Ostwald Ripening of an Emulsion Monitored by PGSE NMR

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Ostwald Ripening of an Emulsion Monitored by PGSE NMR N. Hedin and I. Furo´* Division of Physical Chemistry, Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Received November 16, 2000. In Final Form: May 8, 2001 Coarsening of surfactant-stabilized oil-in-water emulsions (C12E5-decane-D2O) induced by a fast temperature drop from their microemulsion phase is studied by 1H stimulated-echo-type pulsed-fieldgradient spin-echo (PGSE) NMR spectroscopy. The data obtained on a small amount of hexamethyldisilane dissolved in the oil phase display two distinct diffusion coefficients. The slower diffusion is interpreted in terms of large droplets containing the oil that had been expelled from the original microemulsion droplets. The faster diffusion belongs to smaller microemulsion droplets that coexist with the large oil droplets. The results show that the investigated emulsions exhibit regular Ostwald ripening. Both the actual amounts of the expelled oil and the obtained coarsening rates agree well with theoretical estimates. As a consequence of fast surfactant exchange among the different droplets, the diffusion of the surfactant molecules is described by a single diffusion coefficient.

* Corresponding author. Tel: +46 8 790 8592. Fax: +46 8 790 8207. E-mail: [email protected].

been noted, scattering results can be biased toward big droplets if big and small droplets coexist.15 Our present NMR experiments do not seem to suffer from this particular shortcoming (see below). The destabilization process we study is the Ostwald ripening, driven by the difference in Laplace pressure between large and small droplets and controlled by the rate of oil transfer among droplets. One question is if the rates of the coarsening of the emulsion (i.e., the growth of large droplets at the expense of small ones) follow the theoretical predictions. The other question is if this transfer of oil is molecular or mediated by (micellar) aggregates. The particular system we study is the mixture of the nonionic surfactant C12E5 with decane and water24-30 to which a small amount of a charged surfactant (sodium dodecyl sulfate, SDS) was added to suppress other mechanisms4 of destabilization of emulsions. This system, although well studied, was chosen because there is an inconsistency concerning the experimental coarsening rates: the closely related C12E8-decane-H2O and C12E6decane-H2O emulsions, stabilized by charged surfactants,

(1) Kabalnov, A. Curr. Opin. Colloid Interface Sci. 1998, 3, 270. (2) Kabalnov, A.; Wennerstro¨m, H. Langmuir 1996, 12, 276. (3) Bibette, J.; Leal-Calderon, F.; Poulin, P. Rep. Prog. Phys. 1999, 62, 969. (4) Aveyard, R.; Binks, B. P.; Esquena, J.; Fletcher, P. D. I.; Buscall, R.; Davies, S. Langmuir 1999, 15, 970-980. (5) Loudet, J. C.; Richard, H.; Sigaud, G.; Poulin, P. Langmuir 2000, 16, 6724-6730. (6) Talmon, Y. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 364-372. (7) Kabalnov, A. S.; Makarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (8) De Smet, Y.; Danino, D.; Deriemaeker, L.; Talmon, Y.; Finsy, R. Langmuir 2000, 16, 961-967. (9) Lee, H. Y.; McCarthy, M. J.; Dungan, S. R. J. Am. Oil Chem. Soc. 1998, 75, 463-475. (10) McDonald, P. J.; Ciampi, E.; Keddie, J. L.; Heidenreich, M.; Kimmich, R. Phys. Rev. E 1999, 59, 874-884. (11) Katsumoto, Y.; Ushiki, H.; Mendiboure, B.; Graciaa, A.; Lachaise, J. J. Phys.: Condens. Matter 2000, 12, 3569. (12) Katsumoto, Y.; Ushiki, H.; Graciaa, A.; Lachaise, J. J. Phys.: Condens. Matter 2000, 12, 249. (13) Morris, J.; Olsson, U.; Wennerstro¨m, H. Langmuir 1997, 13, 606-608. (14) Kabalnov, A. S.; Shchukin, E. D. Adv. Colloid Interface. Sci. 1992, 38, 69-97. (15) Egelhaaf, S.; Olsson, U.; Morris, J.; Wennerstro¨m, H. Phys. Rev. E 1999, 60, 5681.

