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).
.
Nov., 1959
ADSORPTION ON CONDUCTING SURFACES:POTASSIUM ON ACTIVECARBON
f849
with changes in composition were measured by the volumes of hydrogen evolved. A quantitat,ive interpretation of the results, based on the theory of adsorption on conducting surfaces, has been attempt,ed. Experimental Commercial active carbons, designated A, B and C, were used without purification. Carbons A and B were separate batches of an 8-to-14-mesh coconut charcoal supplied by E. H. Sargent and Company. Carbon C was a 20-to-50mesh coal-based carbon from Pittsburgh Coke and Chemical Company. Analyses of these carbons are given in Table I. Immediately before use, carbon samples were dried by heating to 300' under a stream of nitrogen. Potassium was deposited on the carbon by a procedure conventionally used to disperse sodium on inert solids. Weighed amounts of potassium and carbon were heated with stirring to flask temperatures of 300'. Heatin and stirring were continued for about one-half hour beyonf the time required to obtain visually homogeneous products. All operations were carried out under an atmosphere of high-purity nitrogen. Distilled water was slowly added to the cooled product at room temperature and atmospheric pressure. To ensure the exclusion of air and to avoid transfer errors, the total freshly prepared product was hydrolyzed in the preparation flask. The volume of gas released was measured with a gas buret or by water displacement. In order to determine the amount of hydrogen evolved the measured volume was corrected for the volume of adsorbed nitrogen. The volume of adsorbed nitrogen was determined separately by desorption with either n-heptane on n-dodecane.'
TABLE I ANALYSESOF ACTIVECARBONS ( WEIQHTyo) A
Carbon Hydrogen Oxygen Sulfur Ash, total, as oxides
95.2 0.91 0.94 0.09 3.9
c
B 94.7 1.07 2.12
77.8 1.62 2.25
2.4
18.44
...
...
Results Hydrolytic activities were determined for a series of compositions prepared from each carbon. The hydrogen volumes are plotted as a function of potassium concentration in Fig. 1. The dashed line represents the volumes that would be expected if there were no interaction between the potassium and the carbon. Experimental points for carbon A appear to be best fitted by linear segments, rather than by a curved line. Compositions with a K/C atomic ratio below 0.03 give littleor no hydrogen on hydrolysis. Potassium added beyond the 0.03 ratio leads to the formation of products that displace hydrogen from water. However, to a ratio of 0.12, the slope of the curve is less than that expected for pure potassium; only a fixed fraction of the incremental potassium added in this region displaces hydrogen from water. Beyond the 0.12 ratio, the curve parallels that of pure potassium; the incremental potassium reacts quantitatively with water. The data for carbon B and C define incomplete hydrolytic curves of the type obtained for carbon A. All experimental points are satisfied by completed curves of this type, although they do not define them. The curves for carbon A and B ap(9) National Distillers Chemical Co., "High-Surface Sodium on Inert Solids," New York, N. Y.,1953.
i
"0 D
r >
a Y > 0
>
Y
Fig. l.-Hydrolytic
activity of potassium on three carbons.
pear almost identical, as would be expected for carbons of similar source and composition. That for the dissimilar carbon C falls surprisingly close to those for carbon A and B. Comparison of the experimental curves with that for pure potassium shows that much of the supported metal fails to release hydrogen from water. Four possible causes for this failure were examined. There was no evidence that the activity loss was caused by reaction of potassium with impurities in the carbon or by attack on the preparation flask. Examination of analyses of carbon A and B showed insufficient impurities to account for more than a small fraction of the activity loss. Portions of carbon B were purified by extraction with hydrofluoric acid, followed by heat-treatment a t 800" and l,OOOo in a stream of nitrogen and then of hydrogen.1° Hydrolysis results for potassium on the original and purified carbon are given in Table 11. Although the ash content was reduced from 2.4 to 0.15% and the oxygen from 2.1 to 0.4%, there was little change in the amounts of hydrogen evolved. TABLE I1 EFFECTOF CARBONPURITY ON HYDROLYTIC ACTIVITY W C
atomic ratio
Carbon B Purified carbon B
0.018 .053 .018
.053
Evolved hydrogen, cc./g. carbon
0.7 15.1 0.6 16.5
Attempts to relate the loss in activity to degradative reactions of the potassium with carbon or hydrocarbon constituents were unsuccessful. Little or no gas evolution was observed under typical preparation conditions. I n general, volumes of hydrogen evolved on hydrolysis were unaffected by changes in preparation temperature. Significant changes in activity were obtained only when the compositions were prepared a t temperatures well above 300". Analysis of the hydrogen evolved on hydrolysis showed only 0.1 mole yo hydrocarbon from compositions prepared under (10) Robert B. Anderson and P. H. Emmett, THISJOURNAL, 6Y. 1308 (1947).
