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Articles Surface and Aggregation Behavior of Aqueous Solutions of Ru(II) Metallosurfactants: 4. Effect of Chain Number and Orientation on the Aggregation of [Ru(bipy)2(bipy′)]Cl2 Complexes James Bowers,* Katherine E. Amos, and Duncan W. Bruce Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, United Kingdom
Richard K. Heenan ISIS Facility, CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon. OX11 0QX, United Kingdom Received January 27, 2005. In Final Form: March 22, 2005 The structure of aggregates formed by eight surfactant [Ru(bipy)2(p,p′-dialkyl-2,2′-bipy)]Cl2 complexess which we express as RupqCn, where n ()12 or 19) is the alkyl chain length, p ()4 or 5) refers to the substitution position on the bipyridine ligand, and q ()1 or 2) is the number of substituted alkyl chainssin aqueous solutions has been examined using small-angle neutron scattering for a range of concentrations close to the critical micelle concentration and for several combinations of n, p, and q. A number of general results emerge. The double-chain surfactants possess a smaller headgroup charge but a larger aggregate size than their single-chain analogues. Over the concentration range studied, the micelles of the singlechain surfactants grow as the concentration is increased, whereas for the double-chain systems, the aggregate size remains unchanged. For both single- and double-chain surfactants, an increase in alkyl chain length is accompanied by an expected increase in aggregate size and an increase in average headgroup charge. The aggregates formed in solutions of resolved double-chain complexes are larger than those found in solutions of racemic mixtures. The Ru41C12 and Ru51C12 systems form aggregates with high water content. Variation of the substitution position for the single-chain surfactants produces dramatic changes in the structure of the micelles. The aggregates formed in solutions of Ru41C19 and Ru51C19 display particularly different structures. The Ru41C19 system forms essentially spherical aggregates. In contrast, in the Ru51C19 system, wormlike aggregates are formed in which the rigid rodlike sections appear to undergo a transition from a noninterdigitated to an interdigitated structure as the concentration is increased. For double-chain surfactants, the aggregation number for p ) 4 surfactants is considerably larger than that for p ) 5 surfactants.
1. Introduction 1
The use of metallosurfactants in the development of new materials2,3 has encouraged a number of studies of the aggregate and thin-film structures formed by such surfactants.4-8 As mentioned in our earlier work,5-7 metallosurfactants offer a great deal of flexibility in their molecular design since the headgroup size, charge, and * Author to whom correspondence should be addressed. Email:
[email protected]. (1) Donnio, B. Curr. Opin. Colloid Interface Sci. 2002, 7, 371. (2) Romuelda-Torres, G.; Agricole, B.; Mingotaud, C.; Ravaine, S.; Delhaes, P. Langmuir 2003, 19, 4688. (3) Chu, B. W.-K.; Yam, V. W.-W. Inorg. Chem. 2001, 40, 3324. (4) Griffiths, P. C.; Fallis, I. A.; Willcock, D. J.; Paul, A.; Barrie, C. L.; Griffiths, P. M.; Williams, G. M.; King, S. M.; Heenan, R. K.; Go¨rgl, R. Chem. Eur. J. 2004, 10, 2022. (5) Bowers, J.; Danks, M. J.; Bruce, D. W.; Heenan, R. K. Langmuir 2003, 19, 292. (6) Bowers, J.; Danks, M. J.; Bruce, D. W.; Webster, J. R. P. Langmuir 2003, 19, 299. (7) Bowers, J.; Amos, K. E.; Bruce, D. W.; Webster, J. R. P. Langmuir 2005, 21, 1346. (8) Varughese, B.; Chellamma, S.; Lieberman, M. Langmuir 2002, 18, 7964.
