Dispersion of Latex Particles in a Nematic Solution. 2. Phase

Langmuir 1996, 12, 3789-3792

3789

Dispersion of Latex Particles in a Nematic Solution. 2. Phase Diagram and Elastic Properties V. A. Raghunathan,* P. Richetti, and D. Roux Centre de Recherche Paul Pascal, Avenue A. Schweitzer, F-33600 Pessac, France Received December 18, 1995. In Final Form: May 20, 1996X We have prepared colloidal suspensions of 600 Å diameter latex polyballs in a lyotropic liquid crystal. The phase diagrams of the mixtures have been determined for a few values of the surfactant to water ratio. In the nematic phase, the particles remain suspended at high temperatures but undergo a gas-liquid transition at lower temperatures. The elastic constants and rotational viscosity of the mixtures in the nematic phase have been measured using the Freedericksz transition technique. They are found to be insensitive to the presence of the particles up to a few percent in the particle concentration.

Introduction We have recently reported some preliminary observations on colloidal dispersions in a nematic liquid crystal (NLC).1 In the present paper we describe the phase diagram of the mixtures and studies on the elastic properties of the system. As mentioned in ref 1, compared to an isotropic solvent, at least three additional interactions between the colloidal particles come into play in a NLC. The first is a short-range attractive interaction arising from the gradients in the magnitude of the nematic order parameter close to the particle surfaces.2-4 This would be further enhanced if these surfaces induce a smectic ordering of the micelles in the neighborhood of the particles.5 The second interaction arises from restrictions of the orientational fluctuations in the nematic medium under confinement.6,7 This interaction between two parallel plates immersed in a NLC has been calculated and is found to be attractive and to have the same form as the van der Waals interaction.6,7 However, the interparticle potential between two spheres, which is the case most relevant to the system studied here, has not been calculated so far. The third interaction is elastic in origin. Due to the preferential ordering of the nematic director nˆ on the particle surface, each particle suspended in the NLC carries a disclination, whose detailed topology depends on the specific anchoring conditions on the surfaces. The interactions between these disclinations lead to an effective interaction between the particles. Further, intuitively, we would expect this interaction to be anisotropic and to depend on the elastic constants of the NLC and also on the anchoring strength of nˆ on the particle surfaces. Indeed, a recent calculation, which assumes strong anchoring of nˆ at the particle surfaces, shows that the disclination-mediated interaction energy between two spheres immersed in a uniformly aligned NLC is proportional to Ka6/r5, where K is the elastic constant of the NLC, a a length of the order of the particle size, and r the interparticle separation.8 Further, the interaction is found to be highly anisotropic; it is repulsive if the angle between r and the direction of nˆ at infinity is around 0 or 90°, while * Present address: Raman Research Institute, Bangalore-560 080, India. X Abstract published in Advance ACS Abstracts, July 15, 1996. (1) Poulin, P.; Raghunathan, V. A.; Richetti, P.; Roux, D. J. Phys. II 1994, 4, 1557. (2) Marcˇelja, S.; Radic´, N. Chem. Phys. Lett. 1976, 42, 129. (3) Poniewierski, A.; Sluckin, T. Liq. Cryst. 1987, 2, 281. (4) de Gennes, P. G. Langmuir 1990, 6, 1448. (5) Moreau, L.; Richetti, P.; Barois, P. Phys. Rev. Lett. 1994, 73, 3556. (6) Ajdari, A.; Peliti, L.; Prost, J. Phys. Rev. Lett. 1991, 66, 1481. (7) Ajdari, A.; Duplantier, B.; Hone, D.; Peliti, L.; Prost, J. J. Phys. II 1993, 2, 484.