(16) Wennerstro¨m, H.; Morris, J.; Olsson, U. Langmuir 1997, 13, 6972-6979. (17) Taisne, L.; Walstra, P.; Cabane, B. J. Colloid Interface Sci. 1996, 184, 378. (18) Taisne, L.; Cabane, B. Langmuir 1998, 14, 4744. (19) Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Rippon, S.; Lubetkin, S. D.; Mulqueen, P. J. Langmuir 1998, 14, 5402-5411. (20) Binks, B. P.; Cho, W. G.; Fletcher, P. D. I.; Petsev, D. N. Langmuir 2000, 16, 1025-1034. (21) Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Rippon, S.; Lubetkin, S. D.; Mulqueen, P. J. Langmuir 1999, 15, 4495-4501. (22) De Smet, Y.; Deriemaeker, L.; Parloo, E.; Finsy, R. Langmuir 1999, 15, 2327-2332. (23) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1999, 15, 6745-6754. (24) Olsson, U.; Wennerstro¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113-146. (25) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389-3394. (26) Leaver, M.; Furo´, I.; Olsson, U. Langmuir 1995, 11, 1524-1529. (27) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R. J. Phys. II 1994, 4, 515-531. (28) Leaver, M. S.; Olsson, U. Langmuir 1994, 10, 3449-3454. (29) Rajagopalan, V.; Bagger-Jo¨rgensen, H.; Fukuda, K.; Olsson, U.; Jonsson, B. Langmuir 1996, 12, 2939-2946. (30) Bagger-Jo¨rgensen, H.; Olsson, U.; Mortensen, K. Langmuir 1997, 13 (3), 1413-1421.

Introduction Normal emulsions and microemulsions (Windsor 1) are oil droplets dispersed in water with monolayers of surfactants covering each droplet. These layers lower the tension of the oil-water interface and reduce the free energy penalty for dispersing oil in water. In contrast to microemulsions, emulsions are nonequilibrium states and their time evolution is of both fundamental and technical importance.1-3 This can be studied using indirect or direct techniques. If, as in the present case, one deals with small (∼10-100 nm) droplets, direct techniques, such as optical microscopy,4,5 are excluded (with the possible exception of cryo-transmission electron microscopy6-8). Hence, in this work we use an indirect method, 1H stimulated-echotype pulsed-field-gradient spin-echo (PGSE) NMR spectroscopy, to study the time evolution of emulsions. There exist some PGSE NMR precedents,9,10 while other indirect methods that have been used for the same purpose are X-ray and neutron scattering techniques.7,11-23 As it has

10.1021/la001597z CCC: $20.00 © 2001 American Chemical Society Published on Web 07/10/2001

NMR Study of Ostwald Ripening

coarsened with a rate for the growth of the radius 10-20 times (in units of ms-1/3) quicker than predicted by the theory of molecular-diffusion-mediated transport,19,21 while the coarsening of a C12E5-decane-(H2O/D2O) emulsion proceeded with a rate only ∼2 times larger than predicted by theory.15 The actual setup of our experiment closely follows that in the scattering studies of Egelhaaf et al.15 Hence, emulsions are formed by a temperature drop that brings an initial microemulsion phase out of equilibrium. The growing droplets were in quasi-equilibrium with a phase of microemulsion droplets that shrink because of the higher preferred curvature of the monolayer at lower temperatures.15 Since, as we show below, the exchange of oil among the droplets is slow on the time scale of seconds, PGSE NMR can measure the self-diffusion of the growing bigger droplets as well as that of the coexisting microemulsion droplets. The relative volume fraction of these two compartments can also be extracted from the data. The PGSE NMR data are easier to evaluate when a small amount of another oil (tracer) with a unique 1H NMR signal is mixed into the oil bulk (see below). We chose hexamethyldisilane (HMS) as our tracer. Since HMS has a higher (but still very low on the absolute scale) solubility in water than decane, its distribution among the different droplets during the evolution of the emulsion should match that of decane. Below, we evaluate all our data under this assumption. We avoided adding a less water-soluble oil as tracer since that could have resulted in a tracer redistribution among the different droplets that is slower than the redistribution of the bulk oil.31-33 On the other hand, the amount of added tracer was kept low so that its redistribution among droplets cannot significantly influence the coarsening process. Experimental Section Materials and Samples. The samples were prepared by mixing C12E5 (Nikko Chemicals), decane (Aldrich, 99+), and D2O (Isotec, 99.8%). C12E5 is an oligooxyethylene alkyl ether34 surfactant with 12 carbons in the alkyl chain and 5 oxyethylene groups in the headgroup. We added small amounts of SDS and HMS to each sample. The charged surfactant SDS introduces a net charge on the droplets and stabilizes them against flocculation and coalescence. Note that SDS strongly alters the phase diagram when added in large amounts.29 Three (marked A, B, and C) samples were prepared. The oilto-surfactant volume ratios were χos ) 1.22 for samples A and C and χos ) 2.23 for sample B. The total amount of dispersed material (i.e., oil and surfactant together), expressed in volume fraction φ, was φ ) 0.16 in sample A, φ ) 0.17 in sample B, and φ ) 0.05 in sample C. The weight fraction HMS-to-decane was 0.019 in samples A and C and 0.015 in sample B. The weight fraction SDS-to-C12E5 was 0.018 in all samples which corresponds to 1 SDS molecule per 35 C12E5 molecules. The materials were mixed and filled in 5 mm NMR tubes up to the level of about 1 cm. The tubes were subsequently flame-sealed and stored frozen between the measurements. The microemulsion solutions were prepared by repeating the sequence of heating (∼40-50 °C), mixing, and storing at ∼35 °C. The temperature was set and held constant in the NMR probe using a BVT-3000 regulator unit (Bruker). The initial temperature (300 K for samples A and C and 305 K for sample B) within the probe was set by an external thermometer with its measuring point lowered into the sample space. These temperatures were selected to provide a microemulsion state close to the phase boundary where the oil droplets are close to spherical.24 After (31) Kabalnov, A. S.; Pertzov, A. V.; Shchukin, E. D. Colloids Surf. 1987, 24, 19-32. (32) Webster, A.; Cates, M. Langmuir 1998, 14, 2068. (33) Higuchi, W. I.; Misra, J. J. Pharm. Sci. 1962, 51, 459. (34) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; Macdonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.