architecture can be controlled, as can the length, number, and orientation of the hydrophobic chains. A further option is that resolved enantiomers can be prepared and the effects of chirality studied.9,10 [Ru(bipy)2(p,p′-dialkyl-2,2′bipy)]Cl2 complexes, see Figure 1, are the metallosurfactants considered here and are amenable to such structural variations; the complexes are expressed as RupqCn, where n is the alkyl chain length and p refers to the substitution position on the bipyridine ligand ()4 or 5). For singlechain surfactants, q ) 1, i.e., one of the two alkyl chains is a methyl group, whereas for the double-chain surfactants q ) 2. These complexes are advantageously inert in water. Some of the authors have a special interest in these Ru-based amphiphiles,11 as they have employed them as the surfactant for the production of Ru-doped mesoporous (9) Tamura, K.; Sato, H.; Yamashita, S.; Yamagishi, A.; Yamada, H. J. Phys. Chem. B 2004, 108, 8287. (10) Yashiro, M.; Matsumoto, K.; Yoshikawa, S. Chem. Lett. 1992, 1429. (11) Bruce, D. W.; Holbrey, J. D.; Tajbakhsh A. R.; Tiddy G. J. T. J. Mater. Chem. 1993, 3, 905.
10.1021/la050241q CCC: $30.25 © 2005 American Chemical Society Published on Web 05/17/2005
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Figure 1. Molecular structures for the surfactant cations studied: Ru41C19 (A); Ru51C19 (B); Λ-Ru42C19; (C); ∆-Ru42C19 (D).
silicates12 using a True Liquid Crystal Templating approach.13 On reduction of the nanoparticulate RuO2 produced on calcination, such silicates are hydrogenation catalysts12 whose activity may be greatly enhanced if the conditions of preparation are controlled carefully.14 The as-prepared RuO2-doped materials are also effective oxidation catalysts, for example, in the oxidation of water by acidic CeIV.15 Thus, in addition to ongoing investigations of the lyotropic liquid crystal phase behavior of these materials, there is an inherent interest in investigating their surfactant properties so that we may understand all the factors that influence the use of these materials as porous oxide templates. For related metallosurfactants,5-7 we have reported the structure of micelles formed in aqueous solutions of Ru52Cn surfactants with n ) 12, 15, and 19 and the structure of adsorbed films from aqueous solutions of Ru52Cn with n ) 13 and 19. To conclude this work, we report here the results of small-angle neutron scattering (SANS) experiments examining the effects of variation of p, q, n, and chirality (for q ) 2 surfactants) on the aggregates formed in the aqueous solutions of eight RupqCn metallosurfactants; this work thus builds on our previous work and examines more completely the relationship between the molecular structure of the metallosurfactants and the structure of the aggregates by incorporating a wide range of structural variations. Recently, we have investigated the effect of a similar range of variations on the nature and structure of Gibbs films adsorbed from aqueous solutions of a selection of the surfactants studied here.7 From packing fraction considerations,16 the effects of variation of p, q, and n are not expected to result in any dramatic variation in micelle shape: for q ) 1, spherical micelles are expected; whereas for q ) 2, cylindrical micelles are expected to be produced. However, as we discuss later, such a simple view bears little resemblance to the real structures when the unoccupied volume near (12) Jervis, H. B.; Raimondi, M. E.; Raja, R.; Maschemeyer, T.; Seddon, J. M.; Bruce, D. W. Chem. Commun. 1999, 2031. (13) Attard, G. S.; Glyde J. C.; Go¨ltner, C. Nature (London) 1995, 378, 366. (14) Danks, M. J.; Jervis, H. B.; Nowotny, M.; Zhou, W.; Maschemeyer, T. A.; Bruce, D. W. Catal. Lett. 2002, 82, 95. (15) King, N. C.; Dickson, C.; Zhou, W.; Bruce, D. W. J. Chem. Soc., Dalton Trans. 2005, 1047. (16) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992; Chapter 17.
