Nonionic Mixed Micelles

May 7, 2002 - From the empirical relationship between average mobility and Y, the mobility distributions may be interpreted in terms of a distribution...
1 downloads 0 Views 66KB Size
Download PDF
Langmuir 2002, 18, 4605-4609

4605

Compositional Heterogeneity in Anionic/Nonionic Mixed Micelles Observed by Frontal Analysis Continuous Capillary Electrophoresis Bin Zhang, Gavin F. Kirton, and Paul L. Dubin* Department of Chemistry, Indiana University - Purdue University at Indianapolis, Indianapolis, Indiana 46202-3274 Received December 19, 2001. In Final Form: February 28, 2002 Mixed micelles of sodium dodecyl sulfate (SDS) with Triton X-100 (TX100) or dodecyl octa(ethylene glycol) monoether (C12E8) at different bulk SDS mole fractions (Y) and at two ionic strengths were analyzed by frontal analysis continuous capillary electrophoresis. For most systems, the electropherograms showed a distribution of mobilities, providing evidence of compositional heterogeneity in the mixed micelles. From the empirical relationship between average mobility and Y, the mobility distributions may be interpreted in terms of a distribution of micelle compositions. Broad distributions were observed from 0.1 e Y e 0.6 in all cases, while the mixed micelles were close to monodisperse at Y g 0.8. As similar results were obtained from monodisperse C12E8 and polydisperse TX100, the compositional distributions do not result from the compositional polydispersity of the nonionic surfactant. These results were found to be correlated with the composition dependence of the critical micelle concentration of mixed micelles.

Introduction Surfactants have extensive applications in numerous fields such as detergents, cosmetics, pharmaceuticals, enhanced oil recovery, surfactant-based separation processes, and so forth. In most applications, surfactant mixtures rather than pure species are used, as they are naturally prevalent and less expensive and often perform better than a single surfactant in a particular application.1,2 This improved performance often arises through synergistic interactions between the two surfactants. For example, in skin care applications, synergistic behavior of a surfactant mixture can minimize the total surfactant monomer concentration,3 which in turn has been shown to reduce skin irritation.4,5 The synergistic behavior of surfactant mixtures may also be exploited to reduce the total amount of surfactant, thus reducing both cost and environmental impact. Recently, many papers have dealt with the solution properties of mixed surfactant systems, especially the variations of the critical micelle concentration (cmc) and of the micelle size or aggregation number with the composition of the system.6-10 A number of micellar properties depend on the structural and dynamic features of the aggregates, and these are related to the composition of the micellar phase. Several thermodynamic treatments * To whom correspondence should be addressed. E-mail: dubin@ chem.iupui.edu. Tel: 1-(317)-274-6879. Fax: 1-(317)-274-4701. (1) Abe, M.; Ogino, K. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 1. (2) Hill, R. M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 317. (3) Garcia, M. T.; Ribosa, I.; Leal, J. S.; Comelles, F. J. Am. Oil Chem. Soc. 1992, 69, 25-29. (4) Prottey, C.; Ferguson, T. J. Soc. Cosmet. Chem. 1975, 26, 29-46. (5) Rhein, L. D.; Simion, F. A.; Hill, R. L.; Cagan, R. H.; Mattai, J.; Maibach, H. I. Dermatologica 1990, 180, 18-23. (6) Saiyad, A. H.; Bhat, S. G. T.; Rakshit, A. K. Colloid Polym. Sci. 1998, 276, 913-919. (7) Ruiz, C. C.; Aguiar, J. Mol. Phys. 1999, 97, 1095-1103. (8) Ruiz, C. C.; Aguiar, J. Langmuir 2000, 16, 7946-7953. (9) Burman, A. D.; Dey, T.; Mukherjee, B.; Das, A. R. Langmuir 2000, 16, 10020-10027. (10) Alargova, R. G.; Kochijashky, I. I.; Sierra, M. L.; Kwetkat, K.; Zana, R. J. Colloid Interface Sci. 2001, 235, 119-129.

