1302
J . Phys. Chem. 1986, 90, 1302-1310
SURFACE SCIENCE, CLUSTERS, MICELLES, AND INTERFACES Fluorescence Decay Study of the Adsorption of Nonionic Surfactants at the Solid-Liquid Interface. 2. Influence of Polar Chain Length Pierre Levitz* and Henri Van Damme Centre National de la Recherche Scientifque, Centre de Recherches sur les Solides ci Organisation Cristalline Imparfaite 45071 Orleans Cedex 2, France (Received: January 2, 1985; In Final Form: November 5, 1985)
The method previously developed by us in part 1 of this work for the determination of the average aggregation number in the adsorption layer of a nonionic surfactant (Triton X-100) at the silica-aqueous solution interface has been improved and extended to other surfactants of the octylphenol poly(oxyethy1ene) family, with an average of 6 (TBE6), 12.5 (TX102), 30 (TX305), and 40 (TX405) oxyethylene (OE) units, respectively. The major point resulting from this fluorescence decay study-and this seems to be a fundamental characteristic of the adsorption of these nonionic surfactants on a hydrophilic surface such as silica-is that the adsorption process, which occurs mainly below the critical micellar concentrations (cmc) is strikingly similar to the micellization process which takes place in water above the cmc. Molecules with short polar chains, like TBE6, which form very large micellar aggregates in water, with an average aggregation number (N) too large to be determined by our method (above 200 or 300 molecules per aggregate), also form very large assemblies on the silica surface, below the cmc. On the other hand, for surfactants with medium or long polar chains (TX102, TX305), the adsorbed phase appears as a micellar-like phase, up to the plateau of the isotherms. The average surface aggregation number in the plateau region is very close to the average size of regular micelles in water at high concentration (well above the cmc). An intermediate behavior is displayed by TX100. This molecule, with a moderately short polar chain, nicely fits into the sequence since it forms micellar-like surface aggregates for apparent surface coverages, 0, below 0.8, and very large assemblies beyond 0.8. In a broad domain, from 0 = 0.17 to 0.5, the average surface aggregation number is again close to the size of regular micelles in water. A simple geometrical model is proposed which, when compared to the experimental results for the apparent surface per molecule, suggests that, at 0 = 1, the adsorption layers can be viewed as close-packed assemblies of surface-generated micelles with an oblate ellipsoidal shape. The main conclusion of this work is that the silica below the cmc acts as a “precursor” of the micellization process on the solid surface.
I. Introduction Fluorescence decay spectroscopy (FDS) is now a classical tool for measuring average aggregation numbers in micellar solutions of surfactant molecule^.^-^ The method relies on the kinetic analysis of bimolecular photochemical reactions in confined systems, with a distribution of local probe concentrations.’&” The time course of the monomer and excimer fluorescence emissions (1) (2) (3) (4)
Maestri; Infelta, P. P.; Gratzel, M. J . Chem. Phys. 1978, 69, 1522. Infelta, P. P.; Gratzel, M. J. Chem. Phys. 1979, 70, 179. Lianos, P.; Zana, R. J . Phys. Chem. 1980,84, 3339. A!mgren, M.;Lofroth, J. F. J . Colloid Interface Sci. 1981, 81, 486. (5) Llanos, P.; Dinh-Cao, M.;Lang, J.; Zana, R. J . Chim. Phys. 1981, 78, 487. (6) Lianos, P.; Zana, R. J . Colloid, Interface Sci. 1981, 84, 100. (7) Croonen, Y.; Gelade, E.; Van Der Zegel, M.;Van Der Auweraer, M.; Vandendriessche, H.; de Schryver, F. C.; Almgren, M. J . Phys. Chem. 1983, 87, 1426. (8) Van Der Auweraer, M.; Dederen, J. C.; Palmans-Windels, C.; De Schryver, F. C. J. Am. Chem. SOC.1982, 100, 1800. (9) Roelants, E.; Gelade, E.; Van Der Auweraer, M.; Croonen, Y.; De Schryver, F. C. J. Colloid Interface Sci. 1983, 96, 288. (10) Infelta, P. P.; Gratzel, M.:Thomas, J. K. J . Phys. Chem. 19874, 78, 190. (1 1) Tachiya, M. Chem. Phys. Len. 1975, 33, 289. (12) Selinger, B. K.; Watkins, A. R. Chem. Phys. Left. 1978, 56, 99. (13) Watkins, A. R.; Selinger, B. K. Chem. Phys. Left. 1979, 64, 250. (14) Atik, S. S.; Nam, M.;Singer, L. A. Chem. Phys. Lett. 1979, 67, 75. (15) Tachiya, M. Chem. Phys. Left. 1980, 69, 605. (16) Dederen, J. C.; Van Der Auweraer, M.; De Schryver, F. C. Chem. Phys. Left. 1979, 68, 451. (17) Van Der Aueraer, M.;Dederen, J. C.; Gelade, E.; De Schryver, F. C. J. Chem. Phys. 1981. 74, 1140.
