INCLUSION COMPLEXES OF METWLNAPHTHALENEB
Nov., 1950
was found to give a [q]/ [ 7 7 ] 0 value of 2.25 if unfiltered, while the filterable portion gave [q]/[q]o = 2.04.) On close inspection of the ca1culation.s' involved in the evaluation of [q]/[q]ofrom the distribution functions, i t is found that for the 1.6 MR. sample more than one-third of the value of [q]/[q]ois contributed by that portion of the sample which has mol. wt. greater than 6,000,000. The sensitivity to filtration is, therefore understandable. Another problem was in fixing the gel point R*. If one plots the light scattering Mwo/Mwversus dose, one h d s R* = 1.5 MR. (see equation 29). On the other hand, if one allows the 1.6 MR. sample to swell in toluene for several hours and then shakes the flask vigorously, one finds no entrapment of air bubbles, thus indicating no gel." A sample of dose 1.7 MR. does entrap minute. air bubbles by this 1.65 MR. Since this value gives test. This indicates E* better over-all consistency in the viscosity analysis, i t was adopted in the following calculations for purposes of illustrations. Plots of [q]/[q]o versus R/R* for measurements in the e solvent are given in Fig. 6. Comparison of these with 0.5-1.0. For the measurements in theory yields 2B/a toluene, if we take a 0.75, one obtains 2p/a 1.0-1.5. On the other hand, if Barry's value of a = 0.68 is assumed, one finds 2P/a = 0-1.0. This lack of precision is disappointing; furthermore, studies by A. A. Miller12 of this system by chemical techniques indicates that 2p/a 0.1. The difficulty is the 1ack.of sensitivity of [q] to small amounts of degradation. Thus it appears that although the theory gives the correct qualitative features, the method is only useful in a quantitative manner when 2B/a > 1. It is also desirable to use 8 solvents to improve precision. As an alternative method, the osmotic and light scattering molecular weights of several of the irradiated samples were determined. These are given in Table 111. These data are plotted in Fig. 7. Using R* = 1.5 as determined by equa-
-
--
-
-
(11) W. J. Barnes, H. A. Dewhurst, L. St. Pierre and R. W. Kilb, J . Polymer Sci., 36, 525 (1959). (12) A. A. Miller, private communication.
1843
tion 29, lines were constructed from equation 28 for various values of CY. Although the precision of the osmotic pressure data is rather poor, it is clear that 20/a > 1/2, in rough agreement with Miller's value. In Fig. 6, there are also plotted the data of Shdtz, et aZ.,1 on irradiated polystyrene. At R/R* < 0.6, [q]/[q]ofollows the curve for 2D/a 2 fairly well. At larger values of R/R*, [ T ] / [ ~ falls ] O much below the ex ected values. Some ossible experimental causes are: (1) i t r a t i o n difficulties, nonrandom initial molecular weight distribution, (3) incorrect value of the ex onent a, and (4) the crosslinking is not purely tetrafunctionafand so the theory developed here is not applicable. In any case, the apparent difference in the behavior silicones and polystyrene is unexpected and would be an interesting topic for further study.
-
6)
Conclusion The qualitative features of the change in intrinsic viscosity of a polymer with irradiation are predicted satisfactorily by the above model. Quantitatively, it is found that [ ~ l ] / [ q ]iso not very sensitive to 2p/a (the ratio of number of degradations to crosslinks) unless 1 < 2p/a < 10. Consequently viscosity studies by themselves are practically useful only in this range of 2/3/a. Outside this range, other techniques-such as light scattering, osmotic pressure or chemical scavenging of radicals -must be employed to find the ratio of scission to crosslinking. Acknowledgment.-The author is grateful to Mr. W. J. Barnes and Miss W. E. Bals for the light scattering and osmotic pressure measurements, and to Mr. J. S. Balwit for the irradiations. He also wishes to acknowledge the interesting discussions of the problem with Dr. A, A. Miller.
