Langmuir 1996, 12, 5845-5850
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Surface and Colloidal Properties of Cyclic Amides. 1. Two-Dimensional Virial Coefficients for Adsorbed Monolayers of N-Alkyl-2-pyrrolidones at the Air/Water Interface Anjing Lou, Brian A. Pethica,* and Ponisseril Somasundaran Langmuir Center for Colloids & Interfaces, Columbia University, 500 West 120th Street, Room 911, New York, New York 10027 Received March 11, 1996. In Final Form: August 9, 1996X The N-(n-alkyl)pyrrolidones are low vapor pressure polar solvents which are surface active in aqueous solutions. From measurements at low surface pressures and low concentrations the two-dimensional second virial coefficients B2(T) at the air/water interface are obtained for the series of even-numbered alkyl substituents from ethyl to octyl. At 25 °C, B2(T) is positive for the ethyl compound and becomes increasingly negative as the chain length increases. The effect of temperature on B2(T) is unusual, increasing temperature leading to more negative B2(T) values. The virial coefficients, heats of adsorption, and Traube coefficients are discussed in terms of molecular packing, chain-chain van der Waals attraction, and the interaction of the chains and large molecular dipoles with water.
The N-(n-alkyl)pyrrolidones comprise a class of biodegradable surface-active solvents with low vapor pressures and low toxicity. They are partially or completely miscible with water, depending on the chain length and temperature. These properties have become of increasing industrial interest. The molecules are very polar, with dipole moments close to 4 D1 and liquid dielectric constants at low frequencies in the range 32 (methyl) to 20 (dodecyl).2 The pure liquids are conducting and will dissolve a variety of electrolytes. They are very weak bases and are essentially nonionic, giving neutral solutions in water. The surface activity of the octyl-, (2-ethylhexyl)-, and dodecylpyrrolidones has been studied in the high surface pressure region,3-5 and the close-packed areas for the n-alkyl compounds are given (assuming ideal solutions) as about 0.35 nm2/molecule, indicating that the ring amide head group prevents close chain packing in the monolayer. Measurements of virial coefficients played a major role in the development of theories of intermolecular forces, since they can be related explicitly by statistical mechanical methods to the potentials and forces between molecules.6 The second virial coefficients in particular are a function of pair potentials. Intermolecular pair potentials between like molecules at interfaces are obviously fundamental to understanding monolayers, membranes, and other interfacial or quasi-interfacial structures. It is therefore surprising that there is little information in the literature for two-dimensional virial coefficients of lipid molecules at aqueous interfaces. It is hoped that this paper will help to increase the interest of theoreticians in the topic, particularly in view of the unusual features of virial coefficients for the pyrrolidones. The available low-pressure data for insoluble spread monolayers of nonionic lipids at the air/water (a/w) X Abstract published in Advance ACS Abstracts, November 1, 1996.
(1) Calvin, M. L.; Kumler, W. D. J. Am. Chem. Soc. 1961, 83, 4596. (2) B.A.S.F. Technical brochure, “Specialty Pyrrolidones”, 1995. BASF Corporation, 100, Cherry Hill Road, Parsippany, NJ 07054. (3) Zhu, Z. H.; Yang, D.; Rosen, M. J. J. Am. Oil Chem. Soc. 1989, 66, 998. (4) Rosen, M. J.; Zhu, Z. H.; Gu, B.; Murphy, D. S. Langmuir 1988, 4, 1273. (5) Rosen, M. J.; Gu, B.; Murphy, D. S.; Zhu, Z. H. J. Colloid Interface Sci. 1989, 129, 468. (6) Davidson, N. Statistical Mechanics; McGraw Hill: New York, 1962; pp 315-349.