0022-3654/86/2090- 1302$01.50/0
of pyrene molecules solubilized in the micellar aggregates has been shown to be well suited for this p ~ r p o s e . ~ * ~ , ~ - ~ , ~ We have recently shown that this approach can be fruitfully extended to the characterization of the adsorbed phases formed by nonionic surfactant molecules at the solid-solution interface.18 Our approach is basically parallel to what has been developed for micellar solutions. The idea is to “solubilize” a hydrophobic fluorescent probe molecule (pyrene) within the hydrophobic regions of the adsorption layer and to determine from the time law of the decay the spatial extent of the regions in which the probe is free to move. The probe must explore as selectively as possible the regions of the surface that we are interested in. Partitioning of the probe molecules between two or several hydrophobic environments would clearly be detrimental to the quality of the information. Thus, measurements at equilibrium concentrations above the cmc have to be avoided since under such conditions the probe molecules would most probably partition between the condensed assemblies on the surface on the one hand and the micelles of the solution on the other hand. Fortunately, the plateau of the adsorption isotherms is reached at equilibrium concentrations close to the cmc (Figures 1 and 23, so that the major part of the development of the adsorbed phase can be safely studied without interference with the micellar phase. Our previous paper‘* was devoted to the study of Triton X- 100 (TX 100) adsorbed on silica, in aqueous medium. TXlOO is a polydisperse preparation of p - ( 1,1,3,3-tetramethylbutyl)phenoxypoly(oxyethylene glycol) (18) Levitz, P.; Vand Damme, H.; Keravis, D. J. Phys. Chem. 1984, 88, 2228.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 1303
Adsorption of Nonionic Surfactants
TABLE I: Fluorescence Parameters of IO-* M Micellar Solutions of TX100, TX102, TX305, and TX405 N
this surfactants T X 100
TX102 TX305 TX405
NOE cmc, mol L-’ 9.5
12.5 30 40
2.8 X
7.1 X
13/11 0.74
3.8 X lo4 7 X lo4 7-10 X
1.09 X 1.64 X loF3 2.77 X lo-’
0.71 0.71 0.70
XPm
k2, S-’
kl, s-’ 2.93 X lo6
1.7 X lo7
2.63 X lo6 2.89 X lo6 3.06 X lo6
1.7 X lo7 1.4 X lo7 1.9 X lo7
k,”, s-I
il
work
3.1 X lo6
2.1 X lo6
0.94
132
5.6 X lo6 7.3 X lo6 8.4 X lo6
3.3 X lo6 7.4 X lo6 8.8 X lo6
1.17 0.66 0.85
107 40 30
k,,
s-I
lit. 140‘ lllb 135c 1OOd 120e
‘Reference 44. bReference 47. CReference45. “Reference 46. eReferences 12 and 13.
containing an average of 9.5 oxyethylene units per molecule. The major information which emerges from the work on TXlOO is the similarity of adsorption and micellization. This was already the conclusion of another FDS study, in which we used the phenyl ring of monodisperse surfactant molecules as fluorescent probe.lg Everything happens as if adsorption of TXlOO on silica was approximately a surface-induced and surface-confined micellar-like surface aggregation. The interaction of the hydrophilic surface with the surfactants molecules appears to be strong enough to induce the formation of micellar-like surface aggregates in equilibrium with monomers below the cmc, but, at the same time, weak enough to avoid important structural differences with respect to the micelles which form in water above the cmc. However, before developing a general thermodynamic model of this type of adsorption, a broader experimental investigation is clearly desirable. This is the aim of the present paper. In order to evaluate the influence of the poly(oxyethy1ene) (POE) chain length on the structure of the adsorbed phase, we have performed a FDS study with pyrene as fluorescent probe on four nonionic surfactants of the p-tert-octylphenol group, i.e., the same group as TX100, with an average of 6, 12.5, 30, and 40 oxyethylene units, respectively. As will be shown below the length of the POE chain strongly affects the parameters of adsorption, but the similarity of the molecular assemblies of the silica surface with the aggregates of micellar solution is as striking as in the case of TX100.
11. Experimental Section 1 . Materials. The silica was the same high-purity nonmicroporous Spherosil (Prolabo, Rhone-Poulenc XOBOl5) as previously used. This solid is obtained by association of small spheres with a particule size between 0.1 and 0.2 pm. These elementary spheres formed large spherules with a mean size between 40 and 100 pm, and an average pore size larger than 1300 A. The nitrogen BET surface area of this solid is 25 m2/g. This is also, within experimental error, the surface area obtained from microcalorimetric detemination of the heat of immersion in water, using a modified Harkins-Jura method.20 A similar surface area is obtained by the t-plot method.21 A straight line running through the origin is obtained between PIPo= 0 to PIPo= 0.3. This result is a good verification of the nonmicroporosity of the solid. Three polydisperse p-tert-octylphenol surfactants of the Triton family (Rohm and Haas) were used: TX102 (12.5 O E units), TX305 (30 O E units), and TX405 (40 O E units). One monodisperse p-tert-octylphenol surfactants with 6 O E units (TBE6) was used as received fqom IRCHA. It has a homodispersity better than 95%, as determined by HPLC: The cmc’s, determined as the concentration at which departure from Beer-Lambert law occurs in the UV-visible absorption spectra (276 nm), are collected in Table I. They are in good agreement with literature values
(19) Levitz, P.; El Miri, A.; Keravis, D.; Van Damme, H. J . Colloid Interface Sci. 1984, 99, 484. (20) Partvka, S.; Rouquerol, F.; Rouquerol, J. J . Colloid Interface Sci. 1979, 68, 21: (21) Broekhoff, J. C. P.; Linsen, B. H. “Physical and Chemical Aspects of Adsorbants and Catalysts”; Academic Press: London, 1970; Chapter I, pp 23, 24.
