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Phase Transitions in Colloidal Dispersions in a Liquid Crystalline Medium V. A. Raghunathan,*,†,‡ P. Richetti,† D. Roux,† F. Nallet,† and A. K. Sood§ Centre de Recherche Paul Pascal, Avenue A. Schweitzer, F-33600 Pessac, France, Raman Research Institute, Bangalore-560 080, India, and Department of Physics, Indian Institue of Science, Bangalore-560 012, India Received October 13, 1999. In Final Form: February 7, 2000 We present experimental studies on colloidal suspensions in a lyotropic system exhibiting an isotropicnematic-lamellar phase sequence upon decreasing the temperature. The particles are found to undergo a gas-liquid transition in the nematic phase of the suspending medium, indicating the existence of an attractive interparticle interaction. The resulting liquid phase is weakly anisotropic. Further, the nematiclamellar transition of the liquid crystal is found to be accompanied by a liquid-solid transition of the particles.
Introduction Colloidal suspensions in isotropic liquids have long served as model systems for studying the influence of interparticle interactions on particle organization and dynamics. The much larger length and time scales involved here compared to simple atomic systems, whose behavior they mimic, make them very attractive from an experimental point of view.1 The interparticle interactions in a suspension of colloidal particles in an isotropic liquid such as water are well described by the DLVO potential, which is a combination of the long-range screened Coulomb repulsion arising from the electric charges on the particles and the short-range van der Waals attraction.1 In the case of a micellar liquid, short-range attractive interactions also arise owing to depletion forces.2 On the other hand, if the dispersing medium is a nematic liquid crystal (NLC), which is an orientationally ordered fluid,3 additional interparticle interactions are expected to come into play, provided that the particle size is much larger than the size of the basic units (molecules or micelles) in the NLC. The nematic director nˆ , which describes the orientational ordering in the medium, usually has a preferential alignment at the bounding surfaces. Owing to the alignment of nˆ on its surface, each particle would give rise to disclinations in the NLC, the detailed nature of which depends on the specific anchoring conditions at the surfaces. As these disclinations are bound to the particles, the interactions between the disclinations give rise to an effective interparticle interaction.4 The particle surfaces can also induce a gradient in the magnitude of the nematic order parameter in their neighborhood, leading to an attractive short-range interaction.5 Finally, there can also be interactions arising from the restriction of thermal fluctuations in the director field by the surfaces of the †
Centre de Recherche Paul Pascal. Raman Research Institute. § Indian Institute of Science. ‡
(1) See, for example: Sood, A. K. In Solid State Physics; Ehrenreich; Turnbull, D., Ed.; Academic Press: New York, 1991; Vol. 45. (2) Asakura S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (3) See, for example: de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Oxford University Press: London, 1994. (4) Ramaswamy, S.; Nityananda, R.; Raghunathan, V. A.; Prost, J. Mol. Cryst. Liq. Cryst. 1996, 288, 175. (5) Marcelja, S.; Radic, N. Chem. Phys. Lett. 1976, 42, 129. Poniewierski, A.; Sluckin, T. Liq. Cryst. 1987, 2, 281. de Gennes, P. G. Langmuir 1990, 6, 1448.
