concentrated NH4CI. The unit cell composition of the product was Na7. 5 6fA17. 6 7si40. 3 6FeO. 0 2 7 0 9 61 *23*6H20* NH4-mordenite was prepared in quantity from some of the Na-form by prolonged treat- (NH4)7.4 6[A17. 67si40.3 6FeO. 0 2 7 0 9 61-l 9-5H20. Either the Na- or the NH,-form, as appropriate, was then used to determine the exchange isotherms of Na++Cs+, NH1; +K+, NH t +Na+, NH 1; $Li+, 2NH +Ca2+, 2NH 1; +Sr2+ and 2NHz+Ba2+.Equilibria were normally measured at 25°C with constant solution 2362R. M . BARRER AND J . KLINOWSKI 2363 concentrations of 0.05 equiv. dm-". Weighed amounts of the homoionic zeolite were equilibrated in 60 cm3 polypropylene bottles with solutions containing known proportions of the competing ions. For each point the bottles were rotated for 10 days for uni-univalent exchanges and 21 days for uni-divalent exchanges. The equilibrium compositions of the supernatant solutions were determined for the metal ions by atomic absorption or emission spectrophotometry and the NHZ by the Kjeldahl method. This was also used to find the NHZ content of the crystals. ANALYSIS OF ISOTHERMS The exchange reaction for ions A Z ~ + and B z ~ + is ZA and ZB are the valencies of the ions of A and B and the subscripts s and c refer to solution and crystalline zeolite respectively.The modified selectivity (or Kielland) quotient is then given by where A , and B, are the equivalent cation fractions of A and B in the zeolite, rnt and rn: are the molalities of A and B in solution and YA and YB are the activity coefficients of ions A and B in the mixed solution, Their ratio, r, was evaluated from the formula (AX) ZA(ZB + Zx)/Zx (BX) ZB(ZA + Zx)/Zx = yiA/y? = [YBX 1 ICYAX 1 (3) using the values of the mean activity coefficients of salts AX and BX in the mixed solution, y(Z5) and y(&, evaluated by the method introduced by Glueckauf. l 1 In eqn (3) Z, is the valence of the common anion X. The plots of log& against A, were then fitted by an appropriate polynomial in A,, using a least squares method.The activity coefficients, f, of individual cations and the thermodynamic equilibrium constant, K,, were then obtained by integration using the expressions : log fp = 0.4343(2, - ZA)B, - B, log K, + (4) log K , = 0.4343(Z,-ZA)+ log K , dA,. s: Linear, quadratic and cubic equations of the form logK, = C*+C1A,+C,A,2+. . . (7) where Co, C1 and C2 are coefficients, were each used to fit the experimental curves. The error of fit in each case is reflected in an R-factor already defined.13 The polynomial giving the lowest R was chosen, Although a higher order polynomial will fit a given number of points better than a lower order one, it does not follow that R is lower for the higher order polynomial because the order of the polynomial is one of the factors influencing R.The best fit equations were quadratic or cubic. TRIANGLE RULE I N GENERAL FORM From the values of K, determined as above [eqn (6)j values of K, may be derived for exchange equilibria additional to those actually measured. Let K:9A, KtPC and K:*A denote the thermodynamic equilibrium constants and AGgA, AGEc and AGgA the corresponding standard free energies per equivalent of reaction for reaction (1) and for the respective reactions Z,CF + + Z,BfB + + Z , BFB + + Z,C,Zc +2364 ION EXCHANGE IN MORDENITE and ZCAfA+ 4- z,c,Zc+ + z,cfc+ 4- ZCA:A+. Then per equivalent of reaction (l), (8) and (9) give AGgA = AGgA-AGgc where with similar relations for AGEA and AG&.Thus from eqn (10) and (11) one obtains (12) K ~ , A = (K~,A)ZC/ZBI(K~,C)ZA!ZB as the general form of the triangle rule. If Ka for any two of the equilibria in eqn (l), (8) and (9) has been measured then the third can be evaluated from eqn (12). RESULTS AND DISCUSSION The experimental isotherms are shown in fig. 1 and 2, and were analysed according to the procedures outlined above. 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 equivalent fraction of entering ion in crystal FIG. 1 .