the headgroup for, in particular, the q ) 1 surfactants and the consequence of variation of substitution position p on both this unoccupied volume and the effective headgroup area is considered. Additionally, for q ) 2 surfactants, the effective headgroup area can be tuned by variation of the surfactant’s chirality. It is these effects that this paper sets out to explore with a view to examining their consequences in terms of the range of shapes and sizes and aggregation numbers of micelles that are produced and which, in turn, may influence the choice of surfactant in future applications. 2. Experimental Section Materials. The complexes were synthesized as described in ref 7 but using protonated 1-bromoundecane and 1-bromooctadecane. The purity of the complexes was checked by 1H NMR spectroscopy and elemental analysis, and the hydration of the product was 2-3 H2O molecules per complex. D2O was obtained from Aldrich (>99.9 atom% D). The mass densities of the complexes,7 given in Table 1, were measured using a Quantachrome micropycnometer. Critical micelle concentrations (cmc) were determined by seeking consistency between the concentration at which the SANS intensity becomes indistinguishable from background and breakpoints in conductivity isotherms plotted as κ/c versus c1/2, where κ is the measured conductivity and c the concentration. The conductivities were measured using a Jenway 4520 conductivity meter. Since the concentrations of the solutions are low, it was necessary to leave the extremely low concentration systems in excess of 1 day before a steady conductivity reading was obtained. Solutions of the metallosurfactants were prepared for the SANS (conductivity) measurements by mass in D2O (H2O), either as stock solutions or as appropriate dilutions of the stock solutions. Warming (∼40 °C) was required to solubilize the Ru42C19 surfactants. In the presence of a protic solvent and light, racemization of the resolved complexes occurs. Accordingly, the vessels containing either the ∆-Ru42C12 or the ∆-Ru42C19 solutions were wrapped in aluminum foil to eliminate light. Appropriate transmission measurements were performed to account for the additional attenuation arising from the foil for the SANS measurements. Small-Angle Neutron Scattering Measurements. SANS is an established method for the determination of the size, shape, and polydispersity of aggregates in solution.17 In a SANS experiment, the intensity of a neutron beam with wavelength λ is measured as a function of momentum transfer, Q, where Q ) |Q| ) |ks - ki| ) 4π sin(θ/2)/λ, θ is the angle between the straight through direction and the scattered direction, and ki and ks are (17) See King, S. M. In Modern Techniques for Polymer Characterisation; Pethrick, R. A., Dawkins, J. V., Eds.; John Wiley and Sons Ltd.: New York, 1999; p 171.
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Table 1. Representative Parameters Resulting from Core-Shell Models with Hayter-Penfold S(Q) Describing Sphericala Aggregates Formed by Aqueous Solutions of Rupq Cn Complexes Close to Their cmc
complex Ru41C12 Ru42C12 ∆-Ru42C12 Ru41C19e Ru42C19 ∆-Ru42C19 Ru52C12f Ru52C19f Ru51C12 Ru51C19 typical uncertainty
cmcb mmol dm-3
mass density, F g cm-3
radius of gyration, Rgc Å
core radius, R Å
shell thickness, t Å
agg no., Nagg
headgroup charge, q/e
water content, β
headgroup area, Ahgd Å2
0.5 0.1 0.3 0.3 0.02 0.03 0.3 0.03 1.0 0.1 -
1.309 1.213 1.195 1.208 1.243 1.19 1.158 1.30 1.251 (0.001
10 16 16 15 27 28.5 8 14.0g (0.5
9.5 14.5 15.0 15.0 26.6 27.5 11.0 22.0 (0.5
10.0 7.0 7.0 9.0 9.5 9.5 7.4 10.2 (0.5
11 23 25 29 80 88 11 50 (2
1.1 0.6 0.55 1.5 0.9 0.8 0.7 1.3 (0.2
0.75 0.50 0.50 0.50 0.50 0.50 0.40 0.50 (0.05
100 115 110 85 110 110 150 120 (5
a See text regarding choice of particle shape. b cmc determined by consistency between conductivity and extrapolation of SANS data to zero intensity. c Radius of gyration determined using Guinier analysis. d Minimum headgroup area determined from the spherical surface formed at R. e Radius increases with increasing concentration. See text for details. f From ref 5. g From Guinier rod analysis.
