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Jan 27, 1999 - Diffraction-like effects have been observed by applying pulsed-field-gradient spin−echo (PFG-SE) NMR to a highly concentrated W/O emu...
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Langmuir 1999, 15, 988-991

Structure Determination of a Highly Concentrated W/O Emulsion Using Pulsed-Field-Gradient Spin-Echo Nuclear Magnetic Resonance “Diffusion Diffractograms” Bjo¨rn Håkansson,*,† Ramon Pons,‡ and Olle So¨derman† Division of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden, and Departamento de Tensioactivos, CID/CSIC, C/Jordi Girona 18-26, 08034 Barcelona, Spain Received April 1, 1998. In Final Form: November 17, 1998 Diffraction-like effects have been observed by applying pulsed-field-gradient spin-echo (PFG-SE) NMR to a highly concentrated W/O emulsion, made from the nonionic surfactant C12E4 (CH3(CH2)11(OCH2CH2)4OH), n-decane, and brine (1 wt % NaCl(aq) solution). The q-space plots of the PFG-SE NMR data show one pronounced maximum and the shoulder of a second maximum in the attenuation curve of the NMR signal of water. Such peaks are often referred to as diffraction-like peaks, because of the close analogy of their origin to the origin of peaks observed in scattering experiments. In this paper it is suggested that the peak positions in the “diffusion diffractograms” can be related to the structure of the emulsion, i.e., to the three-dimensional packing of the (nonspherical) emulsion droplets. Furthermore, the characteristic distances in the emulsion system, in this case related to the average size of an emulsion droplet, can be determined from the positions of the diffraction-like peaks. This can be achieved without the need to invoke models for the diffusion.

Introduction During the last 10 years the interest in studying nonGaussian diffusion by means of pulsed-field-gradient spin-echo (PFG-SE, other common abbreviations used in the literature are PFG and PGSE) NMR has increased. This is due to the fact that not only do these experiments give the transport behaviors of the constituents of the system but they also convey structural information. As discussed by Callaghan,1 the PFG-SE experiment can be regarded as an imaging experiment, in which dynamic displacements are probed. This was first experimentally shown by Callaghan et al.,2 using randomly packed polystyrene spheres and measuring the solvent diffusion (in this case water). Another reason for the increased interest in PFG-SE NMR is due to the instrumental developments and improvements that have taken place, as these kinds of experiments require good sensitivity as well as highly reproducible and large magnetic field gradient pulses. An interesting class of systems that has been the object of many recent studies3 are highly concentrated emulsions (also referred to as high internal phase ratio emulsions (HIPREs), gel emulsions, and hydrocarbon gels in the literature) that find great interest in a number of technical applications. Examples can be found in cosmetic and pharmaceutical formulations.4,5 They are also used in applications such as aviation fuels with fire-retarding * Corresponding author. E-mail: [email protected]. Telephone: INT +46 46 222 01 35. Fax: INT +46 46 222 44 13. † Lund University. ‡ CID/CSIC. (1) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Clarendon Press: Oxford, 1991. (2) Callaghan, P. T.; Coy, A.; MacGowan, D.; Packer, K. J.; Zelaya, F. O. Nature (London) 1991, 351, 467. (3) Cameron, N. R.; Sherrington, D. C. High internal phase emulsions (HIPEs)sstructure, properties and use in polymer preparation. In Advances in Polymer Science; Ledwith, A., Ed.; Springer-Verlag: Berlin, 1996; Vol. 126; p 163. (4) Sagitani, H.; Hattori, T.; Nabeta, K.; Nagai, M. Nippon Kagaku Kaishi 1983, 10, 1399.

