2687
NOTES
picture of an electrical double layer given by Helmholtz permits this assumption. The Helmholtz model of a double layer is similar to an electrical condenser made of positively and negatively charged plates situated a molecular distance apart. From the electroneutrality condition of the surface phase, nRJ will be equal to ma+and eq 1 will then assume the form
Gibbs Equation for the Adsorption of Organic
Ions in Presence and Absence of Neutral Salt
by D. K. Chattoraj Chemistry Department, Jadavpur University, Calcutta 98, India (Received December 1, 1966)
Recently, considerable interest has been found to exist in the study of the equations of state for soluble charged monolayers using surface and interfacial tension measurements a t air-water and oil-water interfaces in the presence and absence of neutral A major difficulty in such investigation lies in the uncertainty in the calculation of the area per adsorbed organic ion using the Gibbs equation which assumes “one KT” and “two KT” forms, respectively, in the presence and absence of neutral salt^.^-^ The confusion mainly arises because of the neglect of the part played by different models of the electrical double layer during the application of the Gibbs equation for the adsorption of organic ions. An attempt has been made in the present communication to estimate the dependence of the values of the K T coefficient in the Gibbs equation on the concentration of neutral salts and on the potential of the electrical double layer formed near the phase boundary. The convention of terms to be used in the present treatment is similar to that adopted by Davies and Rideal.lo Let C R ~ represent the aqueous concentration of surface-active organic salt RNa (such as sodium octanoate, sodium lauryl sulfate) in the presence of the neutral salt sodium chloride at a concentration C. The present treatment will be also applicable to the cationic soap in the presence of a salt containing a common anion. Owing to adsorption of R- ions, the liquid surface will be negatively charged as a result of which Na+ ions and in all probability C1- ions will be present in the surface phase to maintain electroneutrality. From the application of the Gibbs equation at constant temperature, it is possible to write -dy = dn
=
nRjdjmr
+ nNa+dpNa++ ncl-dpcl-
(1)
where y and x stand for interfacial tension and pressure, respectively. nRJ, ma+,and ncl- represent the number of R’, Na+, and C1- ions adsorbed per unit , mi- are the corarea of the surface and ~ R J p, ~ , , + and responding equilibrium chemical potentials of the ions concerned. In the earlier treatment,lO nRt has been assumed to be equal to ma+,prohibiting the presence of C1- ions in the surface phase (ie., ncl- is zero). The classical
However, d m will be equal to d m a +since the concentration of R’ and Na+ will increase in equal amount with further addition of long-chain salt to the system + also be taken at constant salt concentration. C N ~ can to be equal to C R ~ c. Therefore
+
(4) where m representing the coefficient of K T will be given by the equation m=1+-
1 l + x
(5)
where x stands for the ratio C / C R ~ . At x equal to zero and infinity, the value of m becomes 2 and l, respectively, in agreement with the limiting values of the coefficient of K T previously estimated. In Figure 1 (curve I), m has been plotted for various values of x using eq 5 . A more recent treatment of the electrical double layer assumes the validity of Gouy and Stern pictures of the double layer in place of that given by Helmholtz. According to the Gouy model, although the negative charge due to adsorbed organic ions will remain on the phase boundary plane, Na+ and C1- ions will be distributed on the aqueous side of the surface phase ~~
~~
(1) J. T. Davies, Proc. Roy. Soc. (London), A208, 224 (1951). (2) J. T. Davies, J . Colloid Sci., 11, 377 (1956). (3) E. Matijevic and B. A. Pethica, Croat. Chem. Acta, 29, 431 (1957). (4) J. N. Philips and E. Rideal, Proc. Roll. Soc. (London), A232, 149 (1955). (5) D. A. Haydon and F. H. Taylor, Phil. Trans. Roy. SOC.(London), A252, 225, (1960). (6) M. van den Tempel, Rec. Trav. Chim., 72, 419 (1953). (7) B. A. Pethica, Trans. Faraday Soc., 50, 413 (1954). (8) E. G . Cockbain, ibid., 50, 874 (1954). (9) D. A. Haydon, J . Colloid Sci., 13, 159 (1958). (10) E. Rideal and J. T. Davies, “Interfacial Phenomena,” Academic Press Inc., New York, N. Y . , 1961, pp 196-199.
