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Diffusion in an inhomogeneous system: NMR studies of diffusion in highly concentrated emulsions
Journal of Colloid and Interface Science 263 (2003) 270–276 www.elsevier.com/locate/jcis
Diffusion in an inhomogeneous system: NMR studies of diffusion in highly concentrated emulsions Carin Malmborg,∗ Daniel Topgaard, and Olle Söderman Division of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden Received 20 November 2002; accepted 5 March 2003
Abstract In this study the self-diffusion of different species in highly concentrated water-in-oil emulsions was investigated by means of the NMR diffusometry approach. The emulsions contained 96% aqueous solutions of salt or other additives; heptane was used as the oil phase. The surfactants, used to stabilize the emulsion, were soybean phosphatidylcholine and C12 EO4 . The water drops were about 1.5 µm in diameter according to diffusion measurements performed on water. Diffusion of tetramethyl ammonium ions and glucose between the emulsion droplets was found to be negligible on the relevant time-scale (<1 s). On the contrary, acetic acid/acetate ions diffused between the droplets and had exchange times which were a function of pH. 2003 Elsevier Science (USA). All rights reserved. Keywords: Diffusometry; Self-diffusion; Highly concentrated emulsion
1. Introduction The aim of this study was to investigate the self-diffusion of different substances in highly concentrated water-in-oil emulsions with NMR diffusometry. These emulsions are also known as gel-emulsions or high internal phase ratio emulsions (see [1] for a recent review). This type of emulsions are important in many technical applications such as in food products, in cosmetic and pharmaceutical formulations, and in emulsion explosives, to name just a few of the many application areas. One particular important application is the use of concentrated emulsions as drug delivery systems, for instance via topical administration. Therefore, it is of interest to study the transport of active substances solubilized in these emulsions. This can be done by measuring the mean square displacement (MSD), z2 , of different substances placed in the dispersed phase with spin–echo and stimulatedecho based NMR pulsed field gradient techniques, a technique which has become known as NMR diffusometry [2]. One advantage of this technique is that it is possible to determine z2 irrespective of whether the diffusion process is unrestricted (Gaussian) or not. In addition, z2 may be de* Corresponding author.
E-mail address: [email protected] (C. Malmborg).
termined as function of time over a wide time-window from a few 100 µs up to several seconds [3–5]. Further advantages of the technique are that it does not require any isotopic labeling or addition of disturbing probes, it is rapid, it only requires a small amount of sample, and it is a nondestructive method meaning, that the same sample can be repeatedly studied. The method measures root-mean-square displacements (RMSDs) of the diffusing molecules in the µm range. As a consequence, the measured value of the MSD conveys easily interpretable information on the structure and obstruction effects in systems where characteristic length scales are in the µm range, such as in emulsion systems. In addition to allowing the measurements of z2 , the plot of the NMR echo signals vs the relevant experimental parameter q (for a definition of q, see below), which we shall henceforth refer to as echo profiles, sometimes show coherence peaks for systems in which the diffusion is not Gaussian [6–14]. The position of these peaks may convey structural information (pore size and shape). In the context of concentrated emulsions, Håkansson et al. have performed earlier work in this area [14]. They showed that the peak position in an echo profile could be related to the emulsion structure in the highly concentrated systems, i.e., to the three-dimensional packing of the nonspherical emulsion droplets.
0021-9797/03/$ – see front matter 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0021-9797(03)00259-5
C. Malmborg et al. / Journal of Colloid and Interface Science 263 (2003) 270–276
Related studies have been performed by Kreilgaard and co-workers, who studied diffusion of a lipophilic and a hydrophilic model drug in microemulsions. They used the selfdiffusion coefficient and the T1 relaxation time obtained from NMR spectroscopy measurements to characterize the microemulsions [15]. Hills et al. discussed the relationship between emulsion microstructure and bulk rheology, focusing on the diffusion propagator of the continuous phase of concentrated oil-in-water emulsions [16]. Properties such as emulsion stability and molecular diffusion of mandelic acid through a dialysis membrane have been studied by Calderó et al. on highly concentrated water-in-oil emulsions [17]. They measured the passage of mandelic acid in a concentration gradient with UV spectrophotometry and investigated the effect of the amount of internal phase, the presence and concentration of electrolytes, and the different surfactant mixtures. In a second paper they performed diffusion studies of mandelic acid in highly concentrated emulsions with different pH values by allowing two emulsions to come into contact and then monitoring the concentration with UV spectrophotometry [18]. The present work is the first in a series of studies aimed at characterizing and determining the transport of various substances in concentrated emulsions. We present data on the transport of water, tetramethyl ammonium (TMA) ions, glucose, and mixtures of acetic acid/acetate ions. The long-time diffusion is interpreted using a cell model, which describes the diffusion in terms of the local (equilibrium) concentrations and local diffusivities [19]. In addition, we present some data pertaining to the characterization of the concentrated emulsions used, in particular with respect to stability.
2. Materials and methods
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phosphatidylcholine (0.3% w/w). To investigate the influence of various salts on the stability of the emulsions, samples were made with 1 wt% of the following salts: NaCl, CaCl2 , MgCl2 , MgSO4 , and K2 SO4 . Three emulsions with acetic acid/sodium acetate were prepared with different pH values of the water phase with the molar ratios of acetic acid/sodium acetate 95/5, 50/50, and 5/95; the total concentration of sodium acetate + acetic acid was 0.25 M in all three samples. Samples with 0.2 M TMACl and 0.25 M glucose were also made. The water used in the sample preparation contained different combinations of Millipore water and heavy water to get a reasonable relationship in intensities between the water and salt/sugar/(acetic ion + acid) NMR peaks. The water phase was added drop-wise to the oil phase (in which the surfactants were solubilized) in a glass tube containing 6–7 glass beads while shaking on a mixer. When the emulsion became viscous the shaking was done by hand. 2.3. NMR self-diffusion measurements NMR experiments were performed on a 200 MHz Bruker DMX spectrometer equipped with a Bruker DIFF-25 gradient probe driven by a Bruker BAFPA-40 unit. The temperature was 25 ◦ C. In most of these experiments we have performed Hahn spin–echoes. The stimulated-echo technique was used in the experiment with glucose. 2.4. Calculating the size of emulsion droplet from echo profiles The plot of the measured intensity vs q, which is calculated from the gradient pulse strength and length (units of m−1 ), gives a broad peak. The value of q at the peak is the inverse of the droplet diameter [14].