INCLUSION COMPLEXES OF METHYLNAPHTHALENES BY JACKMILGROM Contributionfrom the Research and Development Department, Standard Oil Company (Indiana), Whiting, Indiana Received March $6. I960
A chance observation of an unaccountably high melting point prom ted investigation of the system 2-methylnaphthalenen-heptane. T o confirm complex formation, this system waa studiecf by regular and differential thermal analyses, vaporpressure measurement, solids separation and X-ray analysis. Data have been represented by the usual linear phase diagram and a special logarithmicoone. Six different complexes of 2-methylnaphthalene and n-heptane were found a t temperatures between 25 and -92 . Depending upon temperature, eight moles of &methylnaphthalene combine with one, three or eight moles of n-heptane to form three pairs of complexes. The members of each pair have different crystal modifications. Transitions do not proceed readily; some complexes must be cooled below 0" before they transform and one is metastable. These results suggest a mechanism for complex formation. At room temperature a void ap arently exists in the %methylnaphthalene crystal lattice, which can accommodate guest molecules of a definite shape. dmplexes form with both straight- and branched-chain hydrocarbons, althou h molecules as long as n-hexadecane fail to react. Complex formation is not limited to 2-methylnaphthalene. 1-Methyfnaphthalene and perhaps other polycyclic compounds also adduct paraffis. Below room temperature, a new realm of inclusion complexes probably exists.
Introduction During an attempted purification of l-methylnaphthalene in our laboratories, a 30 mole yo solution of 1-methylnaphthalene in n-pentane solidified unexpectedly a t - 70". If an ideal solution had been formed, it would have solidified below - 130°, the freezing point of n-pentane. Solutions of 2-methylnaphthalene and paraffins behaved similarly. These results suggested that both methylnaphthalenes form complexes with alkanes and led to further investigation. Knowledge of solid-liquid equilibria of methylnaphthalene in binary systems is sparse. 2Methylnaphthalene was observed to form a simple
eutectic mixture with triphenylmethane1 and a solid solution with naphthol.* Complexes were formed between methylnaphthalene and acetone, phenol or hydrogen sulfide.8 A recent calorimetric study4 has revealed that both 1- and 2-methylnaphthalene undergo polymorphic transitions sluggishly, exhibiting supercooling and superheating. The system 2-methylnaphthalene-heptane has (1) V. M. Kravchenko. Ulorain. Khim. Zhur., IS, 36 (1952): C. A . , 48, 3776f (1954). (2) G . Nazario, Rev. inst. Adolfo Lute., 8, 137 (1948): C. A . , 44, 421f (1950). (3) E. Terres and A . Doerges, Brennslofl-Chem., 37, 385 (1956). (4) J. P. McCullough. H. L. Finke, J. F. Messerly, 8. S. Todd, T. C. Kincheloe and G. Waddington, THISJOURNAL, 61, 1105 (1957).
1844
JACKMILGROM
(
Vol. 63
nitrogen or a mixture of acetone and Dry Ice. During cooling, a continuous stream of dry nitrogen covered the sample in the flask and prevented absorption of water. Agitation was maintained as long as a liquid phase remained, and cooling was continued through the eutectic temperature. Cooling curves were automatically plotted by a recorder linked to a platinum-resistance thermometer in the sample. Heating curves were similarly plotted after the cold bath surrounding the sample was replaced by a warm bath of acetone or water. Near the melting point, the heating rate was 0.05 to 0.10" per min. Melting points were easily rea! to 0.02' but duplicate analyses differed by as much as 0.05 Supercooling made freezing-point values less accurate than meltingpoint values; therefore, only the latter were used to plot the liquidus curve. However, complete freezing and melting cyrves were used to determine solid-solid transitions. Differential thermal analyses were carried out in a wellinsulated bath equipped with a heater; a constant heating rate of 0.56" per min. was maintained by a controller. Samples were sealed in glass containers having a capacity of 3 ml., and temperature differences A T were measured by an iron-constantan thermocouple having a diameter of 0.065 in. An azelaic acid ester served as the reference material. An X-Y recorder, coupled with a preamplifier, automatically recorded the difference between temperatures of the reference and test samples as a function of time. A mercury thermometer was used to measure the bath temperature. Samples were precooled a t -50" for a t least 24-hr. and then placed in the bath, which was cooled to a temperature just below 0". The samples were allowed to warm and equilibrate in the bath a t 0' before heating was started and the melting curve was obtained. Melting curves for 2-methylnaphthalene and n-heptane mixtures containing 88.5, 81.3 