Langmuir, Vol. 17, No. 16, 2001 4747 performing experiments in the microemulsion samples at these temperatures, the set temperature of the probe has been dropped in one step by 14 or 20 K (see tables). Under the applied experimental conditions, the whole sample volume reached to within (0.1 K of the new set temperature in about 5 min after initiating the temperature drop. Repeated experiments with the same temperature drops yielded identical data within the errors presented in Tables 2 and 3. NMR Experiments. The experiments were performed on a Bruker DMX200 spectrometer equipped with a wide-bore Bruker gradient probe with a maximum gradient of 9.6 T/m. In the actual PGSE NMR experiments, performed by the stimulated-echo pulse sequence,35 the gradient strength was varied up to 6.5 T/m. The self-diffusion coefficient was extracted by fitting the conventional Stejskal-Tanner expression36,37 N

I(g) ) I0

∑Ae

-Diδ2γ2g2(∆-δ/3)

i

(1)

i)1

with N () 1 or 2) diffusing components to the observed signal attenuation on increasing gradient strength g. In eq 1, Ai is the relative weight of the different diffusing components, γ is the magnetogyric ratio of 1H, δ is the length of the gradient pulse, ∆ is the diffusion time, and I0 is the signal intensity at zero attenuation. The phases of the applied radio frequency pulses were cycled in four steps such as φ2 ) (+x, -x), φ3 ) (+x, +x, -x, -x), φR ) (+x, -x, -x, +x) where φn and φR are the phases of the nth radio frequency pulse and the phase of the receiver, respectively. (In some experiments, this phase cycle was extended to φ1 ) (+x, +x, +x, +x, -x, -x, -x, -x), φR ) (+x, -x, -x, +x, -x, +x, +x, -x).) This, in combination with the 32 gradient steps and 11 s recycle time, sets the total experimental time to about 25 min (50 min for the eight-step phase cycle). This value defines our time resolution for observing the evolution of the emulsion. For the dilute sample C, the signal-to-noise ratio for HMS (see below) was low after 4 scans and a total of 16 scans was instead accumulated limiting the time resolution to ∼2 h for that sample. The ethyleneoxide (EO) groups in C12E5 provide a distinct peak in the 1H NMR spectrum of our samples (Figure 1a). Hence, the diffusion coefficient of the surfactant molecules can be easily measured using that peak. On the other hand, the signals from the methylene and methyl groups from C12E5 and decane overlap, which prohibits their use for extracting the oil diffusion coefficient. Hence, the oil diffusion coefficient was measured via our HMS tracer that has a unique and separate 1H NMR spectral peak. Since the small amount of HMS rendered that signal weak (Figure 1a), the spectral overlap from the methyl protons of decane and C12E5 presented a problem. To eliminate this overlap, the first radio frequency pulse, nonselective in the conventional stimulatedecho pulse sequence, was replaced by a 60 ms long, Gaussian shaped pulse. This pulse, applied at the HMS frequency, provided a selective excitation of the HMS peak and suppressed the other peaks. The degree of achieved selectivity is shown in Figure 1 with spectra from PGSE experiments with a nonselective (Figure 1a) and a selective (Figure 1b) first pulse. The signal attenuation with increasing gradient recorded in the microemulsion phase followed a single-component StejskalTanner expression for both C12E5 and HMS. After the temperature drop, the HMS data became a sum of two decays with distinct diffusion coefficients. Such a behavior is a sign of slow exchange on the time scale of the diffusion experiment that is set by the diffusion time ∆ of the stimulated-echo experiment. To prove this point, ∆ was varied in the range of 0.15-4.8 s; at all times, two-component decays were observed for HMS with the same two diffusion coefficients. On the other hand, the surfactant diffusion proceeded with one diffusion coefficient at all diffusion times ∆. Clearly, at the tested time scales there is a slow exchange of the HMS molecules between two different compartments but a fast exchange of the C12E5 molecules. The two-component behavior of the oil signal is the decisive factor behind using the HMS tracer. In principle, one could extract (35) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (36) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288-292. (37) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523-2526.