2.1. Materials Heptane of p.a. quality was purchased from Merck. The surfactant oligo(ethylene glycol) dodecyl ether (C12 EO4 ) was obtained from NIKKO chemicals, Japan. Lucas Meyer supplied the soybean phosphatidylcholine with the trade name Epicuron 200. NaCl was obtained from Riedel-de Haen. The water was of Millipore-Q quality and heavy water was from Dr. Glaser, Basel. Tetramethylammonium chloride (TMACl) and D(+)-glucose was purchased from Fluka Biochemica. The acetic acid, K2 SO4 , MgSO4 , and MgCl2 were obtained from Merck, the sodium acetate from the British Drug Houses, and CaCl2 from Aldrich. All chemicals were used as received. 2.2. Sample preparation The emulsions contained 96% w/w water to which salt, sugar or acetic acid/sodium acetate have been added. The oil phase, making up 2.3% w/w, was heptane, while the emulsifier was a mixture of C12 EO4 (1.4% w/w) and soybean
3. NMR diffusometry The field gradient technique to monitor diffusion was introduced by Hahn in 1950 [20]. Stejskal and Tanner improved the technique by introducing the pulsed gradient technique [21,22]. In its simplest version the technique involves the application of two identical gradient pulses of duration δ and amplitude g a distance apart (from start to start) of on either side of the 180◦ pulse in a Hahn echo experiment. In terms of the parameters of the NMR diffusion experiment, the normalized echo-intensities can be written as [23] E(δ, , g) = ρ(z0 )P (z0 |z, )eiγ gδ(z−z0 ) dz dz0 , (1) where ρ(z0 ) is the initial normalized spin density and P (z0 |z, ) is the probability density of finding a spin at position z after a time , if it was originally at z0 , is the diffusion time, i.e., the time over which the RMSD is monitored, and γ is the magnetogyric ratio of the studied nucleus.
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Equation (1) is valid for infinitely narrow gradient pulses. In short, the conditions for this is that the displacement during the gradient pulse is much smaller than the displacement during the diffusion time and the compartment size, where the latter condition applies for the case of molecules experiencing restricted diffusion. Apart from this limitation, Eq. (1) is valid for all types of diffusion processes. Often, the experimental parameters δ and g are used to define a scaled area of the gradient pulse as q = γ gδ/(2π). For the special case of unrestricted diffusion, where the propagator P (z0 |z, ) is a Gaussian, Eq. (1) gives the Stejskal–Tanner equation for the echo intensities, E(, δ, g) = exp(−γ 2 g 2 δ 2 D),
(2)
where D is the self-diffusion coefficient. As mentioned above, a useful property of NMR diffusometry is that the MSD may be obtained by expanding Eq. (1) to low values of q: lim E(, δ, g) = 1 − 2π 2 q 2 z2 .
q→0
(3)
In concentrated emulsions of the type studied here, water domains are separated from each other by a hydrocarbon film, which is on the order of a few 100 Å thick. Substances, which are soluble in the film, may then diffuse from one droplet to the next. If the emulsion structure is well ordered, at least locally, diffraction peaks may be observed in a plot of the measured echo intensities vs q. The inverse of the q-value of the top of the diffraction peak equals the characteristic distance, from one emulsion droplet to another, which is the diameter of the droplet in these highly concentrated systems [24]. The long-time diffusion coefficient in such a system is given by the concentrations and diffusivities in the water and hydrocarbon domains. For the case of a spherical system, such as the one depicted in Fig. 1, the long-time diffusion coefficient, Deff , is given by [19,25]: Deff = β=
1 − βΦ D2 , 1 − (1 − C1 /C2 )Φ 1 + βΦ/2
D2 C2 − D1 C1 . D2 C2 + 0.5D1 C1
(4)
(5)
In the present case, D1 /C1 is the diffusion/concentration of the species in water and D2 /C2 is the diffusion/concentration of the species in oil. Φ is the volume fraction of the inner droplet (in this case the aqueous component). We note that so far we have not discussed the state of the diffusing species in the oil domain. They may be molecularly dispersed or be solubilized in reversed micelles, which are also present in the oil [1,18]. In the case of solubilization in micelles, D2 is the diffusion of the reversed micelle, while C2 is the effective concentration in the oil domains of the solubilized species. From the measurements presented here it is difficult to differentiate between the two mechanisms (in actual fact, both mechanisms will most likely contribute to the transport across the film). In what follows we will assume
Fig. 1. Illustration of the concentrated emulsion in terms of a spherical cell model. The long-time diffusion is determined by the concentrations and diffusivities in the water and oil domains (cf. Eqs. (4) and (5)).