particles.6 The behavior of the particles in the lamellar phase also depends to a great extent on their relative size compared to the lamellar periodicity d. If their size is much smaller than d, they can be incorporated in the lamellar phase, without creating significant deformation in the medium. Such systems have been the subject of many recent studies.7 In the other limit, where the particle size is much larger than d, they would create strong deformations and, therefore, can be expected to be expelled by the medium. We have recently reported the preparation of stable colloidal suspensions in a lyotropic system exhibiting an isotropic (I)-nematic (N)-lamellar (LR) phase sequence upon decreasing the temperature.8 We have determined the phase diagram of these suspensions for different surfactant concentrations and have investigated the effect of the colloidal particles on the orientational ordering in the nematic phase of the suspending medium.9 In the present article we present studies on the influence of the orientational ordering in the liquid crystal on the interactions between the colloidal particles. As the surfactant used is ionic, the charges on the latex particles are highly screened and the electrostatic interaction between the particles is considerably reduced. In this situation we can expect to see the influence of the interactions arising from the orientational ordering in the medium mentioned earlier. In addition to direct microscopic observations on the suspensions, we have also probed them using small-angle neutron scattering (SANS) and dynamic light scattering (DLS) techniques. From these studies we find that the colloidal particles are in a gaseous state when the dispersing medium is isotropic. In the nematic phase anisotropic liquidlike order develops, the anisotropy increasing with decreasing temperature. Below the nematic-lamellar transition the particles are expelled and form tightly bound clusters trapped in the lamellar matrix. A brief report of these results has already been published.10 (6) Ajdari, A.; Peliti, L.; Prost, J. Phys. Rev. Lett. 1991, 66, 1481. Ajdari, A.; Duplantier, B.; Hone, D.; Peliti, L.; Prost, J. J. Phys. II 1993, 2, 487. (7) Ponsinet, V.; Fabre, P.; Veyssie`, M.; Cabanel, R. J. Phys. II 1994, 4, 1785 and references therein. (8) Poulin, P.; Raghunathan, V. A.; Richetti, P.; Roux, D. J. Phys. II 1994, 4, 1557. (9) Raghunathan, V. A.; Richetti, P.; Roux, D. Langmuir 1996, 12, 3789.
10.1021/la991346u CCC: $19.00 © 2000 American Chemical Society Published on Web 04/09/2000
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Experimental Details The material used was a binary lyotropic system containing the surfactant CsPFO (cesium pentadecafluorooctanoate) and water.11 The micelles formed by the surfactant molecules have a discoid shape with the aspect ratio a/b in the range 0.2-0.55 depending on the temperature and surfactant volume fraction with a ≈ 22 Å.12 The periodicity in the lamellar phase varies from 50 to 75 Å depending on the surfactant volume fraction. The colloidal particles used are polymeric latex particles of diameter about 600 Å, with a surface charge density of about 260 µEq/g. The phase diagrams of the suspensions were determined using a polarizing microscope. The SANS experiments were carried out on the neutron line PAXY at Laboratoire Le´on-Brillouin (Labaratoire mixte CEA/ CNRS), CEN-Saclay, France. The neutron wavelength was 13.6 Å with a sample to detector distance of 6.78 m, so that the range of scattering vector q accessible was from 3.0 × 10-3 to 2.4 × 10-2 Å-1 . A sample-to-detector distance of 1.0 m was also used in some experiments, the accessible range of q in this case being from 2.1 × 10-2 to 1.6 × 10-1 Å-1 . A mixture with 1.5 wt % polyballs was used in these studies; the surfactant concentration was 37 wt %. Both oriented and unoriented samples were investigated. The unoriented samples were prepared in 2-mm thick quartz cells, while 5-mm thick cells containing a set of parallel quartz plates were used for oriented samples. The nematic phase has a strong tendency to align homeotropically at the surfaces, and well-oriented samples were obtained by slow cooling across the I-N transition. Contrast enhancement between the polyballs and the solvent was achieved by using D2O instead of H2O in the mixtures. The DLS studies were carried out using a 72-channel, 4-bit digital correlator (Brookhaven Instruments) and a Kr+ laser (Coherent) operating at 6471 Å. The viscosity of the suspensions was measured using a thermostated Carrimed rheometer in the plane-cone geometry.
