Modeling the Effect of Structural Details of Nonionic Surfactants on

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Modeling the Effect of Structural Details of Nonionic Surfactants on Micellization in Solution and Adsorption onto Hydrophobic Surfaces A. B. Jo´dar-Reyes,*,† J. L. Ortega-Vinuesa,† A. Martıń-Rodrı´guez,† and F. A. M. Leermakers‡ Biocolloid and Fluid Physics Group, Department of Applied Physics, University of Granada, 18071, Granada, Spain, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands Received May 16, 2002. In Final Form: August 14, 2002 Applying the classical one-gradient self-consistent-field (SCF) theory for adsorption and/or association, we can show that the molecular architecture of nonionic surfactants influences strongly the micellization in solution and the adsorption on solid-liquid interfaces. This is illustrated by using two models for the molecule with the same overall structure, one with a linear and one with a more realistic branched hydrocarbon tail. The critical micelle concentration is computed for several lengths of the poly(oxyethylene) headgroup. In addition, the adsorption isotherms of these small surfactants on hydrophobic surfaces were studied. Theoretical results are critically compared to the experimental results for critical micelle concentrations and adsorption isotherms of Triton X-100 and Triton X-405 onto a polystyrene latex dispersion. From this comparison, it was concluded that a SCF model in which homogeneous adsorbed layers are preassumed fails to reproduce experimental findings. It is speculated that lateral inhomogeneities must be included in the SCF model to improve its performance.

Introduction Surfactants adsorb to virtually any surface. By doing so, they influence important properties of surfaces and particles (e.g., wetting, stability, etc.). Considering the importance of surfactants at interfaces, it is a surprise that the theoretical understanding is far from complete. There exist several empirical and semiempirical theories (e.g., Langmuir,1 Zhu-Gu2) to describe nonionic surfactant adsorption onto solid/liquid interfaces. Even though several important aspects such as the molecule length or the interactions between different system components are not treated, they are still extensively applied to describe many experimental results. Their success is partially explained by the fact that the neglected phenomena have opposite effects on the adsorption isotherms. Of course, such primitive models are not able to correctly describe more detailed properties of great industrial and scientific interest such as the structure of the adsorbed layer. There are more detailed models based upon statistical mechanical techniques to obtain structural information including interaction and molecular size effects. Some of these models3-6 have the disadvantage that ad hoc assumptions on the segment (surfactant molecule building units) density distributions have to be made. In this paper, a statistical thermodynamic treatment has been applied to model the behavior of amphiphilic chains on surfaces, in which such distribution assumptions are not needed. * To whom correspondence should be addressed. † University of Granada. ‡ Wageningen University. (1) Langmuir, I. J. Am. Chem. Soc. 1916, 38, 2221. (2) Zhu, B. Y.; Gu, T. J. Chem. Soc., Faraday Trans. 1 1989, 85 (11), 3813. (3) Kronberg, B. J. Colloid Interface Sci. 1983, 96, 55. (4) Kronberg, B.; Stenius, P. J. Colloid Interface Sci. 1984, 102, 410. (5) Kronberg, B.; Stenius, P.; Igeborn, G. J. Colloid Interface Sci. 1984, 102, 418. (6) Koopal, L. K.; Wilkinson, G. T.; Ralston, J. J. Colloid Interface Sci. 1988, 126, 493.

The theory we use is called SCF-A,7 self-consistent-field theory for adsorption and/or association, which is a modification of the self-consistent-field theory by Scheutjens and Fleer, originally developed to study the adsorption of homopolymers from solution.8,9 Besides describing copolymer adsorption, this theory has been combined with information from the literature (Thermodynamics of Micelle Formation10 based on Thermodynamics of Small Systems11) to study the association of amphiphilic molecules in solution.7,12 Our aim is to apply the SCF-A theory to the adsorption of nonionic surfactants with different headgroup lengths on hydrophobic surfaces and to get information on the structure of the interfacial layer. The model needs FloryHuggins type parameters that should be tuned for the systems. This set of parameters can be split up into a set in which the surface participates and a set in which the surface is not important. The last set of parameters can be found from a corresponding analysis of the behavior of the surfactant in solution, that is, the theoretical critical micelle concentration (cmc). We will study the effect of the headgroup size on the adsorption and on the micellization, from both an experimental and a modeling viewpoint: we will compare the SCF-A calculations with experimental results for the micellization of two poly(oxyethylene) p-t-octylphenols, Triton X-100 and Triton X-405, and their adsorption on a polystyrene latex dispersion. (7) Leermakers, F. A. M.; Scheutjens, J. M. H. M.; Lyklema, J. Biophys. Chem. 1983, 18, 353-360. (8) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619. (9) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (10) Hall, D. G. Thermodynamics of Micelle Formation. In Nonionic surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Chapter 5. (11) Hill, T. L. Thermodynamics of small systems; Benjamin: New York, 1963, 1964; Vols. 1 and 2. (12) Leermakers, F. A. M.; Scheutjens, J. M. H. M. J. Colloid Interface Sci. 1990, 136, 231.