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Figure 2. Typical attenuation of the HMS signal with increasing gradient strength in a PGSE NMR experiment in a C12E5-decane-D2O emulsion with χos ) 2.2 and φ ) 0.17. These experimental points were recorded 13 h after the temperature drop from 305 to 291 K, and the lines represent fits to eq 1, with one (dotted) and two (dashed) diffusing components. maximum droplet radii in the order of ∼100 nm were not disturbed.

Background to Ostwald Ripening

Figure 1. 1H NMR spectra of a C12E5-decane-D2O microemulsion with oil-to-surfactant volume ratio χos ) 1.2 and volume fraction of dispersed material φ ) 0.16. Both spectra were recorded by stimulated-echo experiments with a gradient strength g ) 0.7 T/m, gradient pulse length δ ) 3 ms, and diffusion time ∆ ) 150 ms. Under these conditions, the signal from quickly diffusing water molecules (around 4.5 ppm) is completely attenuated. The rightmost signal (0 ppm) from the HMS tracer suffers from strong overlap in spectrum a that was recorded in a conventional experiment. There is no overlap in spectrum b that was recorded with a selective first radio frequency pulse of Gaussian shape and 60 ms length.

Ostwald ripening belongs to the general class of aging processes41,42 where the precipitate, here the expelled oil in large droplets, evolves solely by minimizing the surface energy through decreasing the surface-to-volume ratio. In our nonequilibrium microemulsion created by the temperature drop, the oil molecules outside large and small droplets have different chemical potentials because of the different Laplace pressures. Hence, the local concentration of oil in the vicinity of small droplets becomes higher than that close to large droplets. Consequently, oil flows from the small to the large droplets with a rate that is diffusion limited and those droplets that were initially larger grow at the expense of smaller droplets.1 As a result, the total number of droplets is reduced and the volume of the increasing droplets grows linearly with time. Hence, their radius varies as

the surfactant diffusion coefficient from the EO peaks and that result could be used in the analysis of the methylene and methyl data as a fixed parameter. This approach leads to less reliable results because of the undefined (by spin relaxation) relative intensities of surfactant and oil contributions. Instead, we fitted the HMS signal attenuation by a two-component StejskalTanner expression using the standard Levenberg-Marquardt algorithm. In Figure 2, a typical fit to typical data from sample B in the later stages of coarsening is presented. Clearly, the decay cannot be fitted to a single component. The obtained HMS diffusion coefficients and their relative weights are presented in Figures 3-5. At 305 K, where sample C was kept in its microemulsion phase, there is convection inside the sample tube caused by the temperature gradient within the NMR probe. A doublestimulated-echo sequence38-40 was used to cancel the error introduced by this phenomenon into the PGSE NMR experiment. A related problem is the buoyancy flow that drives the macroscopic phase separation (creaming) by the large oil droplets gliding upward. (In our samples, flocculation is suppressed by charging up the droplets with SDS.) We estimate that this flow becomes important at ∼µm droplet radius R. Since this flow phenomenon scales approximately as ∼R2, our PGSE experiments with

where 〈R(0)〉 is the initial average droplet size in the microemulsion phase and t measures the time after the temperature drop. Note that this representation of Ostwald ripening is valid if the volume of the initial droplets is much smaller than the volume of the growing droplets. In our case (compare the diffusion data below), the volume difference is at least 10- to 100-fold. In the original model,41,42 having treated precipitation in dilute binary systems, C is a universal constant with a scale-invariant distribution around the average size 〈R〉. Later, C was proposed to have a volume-fraction dependence and a distribution broader than predicted43 but with the same general behavior. The extension of the theory has been shown accurate for describing the coarsening of solid Sn-rich particles in a Pb-Sn liquid.44

(38) Jerschow, A.; Mu¨ller, N. J. Magn. Reson. 1997, 125, 372-375. (39) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Clarendon Press: Oxford, 1991. (40) Hedin, N.; Yu, T. Y.; Furo´, I. Langmuir 2000, 16, 7548-7550.