and 59.2 mole % 2-methylnaphthalene are shown in Fig. 1. Vapor-pressure measurements were made in an apparatus that consisted of a flask, an attached mercury manometer and a manifold connected to a series of traps on a high-vacuum line. A mixture of known composition was degassed in the flask until the vapor pressure remained constant. The volatile component was then incrementally distilled into the vacuum line. Before each pressure measurement, the residue in the flask was allowed to equilibrate a t the temperature of the surrounding bath. Measurements were easily read to 0.05 mm. Solids were separated in a Skau tube' or a regular centrifuge tube. The Skau tube was placed in a large centrifuge bottle containing acetone and Dry Ice, which maintained a low temperature during filtration. This apparatus was especially suited to the separation of solids melting near or above 0 " ; below O', the liquid bath surrounding the tube warmed too rapidly in the centrifuge. X-Ray analyses were made by the powder-diffraction method. The apparatus was adapted to low-temperature work by using a stream of cold vapor from liquid nitrogen to cool the capillary tube containing the sample. The temperature of each sample was thus maintained between -20 and 0'. A cellophane box enclosing the sample holder prevented severe icing. Phase Diagram for 2-Methylnaphthalene and n-Heptane. -2-Methylnaphthalene has two crystal forms.4 Crystals I, stable a t a temperature above 15.3", can be supercooled below 0' before they transform into crystals 11, and crystals I1 can be superheated 5" before transformation to I. I n this investigation, polymorphism was confirmed by differential thermal analysis of pure 2-methylnaphthalene. It was first cooled a t -50" for more than 24 hr., and then heated in the regulated-temperature bath. The heatinscurve shown in Fig. 1 has two peaks: one, beginning a t 19 , corresponded to th,e heat absorbed in isothermal transition; the other, at about 34", was the heat of fusion. When mixtures of 2-methylnaphthalene and n-heptane were cooled in the thermal analysis apparatus, their cooling curves showed first a freezing point and then a long halt between -20 and -25', as heat was evolved in a phase transformation. Mixtures freezing below -20" often froze and transformed simultaneously. Cooling curves of mixtures containing 50 mole % or less 2-methylnaphthalene also showed an additional @g halt as the mixtures solidified between -90 and -92 . This halt no doubt corresponds to the eutectic transition.
.
AT.
0
IO
20 TEMPERATURE,
.30
40
OC.
Fig. 1.-Differential thermal analysis of 2-methylnaphthalenelz-heptane mixtures.
been investigated to confirm the existence of methylnaphthalene-paraffin complexes. This system was selected because both materials are available in high purity, and the 2-methyl derivative is conveniently higher-melting than the 1-methyl. To prepare phase diagrams, the system was studied by regular and differential thermal analysis, vapor-pressure measurement and solids separation. Preliminary thermal analyses indicated that the solid precipitated first was metastable and, if cooled below Oo, it transformed t o a stable solid. Therefore, mixtures were precooled before thermal analysis. To compute heats of fusion and transition temperatures, a plot of log mole-fraction against reciprocal temperature was also prepared. Data from the phase diagrams and X-ray studies provided a basis for a mechanism of complex formation in this system and perhaps in analogous ones. Experimental 2-Methylnaphthalene was used without further purification if cryoscopic analysis showed a purity of 98% or higher. When purification was necessary, it was crystallized from an aqueous alcohol solution and dried a t 100" a t 1 m.m. Material 99.8% pure was readily obtained. Crystallization of 2-methylnaphthalene from its own melt proved unsatisFactory. The cryoscopic purity of 1-methylnaphthalene was 96.0'%; of n-heptane., 99.6%; and of n-hexane, 95.0%. Five methods of analysis were used to determine the solidliquid equilibria. The primary method, thermal analysis, defined the liquidus curve in the phase diagram and partially defined phase transitions; however, transitions were more readily and accurately determined by differential thermal analysis and vapor-pressure measurements. Analysis of isolated solids by refragtive-index measurements determiqed their compositions and X-ray studies revealed their structures. Thermal analyses were carried out in an apparatus similar to one used in cryoscopic analysis of pure materials.5 A ten-gram sample, weighed to 0.01 g., was charged to a special Dewar flask and the flask and sample were cooled with liquid (5) Am. SOC.Testing Materials, "ASTM Standards on Petroleum Fuels and Lubricants," Philadelphia, Pa., 1957, Designation D 1015-55.
