E JOURNA
ISTRY
(Registered in
VOLUME66
U. 8. Patent O5ce)
(0Copyright, 1962, by the American Chemical Society)
XUMBER3
MARCH 20, 1962
IDEAL TWO-DIMENSIONAL SOLUTIOPU’S. II. A KEW ISOTHERM FOR SOLUBLE AND “GASEOUS” MONOLAYERS BY FREDERICK M. FOWKES Shell Development Company, Emerydle, California and Martinez Research Laboratory, Shell Oil Company, Martinez, California Received April 24, 1061
The concept that the adsorbed monolayers on binary solutions act like an ideal two-dimensional solution has been extended to monolayers of soluble detergents and “gaseous” monolayers of substances insoluble in the substrate. I n these monolayers water molecules in the surface layer are the solvent and the film pressure can be calculated as a direct result of water molecules crowding into the monolayer (or two-dimensional solution) because of a decrease in their chemical potential resulting from dilution by the surface-active molecules. From these principles a new isotherm is derived which fits pressurearea relatioiw better than the “gas” equations, is more accurate for measuring molecular weights, and represents quantitatively the pressure-area relations for soluble detergents.
Several previous investigators of the surface tension of binary solutions have found it useful to consider the surface layer as a separate phase one, molecule deep in which the composition is related to the two-dimensional tension in the same manner as the equilibrium pressure in an osmometer is related to the composition of the solution inside the membrane.l-* However, these examples were confined to binary systems of small molecules, such as ethanol and water. More recently the author has shown that this treatment gives quantitative relations of film pressure to mole fraction for two component monolayers on aqueous solutions of synthetic detergents with a second surface-active comp ~ n e n t . ~It, ~is now to be shown that the film pressure on aqueous solutions of detergents (or even of very slightly soluble surface-active materials) can be related quantitatively to the mole fraction of water in the monolayer. Theory.-The notation is the same as was used in Part I of this series.8 Let us coiisider a dilute solution of surface-active substance 1 in water 2. (1) 3. A. V. Butler, Proc. R o y . Sac. (London), A135, 348 (1932). ( 2 ) J. E. Verschaffelt, Bull. classe sci., Acad. ray. Belg., 22, 373, 390, 402 (1936). (3) A. Schuchowitzky, Acta Ph~aicochzm. U.R.S.S., 19, 176, 508 (1944). (4) J. W. Belton and M. G. Evans, Trans. Faraday SOC.,41, 1 (1945). (5) E. A. Guggenheim, ibid., 41, 150 (1948). (6) R. Defay and I. Prigogine, J . Chem. Phys., 43, 217 (1946). (7) W. M. Sawyer and 1. M. Fowkes, J . Phys. Chem., 6 2 , 159 (1958). (8) F. M. Fowkes, ibzd., 66, 355 (1961).
