W. R. GILLAP,N. D. WEINER,AND M. GIBALDI
2218
Ideal Behavior of Sodium Alkyl Sulfates at Various Interfaces. Thermodynamics of Adsorption at the Air-Water Interface by William R. Gillap, Norman D. Weiner, and Milo Gibaldil College of Pharmaceutical Sciencee, Columbia University, New York, New York 10085 (Received December 14, 1067)
Adsorption of sodium decyl sulfate (SDS) and sodium dodecyl sulfate (SDDS) has been studied at very high areas per molecule at the air-0.1 M NaCl interface. Ideal gaseous behavior has been observed, and the standard thermodynamic functions for adsorption have been determined and evaluated. As anticipated, both standard free energy ( A G O ) and enthalpy (AH’) decreased with increasing hydrocarbon chain length, Surprisingly, however, the standard entropy (As’) was identical for each surfactant. Nevertheless, in both cases entropy was the major factor in the driving force to adsorption and the importance of hydrophobic bonding in this process is discussed. Based on these data, it is postulated that whereas SDS is present in the bulk and is adsorbed as a monomer, SDDS may be present in the bulk in both monomeric and dimeric forms, and may be adsorbed at the surface in both these forms.
Introduction Considerable work has been reported on the adsorption of sodium alkyl sulfates at the air-water surface. Mankowich2 recently commented that while many data are available in the literature on the molecular areas of adsorbed ionic and nonionic surfactants at air-water surfaces, little work bas been done in estimating the standard free energy, enthalpy, and entropy changes for the adsorption processes of these surfactants. Most thermodynamic functions have been evaluated from surface tension-log concentration curves utilizing the Gibbs equation which assumes complete monolayer adsorption in that portion of the curve immediately preceding the critical micelle concentration. Surface concentrations in this region must be estimated from the Gibbs equation and are probably not equal to surface activities. Although it is well known that surfactants, at low bulk concentrations, will exhibit ideal gaseous behavior at the air-water surface, there is almost a complete lack of published data on the thermodynamics of adsorption in this ideal region. It was the purpose of this investigation to obtain thermodynamic information concerning the adsorption of sodium decyl sulfate and sodium dodecyl sulfate at the air-water surface in the ideal region.
Theoretical Considerations The evaluation of standard thermodynamic functions of adsorption provides an excellent means of quantifying subtle differences in adsorption. Quantitative information regarding differences in extent of adsorption between compounds can be determined from standard free energy values, while standard enthalpy and entropy data may provide information concerning the me&%nism of the adsorption process. While surface activities, rather than concentrations, should be used for rigid thermodynamic quantification The Journal of Physical Chemistry
of the adsorption process with standard functions, these are difficult to evaluate in nonideal regions. Therefore, measurements in very dilute solution, where activity coefficients closely approximate unity, are most commonly used to evaluate the standard thermodynamic functions of adsorption. For dilute solutions of surface-active agents, where solute-solute interactions are absent, the variation of surface pressure (a)with bulk concentration (C) of surface active agent is linear, i.e.
where a is defined as Traube’s constant.a Langmuir4 has elucidated the theoretical significance of this linear region by demonstrating that such a dilute interfacial film also obeys an equation of state which is analogous to the ideal gas law, i.e.
ad = kT
(2)
where A is the surface area, k is Boltzmann’s constant, and T is the absolute temperature. Betts and Pethica5 chose a standard state of unit fugacity (a*)to calculate thermodynamic functions of adsorption. I n their opinion, the choice of a standard state in terms of monolayer thickness, as previously used by Ward and T ~ r d a i , ~is- necessarily ~ arbitrary (1) Department of Pharmaceutics, School of Pharmacy, State University of N~~ Yo& at ~ ~ f ~f ~ lf ~ N, f ~,y . l 14214, ~ , (2) A. M. Mankowich, J . Amer. oil Chem. soc., 43,615 (196s). (3) I. Traube, Ann., 265, 27 (1891). (4) I. Langmuir, J . Amer. Chem. SOC.,39, 1848 (1917). ( 5 ) J. J. Betts and B. A. Pethica, Proceedings of the 2nd International Congress of Surface Activity, Vol. I, London, 1957, p 152. (6) A, F,H. Ward, Trans. Furadag soc., 42,399 (1946). (7) A. F. H.Ward and L. Tordai, ibid., 42, 408 (1946).
