- Email: [email protected]
Time-resolved SANS for surfactant phase transitions
Physica B 276}278 (2000) 326}329
Time-resolved SANS for surfactant phase transitions S.U. Egelhaaf *, U. Olsson, P. Schurtenberger Dept. of Physics and Astronomy, The University of Edinburgh, James C. Maxwell Building, Mayxeld Road, Edinburgh EH9 3JZ, UK Physical Chemistry 1, Lund University, S-22100 Lund, Sweden Institut fu( r Polymere, ETH, CH-8092 Zu( rich, Switzerland
Abstract Surfactants spontaneously self-assemble in solution to form a variety of microstructures. Our understanding of the equilibrium properties of these aggregates, such as their shape and size, has made signi"cant progress. However, only limited information is available on the kinetics and pathways of phase transitions and on the existence of nonequilibrium or metastable states. Fortunately, this unsatisfactory situation can now be overcome owing to recent developments in small-angle neutron scattering (SANS) instrumentation which signi"cantly improve the temporal and spatial resolution. These new, fascinating possibilities are illustrated by two examples. Firstly, time-resolved SANS reveals the structure of the intermediate in a spontaneous transition from micelles to vesicles in aqueous mixtures of lecithin and bile salt. Secondly, a microemulsion containing spherical oil droplets is temperature quenched into a two-phase situation where excess oil separates out. The nucleation and growth of the separating oil droplets is, again, followed by time-resolved SANS. 2000 Elsevier Science B.V. All rights reserved. Keywords: Surfactants; Phase transitions; Non-equilibrium systems; Small angle neutron scattering
Amphiphilic molecules in solution exhibit a complex aggregation behaviour resulting from a delicate balance of opposing forces. The size and shape of the aggregates not only depend on the chemical composition of the amphiphile, but also dramatically change in response to variations in solution parameters, such as temperature, concentration, pH, or ionic strength. While the understanding of such equilibrium properties has made signi"cant progress [1], only limited information is available on their behaviour under non-equilibrium conditions. In particular, neither the kinetics of structural transitions, nor the existence, properties and sequence of intermediate non-equilibrium or metastable states, has been addressed in detail [2].
* Corresponding author. Tel.: #44-131-650-5291; fax: #44131-650-7165. E-mail address: [email protected] (S.U. Egelhaaf) Present address: Physics Department, Soft Condensed Matter Group, University of Fribourg, CH-1700 Fribourg, Switzerland
In equilibrium studies, scattering methods have proven to be particularly powerful techniques in order to investigate surfactant systems, since they allow for a detailed and quantitative characterisation of the structural properties on a broad range of length scales down to an almost molecular level. However, in addition to this spatial, an adequate temporal resolution is necessary for non-equilibrium studies following the relaxation of a system to its equilibrium state. Several time-resolved smallangle neutron scattering (SANS) studies investigate relaxations in di!erent soft condensed matter systems, which are either &slow' or pro"t from high scattering intensities and include surface solutions [3], gelation [4], phase-separation in copolymer solutions [5] or alkane mixtures [6], spinodal decomposition [7,8] or protein crystallisation [9,10]. Recent developments in SANS instrumentation [11] signi"cantly improved the temporal and spatial resolution. Time-resolved SANS now enables us to perform an in situ characterisation of the temporal evolution of surfactant aggregates upon a rapid quench in, e.g., concentration or temperature [12,13]. Here, we only highlight the most important features of D22 (ILL, Grenoble) [11], where these measurements
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 5 2 7 - 6
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
were done. Although similar to other SANS instruments, a number of improvements add up to yield a very high neutron #ux. Depending on the instrument con"guration it provides up to 1.2;10 neutrons s\ cm\ at the sample position. Equally important for real-time experiments is the broad range of scattering vectors q covered in a single setting, which avoids time-consuming changes of the instrument con"guration during a kinetic run. This is accomplished by a large detector with 128;128 cells (each having a size of 0.75 cm;0.75 cm) which can in addition be o!set laterally. In a typical experiment we use a standard beamstop (r +4 cm) and move the de tector laterally such that the direct beam would still be on the detector (which allows for an easy and unambiguous determination of the beamcentre, r +100 cm).