At equilibrium, any change in the free energy of the water in the bulk phase (kT d In czf~)must equal that in the surface phase a t equilibrium kT d In
cJ2
= IcT d In X ~ + Z- u2dy
(1)
where c2 and f 2 are the mole fraction and activity coefficient of the solvent (water) in the bulk, 22 and 4bZ are the mole ir’ractionand activity coefficient for the surface phase, (TZ is the partial molecular area of the solvent in the surface film, and y is the surface tension of the solution. Here cr2 = (bA/ &&,, where A is the total surface of the system and nl and nz are the number of molecules of solute 1 and solvent 2 in the monomolecular surface phase of area A . Equations of State for “Gaseous” Monolayers.It has been customary to describe very dilute insoluble monolayers on aqueous substrates as “gaseous” because the area of surface per molecule of film-forming substance, AI, is such that aA1 approaches kT a t infinite dilution. The parallel has been drawn to ideal gases and it has been inferred that the pressure a is the result of collisions between molecules of the film. However, it is far more appropriate to compare dilute monolayers with a solution in an osmometer with an osmotic pressure II, where C W 1 approaches kT a t infinite dilution ( V I is the volume of solutioii containing one molecule of solute). In the case of an osmometer containing a solution of component 1 in solvent 2 in which molecules of the solute are localized by means of a semi-permeable membrane but the molecules of solute are
385
FREDERICK M. FOWKES
386
Vol. 66
free to diffuse through the membrane, equilibra- calculated for surface active solutes on mater once tion of solvent between the solution and pure sol- u1 is known. vent outside the membrane is governed by the The above thermodynamic equation is far more reduction in chemical potential of the solvent in the accurate than the previously used “gas” equations. solution, which reduces the rate of diffusion from the This is obvious from the steps needed to derive the solution so that there is a preponderance of dif- “gas” equations from equation 4, by a procedure fusion into the solution from the pure solvent be- analogous to that used to derive the limiting form yond the membrane. Because of mechanical con- of the osmotic pressure equation (IIB1 = k T ) from finement, this penetration of more solvent into the the exact equation. For a binary solution film solution section of the osmometer causes a rise in In x2 = In (1 - zl). We may approximate In (1 pressure (n) in that section, which raises the xl) by only the first term (--XI) in the series expansion: this is a close approximation only when x1 partial molar free energy, Gz. At equilibrium is very small. This approximation should not be dGz = kT d In czfi vz dII = 0 used for T-AI isotherms a t high pressures, for the where e2 is the mole fraction of solvent in the solu- error is generally about T% (1% at 1 dynelcm., tion, fi is the pressure-independent activity co- 10% at 10 dynes/cm., but rising to 40% error a t efficient, and 7.12 is the partial molecular volume of 30 dynes/cm.). The above approxiniation results the solvent in the solution. I t can be shown easily in that at infinite dilution the above equation approaches in the limit
+
nvl
kT
Since In the case of a dilute monolayer on the surface + = /Il - (ul - cz) of water in which the molecules of the surface- (n1 +nlnz) $2 = (az - al) + nl active solute 1 are solvated by water molecules 2, AI - (UI - vz)] = kT(approx.) (G) the surface layer behaves like a tvo-dimensional solution in which the solute molecules are localized Variakions of equation 6 have been widely used. by adsorption and sometimes also by insolubility. For extremely dilute monolayers, (01 - u2) beHowever, the solvent molecules are free to diffuse comes negligibly small with respect to A1 and in and out of this surface layer. The solute, being aA1 A kT. However, this equation is of little concentrated in the surface, preferentially lowers value for finite values of a. For protein monothe chemical potential of the water in the surface layers Bull9 and others1° have used the substitulayer so that the preponderance of diffusion of mater tion ATm/Jf = n1 (where N is Avogadro’s number, is into the surface layer and the surface film pres- m the mass of material spread on surface area A , sure (a)rises. The relation of film pressure to mole and &I the molecular weight) to give fraction of water in the surface layer (xz) is given mR T r 4’in x A = -2(ul - u2)(approx.) (7) by equation 1. The term kT d In czfz generally is L W iM negligibly small with the dilute solutions usually , A graph of aA us. T gives a straight line with an considered; consequently intercept from which M is calculable and a slope kT d In aa$2+ u2 d a = 0 (2) from which u1 - up is calculable. J17henused with large molecules (proteins) the further approxiniaand the film pressure is obtained by integration tion of ignoring 6 2 is quite justified. The extension of equation 6 to high pressures is clearly unjustified, and to ignore u2 when u1 is small is also incorrect. Thus, the use of equations