THERMODYNAMICS OF ADSORPTION AT THE AIR-WATERINTERFACE and introduces considerable difficulty when applied to ionized surfaces owing to the variation in thickness of the diffuse double layer with changing surfactant concentration and ionic strength. Surface fugacity is defined by
#A = kT = rfA
(3)
where f is the fugacity coefficient. In the ideal region, where Traube’s relation applies, values off approach unity, and values of T may, therefore, be considered equal to surface fugacities. Thus in dilute regions where the bulk activity can be replaced by concentration, and where Traube’s law applies -AGO
=
k T In a
(4)
where AGO is the standard free energy of adsorption. The standard entropy of adsorption, A s o , can be calculated from
(5) and the standard heat of adsorption, AH’, can be calculated from A G O
A H o - TASO
2219
sence of a change in surface tension with time, throughout the course of the experiment, indicated the absence of surface hydrolysis. The chemical stability of sodium alkyl sulfates a t the interface over reasonable periods of time has also been shown by Jones14 and Bujake and Goddard.’5 Solutions should be prepared for each experiment, however, and not retained for additional studies on succeeding days, since aging can occur if solutions are stored for long periods. Surface tension vs. concentration data were obtained for SDS and SDDS in 0.1 M NaCl at 25,35,and 45 f 0.1”.
Results Surface tension (6) and surface pressure (a) vs. concentration plots for SDS and SDDS are shown in Figures 1-4. The slopes of these curves were calculated by the method of least squares. The variances of the experimental points about these regression lines were calculated, and the data were tested for linear relationships a t the 95% confidence level.16J7 All curves tested statistically in the ideal region satisfied the condition for linearity at this confidence level. The values of the slopes (avalues) are shown in Table I.
(6)
Experimental Section Materials. Fractionally distilled, demineralized water was used in all experiments. Deionized water (Barnstead mixed bed) was fractionally distilled in the presence of basic potassium permanganate. The surface tension of water prepared by this method was within 0.05 dyn/cm of the literature value.’O Sodium chloride was Baker Analyzed reagent grade. The surface tension of a 0.1 M solution of this salt was 0.1 dyn/cm higher than that of distilled water,l0 suggesting the absence of surface active impurities. The use of sodium chloride which was roasted a t 600” for 6 hr produced the same result. The sodium alkyl sulfates, sodium decyl sulfate (SDS), and sodium dodecyl sulfate (SDDS), were synthesized by the SO3 method according to Schick.ll Their purity was confirmed by the absence of minima in surface tension vs. log concentration plots. Before each use, both sodium alkyl sulfates were slurried and washed with ether to remove any alcohol which may have occurred due to hydrolysis. Surface Tension Measurements. All measurements of surface tension were made in 0.1 M NaCl solutions by Critical micelle conthe Wilhelmy plate meth0d.~2>~3 centrations in 0.1 M NaCl solutions were 0.015 M and 0.0012M for SDS and SDDS, respectively. Surface tension wa8 measured after allowing 15 min for equilibrium. At least four readings were made on each solution. The constancy of the readings throughout the experiment indicated that the surface tension values were equilibrium values. Furthermore, the ab-
Table I: Standard Thermodynamic Functions for the Adsorption of Sodium Decyl and Dodecyl Sulfates a t Various Temperatures for the Air-0.1 M NaCl Surface Cornpound
SDS SDDS
Absolute temp, deg
298.2 308.2 318.2 298.2 308.2 318.2
U
2.25 2.11 1.84 2.48 2.20 1.74
X X X X X X
lo4 lo4 104 106 10‘1 10‘
A@, kcal/mol
AHa, kcal/mol
-5.92 -6.06 -6.19 -7.31 -7.45 -7.58
-2.0 -2.0 -2.0
AS‘, eu
13
-3.3 -3.3 -3.3
13
Values for the standard free energies of adsorption the standard entropies of adsorption (AS”),and the standard enthalpies of adsorption ( A H o ) were calculated by means of eq 4,5,and 6,respectively. These (AGO),
