Anionic Surfactant Solution Interfaces | Langmuir

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Langmuir 2000, 16, 157-160

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Cation Selectivity at Air/Anionic Surfactant Solution Interfaces† Vanessa E. Haverd and Gregory G. Warr* School of Chemistry, The University of Sydney, Sydney, New South Wales, 2006, Australia Received June 3, 1999. In Final Form: August 22, 1999 The selective binding of alkali metal and quaternary ammonium ions to anionic surfactant films at the air/solution interface has been investigated using the ion flotation technique. Surfactant anions studied were the dodecyl phosphate monoanion, the hexadecyl phosphate dianion, bis(2-ethylhexyl) phosphate, dodecanoate, and dodecyl sulfate. Alkali metal ions display only weak selectivity at adsorbed films of all surfactants studied. The binding strength increases in the order Na+ < K+ < Rb+ < Cs+, with the exception of films of dodecanoate, for which the ions have equal affinity, and the hexadecyl phosphate dianion, for which the selectivity sequence is Cs+ < Rb+ < K+ < Na+. By contrast, the binding of quaternary ammonium counterions to adsorbed films of anionic surfactants has a striking dependence on the surfactant headgroup. Results are interpreted using a model which includes solvation of the headgroups and competing counterions and is compared with competitive binding of phosphate, sulfate, and acetate ions at cationic surfactant films.

Introduction The selectivity of binding of ions to interfaces remains an important problem in many areas of colloid and surface science. It enters classic problems such as electrocapillarity1 and the meaning of the electrokinetic potential,2 as well as surfactant self-assembly through critical micelle concentration,3 the micelle sphere-to-rod-transition,4 and reaction kinetics in micellar systems.5 The study of selective adsorption of competing counterions at the air/solution interface provides insight into surfactant/counterion interactions in isolation from the effects of self-assembly present in the bulk solution. It is also of industrial interest, since preferential ion adsorption can be exploited to selectively remove ions from wastewater by ion flotation.6,7 The exchange of two counterions, X+ and Y+, at a charged interface can be described by the equilibrium given by

X+(aq) + Y+(ads) h X+(ads) + Y+(aq) where (ads) denotes an ion adsorbed at the interface and (aq) denotes an ion in the bulk solution. The affinity of X+ for the interface, relative to that of Y+, can be quantified by the selectivity coefficient, KYX. It is simply the equilibrium constant in the dilute solution limit given by

KYX ) ΓXcY/ΓYcX

(1)

* To whom correspondence may be addressed. E-mail: [email protected]. † Part of the Special Issue “Clifford A. Bunton: From Reaction Mechanisms to Association Colloids; Crucial Contributions to Physical Organic Chemistry”. (1) Butler, J. A. V. Electrocapillarity; Methuen, London, 1940. (2) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: London, 1981. (3) Rosen, M. J. Surfactants and Interfacial Phenomena; John Wiley & Sons: New York, 1978. (4) Magid, L. J.; Han, Z.; Warr, G. G.; Cassidy, M. A.; Butler, P. D.; Hamilton, W. A. J. Phys. Chem. B 1997, 101, 7919-27. (5) Romsted, L. S.; Bunton, C. A.; Nome, F.; Quina, F. H. Acc. Chem. Res. 1991, 24, 357. (6) Aziz, M.; Shakir, K.; Benyamin, K. Radioact. Waste Manage. 1986, 26, 235. (7) Walkowaik, W. Sep. Sci. Technol. 1991, 26, 559.