Results Phase Diagram. Pseudobinary phase diagrams of the mixtures at fixed values of the ratio R ) ws/(ws + ww), where ws and ww are the weights of the surfactant and water, have been determined for a few values of this ratio.9 Figure 1 shows the phase diagram for R ) 0.41. As the concentration of the particles in the mixture is increased, the I-N coexistence range increases, while the N-LR transition temperature is not significantly affected. The most interesting feature of the phase diagram is the appearance, under a polarizing microscope, of a frozen spinodal-decomposition-like texture at lower temperatures in the nematic phase.8 The onset of this texture is not very well defined and as the temperature is lowered in the nematic phase, it becomes gradually more conspicuous and at the nematic-lamellar transition it becomes abruptly very pronounced. This behavior is found to be reversible on increasing the temperature. Microscopic Observations. Phase contrast microscopic observations indicate that the particles are well dispersed and perform free Brownian motion in the isotropic phase as well as just below the N-I transition of the suspending medium (Figure 2a, 2b). At lower temperatures in the nematic phase small clusters of particles appear, which are in equilibrium with particles in the bulk (Figure 2c). The ordering of the particles within these clusters is liquidlike, and the motion of the particles within them could be easily discerned. When the temperature is lowered, these clusters grow incorporating more and more particles from the bulk. However, there (10) Raghunathan, V. A.; Richetti, P.; Roux, D.; Nallet, F.; Sood, A. K. Mol. Cryst. Liq. Cryst. 1996, 288, 181. (11) Boden, N.; Jackson, P. H.; McMullen, K.; Holmes, M. C. Chem. Phys. Lett. 1979, 65, 476. (12) Holmes, M. C.; Reynolds, D. J.; Boden, N. J. Phys. Chem. 1987, 91, 5257.
Figure 1. Phase diagram of the suspensions at R ) 0.41 (see text). The labels I, N, and LR correspond to the isotropic, nematic, and lamellar phases, respectively. T stands for the texture seen under an optical microscope.
are free particles in the bulk even at the lowest temperature in the nematic phase. As the sample is cooled into the lamellar phase, the movement within the clusters is frozen and all the suspended particles seem to be expelled into the clusters (Figure 2d). Neutron Scattering. The size of the polyballs being about an order of magnitude larger than that of the micelles, the scattered intensities from these two species are well separated in the reciprocal space, as can be seen from Figure 3. Figure 4 shows the angle-averaged scattered intensity profiles due to the latex particles obtained from unoriented samples at a few temperatures. It is interesting to note that even in the isotropic phase of the dispersing medium, there is a shoulder in the intensity profile at q ≈ 6 × 10-3 Å-1 , which corresponds approximately to the particle size, indicating the presence of short-range order in the latex fluid. We may note here that such a shoulder was absent in the case of an aqueous suspension of these particles at the same concentration. As the temperature is lowered, the shoulder becomes more pronounced and becomes a well-defined peak at lower temperatures in the nematic and lamellar phases. The intensity profiles due to the colloidal particles obtained from oriented samples are shown in Figure 5. The sample was aligned with the nematic director normal to the incident beam. The figure shows two slices of the two-dimensional profile in directions parallel and perpendicular to the director. In the isotropic phase, I(q) is isotropic and decays smoothly with q. In the nematic phase, on the other hand, it becomes anisotropic, with the anisotropy increasing with decreasing temperature. The anisotropy is maximum between the two directions shown. When the sample was aligned with the nematic director along the beam, the scattering from it was isotropic at all temperatures. Hence the preferential direction in the anisotropic liquid phase of the latex particles coincides with that of the nematic phase of the micelles. The anisotropy is further enhanced as the sample is cooled into the lamellar phase. The intensity scattered by the particles, which are assumed to be spherical, can be written as
I(q b) ) AP h (q) S(q b)
(1)
where A is a q-independent numerical factor, P h (q) the
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Figure 2. Photographs of the suspensions taken under a phase contrast microscope at different temperatures corresponding to the isotropic (a), higher temperature nematic (b), lower temperature nematic (c), and lamellar (d) phases of the suspending medium. Note that the particles are well dispersed in (a) and (b), while they form clusters in (c) and (d). Magnification: approximately ×1000.