This gives q /q +r /r +25 and yields about
(r !r )/0.75 cm +128 data points.
The value of these new features for time-resolved SANS is demonstrated in recent studies on surfactant phase transitions [2,12,13] and illustrated here by two examples.
327
Fig. 1. (A) Temporal evolution of the scattering intensity I(q, t) as observed during a micelle-to-vesicle transition. In addition, every 30 min I(q, t) is highlighted as solid lines. The intensity of the initial, equilibrated micelles (open squares), the "t to the kinetic model (solid lines) and the resulting intensity I (q) of the intermediate (crosses) are also shown. (B) Schematic representation of the transition.
1. Micelle-to-vesicle transition The micelle-to-vesicle transition is a classical transiton of considerable importance in many areas of biochemistry, pharmacology and physical chemistry. Although extensively studied under equilibrium conditions in a number of systems [14}20], the investigation of its temporal evolution is only beginning. Aqueous mixtures of lecithin and bile salt are prime examples of mixed surfactant solutions that exhibit a spontaneous micelle-to-vesicle transition [14}17]. It can conveniently be induced by rapid dilution of an equilibrated micellar stock solution, which exploits the very di!erent monomer solubilities of bile salt and lecithin. Fig. 1A shows the temporal evolution of the scattering intensity I(q, t) during the course of a dilution-induced micelle-to-vesicle transition. A measurement time of 30 s already results in astonishingly good statistics, although the total surfactant concentration is less than 1 mg/ml to avoid interparticle interaction e!ects. The data indicate that on the time scale of the experiment the initially present worm-like micelles (Fig. 1A, open squares) rapidly change to non-equilibrium, intermediate structures. These intermediates then slowly transform into the "nal, larger vesicles; equilibrium values are reached after approximately 4 h. The positions of the minima and maxima of I(q, t), which provide information on the size and polydispersity of the vesicles, remain constant throughout the experiment, but become more pronounced. This indicates that the vesicles already form with a narrow size distribution around their "nal equilibrium size, while their number fraction increases. These qualitative "ndings suggests that this transition could be described by the scheme shown in Fig. 1B.
Based on this hypothesis a simple kinetic model can be developed to quantitatively describe the temporal evolution of I(q, t) [12]. Since the transition from the micelles to the intermediate structures is instantaneous on the time scale of the experiment, we assume that the contribution of the initial micelles can be neglected and only the intermediates and vesicles contribute to I(q, t) with their relative proportions governed by an exponential decay of the concentration of the intermediates. While the vesicular part can be inferred from the "nal, equilibrated vesicular solution, this leaves the scattering function of the intermediates I (q) together with a q-indepen dent time constant q as the only "tting parameters. An inverse Fourier transformation of the resulting I (q) indi cates a disc-like structure with a thickness of about 50 As . Based on this additional information the intermediates are then described as polydisperse discs, which signi"cantly reduces the number of "tting parameters to the mean radius 1R2 and polydispersity p of the discs and q only. We obtain excellent agreement for q"143 min and polydisperse discs with 1R2"170 As and p"0.2 as the intermediate structures (Fig. 1A, solid lines), which is also consistent with the molar mass calculated from I(qP0, t). In addition, the same qualitative behaviour was revealed by independent light scattering experiments [12]. It thus seems conceivable that the worm-like micelles very quickly change their morphology to discs as a response to the changed average spontaneous curvature of the assembly on removal of the more soluble bile salt (Fig. 1B). The disc-like micelles then transform either directly or via a second, short lived and thus not observable intermediate into closed unilamellar vesicles by
328
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
a much slower process, which can be described by an exponential time dependence. We believe that this represents a signi"cant step towards a full understanding of this important structural transition and may solve the puzzling question on how the initially present worm-like micelles transform into closed bilayer structures.