the wave-vectors of the incident and scattered beams, respectively. After accounting for detector efficiency and pixel solid angles, sample transmission, illuminated volume, and the incidence flux, the differential scattering cross section dΣ/dΩ can be determined. The dΣ/dΩ is calibrated by reference to scattering from a well-defined sample to yield absolute values. SANS measurements were performed on two separate days on the LOQ instrument at the ISIS Facility, Rutherford Appleton Laboratory (Didcot, U.K.). ISIS is a pulsed neutron source, and thus, LOQ is a time-of-flight instrument which, operating at 25 Hz, uses neutrons with wavelengths 2.2 < λ < 10 Å to give 0.006 < Q < 0.24 Å-1 on its main detector located 4.1 m from the sample. Solutions of the metallosurfactants in D2O were placed in Hellma fused-silica spectrophotometry cuvettes with a path length of 5 mm and were thermostated at 298 K. The beam diameter was 12 mm. Scattered neutrons are detected using a 3He gas area detector. The time-of-flight data were corrected for the wavelength-dependent monitor spectrum, sample transmission, and detector efficiency. Background scattering was removed by subtraction of data collected from scattering from D2O in a similar cuvette. Any residual incoherent background scattering from the samples was catered for by inclusion of a flat background term in all fits. This background correction was generally close to zero for the studied solutions. The dΣ/dΩ data were finally normalized to an absolute scale by reference to scattering from a standard sample (a solid blend of protonated and deuterated polystyrene) with known differential scattering cross section.18 For the purposes of this work, sufficient scattering length density contrast between aggregate and solvent is obtained by using protonated surfactants in deuterium oxide. The scattering length densities of the surfactant moieties were calculated using the densities given in Table 1, and the scattering length density of D2O was taken to be 6.33 × 10-6 Å-2. The differential scattering cross section19 for neutrons scattered from a uniform particle is commonly written as
dΣ (Q) ≈ NV2(∆F)2P(Q)S(Q) dΩ
(1)
where V is the volume of one scatterer, ∆F is the difference in scattering length density between the particle and the solvent, P(Q) is the particle shape factor, and S(Q) the (apparent) structure factor. Equation 1 is expressed in the decoupling approximation. Approximate forms of S(Q) can be derived on the basis of particular choices of interaction potential. Because of the ionic nature of the systems under investigation, a suitable choice here (18) Heenan, R. K.; Penfold, J.; King, S. M. J. Appl. Crystallogr. 1997, 1140. (19) See, for example, Spalla, O. In Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter; Lindner, P., Zemb, Th., Eds.; Elsevier Science Publishing: New York, 2002; pp 49-71.
is the RMSA one-component macroion, with penetrating background, model of Hayter and Penfold,20 which is a good approximation, provided the axial ratio of the particles is not significantly greater than unity. For the majority of the surfactant solutions studied here, this S(Q) has been combined with a coreshell ellipsoid model for a uniform ellipsoid with core radii R, R, and XR and shell of constant thickness, t. However, although for the Ru51C12 solutions good quality fits are obtained, the absolute scattered intensities resulting from analysis using the above model are inconsistent. To attempt to understand the aggregation behavior in this system, a form factor for polydisperse spherical particles21 with the Hayter-Penfold S(Q) has been applied. A completely different model is required to interpret the scattering patterns measured for the Ru51C19 solutions. At lower concentrations, the data can be modeled using a disk model. At higher concentrations, the data have been modeled using the Kholodenko worm model, which allows interpolation from rodlike structures through to Gaussian coils.22 The scattering patterns at low Q indicate that a nonunit S(Q) is not required. The SANS data have been analyzed using the multimodel fitting program FISH.23 Fitting was performed using the Marquardt steepest-descent least-squares method. The vast parameter-space was explored starting from many parameter configurations. The internal consistency of the parameters used in the models has been maintained throughout. The measured data and model fits are shown in Figures 3-5. Core-Shell Ellipsoid Model with Hayter-Penfold S(Q). The main model parameters are the core radius, R, the axial ratio, X, the volume fraction of water in the shell of the micelle, β, the overall charge on the micelle, qtot, the inverse Debye screening length, 1/κ, the scattering length densities of solvent, core, and dry shell materials, and an overall scale factor proportional to the volume fraction, φ, of micelles in the solution. In addition to these, the shell thickness, t, was constrained to a value computed for the given core size, β, and the expected shell/ core volume ratio of the dry amphiphile. The volume fraction obtained from the scale factor, φfit, is then compared with the estimated volume fraction, φexp, the fitted β, estimates of the tail and headgroup volumes of the complex, and the known concentration minus the cmc. The Debye length, κ, has at each stage of the analysis been calculated taking into account the free monomeric surfactant and unbound counterions present in the solution. κ has been determined by iteration with respect to the fitted qtot for a particular concentration. The effect of changes in counterion concentration with micellar charge on the molar (20) (a) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (b) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 64, 651. (21) Kotlarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (22) Kholodenko, A. L. Macromolecules 1993, 26, 4179. (23) Heenan, R. K. FISH; Rutherford Appleton Laboratory: Didcot, UK, 1989.