organization, which in general is anisotropic. Assuming the particles to be spherical and their size distribution to be Gaussian, we have
P h (q) )
∫[3(sin(qr) - qr cos(qr))/(qr)3]2 exp[-(r - rj)/ (2σ2)] dr (2)
Figure 3. SANS intensity profile from the nematic phase of the suspension. The peak at small q is due to the scattering by the particles and that at larger q due to the micelles. Note that the two peaks are well separated.
form factor of the particles averaged over the size polydispersity, and S(q b) the structure factor of the particle
where rj is the average radius of the particles and σ the standard deviation. In the aqueous suspension, the interaction between the polyballs is presumably dominated by the repulsive screened Coulomb interaction. At the concentration used (1.5 wt %), the average polyball separation is much larger than their effective size and the interparticle interactions are negligible. Therefore, S(q) in this case can be taken to be unity. On fitting the aqueous suspension data to P h (q) given by eq 2 (Figure 6), we obtain the average radius to be 285 Å with a standard deviation of 53 Å. The S(q) of the particles at different temperatures in the liquid crystalline solvent was then calculated from the data from unoriented samples using eq 1. These are shown in Figure 7. Light Scattering. We have measured the single particle diffusion coefficient (D0) of the polyballs in the
Phase Transitions in Colloidal Dispersions
Figure 4. Variation in the SANS intensity from an unoriented latex suspension in the CsPFO-water system with the wave vector q for a few temperatures corresponding to the isotropic (a), nematic (b), nematic with texture (c), and lamellar with texture (d) phases of the system. Particle concentration: 1.5 wt %. surfactant concentration: 37 wt %.
Figure 5. Scattered neutron intensity from an oriented sample. The open squares correspond to the direction normal to the nematic director and the filled squares to that parallel to it. The labels have the same significance as in Figure 4.
solvent using DLS. From the measured value of D0, the hydrodynamic radius rj of the particles was estimated using the Stokes-Einstein relation D0 ) kBT/(6πηrj). The value of the radius obtained from a very dilute suspension (0.1 wt %) in water is about 315 Å. Interestingly, we obtained a value of 425 Å from a suspension in the isotropic phase of the CsPFO/water system well above the I-N transition, using the measured value of the viscosity. As the viscosity was determined using unoriented samples, the value obtained in the nematic phase can be taken to be an average bulk viscosity. However, when the system is cooled below the N-L transition, the viscosity is found to decrease strongly, indicating flow alignment of the bilayers parallel to the surfaces. As the polyball size is much larger than the lamellar periodicity, the effective viscosity experienced by the particle is not what is measured by the viscometer. We have, therefore, estimated the average bulk viscosity in the lamellar phase by extrapolating the values in the nematic phase (Figure 8a). In suspensions with larger particle concentrations, the interparticle interactions come into play and the intensity
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Figure 6. Scattered neutron intensity from a suspension of the latex particles in D2O. The continuous line is the fit obtained using the polydispersity-averaged form factor of a sphere (eq 2 in the text).
Figure 7. The structure factor of the latex particles at four different temperatures obtained from the SANS data. The labels have the same significance as in Figure 4.
correlation function shows deviation from a singleexponential decay. The short time decay in the correlation of the scattered light gives an effective diffusion coefficient Deff, which is related to the single particle diffusion coefficient (D0) by13
Deff )
D0 S(q)
(3)
Thus if we know D0 it is possible to estimate S(q). Further, as the range of q accessible by DLS lies below the range probed by SANS, eq 3 makes it possible to study the behavior of S(q) at small q. The temperature dependence of D0 arises from that of the viscosity. Therefore, the additional temperature dependence of Deff is due to that of S(q). D0 was calculated from the known values of the particle radius r and η. The T-dependence of S(q) obtained this way from a mixture with 46 wt % surfactant concentration is shown in Figure 8b for two values of q. In the nematic phase at higher temperatures as well as (13) Pusey, P. N.; Tough, R. J. A. In Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy; Pecora, R., Ed.; Plenum: New York, 1985.