at 300 K.22-24 Pyrene from EGA Chemie was used as received (Purity > 99%). 2. Adsorption Isotherms and Sample Preparation. All the measurements were performed at 25 OC, with distilled water, in the pH range 6-6.5. This is close to the point of zero charge of our silica, determined by electrophoretic methods (-4-5). Hence, the silanol groups of the silica surface are essentially in the neutral OH form in our experimental conditions. The adsorption isotherms in pyrene-free solutions were determined by mixing known amounts of silica (- 100-500 mg) with a known volume (- 10-20 mL) of calibrated surfactant solution in a centrifugation cup. The mixture was shaken for 10 h. This was found to be more than enough for the adsorption equilibrium to be reached. The mixture was then centrifuged and the final concentration of the supernatant was determined spectrophotometrically from the optical density at 276 nm. The amount adsorbed was calculated from the difference between the initial and final concentrations of surfactant in water. The same general procedure was used with pyrene-containing solutions. A stock solution of pyrene was first prepared by introducing solid pyrene into a concentrated mol/L) micellar solution of surfactant. Solubilization in the micelles was obtained by stirring the solution for at least 1 or 2 days. The micellar solutions used for the adsorption isotherms were obtained by diluting the stock solution. The initial and final pyrene concentrations in the supernatant were determined from the optical density at 320 and 337 nm. The surfactant concentrations were still determined at 276 nm, but a correction was introduced for the absorbance of pyrene at this wavelength. Calibration curves were therefore established for pyrene at 337, 320, and 276 nm. These calibration curves are practically independent of the polar chain length of the surfactant. For each wavelength, two different extinction coefficients were found: one below and another above the cmc. 3. Steady-State Fluorescence. Steady-state fluorescence spectra were recorded with a FICA 55 Bausch and Lomb spectrometer equipped with a front face accessory. The emission spectrum of pyrene was recorded between 350 and 550 nm, with excitation at 337 nm, in quartz cells. All the solutions, in IO-” quartz cells, were thoroughly deaerated prior to measurements by bubbling dry nitrogen. The silica suspension samples were placed in a 2-mm-path quartz cell with a solid/liquid ratio near of one. This is enough to keep the silica entirely immersed in the liquid. We did not attempt to measure mean aggregation numbers in the adsorption layers by steady-state fluorescence measurements. Indeed, with respect to micellar solutions,*.l2working with concentrated suspensions raises some difficult problems. The general methodology developed by Infelta and Gratze12 for micelles can hardly be applied, because some parameters which are absolutely necessary such as the number of adsorbed photons are no longer accessible to the measurements. It is therefore not (22) Ray, A,; Nemethy, G. J . Phys. Chem. 1971, 75, 809. (23) Crook, E. H.; Fordyce, D. B.; Trebbi, G. F. J . Phys. Chem. 1963,67, 1987. (24) Crook, E. H.; Trebbi, G. F.; Fordyce, D. B. J . Phys. Chem. 1964,68, 3592.
1304
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986
Levitz and Van Damme
t I
CMC
10
1
v
e e
I
I
I
1
I
I
I
I
I
+
(c
io-'m~ie /I Figure 1. Adsorption isotherms of TBE6 and TXlOO on Spherosil XOB015 at 298 K: ( 0 )without pyrene; (V)with pyrene.
possible to perform experiments at variable pyrene concentrations, in which the number of adsorbed photons is kept constant by modifying the excitation wavelength. For the same reason, measurements at consant wavelength for different pyrene concentrations are not possible. In fact, it is not possible to calculate from experiments the correction factor, A2 which is required to apply the method of Infelta and GratzeL2 At first sight, one might think that the approach of Selinger and Watkins12 would avoid these problems, since it is based on the ratio between the monomer and excimer emission. To adjust the aggregation number, these authors have needed the ratio $m/$e, where &, is the maximum monomer quantum yield (excimer formation excluded) and $e the maximum excimer quantum yield (excimer dissociation excluded). This ratio is noted as Cp0/q5,,' in ref 12 and as &,/$e in ref 2. In fact the ratio d m / ~ as e , shown in the formula 18 ref 12, is measured by a series of experiments at constant absorption which are similar to those performed in ref 2 when formula 20 is used. As explained before this is not possible with our system. Finally our concentrated slurries contain solid particules with size slightly smaller than the emission wavelength. In this case, reflection, refraction, and scattering processes must be taken into account. Unfortunately, all those processes depend on the texture of the medium, the emission wavelength, and the pyrene concentration. The latter parameter determines the spatial distribution of the emission light sources in the slurries. As shown e1sewhe1-e~~ some complex corrections are in general prerequisite when one compares two experimental emissions bands measured at two largely different wavelengths in a well-defined direction. 4 . Fluorescence Decay Study. The fluorescence decay spectrometer was a single-photon-counting E.G.G Applied Photophysics instrument. The flash lamp was used at a repetition rate of 30 kHz. Excitation was performed at 320 nm. The pyrene monomer emission was monitorted at 385 nm and the excimer emission at 490 nm. Time calibration was performed with deaerated aqueous solutions of tris(2,2'-bipyridine)ruthenium( 11) (650 nsZ6)and pyrene (10" mol/L, 180 n ~ * ~ ) . 5 . Numerical Analysis of the Decays. As compared to the first paper," the numerical analysis has been improved. The (25) Lipsett, F . R. Prog. Dielecrr. 1967, V7, 217-318. (26) Van Houten, J.; Watts, R. J. J . Phys. Chem. 1976, 98, 4853. (27) Kalyanasundaram, K.; Thomas, J. K. J . Am. Chem. SOC.1977, 99, 2039.