that the transport over the oil film is dominated by molecularly dissolved species in the oil domains, and will return to the question of which of the two mechanisms that dominates below. Species, which are not present in the oil domains, are confined to one emulsion droplet during the experiment. If the droplet size is smaller than the RMSD diffused by the molecules in bulk (with no restrictions), the following relation exists between z2 and the droplet radius R [5]: 2 z2 = R 2 . 5
(6)
4. Results and discussion 4.1. Introduction This section is organized in the following way. We start by discussing some general properties of the investigated emulsions system, such as stability with time, the influence on stability of different ionic species in the dispersed phase, and the size of the (deformed) water droplets. We then present and discuss data about diffusion of species confined to reside in the droplets and for species that exchange between the droplets in the emulsion and end the paper with some concluding remarks. 4.2. General properties of the investigated emulsion system In order to assess the size of the water droplets and the stability of the concentrated emulsion, the water diffusion was measured every hour during a period of 24 h for a system containing 0.17 M NaCl in the dispersed phase. Figure 2 shows that the echo profiles coincide over a period of (at least) 24 h, implying that the emulsion is stable over that time period. The fact that the stability can be monitored as a function of time is a useful feature of the NMR diffusometry approach; from echo profiles taken before and after each experiment one can investigate whether the emulsion is stable
C. Malmborg et al. / Journal of Colloid and Interface Science 263 (2003) 270–276
Fig. 2. Water echo intensity versus q. Three curves, obtained after 0 (!), 10 (1), and 24 (E) h of preparation are given.
or not during the measurement. Such experiments have been carried out before and after each experiment reported on in this work. In addition, the position of the rather broad peak gives information about the droplet size [14]. The position of the peak in q-space corresponds to the inverse of the distance between two droplets, which in these dense emulsions corresponds to the droplet diameter. From Fig. 2, the droplet diameter can be estimated to 1.8 µm. The echo profile peaks are quite broad and hence the evaluation is not very exact. This fact may have different causes. The water droplets are polydisperse in size and/or the emulsion is divided in big domains with different sizes of the droplets in each domain. When the signals are added together both of these situations would give broad peaks with a mean droplet size [14]. Finally, we note that the emulsion droplets studied in Fig. 2 had grown to 2.2 µm in diameter after 9 days. Salt is added to the dispersed phase in order to slow down the rate of Ostwald ripening. Salt increases the osmotic pressure in the water and prevent the emulsion droplets from growth, as water will not leave a droplet since the osmotic pressure in that drop would then increase. We examined whether different salts would give emulsions with different sizes of the water droplets. The salts used were CaCl2 , MgSO4 , MgCl2 , K2 SO4 , and NaCl (all at 1 wt%) and the results are shown in Fig. 3. The type of salt used does not affect the emulsion droplet size and stability (at least not over the time span over which the emulsions were investigated). The droplet diameter was estimated from water echo profiles to 1.8 µm, irrespective of which salt was added. From the size of the droplets some further information about the emulsion may be derived. On the assumption that the droplets are spherical with a radius of 0.9 µm, the thickness of the oil film surrounding each droplet may be calculated from the emulsion composition to approximately 100 Å. Moreover, if the area per surfactant at the droplet interface is taken as 75 Å2 for lecithin and 45 Å2 for C12 E4 , and it is assumed that lecithin resides solely at the interface,
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Fig. 3. Water echo intensities versus q, for emulsions with different salts in the water phase. The salts used are CaCl2 (!), MgSO4 (1), MgCl2 (E), K2 SO4 (P), and NaCl (✁). The concentration was in all cases 1 wt%.
the amount of C12 E4 in the oil film may be calculated from the droplet area. The result is that approximately 15% of C12 E4 resides in the film, in the form of molecularly dispersed C12 E4 and in reversed micelles. 4.3. Diffusion of molecules that do not leave the droplet during the diffusion time We show in Figs. 4 and 5 the long-time RMSDs of TMA ions and glucose as a function of the diffusion time. In both cases the displacement is also given for water. MSDs have been obtained from the slope of the echo intensities at low q-values (see Eq. (3) above). While the MSD for water increases linearly with time, indicating Gaussian diffusion for this species in the long-time limit (we will discuss the water data in the next section), the MSDs of the TMA ion and glucose are independent of time, indicating that these species do not leave the droplet during the diffusion time. In the light of Eqs. (4) and (5), this means that the solubility of glucose and
Fig. 4. Root mean square displacement for TMACl (") and water (F) vs diffusion time. The solid lines are guides to the eye.
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Fig. 5. Root mean square displacement for glucose (") and water (F) vs diffusion time.
TMA ions is low in the oil film, implying that the oil film is an effective barrier that hinders these species from leaving a droplet. The value of the MSD for both glucose and the TMA ion is 4 × 10−14 µm2 , giving further support for the fact that the droplet size is reproducible between different emulsions. Using Eq. (6) the radius of the droplets can be calculated to be 0.3 µm. This is lower than the value obtained from the echo profiles in Figs. 2 and 3. This is a consequence of the fact that the conditions for short gradient pulses are not met for the species diffusing within a droplet [26]. We show in Fig. 6 results of Brownian dynamics simulations using a procedure outlined in [27]. From the simulations the RMSDs have been determined. It is clear from Fig. 6 that the effect of the finite gradient pulses is to decrease the measured RMSD. Hence, too low a value for the droplet radius is derived if Eq. (6) is used. In the present case δ was 2 ms. The data in Fig. 1 were obtained for a droplet radius of 0.9 µm. From Fig. 6, the use of δ = 2 ms yields a value of RMSD of 0.16 µm, in rather good agreement with the obtained value 0.2 µm.
Fig. 6. Root mean square displacements obtained from initial slopes as function of the gradient pulse length as obtained from Brownian simulations. Conditions are for water diffusing within a droplet of 0.9 µm (D = 2 × 10−9 m2 s−1 ).
Fig. 7. Echo profiles for water (") and HAc/Ac− (F). The ratio of HAc to Ac− is 5/95.