2. Nucleation and growth of oil drops in a microemulsion Oil, water and surfactant can form thermodynamically stable phases, where water and oil domains are separated by a surfactant "lm. The maximum volume of oil that can be accomodated in an aqueous surfactant solution is set by the geometrical constraint of a "xed surface of the spherical oil droplets, given by the amount of surfactant available, and the spontaneous curvature H of the sur factant "lm, which determines the radius of the oil droplets. If this volume is exceeded or H increased, excess oil separates out. This process, namely the separation of an oil phase from oil-in-water microemulsion droplets, is here induced by a temperature quench which increases H . The majority of droplets thus decrease in size, while some of the droplets are &sacri"ced' and forced to grow to accomodate the remaining oil (Fig. 2B). Finally, in equilibrium two phases exist; a microemulsion of smaller droplets coexists with an excess oil phase. Initially there are much more small than big microemulsion droplets. To avoid that the overall scattering intensity is completely dominated by the small droplets, we use a H O/D O mixture which minimises the for ward scattering intensity of the small droplets. This is possible, since the average contrast of a droplet depends on the surfactant (C E )-to-oil (D -decane) ratio and thus on the size of the droplets. Following a temperature quench, scattering curves were measured for periods of 30 s. The sequence of scattering curves (Fig. 2A) shows dramatic changes as time progresses. The growing scattering intensity at low qvalues is due to the few large drops. They retain a relatively monodisperse size distribution as can be seen qualitatively from the &hump' in the scattering curves (q+0.02 As \), which corresponds to the second peak in the form factor of a sphere. A Guinier analysis yields the time dependence of the radius of gyration of the large drops. It can be converted to the sphere radius, which at long times is found to grow as the cubic root of time. Furthermore, from the forward scattering cross section, the number density of big drops is obtained, which apart from early times is approximately inversely proportional to time [13]. Due to the broad q-range covered and because only the forward scattering of the small droplets is matched, we can in addition monitor the shrinking small droplets. Their average size is re#ected in the position of the local maximum, which is initially observed at q+0.04 As \
Fig. 2. (A) Sequence of scattering curves recorded during the nucleation and growth of an excess oil phase from oil-in-water microemulsion droplets, which is schematically shown in (B).
and then moves to higher q-values, which indicates a decrease of the microemulsion droplet size. After about 45 min it reaches its "nal position at q+0.065 As \ [13]. Time-resolved SANS experiments thus provide detailed structural information on the evolution of the size distributions of both, the big and small oil droplets. Immediately after the temperature quench there is a fast nucleation followed by the growth of these nuclei via di!usion of oil from the small droplets. After about 45 min the small droplets have reached their (near) equilibrium size and the large drops continue to evolve through Ostwald ripening at constant oil volume.
3. Conclusions Signi"cant improvements in SANS instrumentation open up new opportunities for time-resolved studies of surfactant phase transitions, which give access to detailed structural data down to almost molecular length scales having adequate temporal resolution. They allow to derive quantitative models for the structural evolution of surfactant systems during relaxation to equilibrium. In the "rst example a transition in the aggregate structure from polymer-like micelles to vesicles via intermediate disc-like micelles was investigated, while the subject of the second study was a phase transition in an oil-in-water microemulsion during which the droplets change their size, but retain their spherical shape.
Acknowledgements We gratefully acknowledge support from the Institut Laue-Langevin in Grenoble.
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
References [1] D.F. Evans, H. WennerstroK m, The Colloidal Domain } Where Physics, Chemistry, Biology, and Technology Meet, VCH Publishers, New York, 1994. [2] S.U. Egelhaaf, Curr. Opin. Colloid Interface Sci. 3 (1998) 608. [3] H. Imai, T. Kato, D. Schneider, J. Chem. Phys. 108 (1998) 1710. [4] M. Kobayashi, T. Yoshioka, M. Imai, Y. Itoh, Macromol. 28 (1995) 7376. [5] J.G. Connell, R.W. Richards, A.R. Rennie, Polymer 32 (1991) 2033. [6] E.P. Gilbert, P.A. Reynolds, P. Thiyagarajan, D.G. Wozniak, J.W. White, PCCP 1 (1999) 2715. [7] H. Jinnai, H. Hasegawa, T. Hashimoto, C.C. Han, Macromol. 24 (1991) 282. [8] D. Schwahn, S. Janssen, T. Springer, J. Chem. Phys. 97 (1992) 8775. [9] N. Niimura, Y. Minezaki, M. Ataka, T. Katsura, J. Cryst. Growth 154 (1995) 136.