S0743-7463(96)00232-6 CCC: $12.00
interface for n-alkyl compounds with a variety of head groups have been collected and used earlier to estimate second virial coefficients.7 These were interpreted by summed pair-potential calculations.7 A later study of pentadecanoic acid monolayers at the a/w interface at low pressures gave an improved set of second virial coefficients at several temperatures.8 These results have been interpreted by an improved analysis in which the lipidwater interactions were explicitly included.9,10 There are few virial coefficients in the literature for a/w monolayers adsorbed from aqueous solutions. A second virial coefficient at one temperature has been obtained for propionic acid,10 and coefficients are also available for several longchain esters and alcohols.11 Alkane vapor adsorption to the water surface has been studied by several groups,12-18 the results being mostly interpreted by equations of state,11,19 although some few results were treated by the virial method.19 The available data on alkanes at the a/w interface have been reanalyzed recently, giving acceptable values of B2(T) in the range methane to butane only.20 These results indicate that the alkanes interact at the water surface as they do in the three-dimensional gas phase, with little or no “hydrophobic” contribution from the water to the pair potentials. The best available results for adsorbed alcohol and ester monolayers at the oil/water (o/w) interface have again been mostly interpreted through equations of state,11,19 (7) Pethica, B. A.; Glasser, M. L.; Mingins, J. J. Colloid Interface Sci. 1981, 81, 41. (8) Pallas, N. R. Ph.D. Thesis, Clarkson University, Potsdam, NY, 1983. (9) Hasmonay, D.; Badiali, J. P.; Dupeyrat, M.; Claverie, P. J. Colloid Interface Sci. 1994, 165, 467. (10) Hasmonay, D.; Billoudet, F.; Badiali, J. P.; Dupeyrat, M. J. Colloid Interface Sci. 1994, 165, 480. (11) Chapman, J. Ph.D. Thesis, University of Hull, 1975. (12) Hauxwell, F. Ph.D. Thesis, University of Bristol, 1969. (13) Hauxwell, F.; Ottewill, R. H. J. Colloid Interface Sci. 1970, 34, 473. (14) King, J. W.; Chatterjee, A.; Karger, B. L. J. Phys. Chem. 1972, 76, 2769. (15) Karger, B. L.; Castells, R. C.; Sewell, P. A.; Hartkopf, A. J. Phys. Chem. 1971, 75, 3870. (16) Massoudi. R.; King, A. D., Jr. J. Phys. Chem. 1974, 78, 2262. (17) Massoudi, R.; King, A. D., Jr. In Colloid & Interface Science; Kerker, M., Ed.; Academic Press: New York, 1976; Vol. 3, pp 331-347. (18) Jho, C.; Nealon, D.; Shogbola, S.; King, A. D., Jr. J. Colloid Interface Sci. 1978, 651, 141. (19) Aveyard, R.; Chapman, J. Can. J. Chem. 1975, 53, 916. (20) Pethica, B. A. Langmuir 1996, 12, 5851.
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with some analyses showing that the virial expansion fits the data well for several solutes using only the second virial coefficients, which are all positive due to the screening of the chain-chain interactions of the monolayer molecules by the paraffinic oils. The virial expansion to the second term only is then equivalent to the Volmer equation of state, and Volmer coareas are equivalent to second virial coefficients. The extensive data on o/w spread monolayers of dialkyl phospholipids in the low-pressure region21 have been recently analyzed in depth, largely in terms of repulsive interactions between the zwitterion head groups as the factor leading to the large positive virial coefficients which increase with temperature.22,23 In the present study the surface tensions of four N-alkyl2-pyrrolidones (ethyl to octyl) were measured in the lowpressure region, in equilibrium with dilute solutions shown to be close to ideal. The second virial coefficients for the adsorbed monolayers are derived, and the temperature variations are estimated for the ethyl, butyl, and octyl compounds. The virial coefficients are shown to be primarily related to the van der Waals pair interactions of the methylene groups on the surface. Standard heats of adsorption and Traube coefficients are also presented.
Lou et al.
Figure 1. Ethylpyrrolidone in water. Surface pressures at the air/solution interface at 10, 25, and 40 °C.