(41) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (42) Wagner, C. Z. Elektrochem. 1961, 65, 581. (43) Marqusee, J. A.; Warner, M.; Dill, K. A. J. Chem. Phys. 1984, 81, 6404.

3

〈R(t)〉 ) 〈R(0)〉 + Cxt

(2)

NMR Study of Ostwald Ripening

Figure 3. Self-diffusion coefficients Dmicro of the microemulsion droplets in C12E5-decane-D2O mixtures created by temperature drops. Dmicro is obtained by fitting eq 1 with two components to the experimental data from PGSE NMR; Dmicro is the higher of the two obtained diffusion coefficients. (a) Data from sample with χos ) 1.2 and φ ) 0.16 presented for two different temperature drops, 300 f 286 K (O, ×, two repeated experiments) and 300 f 280 K (0). The typical error ((1σ) for each point is (3%. (b) Data from sample with χos ) 1.2 and φ ) 0.05 for a temperature jump 300 f 286 K. The typical error is (5%. (c) Data from sample with χos ) 2.2 and φ ) 0.17 for a temperature jump 305 f 291 K. The typical error is (2%.

Langmuir, Vol. 17, No. 16, 2001 4749

Figure 4. The fraction of expelled oil from a microemulsion after a temperature jump, obtained from the relative intensities of the two diffusing components in the HMS signal, by fitting eq 1 to the experimental data from PGSE NMR. (a) Data from sample with χos ) 1.2 and φ ) 0.16 presented for two different temperature drops, 300 f 286 K (O, ×, two repeated experiments) and 300 f 280 K (0). The typical error ((1σ) for each point is (4%. (b) Data from sample with χos ) 1.2 and φ ) 0.05 for a temperature jump 300 f 286 K. The typical error is (5%. (c) Data from sample with χos ) 2.2 and φ ) 0.17 for a temperature jump 305 f 291 K. The typical error is (4%.

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For emulsion droplets, C is expressed in terms of the properties of the oil as

C)

(

)

8γsurfDcVM2 9RT

1/3

(1 + 0.74φ)

(3)

where D, c, and VM are the self-diffusion coefficient, the solubility, and the molar volume of the oil, respectively, while γsurf is the oil-water surface tension. Real emulsions are often complex mixtures, and representing the time dependence by eq 2 should be treated as an approximation. Still, the scaling relation between the average size and the elapsed time t holds when Ostwald ripening is dominating over other mechanisms of phase separation.11,12,14 On the other hand, it commands caution that some emulsions were observed to coarse with a rate that is higher by a small factor45 or by several orders of magnitude19-21 than the rate predicted by eq 3. After the temperature drop, the proposed model for this system15 suggests two types of droplets, growing large ones and smaller ones that constitute a microemulsion phase. (Ultimately, this microemulsion phase reaches equilibrium with the expelled oil.) Hence, the size distribution of the oil reservoirs is bimodal in contrast to the unimodal distribution predicted by the original model,41,42 and only the larger droplets grow by Ostwald ripening. We disregard this complication and compare the experimental C with the regular expression in eq 3. 〈R(0)〉 is treated as a free fitting parameter reflecting our uncertainty (imposed by the experimental limitations, see below) about the time when the emulsion destabilization is initiated. Results and Discussion We analyze our data under the assumption that the lower of the obtained two HMS diffusion coefficients, Demul, presented in Figure 5, describes the self-diffusion of large oil droplets while the higher one, Dmicro, presented in Figure 3, belongs to the coexisting small microemulsion droplets. This assumption is supported with the qualitative behavior of the measured diffusion coefficients: Dmicro is approximately constant in time, but Demul decreases (Figures 3 and 5). The time dependence of Demul is supposed to follow Ostwald ripening. The relative amount of oil residing in these two types of environments, obtained as the relative weight of the two components in the decay of the NMR signal of HMS with increasing gradient strength (Figure 2), is given in Figure 4. We relate the measured self-diffusion coefficients to the droplet radius by the Stokes-Einstein equation

D)

