+
+
2418
Langmuir 1996, 12, 2418-2424
Atomistic Simulation of Overbased Detergent Inverse Micelles J. A. Griffiths and D. M. Heyes* Department of Chemistry, University of Surrey, Guildford GU2 5XH, U.K. Received September 29, 1995. In Final Form: January 24, 1996X We describe the results of atomistic simulations of oil-soluble micelles containing a calcium carbonate core, stabilized by either sulfonate or phenate surfactant molecules. Strong Coulombic forces between the ions provide the driving mechanism for the model Ca2+, CO32-, and surfactant molecules to arrange themselves into an inverse micelle structure, with the calcium carbonate in the core and the surfactant anions forming a stabilizing shell around this core. In contrast to conventional water-containing inverse micelles, these structures are quite rigid and show negligible fluctuation in shape with time. They are also relatively insensitive to temperature, explaining their effectiveness at elevated temperatures (∼650 K in engine oil) as slow release acid neutralizers and the ease with which they can be extracted from oil and subsequently redispersed. The shape and properties of the micelles are largely determined by the geometry of the individual surfactant molecules. The sulfonates consist of single alkyl chains, and the phenates, of double alkyl chains joined via sulfur-bridged aryl moieties. Structurally and dynamically the two classes are quite different. Simulations carried out in vacuo and in hydrophobic solvent show the sulfonate systems are spherical, whereas the phenate surfactants self-assemble into more rigid diskshaped structures. The phenate micelles swell out to a certain extent when ‘soaked’ with a model hydrophobic solvent, enabling the alkyl chains to be more effective at covering the carbonate core. This arises from penetration of the solvent molecules in between the phenate alkyl chains, which open out.
1. Introduction Overbased detergents are added to engine lubricants to neutralize corrosive acid byproducts produced by the combustion process. They are particularly important in marine applications, where the fuel typically has a high sulfur content. The additive is formed by carbonation of a mixture of lime in the presence of a surfactant, with sulfonates and phenates being the most widely used surfactants. The term ‘overbased’ refers to the fact that there is calcium carbonate associated with the surfactant to varying levels of nonstoichiometric excess. There is considerable experimental evidence (e.g., from neutron scattering) that calcium carbonate and the surfactant form an inverse micellar structure.1-5 The carbonate is surrounded by a layer of detergent molecules, enabling the carbonate to be soluble in oil. However, in general these systems are not easy to investigate experimentally, as they are dark viscous liquids. The usual investigative procedure is first to extract the active component from the base oil as a powder and then redisperse it in a clear organic solvent (e.g., toluene) in a dilute form.6 However, none of these experiments have been able to provide a detailed atomistic description of the construction of the micelles which would have the resolution to compare micelles formed with different surfactant types. As dynamic atomistic simulation using the molecular dynamics method can provide this information, we have carried out simulations of two commercially important classes of surfactant molecules, i.e., sulfonates and phe* To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +44 1483 259580. Fax: +44 1483 259514. X Abstract published in Advance ACS Abstracts, April 1, 1996. (1) Markovic, I.; Ottewill, R. H.; Cebula, D. J.; Field, I.; Marsh, J. F. Colloid Polym. Sci. 1984, 262, 648. (2) Markovic, I.; Ottewill, R. H. Colloid Polym. Sci. 1986, 264, 65. (3) Markovic, I.; Ottewill, R. H. Colloid Polym. Sci. 1986, 264, 454. (4) Mansot, J. L.; Martin, J. B. J. Microsc. Spectrosc. Electron. 1989, 14, 78. (5) Mansot, J. L.; Allouis, M.; Martin, J. B. Colloids Surf. 1992, 66, 197. (6) O’Sullivan, T. P.; Vickers, M. E.; Heenan, R. K. J. Appl. Crystallogr. 1991, 24, 732.