Experimental Section Materials. The structure of the compounds studied is CH2
CH2
CH2
C
N
O R = n-alkyl
R
The final compounds were analyzed by glc to show the following purities: C2, 99.35; C4, 99.75; C6, 99.54; C8, 99.57%. The residual impurities were mostly shorter chain homologs or methyl ringsubstituted compounds unlikely to interfere with surface tension measurements. A possible exception may be an unidentified component at 0.13% in the hexyl compound. Surface tension measurements were mostly made with a platinum Wilhelmy plate using a Cahn electromicrobalance, the temperature and humidity being maintained inside a thermostat vessel. A number of checks were made by the drop-volume method. Water was triply distilled, the second stage from alkaline permanganate. Tests of the ideality of the solutions were first attempted with a vapor-pressure osmometer, but it proved impossible to obtain steady temperature differences in the detector, presumably due to the effect of the residual low volatility of the pyrrolidones. The freezing point method was therefore chosen, and determinations were made to 0.01 °C using a mercury thermometer in a stirred doublewalled thermostated vessel.
Results The surface tension was routinely checked, giving 72.00 ( 0.05 mN m-l at 25 °C.24,25 Measurements of the surface tension of water over the temperature range reported here (5-40 °C) agreed well with the values in the tabulation of Vargaftik et a1.26 At 40 °C we find 69.52 ( 0.09 mN m-1(69.56), and at 10 °C we find 74.33 ( 0.08 mN m-1 (74.22). The surface tensions of the test solutions showed substantial time effects only at the lowest concentrations, steady state values being observed in a minute or so for (21) Mingins, J.; Taylor, J. A. G.; Pethica, B. A.; Jackson, C. M.; Yue, B. Y. T. J. Chem. Soc., Faraday Trans. 1 1982, 78, 323. (22) Mingins, J.; Stigter, D.; Dill, K. Biophys. J. 1992, 61, 1603. (23) Stigter, D.; Mingins, J.; Dill, K. Biophys. J. 1992, 61, 1616. (24) Pallas, N. R.; Pethica, B. A. Colloids Surf. 1983, 6, 221. (25) Pallas, N. R.; Harrison, Y. Colloids Surf. 1990, 43, 169. (26) Vargaftik, N. B.; Volkov, B. N.; Voljak, L. D. J. Phys. Chem. Ref. Data 1983, 12, 817. These data are also given in abbreviated form in: The Handbook of Physics & Chemistry, 75th ed.; CRC Press: Boca Raton, FL, 1995.
Figure 2. Butylpyrrolidone in water. Surface pressures at the air/solution interface at 25 and 45 °C.
pressures above about 1 mN m-1. At lower pressures, the larger time intervals to reach steady state introduce more uncertainty, and we estimate reproducibility to be (0.l mN m-1for the surface pressures below 1.0 mN m-1 at 25 °C and (0.15 mN m-1 at the other temperatures. Surface tensions measured by the drop-volume and Wilhelmy plate methods agreed within these limits. The freezing point data over a wide concentration range will be presented separately. In the dilute concentration ranges reported here, the osmotic coefficients are given within experimental error by (1 - λm), where m is the molality and λ is 0.16 (ethyl), 0.40 (butyl), and 0.50 (hexyl), (10% in each case. For the octyl compound, the freezing point experiments were not sufficiently sensitive to estimate λ, but by extrapolation from the lower homologs, λ is reasonably sure to be well below 1.0. Since the heats of dilution (to be reported later) are zero within experimental error in the range of dilutions considered here (up to 2 × l0-l molal for ethylpyrrolidone and decreasing by an order of magnitude for each additional pair of CH2 groups in the chain), the activity coefficients can all be taken as unity for the calculations reported for each compound. The largest deviation from ideality is with the ethyl compound (activity coefficient 0.92 at 2 × 10-1 molal), not low enough to influence the estimates as described below, which focus on the low concentration limits. The surface pressure (Π) as a function of concentration (c) is shown for the four compounds in Figures 1-4, and
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Langmuir, Vol. 12, No. 24, 1996 5847
Figure 3. Hexylpyrrolidone in water. Surface pressure at the air/solution interface at 25 °C.
Figure 6. Butylpyrrolidone in water. Π/c as a function of c at 25 and 45 °C.
Figure 7. Hexylpyrrolidone in water. Π/c as a function of c at 25 °C.
Figure 4. Octylpyrrolidone in water. Surface pressure at the air/solution interface at 10, 25, and 40 °C.