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it is attractive for angles around 50°. A NLC is characterized by three bulk elastic constants, corresponding to the three basic modes of deformation called splay, twist, and bend.9 While all three are sensitive to the temperature near the nematic-isotropic transition, the twist and bend elastic constants also vary strongly near the nematiclamellar transition.9 In the binary lyotropic system used here, the nematic phase is sandwiched between an isotropic phase at higher temperatures and a lamellar phase at lower temperatures. As a result, the elastic interactions between the particles can be rather strongly temperature dependent. One of the objectives of the study was to investigate the influence of the disclinations created by the particles on the properties of the nematic medium itself. In this connection, there has been a recent theoretical examination of the role played by disclinations in the nematicisotropic transition, which predicts the possible existence of a novel intermediate phase, where the long-range nematic order is destroyed by the proliferation of disclinations.10 In the experimental system under study, the concentration of disclinations can be varied by simply changing the particle concentration. Hence it is a convenient system for studying the influence of disclinations on the NLC. If these disclinations affect the longrange nematic ordering, it will be reflected in the elastic properties of the medium. With this in mind we have measured the elastic constants of the NLC with and without the latex particles. Experimental Section The NLC used was a binary lyotropic system containing the surfactant CsPFO (cesium pentadecafluorooctanoate) and water. This system exhibits a nematic phase (N) over a temperature range of about 6 °C for a very broad range of the surfactant concentration.11 This phase is bounded on the higher temperature side by an isotropic phase (I) and by a lamellar LR phase at lower temperatures. The micelles formed by the surfactant molecules in the nematic phase have a discoid shape with a thickness of about 22 Å and a diameter in the range 50-120 Å, depending on temperature and concentration.12 The colloidal particles used are polymeric latex of diameter 600 Å with a surface charge density of 360 µequiv/g (Rhoˆne-Poulenc, France). The samples were prepared by weighing the right amounts of the (8) Ramaswamy, S.; Nityananda, R.; Raghunathan, V. A.; Prost, J. To be published. (9) See, for example: de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Oxford University Press: London, 1994. (10) Lammert, P. E.; Rokhsar, D.; Toner, J. Phys. Rev. Lett. 1993, 70, 1650. (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.

© 1996 American Chemical Society

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three components into a test tube, which was then sealed and maintained at a temperature corresponding to the isotropic phase for proper mixing. The samples were also agitated to expediate the mixing process. The transition temperatures were determined using a polarizing microscope, with samples taken in 200 µm thick capillaries. The elastic constants of the NLC were determined using the Freedericksz transition (FT) technique.9 The sample cells employed were similar to the ones used for optical observations. Homeotropically aligned samples were prepared by slow cooling across the I-N transition. It was possible to align mixtures containing up to about 2 wt % of the latex in this manner. Above this concentration it was not possible to prepare well-aligned samples even using a magnetic field. In the experiment, the transmitted intensity of a laser beam, through the sample kept between crossed polarizors, was measured as a function of the applied magnetic field. As the diamagnetic anisotropy (∆χ) of the medium is positive, the direction of the field was normal to the nematic director nˆ . Equating the stabilizing elastic torque with the destabilizing magnetic torque, the critical field of the FT is found to be9

Hc )

[ ]

π K3 d ∆χ

1/2

(1)

where K3 is the bend elastic constant and d the cell thickness. Thus K3/∆χ can be determined from the critical field. The ratio of the splay and bend elastic constants, K1/K3, and the birefringence ∆n can be obtained from fitting the experimentally observed dependence of the transmitted intensity on the magnetic field to that calculated from a model based on the continuum theory of NLCs.13 The director field under supercritical values of the field is described by the following differential equation obtained by minimizing the sum of the elastic and magnetic energies of the system:

K3(cos2 θ + κ sin2 θ)

d2θ 1 dθ 2 + K3(κ - 1) sin 2θ + 2 2 dz dz 1 ∆χH2 sin 2θ ) 0 (2) 2

( )

where θ is the angle nˆ makes with the z-axis and κ ) K1/K3. Assuming rigid anchoring of the nematic director at the cell surfaces, the boundary conditions are θ(z)0) ) θ(z)d) ) 0. In the limit of small birefringence, the transmittance of a homeotropically aligned cell is given by

It π∆n ) sin2 Ii λ

( ∫ sin θ dz) d

2

0

∆χ 2 (H - H2) γ1 c

alignment.14 τ-1 was measured for different values of H and was then fitted to eq 4. This yields the combinations K3/∆χ and K3/γ1 of the material parameters.