10.1021/la025954c CCC: $22.00 © 2002 American Chemical Society Published on Web 09/20/2002

Effect of Surfactant Structure on Micellization

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Table 1. Main Features of Triton Surfactants surfactant

Xa

molecular weight

HLB

cmc (10-4 M)

Triton X-100 Triton X-405

9-10 40

625 1966

13.5 17.9

2.5 8.1

a

Number of ethylene oxide groups.

In addition to just fitting our experimental results leading to an ad hoc set of parameters, we pursue parameters whose values are more coherent with their physical meaning. This will give information on the true performance of the theory. First, we will present results for surfactant molecules designed as linear chains. Unlike other work,13,14 our design allows for some hydrophobic groups to be distributed in the surfactant head as in the real molecule. The effect of the interaction parameter between segments and surface is also studied. It will be shown that the choice of more “realistic” parameters has the effect that the theoretical isotherms differ significantly from the experimental ones. Then we will improve the molecular design. A branched hydrocarbon tail will be considered. At this point, we will show the important effect this structural change has on adsorption and micellization. Of course, there is still a difference between the measured and predicted isotherms. In the discussion, we will speculate on the possible reasons for this difference. Experimental Section Materials. All chemicals used were of analytical grade. Solvent. The water used as the solvent was purified by reverse osmosis, followed by percolation through charcoal and a mixed bed of ion-exchange resins. Surface. Polystyrene latex beads have been used as the adsorbent surface. We synthesized this colloidal system by means of emulsion copolymerization of styrene (Merck) and sodium styrenesulfonate (NaSS) (Fluka) using a thermostatic batch reactor. The solution was stirred with a Teflon palette at 250 rpm, and the synthesis temperature was 45 °C. The latex recipe was as follows: 570 mL of water, 90 g of styrene (previously distilled under low pressure: 10 mmHg and 40 °C), 775 g of NaSS, 820 mg of K2S2O8 (Merck), 508 mg of NaHCO3 (Sigma), and 319 mg of NaHSO3 (Sigma). The reaction lasted 14 h. Subsequently, cleaning was done by serum replacement with DDI water until the electrical conductivity of the replaced liquid was below 2 µS cm-1. Particle size was obtained by transmission electron microscopy. The mean diameter is (138 ( 7) nm and its polydispersity index is 1.007, so the particle size distribution can be considered extremely narrow. The coinitiator NaSS makes particles present some negative charge on the surface. This surface charge density was determined by conductometric and potentiometric titrations. The calculated value was (-6.6 ( 0.2) µC cm-2. The colloidal stability of the dispersion is guaranteed in our experiments. Surfactants. Two nonionic surfactants were employed in this study, Triton X-100 and Triton X-405. They were supplied by Sigma with a high grade of purity. They are both poly(oxyethylene) p-t-octylphenol and differ with respect to the number of ethylene oxide groups. The structural formula of Triton X surfactants is shown in eq 1 where X ) 9-10 for Triton X-100 and X ) 40 for Triton X-405.

The main features of these surfactants are shown in Table 1. (13) Bo¨hmer, M. R.; Koopal, L. K. Langmuir 1990, 6, 1478-1484. (14) Bo¨hmer, M. R.; Koopal, L. K.; Janssen, R.; Lee, E. M.; Thomas, R. K.; Rennie, A. R. Langmuir 1992, 8, 2228-2239.

