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Langmuir 2000, 16, 8926-8931
Equilibrium and Dynamic Adsorption of C12E5 at the Air-Water Surface Investigated Using Ellipsometry and Tensiometry† B. P. Binks, P. D. I. Fletcher,* V. N. Paunov, and D. Segal Surfactant Science Group, Department of Chemistry, University of Hull, Hull HU6 7RX, U.K. Received March 13, 2000. In Final Form: May 2, 2000 We have investigated the equilibrium and dynamic adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at the air-water surface using both ellipsometry and tensiometry. Two simple models for the monolayer structure were used to derive the equilibrium adsorption isotherm from ellipsometric data and tested for their validity by comparison with neutron reflection and tension data. A monolayer model comprising a lower layer containing the ethoxy headgroups plus water and an upper layer containing the dodecyl tail groups was found to yield an isotherm consistent with all the data. The slow adsorption kinetics (minutes to hours) was monitored using both ellipsometry and dynamic tension. Dynamic tension curves reconstructed from the ellipsometric data using the equilibrium adsorption isotherm were in agreement with measured dynamic tensions. The adsorption rate for a C12E5 monomer concentration corresponding to adsorption equal to 75% of the maximum adsorption was found to be diffusion controlled. Lower concentrations of C12E5 showed adsorption rates faster than diffusion-controlled adsorption, probably due to convection.
Introduction A common method to determine the equilibrium adsorption isotherm of a surfactant at the air-water surface is to measure the surface tension as a function of bulk concentration. Differentiation of the plot according to the Gibbs adsorption equation yields the adsorption isotherm. Unfortunately, this method is rather imprecise since even small errors in the tension values may cause large errors in the derived surface excess concentrations. The result of this is that the choice of theoretical adsorption isotherms used to fit experimental surfactant adsorption isotherms remains controversial. More recently, neutron reflection studies have provided direct and more reliable estimates of surfactant adsorption isotherms in addition to revealing more detailed aspects of adsorbed monolayer structures (see, for example, refs 1-4 concerning nonionic surfactants of the type used here). Ellipsometry has the required sensitivity to determine surface concentrations accurately but suffers from the drawback that either a surface structural model must be assumed or the relationship between adsorbed amounts and the ellipsometric parameters must be determined separately in order to derive surfactant surface concentrations from the measurements.5-9 In this work we test two simple models for equilibrium ellipsometric data for the adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at the air†
Part of the Special Issure “Colloid Science Matured, Four Colloid Scientists Turn 60 at the Millennium”. * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Lu, J. R.; Lee, E. M.; Thomas, R. K.; Penfold, J.; Flitsch, S. L. Langmuir 1993, 9, 1352. (2) Lu, J. R.; Li, Z. X.; Thomas, R. K.; Penfold, J. Langmuir 1993, 9, 2408. (3) Lu, J. R.; Li, Z. X.; Thomas, R. K.; Staples, E. J.; Thompson, L.; Tucker, I.; Penfold, J. J. Phys. Chem. 1994, 98, 6559. (4) Lu, J. R.; Li, Z. X.; Thomas, R. K.; Binks, B. P.; Crichton, D.; Fletcher, P. D. I.; McNab, J. R.; Penfold, J. J. Phys. Chem. B 1998, 102, 5785. (5) Manning-Benson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109. (6) Bell, G. R.; Manning-Benson, S.; Bain, C. D. J. Phys. Chem. 1998, 102, 218.