(3)

Results and Discussion

Thus for a given value of the applied field and a set of values of the material parameters, the above differential equation can be solved to obtain the variation of θ across the cell and the transmittance can be calculated. Due to the relatively high rotational viscosity of lyotropic NLCs and also due to the inherent slowing down of the micellar reorientation close to the critical field, the above method is very time consuming. Hence we also used the dynamic FT technique, where the relaxation time of the micellar reorientation is determined from the decay of the transmitted intensity on decreasing the field from supercritical to subcritical values. The relaxation time τ is given by14

τ-1(H) )

Figure 1. Phase diagram of the suspensions of latex particles in the CsPFO/water system, for R ) 0.38 (a), 0.41 (b), and 0.44 (c). The dashed lines correspond to the appearance under an optical microscope of the texture described in the text. The labels I, N, and LR stand for the isotropic, nematic, and lamellar phases, respectively, and T denotes the texture.

(4)

where γ1 is the rotational viscosity of the NLC and H the final subcritical value of the field. It should be noted here that, due to the discoid shape of the micelles, backflow effects are expected to be negligible in the homeotropic case.15 On the other hand, for rodlike systems these effects are small in the case of planar (13) Gruler, H.; Scheffer, T. J.; Meier, G. Z. Naturforsch. 1972, 27a, 966. (14) Pieranski, P.; Brochard, F.; Guyon, E. J. Phys. (Paris) 1973, 34, 35. (15) Lacerda Santos, M. B.; Galerne, Y.; Durand, G. J. Phys. (Paris) 1985, 46, 933.

1. Phase Diagram. Figure 1 shows the pseudo-binaryphase diagram of the mixtures at three values of the ratio R ) WS/(WS + WW), where WS is the weight of the surfactant in the mixture and WW that of water. Parts a-c of Figure 1 correspond to R ) 0.38, 0.41, and 0.44, respectively. The transition temperatures of the pure binary system increase with R, and the above values of R were preferred, as the transition temperatures of these mixtures fall in a convenient range. The surfactant used to determine the phase diagram at R ) 0.44 was slightly impure, leading to lower transition temperatures. The phase diagrams at the three different values of R are similar, but the maximum amount of the latex that can be incorporated in the nematic phase is found to increase with R. It increases from about 3% by weight for R ) 0.38 to about 10% for R ) 0.44. It was found that, on washing the latex, a larger amount of particles could be incorporated in the mixtures. For example, the maximum concentration increased to about 5% in the case of the mixture with R ) 0.38. Further, from Figure 1 we see that the I-N coexistence range grows with increasing particle concentration, while the N-LR transition temperature is hardly affected. The most interesting feature of the phase diagram is the appearance of a frozen spinodal-decomposition-like pattern at lower temperatures in the nematic

Dispersion of Latex Particles in a Nematic Solution

Langmuir, Vol. 12, No. 16, 1996 3791 Table 1. Temperature Dependence of the Material Parameters of the Pure Nematic Obtained Using the Static Freedericksz Transition Technique (R ) 0.41). TNI - T (°C)

K3/∆χ (cgs units)

K1/K3

∆n (10-3)

1.0 2.0 3.0

25.9 ( 0.5 33.2 39.7

0.85 ( 0.05 0.76 0.70

1.13 ( 0.02 1.34 1.53

Table 2. Temperature Dependence of the Material Parameters of the Mixture with 1.5 wt % Latex Particles Obtained Using the Static Freedericksz Transition Technique (R ) 0.41) TNI - T (°C)

K3/∆χ (cgs units)

K1/K3

∆n (10-3)

1.0 2.0 3.0

25.9 ( 0.5 30.7 37.0

0.85 ( 0.05 0.72 0.70

1.19 ( 0.02 1.41 1.62

Figure 2. Variation of the transmittance of a homeotropically aligned cell with the applied field for the pure nematic (a) and for a sample containing 1.5 wt % latex particles (b). The solid lines are fits to the experimental data. R ) 0.41; TNI - T ) 1.0 °C (O), 2.0 °C (4), and 3.0 °C (0).