(13) A . Weissberger, "Technique of Organic Chemistry." Vol. 111, Second Edition, Interscience Publishers, Inc., New York, N. Y., 1955.
Nov., 1959
INCLUSION COMPLEXES OF METHYLNAPHTHALENES
Melting curves of mixtures previously cooled through the transformation, in contrast to freezing curves, exhibited a series of halts. These halts apparently arise from isothermal phase transitions. The data obtained from the melting curves were used to plot the phase diagram in Fig. 2 which shows that five stable complexes having three different compositions are formed in this system. Two pairs of complexes have the same composition, but each member has a different crystal form and all melt incongruently. According to vapor-pressure measurements and thermal analyses, horizontal transition lines in the phase diagram probably extend all the way across the diagram through points B, C, D, E and F. The vapor pressure of a mixture containing 36 mole yo 2-methylnaphthalene was measured a t 0" as heptane was removed in increments; at the composition of the complex, the vapor pressure dropped from 10.0 to 9.0 mm. and remained constant until the residue was solely 2-methylnaphthalene. Solid-solid transitions were often observed beyond the vertical solidus lines. However, in regions having a high concentration of methylnaphthalene, these transitions were difficult to see. Along curve AB, solid 2-methylnaphthalene crystals I is in equilibrium with liquid compositions of 2-methylnaphthalene and n-heptane. This curve coincides almost exactly with the "ideal" solubility curve of 2-methylnaphthalene I, as calculated from the Clausius-Clapeyron equation. A solid com lex of 2-methylnaphthalene and n-heptane precipitates begw 25"; the solubility curve is BC. Cooling and heating curves of a mixture containing 88.9 mole 2methylnaphthalene exhibited a halt between 23 and 26". This mixture solidified as it cooled through the transition temperature. I n contrast, a mixture containin 88.5%only 0.4% less-did not solidify completely wfen cooled below 23". Therefore, the solid stable between temperatures B and C corresponds closely to a combination of eight moles of 2-methylnaphthalene per mole of heptane or an 8: 1 complex. The stable solid in equilibrium with liquid along curve CD apparently has the same composition as the solid melting along BC, but the crystal form is different. Such dimorphism was suggested by results obtained from both regular and differential thermal analyses, which indicated that the solidus transition occurred a t 6" rather than 15". Curves obtained by differential thermal analyses of mixtures containing 88.5 and 81.3% 2-methylnaphthalene had peaks that began between 6 and 8" and ?nded a t the melting point, as shown in Fig. 1. The beginnin of the peak corresponds to the transition line going througt point D in the phase diagram. Because the 88.5'%mixture was warmed through the 25" transition, it absorbed more heat than the 81.3% mixture. Solid melting along curve DE is probably an 8:3 complex. According to regular and differential thermal analyses, the solidus line in the diagram shifts from 6 to 1" a t some composition between 75.6 and 59.2y0 2-methylnaphthalene. For example, differential thermal analysis of a 59.2% mixture was started a t about 0" but, as shown in Fig. 1, AT was displaced. This displacement occurs because heat iz absorbed by the mixture as it is warmed through the 1 solidus transition. Continued slow heating produced a curve with a peak beginning between 6 and 8",similar to the peaks produced by the other mixtures. Results from thermal analysis were more difficult to inberpret because solidus transitions were not readily differentiated from solid-solid transitions. Solid 1:1 complex is in equilibrium with liquid 2-methylnaphthalene and n-heptane at temperatures represented by curve EG. The solid phase isolated a t -20 to -22" contained 50% 2-methylnaphthalene. All melting curves of mixtures containing 60% or less 2-methylnaphthalene exhibit a short halt between - 18and -22". This halt apparently corresponds to a polymorphic change in the 1:1 complex, because the solidus line for these mixtures is at -90.8". The eutectic composition of this binary system a t G, contains less than 1% 2-methylnaphthalene. Adding as little as 0.96'% 2-methylnaphthalene to n-heptane raised the melting point from -90.70 to -90.00'. The heating curve of the dilute solution indicated that the melting point of the eutectic was -90.79". A short halt between -94 and -96" was exhibited by melting and freezing curves of mixtures containing as much as 81% 2-methylnaphthalene. This effect could be the result of incomplete transformation a t temperatures below 0"; however, the same halt occurred
1845
40
I
30
20
10
f
o
W
a
2
-10
4 P W
5 -20 I-
-30
-40
-80 -90
I
IO 20 30 4 0 5 0 60 70 8 0 90 100 MOL V. 2- METHYLNAPHTHALENE.