Figure 5. Ethylpyrrolidone in water. Π/c as a function of c at 10, 25, and 40 °C.
the plots of Π/c as a function of c are shown in Figures 5-8. The virial expansion for monolayers may be expressed as
Π ) kT(Γ + B2(T)Γ2 + B3(T)Γ3 ...)
(1)
where Γ is the surface density, B2(T), B3(T), etc. are the temperature dependent second, third, etc. virial coefficients, k is Boltzman’s constant, and T is the temperature.
Figure 8. Octylpyrrolidone in water. Π/c as a function of c at 10, 25, and 40 °C.
In practice, the series is truncated at a term appropriate to the extent and precision of the available data. In this paper the emphasis is on B2(T), which relates directly to intermolecular pair potentials between the monolayer molecules and to their interaction with the solvent.6,7,9 For insoluble monolayers Γ is the density of the molecules, known directly from the overall surface area and the volume and concentration of the spreading solution of the monolayer substance. For adsorbed films, as shown by Hasmonay et al.,9 the appropriate Γ in eq 1 is the surface excess density as given by the Gibbs Adsorption Isotherm.
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Lou et al.
For the nearly ideal solutions studied here, the surface excess is given by
kTΓ ) c dΠ/dc
(2)
Substituting eq 2 into eq 1, it is straightforward to show that
B2(T) ) (-β/R2)kT
(3)
where
(dΠ dc )
(4)
(dΠ/c dc )
(5)
R ) lim cf0
and
β ) lim cf0
To determine B2(T), the problem is to estimate R and β from the data. A common statistical strategy is to express the data as a polynomial in the form
Figure 9. Propionic acid in water at pH 2. Π/c as a function of c at 27 °C. Data from Hasmonay et al.10
x)x
Π)
axcx ∑ x)0
(6)
where the ax are coefficients which vary with temperature and x ) 0, 1, 2, 3, ... to a limit appropriate to the available data, and then to obtain the coefficients by a least squares computation. This procedure is one of the methods used by Hasmonay et al.10 for aqueous propionic acid solutions. These authors find that a0 is not zero, which is physically incorrect, since Π is necessarily zero at c ) 0. They adopt an empirical correction by subtracting the nonzero intercept from the pressures obtained from the polynomial, which essentially adjusts all the empirical data points. In our calculations with polynomials, we have taken a0 as zero in all cases. The difficulty in using eq 6 is that the values of the coefficients necessarily vary with the number of terms chosen in the polynomial and the range of data chosen for analysis. Some numerical solutions also give physically impossible or improbable behavior on modest extrapolation beyond the experimental range being fitted. For example, the cubic function calculated by Hasmonay et al.10 exhibits a physically improbable increased slope of the Π-c plot a little above the range of the experimental points. The choice of any “smoothing” function for statistical purposes necessarily implies physical assumptions which impose consequences on subsequent calculations. We have preferred, therefore, to emphasize graphical procedures with both Π-c and Π/c-c plots to determine R and β, paying particular attention to the experimental data at low surface pressures and the effect of experimental error, using polynomials in a secondary role in judging the analyses. As an example we may compare the graphical estimation of B2(T) for propionic acid with the values obtained using both a polynomial and a “rational function” by Hasmonay et al.10 This rational function also gives a nonzero Π at c ) 0. They tabulate their experimental data for aqueous propionic acid at pH 2 (additional acid unspecified) at 27 °C. These data are represented as Π/c as a function of c in Figure 9. Taking the solutions as ideal, the values of R and β can readily be estimated, underemphasizing the single point at the lowest concentration, which is the least precise experimentally. The resulting B2(T) from Figure 9 as drawn is 0.36 nm2 molecule-1. Hasmonay et al.10 find values of 0.4 nm2 molecule-1 (obtained using Γ values estimated graphically) and 9 and 7 × 10-2 nm2 molecule-1
Figure 10. Two-dimensional second virial coefficients for adsorbed monolayers of the alkylpyrrolidones at the air/solution interface.