properties,6 in the field of emulsion explosives,7 and as precursors for polymeric materials.3 As a consequence, it is important to understand the basic properties of such systems, and here the noninvasive PFG-SE NMR technique can provide a valuable tool to obtain information such as structural and dynamic properties of the systems. Concepts from diffraction theories were first introduced in NMR by Mansfield and Grannell.8 Two different such concepts can be identified, viz., the “Mansfield (k-space) diffraction” and the “Callaghan (q-space) diffraction”.9 The differences and similarities are thoroughly discussed by Callaghan.10 In this work we will be concerned with the latter, i.e., the “diffusive (q-space) diffraction”. Diffractionlike effects in highly concentrated emulsions have so far only been reported twice, as far as the authors are aware of. This was done in a report by Balinov et al.,11 dealing with a highly concentrated W/O emulsion, consisting of a fluorinated nonionic surfactant (CnF2n+1CH2E2, where n is 6, 8, or 10), perfluorodecalin, and water. Recently, we presented diffraction-like effects from a highly concentrated W/O emulsion.12 This report constitutes an extension of that work. We focus on the interpretation of the positions of the diffraction-like peaks in the “diffusion diffractograms”. The positions are related to the threedimensional packing of the (deformed) emulsion droplets and the characteristic distances that can be found in the system. Furthermore, we suggest that the long-time stability of these interesting systems can be conveniently followed nonevasively by this method. (5) Atwood, D.; Florence, A. T. Surfactant system. In Surfactant Systems; Chapman & Hall: New York, 1983; p 698. (6) Ishida, H.; Iwama, A. Combust. Sci. Technol. 1984, 37, 79. (7) Encyclopedia of Emulsion Technology, Basic Theory, Measurements, Applications; Marcel Dekker: New York, 1988; Vol. 3. (8) Mansfield, P.; Grannell, P. K. J. Phys. C 1973, 6, L422. (9) Callaghan, P. T.; Eccles, C. D.; Xia, Y. J. Phys. E: Sci. Instrum. 1988, 21, 820. (10) Callaghan, P. T. Magn. Reson. Imaging 1996, 14, 701. (11) Balinov, B.; So¨derman, O.; Ravey, J. C. J. Phys. Chem. 1994, 98, 393. (12) Håkansson, B.; Pons, R.; So¨derman, O. Magn. Reson. Imaging 1998, 16, 643.

10.1021/la9803631 CCC: $18.00 © 1999 American Chemical Society Published on Web 01/27/1999

Determination of a Highly Concentrated W/O Emulsion

Experimental Section Materials. Tetraethylene glycol dodecyl ether, C12E4, was obtained from Nikko Chemicals Co. (Tokyo, Japan), and n-decane, from Sigma (St. Louis, MO), was of analytical grade. Both chemicals were used without further purification. The water used was Millipore-Q treated (Millipore Corp., Bedford, MA). Sample Preparation. The sample preparation was carried out according to a method recently introduced by Pons et al.13 The starting point is an isotropic solution, made by first mixing appropriate amounts of surfactant and “oil” and then adding the appropriate amount of water. The sample is then brought to a temperature (in this case approximately 5 °C) that is lower than the HLB (hydrophilic-lipophilic balance) temperature of the system to obtain a homogeneous isotropic solution. The emulsion is then formed by suddenly increasing the temperature to a value above the HLB temperature (which in the present system is 19 °C).14 This is performed by a rapid transfer of the NMR sample tube to warm water (approximately 45 °C). The sample chosen for the study reported here had a composition of 3 wt % C12E4, 7 wt % n-decane, and 90 wt % brine (containing 1 wt % NaCl). NMR Self-Diffusion Measurements. The self-diffusion of water in the emulsion was measured with the FT-PFG-SE technique, monitoring the 1H NMR spectra and following procedures as suggested previously.15 The measurements were performed in 5 mm NMR tubes (with approximately 800 µL sample solution in the tube) on a Bruker DMX 200 spectrometer. The gradient probe used is from Bruker and gives a gradient strength of approximately 0.22 T m-1 A-1. The temperature was 30 ( 0.1 °C in all measurements. The pulse sequence, 90°-τ180°-τ-echo, with a pulsed magnetic field gradient of amplitude g and duration δ inserted on each side of the 180° radio-frequency pulse with a time separation of ∆ (where ∆ is kept equal to τ) was used throughout. A typical experiment was composed of 16 scans, with a repetition time of 5 s. In the presentation the normalized signal intensities (In) will be plotted vs the quantity q, defined as q ≡ γgδ/2π (with the unit of inverse length).