where cX and cY are bulk concentrations and ΓX and ΓY are surface excesses. Note that this expression is only applicable for the exchange of ions of equal valence. Determination of selectivity coefficients for cations at adsorbed films of anionic surfactants at the air/solution interface has so far been limited to ion flotation studies of alkali metal and alkaline earth metal ions with sodium dodecyl sulfate (SDS) and bis(2-ethylhexyl) sulfosuccinate (AOT).8,9 With both of these surfactants, the selectivity order of the group 1 and 2 metal ions is the same; binding increases down the group, that is, increasing with hydrated ion radius or free energy of hydration.9 The observed selectivities of alkali metal ions are small (KYX e 2), and the results for dodecyl sulfate and AOT are all but indistinguishable. A slightly greater selectivity is observed for the alkaline earth ions in AOT-adsorbed films compared with dodecyl sulfate (DS). Further, selectivities derived from ion flotation agree well with interfacial probe studies of alkali metal ion binding by SDS micelles.10,11 The same selectivity order is observed at decyl phosphate and dodecyl phosphate micelle surfaces.10 However critical micelle concentrations for alkyl phosphate salts suggest that the selectivity order might be reversed upon changing from singly to doubly charged phosphate micelles,12 and a similar selectivity order reversal is effected upon increasing the pH of phosphoric acid resins.13,14 In this work we use the technique of ion flotation15 to further investigate the effect of the anionic headgroup type on counterion binding and to ascertain whether varying the headgroup is a means of controlling the order (8) Grieves, R. B.; Burton, K. E.; Craigmyle, J. A. 1987, 22, 1597. (9) Schulz, J. C.; Warr, G. G. J. Chem. Soc., Faraday Trans. 1998, 94, 253. (10) He, Z.; O’Connor, P. J.; Romsted, L. S.; Zanette, D. J. J. Phys. Chem., 1989, 93, 4219. (11) Hafiane, A.; Issid, L.; Lemordant, D. J. Colloid Interface Sci. 1991, 142, 167. (12) Arakawa, J.; Pethica, B. A. J. Colloid Interface Sci. 1980, 75, 441. (13) Marcus, Y.; Howery, D. G. Ion Exchange Equilibrium Constants; Report to IUPAC Commission; International Union of Pure & Applied Chemistry: Oxford, 1975; Vol. 6. (14) Tien, H. T. J. Phys. Chem. 1964, 68, 1021. (15) Morgan, J. D.; Napper, D. H.; Warr, G. G.; Nicol, S. K. Langmuir 1994, 10, 797.

10.1021/la990695l CCC: $19.00 © 2000 American Chemical Society Published on Web 11/17/1999

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Table 1. Alkali Metal Ion Selectivity Coefficients, KNa+X, determined from Flotation Experiments X

C12HPO4-

C10HPO4(micelles, ref 10)

C16PO42-

(C8)2PO4-

C11CO2-

C12SO4(ref 9)

C12SO4(micelles, ref 10)