phase.1 The onset of this texture (T) is not sharp, as it is very faint initially. It becomes more conspicuous on lowering the temperature, though at a given temperature it does not grow with time. On further cooling, it becomes abrupty very pronounced at the N-LR transition. If the sample is now heated, the above behavior is found to be reversible, indicating that the texture is the optical manifestation of an equilibrium process. Small angle neutron scattering (SANS) studies indicate that the appearance of this texture is associated with a vapor-liquid transition of the particles.16 Further, the liquid phase formed is found to be anisotropic. This clearly indicates the existence of anisotropic attractive interparticle interactions in the NLC. The growth of the texture on lowering the temperature can be accounted for by the progressive condensation of the vapor. As the size of the particles is more than an order of magnitude larger than the lamellar periodicity in the LR phase, they create very strong deformations in the medium. Therefore, they can be expected to be expelled by the LR phase, forming isolated clusters. This would explain the abrupt change in the texture observed under the microscope at the N-LR transition. From our SANS studies we infer that the particles in these clusters form an anisotropic solid. Hence it is very likely that these clusters contain some solvent in the nematic phase. 2. Elastic Constants. Figure 2 shows the typical variation with the applied field of the ratio of the transmitted intensity to that incident on the cell, obtained from the static FT experiment. The solid line is the fit to the data using eq 3. We have determined K3/∆χ, K1/K3, and ∆n of the pure NLC with R ) 0.41 at a few temperatures, using this technique. These are shown in Table 1. K3/∆χ is found to be much smaller than that in some other lyotropic NLCs, while K1/K3 is slightly (16) Raghunathan, V. A.; Richetti, P.; Roux, D.; Nallet, F.; Sood, A. K. To be published.

Figure 3. Observed decay of the transmitted intensity on reducing the applied field from supercritical to subcritical values (500 G). The solid lines are exponential fits to the data: (O) pure nematic; (b) sample with 1.5 wt % latex particles. TNI T ) 2.0 °C; R ) 0.41.

larger.17,18 As we have not determined ∆χ of the medium, it is not possible to say whether this difference arises from lower elastic constants or from a relatively higher value of ∆χ. The ∆n values are in good agreement with those reported in the literature on the same system at a similar CsPFO concentration.19 A mixture with 1.5 wt % of the latex particles gave comparable values of these parameters (Table 2); it was not possible to get well-aligned samples with a larger latex concentration. Figure 3 shows the decay of the transmitted intensity observed in the dynamic FT experiment. The lines are exponential fits to the data. The relaxation times in the two cases are comparable, though it is slightly higher for the mixture containing the latex particles. The variation of the relaxation frequency with the final subcritical field is given in Figure 4. The solid line is a fit to the data using eq 4. The values of K3/∆χ and K3/γ1 of the pure nematic with R ) 0.41, obtained using this technique, are shown in Table 3 for a few temperatures. The K3/γ1 values are much smaller than those found in some other lyotropic NLCs17,18 probably indicating lower elastic constants of the system under study. The corresponding values of a mixture containing 1.5 wt % latex with R ) 0.41 are given in Table 4. While the K3/∆χ values of the two systems are (17) Zhou, E.; Stefanov, M.; Saupe, A. J. Chem. Phys. 1988, 88, 5137. (18) Haven, T.; Armitage, D.; Saupe, A. J. Chem. Phys. 1981, 75, 352. (19) Rosenblatt, C. In The Physics of Complex and Supermolecular Fluids; Safran, S. A., Clark, N. A., Eds.; Wiley: New York, 1987; p 373.