nates, in order to discover the relationship between chemical composition and micelle structure. Molecular dynamics, MD, atomistic simulation was first applied to organic molecules by Ryckaert and Bellemans,7 who modeled liquid n-butane. Since then the technique has been extended to consider a wide range of selfassembling surfactant systems, including e.g., Langmuir monolayers8,9 and micelles.10,11 In solution, surfactant molecules self-assemble into micelles, the shape of which depends on the chemical nature of the surfactant and the solvent. Aqueous micelles can be spherical, disk-shaped, or rod-like, depending on the counterion and chemistry of the surfactant head-group and tail. These factors can be combined and rationalized in terms of an effective shape for the surfactant-counterion pair described by a packing parameter, p ) v/a0lc, where v is the volume of the hydrocarbon tail of extended length, lc, and a0 is the area of the head-group. The packing parameter can be used to predict the likely aggregate shape: p < 1/3 for spherical micelles, 1/3 > p < 1/2 for rod-shaped micelles, 1/2 < p < 1 for bilayers, and p > 1 for inverse micelles. For the surfactant molecules considered here, calcium sulfonate, Ca(sulph)2 and calcium phenate, CaPhe, the packing parameter p > 1, and therefore we expect these detergent molecules to form an inverse micelle, which is confirmed by our simulations. Molecular dynamics simulations to date of regular micellar structures have concentrated on aqueous systems, a common system being that formed using sodium octanoate.10,11 The simulations have shown that the micelles are stable and quite disorganized in the core, undergoing major fluctuations in shape over a ∼100 ps time scale. There is significant penetration of the solvent in the head-group region. In contrast to the traditional view of a micelle, only a small fraction of the chains were found in the all-trans conformation; the gauche vs trans (7) Ryckaert, J. P.; Bellemans, A. Chem. Phys. Lett. 1975, 30, 123. (8) Karaborni, S. Langmuir 1993, 9, 1334. (9) Collazo, N.; Shin, S.; Rice, S. A. J. Chem. Phys. 1992, 96, 4735. (10) Jonsson, B.; Edholm, O.; Teleman, O. J. Chem. Phys. 1986, 85, 2259. (11) Watanabe, K.; Ferrario, M.; Klein, M. L. J. Phys. Chem. 1988, 92, 819.
+
+
Overbased Detergent Inverse Micelles
ratio was statistically the same as for the gas phase molecules. Therefore the cores are highly disordered and amorphous. These simulations showed that the percentage of trans conformations in the alkyl chain upon micellization was hardly different compared to that of the isolated molecule in the gas phase. As far as we are aware, the only atomistic simulation study of inverse micelles in an apolar solvent has been performed by Brown and Clarke.12 These authors modeled a core of water molecules and ions surrounded by a surfactant coat, itself in a spherical cavity containing some discrete single-center aprotic solvent molecules. The surfactant molecule was represented by two interaction sites, a cationic head-group and a hydrophobic tail. The inverse micelle structure was found to be stable over a ca. 100 ps simulation, with some fluctuation about the spherical average shape. They found a concentration of anions, head-groups, and water molecules in the same radius range from the center of the cavity, indicating a significant level of internal order within the center of the micelle. The water molecules were orientationally highly ordered in the boundary region between the core and the hydrophobic region. Some penetration of the water molecules into the hydrophobic region was also observed. In a previous work we carried out an experimental characterization of the phenate systems we model below.13 The overbased detergent inverse micelles encountered in lubricating oils are chemically quite different from those normally considered, in which the core is predominantly water. With the overbased detergents, the core is made up of calcium carbonate with no detectable water. The CaCO3 molecules interact more strongly with themselves than with water, and at the temperatures of interest (ca. 100 °C), the core is an amorphous solid.3 It is reasonable to assume therefore that the structure of the core and surfactant coat is much less mobile than for the watercontaining systems and is governed by enthalpic considerations arising from the Coulombic interactions within the micelle rather than by issues of hydrophobicity and entropy which are normally invoked. This class of inverse micelles has not been considered before by atomistic simulation. In this study we have performed molecular dynamics simulations based on two important-types of commercial detergent. We consider sulfonate detergents, which