4.4. Diffusion of molecules that leave the droplet during the diffusion time In order to investigate the diffusion behavior of species that have sufficient solubility in the oil film such that they may leave the droplet and in the long-time limit perform a random walk between the droplets, we have prepared emulsions with solutions of HAc/Ac− in different ratios, in order to produce different pH values in the droplet and hence different degrees of dissociation of the acetic acid. We show in Fig. 7 echo profiles for 5/95 volume ratios of 0.25 M HAc/Ac− and water. The diffraction peaks are observed at the same value of q for both water and HAc/Ac− . This is the expected result, since the location of the diffraction peak only depends on the properties of the emulsion (droplet size and film thickness). The minima in the echo profiles are slightly different on account of different diffusion coefficients for water and HAc/Ac− .
Fig. 8. Root mean square displacements for HAc/Ac− and water (×) vs diffusion time. The solid lines are the results of fitting the relation z2 = 2D to the data. Three different molar ratios of 0.25 M HAc/Ac− have been used: 95/5 (!), 50/50 (E), and 5/95 (1).
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Table 1 Data for long-time diffusion of HAc/Ac− and water Emulsion, investigated species 95/5, HAc/Ac 50/50, HAc/Ac 50/50, water 5/95, HAc/Ac
Deff /10−10 m2 s−1 a 5.0 3.0 1.0 0.4
D1 /10−10 m2 s−1 b
C2 /M
C2calc /M
10.2 9.47 23.0 8.52
1.3 × 10−3
1.3 × 10−3 7.2 × 10−4 – 7.6 × 10−5
6.1 × 10−4 1.6 × 10−2 6.1 × 10−5
C2 is the experimentally determined value of the concentration of HAc and water in the oil-film, while C2calc are calculated values (see text for details). a Obtained from data in Fig. 8. b Obtained from measurements on the water solutions from which the emulsions were made.
We now turn to the MSD of HAc/Ac− . Given in Fig. 8 are the RMSDs as a function of diffusion time for three different ratios of HAc to Ac− and for water (water data from the emulsion with 50/50 HAc/Ac− ). The MSDs for water and acetic acid/acetate ions increase with the diffusion time. As noted above, this means that these species are not confined to one droplet on the relevant time scale, but instead they perform a random walk from droplet to droplet. For such a case, z2 = 2D and the long-time diffusion of these species can be obtained by fitting this relation to the data in Fig. 8, and the results are given in Table 1. Inspection of Table 1 reveals the fact that the long-time diffusion depends on the solubility of the species in the oil film separating the droplets: the solubility is low for the charged acetic ion and higher for the acetic acid molecule. We can carry this analysis one step further. By measuring the diffusion coefficients of 0.25 M HAc/Ac− at the relevant pH values, values of D1 are obtained. Furthermore, by assuming that the diffusion coefficient of HAc in the oil phase can be obtained from the value obtained for the sample with 95/5 HAc/Ac− in water scaled by the ratio of the viscosities of the two solvents we may estimate a value of C1 /C2 (cf. Eqs. (4) and (5)) and hence of the concentration of HAc in the oil film. The results are included in Table 1. It is straightforward to show that the concentration of HAc in the oil phase is given by KD −pH 10 [Ac− ], (7) Ka where KD is the distribution constant for HAc between the oil film and water, and the rest of the quantities have their usual meaning. In deriving Eq. (7), we have assumed that the concentrations in the water droplets of HAc/Ac− remains the same as in the original water solution, from which the emulsion is made and that the concentration of Ac− in the oil film is negligible. Although we do not know KD we know that it is constant. By adjusting the value of KD to the experimental C2 result for the 95/5 case, we can predict the values of C2 for the other ratios of HAc/Ac− . The results are included in Table 1. As can be seen the agreement is reasonable, the deviations are most likely do to the uncertainties in the values of D2 . In conclusion, the long-time diffusion of HAc/Ac− is well described by Eqs. (4) and (5). We now return to the question raised above of whether the diffusing molecules are molecularly dispersed or solubilized in reversed micelles in the oil film. Clearly, there is a [HAc]oil =
specificity in the diffusion: molecules with no or low solubility in the oil are confined to the emulsion droplets during the time of the measurement (cf. Table 1). In the case of reversed micelles, the specificity would then be due to the exchange between the emulsion droplet and the reversed micelle, which process involves transport over a non-polar region. We note that if we take the volume fraction of reversed micelles in the continuous phase to be 20 vol%, then the concentration of HAc/Ac− would be of order 0.05 M, which can be compared with the value 6.1 × 10−5 M obtained on the assumption that HAc/Ac− in the oil domain is molecularly dispersed. Since we essentially determine the product D2 C2 , this means that the diffusion coefficient of the reversed micelle in the oil domain would be of order 1 × 10−12 m2 s−1 , which is rather low (corresponding to a hydrodynamic radius of roughly 0.5 µm). One final aspect concerns where the reversed micelles are situated in the emulsion system. If the bulk of the micelles reside in the Gibbs–plateau borders, then their effectiveness in promoting transport from one droplet to a neighboring droplet is less efficient. None of the arguments above are conclusive. Therefore we cannot exclude that some of the transport over the oil film is mediated by reversed micelles. Finally, from the value of the RMSD of water, solubility (again assuming that water is molecularly dispersed) of water in the oil film may also be calculated. The result is included in Table 1. 4.5. Concluding remarks We have investigated the general properties, such as stability and structure of concentrated water-in-oil emulsions with NMR diffusometry. The mean square displacement of water, salt, sugar, and acetic acid/acetate ion have been measured and the results show that water and acetic acid/acetic ion diffuse between emulsion droplets and that tetramethyl ammonium ions and glucose do not on the relevant time scale. Acetic acid show different diffusion coefficients at different pH values of the water phase, which is expected since ions have lower solubility in the oil phase. The results with regard to the long-time diffusion may be rationalized by means of a cell model that describes the long-time diffusion solely in terms of local diffusivities and (equilibrium) concentrations.