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Figure 4. Variation of the relaxation frequency of the nematic director with the final subcritical field. The solid line is a fit to eq 4. Latex concentration ) 1.5 wt %; TNI - T ) 4.0 °C; R ) 0.41. Table 3. Temperature Dependence of the Material Parameters of the Pure Nematic Obtained Using the Dynamic Freedericksz Transition Technique (R ) 0.41) TNI - T (°C)

K3/∆χ (cgs units)

K3/γ1 (10-8 cgs units)

1.0 2.0 3.0 4.0 5.0

26.5 ( 0.5 35.0 42.7 49.6 65.5

3.3 ( 0.1 2.5 2.2 2.0 1.8

Table 4. Temperature Dependence of the Material Parameters of the Mixture with 1.5 wt % Latex Particles Obtained Using the Dynamic Freedericksz Transition Technique (R ) 0.41) TNI - T (°C)

K3/∆χ (cgs units)

K3/γ1 (10-8 cgs units)

1.0 2.0 3.0 4.0 5.0

28.0 ( 0.5 31.7 37.0 47.2 59.9

2.6 ( 0.1 2.0 1.5 1.2 1.0

almost identical within experimental accuracy K3/γ1 is clearly smaller in the mixtures containing the latex particles, indicating that this system has a larger rotational viscosity γ1. Thus it seems that the presence of the particles hinders the reorientation of the micelles, while not affecting the elastic properties to the medium. Similar slowing down of the director relaxation has also been seen in a NLC containing colloidal clay particles.20 The variation of K3/∆χ of the two systems with temperature obtained using the two techniques is shown in Figure 5. The elastic constants of the NLC are roughly proportional to S2, S being the orientational order parameter, while ∆χ is proportional to S.9,21 Hence the ratio K3/∆χ should be approximately linear in S. Further, ∆n is also approximately proportional to S. Therefore, the insensitivity of K3/∆χ and ∆n of the NLC to the presence of the latex particles clearly shows that the latter do not strongly affect the orientational ordering in the medium, at least up to the concentrations studied. We should point out here that although we tried to incorporate the latex particles in many lyotropic NLCs, only the CsPFO/water system gave stable suspensions. In other materials the latexes were expelled in the nematic phase. Further, even in the present system only one particular type of latex (20) Desando, M. A.; Reeves, L. W. Can. J. Chem. 1984, 63, 2628. (21) Saupe, A. Z. Naturforsch. 1960, 15a, 810.

Figure 5. Variation of the ratio of the bend elastic constant to the anisotropy of the diamagnetic susceptibility with temperature, obtained from static (O, b) and dynamic (0, 4) Freedericksz transition experiments: (b, 0) pure nematic; (O, 4) mixture containing 1.5 wt % latex particles. R ) 0.41.

(styrene/butyl acrylate/acrylic acid copolymer) could be suspended. Others were again expelled from the nematic phase. The additional energy cost in putting a particle in the nematic phase compared to the isotropic phase is just the amount of elastic deformation that the particle creates in the medium. For a given particle size, this deformation energy depends on the elastic constants of the medium and on the strength of anchoring of the nematic director on the particle surface. So it is probable that the mixtures under study are characterized by relatively lower values of either or both of these two parameters. However, the fact that we were unable to get oriented samples with a latex concentration greater than 2 wt % might be an indication of a drastic change in the elastic properties of the medium above this concentration. As the Freedericksz transition technique employed here requires oriented samples, other techniques not having this limitation need to be used to explore this possibility. In conclusion, we have prepared stable suspensions of latex particles in a lyotropic nematic medium. The phase diagrams of these mixtures exhibit an interesting feature in the form of a spinodal-decomposition-like pattern at lower temperatures in the nematic phase. On the basis of SANS studies (not described here) we associate the appearance of this pattern with a vapor-liquid transition of the latex driven by anisotropic attractive interparticle interactions. Further, the insensitivity of the physical properties of the NLC to the presence of latex particles indicates the negligible effect they have on the nematic ordering in the medium, at least up to the maximum latex concentration that gave well-aligned samples. Acknowledgment. It is a pleasure to acknowledge stimulating discussions with F. Nallet, P. Poulin, J. Prost, S. Ramaswamy, A. K. Sood, and J. Toner. This work was funded in part by an Indo-French cooperation grant (IFCPAR Grant No. 607-1) and a European community contract (human capital and mobility grant no. CHRXCTQ4-O6P6). We thank the Rhoˆne-Poulenc Company and Dr. Joanicot for providing us with the colloidal particles. LA951551J