Figure 5. The inverse of the self-diffusion coefficients Demul of the microemulsion droplets in C12E5-decane-D2O mixtures created by temperature drops. Demul is obtained by fitting eq 1 with two components to the experimental data from PGSE NMR; Demul is the lower of the two obtained diffusion coefficients. The increase in 1/Demul reflects the growth of the emulsion droplets formed by the oil expelled from a microemulsion after a temperature drop. (a) Data from sample with χos ) 1.2 and φ ) 0.16 presented for two different temperature drops, 300 f 286 K (O, ×, two repeated experiments) and 300 f 280 K (0). The typical error ((1σ) for each point is (2%. (b) Data from sample with χos ) 1.2 and φ ) 0.05 for a temperature jump 300 f 286 K. The error bars represent (1σ error. (c) Data from sample with χos ) 2.2 and φ ) 0.17 for a temperature jump 305 f 291 K. The error bars represent (1σ error.

kT 6πηRapp

(4)

Combining this with eq 3 provides us with an expression that describes the time evolution of Demul as

1 6πη 1 3 C xt ) + kT app Demul(t) Demul(0)

(5)

The analysis of the diffusion data is complicated by two factors. First, because of the interaction among the droplets, the diffusion coefficients overestimate the droplet radii for concentrated microemulsions.26 To account for this phenomenon, a normalization constant aint is intro(44) Alkemper, J.; Snyder, V. A.; Akaiwa, N.; Voorhees, P. W. Phys. Rev. Lett. 1999, 82, 2725-2728. (45) Kabalnov, A. S. Langmuir 1994, 10, 680-684.

NMR Study of Ostwald Ripening

Langmuir, Vol. 17, No. 16, 2001 4751

Table 1. Self-Diffusion Coefficients of Droplets in C12E5-Decane-D2O Microemulsions Measured by PGSE NMRa

Table 2. Self-Diffusion Coefficients Dmicro of the Microemulsion Droplets in C12E5-Decane-D2O Mixtures Created by Temperature Dropsa

sample and equilibrium temp

D (10-12 m2/s)

Rapp (nm)

RHC (nm)

sample and temp drop

Dmicro (10-12 m2/s)

χos ) 1.2, φ ) 0.16, 300 K χos ) 1.2, φ ) 0.05, 300 K χos ) 2.2, φ ) 0.17, 305 K

8.5 18 4.4

23 11 54

7.5 7.5 12

χos ) 1.2, φ ) 0.16, 300 f 286 K χos ) 1.2, φ ) 0.16, 300 f 280 K χos ) 1.2, φ ) 0.05, 300 f 286 K χos ) 2.2, φ ) 0.17, 300 f 291 K

9.5 9.0

a

The apparent radii Rapp calculated via eq 4 are presented together with the radii of the hydrocarbon cores RHC obtained from scattering experiments (for details see text).

duced as

RHC aint ) Rapp

(6)

where RHC is the radius of the hydrocarbon core measured by independent experiments (see below). Hence, the corrected rate of Ostwald ripening is obtained as

Ccorr ) aintCapp

(7)

This procedure is most accurate for dilute samples where aint is close to 1. As a second complication, the low time resolution (25-50 min, see above) of the experiments together with the fast initial changes render the experimental data useless up to a few hours after the temperature drop. Third, the normalization procedure works differently for small and large droplets, although this difference should not influence the obtained Ostwald ripening rate that depends on the relative increase of the size of the large droplets. Initial and Coexisting Microemulsions. Small-angle neutron scattering (SANS) has determined RHC ≈ 7.5 nm for microemulsion droplets with χos ) 1.2, and an oftenused estimate is RHC ≈ 12 nm for χos ) 2.2.13,15,16,25,30 Even in dilute systems, PGSE NMR measures not RHC but instead the hydrodynamic radius Rhydro. Since the volume with radius Rhydro must include the hydrated headgroup region, one always obtains Rhydro > RHC. As an example, the radius determined by NMR (11 nm, see Table 1) is close to RHC (8 nm) measured by SANS15 in the dilute sample C (φ ) 0.05). The difference between the two values is close to the length of the extended EO5 group (∼2 nm). For microemulsions with higher volume fractions (samples A and B), the results from PGSE NMR and SANS strongly deviate from each other (see Table 1). SANS experiments measure an almost constant radius with increasing volume fraction φ for this particular system,25 while PGSE NMR yields an increasing Rapp (from eq 4) on increasing φ. The probable cause of this difference is droplet-droplet interaction26 which provides Rapp > Rhydro. (Nonspherical shape could lead to the same effect, but there are numerous indications for spherical droplet shape close to the emulsification failure.24,26,46-48) As shown in Figure 3 and presented in Table 2, Dmicro reaches a limiting value some hours after the temperature drop. Since this value is smaller than the diffusion coefficient measured before the temperature drop (Table 1), the microemulsion droplets become indeed smaller after the temperature drop. This behavior is consistent with the known temperature dependence of curvature for monolayers of nonionic surfactants. We observe ap(46) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389-3394. (47) Gompper, G.; Schick, M. Self-Assembling Amphiphilic Systems; Academic Press: London, 1994. (48) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: Reading, MA, 1994.