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Acknowledgment This study was financially supported by the Swedish Foundation for Strategic Research (SSF) through the Colloid and Interface Technology program.
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Diffusion in an inhomogeneous system: NMR studies of diffusion in highly concentrated emulsions Carin Malmborg,∗ Daniel Topgaard, and Olle Söderman Division of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden Received 20 November 2002; accepted 5 March 2003
Abstract In this study the self-diffusion of different species in highly concentrated water-in-oil emulsions was investigated by means of the NMR diffusometry approach. The emulsions contained 96% aqueous solutions of salt or other additives; heptane was used as the oil phase. The surfactants, used to stabilize the emulsion, were soybean phosphatidylcholine and C12 EO4 . The water drops were about 1.5 µm in diameter according to diffusion measurements performed on water. Diffusion of tetramethyl ammonium ions and glucose between the emulsion droplets was found to be negligible on the relevant time-scale (<1 s). On the contrary, acetic acid/acetate ions diffused between the droplets and had exchange times which were a function of pH. 2003 Elsevier Science (USA). All rights reserved. Keywords: Diffusometry; Self-diffusion; Highly concentrated emulsion
1. Introduction The aim of this study was to investigate the self-diffusion of different substances in highly concentrated water-in-oil emulsions with NMR diffusometry. These emulsions are also known as gel-emulsions or high internal phase ratio emulsions (see [1] for a recent review). This type of emulsions are important in many technical applications such as in food products, in cosmetic and pharmaceutical formulations, and in emulsion explosives, to name just a few of the many application areas. One particular important application is the use of concentrated emulsions as drug delivery systems, for instance via topical administration. Therefore, it is of interest to study the transport of active substances solubilized in these emulsions. This can be done by measuring the mean square displacement (MSD), z2 , of different substances placed in the dispersed phase with spin–echo and stimulatedecho based NMR pulsed field gradient techniques, a technique which has become known as NMR diffusometry [2]. One advantage of this technique is that it is possible to determine z2 irrespective of whether the diffusion process is unrestricted (Gaussian) or not. In addition, z2 may be de* Corresponding author.
E-mail address: [email protected] (C. Malmborg).
termined as function of time over a wide time-window from a few 100 µs up to several seconds [3–5]. Further advantages of the technique are that it does not require any isotopic labeling or addition of disturbing probes, it is rapid, it only requires a small amount of sample, and it is a nondestructive method meaning, that the same sample can be repeatedly studied. The method measures root-mean-square displacements (RMSDs) of the diffusing molecules in the µm range. As a consequence, the measured value of the MSD conveys easily interpretable information on the structure and obstruction effects in systems where characteristic length scales are in the µm range, such as in emulsion systems. In addition to allowing the measurements of z2 , the plot of the NMR echo signals vs the relevant experimental parameter q (for a definition of q, see below), which we shall henceforth refer to as echo profiles, sometimes show coherence peaks for systems in which the diffusion is not Gaussian [6–14]. The position of these peaks may convey structural information (pore size and shape). In the context of concentrated emulsions, Håkansson et al. have performed earlier work in this area [14]. They showed that the peak position in an echo profile could be related to the emulsion structure in the highly concentrated systems, i.e., to the three-dimensional packing of the nonspherical emulsion droplets.
0021-9797/03/$ – see front matter 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0021-9797(03)00259-5
C. Malmborg et al. / Journal of Colloid and Interface Science 263 (2003) 270–276
Related studies have been performed by Kreilgaard and co-workers, who studied diffusion of a lipophilic and a hydrophilic model drug in microemulsions. They used the selfdiffusion coefficient and the T1 relaxation time obtained from NMR spectroscopy measurements to characterize the microemulsions [15]. Hills et al. discussed the relationship between emulsion microstructure and bulk rheology, focusing on the diffusion propagator of the continuous phase of concentrated oil-in-water emulsions [16]. Properties such as emulsion stability and molecular diffusion of mandelic acid through a dialysis membrane have been studied by Calderó et al. on highly concentrated water-in-oil emulsions [17]. They measured the passage of mandelic acid in a concentration gradient with UV spectrophotometry and investigated the effect of the amount of internal phase, the presence and concentration of electrolytes, and the different surfactant mixtures. In a second paper they performed diffusion studies of mandelic acid in highly concentrated emulsions with different pH values by allowing two emulsions to come into contact and then monitoring the concentration with UV spectrophotometry [18]. The present work is the first in a series of studies aimed at characterizing and determining the transport of various substances in concentrated emulsions. We present data on the transport of water, tetramethyl ammonium (TMA) ions, glucose, and mixtures of acetic acid/acetate ions. The long-time diffusion is interpreted using a cell model, which describes the diffusion in terms of the local (equilibrium) concentrations and local diffusivities [19]. In addition, we present some data pertaining to the characterization of the concentrated emulsions used, in particular with respect to stability.
2. Materials and methods
271
phosphatidylcholine (0.3% w/w). To investigate the influence of various salts on the stability of the emulsions, samples were made with 1 wt% of the following salts: NaCl, CaCl2 , MgCl2 , MgSO4 , and K2 SO4 . Three emulsions with acetic acid/sodium acetate were prepared with different pH values of the water phase with the molar ratios of acetic acid/sodium acetate 95/5, 50/50, and 5/95; the total concentration of sodium acetate + acetic acid was 0.25 M in all three samples. Samples with 0.2 M TMACl and 0.25 M glucose were also made. The water used in the sample preparation contained different combinations of Millipore water and heavy water to get a reasonable relationship in intensities between the water and salt/sugar/(acetic ion + acid) NMR peaks. The water phase was added drop-wise to the oil phase (in which the surfactants were solubilized) in a glass tube containing 6–7 glass beads while shaking on a mixer. When the emulsion became viscous the shaking was done by hand. 2.3. NMR self-diffusion measurements NMR experiments were performed on a 200 MHz Bruker DMX spectrometer equipped with a Bruker DIFF-25 gradient probe driven by a Bruker BAFPA-40 unit. The temperature was 25 ◦ C. In most of these experiments we have performed Hahn spin–echoes. The stimulated-echo technique was used in the experiment with glucose. 2.4. Calculating the size of emulsion droplet from echo profiles The plot of the measured intensity vs q, which is calculated from the gradient pulse strength and length (units of m−1 ), gives a broad peak. The value of q at the peak is the inverse of the droplet diameter [14].