Result and Discussion Concentrated Emulsions. Before the results of the measurements are presented, a few words about some relevant characteristics of highly concentrated emulsions will be given. These systems can conveniently be prepared in three-component systems in which the surfactant is of the alcohol ethoxylated type,14,16 with the other two components being water (or an electrolyte solution) and aliphatic hydrocarbons. These emulsions may contain more than 99% dispersed phase. Moreover, the emulsions are viscoelastic and show gel-like behavior (for this reason they are sometimes termed gel emulsions). At volume fractions exceeding 0.74 of the dispersed phase, the droplets come in close contact and become polyhedral in shape.3 This is the reason for their elastic behavior; when the structure is deformed, the total surface increases and this increase is opposed by the interfacial tension.17,18 Both theoretical and practical attempts have been made to obtain information about the geometry and the packing of the emulsion droplets in these kinds of systems.3 Because of the strong temperature-dependent phase behavior of alcohol ethoxylates, temperature is one of the most important variables in these systems. Highly concentrated W/O emulsions can only be formed at temperatures above the HLB temperature.14 The structure of these emulsions corresponds to an aqueous surfactant (13) Pons, R.; Carrera, I.; Erra, P.; Kunieda, H.; Solans, C. Colloids Surf. A 1994, 91, 259. (14) Kunieda, H.; Solans, C.; Shida, N.; Parra, J. L. Colloids Surf. 1987, 24, 225. (15) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1. (16) Solans, C.; Azemar, N.; Comelles, F.; Sa´nchez Leal, J.; Parra, J. L. Proceedings of the XVIII Jornadas CED/AID; AID: Barcelona, 1986; p 109. (17) Princen, H. M. J. Colloid Interface Sci. 1979, 71, 55. (18) Pons, R.; Erra, P.; Solans, C.; Ravey, J. C.; Ste´be´, M. J. J. Phys. Chem. 1993, 97, 12320.

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solution (with the surfactant present as monomers) for the dispersed phase, while the continuous phase was shown to be a W/O microemulsion from phase behavior studies,14 SAXS studies,19 and FT-PFG-SE NMR studies.20 The properties of these emulsions such as viscoelasticity, droplet size, and stability were found to have a strong temperature dependence.18 Recently, it was found that highly concentrated W/O emulsions can be formed by merely heating an isotropic solution of an appropriate system.13 At certain compositions, the ternary systems fall in a narrow single-phase region at temperatures below the HLB temperature.13,21 In the system presently under study, PFG-SE experiments showed that the solution consisted of oil-swollen micelles in a continuous water medium in the one-phase region. These clear solutions form highly concentrated W/O emulsions when heated above the HLB temperature. The change of temperature has to be fast enough to prevent any phase separation at intermediate temperatures. It was found that the upper limit of water content for this process to lead to a homogeneous system was around 93 wt % of the dispersed phase.13 This limit can be increased if the system is gently stirred while changing the temperature. The emulsions formed in this way are of small droplet size (radius of around 1 µm just after preparation) and fairly monodisperse as viewed under an optical microscope.13 A narrow droplet size distribution would be expected if the droplet generation follows nucleation kinetics. Simulations of such a process give droplet size distributions with a relative standard deviation of approximately 20%.13 The conductivity of the resulting emulsions was found to be reproducible to within 3%.13 Because of the method of preparation, the formation of these emulsions is almost reversible. The system can be cooled again to the temperature at which it forms a clear solution and heated again to form the emulsion with approximately reproducible properties. These features make this system a good candidate for fundamental studies such as the present one. Finally, we note that the use of brine enhances the stability of the emulsions, presumably by decreasing the rate of droplet coalescence.20 NMR Self-Diffusion Study. The aim of this presentation is not to give a detailed description of the theory behind the observed effects. Detailed accounts can be found elsewhere.22,23 Instead, the focus is on how PFG-SE NMR can be used to study highly concentrated W/O emulsions and in a direct way convey information about the threedimensional packing of the emulsion droplets and the characteristic distances of that packing. The underlying idea of q-space NMR is that the gradient pulses used in the NMR experiment induce a phase shift along the sample (in the direction of the main magnetic field) with a certain wavelength depending on the gradient strength (i.e., the area under the gradient pulse), which can directly be compared to the scattering wave vector in the scattering theory.1 In cases where systems exhibit motional restrictions, diffraction-like peaks can be obtained. Two situations can be identified. First, there may by diffusion inside a confinement with a certain geometry and with totally reflecting barriers. If the displacements of the investigated (19) Pons, R.; Ravey, J. C.; Sauvage, S.; Ste´be´, M. J.; Erra, P.; Solans, C. Colloids Surf. A 1993, 76, 171. (20) Solans, C.; Pons, R.; Zhu, S.; Davis, H. T.; Evans, D. F.; Nakamura, K.; Kunieda, H. Langmuir 1993, 9, 1479. (21) Kunieda, H.; Fukui, Y.; Uchiyama, H.; Solans, C. Langmuir 1996, 12, 2136. (22) Callaghan, P. T.; MacGowan, D.; Packer, K. J.; Zelaya, F. O. J. Magn. Reson. 1990, 90, 177. (23) Callaghan, P. T.; Coy, A.; Halpin, T. P. J.; MacGowan, D.; Packer, K. J.; Zelaya, F. O. J. Chem. Phys. 1992, 97, 651.