Na+ K+ Rb+ Cs+

1.00 1.15 ( 0.07 1.13 ( 0.04 1.43 ( 0.11

1.00 1.33 1.41 2.33

1.00 0.88 ( 0.08 0.78 ( 0.09 0.60 ( 0.04

1.00 1.10 ( 0.05 1.05 ( 0.07 1.26 ( 0.04

1.00 0.93 ( 0.04 0.93 ( 0.06 0.91 ( 0.04

1.00 1.10 ( 0.11 1.51 ( 0.15 1.65 ( 0.15

1.00 1.47 1.70 2.05

and magnitudes of selectivity coefficients. Selectivity coefficients for alkali metal ions and quaternary ammonium ions at adsorbed films of dodecyl sulfate (C12SO4-) and AOT are compared with singly charged dodecyl phosphate (C12HPO4-), doubly charged hexadecyl phosphate (C16PO42-), bis(2-ethylhexyl) phosphate ((C8)2PO4-), and dodecanoate (C11CO2-). Materials and Methods Dodecyl sulfate (C12SO4-) and AOT were obtained as sodium salts from Sigma (>99% purity), while bis(2-ethylhexyl) phosphate ((C8)2PO4-) (>99%, Sigma), dodecyl phosphate (C12HPO4-) (>97%, Rhodia), and dodecanoate (C11CO2-) (>99%, Sigma) were obtained in the acid form. The cationic surfactants dodecyltrimethylammonium chloride (DTAC) and tetradecyltrimethylammonium bromide (TTAB) were supplied by Aldrich at >99% purity. Monohexadecyl phosphoric acid was synthesized from hexadecanol (18.76 g) and pyrophosphoric acid (27.62 g) by violent stirring in toluene for 100 h at 25 °C, according to the method of Tahara et al.16 Due to the insensitivity of the ion flotation technique to impurities, no further purification of the surfactants was undertaken. Solutions of surfactants and the competing counterions of interest were prepared in Milli-Q water. With the exception of the experiments with (C8)2PO4-, concentrations were well below the critical micelle concentration to avoid competing ion exchange at the micellar surface. Alkali metal ions were obtained as hydroxide salts (Sigma, >99%) and used as received. The quaternary ammonium ions, tetramethylammonium (TMA+), tetraethylammonium (TEA+), and tetrabutylammonium (TBA+) were obtained and used as chloride salts (Sigma, >99%). The anionic counterions required were dihydrogen phosphate (H2PO4-), ethyl sulfate (CH3CH2SO4-), hydrogen phosphate (HPO42-), and sulfate (SO42-). All were obtained as sodium salts from Sigma. The acid forms of the anionic surfactants were neutralized with 1 or 2 equiv of hydroxide solution. Monoalkyl phosphoric acids are diprotic, with pKa,1 and pKa,2 values of 1.8 and 6.8, respectively.10 Thus by variation of the pH of a monoalkyl phosphate solution, the charge on the headgroup can be varied. Monododecyl phosphoric acid was reacted with 1 equiv of hydroxide solution to obtain a solution of C12HPO4-. However, as the pH was raised by adding a second equivalent of hydroxide solution, only a transient foam could be formed. To compensate for this effect, the longer-chained, more surface-active hexadecyl homologue was used to study the doubly charged phosphate. Experiments on C16PO42- were carried out maintaining the pH above 9.5. All flotation experiments were carried out in a 1 L glass flotation column fitted with a porous frit at the base, through which nitrogen was passed at a flow rate of 100 mL min-1. Solutions were allowed to foam for 1-3 h, with foam being continuously removed from the top of the column. Samples (4 mL) were removed regularly from the bulk solution and analyzed by ion chromatography coupled with a conductivity detector. Details of the procedure have been described previously.9,15 The selectivity coefficient was obtained from a flotation experiment by monitoring the changing concentrations of the competing counterions in the bulk solution. It has been shown that a material balance on the flotation column yields the (16) Tahara, T.; Satake, I.; Matuura, R. Bull. Chem. Soc. Jpn. 1969, 42, 201.

Figure 1. Determination of selectivity coefficients KNa+X+ for the alkali metal ions and (C8)2PO4-: K+ (b); Rb+ (9); Cs+ (2). following relationship between these concentrations and the selectivity coefficient15

ln cX ) KYX ln cY + C

(2)

where C is a constant that depends on initial solution conditions. Thus the selectivity coefficient is given by the slope of a plot of ln cX vs ln cY.

Results and Discussion Selectivity coefficients obtained in this study for binding of alkali metal ions over Na+ at adsorbed films of C12HPO4-, C16PO42-, (C8)2PO4-, and C11CO2- are listed in Table 1. Figure 1 exemplifies the plots used to obtain selectivity coefficients with eq 2. The proximity to unity of all the values in Table 1 indicates that, as with SDS (also listed) and AOT, these surfactants afford little discrimination between the alkali metal ions, with virtually no discrimination in the case of C11CO2-. Results for C12HPO4- and C12SO4- show that the selectivity coefficient increases down the group, as has been found previously for C12SO4- and C10HPO4- micelles.10 The same trend is observed for the double-chained surfactant, (C8)2PO4-, in agreement with the selectivity order inferred from vesicle fusion studies of dihexadecyl phosphate.17 However, the opposite trend is found for an adsorbed layer of C16PO42-. This selectivity order has not previously been observed with surfactants either at the air/solution interface or at the surface of a micelle. The same trend might be inferred for dodecanoate, although all selectivities are so close to unity that this is somewhat equivocal. Morgan et al. proposed that partial dehydration of the competing counterions dominates their exchange at the interface.18 Counterions, fully hydrated in solution, become partially dehydrated upon association with an exchange site. Thus the free energy of ion exchange is related to the standard free energies of hydration of the counterions, ∆G°hyd,X and ∆G°hyd,Y. The assumption is made that ions within a group undergo equal degrees of dehydration ω, where ω is the fraction of ∆G°hyd lost upon adsorption. (17) Mortara, R. A.; Quina, F. H.; Chaimovich, H. Biochem. Biophys. Res. Commun. 1978, 81, 1080. (18) Morgan, J. D.; Napper, D. H.; Warr, G. G. J. Phys. Chem. 1995, 99, 9458.