Volume 70,Number 8 August 1966
NOTES
2688
potential in esu of the negatively charged interface presently considered; E , K , and T are the electronic charge, Boltzmann constant, and absolute temperature, respectively. For a given thickness of the electrical double layer, m i - / n N a + will be equal to CSC1-/CSNa+. According to the Gouy model, the K T coefficient m’, in eq 8 will be given by eq 11 1
m’ = 1 +
C-2e+/KT
l-cR/
rol
I
I
I
0 ’
SALT PA!%
0
20
-I’
Figure 1. KT coefficient m or m’ as function of salt ratio x equal t o C/CR’: curve I, Helmholtz model or Gouy model with > 40 niv; curve 11, Gouy model with = 30 mv; curve 111, Gouy model with = 10 mv; curve IV, Gouy model with = 5 mv.
+
+
+
+
up to an average Debye-Hiickel thickness 1 / ~ . The surface phase containing this Gouy diffuse double layer as a whole should be electrically neutral so that
+ mi- =
nRt
(6)
nNa+
dmt, as before, will be equal to d C N a + . For a given concentration of neutral salt, dccl- and hence d m - / eel- will be negligibly small. Dropping out therefore ncl-dwl- in eq 1 containing this negligible term, one will obtain
1
- d r = nRl-KT
1
dCR‘ CR
+nR‘ n N a + CRJ
CNa +
Replacing nRt inside the bracket by rearranging
+
-dr = n R s T [ l
nNa+
- mi- and
I’ 1
1--
MI- CR’
+c
nNa*
The surface concentrations c s N a + and c S a - per unit volume for Na+ and C1- will be given for the Gouy model by the Boltzmann distribution equation“ cSN a + =
(CR!
cscl-
+ c)e
-4-+)/KT
= ce e ( - + ) / K T
(9)
(10)
where $ stands for the absolute magnitude of the surface The Journal of Physical Chemistry
CR’
+c
a’+
As before, for x equal to zero and infinity, respective values of m’ will be 2 and 1. I n the intermediate range of x, however, m‘ will depend upon $. For $ varying from 5 to 100 mv (a practical range) we have calculated values of m’ as a function of 2. Some of these calculations have been presented in Figure 1. It has been found that for $ equal to 50 mv or more, the m’ - x curve is identical with the m - x curve throughout the whole range of x. Also, for $ equal to 30 and 40 mv, the maximum difference between m and m’ amounts to 2% using the Gouy and Helmholtz models. From eq 9 and 10, it is evident that a t high potentials, C1- concentration within the double layer is negligible compared to that of Na+, and this is the reason for the identity between Helmholtz and Gouy curves in Figure 1. However, it should be carefully noted that considerable differences between m and m’ in such curves will arise (vide Figure 1, curves I, 111, and IV) for $ equal to 10 and 5 mv. Thus, in this case, strong dependence of the KT coefficient on the model of the electrical double layer is indicated. From the figure, it will be noted that the use of the “one KT” form of the Gibbs equation, corresponding to a C/CW value of 10 will lead to a 10% error for the Helmholtz and Gouy models with $ > 40 mv. The error will rise to 24% if $ (for the Gouy model) is equal to 5 mv. I n the light of this situation, many previously derived forcearea data for the adsorption of organic ions, having carbon atoms equal to or less than ten, should be recalculated. For the safe use of the “one KT” form, x should be 1000. I n considering the above models, the possibility of the presence of R’ ion in the diffuse ion atmosphere part of the double layer has been excluded; otherwise, the meaning of area per organic ion will lose much of its significance. The planar arrangement of all of the ~~
(11) H. R. Kruyt, “Colloid Science,” Vol. 1, Elsevier Publishing Co., Amsterdam, 1952, p 128.