-Ion-exchange isotherms in mordenite. (a) Na+ +NH; ; (b) NH; +Li+ ; (c) NHf +K+ ; (a) Na++Cs+. In all isotherms open circles denote forward isotherm points and filled circles denote reverse isotherm points, all at 25°C and total solution concentration 0.05 equiv. dm-3. In (d) the iso- therm obtained for a natural mordenite is shown as the dashed line.EQUILIBRIUM CONSTANTS AND STANDARD FREE ENERGIES OF EXCHANGE The values of K, and AGe are given in table 1. The experimentally measured equilibria in the table are marked with asterisks. The thermodynamic affinity sequence is Csf > K+ > NHB > Na+ > Ba2+ > Lif.R . M. BARRER A N D J . KLINOWSKI 2365 equivalent fraction of entering ion in crystal FIG. 2.-Ion-exchange isotherms in mordenite. (a) 2NHi +Ca2+ ; (6) 2NHi +Sr2+ ; (c) 2NH: + Ba2+. Open circles denote forward isotherm points and the filled circle in (c) denotes a reverse isotherm point at 25°C and total solution concentration 0.05 equiv. dm-3. In addition in (a) A refers to exchange at 80°C and total solution concentration 0.05 equiv.dm-3, Cl refers to exchange at 80°C and total solution concentration 0.5 equiv. dm-3. TABLE 1 .-THERMODYNAMIC EQUILIBRIUM CONSTANTS AND STANDARD FREE ENERGIES FOR EXCHANGES AT 25°C exchan ye K, AG*/kJ equiv.-' Na++ Cs+ 27.2* Na++K+ 7.28 Na+-+NHz 4.56* 2Na+--+Ba2+ 0.334 Na++Li+ 0.0539 Kf-+ Cs+ 3.74 K+-+NHi 0.627* K++ Li+ 0.007 40 2K+-+Ba2+ 0.006 29 Li++ Csf 505 2Li+--+Ba2+ 1 1 5 Li+-+NHi 84.8* NHi+Cs+ 5.97 2NHi-+Ba2+ 0.01 60" -8.19* - 3.76* 4.21 7.24 -4.92 3.27 1.1 6* 12.2 6.28 - 4.43 5.12* 2Cs+-+Ba2+ 0.000 440 9.58 * Ka and A G e measured experimentally. Other values are derived from the triangle rule. AFFINITY SEQUENCES I N ZEOLITES As the results in table 2 demonstrate, the thermodynamic affinity sequence among monovalent alkali metal ions established in this work for mordenite is repeated for some other zeolites, provided exchanges which do not go to completion are normal- ised l4 by considering the equilibrium only in terms of the fraction of the ions which is exchangeable.The larger alkali metal ions always show the greatest affinity and the smallest (Li) always shows the least affinity for the exchanger. There are a few irregularities in the table, but the trend is very clear. The zeolites considered are all so open that ion sieve effects of the kind that have been reported for analcite 2 5 or sodalite 26 are absent. The regularity of the results does not conform with the diverse2366 ION EXChANGB I N MORbENITE affinity sequences which Eisenman’s theory predicts,27 but does conform to the rule that smaller, more energetically solvated cations concentrate preferentially over larger, less energetically solvated ions in the aqueous solution, while within zeolite crystals of diverse structures the opposite is the case.TABLE 2.-THERMODYNAMIC AFFINITY SEQUENCES IN SOME ZEOLITES zeolite reference sequence mordeni te pliillipsite Na-P Na-X Na-X Na-Y zeolite A cha bazi te zeolite K-GI hectori te* this work 15 16 17 18 18, 19 20 21,22 23 24 Cs > K > Na > Li Cs > K > Rb > Na > Li Cs, Rb, K > Na > Li Rb > Cs > K > Na > Li Cs > Rb > Na > K > Li Cs > Rb 3 K > Na > Li Cs > Na > Rb > K > Li Cs > K > Rb > Na > Li Cs > K > Na > Li Cs > Rb > K > Na * For the clay mineral hectorite a mass action rather than the thermodynamic selectivity is given, based on shapes of forward isotherms only.Those exchanges in table 2 which do not go to completion have in some instances already been normalised by the various authors. Those for Na-X in ref. (1 8) have been normalised by us for the experimental exchange limits for Na+-+Rb+ of 65 % and for Na+-+Cs+ of 72 %. In ref. (18) the exchange limit for Na-X had been assumed for both Rb and Cs to be 82 %. Normalisation in ref. (20) was made for exchange limits Na++Rb+ of 76 % and for Na+--+Cs+ of 63 %. Originally these experimental ex- change limits had been disregarded when calculating K, and AG*, and as a result the affinity sequence in ref. (20) was Na > K > Rb > Li > Cs. Thus the regularity of the affinity sequences appears only after normalisation. Homoionic Ca-, Sr- and Ba-mordenites