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Figure 9. Structure factor of the sticky hard sphere model for a few values of the well depth u0 (after ref 10). -u0/kT ) 0.09 (a), 1.5 (b), 2.0 (c), and 2.1 (d). The inset gives the definitions of the different parameters involved in the model. ∆/σ ) 0.1, volume fraction ) 0.07. Figure 8. (a) Variation of the viscosity measured using a plate-cone viscometer. The open squares corresponds to the extrapolated data used in estimating S(q) (see text). (b) Variation of S(q) with temperature obtained from the DLS data for q ) 2.6 × 10-3 Å-1 (open squares) and q ) 7.0 × 10-4 Å-1 (filled squares). Particle concentration, 0.5 wt %, surfactant concentration, 46 wt %. The dashed lines are guides for the eye. (c) Variation of S(q) with temperature at q ) 2.7 × 10-3 Å-1 for a mixture with 37 wt % surfactant concentration.
in the isotropic phase, S(q) ≈ 1 and is not sensitive to T. However, at lower temperatures in the nematic phase, it begins to decrease for q2 ≈ 2.6 × 10-3 Å-1 and increase for q1 ≈ 7.0 × 10-3 Å-1. Interestingly, this trend sets in near the temperature where the texture is seen under a microscope. We were unable to determine S(q) at q1 in the lamellar phase, as the decay of the correlation function is very slow with a time constant of the order of a few seconds, resulting in very large errors in the values of Deff. It may be noted here that the decreasing trend of S(q) with decreasing temperature at q2 is also obtained from the SANS data for comparable values of q (Figure 7). The temperature dependence of S(q) just below the N-I transition seems to be different at lower surfactant concentration. In a mixture with 37 wt % surfactant concentration, S(q) at q2 is found to increase just below TNI. It reaches a broad peak a few degrees below and then begins to decrease (Figure 8c). Discussion The phase contrast microscopic observations provide the most direct evidence for the occurrence of a gas-liquid transition of the colloidal particles in the nematic phase of the suspending medium. The liquid clusters formed at lower temperatures in the nematic phase presumably gives rise to the spinodal-decomposition-like texture seen under the polarizing microscope. The absence of any noticeable Brownian motion of the particles below the nematiclamellar transition seems to indicate that they are expelled by the medium and trapped in tightly bound clusters. The insensitivity of the nematic-lamellar phase boundary to the concentration of the particles supports this conclusion. Referring to Figure 7, which shows S(q) of the particles determined using SANS, we see that there is some structure in the particles even when the medium is in the isotropic phase. The peak in S(q) is not very pronounced
(Smax ≈ 1.1). This low value of Smax corroborates the phase contrast microscopic observations of only free particles in the medium. The increase in S(q) at small q indicates the attractive nature of the interparticle interaction responsible for the structure.14 As the temperature is lowered, the degree of order in the particles increases and the peak in S(q) grows, becoming very pronounced at the N-L transition of the solvent. The fact that the evolution of the peak value does not show any discontinuity reflecting the gas-liquid transition may be due to the presence of a biphasic region, which would smooth out any such discontinuity. The microscopic observations indeed show free particles coexisting with liquid clusters at lower temperatures in the nematic phase. In the lamellar phase the motion of particles within the clusters is frozen and the ordering within them can be either glasslike or crystalline. The hydrodynamic radius of the particles measured using DLS from a suspension in the isotopic phase of the lyotropic system is about 1.3 times the value obtained from a suspension in water. This large difference probably indicates some localized disturbance in the micellar ordering near the particle surface, which increases its effective size.15 It has been reported that the size of the micelles in the CsPFO/water system depends on the surfactant concentration. It is, therefore, conceivable that the degree of the disturbance caused by the colloidal particles also varies with the surfactant concentration. Perhaps this is the reason for the difference in the temperature dependence of S(q) at two values of this parameter shown in Figure 8. Further experiments are required to clarify this point. The observed temperature dependence of S(q) at q1 and q2 (Figure 8b) is similar to that expected from the sticky hard sphere model.16 Figure 9 shows the variation of S(q) with qa, a being the sum of the hard core diameter and the well width (a ) ∆ + σ), for a few values of the well depth, calculated using the expressions given in ref 16. As can be seen from this figure, the short-range attraction results in the increase of S(q) with increasing magnitude of the interaction only at very (14) Bibette, J.; Roux, D.; Pouligny, B. J. Phys. II 1992, 2, 401. (15) Moreau, L.; Richetti, P.; Barois, P. Phys. Rev. Lett. 1994, 73, 3556. (16) Menon, S. V. G.; Manohar, C.; Rao, K. S. J. Chem. Phys. 1991, 95, 9186.