Due to the aromatic ring in the molecules, the detection of these surfactants in aqueous media is possible by means of a direct spectrophotometry method. Triton concentrations were determined by using a Beckman DU 7400 spectrophotometer at 275 nm. The cmc’s of Triton X-100 and Triton X-405 can be determined by measuring the absorbance at 275 nm for different surfactant concentrations.15 The point of change in the slope of the absorbance versus concentration curve corresponds to the cmc. However, this change is rather soft for our surfactants and the value for the cmc is not extremely sharply defined. We have taken into account these results to know the surfactant concentrations used in the adsorption experiments to avoid the starting of association phenomena. As we are interested in a rigorous critical micelle concentration, we have chosen data from another method. The cmc value of Triton X-100 in water at 25 °C using the pyrene 1:3 ratio16 was found to be 0.25 mM. This value is in fair agreement with data published in the literature obtained from surface tension measurements17 and from spectrophotometry.18 For Triton X-405, the value provided by suppliers is 0.81 mM. Methods. Adsorption Isotherms. Adsorption isotherms were determined by using the depletion method. Known values of polystyrene latex, surfactant, and ultrapure water were mixed. The amount of latex was chosen so that the overall area presented by the spherical particles was 0.3 m2. The kinetics of adsorption was monitored in order to determine the best conditions for the equilibrium adsorption experiments. The samples were kept in a thermostatic bath at 25 °C and subjected to shaking. After 4 h, the supernatant was separated by centrifugation and filtered using a filter with an extremely low affinity for protein adsorption (Millipore, pore diameter ) 0.1 µm). There exists a linear relation between absorbance and surfactant concentration for the values in which we are interested. Making a previous determination of the molar extinction coefficient (1.91 × 103 M-1 cm-1 for Triton X-100 and 1.01 × 103 M-1 cm-1 for Triton X-405), we thus know the surfactant concentration in solution by means of a direct absorbance measure.

Theory Due to the extremely high number of possible conformations a surfactant chain can adopt when it is in solution near a surface, we apply a statistical thermodynamic treatment. The exact solution is extremely hard, and typically the problem is “solved” by making mean-field approximations. In such an approximation scheme, the best approach leads to the so-called self-consistent-field (SCF) models. Here we use a SCF approach that solves the problem using lattice approximations. It was first developed for homopolymers by Scheutjens and Fleer,8,9 and then it was extended to treat copolymers.7 In this treatment, the solution is supposed as divided in two regions: on one hand the bulk, far from the interface, and on the other hand a region adjacent to the surface in which a mixture of polymer (represented as a chain of segments) and solvent molecules is distributed on a lattice. Every lattice site is considered to be occupied by a segment that has the same size as a solvent molecule. The lattice consists of M layers parallel to the surface each containing L indistinguishable sites. In this case, there only exists one gradient in the direction perpendicular to the surface and a mean-field approximation is applied to each layer. Therefore, the volume fraction of chain segments in a layer z (φ(z)) is defined as the number of chain segments in this layer divided by L. For the solvent, the volume fraction of molecules in each layer (φw(z)) is defined as the number (15) Romero-Cano, M. S.; Martıń Rodrı´guez, A.; Chauveteau, G.; de las Nieves, F. J. J. Colloid Interface Sci. 1998, 198, 266-272. (16) Molina-Bolı´var, J. A.; Aguiar, J.; Carnero Ruiz, C. Mol. Phys. 2001, 99 (20), 1729-1741. (17) Carnero Ruiz, C.; Molina-Bolı´var, J. A.; Aguiar, J.; MacIsaac, G.; Moroze, S.; Palepu, R. Langmuir 2001, 17, 6831-6840. (18) Ray, A.; Ne´methy, G. J. Phys. Chem. 1971, 75, 809.

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Jo´ dar-Reyes et al.

of solvent molecules in the layer z divided by L. In the bulk, these values are φb and φwb. The physical procedure followed in the SCF theory consists of finding the number of chains of each conformation in the equilibrium by means of the maximization of the partition function with respect to the number of polymer chains in a given conformation. If the total amount of segments is fixed, we have a closed system and the canonical partition function can be used. If we adopt the Bragg-Williams mean-field approximation, this partition function can be expressed as the product of a factor representing the configurational entropy and a factor including the energy of the system. This energy contains adsorption energy for each kind of segments, solventsegment and segment-segment interaction parameters. After maximization, the “segment weighting factor” for each segment in layer z is obtained. Using these factors, the set of M volume fractions of chain segments can be calculated. However, this set of volume fractions has to be introduced in the equations to obtain those weighting factors. Therefore, M implicit equations must be solved by an iteration procedure and a self-consistent solution is found. A numerical method that guarantees convergence must be used. An important observable is the equilibrium segment density profile. Summation over the segment profiles gives the adsorbed amount expressed in number of segments per surface site. Dividing by the number of segments in the chain (N), we obtain exc

n

)