have been developed.11-16 However, the question of micellar compositional heterogeneity in mixed surfactant systems has been little addressed and it is commonly assumed that the composition of the mixed micelles is rather uniform, at least at high surfactant concentration. On the other hand, Dennis et al. have reported the existence of more than one population of thermodynamically stable mixed micelles in systems of nonionic detergents and phospholipids.17 Abe et al. observed micelle demixing for sodium 3,6,9-trioxaicosanoate and alkyl polyoxyethylene ethers.18 Our quasi-elastic light scattering studies of the DMDAO/C12E8 system showed that at lower pH, the two surfactants are partially mixed and there are two micellar forms, with one identical to the pure C12E8 micelle.19 Capillary electrophoresis (CE) was previously employed to analyze the polydispersity of Triton X-100 (TX100)/ sodium dodecyl sulfate (SDS) and C12E8/SDS, two widely studied anionic/nonionic mixed micelle systems.20 That work reported on the coexistence of micelles rich in either a nonionic or an anionic component and the dependence of the electropherogram pattern of the distribution on the SDS mole fraction (Y). No attempt was made to extract distributions of composition from the electropherograms due to the possibility that the flow conditions in conventional CE may perturb the micelle distribution. On the (11) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 13271334. (12) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 337. (13) Holland, P. M. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986; p 102. (14) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 19841990. (15) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 1618-1636. (16) Maeda, H. J. Colloid Interface Sci. 1995, 172, 98-105. (17) Robson, R. J.; Dennis, E. A. Acc. Chem. Res. 1983, 16, 251-258. (18) Abe, M.; Tsubaki, N.; Ogino, K. J. Colloid Interface Sci. 1985, 107, 503-508. (19) Xia, J.; Dubin, P. L.; Zhang, H. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; p 234. (20) Zhang, H.; Dubin, P. L. J. Colloid Interface Sci. 1997, 186, 264270.

10.1021/la015750g CCC: $22.00 © 2002 American Chemical Society Published on Web 05/07/2002

4606

Langmuir, Vol. 18, No. 12, 2002

Zhang et al.

other hand, frontal analysis continuous capillary electrophoresis (FACCE) is a technique that minimizes such perturbation by continuous injection of the sample.21 Thus, the compositional heterogeneity of charged synthetic copolymers22,23 has been observed by FACCE. In this paper, FACCE is used to probe the distributions of micelle compositions for the SDS/TX100 and SDS/C12E8 systems. Experimental Section Materials. Triton X-100 (TX100), mesityl oxide, and Orange OT were purchased from Aldrich (Milwaukee, WI), sodium dodecyl sulfate (purity > 99%) from Fluka (Buchs, Switzerland), naphthalene from Fisher Scientific Co. (Fair Lawn, NJ), and ethyl alcohol (absolute, 200 proof) from Apper Alcohol and Chemical Co. (Shelbyville, KY). Dodecyl octa(ethylene glycol) monoether (C12E8) was a gift from Osaka University, Japan. All were used without further purification except Orange OT, which was purified following the procedure in ref 24. Borate buffers were prepared from 1 N sodium hydroxide solution (Fisher) and boric acid (Sigma, St. Louis, MO). Milli-Q water was used throughout this work. Capillary Electrophoresis. CE was performed with a Beckman P/ACE 5500 instrument (Beckman, Fullerton, CA) with a UV detector and a voltage of 25 kV. The uncoated fused silica capillaries of 50 µm i.d., 57 cm length, were from Restek (Bellefonte, PA). Capillaries were thermostated at 25 °C with fluorocarbon coolant. Run buffers were pH 9.0, I ) 0.03 M (or 0.01 M) borate buffer, filtered through 0.2 µm PP W/GMF filters (Whatman). The total concentration of mixed micelles was 50 mM. TX100/SDS micelles were detected at 254 nm for the strong chromophore of TX100, and C12E8/SDS micelles were detected at 214 nm by the combination of 20 µL of 30 mM naphthalene dissolved in ethanol with 600 µL of 50 mM total mixed surfactants (mixed surfactants were added to the solution after evaporation of ethanol). For most CE experiments, a single 3 s injection of neutral marker (mesityl oxide) preceded the FACCE. Between runs, the capillary was subjected to a 3 min rinse with 0.1 N NaOH, water, and run buffer in that order. The detailed description of FACCE can be found elsewhere.21 The electrophoretic mobility was calculated as