were not prepared.The largest equiva- lent cation fractions actually reached were 0.60, 0.62 and 0.84 for Ca2+, Sr2+ and Ba2+ respectively (compared with 0.72, 0.49 and 0.73 reported earlier ’). At least in part this behaviour is thought to be associated with the strong hydration of alkaline-earth metal ions, which makes it difficult for such ions to enter the side pockets in mordenite (see Introduction). This difficulty of access cannot be explained in terms of the radii of the anhydrous cations because Cs+, a much larger cation, readily replaces sodium [(fig. 1 (d)]. Because of uncertainty over the limiting extents of exchange [fig. 2(a) and (b)] the equilibria 2NH: +Ca2+ and 2NHi +Sr2+ were not submitted to thermodyn- amic analysis. However, for 2NHi +Ba2+ the form of the isotherm clearly suggests that full exchange could be effected [fig.2(c)] and this exchange was analysed accord- ingly. The exchange 2NHi +Ca2+ was also studied using more concentrated solutions. It was found that the selectivity at 80°C decreased when the concentration of the electrolyte was raised from 0.05 to 0.5 equiv. dm-3 [fig. 2(a)]. This behaviour agrees qualitatively with an earlier study 28 and with the quantitative treatment 29 showing how the selectivity for the ion of higher valence increases with dilution of the aqueous solution. However, this increase is less than expected, which is a further indication that the low-concentration isotherm has not reached equilibrium.Also, for a given electrolyte concentration the isotherm for exchange of NH; by Ca2+ was, as found in earlier equilibrium studies on various zeolites,26 little changed when the temperature was altered from 25 to 80°C. Other notable features are the very low selectivity forR . M. BARRER AND J. KLINOWSKI 2367 Li+[fig. 1(6)] and the extremely good selectivity for Cs+ [fig. l(d)]. The selectivity based on the mass action quotient for Na-i-+Cs+ is greater in the synthetic mordenite than is that recorded by Rao and Rees for the natural mineral from Nova Scotia [fig. Wl. R. M. Barrer, J. Chem. SOC., 1948, 2158. L. L. Ames Jr., Amer. Mineral., 1961, 46, 11 20. H. Takahashi and Y . Nishimura, Seisan-Kenkyu, 1968, 20,466. D. B. Hawkins, Materials Res. Bull., 1967, 2, 1021. G. Lenzi and A. Pozzuoli, Rend. Accad. Sci. Fis. Mat. Naples, 1969, 36, 235. V. A. Chumakov, V. I. Gorshkov, A. M. Tolmachev and V. A. Fedorov, Vestnik Moskov Uniu., 1969, 24, 22. N. F. Erinolenko, L. N. Malashevich, S. A. Levina and A. A. Prokopovich, Vestsi Akad. Nawk Belarus. S.S.R., Ser. Khim. Navuk, 1968, 5 , 18. L. V. C. Rees and A. Rao, Trans. Faraday SOC., 1966, 62, 2103. A. Rao and L. V. C . Rees, Trans. Faraday SOC., 1966, 62,2505. l o W. M. Meier, 2. Krist., 1961, 115, 439. E. Glueckauf, Nature, 1949, 163,414. l2 G. L. Gaines and H. C . Thomas, J. Chem. Phys., 1953, 21(4), 714. l 3 B. M. Munday, Ph.D. Thesis (University of London, 1967). l4 R. M. Barrer, J. Klinowski and H. S . Sherry, J.C.S. Faraday II, 1973, 69, 1669. l 5 R. M. Barrer and B. M. Munday, J. Chern. SOC. A, 1971, 2904. l 6 R. M. Barrer and B. M. Munday, J. Chem. SOC. A, 1971, 2909. l7 R. M. Barrer, L. V. C. Rees and M. Shamsuzzoha, J. Inorg. Nuclear Chem., 1966, 28, 629. l 9 R. M. Barrer, J. A. Davies and L. V. C. Rees, J. Inorg. Nuclear Chem., 1968, 30, 3333. 2o R. M. Barrer, L. V. C . Rees and D. J. Ward, Proc. Roy. SOC. A, 1963, 273, 180. 21 R. M. Barrer and D. C. Sammon, J. Chem. Soc., 1955, 2838. 2 2 R. M. Barrer, J. A. Davies and L. V. C. Rees, J . Inorg. Nuclear Cheni., 1969, 31, 219. 2 3 R. M. Barrer and J. Klinowski, J.C.S. Faraday 1, 1972, 68, 1956. 24 R. M. Barrer and D. L. Jones, J. Chem. SOC. A, 1971, 503. 2 5 R. M. Barrer and D. C. Sammon. J. C12ein. Suc., 1956, 675. 26 R. M. Barrer and J. D. Falconer, Proc. Roy. Sor. A, 1956. 235, 227. ’’ G. Eisenman, Biuphys. J., 1962, 2(2) Suppl., 259. ’’ H. C. Subba Rao and M. M. David, A.I. Cheni. Eng. J., 1957, 3, 187. 29 R. M. Barrsr and J. Klinowski, J.C.S. Faraday I, 1974, 70, 2080. H. S. Sherry, J. Phys. Chem., 1966,70, 1158.