such asll For water Q is virtqally independent of film presr(A1 - UI) = kT (very approx.) sure, so that cr2 (9.7 A.2) may be used for 5 2 . Since for ionized monolayers a t high pressures is to be ._ . +2 is usually ~ n i t y ~ film ~ ’ pressures ~~ of soluble avoided. monolayers are calculable as New Eauation of State for “ G a s e ~ u s ’or~ Soluble -k l ‘ Monotayek-Spread monolayers may be “ina=In a2 (4) U2 soluble” in an aqueous substrate for the practical The value of xp is easily calculated from known purpose of maiiipulat,ing with a film balance and values of u1 and u2 for each value of A , (the total yet up to some limiting film pressure be soluble in surface 4, divided by nl, the number of molecules of the surface layer, as indimted by the transition component 1 in it). For water, o2 is invariably from “gaseous” film to a more condensed phase. 9.7 and for each surface-active solute there ap- This transition has been clearly discussed by Ter for Minassian-Saraga and Prigogine. l 2 The greater pears to be just one value of cr1 (e.g., 26 sodium dodecyl sulfate) which applied over the en- solubility in the monolayer is illustrated by myristic tire range of film pressures. This is not entirely acid at 20°, which shows ideal tmo-dimensional soluexpected, but is demonstrated in examples to follow tion behavior up to a mole frsction of 7 X lop3, and in the first paper of this series.8 For sodium but is soluble in the bulk phase only up to 1.6 X dodecyl sulfatefilms (on salt soh$ions), xp = 0.50 (9) 11. B. Bull, J. B i d . Chem.. 186, 27 (1950). ( I O ) E. Mischuck and F.Eirioh in “Monomolecular Layers,” Ed. a t A I = 35.7 A.2, 0.76 at 55.1 A.2, 0.90 a t 113.3 H. Sobotka, A.A.A.S., Washington, D. C . , 1954. etc. The corresponding film pressures a t 2 5 O , by (11) I. Langmuir, J . Chem. P h y s . , 1, 756 (1933). calculated from equation 4, are 29.3, 12.2, and 4.5 (12) L. Ter Minassian-Saraga and I. Prigogine, ~Mem.des services dynes/cm. Thus a complete T-XI isotherm can be chim de l’etat, 38, 109 (1953).
+
March, 1962
A
IL’EW ISOTHERM FOR SOLUBLE llND
It appears that the activity coefficient for the water in the monolayer (42) is unity up to this transition point, and a t higher pressures, when only a more condensed phase is present, +2 is very large. If an unknown substance is spread as a dilute monolayer under conditions that 42 is unity, its molecular weight and UI may be determined with a graph of A os. n2/n1 as shown in Fig. 1. The relationship of n2/n1to 7 is calculated from equation 4 and is the same for all (except polymer) monolayers on a given substrate. It is obvious that
“GASEOUS”MOKOLAYERS
387
2.0
1.8
h
bi: 1.6
E
-2-
i
v
k 1.4
4
so that a graph of A / m (area per mg. of film) vs. nz/nl has a sIope of nlFz/m,from which the molecular weiglit can be determined, and the intercept is n l u l / m , from which g1 may be calculated. The data of Mischuck and EirichlO for egg albumen on 2.6 M amrGonium sulfate are plotted in Fig. 1 using F~ == 9.7 A.2. The slope gives M , the molecular yeight (41,500) and a molecular area (CTI) of 9900 A.2. Tightest hexagonal packing of these molecules with a peripheral line of water molecules separating them would require nz/nl to equal 50. Actually the change in slope from single molecules to more aggregated species appears to take place at about 60 molecules of water per molecule of albumen, as judged by the deviation of points from the slraight line in Fig. 1. The proposed method of plotting is easier to use in that the molecular weight is obtained from a slope rather than from a difficult extrapolation of a steep line to an intercept near the origin.13 Moreover there is only one approximation used, the assumption of ideal solution behavior (42 = 1). Furthermore, the additional information concerning n2/n1is of value for it indicates the maximum film pressures a t which the solute molecules actually can be separated by solvent molecules (0.7 dynes/cm. in the example cited). Extension to Concentrated Soluble Monolayers. -In the case oi monolayers of fatty acids the surface-solution region does not extend beyond pressures of about 0.1 dyne/cm., and with protein monolayers on concentrated salt solutions the surface-solution region extends to about 0.5 dyne/cm. However, in the case of water-soluble detergents the surface layers are soluble in water at nearly all film pressures. Consequently, all the arguments and the equation of state for dilute monolayers apply for most of the pressure-area curves. Figure 2 shows the pressure-area relation for sodium dodecyl sulfate (SDS) at, 20 and 25’, using data from the literature14-“j obtained by Gibbs adsorption equation and surface tension measurements. In Fig. 2 , the data are plotted according to the equation (13) . I J Cr Allan and 4 E Alexander T (cns F a a d a y hoc 6 0 , e63 (1954) (1%)A P Hiads and I C Brown, in ‘ ILIonomolecular Layers” (ref 10) (15) E J Clayfield and Mattheus “Proc I11 Intern Conyr Surface I c t i r i l y ” Butteruorths London 1957, T’ol I, p. 172 (16) E RIatijeiic and B A Pethica, Trans Faraday Soc , 64, 1382 (1958)
1.2
1.o 100
300
200 n&.