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small values of q. There is a range of q below qm (at which the peak in S(q) occurs), where S(q) decreases with increasing magnitude of the attractive potential. We may now speculate on the interaction responsible for the observed gas-liquid transition of the colloidal particles. As this transition always occurs in the nematic phase of the suspending medium, this attractive interaction can be expected to result from the orientational ordering in the NLC. As mentioned in the Introduction, there are at least three such interparticle interactions in the NLC. If the anchoring of the nematic director at the particle surface is strong, we would expect the interaction mediated by the disclinations to dominate. Recent calculations show that this intertaction between two spherical particles immersed in a uniformly aligned nematic is ∝(Ka6)/r5, where a is length comparable to the particle size and r the interparticle separation. It is highly anisotropic, being attractive for r oriented in a range around 50° to the nematic axis nˆ , and repulsive for r normal or parallel to nˆ .4 Moreover, the value of the potential at particle contact is a few orders of magnitude larger than the thermal energy kBT. Therefore, it is unlikely to lead to a temperature-driven gas-liquid transition. From the experimental observation of such a transition, we may conclude that the anchoring of the nematic director at the particle surface is not strong and that the particles do not produce significant deformation in the director field. The pseudo-Casimir interaction arising from thermal fluctuations of the director field has been calculated only for the case of two parallel plates immersed in a nematic.6 In this geometry this interaction has the same form as the van der Waals interaction. Further, it has the same value irrespective of whether the anchoring is strong (rigid) or weak (free). However, this interaction between two spheres has so far not been calculated, and hence we are not in
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a position to infer its importance in the present experimental system. As discussed earlier, the DLS studies show that the particles disturb the local arrangement of the micelles. Therefore, it is probable that the magnitude of the nematic order parameter near the particle surface is different from that in the bulk, resulting in a short-range attractive interparticle interaction.5 It is conceivable that this interaction is responsible for the observed condensation of the particles. However, it is at present not clear if this interaction can account for the observed anisotropy of the liquid phase. Conclusion In conclusion, we have observed a gas-liquid transition of colloidal particles suspended in a nematic solvent. Below the nematic-lamellar transition of the suspending medium, the particles are expelled and form tightly bound clusters dispersed in the lamellar matrix. The ordering of the particles within these clusters is solidlike. Both the liquid and solid phases are found to be anisotropic. The attractive interparticle interaction responsible for the condensation of the particles probably arises from the gradient in the nematic order parameter induced by the particles near their surfaces. Acknowledgment. We thank P. Poulin, J. Prost, S. Ramaswamy, J. Toner, and R. Nityananda for helpful discussions and L. Noirez for technical assistance on the beam line at LLB. This work was funded in part by the Indo-French Center for the Promotion of Advanced Research (Grant No. 607-1). We thank the Rhoˆne-Poulenc Company and Dr. Joanicot for providing us with the colloidal particles. LA991346U