Fig. 2.-The phase diagram for the system 2-methylnaphthalene-n-heptane: open circles are melting points and full squares are transition temperatures. Both temperatures were determined from the heating curves obtained by thermal analysis. 4o
7-
-40
4
0
10 20 30 40 50 60 70 8 0 90 100 MOL a/a 2 - M E T H Y L N A P H T H A L E N E ,
Fig. 3.-Metastable
phase.
even after the sample was cooled at -30" for as long as 24 hr. Perhaps the halt corresponds to still another isothermal transition, if not to supercooling of the -22" transition. Metastable Phase.-Each mixture freezing below 15' could have two melting points, as shown by Fig. 3. If the mixture was cooled to a temperature slightly lower than its freezing point and than allowed to warm, it melted not along curve CG but along curve IJ. The mixture melted a t a higher temperature along curve CG only if i t was cooled t o -20". Thus, 2-methylnaphthalene reacts with heptane to form one metastable and five stable complexes. The metastable solid precipitated along curve IJ is a com-
1846
JACK MILGROM
plex containing eight moles of 2-methylnaphthalene and three moles of n-he tane. The solid was actually isolated at 5" and analyzed. bowever, pure metastable complex could not be isolated below OD, because i t transformed rapidly to the stable 1:l complex. Existence of this metastable 8:3 complex supports the assumption that the solid stable between D and E in the phase diagram is also an 8:3 complex. Thus, this system has three pairs of complexes. In the transformation from metastable to stable form, two effects were evident. Cooling curves showed a long halt as the mixture evolved heat. The crystals, which were transparent initially, became fine and opaque. Temperature affectedthe rate of transformation. Between 2 and 0", transformation was sluggish and complete only after six hours, but, between -20 and -30°, it was rapid and complete in a few minutes. Seeding had no effect; the rate was not increased when a 44% mixture was cooled just below its 5" freezing point and seeded with stable crystals. Therefore, the sluggish rate is not the result of supercooling. Transformation did not always go to completion, particularly when the mixtures froze between 0 and -20". If these mixtures were cooled slightly below the freezing point and then heated slowly, the solid began to transform but melted before the reaction was complete. These melting points were lower than those of mixtures containing 1 :1 complex and heptane. Because the transformation was rapid belowoO", only freezing points were used to plot curve IJ below 0 When the freezing point of the mixture was lower than -20", transformation accompanied freezing. Mixtures freezing a t temperatures above 15' underwent the metastable-stable transformation when cooled below O", but the melting point remained unchanged. Apparently the transformation proceeds reversibly only if thz mixture is heated through the transition temperature a t 15 Logarithmic Diagram.-A plot of the logarithm of mole fraction against reciprocal temperature is often prepared for simple binary systems containing no complexes. Over a short concentration range, a straight line is then obtained with a slope that varies, according to the Clausius-Clapeyron equation, with the heat of fusion of the solute. The heat of fusion determined in this manner can be compared with that determined experimentally to measure the deviation of the solvent from "ideal".' In this study, the Clausius-Clapeyron equation was applied to binary systems containing complexes having incongruent melting points. The modified equation is
.
.
Vol. 63
are only approximate, because the solutions of the complexes in n-heptane are not completely "ideal." Nevertheless, the straight-line correlation in Fig. 4 does suggest that the AHt values are sufficiently valid for an internal comparison. The calculated AHi of pure 2-methylnaphthalene agrees well with the value of 2.898 kcal. per mole determined by experiment.( Thus, n-heptane probably forms an "ideal" solution with 2-methylnaphthalene when the heptane is present in low concentration.