µ)

(

)

lL 1 1 V ts t0

(1)

where l is the effective length of the capillary, and L is the total length of the capillary (both in cm); V is the applied voltage; t0 and ts are the migration times of the reference marker (mesityl oxide) and the sample, respectively. Multiple runs showed that the reproducibility of µ is within (0.8%. Dynamic Light Scattering (DLS). Solutions of 50 mM mixed micelles at various SDS mole fractions and different ionic strengths filtered through 0.1 µm Whatman filters were analyzed with a DynaPro-801 DLS instrument (Protein Solutions, Inc., Charlottesville, VA) equipped with a 30 mW solid state 780 nm laser. The intensity of light scattered from the 7.0 µL cell was detected by an avalanche photodiode detector at a 90° scattering angle. The mean apparent translational diffusion coefficient (DT) was determined by fitting the autocorrelation function using the method of cumulants. The hydrodynamic radius (Rh) of particles was determined from the Stokes-Einstein equation:

Rh ) kbT/6πηDT

(2)

where kb is Boltzmann’s constant, T is the temperature (K), and η is the solvent viscosity. (21) Gao, J. Y.; Dubin, P. L.; Muhoberac, B. B. Anal. Chem. 1997, 69, 2945-2951. (22) Staggemeier, B.; Huang, Q. R.; Dubin, P. L. Anal. Chem. 2000, 72, 255-258. (23) Zhang, B.; Hattori, T.; Dubin, P. L. Macromolecules 2001, 34, 6790-6794. (24) Schott, H. J. Phys. Chem. 1964, 68, 3612-3619.

Figure 1. FACCE electropherograms of SDS/TX100 (A) and SDS/C12E8 (B) in pH 9.0, I ) 0.03 M NaOH/H3BO3 buffer at different bulk SDS mole fractions (Y) shown. Electropherograms in (A) are shifted vertically for clarity. UV Spectroscopy. The cmc’s of pure and mixed anionic and nonionic surfactants were measured by dye solubilization.25 The absorbance of dye in the surfactant solution below the cmc is essentially zero but increases linearly with increasing surfactant concentration above the cmc. Solutions containing different total surfactant concentrations at varying SDS mole fractions and different ionic strengths were prepared. An excess of Orange OT was added, and the solutions were tumbled at room temperature for 2 days with a Carnstead/Thermolyne Speci-Mix model 26125 (Dubuque, IA). Unsolubilized dye was removed using disposable Whatman filters. The solution absorbance was measured at 488 nm using a Perkin-Elmer Lambda 19 UV/VIS/NIR spectrometer.

Results Figure 1 shows the FACCE electropherograms for SDS/TX100 and SDS/C12E8 mixed micelles at varying bulk SDS mole fractions (Y) in pH 9.0, I ) 0.03 M NaOH/ H3BO3 buffer. In both cases, a single abrupt plateau was detected at Y ) 0. Upon addition of SDS, plateaus with a preceding slope were observed from Y ) 0.1 to Y ) 0.5, the slope decreasing with Y. When Y increased to 0.9, a single abrupt plateau was detected again. The single abrupt plateau was also observed at Y ) 0.7 for SDS/ C12E8, while SDS/TX100 showed a more complex electropherogram at Y ) 0.7. Differentiation of the electropherograms of SDS/TX100 and SDS/C12E8 mixed micelles in Figure 1 leads to the differential distributions shown in Figure 2 in which the abscissa is converted from migration time to mobilities via eq 1. Broad distributions of mobilities were seen from 0.1 e Y e 0.7 for SDS/TX100 and from 0.1 e Y e 0.5 for SDS/C12E8; narrow distributions were observed at Y ) 0.9 for SDS/TX100 and at Y ) 0.7 and 0.9 for SDS/C12E8 (the sharp peak of SDS/TX100 at Y ) 0.9 has the same position as that of SDS/C12E8). The empirical relationship between bulk SDS mole fraction and average mobility of mixed micelles (from the half-height position of the electropherogram) in pH 9.0, I ) 0.03 M NaOH/H3BO3 buffer is shown in Figure 3. If the average mobility of a distribution represents typical micelles formed from a system with bulk composition Y, Figure 3 can then be used to associate mobilities with bulk compositions. In this way, Figure 2 can be converted to the compositional distributions in Figure 4. A possible explanation for the observed mobility distributions is a distribution in micelle sizes, this being checked by dynamic light scattering. The mean apparent (25) Sudbeck, E. A.; Dubin, P. L.; Curran, M. E.; Skelton, J. J. Colloid Interface Sci. 1991, 142, 512-517.