18.0 9.5

Rapp (nm)

RHC (nm)

fraction of expelled oil

13

4.2

0.35

12

3.9

0.45

4.8

0.35

3.8

0.50

7.1 17

a D micro, presented in Figure 3, is obtained by fitting eq 1 with two components to the experimental data from PGSE NMR; Dmicro is the higher of the two obtained diffusion coefficients. The apparent radii Rapp are calculated via eq 4, while the radii of the hydrocarbon cores RHC are obtained from Rapp via eq 6 with aint calculated from the data for equilibrium microemulsions in Table 1. The fraction of expelled oil is estimated from the relative intensities of the two diffusion processes involved in the fit and is expressed as the fraction of all oil contained in the sample (see also Figure 4).

proximately the same relative shrinkage, ∼1.8 for the sample with φ ∼ 0.16 and χos ∼ 1.2 for a 300 f 286 K temperature drop, as Egelhaaf et al.15 The droplet size decreases even more if the drop in temperature was set larger. Moreover, the relative shrinkage increases on increasing χos. As shown in Figure 4, the amount of expelled oil is constant after some initial time. This behavior is expected since the radius of the microemulsion droplets behaves on the same way as shown in Figure 3. The amount of oil expelled from the microemulsion droplets can be estimated from the radii in Tables 1 and 2 obtained from diffusion data in Figure 3. Under the crude assumption that all surfactant molecules stay in the water-rich phase, one new obtains 1 - (Rold HC/RHC ) for the expelled oil (the old and new radii are the data given in Tables 1 and 2, respectively). For the temperature drop of 300 to 286 K, the measured amount of expelled oil was ∼35% which is in rather good agreement with this ballpark estimate of 45%. Ostwald Ripening Rates. As shown in Figure 5, the inverse of the self-diffusion coefficient Demul evolves approximately proportional to t1/3. Hence, the data support the notion of regular Ostwald ripening in these emulsions. Capp and the zero-time diffusion coefficient were determined by a two-parameter fit of eq 5 to the data. The zero-time intercept (obtained to about zero or negative from the fits) is of little value because (i) it takes some initial time for Ostwald ripening to become dominant and (ii) our experimental setup has a limited time resolution. The obtained Capp values are given in Table 3. The robustness of the Capp parameter was tested by successive fits after removing point after point in a forward manner (see Figure 6). Hence, although the droplets grew in an environment of coexisting microemulsion droplets, no acceleration of the ripening with time was found. The depth of the temperature jump hardly affected Capp, but a difference was found when more oil was added. This difference between dilute and concentrated samples vanished when the effect of droplet-droplet interaction was taken into account via eq 7. It is as yet unclear to us what is the source of the 2-fold difference between the coarsening rates for samples with low and high χos. Theoretical estimates of the coarsening rates Ctheor were obtained via eq 3 with the decane solubility49,50 set to c ) (49) McAuliffe, C. Science 1969, 163, 478. (50) Coates, M.; Connell, D. W.; Barron, D. M. Environ. Sci. Technol. 1985, 19, 628-632.

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Hedin and Furo´

Table 3. Rates of Ostwald Ripening Obtained from the Variation of Demul with Time t after the Temperature Dropa sample and temperature drop

Capp

χos ) 1.2, φ ) 0.16, 300 f 286 Kb 4.4 ( 0.3 4.7( 0.5 χos ) 1.2, φ ) 0.16, 300 f 280 K 4.5 ( 0.2 χos ) 1.2, φ ) 0.05, 300 f 286 K 2.6 ( 0.5 χos ) 2.2, φ ) 0.17, 305 f 291 K 3.2 ( 0.2

Ccorr CSANS Ctheor 1.4 1.5 1.5 1.7 0.7

1.3 2.5

1.2 1.3 1.3

a D emul, presented in Figure 5, is obtained by fitting eq 1 with two components to the experimental data from PGSE NMR; Demul is the lower of the two obtained diffusion coefficients. The apparent rates Capp are extracted via eq 5, and the corrected rates Ccorr are extracted via eq 7. Available experimental rates CSANS from SANS (ref 15) experiments are also presented together with theoretical estimates Ctheor; see text. All rates are expressed in nm/s1/3 units. The errors of the experimental rates are (2σ. b Results from two repeated experiments; see Figures 3-5.