water surface by comparison of the derived adsorption isotherm against independent measurements using neutron reflection and tensiometry. Adsorption dynamics are commonly estimated using only dynamic surface tension measurements, the interpretation of which is highly sensitive to the particular form of equilibrium adsorption isotherm assumed. From such dynamic tension studies, the adsorption kinetics of a range of nonionic surfactants at low surface coverage are believed to be diffusion-limited with the monolayer being in rapid equilibrium with the subsurface concentration. At high surface coverage, adsorption is estimated to be slower than diffusion controlled owing to the presence of an energy barrier to monolayer entry and exit.10-13 It is noteworthy that a recent study in which the dynamic adsorption of a cationic surfactant was measured directly does not indicate the presence of an adsorption energy barrier, even at high surface coverage.9 In the present work, we have measured the time-dependent adsorption using both ellipsometry together with dynamic tensions with a view to checking for consistency between the two methods and avoiding the necessity to assume any particular form for the adsorption isotherm. Experimental Section n-Dodecyl pentaoxyethylene glycol ether (C12E5) was a chromatographically pure sample from Nikkol, Japan (and obtained via Chesham Chemical Ltd. in the U.K.), and was used without further purification. The gas chromatogram of the sample (supplied by the manufacturer and run using a Diasolid ZT 80(7) Bain, C. D. Curr. Opin. Colloid Interface Sci. 1998, 3, 287. (8) Goates, S. R.; Schofield, D. A.; Bain, C. D. Langmuir 1999, 15, 1400. (9) Hutchison, J.; Klenerman, D.; Manning-Benson, S.; Bain, C. D. Langmuir 1999, 15, 7530. (10) Chang, C.-H.; Franses, E. I. Colloids Surf., A 1995, 100, 1. (11) Lin, S.-Y.; Tsay, R.-Y.; Lin, L.-W.; Chen, S.-I. Langmuir 1996, 12, 6530. (12) Tsay, R.-Y.; Lin, S.-Y.; Lin, L.-W.; Chen, S.-I. Langmuir 1997, 13, 3191. (13) Eastoe, J.; Dalton, J. S.; Rogueda, P. G. A.; Crooks, E. R.; Pitt, A. R.; Simister, E. A. J. Colloid Interface Sci. 1997, 188, 423.
10.1021/la000371t CCC: $19.00 © 2000 American Chemical Society Published on Web 06/22/2000
Adsorption of C12E5
Figure 1. Schematic representation of models 1 and 2 used to derive Γ from ellipsometric data. Model 1 contains a single layer of C12E5 with density and refractive index equal to those of bulk C12E5. Model 2 comprises a layer of E5 heads mixed with water. At low coverages the tail layer contains horizontal tails mixed with water. At higher coverages, the tail layer contains nonhorizontal chains with density equal to liquid dodecane. 100 mesh column and a temperature ramped from 70 to 320 °C at 10 °C/min) showed a single peak indicating the level of any impurity was less than 0.2%. Water was purified by reverse osmosis and treated with a Milli-Q reagent water system. Ellipsometry measurements were made using a Plasmos 2300 instrument equipped with a HeNe laser (wavelength 632.8 nm). The incidence angle used was 50°, approximately 3° lower than the Brewster angle for pure water substrates. For most of the ellipsometry measurements, the samples were held in a thermostated glass dish (diameter approximately 5.5 cm and solution depth 5 cm) open to the air and mounted on a Sandercock antivibration table. The liquid surface was sucked off twice using a Pasteur pipet attached to a vacuum pump prior to the start of each kinetic run. For some later runs, samples were held in a Teflon trough (solution depth 1 cm) fully enclosed within a brass cell with thermostated walls. Pure water samples were used to check for the absence of artifacts due to instrumental drift. Measurements of the ellipsometric parameters Ψ and ∆ were the mean of 20 consecutive measurements taking approximately 60 s and were reproducible to 0.02 and 0.04° respectively. Control experiments using pure water showed that constant results within this level of accuracy were maintained over runs of 2 h indicating that effects due to impurity adsorption and instrumental drift were negligible over this time period. Tensions were measured for the same sample dish geometry and surface cleaning procedure as in the ellipsometry glass dish using a home-built tensiometer in which the static, maximum pull on a Pt/Ir du Nouy ring (supplied by Kru¨ss) was recorded and the tension calculated according to the details given in ref 14. Tensions were reproducible to 0.2 mN m-1. All measurements were made at 25.0 °C.
Results and Discussion Equilibrium Adsorption. The equilibrium values of the ellipsometric parameters Ψ and ∆ measured at long times were used to estimate the surface concentration Γ of the C12E5 according to two different “slab” models for the microstructure of the surface (Figure 1). For each model, initial guesses for Γ were used to compute the thickness and refractive index of each slab. These values, in turn, were used to compute Ψ and ∆ according to the procedures described by McCrackin.15,16 Γ was then adjusted until agreement between measured and calculated values was obtained. For the ellipsometry configuration used in this work, Ψ is primarily determined by the refractive index of the subphase whereas ∆ is primarily determined by the adsorbed film. Adjustment of Γ until measured and calculated values of ∆ alone were in (14) Binks, B. P.; Crichton, D.; Fletcher, P. D. I.; MacNab, J. R.; Li, Z. X.; Thomas, R. K.; Penfold, J. Colloids Surf., A 1999, 146, 299. (15) Tompkins, H. J. A User’s Guide to Ellipsometry; Academic Press, Inc.: Boston, 1993. (16) McCrackin, F. L. Natl. Bur. Stand. (U.S.) Tech. Note 1969, 479.