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Håkansson et al.

Figure 2. Schematic picture of the ordered packing of deformed droplets in a highly concentrated emulsion. The characteristic distances indicated in the figure correspond to the maxima in Figure 1.

Figure 1. Normalized intensities (b) vs q (q ≡ γgδ/2π) for one diffusion time (∆ ) 70 ms). Also plotted is qIn (O) vs q, to enhance the appearance of the maxima. The arrows in the figure indicate the positions of the expected characteristic distances of hexagonal packing (see text and Figure 2 for details), and the characteristic distances are (a) 2b; (b) x3b; (c) 2b, b; (d) x3b, x3b/2; and (e) 2b, b, b/2. The solid lines are guides for the eye. Parameters used in the experiment were δ ) 3 ms and a maximum gradient strength of 8.37 T m-1.

entities are of the same order or bigger as the dimension of the confinement, a signal decay which is a fingerprint of the geometry in question and its dimensions will be obtained.24 Second, there may be diffusion where the barriers of the confinements are partly permeable and the three-dimensional structure of the confinements are well-defined. Diffraction-like peaks will now occur at q values equal to the inverse of the characteristic distances (determined by the structure) or, expressed in another way, at multiples of wavelengths of the phase shift along the sample that match the characteristic distances. Here, the latter case is responsible for the observed diffractionlike effects. Furthermore, we note that also for this case there may still be contributions to the signal decay from diffusion inside the confinement (see above). In Figure 1 the normalized intensities of the water NMR signal is shown vs the parameter q (defined above), for one diffusion time (∆ ) 70 ms). The “diffusion diffractogram” shows one pronounced maximum and the shoulder of a second maximum. To enhance the features of the signal intensities, we have also included a plot of qIn vs q (see Figure 1). Let us first consider the long-range water diffusion (over distances larger than the droplet size). The systems presently under study consist of densely packed water droplets separated by a thin oil film (on the order of 100 Å; in fact, the structure of these emulsions is similar to that of a foam, in which the gas is substituted by the dispersed phase). As a consequence, the water molecules are able to permeate the film. The mechanism whereby the water molecules cross the film is not of importance in the present application and will not be considered here. As discussed by Callaghan,1 the attenuation of the signal intensities in the limit of q f 0 yields the mean square displacement (〈Z2〉) of the investigated components. Thus, the effective long-range diffusion coefficient (Deff ) 〈Z2〉/ 2∆) can be obtained by assuming a Gaussian distribution of the displacements, where the displacements now correspond to a random walk with a step length of b, where b is the center-to-center distance between the droplets. In the present case we obtain Deff ) 9 × 10-11 m2 s-1 (where (24) Callaghan, P. T. J. Magn. Reson. A 1995, 113, 53.

the first five points in Figure 1 have been used in the nonlinear least-squares fitting procedure), which corresponds to a reduction of the bulk water self-diffusion coefficient by a factor of over 20. From this value we can estimate the lifetime (τR) of the water molecules in the emulsion droplet from the relation25

τR ) b2/6Deff

(1)

Letting b ) 2.1 µm (see below), we obtain τR ) 8 ms. Thus, during a diffusion time of 70 ms, the water molecules sample a limited number of emulsion droplets. Let us now return to the origin of the maxima in Figure 1. As indicated above, we measure on a time scale where some of the water molecules visit two or more droplets during the experimental time. In cases where the systems under study have a well-defined structure, the distances traveled by the spin-bearing molecules will be determined by the structure. This implies that the fraction of water molecules that visits two or more droplets will only move certain distances, the values of which will be given by the structure of the system in question. For the preferred distances, diffraction-like peaks will be obtained at q values equal to the inverse of the distances (see Figure 1). As can be inferred from Figure 1, diffraction-like peaks occur at q values of 5.5 × 105 and 9.6 × 105 m-1, respectively. These correspond in real space to 1.8 and 1.0 µm, respectively. The ratio between these numbers is close to x3. To rationalize these numbers, we recall the fact that the droplets are polyhedral in shape. In Figure 2 an ensemble of droplets has been packed in a hexagonal symmetry (Figure 2 shows only a two-dimensional slice of the ensemble, cut in the middle of the droplets). This is certainly not a true picture of a highly concentrated emulsion but serves as a guide for the relationship we would expect among the characteristic distances in the system. Clearly, there are three characteristic distances indicated in the representation of Figure 2. In terms of the distance b, these are b:x3b/2:b/2. The two maxima seen in the “diffusion diffractogram” of Figure 1 would then correspond to the two last of these characteristic distances, and we obtain for b a value of 2.1 µm. Furthermore, we note that a multiple of the characteristic distances mentioned above will also be represented at the same q value, i.e., a whole number of wavelengths (see Figure 1). The “radius” is then approximately 1 µm, in good agreement with independent experiments on these kinds of emulsions.13 The reason that the peak corresponding to b is not visible is presumably due to the fact that a smaller fraction (see Figure 2) of the spin-bearing molecules are able to move this characteristic distance. (25) Balinov, B.; Linse, P.; So¨derman, O. J. Colloid Interface Sci. 1996.