(8) A. F. H. Ward and L. Tordai, Trans. Faraday SOC.,42,413 (1946). (9)A. F. H. Ward and L Tordai, Nature, 158,416 (1946). (IO) “Handbook of Chemistry and Physics,” 42nd ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1960. (11) M. J. Schick, J . Phys. Chem., 68, 3585 (1964). (12) W. R. Gillap, N. D. Weiner, and M. Gibaldi, J . Amer. Oil Chemists’ SOC.,44, 71 (1967). (13) A. W. Adamson, “Physical Chemistry of Surfaces,” Interscience Publishers, Inc., New York, N. Y.,1960,p 110. (14) H.L.Jones, Amer. Dyestuff Reptr., 27, 621 (1938). (15) J. E.Bujake and E. D. Goddard, Trans. Faraday SOC.,61, 190 (1965). (16) W. J. Dixon and F. J. Massey, Jr., “Introduction to Statistical Analysis,” 2nd ed, McGraw-Hill Book Go., Inc., New York, N. Y., 1957, Chapter 11. (17) 0.J. Dunn, “Basic Statistics,” John Wiley and Sons, Inc., New York, N. Y . , 1964,Chapter 12.
Volume 72, Number 6 June 1968
W. R. GILLAP,N. D, WEINER,AND M. GIBALDI
2220
Figure 1. Surface tension
( 7 )v 5 .
molar concentration of sodium decyl sulfate in the ideal region a t various temperatures.
25”
3.0
7
i
2.0
1.0
MOLAR coNcmRATxoN x 10s
Figure 2. Surface pressure ( n ) us. molar concentration of sodium decyl sulfate in the ideal region a t various temperatures.
values are also reported in Table I. Free energy os. temperature plots used to determine the entropy terms are shown in Figure 5.
Discussion The standard free energies of adsorption of SDS and SDDS determined in the present study are in good agreement with the findings of Betts and Pethica.18 These workers calculated AGO values (from the initial slopes of &log C plots in 0.1 M NaC1 solutions) of -4.8 to -4.9 kcal/mol for sodium octyl sulfate, -5.9 to -6.0 kcal/mol for SDS, and -7.1 to -7.2 kcal/mol for SDDS. The data in Table I indicates the predicted decrease in AGO with increasing chain length. The present thermodynamic evaluation confirms the importance of entropy, which represents the major driving force for the adsorption process, as suggested by Weiner, et aL19 The reason for the entropic driving force is speculative. One possibility for the entropy gain is the loss of icelike structure of water molecules associated with the hydrocarbon chain in the bulk phase when the Surface-active agent is adsorbed at the surface. The Journal of Physical Chemistry
Several investigations20-a0have, supported the importance of changes in water structure, or hydrophobic bonding, in the association of surfactant molecules. The discovery that heats of micellization were either positive (as in the case of nonionic surface-active agents and some ionic surface-active agents below 25”J or weakly negative, has led to the conclusion that entropy rather than enthalpy is the major driving force for agg r e g a t i ~ n . l l J ~ -It ~ ~has been proposed that the hydrocarbon chain of the single ion or monomer is surrounded by highly structured water, or “icebergs,” which results in a comparatively low energy state. However, the concomitant restricted motion of the water molecules in the iceberg, by this high degree of structuring, provides a strong driving force to aggregation. Although there is a decrease in the entropy of the system owing to aggregation of the monomers, there is a greater and offsetting increasein entropy as a result of the desolvation of the hydrocarbon chains. A plausible extension of this theory would be a consideration of adsorption a t an interface in mecha(18) J. J. Betts and B. A. Pethica, Trans. Faraday SOC.,56, 1515 (1960). (19) N. D.Weiner, H. C. Parreira, and G. Zografi, J . Pharm. Sci., 5 5 , 187 (1966). (20) F. Franks and H. T. Smith, 3’. Phys. Chem., 68, 3581 (1964). (21) E. D.Goddard, C. A. J. Hoeve, and G. C. Benson, ibid., 61, 593 (1957). (22) E. D. Goddard and G. C. Benson, Can. J . Chem., 35, 986 (1957). (23) P. Mukerjee and A. Ray, J. Phys. Chem., 67, 190 (1963). (24) W. Bruning and A. Holtzer, J . Amer. Chem. SOC.,83, 4865 (1961). (25) K.W. Herrmann, J . Phys. Chem., 66, 295 (1962). (26) M. J. Schick, ibid., 67, 1796 (1963). (27) P. Mukerjee, P. Kapanan, and H. G. Meyer, ibid., 70, 783 (1966). (28) D. C. Poland and H. A. Scheraga, J . Colloid Interfac. Sci., 21, 273 (1966). (29) D. C. Poland and H. A. Scherega, J. Phys. Chem., 69, 2431 (1965). (30) D.C.Poland and H. A. Scherega, ibid., 69,4425 (1965). (31) B.D.Flockhart, J . Colloid Sci., 16,484 (1961).