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volumes and scattering length density of the headgroup region have been accounted for. Aggregation numbers have been determined from the ratio of the core volume to the presumed volume of the tail group in the core, and the charge per surfactant headgroup subsequently estimated. The models used are not particularly sensitive to the choice of core and shell scattering length densities, and hence, the assumption that the densities used in the calculation of the scattering length densities being directly translatable is not crucial. In the S(Q) function, the volume fraction of scatterers is fixed at the value of φexp to maintain model consistency. The scale factor and the core radius, R, were the only actual fitting parameters employed in the complete analysis; the remaining parameters were fixed at values that maintained consistency for the specific model conditions. Subject to this consistency, R was optimized over a range of X values, with the initial choice of R guided by consideration of molecular structure. Polydisperse Sphere Model. For this model, in eq 1 the shape factor P(Q) ) 〈|F(Q)|2〉, where F(Q) is the particle form factor, is replaced with P(Q) ) ∫∞0 dR|F(QR)|2f(R) in which f(R) is the particle radius distribution function. For the modified Schultz distribution, this is21
f(R) )
[ ] Z+1 R h
Z+1
{
}
-(Z + 1)R RZ exp R h Γ(Z + 1)
(2)
where R h is the mean particle radius and Z is a width parameter defined as Z ) (R h /σ)2 - 1, in which σ is the standard deviation of the particle size distribution from R h . The fitted scale factor is used to determine φfit by further assuming the average water content of the particles. This is then compared with φexp. For each solution concentration, the fitting procedure involved choosing a reasonable value of R h , such as the molecular or alkyl chain length, and analyzing the sensitivity of the fit to the choice of σ. This was systematically repeated for further choices of R h, exploring values both above and below this initial choice, and the resulting ranges of R h and σ yielding high quality fits. The scale factor was also fitted to the data. Kholodenko Worm Model. This statistical mechanical model applies to the conformations adopted by semiflexible polymers22,24 and caters for a range of structures interpolating smoothly between rigid rods and Gaussian coils. Its applicability has been demonstrated for ladder polymers25 and dendron rod-coil molecules.26 The shape factor is
Pworm(Q) )
2 3n
[∫
3n
0
(
dy 1 -
y f(y) 3n
) ]
(3)
with
f(y) )
sinh(Ey) Ql and E ) 1 3 E sinh(y)
f(y) )
sin(Fy) Ql 2 with F ) -1 3 F sinh(y)
2 1/2
[ ( )]
3 for Q e l
and
[( )
]
1/2
for Q >
3 l
The contour length is L ) nl, with l the statistical chain element (Kuhn) length, which is twice the persistence length, lp, and n the statistical number of segments. Polydispersity has not been included in the present modeling and neither has a structure factor. Only the highest concentration studied Ru51C19 reveals a hint of requirement of an S(Q), as suggested by weak oscillations appearing in the scattering pattern. Core-shell models can further be applied, with the rodlike sections possessing a core radius R and shell thickness t, with a fraction β of water in the shell. The fitted scale factor is used, as appropriate for the homogeneous or core-shell models, to determine φfit which is then compared via assumed β with φexp. Although with this model (24) Kholodenko, A. L. J. Chem. Soc., Faraday Trans. 1995, 91, 2473. (25) Hickl, P.; Ballauff, M.; Scherf, U.; Mu¨llen, K.; Lindner, P. Macromolecules 1997, 30, 273. (26) De Gans, B. J.; Wiegand, S.; Zubarev, E. R.; Stupp, S. I. J. Phys. Chem. B 2002, 106, 9730.