5
monomer and the excimer decays were simultaneously fitted to the data with a nonlinear least-squares method using the Powell algorithm2* Reconvolution of the theoretical model with the flash profile was performed by using the algorithm of the centered 6 pulse.29 The reconvolution permits to take into account the rise of the excimer emission at short time and to optimize ( k 2 , ke, k,", ii) or ( k 2 ,k-e, k,") (see section 111). k , is determined from the experiments at very low pyrene concentration (no excimer formation). All calculations are performed on line with a MINC DECLAB 23 DEC computer. 6. Solubilization of Pyrene in Adsorption Layer. As shown in Figures 1 and 2, the presence of pyrene does not modify the adsorption isotherms of nonionic surfactants, from one probe for 30 surfactants to one probe for 1000 surfactants. In the case of TBE6, TX100, and TX102, and for equilibrium surfactant concentrations below the cmc, pyrene is totally dissolved in the adsorption layer. Only traces of pyrene are observed in the supernatant. Above the cmc, the fluorescent probe molecules partition between the adsorption layer and the micellar supernatant. However, even in the measurements performed somewhat above the cmc, the ratio [pyrene in the solution/pyrene in the adsorption layer] was always kept below 0.01. This was made possible by the low values of the cmc, the large adsorption, and the solid/liquid ratio used in the fluorescence experiments. A successful solubilization can be described as a situation where the pyrene molecules are dispersed as individual species (in their ground state) in the hydrophobic regions of the medium. A missed solubilization is a situation where the pyrene molecules remain at least partially (for steric reasons) in the polar regions of the medium. Due to their poor solubility in polar solvents, they aggregate and form microcrystallites. There are at least four ways for checking the quality of the solubilization: (i) Monitoring the Z J I , ratio of the vibronic components of the steady-state fluorescence spectrum.27 This ratio is close to 0.75 when pyrene is in the hydrophobic core of the nonionic micelle^'*^^^ (or, more exactly, in the boundary region of the hydrophobic core). It is much lower when pyrene is in a polar environment. For instance, Bauer et aL3' report 13/1,= 0.55 for (28) Powell, M. J. D. Compur. J . 1965, 7, 303. (29) Bouchy, M.; Jezequel, J. Y.;Andre, J. C.: Bordet, J. In "Deconvolution et reconvolution de signaux analytiques. Application i la spectroscopie de fluorescence": Bouchy, M., Ed.; ENSIC-INPL: Nancy, France, 1982; p 398.
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986
Adsorption of Nonionic Surfactants
A
1305
CMC
Nads TX102
. I
0
TX305
0
-
m
-
TX405
-
CMC
l 1
l
l
1
1
1
I
1
5
l
1 10
1
1
1
1
1
1
1
1
l
c ( 1o-‘mo
15
Figure 2. Adsorption isotherms of TX102, TX305; and TX405 on Spherosil XOB015 at 298 K: (0)without pyrene, (V)with pyrene.
pyrene directly deposited on a silica surface. (ii) Analyzing the rise of the excimer emission. This rise is diffusion limited (dynamic excimer formation) in a good “solution”. It is almost instantaneous, as expected (static excimer formation in a nanosecond scale) when the molecules are involved in ground-state aggregates or crystallite^.^' (iii) Verifying the validity of Beer-Lambert law for pyrene at 320 and 338 nm (in the case of micellar solutions). (iv) Testing the presence of pyrene microcrystallites in the supernatant after natural sedimentation of the silica, which is rapid due to the large granulometry (40-100 pm). This test was performed by mixing a well-defined quantity of supernatant in a highly micellar solution. After equilibrium, pyrene is redissolved in micelles and its concentration can be determined by UV absorption at 320 and 337 nm. Serious problems were encountered when we tried to solubilize pyrene in the micelles or in the adsorbed phases of TX305 and TX405. In order to obtain a satisfying solubilization in the micellar solutions, we had to use surfactant concentrations larger mol/L, Le., significantly beyond the cmc’s (bethan 2-4 X tween 7 X and 10 X mol/L). In order to avoid any problem, the determinations of the micellar aggregation number were performed at mol/L. These difficulties are most probably due to the slightly too small size of the micellar cores, just above the cmc. In the adsorbed phases the problem was even more serious. With TX305, pyrene could be solubilized in the hydrophobic regions of the surface layer only at 0 larger than 0.5 where 0 is defined as the ratio “amount adsorbed surfactants/ amount adsorbed surfactants at the plateau of isotherm”. With TX405, it could not be solubilized campletely, even at fJ = 1. As a consequence, we were unable to perform the FDS study on the adsorbed layer of TX405, but we will nevertheless use the adsorption isotherm and the average micellar aggregation number in mol/L solution to discuss the structure of the adsorbed layer of TX405 at the plateau of adsorption isotherm (cf. section V). (30) Bauer, R. K.; De Mayo, P.; Ware, W. R.; Wu, K. C. J . Phys. Chem. 1982, 86, 3781. (31) Bauer, R. K.; De Mayo, P.; Okada, K.; Ware, W. R.; Wu, K. C. J .