2221
THERMODYNAMICS OF ADSORPTION AT THE AIR-WATERINTERFACE
I
66
I
I
[PDDS-*pHkO*] Ft: [(DDS)22-*rH20]
+ (n - r)H2O
where H20*refers to structured water. If the driving force for the formation of the dimer (AGD)is assumed to be the formation of the hydrophobic bond, then for a homologous series
3.0
c: E \
a 2,o
AGD = -RT In K D = nAG,
B
9 r
1.0
0
5 .O
10.0
-
15.0
MOLAR CONCENTRATION X 10'
Figure 4. Surface pressure ( P ) us. molar concentration of sodium dodecyl sulfate in the ideal region a t various temperatures.
nistically similar terms. It seems reasonable that the entropy to be gained from the disruption of the hydrocarbon-iceberg structure in the bulk would be a significant driving force to adsorption at an interface. The loss of one degree of rotational freedom and the possible uncoiling of the hydrocarbon a t the air-water surface probably result in only small entropy effects. Of particular interest in our investigation was the lack of difference between the entropies of adsorption of the two alkyl sulfates. Ward and Tordais have shown, for a homologous series of fatty acids, that the dependence of free energy on the entropic component becomes more pronounced with increasing chain length. A similar entropy-chain length relationship was expected in comparing the adsorption of SDS and SDDS. A possible explanation of the discrepancy between the experimental and expected findings is that the adsorption of SDDS may not truly reflect a bulk monomer-adsorbed monomer equilibrium because of precriticalmicelle-concentration association. Franks and Smith,20 on the basis of deviations in density measurements, have proposed the following equilibrium for sodium dodecyl sulfate in the submicellar range
+
AGmi,
(7)
where AG, is the free energy of formation of a hydrophobic bond, AGmix is the free energy of demixing associated with the formation of the dimer, and KD is the dimerization constant. Measurements of pNa+ for a series of alkyl sulfates indicate that K D is affected significantly by the length of the hydrocarbon chain and, therefore, dependent on AG,.20 The behavior of sodium decyl sulfate closely followed that of NaC1, but progres-
TEEIPEBATUPB ("0)
Figure 5. Free energy of adsorption (AGO) DS. temperature plots derived from surface tension data for sodium dodecyl sulfate (0) and sodium decyl sulfate ( 0 ) . Volume 7.9, Number 6 June 1868
2222
W. R. GILLAP,N. D. WEINER,AND M. GIBALDI
sively larger deviations occurred for sodium dodecyl and tetradecyl sulfates. It is quite likely that the results observed in the present study reflect the difference in dimerization potential of SDS and SDDS. Mukerjee, et ~ l . , ~have ’ also suggested that certain discrepancies in the results of their study of hydrophobic bonding in micelle formation may be due to dimerization of long-chain ions in submicellar concentrations. Since dimerization depends primarily on the hydrophobic interactions between hydrocarbon chains and since SDDS exhibits a much greater tendency to dimerize than SDS, the entropy for the bulk monomer-adsorbed ion equilibrium for SDDS would be
greater than the apparent measured value. The present determination may reflect an equilibrium of the type bulk monomer
21
bulk dimer
Jl”
adsorbed species
Hence, the difference in the driving force to adsorption between the SDS and SDDS systems must be enthalpic. However, when considering the microscopic process of bulk monomer -+ surface monomer, the difference in driving force between the two surface-active agents may still be predominantly entropic on origin.