Compositional Heterogeneity in Mixed Micelles

Figure 2. Mobility distributions of SDS/TX100 (A) and SDS/ C12E8 (B) obtained by differentiation of Figure 1, presented as d(Abs)/dt (arbitrary units) vs µ. Distributions in (A) are shifted vertically for clarity.

Figure 3. Dependence on SDS mole fraction (Y) of average mobility of SDS/TX100 (9) and SDS/C12E8 (b) in pH 9.0, I ) 0.03 M NaOH/H3BO3 buffer.

Langmuir, Vol. 18, No. 12, 2002 4607

Figure 5. Variation of the hydrodynamic radius of mixed micelles with bulk SDS mole fraction: (2) SDS/TX100 at pH 9.0, I ) 0.01 M; (9) SDS/TX100 at pH 9.0, I ) 0.03 M; (b) SDS/C12E8 at pH 9.0, I ) 0.03 M.

Figure 6. Critical micelle concentration as a function of SDS mole fraction for mixed micelles: (2) SDS/TX100 at pH 9.0, I ) 0.01 M; (9) SDS/TX100 at pH 9.0, I ) 0.03 M; (b) SDS/C12E8 at pH 9.0, I ) 0.03 M.

of interactions of the component surfactants. Figure 6 shows the dependence of the cmc on Y for the three mixed micelle systems. In each case, the cmc values are nearly constant in the range 0.1 < Y < 0.6 but increase steeply at larger Y. Such plots are characteristic of anionic/ nonionic surfactant mixtures at low salt in which the cmc of the ionic surfactant is typically large relative to that of the nonionic component. Discussion

Figure 4. Bulk compositional distributions of SDS/TX100 (A) and SDS/C12E8 (B) converted from Figure 2 according to the curves in Figure 3. Distributions in (A) are shifted vertically for clarity.

hydrodynamic radii (Rh) of mixed micelles is presented in Figure 5 as a function of Y for SDS/TX100 micelles (I ) 0.01 M and I ) 0.03 M) and SDS/C12E8 micelles (I ) 0.03 M) in pH 9.0 borate buffer. The vertical bars represent the polydispersities in Rh as obtained by cumulants analysis of the autocorrelation function. From Y ) 0 to Y ) 0.4, Rh is observed to decrease significantly, and for Y > 0.4, Rh is relatively invariant. Mixed micelle systems are often characterized by the dependence of the cmc on composition, which is indicative

The electrophoretic mobility depends on both micelle charge (q ) ny) and the friction coefficient f ) 6πηRh, where n is the micelle aggregation number, y is the microscopic micelle composition (mole fraction SDS), η is the solvent viscosity, and Rh is the Stokes radius; to a first approximation, µ ) q/f. If the aggregation number were not dependent on the bulk composition, the electropherograms could be taken as a distribution of micelles of uniform size but varying microscopic composition, y. Otherwise, it is necessary to consider micelle sizes in interpreting the mobility distributions in Figure 2. As the hydrodynamic radius of a micelle can reflect both the aggregation number and the degree of hydration, these two factors may not be easily resolved. The largest change in Rh occurs at bulk compositions with low SDS (Y < 0.4), as seen in Figure 5. Although the micelle microscopic compositions (y) are not necessarily equal to the bulk composition Y, the relationship is sufficient to show that the aggregation number probably increases when y

4608

Langmuir, Vol. 18, No. 12, 2002

Zhang et al. Table 1. Regular Solution Theory β Parameters Obtained from Mixed Critical Micelle Concentration Measurements for the SDS/TX100 System at I ) 0.03 M, pH 9.0a Y

cmc (mM)

β

Y

cmc (mM)

β

0.1 0.2 0.4

0.35 0.40 0.50

-1.92 -0.83 -0.41

0.6 0.8 0.9

0.60 0.90 1.40

-0.79 -0.55 +0.12

a Y is the SDS mole fraction of the system, cmc is the measured critical micelle concentration.