(from the polynomial and rational functions). They conclude that, to an order of magnitude, B2(T) is 10-1 nm2 molecule-1. However, it seems clear from Figure 9 that their value from graphical estimates of Γ is the more reliable and that the statistical calculations from both the polynomial and rational functions are misleading. To obtain a B2(T) as low as 0.1 nm2 molecule-1 requires a much lower β and/or a higher R than is shown in Figure 9, which is plainly improbable. Accordingly, we conclude that, for propionic acid monolayers, the data give B2(T) as nearer to 0.4 nm2 molecule-1. Turning to the data for the alkylpyrrolidones, the R and β values from the lines as drawn in Figures 1-8 (noting that R is obtainable from either Π-c or Π/c-c plots) were used to obtain the B2(T) values shown in Figure 10. The second virial coefficients for the C2, C4, and C8 alkyl substituents are also given at several temperatures. The bars in Figure 10 give the estimated error range of B2(T) values by drawing reasonable limits for the required slopes and comparing R values from both types of plots. The
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Figure 12. Dependence of the initial slope of the Π-c isotherms (R) at 25 °C on the chain length of the alkylpyrrolidones. Figure 11. Variation of the initial slopes of the Π-c isotherms (R) with temperature for ethyl- and octylpyrrolidones. Table 1. Standard Thermodynamic Parameters of the Adsorption of Pyrrolidones at the Air/Water Interface, 25 °C compound
-∆G° (kJ/mol)
-∆H° (kJ/mol)
∆S° (J/mol)
EP BP HP OP
10.8 15.3 21.9 27.3
10.2 -3.1
2 62
-6.0
112
plots of log R against 1/T are linear (Figure 11), leading to estimates of the molar standard heats of adsorption according to27,28
d(log R)/d(1/T) ) ∆H0/R
(7)
where R is the gas constant. The standard free energies (2.3RT log R), heats and entropies, are shown in Table 1. The standard states are the ideal surface pressure of l mN m-1 and ideal unit molality. The plot of log R against chain length (Figure 12) gives a Traube coefficient of 3 at 25 °C. Discussion The B2(T) values for the homologous series of pyrrolidones show that the intermolecular attraction increases with chain length, as expected. The effect of temperature on the B2(T) values was unexpected, with B2(T) becoming more negative at higher temperatures. It will be useful to discuss the chain length effect first, using a theoretical framework developed previously7 for insoluble monolayers of single-chain lipids at the a/w interface, which used the customary relation6,7,9
∫
B2(T) ) π [1 - exp(-φ(r)/kT)]r dr
(8)
where φ(r) is the intermolecular pair potential energy and r is the molecular separation. The integral was evaluated on the assumption that the water provides a force (not dependent on r) holding the molecules in the surface layer. The pair potential was considered to be dominated by the interaction between parallel extended chains lying flat in (27) Betts, J. J.; Pethica, B. A. Second International Congress on Surface Activity; Butterworths: London, 1957; Vol. 1, p 44. (28) Matijevic, E.; Pethica, B. A. Trans. Faraday Soc. 1958, 54, 1390.
the surface. φ(r) was accordingly expressed as a variant of the Lennard-Jones function
φ(r) ) 4[(σ/r)1/2 - (σ/r)5]
(9)
where σ is the lower value of r for which φ(r) is zero and is essentially the exclusion diameter of the extended molecules. The fifth power for the dispersive attraction term was taken from Salem,29,30 who showed that this form applies to long parallel chains at distances small compared to the chain length. The dispersion attraction term is proportional to the effective chain length for lipids such as long chain fatty acids and has been calculated by Salem.29 The B2(T) values (on a scale of πσ2) were computed as a function of 4/kT.7 The interpretation for the insoluble long chain fatty acids then proceeded from the measured B2(T) values by identifying a single value of σ for a given homologous series to give the Salem dispersive attraction term varying linearly with chain length, treating CH2 and CH3 groups as approximately equivalent. This procedure gave physically reasonable results for long chain fatty acids, with σ corresponding to an acceptable close-packed area of 0.19 nm2 molecule-1 at high surface pressure and a corresponding effective chain length one carbon less than the actual number. The remaining CH2 is presumably associated with the acid group immersed in the water and correspondingly screened. Use of the Salem r-5 potential function for the chains of CH2 groups presumes that the chains are long and pack as extended linear alkanes. Correspondingly, eq 9 will apply only qualitatively for the pyrrolidones with their ring-chain sequences of methylene groups, and then only for the higher homologs. The close-packed area for the octyl- and dodecylpyrrolidones is found to be 0.35 nm2/ molecule.4,5 Taking a corresponding value of σ of 0.635 nm, the “effective chain length” can be calculated from B2(T) using the r-5 law to give values of 7, 8.5, 10, and 11.5 for the C2, C4, C6, and C8 pyrrolidones, respectively. These may be compared to the sums of chain and ring methylene groups of 5, 7, 9, and 11 for the four compounds. Since the r-5 function probably leads to an overestimate of the magnitude of the total dispersion energy for the methyl groups in the pair interactions with these compounds, (29) Salem, L. Nature 1962, 193, 476. (30) Salem, L. Prog. J. Chem. Phys. 1962, 37, 2100.