1850
W. F. WOLFF
the usual conditions. Samples prepared a t higher temperatures gave up to 5% hydrocarbons. To test the possibility that some of the potassium was physically inaccessible, several compositions of this type were repeatedly washed with distilled water a t room temperature. In all cases, the alkali metal was quantitatively recovered as titrated base. Complete removal was confirmed by the spark spectrum of the leached carbon. The possibility that the activity loss was caused by interaction of either the potassium or liberated hydrogen with unsaturated regions in the carbon was also investigated. I n either case, potassium treatment followed by hydrolysis should lead to an increased hydrogen content of the carbon. The hydrogen content of untreated carbon B was compared with that of the carbon after potassium treatment, hydrolysis, leaching, and drying. The treated carbon showed a significantly higher hydrogen content, 1.34 weight %, on an ash-free basis, as compared with 0.97% for the original carbon. A slight increase in oxygen content, from 1.01 to 1.14%, was obtained, but the difference is less than the estimated experimental error. The theoretical increase in hydrogen content was calculated from the K/C atomic ratio (0.083) and the amount of hydrogen released on hydrolysis (35.2 cc. per g. of carbon). The calculated increase in the hydrogen content of the carbon 0.40%, is in satisfactory agreement with the observed value 0.37%. Thus the data are consistent with a limited hydrogenation of the active carbon.
Discussion A possible interpretation of the experimental data is that some of the potassium atoms give up their valence electrons to the surface, forming ions incapable of displacing hydrogen from water. The fraction of atoms transformed into ions presumably is determined by the extent of surface coverage. This type of adsorption has been proposed by Becker to account for the results of thermionic-emission studies with cesium on tungsten. 11.12 Such a view represents one of the two principal approaches that have been used in developing the theory of the adsorption bond. I n the other approach, the adsorption of identical particles on a uniform surface is generally treated as giving identical adsorption bonds.’$ The properties of potassium on active carbon might be expected to be similar to those of cesium on tungsten. The graphitic adsorption surfaces postulated for active carbon’ not only should show a metallic character but also should have electron affinities approaching those of tungeten. In both systems, the adsorbed species are alkali metals with low ionization potentials. Thus relationships valid for cesium on tungsten should be applicable to potassium on charcoal. I n developing a quantitative treatment of thermionic-emission data for cesium on tungsten, BeckerI2 (11) J. A. Becker, Trans. Am. EZEsclrochem. SOC.,56, 169 (1929). (12) J. A. Becker, “Advances in Catalysis,” Vol. VII, Academia Press, Ino., New York, N. Y.,1956, pp. 135-59. (13) For a treatment of the adsorption of alkali and alkaline earth Eyring, I. J . Am. Chsm. Soc., 77, metals, see I. Higuchi, T. Ree and € 4969 (1955); 79, 1330 (1957).
Vol. 63
calculated the number of alkali-metal ions per square centimeter of surface, N,, by Np =
A+*
1.8 x 10-8I.l
where A& is the reduction in the electron work function of the support caused by the adsorption of the alkali metal, in electron volts, and L is the distance in 8.between the nucIeus of an adsorbed ion and the electronic surface of the tungsten.14 The number of adsorbed atoms per square centimeter, N,, was determined from the Npvalue N . = ye
- N,
(2)
where y is the number of sites available for alkalimetal adsorption per square cent,imeter of surface, and 0 is the fraction of sites filled. The surface ionization potential, Is,for a system of this type was defined as the energy required to convert an adsorbed alkali-metal atom to an adsorbed ion. Values of this variable can be calculated, by means of a Born cycle, from emission data for atoms, ions and electrons, or by the equation (3)
where T is the absolute temperature and I, is measured in electron volts.12 Although the preceding equations are presumably valid for potassium on active carbon, Becker’s approach must be exbended if a significant interpretation of the hydrolytic results is to be obtained. Such an extension is suggested by the probable dependence of the surface ionization potential on the concentration of electrons within the support. If changes in the concentration of ions adsorbed on the surface-and thus of excess electrons in the support-are assumed to cause directly proportional changes in the surface ionization potential dl.