are predominantly straight single-chain molecules. For each Ca(sulp)2 molecule there are two unattached alkyl chains. We also have investigated double-chain sulfur-bridged phenate surfactants with calcium counterions (CaPhe). In the phenate the two alkyl chains originate from the same aryl head-group, whereas in the sulfonate the two alkyl chains come from separate aryl head-groups. We are interested in the influence of the surfactant type on the assembled microscopic structure. These inverse micelles are quite small compared with conventional colloidal systems (2.5 nm vs ∼100 nm, respectively), and the effect of curvature and the geometrical features of the surfactant molecules is likely to be more important. It is thought that branched alkyl chains are more effective at forming a compact stabilizing shell, as they fill space more efficiently. An alternative explanation was given by Ruckenstein,14 who suggested that nonaqueous dispersions are better stabilized by branched-chain surfactants with two chains per molecule, because these form more open structures which can be filled with the liquid medium. The Hamaker constant of the shell then tends more to that of the solvent, reducing the attraction between cores. (12) Brown, D.; Clarke, J. H. R. J. Phys. Chem. 1988, 92, 2881. (13) Griffiths, J. A.; Bolton, R.; Heyes, D. M.; Clint, J. H.; Taylor, S. E. J. Chem. Soc., Faraday Trans. 1995, 91, 687. (14) Ruckenstein, E. Colloids Surf. 1993, 69, 271.
Langmuir, Vol. 12, No. 10, 1996 2419
We give simulation evidence below for solvent penetration and restructuring of the surfactant coats for the phenate. 2. Computational Details Atomistic simulations were carried out using a commercial software package. Three types of simulation, increasing in complexity, were carried out: (i) Construct the single surfactant molecule, investigating the effect of chain length and level of branching. (ii) The inverse micelles were constructed in vacuo using numbers of surfactant and CaCO3 molecules corresponding to samples synthesized in the laboratory.13 (iii) Several simulations were carried out of a micelle in a model hydrophobic (nhexane) solvent, which is the normal environment for these particles. All simulations were performed on a Silicon Graphics IRIS INDIGO XZ4000 workstation using the BIOSYM modules INSIGHTII and DISCOVER(2.9). InsightII is a graphics-based molecular modeling program. Used in conjunction with the molecular mechanics/dynamics package DISCOVER, model molecules can be built and simulated at the atomistic level. Molecular mechanics was used to minimize the energy of the molecules and to approach the global minimum energy state. Molecular dynamics was then performed on these molecules for a period until they reached dynamic equilibrium. Both techniques treat the molecules as a collection of interaction centers (‘atoms’) held together by parameterized intramolecular forces used to represent the bonds between atoms and the van der Waals forces between nonbonded atoms. Within the MD simulation the molecules adjust their conformations to optimize the bond lengths and angles to achieve a near ‘minimum energy’ least strained structure, attained by a compromise minimum distortion. The force field is the sum of the various contributions derived from a potential. The force field used was the all-atom ‘constant valence force field’, which includes explicit hydrogens. The total energy is a sum of the intramolecular and intermolecular interactions. The intramolecular interactions are given in eq 1,
Eintra )
∑E
stretch
+
∑E
bend
+
∑E
torsion
+
∑E
out-of-plane
(1)
There are explicit forms for each term in eq 1, which are given in eqs 2-5. The bond stretching term is given by eq 2,
Estretch )
∑k (b - b )
2
b
0
(2)
where kb is the bond stretching force constant, b0 is the equilibrium bond length, and b is the optimum (minimum energy) bond length. The bond bending term is given by eq 3,
Ebend )
∑k (θ - θ )
2
0
θ
(3)
where kθ is the bond bending force constant, θ0 is the equilibrium bond angle, and θ is the actual bond angle. The torsional contribution to the intramolecular energy is represented by a cosine series (eq 4),
Etorsion )
∑k (1 + S cos(nφ)) φ
(4)
where kφ is the torsional force constant, S is a phase factor, n is the periodicity, and φ is the torsion angle. The out-of-plane term describes the resistance to out-of-plane bending and is expressed by a quadratic distortion potential function,
Eout-of-plane )
∑k χ
2
χ
(5)
The general expression for the nonbonded interactions is given in eq 6,
Einter )
∑E
vdw
+
∑E
Coulombic
(6)
The Lennard-Jones (12-6) pair interaction is used for the van der Waals energy, Evdw, and Coulombic terms involve partial and full point charges.