NOTES
organic ions on the phase boundary is most probably a kind of thermodynamic requirement arising from the high energy of absorption. The slight ionization of water has been neglected for convenience. ncl- in eq 6 represents the actual concentration of C1- ions within the interfacial double layer. The neglected term ncl-dkcl- of eq 1 represents the negative surface excess value. The consideration of the Gibbs equation on the basis of Stern’s model of a double layer requires no special treatment. Here, the fixed part of the double layer which is similar to that of Helmholtz does not contain any chloride ions. However, both chloride and sodium ions will be present in the diffuse part of the double layer so that m’ will be given by eq 11 with replacement of $ by $d, which is the potential of the diffuse double layer in Stern’s model. In the recent model of the penetration double layer proposed by Haydon and Taylor5 for the oil-water interface, the possibility of distributing only counterions in the space between the plane containing charged head groups and the phase boundary plane has been considered. For such a model, m’will be same as that for Stern’s model. I n fact, the K T coefficient occuring in the bracketed expression of eq 8 and containing the term, ncl-/nNa+is quite general in form. For the Helmholtz model, this ratio is zero, and for the Gouy and Stern models this is dependent on and +d, respectively.
+
Crystallographic Data for Some New Type I1 Clathrate Hydrates’
by D. F. Sargent2 and L. D. Calvert Division of Applied Chemistry, National Research Council, Ottawa, Canada (Received February 83, 1966)
The present paper establishes the structure of and presents lattice parameter measurements for five clathrate hydrates not previously characterized by Xray examination. The work was undertaken in an attempt to explain the anomalies described below. Davidson and c o - ~ o r k e r s ~have - ~ recently reported dielectric absorption studies of the clathrate hydrates of tetrahydrofuran (THF), 2,s-dihydrofuran (DHF), propylene oxide (PO), 1,3-dioxolan (DO), cyclobutanone (CB), trimethylene oxide (TMO), and ethanol (E). It was known’ that the hydrate of T H F was Type I1 (8M.136H20, a = 17.0-17.5 A, Fd3m) and the others were thought to be Type I1 from their
2689
dielectric behavior and approximate stoichiometry. Davidson, et u Z . , ~ suggested that the vhf absorption regions were associated with “hindered” rotation of the guest molecule in the cavities of the clathrate structure. Free rotation of the T H F molecule was deduced by Maks for the THF-H2S double hydrate. Hindered rotation of the ethylene oxide molecule was described by McMullan and Jeffreys for the Type I ethylene oxide hydrate. Davidson and his eo-workers observed certain differences between the results for trimethylene oxide and ethanol hydrates and the results for the other hydrates. It was tentatively suggested that these two might have a structure different from the normal Type I1 hydrate, either a new kind, one with modified hydrogen bonding, or one of those described by Jeffrey and co-w~rkers.~The present work was undertaken to investigate this possibility and to see if the observed lattice parameters might be correlated with the size of the guest moleculeloor with the frequencies of the dielectric absorption.
Experimental Section Powder specimens were prepared in thin-walled glass capillaries containing mixtures of the compound and distilled water in the approximate mole ratio M.17Hz0. These were frozen in liquid nitrogen. The best composition, usually slightly rich in the organic compound, was found by trial and error. For the compounds with an incongruent melting point, samples were annealed for a suitable time in an appropriate freezing bath. Both dihydrofuran and cyclobutanone were immiscible with water in the concentrations used. Samples were taken after thorough shaking. To obtain lattice parameters, further specimens were prepared containing - silicon as internal standard. This-silicon (99.9%, -325 mesh) had a = 5.4304 A at 25” in good agreement with a = 5.4305 A found for a specimen of the IUCr lattice parameter (1) N.R.C. No. 9107. (2) N.R.C. Summer Student. (3) D. W. Davidson and G. J. Wilson, Can. J . Chem., 41, 1424 (1963). (4) D. W. Davidson, M. M. Davies, and K. Williams, J. Chem. Phys., 40, 3449 (1964). ( 5 ) D. W. Davidson and R. E. Hawkins, J . Phgs. Chem., 70, 1889 (1965). (6) A. D. Potts and D. W. Davidson, ibid., 69, 996 (1965). (7) M. yon Stackelberg and B. Meuthen, Z . Elektrochem., 62, 130 (1958). (8) T. C. W. Mak and R. K. McMullan, J . Chem. Phys., 42, 2732 (1965). (9) R. K. McMullan and G . A. Jeffrey, ibid., 42, 2725 (1965). See also earlier papers in this valuable series. (10) M. von Stackelberg and W. Jahns, Z . Elektrochem., 58, 162 (1954).
Volume 70, Number 8 August 1966