ISSN:0300-9599    

DOI:10.1039/F19747002362

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

CORRIGENDUM Accurate Representation of Thermodynamic Properties near the Critical Point By G. A. CHAPELA and J. S. ROWLINSON J.C.S. Faraday I, 1974, 70, 584 The calculated heat capacities at constant volume shown in fig. 2 are wrong, because of an error in a computer programme. At 305.15 K the correct curves shows a larger peak (1.8 J g-' K-l) at the critical density and also agrees better with the experimental results at higher densities. At 306.15 K, an isotherm which passes close to the upper end of the critical region (as defined by the contour r = 0.01), the peak is lowered and the calculated values at higher densities fall to about 0.6 J g-l K-l at a density of 1 g ~ m - ~ . This discrepancy suggests that the precise form of the switching function (27) must be chosen with greater care if good values of C, (a second derivation of the free energy) are to be obtained on iso- therms which just " cut " the critical region. The calculated pressure is unaffected, and no sensible change is made in the calculated value of the energy or entropy.We are indebted to Mr. B. Armstrong of the I.U.P.A.C. Thermodynamic Tables Project Centre for discovering this error. A full account of the use of the equations of this paper will be published : S. Angus, B. Armstrong and K. M. de Reuck, International Thermodynamic Tables of the Fluid State, Carbon Dioxide, 1973 (Butterworth, to be published). 2368 CORRIGENDUM Accurate Representation of Thermodynamic Properties near the Critical Point By G. A. CHAPELA and J. S. ROWLINSON J.C.S. Faraday I, 1974, 70, 584 The calculated heat capacities at constant volume shown in fig. 2 are wrong, because of an error in a computer programme.At 305.15 K the correct curves shows a larger peak (1.8 J g-' K-l) at the critical density and also agrees better with the experimental results at higher densities. At 306.15 K, an isotherm which passes close to the upper end of the critical region (as defined by the contour r = 0.01), the peak is lowered and the calculated values at higher densities fall to about 0.6 J g-l K-l at a density of 1 g ~ m - ~ . This discrepancy suggests that the precise form of the switching function (27) must be chosen with greater care if good values of C, (a second derivation of the free energy) are to be obtained on iso- therms which just " cut " the critical region. The calculated pressure is unaffected, and no sensible change is made in the calculated value of the energy or entropy. We are indebted to Mr. B. Armstrong of the I.U.P.A.C. Thermodynamic Tables Project Centre for discovering this error. A full account of the use of the equations of this paper will be published : S. Angus, B. Armstrong and K. M. de Reuck, International Thermodynamic Tables of the Fluid State, Carbon Dioxide, 1973 (Butterworth, to be published). 2368

ISSN:0300-9599    

DOI:10.1039/F19747002368

出版商:RSC    

年代:1974

数据来源: RSC