329
[10] P.A. Marone, P. Thiyagarajan, A.M. Wagner, D.M. Tiede, J. Crystal. Growth 191 (1998) 811. [11] http://www.ill.fr/Yellow Book/D22. [12] S.U. Egelhaaf, P. Schurtenberger, Phys. Rev. Lett. 82 (1999) 2804. [13] S. U. Egelhaaf, U. Olsson, P. Schurtenberger, J. Morris, H. WennerstroK m, Phys. Rev. E 60 (1999) 5681. [14] R.P. Hjelm, P. Thiyagarajan, H. Alkan-Onyuksel, J. Phys. Chem. 96 (1992) 8653. [15] M.A. Long, E.W. Kaler, S.P. Lee, Biophys. J. 67 (1994) 1733. [16] S.U. Egelhaaf, P. Schurtenberger, J. Phys. Chem. 98 (1994) 8560. [17] J.S. Pedersen, S.U. Egelhaaf, P. Schurtenberger, J. Phys. Chem. 99 (1995) 1299. [18] E.W. Kaler, A. Kamalakara Murthy, B.E. Rodriguez, J.A.N. Zasadzinski, Science 245 (1989) 1371. [19] A. Walter, P.K. Vinson, A. Kaplun, Y. Talmon, Biophys. J. 60 (1991) 1315. [20] E. SchoK nfelder, H. Ho!mann, Ber. Bunsenges. Phys. Chem. 98 (1994) 842.
Time-resolved SANS for surfactant phase transitions S.U. Egelhaaf *, U. Olsson, P. Schurtenberger Dept. of Physics and Astronomy, The University of Edinburgh, James C. Maxwell Building, Mayxeld Road, Edinburgh EH9 3JZ, UK Physical Chemistry 1, Lund University, S-22100 Lund, Sweden Institut fu( r Polymere, ETH, CH-8092 Zu( rich, Switzerland
Abstract Surfactants spontaneously self-assemble in solution to form a variety of microstructures. Our understanding of the equilibrium properties of these aggregates, such as their shape and size, has made signi"cant progress. However, only limited information is available on the kinetics and pathways of phase transitions and on the existence of nonequilibrium or metastable states. Fortunately, this unsatisfactory situation can now be overcome owing to recent developments in small-angle neutron scattering (SANS) instrumentation which signi"cantly improve the temporal and spatial resolution. These new, fascinating possibilities are illustrated by two examples. Firstly, time-resolved SANS reveals the structure of the intermediate in a spontaneous transition from micelles to vesicles in aqueous mixtures of lecithin and bile salt. Secondly, a microemulsion containing spherical oil droplets is temperature quenched into a two-phase situation where excess oil separates out. The nucleation and growth of the separating oil droplets is, again, followed by time-resolved SANS. 2000 Elsevier Science B.V. All rights reserved. Keywords: Surfactants; Phase transitions; Non-equilibrium systems; Small angle neutron scattering
Amphiphilic molecules in solution exhibit a complex aggregation behaviour resulting from a delicate balance of opposing forces. The size and shape of the aggregates not only depend on the chemical composition of the amphiphile, but also dramatically change in response to variations in solution parameters, such as temperature, concentration, pH, or ionic strength. While the understanding of such equilibrium properties has made signi"cant progress [1], only limited information is available on their behaviour under non-equilibrium conditions. In particular, neither the kinetics of structural transitions, nor the existence, properties and sequence of intermediate non-equilibrium or metastable states, has been addressed in detail [2].
* Corresponding author. Tel.: #44-131-650-5291; fax: #44131-650-7165. E-mail address: [email protected] (S.U. Egelhaaf) Present address: Physics Department, Soft Condensed Matter Group, University of Fribourg, CH-1700 Fribourg, Switzerland
In equilibrium studies, scattering methods have proven to be particularly powerful techniques in order to investigate surfactant systems, since they allow for a detailed and quantitative characterisation of the structural properties on a broad range of length scales down to an almost molecular level. However, in addition to this spatial, an adequate temporal resolution is necessary for non-equilibrium studies following the relaxation of a system to its equilibrium state. Several time-resolved smallangle neutron scattering (SANS) studies investigate relaxations in di!erent soft condensed matter systems, which are either &slow' or pro"t from high scattering intensities and include surface solutions [3], gelation [4], phase-separation in copolymer solutions [5] or alkane mixtures [6], spinodal decomposition [7,8] or protein crystallisation [9,10]. Recent developments in SANS instrumentation [11] signi"cantly improved the temporal and spatial resolution. Time-resolved SANS now enables us to perform an in situ characterisation of the temporal evolution of surfactant aggregates upon a rapid quench in, e.g., concentration or temperature [12,13]. Here, we only highlight the most important features of D22 (ILL, Grenoble) [11], where these measurements
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 5 2 7 - 6
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
were done. Although similar to other SANS instruments, a number of improvements add up to yield a very high neutron #ux. Depending on the instrument con"guration it provides up to 1.2;10 neutrons s\ cm\ at the sample position. Equally important for real-time experiments is the broad range of scattering vectors q covered in a single setting, which avoids time-consuming changes of the instrument con"guration during a kinetic run. This is accomplished by a large detector with 128;128 cells (each having a size of 0.75 cm;0.75 cm) which can in addition be o!set laterally. In a typical experiment we use a standard beamstop (r +4 cm) and move the de tector laterally such that the direct beam would still be on the detector (which allows for an easy and unambiguous determination of the beamcentre, r +100 cm).
This gives q /q +r /r +25 and yields about
(r !r )/0.75 cm +128 data points.
The value of these new features for time-resolved SANS is demonstrated in recent studies on surfactant phase transitions [2,12,13] and illustrated here by two examples.
327
Fig. 1. (A) Temporal evolution of the scattering intensity I(q, t) as observed during a micelle-to-vesicle transition. In addition, every 30 min I(q, t) is highlighted as solid lines. The intensity of the initial, equilibrated micelles (open squares), the "t to the kinetic model (solid lines) and the resulting intensity I (q) of the intermediate (crosses) are also shown. (B) Schematic representation of the transition.
1. Micelle-to-vesicle transition The micelle-to-vesicle transition is a classical transiton of considerable importance in many areas of biochemistry, pharmacology and physical chemistry. Although extensively studied under equilibrium conditions in a number of systems [14}20], the investigation of its temporal evolution is only beginning. Aqueous mixtures of lecithin and bile salt are prime examples of mixed surfactant solutions that exhibit a spontaneous micelle-to-vesicle transition [14}17]. It can conveniently be induced by rapid dilution of an equilibrated micellar stock solution, which exploits the very di!erent monomer solubilities of bile salt and lecithin. Fig. 1A shows the temporal evolution of the scattering intensity I(q, t) during the course of a dilution-induced micelle-to-vesicle transition. A measurement time of 30 s already results in astonishingly good statistics, although the total surfactant concentration is less than 1 mg/ml to avoid interparticle interaction e!ects. The data indicate that on the time scale of the experiment the initially present worm-like micelles (Fig. 1A, open squares) rapidly change to non-equilibrium, intermediate structures. These intermediates then slowly transform into the "nal, larger vesicles; equilibrium values are reached after approximately 4 h. The positions of the minima and maxima of I(q, t), which provide information on the size and polydispersity of the vesicles, remain constant throughout the experiment, but become more pronounced. This indicates that the vesicles already form with a narrow size distribution around their "nal equilibrium size, while their number fraction increases. These qualitative "ndings suggests that this transition could be described by the scheme shown in Fig. 1B.
Based on this hypothesis a simple kinetic model can be developed to quantitatively describe the temporal evolution of I(q, t) [12]. Since the transition from the micelles to the intermediate structures is instantaneous on the time scale of the experiment, we assume that the contribution of the initial micelles can be neglected and only the intermediates and vesicles contribute to I(q, t) with their relative proportions governed by an exponential decay of the concentration of the intermediates. While the vesicular part can be inferred from the "nal, equilibrated vesicular solution, this leaves the scattering function of the intermediates I (q) together with a q-indepen dent time constant q as the only "tting parameters. An inverse Fourier transformation of the resulting I (q) indi cates a disc-like structure with a thickness of about 50 As . Based on this additional information the intermediates are then described as polydisperse discs, which signi"cantly reduces the number of "tting parameters to the mean radius 1R2 and polydispersity p of the discs and q only. We obtain excellent agreement for q"143 min and polydisperse discs with 1R2"170 As and p"0.2 as the intermediate structures (Fig. 1A, solid lines), which is also consistent with the molar mass calculated from I(qP0, t). In addition, the same qualitative behaviour was revealed by independent light scattering experiments [12]. It thus seems conceivable that the worm-like micelles very quickly change their morphology to discs as a response to the changed average spontaneous curvature of the assembly on removal of the more soluble bile salt (Fig. 1B). The disc-like micelles then transform either directly or via a second, short lived and thus not observable intermediate into closed unilamellar vesicles by
328
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
a much slower process, which can be described by an exponential time dependence. We believe that this represents a signi"cant step towards a full understanding of this important structural transition and may solve the puzzling question on how the initially present worm-like micelles transform into closed bilayer structures.
2. Nucleation and growth of oil drops in a microemulsion Oil, water and surfactant can form thermodynamically stable phases, where water and oil domains are separated by a surfactant "lm. The maximum volume of oil that can be accomodated in an aqueous surfactant solution is set by the geometrical constraint of a "xed surface of the spherical oil droplets, given by the amount of surfactant available, and the spontaneous curvature H of the sur factant "lm, which determines the radius of the oil droplets. If this volume is exceeded or H increased, excess oil separates out. This process, namely the separation of an oil phase from oil-in-water microemulsion droplets, is here induced by a temperature quench which increases H . The majority of droplets thus decrease in size, while some of the droplets are &sacri"ced' and forced to grow to accomodate the remaining oil (Fig. 2B). Finally, in equilibrium two phases exist; a microemulsion of smaller droplets coexists with an excess oil phase. Initially there are much more small than big microemulsion droplets. To avoid that the overall scattering intensity is completely dominated by the small droplets, we use a H O/D O mixture which minimises the for ward scattering intensity of the small droplets. This is possible, since the average contrast of a droplet depends on the surfactant (C E )-to-oil (D -decane) ratio and thus on the size of the droplets. Following a temperature quench, scattering curves were measured for periods of 30 s. The sequence of scattering curves (Fig. 2A) shows dramatic changes as time progresses. The growing scattering intensity at low qvalues is due to the few large drops. They retain a relatively monodisperse size distribution as can be seen qualitatively from the &hump' in the scattering curves (q+0.02 As \), which corresponds to the second peak in the form factor of a sphere. A Guinier analysis yields the time dependence of the radius of gyration of the large drops. It can be converted to the sphere radius, which at long times is found to grow as the cubic root of time. Furthermore, from the forward scattering cross section, the number density of big drops is obtained, which apart from early times is approximately inversely proportional to time [13]. Due to the broad q-range covered and because only the forward scattering of the small droplets is matched, we can in addition monitor the shrinking small droplets. Their average size is re#ected in the position of the local maximum, which is initially observed at q+0.04 As \
Fig. 2. (A) Sequence of scattering curves recorded during the nucleation and growth of an excess oil phase from oil-in-water microemulsion droplets, which is schematically shown in (B).
and then moves to higher q-values, which indicates a decrease of the microemulsion droplet size. After about 45 min it reaches its "nal position at q+0.065 As \ [13]. Time-resolved SANS experiments thus provide detailed structural information on the evolution of the size distributions of both, the big and small oil droplets. Immediately after the temperature quench there is a fast nucleation followed by the growth of these nuclei via di!usion of oil from the small droplets. After about 45 min the small droplets have reached their (near) equilibrium size and the large drops continue to evolve through Ostwald ripening at constant oil volume.
3. Conclusions Signi"cant improvements in SANS instrumentation open up new opportunities for time-resolved studies of surfactant phase transitions, which give access to detailed structural data down to almost molecular length scales having adequate temporal resolution. They allow to derive quantitative models for the structural evolution of surfactant systems during relaxation to equilibrium. In the "rst example a transition in the aggregate structure from polymer-like micelles to vesicles via intermediate disc-like micelles was investigated, while the subject of the second study was a phase transition in an oil-in-water microemulsion during which the droplets change their size, but retain their spherical shape.
Acknowledgements We gratefully acknowledge support from the Institut Laue-Langevin in Grenoble.
S.U. Egelhaaf et al. / Physica B 276}278 (2000) 326}329
References [1] D.F. Evans, H. WennerstroK m, The Colloidal Domain } Where Physics, Chemistry, Biology, and Technology Meet, VCH Publishers, New York, 1994. [2] S.U. Egelhaaf, Curr. Opin. Colloid Interface Sci. 3 (1998) 608. [3] H. Imai, T. Kato, D. Schneider, J. Chem. Phys. 108 (1998) 1710. [4] M. Kobayashi, T. Yoshioka, M. Imai, Y. Itoh, Macromol. 28 (1995) 7376. [5] J.G. Connell, R.W. Richards, A.R. Rennie, Polymer 32 (1991) 2033. [6] E.P. Gilbert, P.A. Reynolds, P. Thiyagarajan, D.G. Wozniak, J.W. White, PCCP 1 (1999) 2715. [7] H. Jinnai, H. Hasegawa, T. Hashimoto, C.C. Han, Macromol. 24 (1991) 282. [8] D. Schwahn, S. Janssen, T. Springer, J. Chem. Phys. 97 (1992) 8775. [9] N. Niimura, Y. Minezaki, M. Ataka, T. Katsura, J. Cryst. Growth 154 (1995) 136.
329
[10] P.A. Marone, P. Thiyagarajan, A.M. Wagner, D.M. Tiede, J. Crystal. Growth 191 (1998) 811. [11] http://www.ill.fr/Yellow Book/D22. [12] S.U. Egelhaaf, P. Schurtenberger, Phys. Rev. Lett. 82 (1999) 2804. [13] S. U. Egelhaaf, U. Olsson, P. Schurtenberger, J. Morris, H. WennerstroK m, Phys. Rev. E 60 (1999) 5681. [14] R.P. Hjelm, P. Thiyagarajan, H. Alkan-Onyuksel, J. Phys. Chem. 96 (1992) 8653. [15] M.A. Long, E.W. Kaler, S.P. Lee, Biophys. J. 67 (1994) 1733. [16] S.U. Egelhaaf, P. Schurtenberger, J. Phys. Chem. 98 (1994) 8560. [17] J.S. Pedersen, S.U. Egelhaaf, P. Schurtenberger, J. Phys. Chem. 99 (1995) 1299. [18] E.W. Kaler, A. Kamalakara Murthy, B.E. Rodriguez, J.A.N. Zasadzinski, Science 245 (1989) 1371. [19] A. Walter, P.K. Vinson, A. Kaplun, Y. Talmon, Biophys. J. 60 (1991) 1315. [20] E. SchoK nfelder, H. Ho!mann, Ber. Bunsenges. Phys. Chem. 98 (1994) 842.