Fig. 1.-Data of Nischuck and Eirichlo for “gaseous” monolayers of egg albumen on 2.6 M ammonium sulfate plotted according to equation 8.
0
No a . l t
A
No s a l t
v
0 A
0,001 N
Ref (141
Fkf 115)
NaCI
0.1 N NaCI 0 . 2 N NaCI
Ref ( 1 6 1 Ref 1141
Ref 116)
0 5 10 15 Ratio of water to detergent molecules in surface film (nzz/ nd. Fig. 2.-Solutions of sodium dodecyl sulfate, with and without salt. Test of proposed isotherm: AI = U I u,z[e-ruz/kT/( 1 - e-rw‘k?’)].
+
(9)
where x is the number of particles per molecule of SDS. If the surface solute is dissociated into z particles, this must be taken into account in using 2 2 , the mole fraction of water molecules. Since equation 4 relates x2 to T without any assumption regarding the kind of solute particles, the ratio xp/(1 - x2) = nz/nlz,where n1 is the total number of solute molecules (associated and undissociated). We may write n2/n,xas an exponential expression
FREDERICK M. FOWKES
388
I
01
0
50 100 150 AI, area per molecule of SDS, Fig. 3.-Equations of state for soluble monolayers of sodium dodec l sulfate in the presence and absence of salt. The first eq. in {oth cases should read T = - (IcT/a~)In 22. 140 120
2 100
-2
a?
2 80
8
E
60
li: rd
4 40 20
a 2 4 6 8 10 12 Water molecules per SDS molecule ( n d n i ) . Fig. 4.-Ideal solution isotherms for sodium dodecyl sulfate adsorbed on the surface of water (ref. 15), calculated for water lagers one or two molecules in depth.