2.1. Materials Heptane of p.a. quality was purchased from Merck. The surfactant oligo(ethylene glycol) dodecyl ether (C12 EO4 ) was obtained from NIKKO chemicals, Japan. Lucas Meyer supplied the soybean phosphatidylcholine with the trade name Epicuron 200. NaCl was obtained from Riedel-de Haen. The water was of Millipore-Q quality and heavy water was from Dr. Glaser, Basel. Tetramethylammonium chloride (TMACl) and D(+)-glucose was purchased from Fluka Biochemica. The acetic acid, K2 SO4 , MgSO4 , and MgCl2 were obtained from Merck, the sodium acetate from the British Drug Houses, and CaCl2 from Aldrich. All chemicals were used as received. 2.2. Sample preparation The emulsions contained 96% w/w water to which salt, sugar or acetic acid/sodium acetate have been added. The oil phase, making up 2.3% w/w, was heptane, while the emulsifier was a mixture of C12 EO4 (1.4% w/w) and soybean
3. NMR diffusometry The field gradient technique to monitor diffusion was introduced by Hahn in 1950 [20]. Stejskal and Tanner improved the technique by introducing the pulsed gradient technique [21,22]. In its simplest version the technique involves the application of two identical gradient pulses of duration δ and amplitude g a distance apart (from start to start) of on either side of the 180◦ pulse in a Hahn echo experiment. In terms of the parameters of the NMR diffusion experiment, the normalized echo-intensities can be written as [23] E(δ, , g) = ρ(z0 )P (z0 |z, )eiγ gδ(z−z0 ) dz dz0 , (1) where ρ(z0 ) is the initial normalized spin density and P (z0 |z, ) is the probability density of finding a spin at position z after a time , if it was originally at z0 , is the diffusion time, i.e., the time over which the RMSD is monitored, and γ is the magnetogyric ratio of the studied nucleus.
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Equation (1) is valid for infinitely narrow gradient pulses. In short, the conditions for this is that the displacement during the gradient pulse is much smaller than the displacement during the diffusion time and the compartment size, where the latter condition applies for the case of molecules experiencing restricted diffusion. Apart from this limitation, Eq. (1) is valid for all types of diffusion processes. Often, the experimental parameters δ and g are used to define a scaled area of the gradient pulse as q = γ gδ/(2π). For the special case of unrestricted diffusion, where the propagator P (z0 |z, ) is a Gaussian, Eq. (1) gives the Stejskal–Tanner equation for the echo intensities, E(, δ, g) = exp(−γ 2 g 2 δ 2 D),
(2)
where D is the self-diffusion coefficient. As mentioned above, a useful property of NMR diffusometry is that the MSD may be obtained by expanding Eq. (1) to low values of q: lim E(, δ, g) = 1 − 2π 2 q 2 z2 .
q→0
(3)
In concentrated emulsions of the type studied here, water domains are separated from each other by a hydrocarbon film, which is on the order of a few 100 Å thick. Substances, which are soluble in the film, may then diffuse from one droplet to the next. If the emulsion structure is well ordered, at least locally, diffraction peaks may be observed in a plot of the measured echo intensities vs q. The inverse of the q-value of the top of the diffraction peak equals the characteristic distance, from one emulsion droplet to another, which is the diameter of the droplet in these highly concentrated systems [24]. The long-time diffusion coefficient in such a system is given by the concentrations and diffusivities in the water and hydrocarbon domains. For the case of a spherical system, such as the one depicted in Fig. 1, the long-time diffusion coefficient, Deff , is given by [19,25]: Deff = β=
1 − βΦ D2 , 1 − (1 − C1 /C2 )Φ 1 + βΦ/2
D2 C2 − D1 C1 . D2 C2 + 0.5D1 C1
(4)
(5)
In the present case, D1 /C1 is the diffusion/concentration of the species in water and D2 /C2 is the diffusion/concentration of the species in oil. Φ is the volume fraction of the inner droplet (in this case the aqueous component). We note that so far we have not discussed the state of the diffusing species in the oil domain. They may be molecularly dispersed or be solubilized in reversed micelles, which are also present in the oil [1,18]. In the case of solubilization in micelles, D2 is the diffusion of the reversed micelle, while C2 is the effective concentration in the oil domains of the solubilized species. From the measurements presented here it is difficult to differentiate between the two mechanisms (in actual fact, both mechanisms will most likely contribute to the transport across the film). In what follows we will assume
Fig. 1. Illustration of the concentrated emulsion in terms of a spherical cell model. The long-time diffusion is determined by the concentrations and diffusivities in the water and oil domains (cf. Eqs. (4) and (5)).