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agreement was found to yield calculated Ψ values simultaneously in agreement with experiment. In model 1, the surface film is assumed to be isotropic and to consist of pure C12E5 with a density and refractive index equal to that of the pure, bulk surfactant. The thickness of the adsorbed film h is then related to Γ by h ) Γv where v is the molecular volume of C12E5 calculated from its bulk density. Model 1 is the simplest possible model for adsorption but is certainly unrealistic in that the headgroup region of the monolayer is expected to contain water of solvation. In model 2 we have attempted to capture a more realistic structure of the monolayer while also trying to avoid the introduction of unknown adjustable parameters. In this context, it is important to note that ellipsometry essentially yields only a single measured parameter (∆) reflecting the adsorbed film structure which can reliably yield only a single unknown, Γ in this case. Thus, although ellipsometric data is precise, it is “information poor”. In model 2, the film is assumed to consist of a first, optically isotropic slab consisting of surfactant ethoxy headgroups mixed with water plus a second, optically isotropic slab consisting of surfactant tailgroups. The thickness of the headgroup slab is assumed to be a constant (i.e., independent of Γ) fraction of the fully extended length of the E5 headgroup (1.9 nm). The value of this fraction x was taken to be 0.8, i.e., hE5 ) 1.52 nm. It was found by calculation that varying the fraction x between 0.5 and 1 had no significant effect on the derived values of Γ. The volume fraction of E5 headgroups in the slab was calculated according to φE5 ) ΓvE5/hE5 where vE5 is the molecular volume of the E5 group. The remaining volume fraction of headgroup layer was assumed to be filled with water of solvation. The refractive index of the headgroup slab was calculated from the volume fraction using nhead ) φE5nE5 + (1 - φE5)nwater. The value of nE5 was estimated from data for polyoxyethylene glycols (i.e., E chains) of different chain length taken from the manufacturer’s (Fluka) catalog. For the tailgroup slab at low surface coverages such that the dodecyl chain had sufficient area to lie flat, the slab thickness was set equal to the thickness of a horizontal alkyl chain (htail ) 0.4 nm). At very low coverages, the horizontal chains were assumed to be mixed with water and the slab refractive index was calculated using a volume fraction relationship similar to that described above. At high surface coverages such that the chains have insufficient room to lie flat, they are assumed to form a slab with a density and refractive index equal to that of bulk dodecane. In this situation htail ) Γvtail, where vtail is the molecular volume of the dodecyl chain, calculated from the density of dodecane. Molecular dimensions (estimated using CPK molecular models), molecular volumes (calculated from densities), and refractive index values required for the calculations of models 1 and 2 are listed in Table 1.17 Because the calculations of Γ using model 2 are found to be insensitive to the fraction x, both models 1 and 2 yield the single unknown (Γ) from the single measured quantity (∆) with all other model parameters being taken from molecular dimensions and bulk material properties. The overall aim of this exercise was to attempt to determine the simplest possible microstructural model of the monolayer capable of yielding consistent adsorption isotherm results. This type of information is useful in order to utilize the advantages of ellipsometry for surfactant adsorption (17) Selected Values of Properties of Hydrocarbons and Related Compounds; Haas, C. W., Ed.; Thermodynamics Research Center API 44 Hydrocarbon Project Publications: Thermodynamic Research Center, Texas A&M University, College Station, TX, 1978.
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Binks et al.
Table 1. Molecular Parameters (25 °C) for C12E5 Used in the Calculation of Γ from Ellipsometric Data According to Models 1 and 2 Value
Source
Model 1 Parameters density C12E5/g cm-3 0.93 0.725 vC12E5/nm3 nC12E5 1.452
a derived measured
Model 2 parameters density C12 tail/g cm-3 0.745 density E5 head/g cm-3 1.12 vC12 tail/nm3 0.377 3 vE5 head/nm 0.351 nC12 tail 1.4181 1.46 nE5 head minimum hC12/nm 0.4 maximum hE5/nm 1.9
ref 17 b derived derived ref 17 b CPK models CPK models
a The measured C E density value (0.9609 g cm-3) was adjusted 12 5 slightly to obtain agreement between the molecular volume and the sum of the molecular volumes of the head and tail. b Estimated by interpolation of manufacturer’s (Fluka) data for polyoxyethylene glycol of different chain lengths.