Figure 7. Effect of SDS mole fraction on the compositional distribution breadth (∆Y) of mixed micelles: (2) SDS/TX100 at pH 9.0, I ) 0.01 M; (9) SDS/TX100 at pH 9.0, I ) 0.03 M; (b) SDS/C12E8 at pH 9.0, I ) 0.03 M.

decreases. However, the aggregation number and compositions of the micelles may be independent variables with separate distributions. With significant variation in aggregation number, the relationship between mobility µ and the bulk composition is complex. It is possible, for example, that a given micelle mobility obtained from FACCE may represent two types of micelles: one having large q and Rh and another having small q and Rh. For bulk compositions of Y > 0.4, the relationship is simplified. As the average micelle Rh is relatively invariant for these compositions, the distribution width of micelle aggregation numbers is at most the indicated polydispersity for each bulk composition in this range. Thus, at Y > 0.4, a given mobility from FACCE represents micelles of a particular composition y. The correlation between µ and Y is empirically sound; the difficulty arises from equating this to the dependence of µ on y, particularly in those cases where a twodimensional description of the distribution at any Y with respect to both n and y may be warranted. Dynamic light scattering measurements for Y > 0.4 show little variation in n, so identifying the electropherograms with the polydispersity of microscopic composition y seems justifiable. For Y < 0.4, we can still maintain that a given mobility range corresponds to a particular group of micelles characterized by certain microscopic compositions and aggregation numbers and that this correspondence is valid regardless of the bulk composition (Y) mixture in which they are found. This assumption forms the basis of the transformation to Figure 4 via Figure 3. Considering the distributions in Figures 2 and 4 at the larger Y values, the changing width of the distribution must be due to changes in the composition distribution because of the weak dependence of Rh on Y. The dependence of the electropherogram baseline widths (converted to compositional breadths ∆Y by the procedures used for Figures 1-4) on Y is plotted in Figure 7. In all cases, the broad compositional distributions from 0.1 e Y e 0.6 correspond to the regions of relatively constant cmc in Figure 6, while the narrower distributions from 0.7 e Y e 0.9 in Figure 7 (nearly monodisperse for Y g 0.9) correspond to regions in Figure 6 in which cmc rises rapidly with Y. This correlation is probably due to the intramicellar repulsions of SDS headgroups. Such interactions would elevate the cmc and concomitantly preclude the formation of micelles with microscopic compositions higher than the average y, especially when y is high. The skewing of the distributions in Figure 4 toward low Y is consistent with this explanation.

The changes in the composition distributions must be a consquence of the relative micellization energies for micelles of different y. For binary surfactant systems such as the anionic/nonionic systems studied here, the free energy of micellization, with the pseudo-phase separation model, is given by the general equation16

[

]

Gmic(RM) 1 - R1 ) ln cmc + (1 - RM) ln + RT 1 - RM

[ ]