+
2420
+
Langmuir, Vol. 12, No. 10, 1996
Figure 1. Branched-chain phenate molecule used in the single calcium phenate molecule simulations. A computer-generated structure showing a representative conformation is shown.
Griffiths and Heyes
Figure 2. Total energy vs number of carbon atoms in each chain for the straight chain (A) and branched chain (B) phenate molecules.
3. Results and Discussion Several distinct classes of simulation were carried out. 3.1. Isolated Molecules. The structure and dynamics of the individual surfactant molecules are of some interest because they form the building units for the self-assembled structures. Although in the real systems the chains are branched, some of our simulations were performed on straight chain model surfactants, as useful reference systems, to assess the effect of the level of branching on the molecule’s structure. A series of model molecules was constructed in vacuo using this package. First a model calcium methyl phenate molecule was prepared and equilibrated. Then the chain length was extended in the sequence n-C2H5, n-C3H7, and so on, while monitoring the properties of the molecule at each step. The molecules were constructed in stages by adding a methyl group to both alkyl chains each time using INSIGHTII. The structure was energy minimized at 0 K for each stage in the construction process using molecular mechanics. Molecular dynamics simulations using the DISCOVER program were then performed at 300 K on these optimized structures to thermalize the molecules and prepare a state closer to that of the molecule in its working environment. Each additional methylene group was equilibrated for ca. 20 ps. Simulations for each molecule at each stage in the ‘growth’ path typically required several hours of computational time. In Figure 1 we show the structure for the branchedchain calcium phenate molecule we considered for most of our studies. A comparison between the chain length dependence of the total energy of the reference straight chain system and that of the branched structure is given in Figure 2. Increasingly above C4 the two curves deviate, with the branched structure having a more positive energy. As noted previously13 a straight chain length of C8 marks the onset of a departure in the relative chain orientations, which is reflected as a ‘kink’ in the total energy plot. This also occurs for the branched chain, but at one total carbon number higher (i.e., C9). The corresponding backbone chain length is C6, which is consistent with the enhanced steric repulsion between the chains arising from the sidegroup methyls. The branched alkyl chains are ‘driven’ apart at lower backbone carbon numbers than for the straight chain cases. Computer generated structures show that the alkyl chains in both the straight and branched molecules bend over increasingly with chain length, with a tendency for the chains to be directed away from their original axis formed through the para positions of the phenyl ring. The straight chains are more effective in
Figure 3. Ball and stick computer-generated structures showing a representative conformation adopted by a C18 sulfonate molecule. Note that there are two sulfonate chains per calcium in the molecule.