Cation Selectivity

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Table 2. Selectivity Coefficients, KYX, for Selected Anions with Quaternary Ammonium Surfactants X

Y

CH3CH2SO4CH3CH2SO4BrH2PO4CH3COO-

ClBrClBrBr-

SO42-

HPO42-

surfactant

KYX

monovalent DTAC 4.0 ( 0.3 1.3 CTAB 3.02 TTAB 0.25 ( 0.05 TTAB 0.078 divalent DTAB

4.2 ( 0.9

reference this work calculated ref 15 this work ref 22 this work

The standard free energy of exchange, ∆GYX, is therefore given by

∆GYX ) ω(∆G°hyd,Y - ∆G°hyd,X)

(3)

This equation adequately describes Morgan’s results for halides15,18 as well as Schulz’s results for alkali metal ions with dodecyl sulfate and AOT.9 Alkali and alkaline earth metal ion exchanges on sulfonate ion exchange resins are also well described by this model.18 Its plausibility in the present systems is easily tested by plotting RT ln KYX vs (∆Ghyd,X - ∆Ghyd,Y), which has a slope yielding the fractional dehydration, ω. Such plots give ω ) 0.7% for C12SO4- and ω ) 0.6% for C12HPO4-. This is consistent with small extents of dehydration expected for alkali metal ions and known to occur at the mercury/solution interface19 and in sulfonated ion exchange resins.18 However the slope of such a plot for C16PO42- is negative. Since ω lies between 0 and 1 by definition, partial dehydration of the counterions cannot account for the exchange of alkali metal ions at an adsorbed film of C16PO42- at the air/solution interface. Extending the partial dehydration model by adding electrostatic effects through an ion size dependence,20

∆GYX ) ∆G°el + ∆G°dehyd

(4)

also fails to an adequately describe the results for C16PO42-, indicating that there must be additional, specific complexation between the doubly charged phosphate headgroups and the alkali metal counterions. The selectivity coefficients, particularly KNa+Cs+ and KNa+Rb+, in Table 1 reveal an increased selectivity between alkali metal ions as the headgroup of the singly charged surfactants is changed from carboxylate to phosphate(1-) to sulfate. Kellaway and Warr21 report a similar enhancement of halide selectivity coefficients, KCl-Br- and KBr-I-, upon increasing the degree of methyl substitution of alkylammonium surfactants. This finding is consistent with counterion binding being favored by easier headgroup desolvation. To establish whether the relative ease of desolvation of the R-CO2-, R-HPO4-, and R-SO4- headgroups can account for the observed differences in alkali metal ion selectivities, we compare their selectivities as counterions against a reference ion, bromide, using a quaternary ammonium surfactant as the cationic group. Dihydrogen phosphate (H2PO4-), acetate (CH3COO-), and ethyl sulfate (CH3CH2SO4-) are three anions of equal valence, each closely resembling one of the anionic surfactant headgroups. The selectivity coefficients of H2PO4- and CH3CH2SO4- against Br- are listed in Table 2, together (19) Grahame, D. C. Chem. Rev. 1947, 41, 441. (20) Jorne´, J.; Rubin, E. Sep. Sci. 1969, 4, 313. (21) Kellaway, L.; Warr, G. G. J. Colloid Interface Sci. 1997, 193, 312.