rate is the net difference of the molecular currents among the different environments. It is important to note that these molecular currents are not directed and “flow” through the common (for microemulsion and emulsion droplets) aqueous reservoir of the respective molecules, such as molecular decane dissolved in water. The microemulsion droplets exhibit an equilibrium exchange of material with the reservoir at times t > 104 s after the temperature drop as shown by the constancy of Dmicro in Figure 3. This exchange is fast on the 150 ms time scale for the surfactant molecules and slow on the 5 s time scale for the decane molecules. Considering that the oil and surfactant volumes per microemulsion droplets are roughly equal (χos ) 0.7-0.8, if one accounts for the expelled oil) and the molecular volume of C12E5 is roughly twice that of decane, this observation sets the ratio of the oil and surfactant molecular currents to ,0.06 ≈ (2*0.15 s)/(5 s). If the exchange of both oil and surfactant proceeds through a reservoir consisting of individual oil and surfactant molecules in the water phase, the ratio of the two molecular currents should be approximately equal to the ratio of the products of the molecular solubilities and diffusion coefficients of the oil and the surfactant which is 10-2 > cdecaneDdecane/cC12E5DC12E5 > 10-3, where cC12E5 is set to the critical micelle concentration. Hence, the current data are consistent with a molecular reservoir. Future PGSE NMR experiments with a wider range of diffusion times (∆ , 100 ms and ∆ ∼ 10-20 s) could verify this point in a more convincing way. Conclusions

Figure 6. Capp values obtained by fitting eq 5 to the data in Figure 5c by involving less and less experimental points from tstart until the time of the last measured point. The obtained Capp values are constant within error.

0.39 mmol/m3. The other used material parameters were D ) (0.57; 0.7; 0.8) × 10-9 m2/s15,51 at temperatures T ) (280.0; 286.2; 291.2) K, Vm ) 0.195 dm3/mol, γ ) 0.6 mJ/ m2, and the viscosity of water from ref 52. The value used for the surface tension is estimated for the χos ∼ 1.2 microemulsion droplets without added SDS from the spontaneous curvature53 of the monolayer and is higher than other estimates.54 We assume that the addition of 1 SDS molecule for 35 C12E5 molecules increases the surface tension but only weakly. Note that the coarsening rate is only weakly (∼γ1/3) dependent on the surface tension. Further studies should rely on theoretical estimates of this effect supplied by extending existing theoretical treatments.55 The obtained volume transfer rate (∼C3) for the oil is in the order of 10 nm3/s per droplet. The volume transfer (51) Price, W. S.; So¨derman, O. J. Phys. Chem. A 2000, 104, 58925894. (52) Cho, C. H.; Urquidi, J.; Singh, S.; Robinson, G. W. J. Phys. Chem. B 1999, 103, 1991-1994. (53) Le, T. D.; Olsson, U.; Wennerstro¨m, H.; Schurtenberger, P. Phys. Rev. E 1999, 60, 4300-4309. (54) Sottmann, T.; Strey, R. J. Chem. Phys. 1997, 106, 8606-8615. (55) Daicic, J.; Fogden, A.; Carlsson, I.; Wennerstro¨m, H.; Jo¨nsson, B. Phys. Rev. E 1996, 54, 3984-3998.

Rapid drops in temperature destabilize the microemulsion droplets in the C12E5-decane-D2O system. The emulsion droplets that appear grow in a way and with a rate that are predicted by theories of Ostwald ripening. Our results expand the range in which the validity of the theory has been tested. Earlier experiments used SANS15 where there are limitations on the length of the available experimental periods. NMR, not having centered around a nuclear reactor but instead around cheaper and more abundant spectrometers, is less limited by the length of a single experimental session. We exploited this fact. A weak point of the present study is the use of the molecular probe HMS instead of directly measuring the distribution of decane among different droplets. Further NMR experiments with molecular probes other than HMS might help, if supplying identical results, to convince those readers who would doubt that the distribution of HMS truly represents the decane distribution in the studied system. An experiment without a foreign probe molecule (as HMS is in the present study) would be possible if one used (expensive) surfactants with a deuterated alkyl chain. Hence, the 1H NMR signal of methylene groups would exclusively reflect the motion of decane molecules. A third option is to use 2H PGSE NMR with emulsions prepared by deuterated decane although this demands a higher (∼40 T/m that is technically difficult) magnetic field gradient strength. Acknowledgment. The Swedish Natural Science Research Council (NFR) has supported this work. N.H. thanks the Ernst Johnsson Foundation for a scholarship. Ulf Olsson is thanked for helpful comments. LA001597Z