Figure 2. Conductivity isotherms measured at 298 K for aqueous solutions of (a) Ru41C12 (9), Ru41C19 (b), Ru51C12 (0), Ru51C19 (O); (b) racemic Ru42C12 (9), ∆-Ru42C12 (0), racemic Ru42C19 (b), ∆-Ru42C19 (O). The dotted lines are guides to the eye to indicate departures from linearity; the error bars designate the region of concentration in which the SANS intensity becomes indistinguishable from the background. The data for each surfactant have been subjected to a linear shift relative to one another for clarity. it is very difficult to obtain an unambiguous set of parameters, it is nonetheless possible to determine the minimum radius, R, the minimum number of segments, nmin, and the persistence length, lp, emerges from the analysis relatively well defined. Elaboration of the model by employing core-shell structure leads to no further consolidating information. Therefore, the coreshell model version was not used in the analysis reported later. In the fitting, the values of R, lp, and n were assessed via a sensitivity analysis. For a chosen R, again chosen initially to correspond to a molecular length, the coupling of lp to n was examined. R was then varied around this initial choice, and for the new fixed value of R, the coupling of lp and n assessed. This process was repeated until all three parameters resulted in highquality fits for all solution concentrations studied. The scale factor was also fitted to the data.
3. Results Critical Micelle Concentrations. As mentioned earlier, consistency between concentrations corresponding to breakpoints in the conductivity isotherms and negligible scattered intensity was used as a means of determining the cmc values. Figure 2 shows the conductivity isotherms, together with error bars indicating the concentration range over which the scattered intensity becomes indistinguishable from the background. The values given in Table 1 are determined nominally from the midpoint of these error bars, and where convincing break points occur in the conductivity isotherms, the conductivity measurements are used to refine the determination of the cmc value. As can be seen, the cmc is not always associated with the lower concentration breakpoint in the conductivity isotherm. Such breakpoints may be associated with ion association or some form of premicellar aggregation. In any event, the scattering measurements are not sensitive to the presence of any structure at these lower concentrations. For the single-chain surfactants with n ) 12, there is no conductivity break point associated with the SANSdetermined cmc. The data serve to reasonably locate the cmc values; fortunately, the precise values of the cmc are not crucial for the purpose of this paper. Preliminary Remarks. The SANS data are shown in Figures 3-5 for several concentrations for the eight surfactant systems studied. Before discussing the results in detail, some general remarks regarding the appear-
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Figure 3. Measured (points) and modeled (lines) differential scattering cross section dΣ/dΩ as a function of momentum transfer Q for aqueous solutions of (a) racemic Ru42C12 (b), ∆-Ru42C12 (O), with, from bottom to top, concentrations of 0.5, 1.5, and 2.5 mmol dm-3; (b) racemic Ru42C19 (b) ∆-Ru42C19 (O) with concentrations, from bottom to top, of 0.1, 0.5, 1.0, 2.0, and 3.0 mmol dm-3.
ance of the patterns and the relative scattered intensities and the results of a preliminary Guinier analysis are given. The scattering patterns for the double-chain Ru42Cn surfactants with n ) 12 and 19 (Figure 3a and b, respectively) are similar to those found for the Ru52Cn surfactants reported before5 with evident structure peaks appearing in the patterns for the samples studied at higher concentrations. Since the concentrations are generally low, these peaks imply charged aggregates. At the same concentration, the scattered intensity from the solutions of racemic Ru42Cn is slightly lower than that for the resolved Ru42Cn. The solutions of Ru41Cn and Ru51C12 (Figure 4a and b) display patterns similar to those for the Ru42Cn solutions. However, the patterns for the Ru51C19 solutions (Figure 5a) are dramatically different, both in shape and intensity. The scattered intensities for the Ru41C12 and Ru51C12 are weak, suggesting the presence of small aggregates or aggregates with high water content. To guide the choice of shape and size of aggregates for the quantitative analysis, plots of ln(dΣ/dΩ) vs ln Q have been employed (not shown), and despite the presence of the structure peaks in the SANS data, a Guinier analysis has been performed. Thus, ln QR dΣ/dΩ has been plotted
Bowers et al.