A Mechanism for Complex Formation According to X-ray diagrams, the two polymorphic forms of 2-methylnaphthalene belong to the monoclinic crystal system. Moreover, the unit-cell volume of crystals I1 is smaller than that of crystals I. Therefore, 2-methylnaphthalene crystals contract a t the transition temperature. Crystals I1 do not form complexes; pure 2-methylnaphthalene cooled to a temperature of -30", where the polymorphic transformation is complete, can be mixed with cold n-heptane without reaction. Apparently a void exists in the lattice structure at ordinary temperatures. But a t low temperatures, where van der Waals forces become more important, a compact crystal lattice forms that prevents the inclusion of heptane. The cavity in the 2-methylnaphthalene crystal lattice probably extends through two unit cells, because each cell has four molecules8 and the complexes involve units of eight. Furthermore, the complexes form in pairs; the 8:l and 8:3 complexes that precipitate initially are less stable, according to the heats of fusion, than the 8:l and 8:3 complexes that form after the low-temperature transformation. The complexes that precipitate first probably belong to the same structural family and those that form after the transformation belong to another. TABLE I RESULTSCALCULATED FROM LOG DIAGRAM
where N is the mole fraction of component A in the binary mixture melting a t T,z is the mole fraction of A in the complex A,B,, AHf is the heat of fusion of the complex, and TO is the theoretical melting point of the complex. This equation was derived, as given in the Appendix, by assuming that the amount of B was always more than required for the complex, AHf was constant, and the solute formed an "ideal" solution with the solvent. A plot of log N against 1 / T then gives a straight line for A and each complex formed by A, the slope varying with AH8 and the intercept varying with x and TO. Advantages of this graphic representation are manifold. Straight lines are useful for correcting small experimental errors and intersections between them give more accurate values for transition temperatures. Heats of fusion can be easily estimated and compared. If x is known, TOcan be calculated; it cannot be determined experimentally because the complex decomposes before it melts. Figure 4 shows such a logarithmic plot applied to the system 2-methylnaphthalene-n-heptane. For easy comparison with the composition-temperature phase diagram, the lettered solubility curves and lines refer to the same solid phases. The data points between C and F might be described by a single straight line; however, evidence indicates the points belong to three different lines having similar slopes that correspond to similar AHf values for the solid phase:. The broken line below 0" deviates from the line above 0 , because the metastable solid reacted in this temperature region. Heats of fusion and incongruent melting points were computed by the least-squares method and are summarized in Table I. The values for the heats of fusion of the complexes (7) F. S. Mortimer, J . A m . Chem. SOC.,44, 1416 (1922).
SOlll-
bility curve
AB BC CD DE EF
IJ
Solid phase
2-Methylnaphthalene 8:1 Complex 8 : l Complex 8:3 Complex 1:l Complex 8 : 3 Complex
Heat of Crystal fusion, form kcal./mole
Incongruent
m.p., OC.
...
I
2.94
I I1 I
4.7 8.7 0.6 7.2
B: 25.4 C: 14.8 D : 6.0 E: 1.2
I
6.4
I: 15.4
I1
A mechanism of complex formation is thus apparent. Molecules as large as n-heptane can be trapped in the void as methylnaphthalene begins to crystallize at temperatures below 25". As the crystals are cooled through the 15' transition, the void in the lattice and the increased importance of van der Waals forces permit the inclusion of additional n-heptane. On further cooling, methylnaphthalene molecules try to move closer to conform to the arrangement of crystals I1 but are prevented by heptane already in the crystal lattice. The lattice structure becomes strained, such that the molecules realign into a stable-though expanded-unit cell. This rearrangement corresponds to the metastable-stable transformation (8) Armour Research Foundation, Anal. Chem., 20, 1249 (1948).