0
The data in Fig. 2 show the effect of salt on the value of x , which is 2.0 on salt-free substrates and decreases to 1.0 with increase in salt content of the substrate. The data of Clayfield and Matthews16 were especially useful for the salt-free solutions because time-effects were taken into account better than with other studies without salt. It is obvious that these data fit eauation 9 verv well and the intercept a t c1 = 26 of both lines helps confirm the validity of applying the ideal two-dimensional
Vol. 66
solution equations to soluble monolayers in the region of high film pressures. Note that ul is constant over the whole pressure-area isotherm. Figure 3 shows the same data and isotherms plotted in the customary fashion and compares them with the “gas” equations. It is obvious that the proposed ideal two-dimensional solution equations not oiily have a better theoretical basis than “gas” equations, but fit the data far better. At larger areas per molecule the “gas” equation gives values of A1 which are too large by the value of ciz (9.7 as discussed earlier. However, the error in the linear approximation of In 22 becomes quite a bit larger at high film pressures. The main point is that concentrated soluble monolayers a t high film pressures act as ideal twodimensional solutions and that pressure-area curves for such systems may be calculated accurately using the ideal solution equations. Some soluble monolayers have been studied by adding so much salt to the substrate that they become insoluble. l’ The pressure-area isotherms, when plotted as in Fig. 2, ,give x-values of a few tenths. This is taken to indicate that the high salt content has so reduced the activity of water in the surface layer that it thereby has promoted the formation of dimers, trimers, and higher aggregates in the monolayer as part of the salting-out process. Other Soluble R/Bonolayers.-PayensI8 has presented some pressure-area curves for soluble monolayers of n-octylamine on aqueous substrates. The data obtained on a substrate of 0.2 M acetate buffer a t pH 6 with 1 M KaC1 give a straight line plot according to equation 9 with a z-value of 1.0 because of the high ionic strength. The intercept The data for a film of the same gives m = 20 material on a substrate of 0.2 M acetate buffer a t pH 6 without added salt gave the same intercept and a z-value of 1.5, indicating partial conversion of the amine to octylammonium acetate. TJ7ith a weaker buffer and lower pH, x should become as large as 2.0. Data obtained on substrates other than water require a value of $2 for the molecular area of the solvent molecules. In the case of water and propylene carbonatelg the two-thirds power of the molecular volume (9.7 and 30 respectively) has proved adequate. Jarvis and Zismanlg have measured the pressure-area isotherm for some fluorochemicals adsorbed a t the surface of their solutions in polar organic solvents. One such pair is bis-(+’-butyl) 3-methylglutarate in propylene carbonate. The plot of the pressure area data as A I os. nz/nl gives a straight line with an intercept of u1 = 35 A.z and a surprisingly small slope (15 A.2). This slope means either that uz is really only half the estimated 30 if.2or that there is a z-value of 0.5, indicating that this solute is associated as dimers on the surface of the propylene carbonate. Dimerization of this solute is not expected but appears more reasonable than Q = 15 A.2. Depth of the Surface Phase.-The calculations of mole fraction of water in the surface solution (17) B. A. Pethica, Trans. Faraday Sac., BO, 4 1 3 (1954). (18) Th. A. J. Payens, Philips Research Repts., 10, 426 (1955). (19) , ~ . ,N. L. Jarvis and W. A. Zisman. J. Phvs. Chem.. 64, 157 (1960). ~
March, 1962
HEATSOF SOLUTION OF NICKELAND COPPER DIMETHYLGLYOXIMES 389
of monolayers all have been made by assuming that only the surface layer of water molecules is involved in the surface solutions. However, since water mollecules are very small and have strong cohesive forces, it appears possible that two or more layers of -water molecules could be involved in surface solutions. In the case of solutions of sodium dodecyl sulfate, where the partial molecular area ul of 26 14.2includes a contribution of the cation as well an the sulfate group, we calculate a mole fraction x2 of 0.33 a t 36 A.2. However, if two layers of water molecules were involved in surface solutions, x2 would be 0.50; a t the same time the partial molecular surface area uz would be reduced to 4.85 instead of 9.7 The two effects do not quite cancel out, as is shown in Fig. 4, which makes use of the data of Clayfield and Matthews16 for saltfree solutions of sodium dodecyl sulfate (SDS) a t 25’. Here the ratio of water to detergent molecules in the surface solution (nzln,) was calculated (from the measured film pressure) for two cases: water layers one molecule deep or two molecules deep. The experimental slopes (UZ = 10.0 u2/2 = 5.05 agree with theory (UZ = 9.7 u2/2 = 4.85 but the intercepts are signifi-
cantly different and only the intercept for the monomolecular layer fits the experimental data. The intercept gives ul,the partial molecular area of the solute; in the monomolecular layer calculation u1 is 26-27 A . 2 , while in the bimolecular layer calculaSince it already is known tion ul is 21-22 that u1 for dehydrated monolayers (on salt solutions’’) is 26-27.5 A.2,it appears entirely justified to use the monomolecular layer calculation. In Fig. 4 the monomolecular layer plot includes (in the lower left corner) Clayfield and Matthews data a t pressures over 25 dynes/cm., where the ratio of water molecules to detergent molecules approaches 1:l. It is most interesting to see that a t this ratio there is a sharp transition from an ideal solution monola,yer to a dehydrated monolayer (in whichoA1 = m). The five measurements of AI = 26.3 A.2 in this region agree well with the 26-27.5 A.2 found on salt solutions. Acknowledgment.--The section on depth of the surface phase was inspired by the helpful criticism of Professor N. K. Adam. The advice of Dr. W. A. Zisman in revision of the manuscript is gratefully acknowledged.