Figure 4. Measured (points) and modeled (lines) differential scattering cross section dΣ/dΩ as a function of momentum transfer Q for aqueous solutions of (a) Ru41C12 (O) and Ru51C12 (b) with concentrations, from bottom to top, of 5.0, 7.5, 10.0, and 20.0 mmol dm-3; (b) Ru41C19 with, from bottom to top, concentrations of 0.5, 1.0, 3.0, 5.0, and 10.0 mmol dm-3.
against Q2, with R ) 0, 1, or 2 for spheres, rods, and disks, respectively. The ln-ln plots reveal that, with the exception of the Ru41C12 and Ru51C12 systems, a Porod Q-4 dependence is found at high Q. This implies that large objects with clear interfaces between object and solvent matrix are present. At low Q, the slope of the ln-ln plots can suggest, if S(Q) ) 1, whether the aggregates are spherelike, (infinite)rodlike, or sheetlike in character. Ambiguity is introduced if a Q-2 dependence is found because Gaussian coils also display this behavior at middle Q. With the exception of Ru51C19, the presence of the structure peak hinders shape determination. However, Guinier plots for spherical particles do consistently produce straight lines, the slopes of which yield radii of gyration, Rg. It is found that the Rg for the double-chain surfactant aggregates are independent of concentration for the range studied and that the aggregates formed by the resolved Ru42C19 are larger than those found for the racemic counterpart, although a similar result is not found for the Ru42C12 case. In contrast, the Rg of the single-chain surfactant aggregates are concentration dependent, with the Rg increasing with increasing concentration. Table 1 shows the Rg determined at the concentration studied closest to the cmc for comparative purposes for all the surfactant systems studied here.
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Langmuir, Vol. 21, No. 13, 2005 5701 Table 2. Significant Parameters Resulting from Modeling the Ru51C19 SANS Data Using the Kholodenko Worm Form Factor
Figure 5. (a) Measured (points) and modeled (lines) differential scattering cross section dΣ/dΩ as a function of momentum transfer Q for aqueous solutions of Ru51C19 with, from bottom to top, concentrations of 0.1, 0.5, 1.0, 3.0, 5.0, and 10.0 mmol dm-3. (b) The data given in (a) displayed as a Holtzer (bending rod) plot. The indicated value of Qc is used to determine the flexibility of the wormlike micelle.
The Ru51C19 ln-ln plot possesses a slope ≈-2 for all concentrations studied above the cmc, suggesting the presence of sheets or Gaussian coils. Guinier analysis suggests that sheets or Gaussian coils form at lower concentrations with a transition to rigid rods occurring between 1 and 3 mmol dm-3. The nature of this transition is examined later. Aqueous Solutions of Double-Chain Surfactants. Table 1 lists some typical structural parameters resulting from the quantitative analysis with the model fits shown as the solid lines in Figure 3. Many of the results indicated by the Guinier analysis are consolidated. For all doublechain surfactants studied, the particle radius is not concentration dependent in the range studied. The micelles formed by the racemic mixture of surfactants are smaller than the corresponding resolved isomers. Although this distinction is modest, particularly for the n ) 12 case, it unambiguously emerges from the data analysis regardless of the choice of model for the particle shape. This is consistent with the trend in the differences in bulk densities, as reported in Table 1, which imply a closer packing in the racemic mixture. The shapes of the particles are, unfortunately, not unambiguously determined. Models with 0.5 e X e 1.5 have been applied, and in each case, the fit quality is good
concn, c mmol dm-3
persistence length, lp Å
min no. stat. seg. nmin
radius rod, R Å
0.1 0.5 1 1 3 5 10
38 ( 2 67 ( 2 100 ( 2 45 ( 2 103 ( 2 136 ( 4 239 ( 3
∼ 500 ∼ 400 ∼ 300 ∼200 50 ( 5 30 ( 5 25 ( 5
30 30 30 15 15 15 15
and the absolute intensities are in reasonable agreement with the model (i.e., φfit ≈ φexp). (For comparative reasons, the fits shown in Figure 3 are for spherical models but no differences are evident over this X range.) There is, as expected, strong coupling between X and R, with R decreasing with increasing X. Estimation of average headgroup area per molecule by dividing the surface area of the ellipsoids (strictly spheroids) by the aggregation number, Nagg, can be used to establish reasonable upper and lower cutoffs for X. On these grounds, the prolate ellipsoidal models may be rejected as the headgroup area becomes extremely small and layering of headgroups is not consistent with the modeled shell thickness. If the calibration of the absolute intensity is within (10%, then the oblate model with X ≈ 0.5 is favored for all the doublechain surfactants studied here because the agreement between φfit and φexp is consistently close as a function of concentration, unlike for the other shapes where deviations greater than 10% are found, although these deviations are