that the transport over the oil film is dominated by molecularly dissolved species in the oil domains, and will return to the question of which of the two mechanisms that dominates below. Species, which are not present in the oil domains, are confined to one emulsion droplet during the experiment. If the droplet size is smaller than the RMSD diffused by the molecules in bulk (with no restrictions), the following relation exists between z2 and the droplet radius R [5]: 2 z2 = R 2 . 5
(6)
4. Results and discussion 4.1. Introduction This section is organized in the following way. We start by discussing some general properties of the investigated emulsions system, such as stability with time, the influence on stability of different ionic species in the dispersed phase, and the size of the (deformed) water droplets. We then present and discuss data about diffusion of species confined to reside in the droplets and for species that exchange between the droplets in the emulsion and end the paper with some concluding remarks. 4.2. General properties of the investigated emulsion system In order to assess the size of the water droplets and the stability of the concentrated emulsion, the water diffusion was measured every hour during a period of 24 h for a system containing 0.17 M NaCl in the dispersed phase. Figure 2 shows that the echo profiles coincide over a period of (at least) 24 h, implying that the emulsion is stable over that time period. The fact that the stability can be monitored as a function of time is a useful feature of the NMR diffusometry approach; from echo profiles taken before and after each experiment one can investigate whether the emulsion is stable
C. Malmborg et al. / Journal of Colloid and Interface Science 263 (2003) 270–276
Fig. 2. Water echo intensity versus q. Three curves, obtained after 0 (!), 10 (1), and 24 (E) h of preparation are given.
or not during the measurement. Such experiments have been carried out before and after each experiment reported on in this work. In addition, the position of the rather broad peak gives information about the droplet size [14]. The position of the peak in q-space corresponds to the inverse of the distance between two droplets, which in these dense emulsions corresponds to the droplet diameter. From Fig. 2, the droplet diameter can be estimated to 1.8 µm. The echo profile peaks are quite broad and hence the evaluation is not very exact. This fact may have different causes. The water droplets are polydisperse in size and/or the emulsion is divided in big domains with different sizes of the droplets in each domain. When the signals are added together both of these situations would give broad peaks with a mean droplet size [14]. Finally, we note that the emulsion droplets studied in Fig. 2 had grown to 2.2 µm in diameter after 9 days. Salt is added to the dispersed phase in order to slow down the rate of Ostwald ripening. Salt increases the osmotic pressure in the water and prevent the emulsion droplets from growth, as water will not leave a droplet since the osmotic pressure in that drop would then increase. We examined whether different salts would give emulsions with different sizes of the water droplets. The salts used were CaCl2 , MgSO4 , MgCl2 , K2 SO4 , and NaCl (all at 1 wt%) and the results are shown in Fig. 3. The type of salt used does not affect the emulsion droplet size and stability (at least not over the time span over which the emulsions were investigated). The droplet diameter was estimated from water echo profiles to 1.8 µm, irrespective of which salt was added. From the size of the droplets some further information about the emulsion may be derived. On the assumption that the droplets are spherical with a radius of 0.9 µm, the thickness of the oil film surrounding each droplet may be calculated from the emulsion composition to approximately 100 Å. Moreover, if the area per surfactant at the droplet interface is taken as 75 Å2 for lecithin and 45 Å2 for C12 E4 , and it is assumed that lecithin resides solely at the interface,
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Fig. 3. Water echo intensities versus q, for emulsions with different salts in the water phase. The salts used are CaCl2 (!), MgSO4 (1), MgCl2 (E), K2 SO4 (P), and NaCl (✁). The concentration was in all cases 1 wt%.
the amount of C12 E4 in the oil film may be calculated from the droplet area. The result is that approximately 15% of C12 E4 resides in the film, in the form of molecularly dispersed C12 E4 and in reversed micelles. 4.3. Diffusion of molecules that do not leave the droplet during the diffusion time We show in Figs. 4 and 5 the long-time RMSDs of TMA ions and glucose as a function of the diffusion time. In both cases the displacement is also given for water. MSDs have been obtained from the slope of the echo intensities at low q-values (see Eq. (3) above). While the MSD for water increases linearly with time, indicating Gaussian diffusion for this species in the long-time limit (we will discuss the water data in the next section), the MSDs of the TMA ion and glucose are independent of time, indicating that these species do not leave the droplet during the diffusion time. In the light of Eqs. (4) and (5), this means that the solubility of glucose and
Fig. 4. Root mean square displacement for TMACl (") and water (F) vs diffusion time. The solid lines are guides to the eye.
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Fig. 5. Root mean square displacement for glucose (") and water (F) vs diffusion time.
TMA ions is low in the oil film, implying that the oil film is an effective barrier that hinders these species from leaving a droplet. The value of the MSD for both glucose and the TMA ion is 4 × 10−14 µm2 , giving further support for the fact that the droplet size is reproducible between different emulsions. Using Eq. (6) the radius of the droplets can be calculated to be 0.3 µm. This is lower than the value obtained from the echo profiles in Figs. 2 and 3. This is a consequence of the fact that the conditions for short gradient pulses are not met for the species diffusing within a droplet [26]. We show in Fig. 6 results of Brownian dynamics simulations using a procedure outlined in [27]. From the simulations the RMSDs have been determined. It is clear from Fig. 6 that the effect of the finite gradient pulses is to decrease the measured RMSD. Hence, too low a value for the droplet radius is derived if Eq. (6) is used. In the present case δ was 2 ms. The data in Fig. 1 were obtained for a droplet radius of 0.9 µm. From Fig. 6, the use of δ = 2 ms yields a value of RMSD of 0.16 µm, in rather good agreement with the obtained value 0.2 µm.
Fig. 6. Root mean square displacements obtained from initial slopes as function of the gradient pulse length as obtained from Brownian simulations. Conditions are for water diffusing within a droplet of 0.9 µm (D = 2 × 10−9 m2 s−1 ).
Fig. 7. Echo profiles for water (") and HAc/Ac− (F). The ratio of HAc to Ac− is 5/95.