THE HEATS OF SOLUTION OF NICKEL AND COPPER DIMETHYLGLYOXIMESX BYDAVIDFLEISCHER AND HENRY FREISER* Department of Chemistry, University of Pittsburgh, Pittsburgh 13, Pennsylvania Received July 18, 1961
The solubilities of nickel and copper dimethylglyoximes have been determined as a function of temperature in a series of solvents. The differences in the derived heats of solution indicate that solvation effects are more important than the difference in crysbal energies in determining the relative solubility of these two compounds in water, and that the crystal form of the copper compound is more stable than the crystal form of the nickel compound. The postulated nickel-nickel bond in the solid chelate would seem to be very weak.
The specificity of dimethylglyoxime for nickel(I1) has been shown to be a result of a solubility effect, as copper(I1) dimethylglyoxime has a larger formation constant than the less stable nickel(I1) chelate. a When comparing the solubilities of a compound there are two energy terms t o be considered: the relative crystal energies and the relative energies of solvation of the species in solution. I n order to examine the solubility difference of copper(I1) and nickel(I1) dimethylglyoximes in terms of these two energies, the heats of solution of these complexes have been determined, from the temperature dependence of the solubility, in water, chloroform, benzene, and n-heptane. Experimental Apparatus.-The solutions were contained in a doublewalled glass vessel and were mixed with a magnetic stirrer. Water, maintained at constant temperature, was circulated through the vessel jacket. The vessel was sealed with a standard taper joint held in place by a metal screw clamp.
__--
(1) Taken in part from the Ph.D. dissertation of David Fleischer, August, 1958. (2) .Department of Chemistry, University of Arizona, Tucson 25. Arizona. (3) R. G. Charles and H. Freiser, AnaZ. Chim. Acta, 11, 101 (1954).
A capillary tube, sealed through this joint, terminated a t the bottom of the vessel in a fine glass frit. The other end of the capillary terminated in a small outer standard-taper joint to which could be fitted a short capillary take-off tube or a heated pipet. The pipet was so constructed that its tip consisted of only the necessary inner standard taper joint. The rest of the pipet was wrapped with resistance wire and insulated with asbestos. The pipet was kept at a constant temperature by maintaining a specific voltage across its resistance. The photometric measurements were made using a Beckman Model DG spectrophotometer. A Model E Leeds and Northrup polarogra h was used for the polarographic measurements. The pofarograph cell was of the conventional H-type, using a saturated calomel half cell with an agar bridge supported by a glass frit. Reagents.-Both nickel(11) and copper( 11) dimethylglyoximes were prepared from a 2:1 mole ratio of 0.1 M ethanolic dimethylglyoxime and reagent grade nitrate salts of the metals. The metal salts were prepared as 0.001 M water solutions, to which was added the alcoholic dimethylglyoxime solution. It was necessary to evaporate the copper(I1) dimethylglyoxime solution before precipitation occurred. The preparation of the copper compound was very sensitive to excessefiof either component, and an amorphous solid, instead of crystals, resulted unless exactly stoichiometric amounts were used. The analysis of the copper(I1) dimethylglyoxime crystals gave these percentages:
