J . Phys. Chem. 1994,98, 393-395
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Diffraction-like Effects Observed in the PGSE Experiment When Applied to a Highly Concentrated Water/Oil Emulsion B. Balinov and 0. Weman' Division of Physical Chemistry 1, University of Lund, Box 124, S-221 00 Lund, Sweden
J. C. Ravey Luboratoire de Physico-Chimie des Colloides Lesoc, UA CNRS 406, University Nancy I, Vandoeuvre, France Received: September 24, 1993; In Final Form: November 23, 1993' The N M R pulsed gradient spin echo (PGSE) self-diffusion technique is applied to a system with permeable barriers. The system is a highly concentrated emulsion consisting of 97% water, and its internal structure is one of closely packed water droplets which are separated by thin oil films. These oil films are permeable to water, and the emulsion can therefore be considered as belonging to the general class of porous systems. Recently, Callaghan and co-workers showed both theoretically and experimentally that under certain conditions one may actually detect diffraction-like effects when the PGSE experiment is applied to porous systems. We report here for the first time such diffraction-like effects in an emulsion system, which were observed when examining the water diffusion in the emulsion system mentioned above with the PGSE experiment. From the experiment the mean droplet size may be determined.
Introduction The pulsed gradient NMR techniques are powerful tools for investigating the molecular transport in homogeneous as well as heterogeneous When the transport of liquids in hetereogeneous systems is studied by this method, the observed diffusion behavior of the liquid depends on the time during which the transport is monitored. At short times, the observed mobility depends on the local environment of the medium. At long enough diffusion times an average uniform mobility of the liquid is measured because of prolonged motion in different environments. Of particular interest are systems which consist of physical barriers in an otherwise homogeneous medium. In practice, the barriers are often permeable, and several examples exist such as cell membranes, some minerals, continuousand dispersed phases in emulsions, and some liquid crystals. Such systems are generally classified as being porous. Recently, Callaghan et al.2+6 applied the PGSE NMR to fluids in porous structures and interpreted the spin echo signal using mathematics of diffraction theory. The method was applied to water diffusion in the void space of a closely packed assembly of polymer spheres.5 In the dependence of the water echo intensity on the relevant experimental parameters, a diffraction-likeeffect was observed in this system. Thus, a new imaging concept called "q-space imaging"2 was developed which allows structural resolution of identical objects far beyond the size resolution of the conventional NMR (k-space) imaging. The same topic was also discussed recently in ref 7. In this paper we report a study on a highly concentrated emulsion. Such systems contain high amounts of dispersed phase (typically up to 99 wt %) as droplets dispersed in a continuous phase.*s9 The droplets are separated by a thin liquid film, which may or may not be permeable to the dispersed phase. In this work we have studied a water/oil (w/o) highly concentrated emulsion, in which the oil component is a fluorocarbon. Although the water solubility in fluorocarbons is known to be very low, PGSE NMR data imply that the water may actually diffuse through the thin films, which are actually made up of a (inverse) water-swollen micellar phase. Thus, the water droplets appear to be interconnected (on a certain time scale), with a distance between the repeating units corresponding to the droplet size. This highly concentrated emulsion can therefore be considered *Abstract published in Advance ACS Abstructs, January 1, 1994.
as a porous system and may show diffraction-likeeffects under certain conditions in the PGSE experiment.
Experimental Section Materials. The highly concentrated emulsion was stabilized by a fluorinated nonionic surfactant. The surfactant system was a mixture of fluorinated nonionic surfactants with the general formula CnFzn+lCH2(E0)2where n is 6, 8, or 10. The oil was perfluorodecalin, purchased from Ventron GmbH. The emulsion contains 97 wt % water and was prepared by the procedure described in ref 10. The oil-to-surfactantratio was 3: 1 by weight. NMR Experiments. TheNMR self-diffusion experimentswere performed on a spectrometer of in-house design, equipped with a Varian 2.3 T electromagnet. The gradient drivers were of inhouse design and construction. The NMR probe is quipped with quadrupole coils delivering linearly homogeneous field gradients. The experiments were performed with a gradient strength of 0.3 T/m and gradient pulse lengths varying between 3 and 60 ms. The experimentswere performed with the ordinary Carr-Purcell sequence.11 The time between the 90° and 180° pulseswasvaried in the range from 100 ms to 1 8. The temperature for all measurements was 25 OC.
Results and Discussion In the discussion presented here we have concentrated on the conceptual featuresof the work. Thus, we will not go into detailed explanations regarding the observed effects. Those interested in more rigorous accounts of the effects observed may find such accounts in refs 4-6 and 12. The pulsed gradient spin echo (PGSE) NMR experiment is based on the application of two radio-frequency (rf) pulses and two magneticfield gradient pulses to the sample.11 By means of the first gradient pulse, the molecules are spatially "tagged" by means of a phase shift of the spin produced by the field gradient. The second field gradient is used to determine the mean displacementsof the molecules in the time interval (termed A in the PGSE experiment) between the two gradient pulses. Observing the NMR echo intensityas a function of the intensity, g, and duration, 6, of the applied field gradient pulses, therefore, provides direct information on the molecular motion during the time interval between the two gradient pulses. To investigate the structure of the medium in which the molecules diffuse, one can proceed in two ways. In the first procedure, a model is required which yields the decay of the echo
0022-3654/94/2098-0393$04.50/0Q 1994 American Chemical Society
394 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
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Figure 1. Echo intensity as a function of q. The curve was obtained with a value of A = 250 ms and g = 0.3 T m-I. The experimental data points were obtained by varying 6 from 5 to 60 ms. Please note that, for each value of q, there are two independent data points displayed in the figure.
intensity as a function of the relevant experimental parameters. Such models have been derived for simple geometries like diffusion in spherical,13*14cylindrical,14J5 or planar impermeable barriers.14J6J7 Examples of permeablebarriers also exist for the case of parallel planes1*and spheres.19 The other approach gives directly the molecular displacement profile. Kirger and Heink showed that the Fourier transform of the echo amplitude E(q), where the quantity q is analogous to a wave vector and is defined by q = (2?r)-Iyg6 (y is the magnetogyric ratio), with respect to q, yieldsdirectly thediffusion displacement profile.20 It can be determined by varying the strength of the field gradient pulse while keeping the pulse delay A constant. This approach was taken by Cory and Garroway21 for cells with impermeable walls. We have performed a series of PGSE-NMR measurementson the water diffusion in a w/o highly concentrated emulsion, a system described in detail in ref 10. One set of the results is presented in Figure 1, where the echo intensity as a function of q is presented. (A complete account of the entire data set will appear elsewhere.22) Of special interest is the slight increase in the echo intensity indicated by an arrow in Figure 1. Although the increase is not very large, it is certainlysignificant and above the noise level. That this is the case can be inferred from the fact that, for each value of q, two independent measurements were performed (cf. Figure 1). Such an increase was observed also by Callaghan et al.5 in a system of gently packed monodisperse polystyrene spheres, but apart from this system, it has to the best of our knowledge not been observed in any other system. Its origin may be understood from the following reasoning. As mentioned above, this system consists of densely packed water spheres which are separated by thin (of the order of 100 A) oil films. This film is in fact permeable to water, a fact that can be ascertained by performing PGSE experimentsat different diffusion times, A. The mechanism whereby water molecules cross the oil layers need not us concern us here, but it can originate either from single water molecules dissolved in the continuous phase or from existing reversed micelles in the continuous phase. The conseqeunce of this fact is that at low diffusion times the water will mainly diffuse within a single emulsion droplet, and negligible amounts will actually leave the droplet they reside in. At long enough diffusiontime the water migrates between droplets, and one can measure an effective long-rangediffusion coefficient of the water. On some intermediate time scale the following may happen. Consider a water molecule in a particular droplet. It will diffuse within this droplet but will also, with some finite probability,
Figure 2. Image obtained by optical microscopy of the emulsion studied in the present work. The emulsion has been diluted with decane. Please note the scale as indicated in the figure, which indicates that the droplet size is around 2 pm. Note also that the emulsion droplets are fairly uniform in size.
leave this droplet and migrate to any of the neighboringdroplets. This will, on the time scale of the diffusion experiment, result in the displacements of a large fraction of molecules a distance which is of the order of the droplet diameter. If the system is well ordered with a regular distance, b, between the centers of two neighboring droplets, one may for such a case expect to detect a diffraction peak at a q vector of around 6-I. As can be seen in Figure 1, the position of the diffraction-like peak occurs at a q value of approximately 0.3 X 106 m-1, which correspondsin real space to a distanceof 3.3 pm. Following the reasoning above, this should be compared to the size of the emulsion water droplets. Presented in Figure 2 is a picture as obtained by a microscope, after addition of decaneto the emulsion in order to dilute the emulsion dropletsso as to make them visible under the microscope. Two things are immediately apparent from Figure 2. First, the emulsion droplets appear rather uniform in size, which is a prerequisite for obtaining the diffraction-like peak in Figure 1. One should note that the width of the peak is indicative of the spread in droplet size: as the size distribution gets wider, the peak broadens and will eventually disappear. Second, the size of the droplet is approximately 2 pm, which is close to what one would expect from the position of the peak in Figure 1. In order to establish the droplet size from the position of the peak in Figure 1, one would require a model along the lines presented in ref 4. One problem in this regard is that the data in Figure 1were not obtained in the so-called short gradient pulse limit, which makes the development of such a model considerably more complicated. Finally, we note that the case of water molecules performing completely restricted diffusion within a droplet may alsoleadtopeaksin theechodecay (see thediscussion in Chapter 7 of ref 2). For such a case the peak would correspond to a droplet radius of approximately3 pm, which is not compatible with the sizes observed in Figure 2, excluding this mechanism as the origin of the peak in Figure 1. In conclusion, we have demonstrated for the first time the appearanceof a diffraction-like peak in the PGSEexperimentas applied to a system with semipermeablebarriers. The particular system is a w/o concentrated emulsion, and the position of the peak correlates with the mean droplet size, as determined by optical microscopy.
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References pnd Notes (1) Callaghan, P. Aust. J. Phys. 1984, 37, 359-387. (2) Callaghan, P. T.Principles of &clear Magnetic Resonance Microscopy; Clarendon Reas: Oxford, 199l. (3) Stilbs, P. Prog. Nucl. Magn.Reson. Spectrosc. 1987, 19, 1-45. (4) Callaghan, P. T.; Coy, A.; Halpin, T. P. J.; MacGowan, D.; Packer, J. K.; Zelaya, F. 0. J . Chem. Phys. 1992, 97,651462. ( 5 ) Callaghan, P. T.; Coy, A.; MacGowan, D.; Packer, K. J.; Zclaya, F. 0. Nature (London) 1991,351, 467-9. (6) Callaghan, P. T.; MacGowan, D.; Packer, K. J.; Zelaya, F. 0. J. Magn.Reson. 1990, 90,177-182. (7) Barral, G. A.; Frydman, L.; Chungas, G. C. Science 1992,255,714717. ( 8 ) Lissant, K. J. J. Colloid Interface Sci. 1966, 22, 462-468. (9) Solance, C.; Dominguez, J. G.; Parra, J. L.; Heuser, J.; Friberg, S. E. Colloid Polym. Sci. 1988, 266, 570-574.
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