1

M

(φ(z) - φb) ∑ Nz)1

(2)

This quantity is called the excess amount of chains per surface site. This can be done for each volume fraction of surfactant in the bulk, and the adsorption isotherm is obtained. The SCF-A7 is also used to obtain the theoretical cmc of our surfactants. This theory was the first statistical approach that successfully applied the information in Thermodynamics of Small Systems11 for self-assembly processes. In this case, the SCF procedure is applied in a spherical geometry and density gradients in the radial direction r are found. The center of the lattice corresponds to r ) 0. The key thermodynamic quantity is the translationally restricted grand potential Ξ of the micelle which is a function of its size, that is, the surfactant aggregation number nexc: Ξ(nexc). The Ξ must be compensated by the entropy of mixing which leads for low micelle concentrations (near cmc) to φmicelles ) exp(-Ξ(nexc)/KBT where φmicelles is the volume fraction of micelles in the system. At the cmc, the concentration of surfactants that can exist with micelles is minimum. This point coincides with a maximum of Ξ(nexc). All told, the micelle size and the structure of the micelle are known at the cmc. Statistical and computational aspects including the details of how to account for surfactants with branched tails are found in the literature.22 (19) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; Wiley: New York, 1989. (20) Bo¨hmer, M. R.; Koopal, L. K.; Lyklema, J. J. Phys. Chem. 1991, 95, 9569. (21) Leermakers, F. A. M. Ph.D. Thesis, Wageningen Agricultural University, Wageningen, The Netherlands, 1988. (22) Leermakers, F. A. M.; Scheutjens, J. M. H. J. Chem. Phys. 1988, 89, 3264.

Figure 1. Experimental adsorption isotherms for Triton X-100 (b) and Triton X-405 (O) on latex.

Results and Discussion Experimental Adsorption Isotherms. The adsorbed amount (Γ) versus the equilibrium surfactant concentration (Csurfactant) (adsorption isotherm) for Triton X-100 and Triton X-405 on latex is shown in Figure 1. Several aspects related to the effect of the size of the hydrophilic moiety may be emphasized: I. There are no significant differences between the two isotherms at low surfactant concentration. This means that when surfactant molecules have enough free sites on the surface the effect of interaction among chains is negligible. Therefore, the adsorption mechanism involves mainly hydrophobic interaction between the polymer surface and the tail that is similar in both surfactants. II. The maximum adsorbed amount decreases as the number of ethylene oxide groups increases. When there are already molecules on the surface, the repulsive interaction energy among hydrophilic heads begins to be important for the molecules going onto the interface. The longer the hydrophilic moiety, the higher the repulsion. III. The shapes of the isotherms for Triton X-100 and Triton X-405 are significantly different. The shorter surfactant has a step in the isotherm, whereas the longer one reaches a well-defined plateau starting already at very low concentrations. Points I and II agree with published data.15 Theoretical Results. Choice of Parameters. Any molecularly realistic modeling effort needs a set of parameters. In the SCF-A theory, there are lattice parameters, parameters associated with the structure of the molecules, and finally, quantities that specify the interactions. We will discuss these in this order. First, we have to choose the type of lattice as expressed in the coordination number (the number of nearest neighbors) of which fractions λ0 and λ1 are in the same and in adjacent layers, respectively. Theoretical results must be qualitatively independent of the lattice type, and only minor quantitative differences may occur. However, lattice artifacts have been reported in the literature.14,20 It was found that the best choice to avoid these artifacts is the face-centered cubic (fcc) lattice for which λ0 ) λ1 ) 1/3. Each segment in the surfactant chain is supposed to have a size of 0.3 nm. This corresponds to the effective CH2 unit size. One of the most controversial choices in using this theoretical model is concerning the surfactant design: chain architecture, number of segments in the chain, and number and position of hydrophobic and hydrophilic segments in the chain, for example. This choice must be close to the Triton’s structure (eq 1). In this paper, two


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different designs have been considered. First, we have analyzed the results for a linear chain, with overall correct hydrophilic and hydrophobic units. As the parameters will depend on the way the chain is defined, we will discuss the interactions in combination with the presentation of the molecules. Unlike other authors,13,14 we allow hydrophobic segments to be in the headgroup. Second, we have studied a more realistic model with a branched hydrocarbon tail. Linear Chain Model. In the most simplistic case, the structure of the Triton surfactants (eq 1) is modeled as a flexible linear chain. They have the same number of hydrophobic segments (C) in the tail and a different number of both hydrophilic (O) and hydrophobic segments in the head:

C14-(OC2)X-O

(3)

where X ) 10 for Triton X-100 and X ) 40 for Triton X-405. Once the chain design is chosen, it is possible to fix a set of interaction parameters between segments (C, O, and solvent (W)) by means of the theoretical determination of the cmc described above. Our surfactants are composed of the same kind of segments, so this set of parameters must explain the experimental cmc values for Triton X-100 and Triton X-405. In addition, the poor solubility of the aliphatic segments in water, the affinity of the hydrophilic segments for water, and the repulsion between the two kinds of segments must be guaranteed. To compare experimental and theoretical data for cmc’s, it is necessary to translate molar concentrations (Csurfactant) to segment volume fractions (φb) by using b

φ ) NAVsegmentNCsurfactant

(4)

where NA is Avogadro’s number and Vsegment is the segment volume. The translated experimental values for our surfactants are φb(cmc) ) 1.76 × 10-4 for Triton X-100 and φb(cmc) ) 1.78 × 10-3 for Triton X-405. The best set of parameters we could find is χCO ) 1.6, χCW ) 1.65, and χWO ) -0.4 for the CO, the CW, and the WO contacts, respectively. The theoretical values obtained for the cmc are 4 × 10-4 (Triton X-100) and 5.3 × 10-4 (Triton X-405). The order of magnitude for these cmc’s is the same as for the experimental ones. This choice of parameters gives the headgroups enough hydrophilic properties to have a stopping mechanism for self-assembly. Therefore, thermodynamically stable micelles are present in the system. In agreement with experimental results, we found that the cmc increases slightly with increasing length of the poly(oxyethylene) headgroup. The interaction parameters between segments and surface will be our fitting parameters. They must explain the experimental adsorption results for both Triton X-100 and Triton X-405 chains. If a completely hydrophobic surface is considered, hydrophilic segments should not be adsorbed, so χOS ) 0 and χWS ) 0 for the O-surface and W-surface contacts, respectively. We studied the effect of increasing attraction between surface and hydrophobic segments which means more negative values for χCS. Theoretical results for Triton X-100 and Triton X-405 are presented in Figure 2a,b for a range of χCS values, in combination with the experimental data. To compare the theoretical and experimental results, data have been rescaled. The adsorbed amount has been translated from the number of moles per unit surface area (Γ) to the excess amount of chains per surface site (nexc)

Figure 2. Adsorption isotherms for Triton X-100 (a) and Triton X-405 (b) on a hydrophobic surface. Experimental results for latex (b) are shown. Theoretical results: χCS ) -3 (short dash), χCS ) -6 (dash), χCS ) -9 (dot), χCS ) -12 (solid), χCS ) -15 (dash-dot).

by using the following approximation:

nexc ) ΓAsegmentNA

(5)

where Asegment is the segment area or the area of a lattice site of length l. As discussed before, in this work we have chosen a segment size of 0.3 nm and a fcc lattice for which Asegment ) (6λ1)1/3l2 with λ1 ) 1/3. The equilibrium surfactant concentration has been translated from molar concentration (Csurfactant) to segment volume fraction (φb) by means of eq 4. Several aspects can be underlined in relation to these results: I. Nonstepwise isotherms are obtained. II. Increasing attraction between surface and hydrophobic segments increases the affinity and the maximum adsorbed amount. However, above certain value for χCS this effect is negligible. In Figure 3, the effect of the chain length on the isotherms is shown. For a fixed χCS, isotherms at low concentration are independent of the chain length. This means that chains are adsorbed through the tail. At higher concentrations, steric repulsion between hydrophilic heads determines that nexcmax for Triton X-100 is always higher than for Triton X-405. The difference between nexcmax for Triton X-100 and Triton X-405 is the same for χCS ) -3 and χCS ) -12. This supports the role of hydrophilic interactions at these concentrations. However, at low concentrations, the effect of the chain length is more important for χCS ) -12. This

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Figure 3. Effect of the chain length on the theoretical isotherms. Triton X-100: χCS ) -3 (solid) and χCS ) -12 (dash). Triton X-405: χCS ) -3 (dot) and χCS ) -12 (dash-dot).

is in agreement with the main role of the hydrophobic interaction in this stage of the adsorption process. In Figures 4 and 5, the effect of χCS on the segment profiles for Triton X-100 and Triton X-405 is presented at low concentrations (a) and at the plateau (b). For Triton X-100 at low concentration (Figure 4a), the total segment profile is affected by a change in χCS. Higher attraction (more negative χCS) leads to a higher number of segments in the layer adjacent to the surface. In the next three layers, the effect of χCS is rather small, but after that a new increase in sensitivity for χCS is found. At the 15th layer, the segment volume fraction in the bulk is reached. The number of hydrophilic segments in the first layer decreases when χCS is made more negative. At the plateau (Figure 4b), the effect of χCS is less


important, but still higher attraction leads to a higher number of segments in the first layer. The segment distribution is more extended at this concentration. For Triton X-405 at low concentrations (Figure 5a), the effect of χCS in the first layer is the same as for Triton X-100. In addition, a less flat chain distribution and a rise in the number of hydrophilic segments in the second layer are found. At the plateau (Figure 5b), the effect of χCS is the same as at low concentrations, but for χCS ) -3 the segment distribution is more extended. If we compare Figures 4 and 5, we can see how the molecule size affects the adsorbed surfactant layer. The total segment profile drops more sharply in the first layers for the longer molecule, but at the same time the distribution is more extended. The length of the hydrophilic block thus dominates the total thickness. Despite these reasonable results, they should explain the experimental behavior. In Figure 2b, it is shown that the theoretical isotherm for χCS ) -12 fits the experimental isotherm for Triton X-405, both qualitatively and quantitatively. However, this value cannot explain the more rich behavior of Triton X-100. If polar patches on the surface are taken into account according to the charged groups present on the latex surface, some attraction between hydrophilic segments and surface must be allowed for. In a mean-field picture, where the layers parallel to the surface have constant composition, one can consider such patches only in a very rough manner, for example, by assigning some surface affinity for both the headgroups and the tail segments. Isotherms including this effect are shown in Figure 6a for Triton X-100 and in Figure 6b for Triton X-405. In both cases, this effect is not really important, although this result may be caused by the lateral homogeneity on

Figure 4. Effect of χCS on the segment profiles for Triton X-100 at low concentration (a) and at the plateau (b). χOS ) 0. χCS ) -3: φC(z) (b), φO(z) (2), φ(z) (solid line). χCS ) -9: φC(z) (O), φO(z) (4), φ(z) (dotted line).

Figure 5. Effect of χCS on the segment profiles for Triton X-405 at low concentration (a) and at the plateau (b). χOS ) 0. χCS ) -3: φC(z) (b), φO(z) (2), φ(z) (solid line). χCS ) -9: φC(z) (O), φO(z) (4), φ(z) (dotted line).


Figure 6. Effect of χOS on the isotherm for Triton X-100 (a) and Triton X-405 (b). Experimental results for latex (b) are shown. Theoretical results: χCS ) -12. χOS ) 0 (solid), χSO ) -3 (dash), χSO ) -6 (dot).

assumption in the SCF model. By inspection of the profiles for Triton X-100 (Figure 7), it is found that a more negative χOS leads to the same number of segments in the first layer but to a lower number in the remainder of the profile. In addition, there exists a higher probability for hydrophilic segments to be next to the surface. For Triton X-405 (Figure 8), the effect of χOS is more important. At low concentrations (Figure 8a), increasing O segment-surface attraction leads to a rise in the number of segments (hydrophilic and total segments) in the first layer and to a flatter chain conformation. At the plateau (Figure 8b), the number of segments in the first layer is the same but again, the conformation is flatter for χOS ) -6. None of the parameter sets discussed so far can explain the shape of the Triton X-100 isotherm. The next step