Nov., 1959
*
INCLUSION COMPLEXES OF METHYLNAPHTHALENES
observed during cooling of mixtures to temperatures below 0". X-Ray analysis of the 1:l complex confirmed that the largest side of the unit cell expanded. These X-ray results, and the data showing formation of complexes containing an integral number of molecules, suggest that 2-methylnaphthalene behaves much like graphitee or the clay minerals halloysite and montmorillonite,'O which form layertype inclusion complexes. During the transformation, therefore, 2-methylnaphthalene molecules form a structure with enough space t o accommodate as much as one molecule of n-heptane per molecule of naphthalene. As the crystal is warmed, the void in the lattice remains, but the heptane escapes because van der Waals forces become less significant. Thus, melting curves show short halts as five molecules, and then two more molecules, of n-heptane are removed from the void in two unit cells. Although the temperature of isothermal transition of pure 2-methylnaphthalene is the same as that of the 8:l complex, the two transitions correspond to different arrangements of the crystal lattice. The heat of transition of 2-methylnaphthalene is 1.34 kcal. per mole,a but that of the 8:l complex is approximately four kcal. per mole, according to Table I. The transition of the 8:1 complex from crystals I1 to crystals I involves the largest energy change of any transition in the system 2-methylnaphthalene*-heptane. This large absorption of heat probably corresponds to the collapse of the expanded crystal lattice to the normal lattice of crystals I. The magnitude of the forces binding the naphtha1ene complexes together is by the large heats Of fusion Of the complexes* low temperature, these forces are as strong as the dipole-dipole forces in urea complexes at room temperature* Thus, in a the methylnaphthalene molecule probably becomes dipo1e at low temperature, because the electrons are undoubtedly localized. The intensity of the cohesive forces in urea and nLethylnaphthalene complexes can be compared by rneasurernent of their respective dissociation pressures. At O", the dissociation pressure Of heptane-urea is 3'3 mm*''; that Of heptane-2-methylnaphthalene is 9.0. Other Comp'exes Of If this mechanism is correct, formation of complexes should not be limited to n-hePtane. A survey of binary systems containing 2-methYlnaphthalene and Other hydrocarbons, as as with a variety of functional groups, has demonstrated that complex formation is general. Cornplexes are formed with both straight-chain and branched hydrocarbons; however, molecules as long or longer than n-hexadecane do not fit into the cavity i n the crystal I lattice of 2-methylnaphthalene. Flat aromatic ComPoUnds, such as toluene, form complexes easily. k k t u r e s of 2-methYlnaPhthalene and toluene evolve heat below 0" and melt (9) H. L. Riley, Fuel i n Science and Practice, 24, 1 (1945). (10) W. Sohlenk, Fortschv. chem. Forsch., 2, 92 (1951). (11) W. Schlenk, Ann., 666, 204 (1949).
IO
1847
20 30 40 50 60 70 8090100 MOL % 2-METHYLNAPHTHALENE,
Fig. 4.-Log diagram.
a t temperatures higher than theoretical, Although the binary system was not studied completely, initial results suggest that the phase diagram resembles the system 2-meth~lnaphthalene*-heptane. ~ o l e c u l e sas large as PhenYlcYclohexane and decalin complex with 2-methylnaphthalene a t temperatures below 0", but above 0" 2-methylnaphthalene complexes only with decalin. Thus, the cavity in crystals I of 2-methylnaphthalene accommodates the compact decalin molecule and not the slightly larger phenylcyclohexane molecule. However, below oo, where the crystal lattice Can expand, even phenylcyclohexane is accommodated. I-Methylnaphthalene behaves like the '&methyl derivative; the comp~exes,as might be expected, are lower-melting. Preliminary thermal analysis of the l-methylnaphthalene7-hexane system indicates that it also is composed of incongruent-melta mixture was cooled below ing comp~exes. men its freezing point, it transformed at to a higher-melting form. Apparently the transformation is similar to that observed in the 2-methylnaphthalene+-heptane system and corresponds to an expansion of the unit cell, Formation of these novel inclusion complexes is not limited to methylnaphthalenes. Initial experiments indicate that other naphthalene derivatives and other polycyclic compounds react similarly. Future work will be directed toward determining the dimensions of the cavity in the methylnaphthalene lattice and delineating the scope of the reaction that occurs below room
temperature.