Phys. Chem. 1983,87, 460.
111. Determination of the Average Aggregation Number by FDS 1 . General Theory of Pyrene Monomer and Excimer Decay. It is well established that the photokinetic properties of pyrene can be described satisfactorily by the following reaction mechanisms. P huo P* (1)
+
P*
-+ -+
k!‘
P
NR
k!
P*
hUl
P
(4) k,’
P2* P2*
P
+ P + hV2
-+ kl
P
P
(5)
(6) klr,klNRand kZr,kZNR are the radiative and nonradiative rate constants for the monomer and excimer, respectively. k, and k, are the rate constants for excimer formation and dissociation, respectively. In our previous work18 we assumed that the dissociation rate of the excimer (k,) is negligible. This is a common practice but, in fact, does not rely on adequate justifications as pointed out to use by one of the reviewers. Therefore we shall consider k-, as an adjustable parameter in what follows. Let us consider first a micellar-like medium formed by molecular aggregates with a small average aggregation number N . The equilibrium distribution of probe molecules over the aggregates n is reported to follow Poisson statistics. As discussed in our first paperI8 this implies some well-defined conditions, one of them being that the average number of probe molecules per aggregate, ii, is close to 1. Under these conditions, the time dependences of the pyrene monomer and excimer fluorescence following pulsed excitation are
1306
Levitz and Van Damme
The Journal of Physical Chemistry, Vol. 90, No. 7 , 1986
with
+ k, = k I N R+ k l R k2 = kZNR k 2
+ k t ( n - 1) + k-,
= k,
p,
(9) (10) (11)
v = k2
+
a, = Y2[(p,, u ) Pn
=
f/2[(pn
(12)
- {(p,, - v ) +~ 4k: k-,(n
+ V) + {(Y,
-v )+ ~ 4k:
- 1))1’23 (13)
k-e(n - 1)1”21 (14)
k,“ is a first-order rate constant which is assumed to be equivalent to the intramicellar encounter frequency of the probes. In micelles containing n pyrene, the rate of excimer formation (eq 4) is supposed to be proportional to ( n - l ) , with k: as proportional factor. At short times, the monomer and excimer decays are multiexponential functions. A single-exponential limit is reached at long times for the monomer decay. This comportment is assigned to aggregates containing only one pyrene molecule where excimer formation is not possible. On the other hand, for very large aggregates or continuous media, the distribution of probe molecules is homogeneous and the monomer and excimer decays are given by the following expressions, re~pectively)~
with
CY
= X[(p
+
V)
+
- ( ( p - v ) ~ 4kek-e[P])1’2]
P = ~/Z[(IL + V) + { ( K - vI2 + 4kek-e[Pl)”21
(19) (20)
[PI is the pyrene concentration. ke” is the second-order rate constant for dynamic quenching through excimer formation. From (19) and (20) we have P>a
and from the inequality
IU
+
- pi C [ ( p - v ) ~ 4k,k-e[P]]’/2
it is easy to verify
-P>- oP P-.
CL-a
-> O P-a
At long times, the monomer and excimer decays are practically monoexponential. They run parallel to each other (in logarithmic scale) with a common slope a. This situation is not obtained in the case of small aggregates. Between the two previous well-defined situations (very small aggregates on the one hand, and very large or “infinite” aggregates on the other hand), there is clearly room for intermediate cases. Aggregates with a typical half-size somewhat larger than the diffusion length of a pyrene molecule during its monomer excited-state lifetime would, for instance, belong to this category. In this case, two main problems appear: (i) As pointed out by Lianos and Zana3 the limited exploration volume of the pyrene probes during their excited-state lifetimes does not justify the proportionality between the rate of excimer formation (eq 4) and ( n - l), as admitted in eq 7-14. (ii) The amplitude of the pyrene concentraion fluctuations in these large aggregates decreases as (32) Nataga, N.; Kubota, T. “Molecular Interactions and Electronic Spectra”; Marcel Dekker: New York, 1970; Chapter 9.