Determination of a Highly Concentrated W/O Emulsion

The agreement is surprisingly good, and one might argue that the position of the second peak is somewhat inexact (as we do not have any pronounced maximum). Nevertheless, the effect of shifting the position one point to the left or to the right is marginal. One should also note that the signal attenuation predicted by the above reasoning is modulated by diffusion within each droplet as discussed earlier. In the scattering analogy, the decay due to the diffusion between droplets is modulated by the form factor of the droplet as such. The contribution of the form factor to the signal decay will certainly depend on how easy the molecules can leave the confinement (in other words, how long the lifetime is). In the case of highly concentrated W/O emulsions, the initial NMR signal decay of water indicates that the lifetime is indeed short (on the order of milliseconds) and the form factor will then contribute less to the signal decay. The lifetime is probably determined by the film thickness between the droplets; i.e., water in bigger droplets will have longer lifetimes than water in smaller droplets, as the film thickness increases with increasing droplet size. Moreover, we may conclude that the “diffusion diffractograms” are probably broadened by the polydispersity in size of the emulsion droplets, which will give a polydispersity in characteristic distances of the system as well. This will broaden the diffraction-like peaks, and as a consequence they will be less pronounced. In conclusion, we have shown that it is possible to rationalize the PFG-SE NMR signal decay of water in terms of ordered (at least over distances of a few droplets) deformed droplets. From the data, we obtain an estimate of the size of the droplet as well as a fairly good picture of the packing of the emulsion droplets and the characteristic distances in the concentrated emulsion system. The information is obtained directly from the PFG-SE NMR data without the need to invoke any models. Crucial for this approach is the observation of more than one peak (in order to obtain the scaling behavior). The ratio between the g values of the two peaks will determine the structure of the three-dimensional packing of the (nonspherical) emulsion droplets. Finally, we note that Callaghan and co-workers have developed a pore-hopping (PH) formalism,2,22,23 which describes the diffusion in a pore glass. The PH formalism has been successful in describing the diffusion of water between randomly packed polystyrene spheres.2 We have been less successful in using the PH formalism to describe the attenuation curve in Figure 1. Some likely reasons for this failure are that the structure factor may not be described as a pore glass, because of ordering of the droplets. Long-Time Stability. The stability of the emulsion system with time can be conveniently followed by this

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Figure 3. Normalized intensities vs q (q ≡ γgδ/2π) for one diffusion time (∆ ) 50 ms) at 2 (b) and 8.5 (O) h after preparation, respectively. The solid lines are guides for the eye. Parameters used in the experiment were δ ) 3 ms and a maximum gradient strength of 8.37 T m-1.

method. This is illustrated in Figure 3, where the signal attenuation of the water signal is shown for two different times after preparation of the emulsion, using the same diffusion time in both cases (∆ ) 50 ms). From Figure 3 we clearly see how the maximum moves toward lower q values (i.e., larger distances and bigger droplets). We also note that the maximum is becoming less pronounced. The emulsion is breaking. Such data are important in the development of theories for the stability of emulsions.26 Concluding Remarks This study has shown that it is possible from PFG-SE NMR “diffusion diffractograms” to obtain a rather detailed picture of a highly concentrated W/O emulsion without invoking any complicated modeling. Furthermore, it is possible to follow the long-time stability of the emulsion. The PFG-SE NMR method may be a complement to other methods to obtain structural information of such systems. Acknowledgment. This work was financially supported by the Swedish Natural Science Research Council and the Swedish Institute. The spectrometer was purchased with a grant from the Swedish Council for Planning and Coordination of Research (FRN). R.P. acknowledges financial support from Generalitat de Catalunya (CUR, BEAI). LA9803631 (26) Kabalnov, A.; Wennerstro¨m, H. Langmuir 1996, 12, 276.