extending through space in this manner than the more compact branched structures. Figure 3 shows the comparable figure for the sulfonate systems. The energy vs chain length for the sulfonate surfactant types is almost linear, without a discontinuity of slope at ca. C8 as we observed for the phenate. Although the longer chains do have a statistical distribution of gauche defects, they are not associated with a release of strain energy, as is the case for the phenates. The two chains in the sulfonate molecule are as far apart as they can get and therefore have little interaction with each other. Therefore the sulfonates experience no great steric energy penalty growing beyond ca. C8, as the two alkyl chains are unattached. In contrast, for the phenates, the two alkyl chains are chemically connected via the sulfur bridge. The molecule undergoes a structural transformation at ca. C8, which we suggest has implications for the structure of the assembled micelle. 3.2. Overbased Clusters In Vacuo. The clustering of the branched phenate surfactant molecules with calcium carbonate molecules was investigated. From experimental work13 the relative number of calcium carbonate and
+
+
Overbased Detergent Inverse Micelles
Langmuir, Vol. 12, No. 10, 1996 2421
Table 1. Cluster Characteristics Determined by Experiment and Molecular Simulationsa cluster
n(CaCO3)
n(CaPhe)
a / dcore nm
a dtotal / nm
b dcore / nm
b dtotal / nm
I II III
2 10 16
2 6 8
0.59 1.05 1.25
2.49 2.95 3.15
0.61 1.03 1.26
1.85 2.85 2.90
a The number, n, of each species in the cluster is given. The core and total diameters, d, from Langmuir trough experiment (a) and simulation (b) are also presented. The simulation diameters are based on their maximum area projections. The area of cluster type I was based on a triangular representation, and those of types II and III on disks. Simulation diameters have estimated uncertainties of (0.03 nm.
surfactant molecules for particular levels of overbasing has been determined, and these are given in Table 1. We have simulated many clusters but analyze in particular detail examples I, II, and III with increasing base content, which corresponds to those we synthesized in our previous work.13 The number of each species in clusters I, II, and III is given in the table, and these were used in the simulations. The simulation procedure was to add one molecule at a time, at an unbiased starting position some way from the cluster, and then equilibrate this new structure. Additional molecules were added until the correct ratios of carbonate to phenate moieties were achieved for a desired class of particle. We found that not only did the predetermined ratios of clusters I, II, and III lead to stable structures but ratios differing from these specified values were also stable. Therefore there are no ‘magic’ numbers of building components for this class of cluster, as there are for noble gas clusters, for example.15 The accumulated simulation time for cluster III was in excess of 1000 ps. The micelles formed without any biased positioning of the units. The structures adopted we were quite rigid and extremely stable over a wide temperature range, 0-700 K, well within engine operating temperatures. Unlike the individual surfactant molecules, the geometry of these clusters hardly changes with time and was found to be insensitive to temperature within the studied range. There was negligible fluctuation of the assembly over the simulation, except some small oscillations within the tails of the alkyl chains. The coherence of the structure is caused by a combination of strong Coulombic forces in and around the carbonate core, binding the species together, and steric hindrance imposed by the proximity of neighboring alkyl chains, ‘wedging’ the surfactant molecules together. The alkyl chains are more immobile, even for the open phenate structure I (shown in Figure 4) because the surfactant chains associate over only part of the cluster. Therefore, locally they are sterically hindered. The structure of cluster I does not conform to the average spherical geometry normally associated with inverse micelles. This is to be expected, as there are not enough surfactant molecules present to achieve a complete coat. The alky chains tend to associate over only part of the surface of the core. A cluster of type II has a higher carbonate/phenate ratio, and as the cluster is allowed to self-assemble, it forms a nonspherical shape, which is quite flat and discus shaped. The carbonate is in the core, and the surfactant forms a shell around it. If these structures are present in an oil, it would imply that the core is significantly exposed to the solvent on two sides of the micelle. Interestingly, some of the chains project out of the plane of the cluster, presumably owing to steric constraints within the ‘equatorial’ plane of the micelle. Figure 5 shows a cluster of type III, which is similar to type II except that the phenate molecules are more tightly (15) Wales, D. J.; Berry, R. S. J. Chem. Phys. 1990, 92, 4283.
Figure 4. Ball and stick projections of typical conformations adopted by cluster I (2CaPhe and 2CaCO3) during the simulation.