Figure 2. Estimates of the equilibrium adsorption isotherm for C12E5 at the air-water surface at 25 °C. The symbols refer to ellipsometry, model 1 (open circles), ellipsometry, model 2 (filled circles), and neutron reflection (open triangles). The vertical dashed line shows the cmc.
studies (precision, noninvasive nature, and, relative to neutron reflectivity, low cost). Figure 2 shows the equilibrium adsorption isotherm derived from the ellipsometric data using models 1 and 2. Data by neutron reflection is also shown for comparison.4 Estimation by model 2 shows reasonable agreement with neutron reflection data recorded at surfactant concentrations lower than the critical micelle concentration (cmc). Values of Γ at the cmc and above appear slightly low relative to the neutron data, possibly owing to the neglect of the influence of micelles within the surface structure assumed in model 2. Model 1 underestimates the adsorption at all concentrations. The validity of the adsorption isotherms was further tested by integration of the empirical isotherms (using the polynomial fitting curves shown) to yield the variation of surface tension σ with surfactant concentration (see eq A.4 in Appendix 1). The resultant surface tension curves are compared with direct experiment in Figure 3. Again, it can be seen that model 2 provides a reliable estimate of the isotherm whereas model 1 clearly underestimates the adsorption for all concentrations below the cmc. Adsorption data at low C12E5 concentrations ( 0), C(0,0) ) C*
(A.7)
To solve the diffusion problem numerically, we use a fully implicit Crank-Nicholson scheme,18 similar (but not identical) to that proposed by Miller and co-workers.19 For the readers convenience we present here the details of the scheme, which allows calculation for subsurfaces (18) See, for example: Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flanery, B. P. Numerical Recipes in FORTRAN, 2nd ed.; Cambridge University Press: Cambridge, 1992. (19) Miller, R. Colloid Polym. Sci. 1981, 259, 375.
(A.9)
with the derivatives approximated by finite differences as follows
(A.2)
Here C is the local surfactant concentration, x is the depth position within the subphase, t is time, Γ ) Γ(Cs) is the surfactant adsorption, and Cs ) C(0,t) is the subsurface concentration. In our calculations, we use the following empirical adsorption and surface tension isotherms
(A.8)
i,j
i,j
(A.10)
[( ) ( ) ]
( )
Γj+1 - Γj 1 ∂Γ ∂Γ + O(∆t) ) ) C ∂t j ∆t ∆t ∂Cs j+1 1,j+1 ∂Γ C + O(∆t) (A.11) ∂Cs j 1,j
( ) ∂2C ∂x2
)
Ci+1,j - 2Ci,j + Ci-1,j ∆x2
i,j
+ O(∆x2)
(A.12)
Thus, the discrete form of the diffusion equation, eq A.8, is
Ci-1,j+1 - (2 + β)Ci,j+1 + Ci+1,j+1 ) -(Ci-1,j - (2 - β)Ci,j + Ci+1,j) (A.13) i ) 2, ..., n - 1 where β ) 2∆x2/(D∆t). The combination of eq A.13 with the discrete form of eq A.9 gives (for i ) 1)
[
- 2+β+λ
( ) ] [ ∂Γ ∂Cs
C1,j+1 + 2C2,j+1 )
j+1
2-β-λ
( )] ∂Γ ∂Cs
C1,j - 2C2,j (A.14)
j
where λ ) 4∆x/(D∆t). When eq A.5 is used as a boundary condition away from the air-water interface, the system of eqs A.13 and A.14 is solved together with the equation
Cn,j+1 ) C0
(i ) n)
(A.15)
In the case of a solution of finite depth, the system of eqs A.13 and A.14 is solved together with the equation
2Cn-1,j+1 - (2 + β)Cn,j+1 ) -(2Cn-1,j - (2 - β)Cn,j) i)n
(A.16)
instead of eq A.15. We stress that while eqs A.13, A.15 and A.16 are linear, eq A.14 is nonlinear with respect to C1,j+1. The nonlinearity comes from the adsorption isotherm, eq A.3. We solve the whole system of eqs A.13A.16 by using subsequent iterations. At each time step, the coefficient in brackets in the left-hand side of eq A.14
Adsorption of C12E5
is estimated by using information for C1,j+1 from the previous time step and then the system of linearized equations is solved iteratively until a convergence between two subsequent values of C1,j+1 is reached. Usually two to five iterations give enough accuracy for practical purposes. We use the Thomas algorithm18 to solve the three-diagonal
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system of linear equations. The described method is unconditionally stable for arbitrary values of the time and spatial steps. LA000371T