compared to those in small aggregates, and Poisson statistics must be replaced by a binomial or another more realistic statistic^.^^ In the case of p-tert-octylphenol poly(oxyethy1ene) micelles, our estimate for the upper limit of the aggregation number which we can determine with confidence using eq 7-14 is between 200 and 300 surfactant molecules per aggregate.34 This estimation is very similar to that obtained by Lianos and ZanaS3v6 2. Determination of the Average Aggregation Numbers in the Adsorption Layer. For aggregates of less than 200 or 300 molecules, eq 7 and 8 permit us to calculate ri. rt is related to the total number of pyrene molecules np and the total number of aggregates Nagby ri
= np/Nag
(21)
whereas the average aggregation number N is defined as
=
NSA/Nag
(22)
where NSA is the total number of surfactant molecules involved in aggregates. Equations 21 and 22 lead to The use of eq 23 for the determination of N is straightforward in micellar solutions. Indeed, np is a well-controlled experimental parameter and NSA is the amount of molecules in excess of the amount of monomers, determined by the cmc. The use of eq 23 for the determination of average aggregation numbers in adsorbed phases is less straightforward. First, one has to make sure that all the pyrene molecules are “solubilized” within the surface aggregates and not simply adsorbed on the bare surface. This can be checked by monitoring the 13/Z, vibronic ratio as explained below. It was always the case in this work. Second, NSA is not as easily calculated as in micellar solution because we do not even know if there is a quantity equivalent to some ”critical surface aggregate concentration”. Fortunately, there is some experimental evidence that, for the type of molecules we are dealing with, the amount of adsorbed molecules not involved in aggregates is always negligible with respect to the amount of molecules involved in aggregates. This evidence comes from our FDS investigation on the phenoxy group fluorescence of monodisperse cctylphenol POE adsorbed on silica,I9in which we showed that, from the outset of adsorption, the overwhelming majority of molecules is involved in aggregates. Although this was only shown for surfactants with 8 and 10 OE units, we will assume that it is also true for the other POE chain lengths examined in this paper. In these conditions, N S Ais simply taken as the total amount of adsorbed molecules, Nads,and eq 23 may be applied. Nevertheless, the determination of aggregation numbers by FDS is submitted to two limitations, in very small aggregates on the one hand and very large aggregates above 200-300 molecules on the other hand. In very small aggregates (or, more exactly, in aggregates with very small aggregation numbers), the hydrophobic nucleus may not be large enough to accommodate one or more pyrene molecules. In this case, the FDS study is just not feasible. This might be the problem encountered in the adsorbed phase of TX305 at low surface coverage and in the adsorbed phase of TX405 at all coverages. The limitation encountered in very large aggregates is of an entirely different nature, as explained above. IV. Results 1. Micellar Solution (at 1r2 mol/L). For TX100, TX102,
TX305, and TX405, the pyrene monomer and excimer decays can be fitted by eq 7 and 8. A typical fit is shown in Figure 3, for the micellar solution of TX305. For very low (200 210 97 42 30
10.8 17.1 22.5 54 72
43 29. 19 16
"Surface aggregates are assumed to be oblate ellipsoids (see text).
(between 35 and 42). This is again very close to the average aggregation number of regular TX305 micelle at lo-* mol/L ( N = 40). An intermediate behavior is displayed by TX100. This molecule, with a moderately short polar chain, nicely fits into the sequence (cf. Table V and Figure 6) since its forms micellar-like aggregates for apparent surface coverages 0 below 0.8 and certainly large surface assemblies, as in the case of TBE6, beyond 0.8. In a broad domain, from 0 = 0.17 to 0.5, the average surface aggregation number is again close to the size of regular micells well above the cmc. Similar conclusions were obtained in our first paperI8 where a simplified analysis of the fluorescence decays were used.
V. Discussion. Structure of the Adsorbed Phase The major point resulting from this work is undoubtedly the striking similarity of the adsorbed phases with the micellar solutions. Molecules with short polar chains (TBE6, 6 OE units) form large assemblies on the silica surface. The same situation is encountered in aqueous medium with the micellar aggregates. Their average aggregation number is too large to be determined by our method. On the other hand, molecules with long polar chains (TX102, TX305; 12.5 and 30 O E units) form adsorbed phases which always appear as fragmented media to the fluorescence probes, at all coverages. The average aggregation numbers of the surface assemblies are close to those of regular micelles, and at 0 = 1, they are equal to each other, within experimental error. TX100, with a moderately long polar chain (9.5 OE units), appears as an intermediate case which nicely fits into the general picture. In order to evaluate the limits of the similarity of the surface aggregates with the regular micelles, we calculated the apparent surface per molecule (a,) at the plateau of isotherm and we compared this value to that from the experiment. The experimental value of a, is obtained by dividing the specific surface area of the solid by the number of molecules adsorbed at the plateau of the isotherm (or at 0 = 0.8 in the case of TXl00, see below). In order to calculate up a priori, we assumed that the surface aggregates are oblate ellipsoids. This hypothesis is a good approximation for regular micelles of alkylphenol POE surfactants in ~ a t e r . ~We ~ .assume ~ ~ that the minor semiaxis, La, of the aliphatic core is perpendicular to the solid surface. The projected circular area of such ellipsoids, aagis where Lb is the major semiaxis of the oblate ellipsoid aliphatic core (including the phenol ring), and Lp, the thickness of the polyoxyethylenic palisade. Lb can be calculated from the volume of the aliphatic core ua and the aggregation number N . The volume of the oblate ellipsoidal aliphatic core is3*
b=
limN,,
11.3 14.7 17.1 27.3 31.6
30b 59 95 440 896
Lb =
[ 1(%)I1/' 4.n
La
33 60 78 250 333
up.