with the literature value for CH3COO-.22 The quaternary ammonium surfactant headgroup avoids the effects of headgroup hydration and eliminates the possibilities of hydrogen bonding and specific complexation between the headgroup and the counterions. Thus the selectivities of the competing counterions are determined by their ease of desolvation, as has been demonstrated previously.18,21,22 Of the cationic nitrogen surfactants, the quaternary ammonium surfactants are also those which display the most discrimination between counterions.21 We therefore expect to be able to clearly observe any differences in solvation of the model headgroup ions. KBr-CH3COO- and KBr-H2PO4- were determined directly with TTAB as surfactant. KBr-CH3CH2SO4- was determined from the product of KCl-CH3CH2SO4- using DTAC and the literature value15 for KCl-Br-. Selectivity coefficients lie in the order KBr-CH3COO- < KBr-H2PO4- < KBr-CH3CH2SO4-. Since the quaternary ammonium headgroup ensures the absence of binding mechanisms other than partial dehydration of the counterions, this is also the order of increasing ease of desolvation. This is consistent with the order of measured gas-phase first and second solvation free energies for these ions.23 The higher affinity for the interface of ethyl sulfate is not attributable to the ethyl moiety. In a study of binding of carboxylates at air/solution interfaces, Thalody and Warr22 report that acetate is the most weakly binding ion among the carboxylates, being marginally less bound than formate. Propionate and butyrate also bind very weakly to tetradecyltrimethylammonium, whereas pentanoate and longer chain carboxylates bind very strongly. This indicates that the counterions do not act as cosurfactants until the alkyl chain length exceeds four carbons. As above, first and second solvation energies of hydrogensulfate and ethyl sulfate ions are indistinguishable.23 In a separate experiment the selectivity coefficient KHPO42-SO42- was determined using DTAB as a surfactant. It was found that KHPO42-SO42- ) 4.2 ( 0.9, offering further support that sulfate anion selectivity over dihydrogen phosphate is not attributable to the ethyl moiety. We now turn to quaternary ammonium ions not as surfactants but as counterions. Table 3 lists selectivity coefficients for TMA+, TEA+, and TBA+ over Na+ at the air/solution interface for a range of surfactants. Selectivity coefficients of all three quaternary ammonium ions with C12SO4- are significantly greater than 1, indicating that they bind more strongly to the interface than any of the group 1 ions. There is a large increase of KNa+X as the chain length of the alkyl substituents of the counterions is increased, with tetrabutylammonium exhibiting a remarkable 100-fold selectivity over sodium.24 This shows that selectivity is dominated by the hydrophobicity of the counterions, with the free energy of the system being lowered by removal of the hydrophobic counterions from the bulk solution to the interface. Similar observations have been reported for the exchange of tetraalkylammonium ions with Na+ at the surface of dodecyl sulfate micelles.25 (22) Thalody, B.; Warr, G. G. J. Colloid Interface Sci. 1997, 188, 305. (23) Blades, A. T.; Klassen, J. S.; Kebarle, P. J. Am. Chem. Soc. 1995, 117, 10563. (24) This strong counterion binding may explain the anomalous demixing behavior of alkyltributylammonium surfactants reported by Warr et al. (Warr, G. G.; Zemb, T. N.; Drifford, M. J. Phys. Chem. 1990, 94, 3086. Buckingham, S. A.; Garvey, C. J.; Warr, G. G. J. Phys. Chem. 1993, 97, 10236) and the similar behavior of sodium tetradecyl sulfate solutions containing added tetrabutylammonium salts (Yu, Z.-J.; Xu, G. J. Phys. Chem. 1989, 93, 7441. Yu, Z.-J.; Zhou, Z.; Xu, G. J. Phys. Chem. 1989, 93, 7446.) (25) Bonilha, J. B. S.; Georgetto, R. M. Z.; Abuin, E.; Lissi, E.; Quina, F. J. Colloid Interface Sci. 1990, 135, 238.

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Table 3. Quaternary Ammonium Selectivity Coefficients, KNa+X, Determined from Flotation Experiments X

C12HPO4-

TMA+

0.5 ( 0.1 0.5 ( 0.1 0.8 ( 0.1

TEA+ TBA+ a

C16PO421.2 ( 0.1 1.2 ( 0.2

(C8)2PO4-

C12SO4-

6.4 ( 0.6

3.1 ( 0.2, 7.7 ( 0.2, 6.0a 110 ( 10 3.0a

AOT

C11COO-

2.2 ( 0.2 19 ( 4

20 ( 5

Micellar selectivity coefficients, ref 25.