Acknowledgment.-The author is indebted to Dr. George 5. John for help and advice on the mathematical development of the logarithmic representation of the data, Appendix Application of Clausius-Clapeyron Equation to
W. F. WOLFF
1848
Binary Systems Containing Incongruent-Melting Complexes. General Equation.-If N Bis the mole fraction of the solute in an ideal solvent
where AHf is the heat of fusion of the solute, To is the melting point of the solute and T is the melting point of the mixture. Reaction.CIA
+ bB = A,B,
(3)
Derivation.-In a mixture of A,B, and B formed by reaction of u” moles of A and“ b” moles of B moles A,B, = a/x
(4)
and moles of B = b
- ay/z
or, in terms of the logarithm In Nz =
- In (1 + bx/(a
- y))
(7)
The value for y from equation 3 can be substituted into equation 7 to give In N Z =
- In (1 + bx/a - (1 - 2))
(8)
- In x(1 + b/a)
(9)
which reduces to In N Z =
But
(2)
where A,B, is an incongruent-melting complex. Definitionx + y = l
Vol. 63
1
+ b/a
= l/mole fraction A = 1/N
(10)
Therefore, substitution of expression 10 into equation 9 gives lnNz= -lnx(l/N)=
-lnx+lnN
(11)
Substitution of this expression for In N Z into the general equation 1 and rearrangement of terms leads to the new expression
(5)
Therefore, when N z represents the mole fraction of complex A,B, in the solvent
or, in terms of common logarithms - l o g N = _ _ _AH f_2.303R T
mf + log x] [___ m 0 3 R To
(14)
ADSORPTION ON CONDUCTING SURFACES. HYDROLYSIS OF POTASSIUM ON ACTIVE CARBON BY W. F. WOLFF Research and Development Department, Standard Oil Company (Indiana), Whiting, Indiana Received April 1, 1060
Recent work suggests that certain active carbons provide uniform, essentially graphitic surfaces suitable for use in studying adsorption phenomena. Compositions prepared by depositing otassium on active carbon have been studied by reacting them with water. Significant changes in the amounts of hygogen evolved are observed as functions of potassium and carbon content. The results are interpreted in terms of the potassium being discretely adsorbed both atomically and ionically on a conducting surface, as has been proposed for cesium on tungsten. An extension of the mathematical treatment developed for cesium on tungsten seems to apply to potassium on active carbon, as well as to alkali and alkalineearth metals on tungsten.
Recent work on the structure of gas-adsorbent carbons1 suggests that active carbons of this type provide graphite-like surfaces suitable for use in the study of adsorption phenomena. If this is the case, electrons are presumably mobile within the small graphitic planes that make up such a surface. These carbons might be expected to show adsorption properties characteristic of metallic conducting surfaces. A study of the behavior of potassium deposited on gas-adsorbent carbons should be of particular interest; the alkali metals are known to react with graphite and much attention has been given to the products obtained from p o t a ~ s i u m . ~ -Vapor~ (1) W.E’. Wolff, THISJOURNAL, 62, 829 (1958); 68, 653 (1959). (2) K. Fredenhagen and G. Cadenbach, Z . anorg. Chem., 168, 249 (1926). (3) H.L. Riley, Fuel, 84, 8 (1945). (4) A. HBrold, BUZZ. a m . chim. Francs, 999 (1955). (5) F. R . M. McDonnell, R. C. Pink and A. R . Ubbelohde, J . Chem. Soc., 191 (1951). (6) R. C. Asher and S. A. Wilson, Nature, 181, 409 (1958). (7) G. R. Hennig, “Prooeedinga of the First and Second Conferences on Carbon,” The Waverly Press, Baltimore, Md., 1956, pp. 103-112.
pressure measurements and X-ray studies indicate that potassium, rubidium, and ’ cesium penetrate the plane structure of graphite to give series of ordered sandwich compounds, with limiting compositions containing one metal atom per eight carbon atoms.8 Although the X-ray evidence has been interpreted in terms of the alkali metal being present in an atomic for^,^-^ electrical studies favor ionic or partially ionic structure^.^^^ Little information is available in the literature on products obtained by the interaction of alkali metals with active carbons or other microcrystalline forms of carbon. X-Ray and conductance techniques are difficult to apply in such cases and the structures of the carbons are not known with certainty. However, vapor-pressure studies suggest that compositions similar to those obtained with graphite are formed.2s8 To study the systems formed by potassium and gas-adsorbent carbons, three series of such compositions with different carbons were treated with water. Changes in hydrolytic activity associated (8) N. Platzer, Cornpt. rend., 245, 1925 (1957).
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