300.
200.
100.
10
20
30
40 NO€
Figure 7. Apparent surface area (up) per surfactant molecule on the Spherosil XOB015 vs. NOE,the number of oxyethylenic groups in the polar chain: (*) experimental results; (0)theoretical calculations at 8 = 1 for surfactants with long polar chains, assuming a random coil conformation for the POE chains, an oblate ellipsoid shape for the surface aggregates, and a close-packed arrangement. N = 97, 42, and 30 for theoretical estimate for TX102, TX305, and TX405, respectively; (0) TX100, assuming that the polar chains are in meander conformation and that close-packed arrangement is reached at 8 = 0.8;18the horizontal dotted line is the limit up = 30 A2 obtained for very large oblate ellipsoids.
u, is the average volume per octylphenol chain estimated at 363
A3 by Robson and Dennis,37assuming that the hydrophobic interior resembles a droplet of liquid hydrocarbon. La is simply taken as the length of the alkyl chain (10 A, for our ocylphenol chaid7). A good estimate for L, is more difficult. For long polar chains (TX102, TX305, and TX405), L, can be approximated by the end to end distance of a POE chain in the random coil conform a t i ~ n .In~ this ~ case, the calculations of Mark and F 1 0 r y ~ ~ ~ ' can be used. For shorter polar chains, a meander conformation would be more realistic.37 In this case, we have L, = 1.8NoE
(27)
We further assumed that, at the plateau of the isotherm, the micellar-like aggregates population is in dense packing. upis then readily obtained from up
and
30b 54 76 177 263
= .,p/Wr)
(28)
where r is the surface occupancy in a close-packed arrangement of hard disks, Le., 0.907.42 (39) Flory, P. J. 'Statistical Mechanics of Chain Molecules"; Wiley: New
York, 1969; Chapter V. (36) Tanford, C.; Nozak, V.; Rohde, N . J. J . Phys. Chem. 1977,81, 16. (37) Robson, R. J.; Dennis, E. A. J . Phys. Chem. 1977, 81, 1075. (38) 'Handbook of Chemistry and Physics", 44th ed.; Hodgman, C. D.; Ed.; CRC Press: Boca Raton, FL, 1962-1963; p 347.
(40) Mark, J. E.; Flory, P. J. J . Am. Chem. SOC.1965, 87, 1415. (41) Mark, J. E.; Flory, P. J. J . Am. Chem. SOC.1966, 88, 3702. (42) Helfand, E.; Frisch, H. L.;Letmwitz, J. L. J . Chem. Phys. 1961, 34, 1037.
1310 The Journal of Physical Chemistry, Vol. 90, No. 7 , 1986 The results obtained from this simple geometrical model are compared with those from experiments in Table VI and in Figure 7 . In the case of TXlOO, the calculations were performed at 0 = 0.8 with N = 210. For TX405, the size of the surface aggregate at 0 = 1 is assumed to be equal to that of regular micelles at lo-, mol/L ( N = 30). The main conclusions are as follows: for long polar chain surfactants (TX102, TX305, and TX405), the random coil conformation hypothesis is in acceptable agreement with experiments. However the calculated values are all somewhat lower than the observed values. This probably stems from the fact that the actual thickness of the POE palisade is larger than than that predicted from the random coil conformation, due to excluded volume interactions between ethoxy groups in the polar corona of the surface aggregate.43 These interactions certainly increase the value of up by stretching the POE chains. However, going from the random coil to the meander conformation (cf. Table VI), which is very elongated for long polar chains, leads to a large overestimation of up beyond 10 O E units. It is therefore likely that the POE chains are only modestly stretched. For a surfactant with long polar chains, the polymeric aspect of the POE chain must be taken into account. A similar observation was made by Tanford et al.36 concerning the structure of aqueous micelles. For TX100, the two conformation hypotheses give similar estimations of up (at 0 = 0.8). However, the meander conformation appears to be in better agreement with the experiment. As shown before,’, the adsorbed phase can be described as an assembly of surface aggregates in close packing at 0 = 0.8. Molecules with very short polar chains (TBE6) raise a problem because we know their average aggregation number neither in the micellar solution nor on the silica surface. We merely know that the aggregates are very large, well above 200-300 molecules. Two asymptotical models for the adsorption layer at the plateau were examined: an infinite bilayer on the one hand, or an ensemble -) oblate ellipsoids on the other hand. Asof very large ( N suming that the steric constraints in a bilayer structure are due essentially to the alkyl chains (including the phenol group), the volume of a bilayer portion, or a disk, of N molecules is
-
-
V, = Nu, = aR2(2L,)
(29)
with R the radius of the disk (or of the bilayer portion). In this case, the apparent surface area per molecule would be
rR2 Nr
up = - = -
c’a
2L,r