The effect is similar with AOT, although the binding of tetrabutylammonium is not as dramatic as with dodecyl sulfate. This can be attributed to the presence of ester groups near the AOT headgroup reducing access of the quaternary ammonium surfactant to a hydrophobic environment. The binding of quaternary ammonium counterions to C12HPO4- films is remarkably different. While C12SO4shows a 100-fold preference for TBA+ over Na+, C12HPO4actually binds Na+ more than TBA+. Moreover, results for C12HPO4- show that there is scarcely any discrimination between quaternary ammonium ions with different alkyl chain lengths (Table 3). This indicates an absence of the hydrophobic interactions which are so clearly evident with C12SO4-, an effect which is at least partly attributable to the relative eases of desolvation of the phosphate and sulfate headgroups. Headgroup solvation effects are also manifested by selectivity coefficients for C16PO42-. The doubly charged phosphate headgroup also discriminates negligibly between Na+, TEA+, and TBA+ and is consistent with strong solvation of the phosphate(2-), as inferred from the selectivity coefficient KHPO42-SO42- ) 4.2 ( 0.9. This lack of selectivity for quaternary ammonium ions over sodium by decyl phosphate micelles at various pH values has been reported previously based on 23Na NMR results.26 Results in Table 2 show that the affinity of selected anions for an adsorbed film of a quaternary ammonium surfactant increases in the order CH3CO2- < H2PO4- < CH3CH2SO4-. We therefore expect the affinity of a quaternary ammonium counterion for an adsorbed film of C11CO2-, C12HPO4- or C12SO4- to increase in the order C11CO2- < C12HPO4- < C12SO4. This is not so however, and Table 3 indicates that the actual order of affinity, KNa+TBA+, is C12HPO4- < C11CO2- < C12SO4-. The order of the phosphate and carboxylate is switched. This suggests that there is an additional energy cost associated with the binding of a quaternary ammonium ion to an adsorbed film of C12HPO4-, compared with the binding of H2PO4to an adsorbed film of a quaternary ammonium surfactant. It is possible that this additional energy cost arises from hydrogen bonding between the phosphate headgroups in the adsorbed film, hindering access of these hydrophobic counterions to the nonpolar part of the interface. This is supported by the value of KNa+TBA+ with (C8)2PO4-. A double-chained phosphate, this surfactant does not have a protonated headgroup and therefore lacks the capacity (26) Romsted, L. S.; Yoon, C.-O. J. Am. Chem. Soc. 1993, 115, 989.

for hydrogen bonding between the headgroups. TBA+ has a significantly higher affinity for an adsorbed film of (C8)2PO4- (KNa+TBA+ ) 6.4 ( 0.6) than for a film of C12HPO4(KNa+TBA+ ) 0.8 ( 0.1). Hydrogen bonding has also been invoked in related systems to account for, e.g., minimal polymer/micelle interactions in phosphate surfactants,27 pH-dependent fusion of didodecyl phosphate vesicles,28 and reduced permeability of methyl viologen across a dihexadecyl phosphate bilayer29 and also in sphere to rod transitions in micellar solutions of dimethyldodecylamine oxide.30 Conclusion For all the anionic surfactants studied, discrimination between alkali metal ions at the air/solution interface is minimal. Nonetheless, a the selectivity order Na+ < K+ < Rb+ < Cs+ is distinguishable for C12HPO4- and (C8)2PO4-, in agreement with previous results for C12SO4and AOT. For C16PO42-, this order is reversed. Discrimination between quaternary ammonium ions is also minimal for C12HPO4- and C16PO42-, while the selectivity order for C12SO4- is Na+ < TMA+ < TEA+ , TBA+. These observations are largely attributable to partial dehydration both of the counterions and of the surfactant headgroups. Partial dehydration of the alkali metal ions adequately describes the discrimination between them for C12HPO4-, (C8)2PO4-, C12SO4-, and AOT but not for C16PO42-. The observed selectivity order for this surfactant remains unexplained. Partial dehydration of the anionic surfactant headgroups accounts for the varying abilities of C12SO4, C11CO2-, and C12HPO4- to discriminate between alkali metal counterions and for the vastly stronger binding of quaternary ammonium counterions to films of C12SO4- than to films of C12HPO4-. It is also likely that quaternary ammonium ion binding to films of C12HPO4is further weakened by hydrogen bonding between the surfactant headgroups. Acknowledgment. The authors thank Dr. R. Reierson of Rhodia Inc. for the kind gift of the dodecyl phosphoric acid used in this study. LA990695L (27) Brackman, J. C.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1988, 132, 250. (28) Rupert, L. A. M.; van Breemen, J. F. L.; Hoekstra, D.; Engberts, J. B. F. N. J. Phys. Chem. 1988, 92, 4416. (29) Tricot, Y. M.; Furlong, D. N.; Sasse, W. H. F.; Daivis, P.; Snook, I.; van Megen, W. J. Colloid Interface Sci. 1984, 97, 380. (30) Ikeda, S.; Tsunoda, M.; Maeda, H. J. Colloid Interface Sci. 1979, 70, 448.