=
kcW,
(4)
The postulate is in reasonable accord with both the free-electron and band theories for metals.I6 Upon integrating from a clean surface to an ion concentration of N,, the surface ionization potential is obtained as a function of N , Is - (1.10 = kN, (5) where (&J0 is the limiting value of the surface ionization potential as 0 approaches zero. If ( N p ) e l is defined as the concentration of ions on the surface a t a concentration such that N p = N a , equations 3 and 5 give 1 8
= (Is)o[1
- Np/(Np)e~l
(6)
and (7)
If these equations are valid, ion-distribution curves obtained by plotting log ( N p / N a ) against Np should be linear. Thermionic-emiseion data for (14) The conatant in this equation may be in error by a factor of two. See G. E. Moore and H. W. Allison, J . Chem. Phus., 28, 1609 (1955). (15) The fractional change in the N ( E ) value of the electrondistribution curve is assumed to be small over the region in which electrons are introduced. Should this region include the completion or initial filling of a band, marked deviationp from tbe linear relationpkip migbt be expected.
Nov., 1959
ADSORPTION ON CONDUCTING SURFACES : POTASSIUM ON ACTIVECARBON
1851
cesium on tungstenI2 and barium on tungsten16 have been plotted in this manner so as to test the equations; the plots are given in Fig. 2. Two distribution curves are given for cesium on tungsten. One is based on published Np and N , values corrected for the polycrystalline nature of the surface by adjusting the values of L in equation 1 as a function of 0.l2 If L is treated as a constant, the second plot is obtained. The plot for barium on tungsten is also uncorrected for polycrystallinity. With the possible exception of values calculated for low Np values-hence, low surface coverages-the points fall on straight lines. The applicability of equation 7 to the activity data for potassium on active carbon is readily tested. The experimental data give the ratio N , / N , directly, by the relationship where V is the molar volume of hydrogen under the experimental conditions, a is the weight of metal deposited on the support, M is the atomic weight of the metal, and g is the volume of hydrogen released. The concentration of ions on the surface, N,, is given by where N is the Avogadro number, W is the weight of the support in grams, and A is the surface area accessible to the metal, in square meters per gram. All factors except A are obtained directly from experiment. An error in A will displace the values of N , by a constant factor but will not affect the linearity of a plot of log (Np/N,) vs. N,. By assuming an effective surface area of 1310 square meters per gram, equations 8 and 9 have been used to determine values of log (NJN,) and of Np for potassium on carbon A. The values for less than monolayer coverage are plotted in Fig. 3. Excluding values for low potassium concentration, the points define a straight line. The hydrolytic curve back-calculated from this line, and extended to greater than monolayer coverage, is shown in Fig. 4. With one possible exception, the composite curve fits all experimental points. The agreement between the experimental and calculated values supports the hypotheses inherent in this treatment ; however, other possibilities are not precluded. The data indicate that the potassium or hydrogen reacts with unsaturated regions in the carbon, but fail to define either the type of reaction or the nature of the unsaturation. Furthermore, interpretation of the results is complicated by the heterogeneity of the support and by its possible modification during the course of the hydrolysis. The hydrolysis results reflect an unknown distribution of graphitic plane sizes, and may indicate average atom-ion distributions significantly different than those existing before the water was added. Conclusion The major properties of potassium on active carbon appear t o be explainable in terms of the hypotheses inherent in equation 7. However, the (16) J. A. Beoker, P h y s . Rev., 84, 1323 (1929).
0
0
Fig. 3.-Ion
distribution for potassium on carbon A.
O/ /
/
/ I
/ /
O /
W
/
P/
' 0
LT
O/
40
n w
"0
005
Fig. 4.-Calculated
I
I
0 10 K / C ATOMIC R A T I O ,
0 I5
0 20
hydrolytic activity of potassium on carbon A.
equation fails to account for the apparent linearity of the principal segments of the experimental curves. Indications that this deviation is associated with the formation of compositions corresponding to the potassium graphites are being studied. Work with other metals on carbon is also in progress, to test the hypothesis that the observed changes in hydrolytic activity primarily reff ect the electronic state of the metal. Data from this work
1852
ARNIMHENGLEIN
should permit direct testing of the exactness and validity of equations 4 and 7, and should provide a sound basis for studying the dependence of the constants (I& and ( N p ) e l on the properties of the systern. The apparent similarities between potassium on active carbon, barium on tungsten, and cesium on
Vol. 63
tungsten may apply to adsorption on metallic conducting surfacesin general. If such is the case, many effects that have been ascribed to surface heterogeneity could simply reflect the formation of adsorbed ions on essentially uniform surfaces, Acknowledgment.-The author thanks G. S. John and C. E. Johnson for helpful discussions.