where r = 1 for an infinite bilayer and r = 0.907 for a close-packed arrangement of disks. This leads to up = 18 or 20 A,, in poor agreement with the experimental value of 33 A at 0 = 1. On the other hand, in an oblate ellipsoid with a very large aggregation number, the thickness of the polyoxyethylenic palisade is negligible with respect to the major axis Lb of the aliphatic core; then uag
XLb*
(N
-
+m)
and from (26) = 3/Nu,/ L,
gag
(N
+a)
-+
(32)
The asymptotic value of up is lim up = 3/qv,/rL,
.V-m
(33)
Levitz and Van Damme with the experimental value (cf. Figure 7 and Table VI). VI. Conclusion The adsorption isotherms of nonionic surfactants with short ~ - ~ ’a typical and medium POE chains lengths on s i l i ~ a ~ have sigmoidal shape. The rising part of the isotherms is always situated below but near the cmc, whereas the plateau is always reached slightly above the cmc. A parallel behavior is observed in the kirietics of a d ~ o r p t i o n . ~ ’The , ~ ~ adsorption rate is directly correlated to the monomer surfactant concentration in water as long as the concentration is below the cmc and becomes constant as the cmc is crossed. Hence the equilibrium as well as the kinetic data show that the adsorption layer is built from isolated molecules coming from the aqueous solution and not by direct adsorption of micelles. The plateau in the adsorption isotherms stems from the stabilization of the monomer surfactant chemical potential slightly above the cmc. The proximity of the rising part of the isotherms with the cmc (at least for short and medium POE chains) is typical of a “weak normal bond adsorption isotherm”. In fact, this is not unexpected since adsorption merely involves the replacement of a silanol-water hydrogen bond by a silanol-ethoxy hydrogen bond.5’ Hence, the resulting exchange energy is certainly weak. Nevertheless, for nonionic surfactants with very long POE chains, this weak interaction energy (per ethoxy unit) can be overwhelmed by the very large number of POE surface bonds just as in the case of polymer adsorption. As shown by Partyka et al.,50 monodisperse poly(oxyethyleneglycols (molecular weight 400 (EO,) and 1000 (EO,,)) are only weakly adsorbed on the Spherosil XOB015 compared to the adsorption level of corresponding octylphenol POE surfactants. This observation is in good accord with a weak interaction between POE chains and solid surface. The FDS study presented in this work reinforces our previous conclusion18 about the micellar character of the adsorbed phase formed by alkylphenol POE nonionic surfactants on a hydroxylated silica surface. Below the cmc, the surface of silica acts as a precursor of the micellization process. Surface aggregates are created on the solid from isolated surfactants in the solution. Their properties are close to those of aqueous micelles well above the cmc. Two facts account for this result. First, in many instances, the POE chains can be considered as relatively flexible. On the surface solid, they can “explore” the surface and stick to it at different points. Second, the weak interaction between the POE chains and the solid allows for a rebuilding of a micellar-like aggregate on the surface below but near the cmc without a deep perturbation due to the solid surface field. Two stages appear to be necessary in order to rationalize this adsorption process. A logical thermodynamic approach would be, in a first step, to account for the formation of isolated micelles of nonionic surfactants in water above some cmc, and in a second step, to understand how the weak interaction of monomers with a hydrophilic surface can generate a set of surface aggregates at equilibrium concentration below or close to that cmc. This is the purpose of a thermodynamic model53which will be published soon.
Acknowledgment. We thank J. E. Poirier of CRVM (Nancy) for performing the electrophoretic measurements. This work has been supported by the MRI Grant 83E 0968, and the PIRSEM of C.N.R.S. Registry No. tert-Octylphenol poly(oxyethylene), 9002-93-1; silica, 7631-86-9; pyrene, 129-00-0. (48) Doren, A.; Vargas, D.; Goldfard, J. Imt. Min. Metall., Tram., Secr.
This leads, with r = 0.907, to u = 30 AZ,in much better agreement
B 1975, 84, C.34.
(43) Kjellander, R.; Florin, E. J . Chem. Soc., Faraday Tram. 1 1981, 77, 2053. (44) Kushner, L M.; Hubbard, W. D. J . Phys. Chem. 1954, 58, 1163. (45) Mankowich, A. M. Ind. Eng. Chem. 1955, 47, 2175. (46) Dwiggins, C. J.; Bolen, R. J.; Dunning, H. N. J . Phys. Chem. 1960, 64, 1175. (47) Mankowich, A. M. J . Phys. Chem. 1954, 58, 1027.
(49) Furlong, D. N.; Aston, J. R. Colloid Surj. 1982, 4, 121. (50) Partyka, S.;Zaini, S.; Lindheimer, M.; Brun, B. Colloids Surf. 1984, 12, 255. (51) Clunk, J. S.; Ingram, B. T. In “Adsorption From Solution at the Solid/Liquid Interface”, Parfitt, G. D., Rochester, CH., Eds.; Academic Press: New York. 1983: Chanter 111. (52) Klinenko, N. i.; Permilovskaya, A. A.; Tryasorukova, A. A,; Loganovski, A. M. Kolloidn. Zh. 1975, 37, 972. (53) Levitz, P. Thtse d‘Etat, Universitt d’orltans, Orleans, France, 1985.