4.4. Diffusion of molecules that leave the droplet during the diffusion time In order to investigate the diffusion behavior of species that have sufficient solubility in the oil film such that they may leave the droplet and in the long-time limit perform a random walk between the droplets, we have prepared emulsions with solutions of HAc/Ac− in different ratios, in order to produce different pH values in the droplet and hence different degrees of dissociation of the acetic acid. We show in Fig. 7 echo profiles for 5/95 volume ratios of 0.25 M HAc/Ac− and water. The diffraction peaks are observed at the same value of q for both water and HAc/Ac− . This is the expected result, since the location of the diffraction peak only depends on the properties of the emulsion (droplet size and film thickness). The minima in the echo profiles are slightly different on account of different diffusion coefficients for water and HAc/Ac− .
Fig. 8. Root mean square displacements for HAc/Ac− and water (×) vs diffusion time. The solid lines are the results of fitting the relation z2 = 2D to the data. Three different molar ratios of 0.25 M HAc/Ac− have been used: 95/5 (!), 50/50 (E), and 5/95 (1).
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Table 1 Data for long-time diffusion of HAc/Ac− and water Emulsion, investigated species 95/5, HAc/Ac 50/50, HAc/Ac 50/50, water 5/95, HAc/Ac
Deff /10−10 m2 s−1 a 5.0 3.0 1.0 0.4
D1 /10−10 m2 s−1 b
C2 /M
C2calc /M
10.2 9.47 23.0 8.52
1.3 × 10−3
1.3 × 10−3 7.2 × 10−4 – 7.6 × 10−5
6.1 × 10−4 1.6 × 10−2 6.1 × 10−5
C2 is the experimentally determined value of the concentration of HAc and water in the oil-film, while C2calc are calculated values (see text for details). a Obtained from data in Fig. 8. b Obtained from measurements on the water solutions from which the emulsions were made.
We now turn to the MSD of HAc/Ac− . Given in Fig. 8 are the RMSDs as a function of diffusion time for three different ratios of HAc to Ac− and for water (water data from the emulsion with 50/50 HAc/Ac− ). The MSDs for water and acetic acid/acetate ions increase with the diffusion time. As noted above, this means that these species are not confined to one droplet on the relevant time scale, but instead they perform a random walk from droplet to droplet. For such a case, z2 = 2D and the long-time diffusion of these species can be obtained by fitting this relation to the data in Fig. 8, and the results are given in Table 1. Inspection of Table 1 reveals the fact that the long-time diffusion depends on the solubility of the species in the oil film separating the droplets: the solubility is low for the charged acetic ion and higher for the acetic acid molecule. We can carry this analysis one step further. By measuring the diffusion coefficients of 0.25 M HAc/Ac− at the relevant pH values, values of D1 are obtained. Furthermore, by assuming that the diffusion coefficient of HAc in the oil phase can be obtained from the value obtained for the sample with 95/5 HAc/Ac− in water scaled by the ratio of the viscosities of the two solvents we may estimate a value of C1 /C2 (cf. Eqs. (4) and (5)) and hence of the concentration of HAc in the oil film. The results are included in Table 1. It is straightforward to show that the concentration of HAc in the oil phase is given by KD −pH 10 [Ac− ], (7) Ka where KD is the distribution constant for HAc between the oil film and water, and the rest of the quantities have their usual meaning. In deriving Eq. (7), we have assumed that the concentrations in the water droplets of HAc/Ac− remains the same as in the original water solution, from which the emulsion is made and that the concentration of Ac− in the oil film is negligible. Although we do not know KD we know that it is constant. By adjusting the value of KD to the experimental C2 result for the 95/5 case, we can predict the values of C2 for the other ratios of HAc/Ac− . The results are included in Table 1. As can be seen the agreement is reasonable, the deviations are most likely do to the uncertainties in the values of D2 . In conclusion, the long-time diffusion of HAc/Ac− is well described by Eqs. (4) and (5). We now return to the question raised above of whether the diffusing molecules are molecularly dispersed or solubilized in reversed micelles in the oil film. Clearly, there is a [HAc]oil =
specificity in the diffusion: molecules with no or low solubility in the oil are confined to the emulsion droplets during the time of the measurement (cf. Table 1). In the case of reversed micelles, the specificity would then be due to the exchange between the emulsion droplet and the reversed micelle, which process involves transport over a non-polar region. We note that if we take the volume fraction of reversed micelles in the continuous phase to be 20 vol%, then the concentration of HAc/Ac− would be of order 0.05 M, which can be compared with the value 6.1 × 10−5 M obtained on the assumption that HAc/Ac− in the oil domain is molecularly dispersed. Since we essentially determine the product D2 C2 , this means that the diffusion coefficient of the reversed micelle in the oil domain would be of order 1 × 10−12 m2 s−1 , which is rather low (corresponding to a hydrodynamic radius of roughly 0.5 µm). One final aspect concerns where the reversed micelles are situated in the emulsion system. If the bulk of the micelles reside in the Gibbs–plateau borders, then their effectiveness in promoting transport from one droplet to a neighboring droplet is less efficient. None of the arguments above are conclusive. Therefore we cannot exclude that some of the transport over the oil film is mediated by reversed micelles. Finally, from the value of the RMSD of water, solubility (again assuming that water is molecularly dispersed) of water in the oil film may also be calculated. The result is included in Table 1. 4.5. Concluding remarks We have investigated the general properties, such as stability and structure of concentrated water-in-oil emulsions with NMR diffusometry. The mean square displacement of water, salt, sugar, and acetic acid/acetate ion have been measured and the results show that water and acetic acid/acetic ion diffuse between emulsion droplets and that tetramethyl ammonium ions and glucose do not on the relevant time scale. Acetic acid show different diffusion coefficients at different pH values of the water phase, which is expected since ions have lower solubility in the oil phase. The results with regard to the long-time diffusion may be rationalized by means of a cell model that describes the long-time diffusion solely in terms of local diffusivities and (equilibrium) concentrations.
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Acknowledgment This study was financially supported by the Swedish Foundation for Strategic Research (SSF) through the Colloid and Interface Technology program.
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