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the “effective chain lengths” suggest tentatively that the lactam group is contributing to the attraction potential. Further calculations based on the summing of all methylene group interactions over all orientations, allowing for the chain ring structures, are necessary to make further progress. A recent detailed analysis of intermolecular potentials in lipid monolayers has advanced the account given earlier7 by expressly introducing the interactions between the water phase and the lipid molecules in the monolayer.9 It was shown that for fatty acids in an insoluble monolayer or in an adsorbed monolayer in contact with a very dilute solution of the monolayer species (typical for surfactants) the use of eq 8 on the assumption that the pyrrolidonewater interaction holding the adsorbed molecules at the surface does not vary with r is a good approximation. The φ(r), however, should also include terms for the head groups and for interaction with water molecules at all r values. It would appear that for fatty acids these extra corrections to the pair potentials are of secondary importance, since the Salem chain-chain potentials cover the B2(T) estimates for n-pentadecanoic acid reasonably well with realistic σ values.7,9,10 For the alkylpyrrolidones, the head group is probably of larger importance, and extended theoretical interpretation along the line given by Hasmonay et al. will be valuable. The required new theoretical analysis must also account for the unexpected effects of temperature on the B2(T) values. With the apparent exception of the butyl compound (which was studied at only two temperatures), B2(T) becomes significantly more negative as the temperature rises. The same trend has been found with cyclohexylpyrrolidone.31 This finding does not correlate with the heats of adsorption, which are endothermic for the butyl and octyl homologs and exothermic for the ethyl compound. It has been shown that both the butyl- and hexylpyrrolidones exhibit lower consolute points in mixtures with water.32 The mutual solubility of octylpyrrolidone and water increases as the temperature is lowered, but no consolute point is reached before a solid phase freezes out. Lower consolute points imply that the balance of interaction in solution between the pyrrolidone molecules themselves and with the water favors clusters and phase separation as the temperature rises. The same process is presumably occurring in the monolayer at the air/water interface. The results also suggest that a similar (31) Zhu, Z. H.; Pethica, B. A. Unpublished observations. (32) Lou, A.; Pethica, B. A. Unpublished observations.
Lou et al.
Figure 13. Freezing points of the alkylpyrrolidones.
increase in net attractive potentials with temperature will be found in adsorbed films of other surfactants with lower consolute behavior, polyoxyethylenes, for example. The apparently anomalous position of butylpyrrolidone (B2(T) not varying significantly with temperature) is not yet understood. Experiments over a wider temperature range are clearly desirable. We may note that butylpyrrolidone has other unusual properties in the homologous series. For example, the freezing point is unusually low (-105 °C),2 as shown in Figure 13. This suggests that close packing in the solid state is energetically relatively unfavorable, corresponding to a weaker overall attractive interaction compared to those of the other homologs. Further studies on heats of dilution, phase diagrams, and aggregate formation in alkylpyrrolidone-water mixtures and measurements at high surface pressures are to be reported. Acknowledgment. Part of this study was supported by a generous grant from International Specialty Products. We wish to thank Dr. Ray Anderson and Dr. Walter De Thomas of ISP for the synthesis and purification of the compounds used in this study and Rose Mackey for the analytic results reported here. LA9602325