Figure 5. As for Figure 4, except that structure III (8CaPhe and 16CaCO3) is shown. Two orthogonal projections are shown in parts a and b, illustrating the flat discus shape of the cluster. Note the alkyl chains projecting out of the equatorial plane of the cluster.
packed around the equator of the cluster. There is a greater tendency for the chains to extend over the exposed
+
2422
+
Langmuir, Vol. 12, No. 10, 1996
Figure 6. Sulfonate cluster (3Ca(C18H37SO3)2 and 3CaCO3) similar to phenate cluster I shown in Figure 4.
Figure 7. Sulfonate cluster (6Ca(C18H37SO3)2 and 10CaCO3) analoguous to phenate cluster II, represented as a space-filled structure.
part of the core (where there is considerable free space), providing more protection for the inorganic species from any solvent. Sulfonate cluster calculations were carried out as for the phenates, by adding carbonate and surfactant molecules in the same ratio as for the phenates. Figure 6 shows a cluster with the same stoichiometry as the phenate cluster I (Figure 4). There is a marked difference between the two: the phenate cluster is wedge shaped with a rather exposed carbonate core (see Figure 4), whereas the sulfonate cluster shows evidence of more complete coverage of the carbonate core. We ascribe this difference to the fact that the aryl rings are not joined together in the sulfonate, so that there is greater freedom for the detergent molecules to organize into a more spherical shape. This trend continues up to the sulfonate equivalent of the phenate cluster II, shown in a space-filled representation in Figure 7. The sulfonate alkyl chains are longer than those of the phenates, and they are better at bending over and covering the core. (Typical commercial sulfonate systems consist of highly branched chains between C15 and C36 chain length.) Core diameters of 2.2 and 6.7 nm have been obtained for the sulfonates, and a shell thickness of 1.9 nm was derived.1-3 These are larger than the phenate particles. With the benefit of these simulations, we can speculate that this arises from the difference in
Griffiths and Heyes
geometries between the sulfonate and phenate molecules. The phenate molecule is a wedge-shaped surfactant (such as sodium bis(2-ethylhexyl)sulfosuccinate (AOT)), which naturally forms an inverse micelle, and has an upper limit to its size. In contrast the sulfonate molecule is a conventional straight chain surfactant which can form larger particles. The cluster core and total diameters are known from previous Langmuir trough measurements.13 We estimated the equivalent sphere radii for the computed clusters from the maximum area projections. As the extent of overbasing increases, the clusters swell in size. For clusters II and III a disk projection was used. For type I a triangle was ascribed to the cluster because of the small number of molecules in this case. The agreement between experiment and simulation is very good, as shown in Table 1, especially for type II and III clusters. However, this could be fortuitous, as these clusters are certainly not spheres, which is assumed in interpreting the Langmuir trough data. However, in the absence of any ordered liquid crystalline arrangement on the water surface, it is likely that the clusters are randomly orientated, and therefore it is reasonable to ascribe an average particle diameter to these particles. Also the water environment on the trough is markedly different from that in which these clusters are normally found, i.e., in a bulk hydrophobic medium. Indeed, previous neutron scattering of these phenates has shown that they are smaller on the trough surface than in a hydrophobic solvent.16 As the ratio of the number of carbonate to phenate molecules, n(CaCO3)/n(CaPhe), increases (through type II to type III), the shape of the cluster does not change significantly. The number of carbonate molecules and phenate molecules increases, with the calcium phenate molecules tending to fill in the free space between the other surfactant molecules. In addition, the core is covered better in type III than type II, with the chains extending to a greater extent out of the equatorial plane of the cluster, covering to a greater extent the exposed cores. Figure 8 shows the total energy of an individual cluster for a range of phenate clusters with different base content. (Examples I, II, and III are annotated on the figure.) In Figure 8a we show the energy per molecule in the cluster (not discriminating between CaCO3 and CaPhe), and in Figure 8b we show the total energy per CaPhe molecule in the cluster. On these figures we present the computed total energy of the cluster and the predicted energy of the cluster on the basis of a sum of the energies of the isolated component molecules. An individual calcium carbonate molecule has an energy of -2134 kJ mol-1, and CaPhe has an energy of -1556 kJ mol-1. From left to right on the figures the relative proportion of carbonate increases, so the energy per molecule (Figure 8a) becomes more negative but is bounded by these two limiting values, going from that of the phenate molecule to that of the carbonate molecule. The two curves show the same qualitative trend and intersect at a ratio of ca. 0.8, which is overbased to an extent below that of the type I cluster. For higher relative carbonate content (which corresponds to all the synthesized examples in ref 13) the computed energies are more negative than predicted on a per molecule additive basis (the other curve). This indicates that (largely Coulombic) interactions between molecules of the same type and interactions between molecules of different type lead to an overall more energetically stable structure. The maximum difference is -161, -358, and -360 kJ mol-1 per carbonate for the type I, II, and III clusters. On a per cluster basis this corresponds to -322, -3580, and -5760 kJ mol-1 more negative energies. (16) Clint, J. H.; Taylor, S. E. Colloids Surface 1992, 65, 61.