Ideal Behavior of Sodium Alkyl Sulfates at Various Interfaces. Thermodynamics of Adsorption at the Oil-Water Interface by William R. Gillap, Norman D. Weiner, and Milo Gibaldi College of Pharmaceutical Sciences, Columbia University, New York, New York 10026 (Received December 14, 1967)
Adsorption of sodium decyl sulfate and sodium dodecyl sulfate has been studied at very high areas per mole,> ,. cule at the hydrocarbon-0.1 M NaCl interface for a homologous series of n-alkanes (CC Ideal gaseous behavior was observed in all systems studied. The chain length of the oil had no apparent effect on adsorption in the ideal region. The standard thermodynamic functions for adsorption at the dodecane-0.1 M NaCl interface were determined and evaluated. Based on comparisons of the data obtained for both air-water and hydrocarbon-water interfaces and on evaluation of the results in terms of the major forces involved in the adsorption process, it is suggested that sodium dodecyl sulfate dimers, which are present in the aqueous bulk, dissociate at the oil-water interface and that the monomer is the exclusive adsorbed species. The importance of hydrophobic bonding and entropy as a driving force to adsorption at the oil-water interface is discussed.
Introduction Few data are available regarding the energetics of adsorption at the oil-water interface. Haydon and Taylor’ calculated the free energy of adsorption per methylene group, from the “initial” slopes of interfacial tension us. concentration curves for solutions of sodium alkyl sulfates (C8,Cl0,and Clz) in 0.1 M NaC1, to be 758 cal/mol of CH2. A review of their data, however, indicates that the bulk concentrations employed exceeded those required to maintain ideality at the interface.2 Davies8 has reported an energy of adsorption per methylene group for the petroleum ether (bp >120°)-water interface of 811 cal/mol of CH2. This was calculated by comparing rates of desorption (by measuring changes in interfacial tension at constant area) of monolayers of cetyltrimethylamnionium bromide injected into a spreading solution at the 0.01 N HC1-petroleum ether The Journal of Physical Chemistry
interface and rates of desorption of monolayers of octadecyltrimethylammonium chloride at the air-0.01 N HC1 surface. Since rates of desorption were measured (which could differ significantly from rates of adsorption, particularly as a function of chain length), two different interfaces were employed, and the difference in the rates of desorption of the spreading solvent (propyl alcohol) at the two interfaces was not considered: the significance of this value is doubtful. Cassie and Palmer14using the data of Powney and Addison16report (1) D. A. Haydon and F. H. Taylor, Trans. Faraday SOC.,58, 1233 (1962). (2) W. R. Gillap, N. D. Weiner, and M. Gibaldi, J . Colloid Interfac. Sci., 25, 441 (1967). (3) J. T. Davies, Trans. Faraday Soc., 48, 1052 (1952). (4) A. B. D. Cassie and R. C. Palmer, ibid., 37, 156 (1941). (6) J. Powney and C. C. Addison, ibid., 33, 1243 (1937).