Langmuir, Vol. 18, No. 22, 2002 8711

could be to study the effect of some competition between segments O and C for the surface. This may lead to a small adsorption at the “beginning” of the isotherm through the adsorption of tails, followed by a sharp rise in the adsorbed amount when surfactant concentration is increased. This sharp change is expected because of the adsorption of the headgroup segment that involves both hydrophobic and hydrophilic segments (a monolayer to bilayer transition). This choice indeed gives rise to a stepwise isotherm. When doing so, the best parameters found to fit the experimental results are χOS ) -12 and χCS ) 0.5. However, these parameters are not consistent with the overall hydrophobic nature of the particles. In other words, there is an unrealistic strength by which O is bound to the surface. Our objective is not fitting the experimental isotherms at any cost with whatever set of parameters. Therefore, we also choose a more realistic physical approach. As our surface is made of polystyrene, its nature could be the same or very similar to that of a hydrophobic segment. In this case, the following approximation is very reasonable: χWS ≈ χCW, χCS ≈ 0, χSO ≈ χCO. In Figure 9a,b, adsorption isotherms using this set of parameters for Triton X-100 and Triton X-405 are shown. Despite having a more sound physical meaning, this choice leads to predictions that are far from the experimental results. Perhaps this could be due to the simplified linear model used for the molecule. For this reason, the molecular structure is altered, leading to the second model. Branched Chain Model. Keeping the more physically reasonable set of parameters used above, we decided to improve the chain model. With the aim of simulating a more accurate surfactant structure (eq 1), we designed a branched model. In addition, the higher hydrophobicity of the CH3 group in the molecule, as is known experimentally, is taken into account including two kinds of hydrophobic segments, C and K (more hydrophobic):

where X ) 10 for Triton X-100 and X ) 40 for Triton X-405. We decided to mimic the aromatic ring as two groups of three CH2 segments (the segments in the branches of the ring do not have the same hydrophobic character as the CH3). Extensions of the theory to incorporate branched molecules have been published elsewhere.22 However, the effect of this change in the structure on surfactant

Figure 7. Effect of χOS on the segment profiles for Triton X-100 at low concentration (a) and at the plateau (b). χCS ) -9. χOS ) 0: φC(z) (b), φO(z) (2), φ(z) (solid line). χOS ) -6: φC(z) (O), φO(z) (4), φ(z) (dotted line).

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Figure 8. Effect of χOS on the segment profiles for Triton X-405 at low concentration (a) and at the plateau (b). χCS ) -9. χOS ) 0: φC(z) (b), φO(z) (2), φ(z) (solid line). χOS ) -6: φC(z) (O), φO(z) (4), φ(z) (dotted line).

Figure 9. Approximation of the surface as hydrophobic segments: isotherms for Triton X-100 (a) and Triton X-405 (b). Experimental results for latex (b) are shown. Theoretical results: χCS ) 0, χOS ) 1.6, χSW ) 1.65 (solid); χCS ) -0.1, χOS ) 1.6, χSW ) 1.65 (dash); χCS ) 0, χOS ) 1.5, χSW ) 1.55 (dot).

properties such as cmc or adsorption on surfaces has not been studied in depth. If we calculate the cmc for our surfactants with the branched design using the same set of interaction parameters as with the linear one, results are different. Therefore, we need a new set of parameters to obtain theoretical cmc’s for the branched model close to the experimental ones for Triton X-100 and Triton X-405. The best set of parameters found was χCO ) 1.6, χCW ) 1.4, χWO ) -0.5, χKC ) 0.5, χKO ) 1.65, and χKW ) -0.5. The theoretical values obtained were cmc(Triton X-100) ) 1.25 × 10-4 and cmc(Triton X-405) ) 1.29 × 10-3.

Figure 10. Segment density distributions through a cross section of a globular micelle of Triton X-100 (a) and Triton X-405 (b). Branched chain: Triton molecule (-b-), CH3 (- -b- -), O (‚ ‚b‚ ‚). Linear chain: Triton molecule (solid line), CH3 (dashed line), O (dotted line).