+
Overbased Detergent Inverse Micelles
+
Langmuir, Vol. 12, No. 10, 1996 2423
Figure 8. Average computed total energy for various sized clusters. Key: (crosses) computed cluster energies; (diamonds) energies computed from the individual molecules summed up. The clusters I-III considered for special attention in the text are indicated on the figure. Part a shows the total energy of the cluster per molecule, not discriminating between carbonate or phenate, and part b shows the total energy per phenate molecule in the cluster. In both cases the energies are plotted against the ratio of the number of carbonate molecules in the cluster divided by the number of phenate molecules in the cluster.
For these overbased micelles, the Coulomb ‘enthalpic’ contribution to the Gibbs free energy far exceeds the ‘entropic’ contribution from the association of the surfactant molecules. Therefore there is an ‘enthalpic’ driving force to cluster formation which overrides the unfavorable entropic decrease arising from association of the individual molecules (which is also present for aqueous-based inverse micelles). The clusters with the carbonate/phenate ratio of type I and higher are more thermodynamically stable than the sum total of their individual components. Figure 8b shows the energy per phenate, which becomes more negative as the relative carbonate content increases. The lowest carbonate/phenate system considered ()0.5) corresponds to two phenates to one carbonate. The indication is that this cluster is not thermodynamically stable on the basis of our enthalpic interpretation. In the 1:1 case, we considered two clusters that had the same carbonate/ phenate ratio (two phenates and carbonates, and four phenates and carbonates, respectively). These gave the same energy per carbonate, within the simulation statistical uncertainty, which is ca. the size of the symbols on the figures. Therefore there appears to be a minimal system size effect here. We constructed sulfonate clusters compositionally very close to those of the phenates. Although commercial sulfonates tend to have a somewhat larger core, the chain lengths used in the simulations, C18, are close to those of the real surfactants. We have calculated the sulfonate cluster energies as a function of composition, as for the phenates of Figure 8. An individual Ca(sulph)2 molecule has an energy of -282 kJ mol-1. In the latter case, the
Figure 9. Ball and stick cluster structure surrounded by solvent molecules. Key: (a) cluster II side view (solvent not shown); (b) same projection as in part a but only showing the solvent molecules.
surfactant has a more positive energy than the phenate, largely attributable to the longer chain length (C18 vs C12 in the case of the phenate). It is not so much the absolute energy for the individual molecules that is important (these energies are not trivially related to thermodynamic energies and will depend on the model adopted) but whether these molecules assembled into a cluster have a more negative energy than the sum total of their individual molecules. This difference in energy is the Gibbs free
+
2424
+
Langmuir, Vol. 12, No. 10, 1996
Griffiths and Heyes
Figure 10. Color photographs of space-filled representations of phenate cluster type II. Key (in vacuo): (a, left) down view, with the calcium carbonate molecules in the center; (b, center) side-on perspective; (c, right) side-on perspective in a generic hydrophobic solvent.