CROSSLINKING OF POLYMERS IN SOLUTION UNDER THE INFLUENCE OF ?-RADIATION1 ARNIMHENGLEIN~ Contribution from the Radiation Research Laboratories, Mellon Institute, Pittsburgh, Pa. Received April
4, 1969
Polyvinylpyrrolidone, r l y v i n y l acetate and polystyrene simultaneously undergo intermolecular crosslinking and degradation of their main c ains when irradiated in solution. Below a critical concentration which depends on the solvent no continuous network is built up since degradation is the predominant reaction in dilute solutions. Only a few solvents or mixtures of solvents in which this critical concentration is smaller than 10 g./lOO cc. have been found for each of these polymers. No relation exists between the radiation sensitivity of the solvent and the rate of crosslinking of dissolved polymers. However, crosslinking seems to be slightly favored in poor solvents. Observations on the gel dose show that this often increases with increasing polymer concentration in concentrated solutions. Radical scavengers inhibit crosslinking of these polymers and often are incorporated into the polymers. A mechanism is proposed in which the formation of macroradicals and low molecular weight radicals from the solvent by direct action of radiation are the primary steps. Crosslinks are formed by combination of macroradicals. The solvent radicals sensitize or retard crosslinking by attacking the polymer to form additional macroradicals or by deactivating macroradicals, respectively. The increase in gel dose in concentrated solutions is attributed to the decrease in the rate constant for the combination qf the free macroradica!s in viscous solutions as is well known from the autoacceleration observed in the bulk polymerization of a number of vinyl monomers.
Introduction I n secent years considerable research on the radiation chemistry of macromolecular substances has been devoted to changes which occur in polymers when they are irradiated in the solid state.3 Only a few investigations concerned with the effects of ionizing radiation on macromolecules in solution have been reported. These, however, have revealed that polymers in solution undergo changes similar to those observed in solid state irradiations, Le., degradation of their main decomposition of side g r o ~ p sand ~~ also intermolecular crosslinking. lo*l1 However, the mechanisms responsible for these changes are more complex since they may result from either indirect or direct action of radiation or both. I n early investigations on the radiation chemistry of polymers in solution no attempts were made to study the dependence of the reactions on the (1) This work was supported, in part, by the U. S. Atomic Energy Commission. (2) Visiting fellow on leave from the University of Cologne, Cologne, Germany. (3) See, for example, F. A. Bovey, "The Effects of.Ionizing Radiation on Natural and Synthetic High Polymers," lntersoience Publishers, New York, N. Y., 1958. (4) P. Alexander and M. Fox, Trans. Faraday Soc., 60, 605 (1954). (5) P . Alexander and M. Fox, J . chim. phys., 60, 415 (1953). (0) L. A. Wall and M . Magat, ibid., 60, 308 (1953). (7) A. Chapiro, J. Durup, M. Fox and M. Magat, International symposium in macromolecular chemistry, Milan-Turin, 1954, Supplemento a "la Ricerca Scientifioa," 1955, p. 207. (8) A. Henglein and M. Bcysen, Makromol. Chem., 20, 83 (1956). (9) A. Henglein, M . Boysen and W. Sohnabel, 2.physik. Chem. Neue Folge, 10, 137 (1957). (10) P. Alexander and A. Charleaby, J . chim. phys., 6 2 , 094 (1955). (11) P. Alexander and A. Charlesby, J . Polymer Sei., 28, 355 (1957).
nature of the solvent. I n recent communicai t has, however, been shown that the rate as well as the nature of the chemical changes in the dissolved polymer depend strongly on the properties of the solvent. Certain generalizations for the various interactions that take place between the dissolved polymer and the solvent during irradiation have been established. Polymers such as polymethyl methacrylate and polyisobutylene which undergo a degradation of their main chains in the solid state are also degraded in ~,~~ and Charlesby found ~s o l ~ t i o n . ~Alexander that several water-soluble polymers crosslink when they are irradiated in aqueous solutions at concentrations above 0.5 weight yo. Recent studiesis on the radiation chemistry of polystyrene in solution showed that this phenomenon is not limited to aqueous solutions. It appears that every polymer that crosslinks in the solid state may also be crosslinked in solution under suitable conditions. The studies reported here are concerned with the radiation chemistry of polyvinylpyrrolidone and polyvinyl acetate in solution. Viscosity measurements were carried out to study the changes in these polymers. The results obtained are compared with earlier investigations on the crosslinking of polystyrene in solution. Each of these polymers (12) A. Henglein, Ch. Schneider and W. Sohnabel, I.physik. Chem. Neue Folge, 12, 339 (1957). (13) A. Henglein and Ch. Schneider, ibid., 18, 56 (1958). (14) A. Henglein and Ch. Schneider, ibid., in press. (15) A. Henglein, K. Heine, W. Hoffmeister, W . Sohnabel, Ch. Schneider and H. Url, International Conference on the peaceful mea of atomic energy in Geneva, Sept. 1958 (United Nations), contribution No. 962.