RM ln

R1 (3) RM

where RM (i.e., y) is the mole fraction of anionic surfactant in the mixed micelle, R1 is the mole fraction of anionic surfactant in the free monomers, and R and T have their usual meanings. The (hypothetical) standard states for the micelles, anionic surfactant monomers, and nonionic surfactant monomers are the pure states in infinite dilution in the buffer solution. The relationship between RM and R1 depends on the total surfactant concentration, their values becoming more similar at higher concentrations due to mass balance requirements. Obtaining relative micellization energies via eq 3 therefore requires the variation of cmc with the microscopic micelle composition (y), rather than with the bulk composition as presented in Figure 6. Regular solution theory12,26 is commonly used for carrying out the transformation between the bulk composition and the microscopic micelle composition. In this pseudo-phase separation method, deviations from ideal binary mixing are assumed to arise from pairwise attractive or repulsive interactions between the two surfactants and consequently expressed by an interaction parameter, β. β may be calculated directly from the cmc’s for pure and mixed systems: the measured cmc’s for SDS (3.5 mM at I ) 0.01 M; 2.0 mM at I ) 0.03 M), TX100 (0.35 mM), and C12E8 (0.15 mM) required for the calculations compare well with those reported elsewhere.7,27 Table 1 presents as an example β interaction parameters for the SDS/TX100 system at I ) 0.03 M, pH 9.0. While good fits to the cmc over a wide range of compositions using a single β value have been frequently reported for binary surfactant systems, we found the interaction parameter for all of our systems to vary significantly with composition, including strongly negative and weakly positive values. Similar results have been reported elsewhere.28,29 For the SDS/ C12E8 system, no β values could be found for low Y. The difficulty of assigning a single β parameter to a given system may indicate shortcomings in describing (26) Holland, P. M. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; p 31. (27) Cifuentes, A.; Bernal, J. L.; Diez-Masa, J. C. Anal. Chem. 1997, 69, 4271-4274. (28) Vora, S.; George, A.; Desai, H.; Bahadur, P. J. Surfactants Deterg. 1999, 2, 213-221. (29) Park, J. W.; Chung, M.-A.; Choi, K. M. Bull. Korean Chem. Soc. 1989, 10, 437-442.

Compositional Heterogeneity in Mixed Micelles

some mixed micelle systems by means of regular solution theory. The enthalpic driving force for mixing in these systems arises largely from intramicellar electrostatic repulsive forces that destabilize highly anionic micelles with respect to those of lower Y. These long-range forces involve multiple interactions among numerous charged sites, subject to screening by small ions. The use of a pairwise nonionic-anionic interaction parameter to account for such complex interactions may be an oversimplification that leads to the absence of unique parameters. With regular solution theory being unsuitable for the mixed micelle systems studied, relative micellization energies could not be derived from the trends in the cmc. A further difficulty is that pseudo-phase separation methods such as regular solution theory ignore distributions in microscopic composition, as well as aggregation number distributions. Detailed and extensive theoretical treatments of micellar compositional and size distributions have appeared, incorporating a number of molecular properties of the surfactants involved.15,30-34 In these analyses, while the composition distribution is generally shown to be narrow so that the focus is on the aggregation number of the micelles, the coupling of distributions of aggregation number and composition in mixed micelles has also been considered.15,30,34 Such treatments may form the basis for a theoretical method to account for the mobility distributions observed by FACCE. (30) Shiloach, A.; Blankschtein, D. Langmuir 1998, 14, 7166-7182. (31) Barzykin, A. V.; Almgren, M. Langmuir 1996, 12, 4672-4680.

Langmuir, Vol. 18, No. 12, 2002 4609

Conclusions Broad distributions of micellar electrophoretic mobility were observed by FACCE for several anionic/nonionic mixed micelle systems. These distributions, which varied with the bulk composition Y, were similar for the two nonionic surfactants (TX100 and C12E8), showing that the distributions were not as a result of surfactant polydispersity. The distributions were found to be broad for 0.1 < Y < 0.6 and narrow for Y > 0.6. From empirical relationships between the average mobility and Y, it was possible to evaluate the distribution of microscopic micelle composition, in part because dynamic light scattering showed that the mobility distributions could not be simply from distributions of aggregation numbers. The mobility distributions were found to be correlated with the dependence of cmc on Y, but a detailed understanding of the interrelationship among aggregation number distribution, microscopic composition distribution, and composition dependence of the cmc would require a sophisticated theoretical treatment. Acknowledgment. Support from Grant NSF CHE 9987891 is acknowledged. LA015750G (32) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 55675579. (33) Ben-Shaul, A.; Rorman, D. H.; Hartland, G. V.; Gelbart, W. M. J. Phys. Chem. 1986, 90, 5277-5286. (34) Nagarajan, R. Langmuir 1985, 1, 331-341.