energy of formation of the cluster from the component molecules. The energy per sulfonate is more negative than predicted on the summation of the component molecules, as was the case for the phenates. The two curves show the same trends and intersect at a ratio of ∼0.25 (cf. phenates 0.8), which would correspond to four sulfonate molecules and one calcium carbonate molecule. As the sulfonate head-groups are not attached to each other, they can more readily form a stable (negative energy) structure than the phenates, in which the two Oatoms are constrained to fixed distances from each other. 3.3. Overbased Clusters in Hydrophobic Solvent. All simulations up to this point were performed in vacuo. While these simulations are of interest in their own right, e.g., as the powdered carbonated detergent is of experimental interest,13 they are found in commercial applications dispersed in a paraffinic solvent (consisting mainly of C12 straight chains). In order to obtain some indications of the effect of a solvent on the micelle structures, simulations on a type II model phenate micelle, surrounded by a cluster of solvent molecules were carried out. (Computational limitations prevented us from adopting a more complete representation of the solvent.) Model n-hexane was employed as the solvent, which was considered to be a reasonable compromise. It is doubtful whether the cluster is significantly influenced by the long chain nature of the solvent molecules beyond n ∼ 6, as the segment interactions with the cluster are probably similar in hexane and, for example, dodecane. (The molecule chosen for the solvent is a liquid at room temperature.) The procedure we adopted was to build a box of these solvent molecules, equilibrate it for 100 ps by MD, and then insert the detergent cluster in a cavity formed in the solvent. In Figure 9 we show the effect of solvent on the structure of the cluster. For clarity, the cluster omitting the solvent molecules is given in Figure 9a and then only the solvent molecules are shown in Figure 9b. In both cases the same projection and ‘snapshot’ are taken. Comparison with the corresponding cluster in a vacuum indicates that the solvent does have a significant effect in opening out the chains so that it presents more of a ‘bow tie’ shape in cross section rather than a discus. The solvent molecules penetrate between the chains of the phenate, swelling that part of the cluster. As a result, the chains bend out of the plane more when compared with the same cluster in vacuo. The carbonate core and aryl part of the
surfactant appear to be largely unaffected by this (although our diagnostic tools were somewhat limited in this respect). The important point here is that the solvent does have some effect on the structure of the cluster. With a more complete solvent ‘soak’ we expect this trend to continue. Nevertheless even in a solvent these clusters are still far from being spherical. The comparable sulfonates are statistically spherical, even in the absence of a hydrophobic solvent. Therefore the natural inclination for the phenate particles is for them to form highly anisotropic particles with large regions of ‘exposed’ carbonate core, which are quite different from those formed from sulfonate surfactants. Figure 10 shows space-filled representations of the type II phenate cluster with and without solvent. 4. Conclusions We have been able to model oil-soluble sulfonate and phenate micelles containing a calcium carbonate core. In contrast to conventional inverse micelles, these structures are relatively insensitive to temperature and show insignificant fluctuations with time. We have no evidence that surfactants with two alkyl chains tend to selfassociate more than single-chain surfactants. However, we have found that the geometry of the surfactant molecule has a pronounced effect on the shape of the micelle which it forms. In vacuo the sulfonates form micelles that are spherical on average over time, with significant ‘bending’ over of the C18 alkyl chains to protect the carbonate core. In contrast, the phenate molecules tend to pack around the carbonate in an ‘equatorial’ plane, giving rise to a discus shape, with large regions of exposed carbonate. The phenate micelles swell out to a certain extent when ‘soaked’ with a model hydrophobic solvent, caused by a penetration of the solvent molecules in between the phenate alkyl chains. They are, nevertheless, still far from being spherical. Acknowledgment. J.A.G. thanks Adibis plc for the provision of a Research Studentship and Dr. J. Crawford and Dr. A. Psaila (Adibis, Redhill, U.K.) for useful discussions. Dr. P. J. Mitchell is thanked for invaluable technical assistance carrying out the molecular simulations. LA950816R