If we compare these results with the experimental ones, we can see that the branched chain is closer to the reality than the linear one including the two kinds of hydrophobic segments:

K3C2K2C7-(OC2)X-O

(7)

where X ) 10 for Triton X-100 and X ) 40 for Triton X-405. In Figure 10a,b, the effect of the molecule design on the radial density profile for the micelle at the cmc is shown for Triton X-100 and Triton X-405. First, these profiles correspond to those of a typical micelle in water formed by a hydrophobic core decorated


by hydrophilic segments in the corona. The water present in the interior of the micelle is an artifact due to the poor model for the solvent.13 The total segment profile for both Triton X-100 and Triton X-405 is only weakly affected by the change of design. However, a higher density of CH3 segments is found in the core with the more compact branched model. The hydrophobic core of the micelles formed by the small surfactant is much bigger than the one formed by the larger Triton due to the increase in the steric hindrance between the headgroups.13 The larger size of the hydrophilic head in Triton X-405 makes the segment profile more extended, especially in the hydrophilic corona regime. Using the same set of parameters, we can see the effect of the molecule design on the theoretical adsorption isotherms for Triton X-100 and Triton X-405 (Figure 11a,b). Indeed, the theoretical results still do not fit the experimental isotherms. However, some important aspects must be noted: I. The effect of the molecule design is significant both qualitatively and quantitatively on the adsorption behavior, especially for the smaller surfactant. II. The isotherm shapes are closer to the real ones for the branched chains. A step isotherm for Triton X-100 is possible with this model, and at the same time it can explain the more gradual increase for Triton X-405. There is a “condensation” loop at concentrations above the cmc for the smaller surfactant (not indicated in Figure 11a). This means that the theory will predict a monolayer coverage, but just at a surfactant concentration that is too high. As the Triton molecules have a relatively large hydrophilic head, it is possible that the surfactant prefers to form aggregates on the surface instead of homogeneous layers. This may explain in part why the theory with reasonable interaction parameters still gives poor predictions. It is possible to apply a 2D-SCF theory to study the adsorption of these branched small surfactants, and this will enable us to study the inhomogeneous adsorbed layer. Then also a more systematic study is possible on the effect of the hydrophilic patches along a predominantly hydrophobic surface. We believe that a model with realistic interaction parameters must be complemented with these effects before a match with experiments is possible. Work along this line is in progress. Conclusions The adsorption of nonionic surfactants on a hydrophobic surface was studied both experimentally and theoretically. The self-consistent-field theory of Scheutjens and Fleer was applied in the adsorption and the micellization process for two chains with the same hydrophobic tail and different headgroup lengths. A comparison with experimental results for Triton X-100 and Triton X-405 was performed. Effects of the molecule size on the adsorption isotherms, segment density profiles at low and plateau concentrations, cmc determination, and micelle profiles found theoretically are in agreement with the experimental behavior of these surfactants. A more realistic design of the molecule including a branched tail leads to important changes in micellization and adsorption processes for these molecules. Although

Langmuir, Vol. 18, No. 22, 2002 8713

Figure 11. Effect of the molecule design on the adsorption isotherm for Triton X-100 (a) and Triton X-405 (b). Experimental results for latex (b) are shown. Theoretical results: χCS ) 0, χKS ) 0, χOS ) 1.6, χSW ) 1.4, χCO ) 1.6, χCW ) 1.4, χWO ) -0.5, χKC ) 0.5, χKO ) 1.65, χKW ) 2.5. Branched chain (solid line), linear chain (dotted line).

the results do not fit the experimental data, the branched model makes the isotherms qualitatively better than those for the linear model. It is still necessary to improve the model. More realistic surface structures must be considered. It was shown that making some hydrophilic contributions to the surface did not affect the isotherms much. However, in that case the layers were still assumed to be laterally homogeneous. If lateral inhomogeneity is allowed for, hydrophilic patches modeling polar groups on the surface can be studied. This more physically realistic system will be studied in a future work. As discussed above, inhomogeneous adsorption could be expected for our surfactants due to their large headgroups. Research on the possible formation of aggregates on the surface in the branched case is in process. It is expected that only a complete model will give reasonable correspondence with experimental data. Only then will the interaction parameters of the model give true information on the system. Acknowledgment. Financial support from “Comisioń Interministerial de Ciencia y Tecnologıá” Project MAT2001-2843-C02-01 is gratefully acknowledged. Ana Beleń Jo´dar Reyes thanks the Spanish Ministry of Education, Culture and Sport for supporting her research at the University of Granada. LA025954C

Modeling the Effect of Structural Details of Nonionic Surfactants on

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