pubs.acs.org/Langmuir © 2009 American Chemical Society
Anisotropic Reversible Aggregation of Latex Nanoparticles Suspended in a Lyotropic Nematic Liquid Crystal: Effect of Gradients of Biaxial Order V. M. Alves,† S. Nakamatsu,† E. A. Oliveira,*,† B. Zappone,‡ and P. Richetti§ †
Instituto de Fı´sica, Universidade de S~ ao Paulo, 05508-090 S~ ao Paulo, Brazil, ‡Liquid Crystal Laboratory, CNR-INFM and Centro di Eccellenza, CEMIF.CAL c/o University of Calabria, Calabria, Italy, and § Centre de Recherche Paul Pascal (CNRS), Pessac, France Received April 28, 2009. Revised Manuscript Received August 4, 2009
We studied the anisotropic aggregation of spherical latex particles dispersed in a lyotropic liquid crystal presenting three nematic phases: calamitic, biaxial, and discotic. We observed that in the nematic calamitic phase aggregates of latex particles are formed, which become larger and anisotropic in the vicinity of the transition to the discotic phase, due to a coalescence process. Such aggregates are weakly anisotropic and up to 50 μm long and tend to align parallel to the director field. At the transition to the discotic phase, the aggregates dissociated and re-formed when the system was brought back to the calamitic phase. This shows that the aggregation is due to attractive and repulsive forces generated by the particular structure of the nematic phase. The surface-induced positional order was investigated by surface force apparatus experiments with the lyotropic system confined between mica surfaces, revealing the existence of a presmectic wetting layer around the surfaces and oscillating forces of increasing amplitude as the confinement thickness was decreased. We discuss the possible mechanisms responsible for the reversible aggregation of latex particles, and we propose that capillary condensation of the NC phase, induced by the confinement between the particles, could reduce or remove the gradient of order parameter, driving the transition of aggregates from solidlike to liquidlike and gaslike.
1. Introduction Colloidal particles suspended in an aqueous isotropic medium are subjected to repulsive interactions of an electrostatic nature and to attractive van der Waals interactions.1,2 In water, other forces between particles can also be present such as hydrophobic, hydration depletion, etc.2 The balance of such interactions results in different types of particle organization or microphase separation, and this is a relevant aspect in preparing composite materials3-5 and in biological processes.6-8 There has been growing interest in the use of liquid crystals to prepare colloids due to the anisotropic interactions between particles. Such interactions, mediated by the elastic distortions introduced into the ordered medium, can be a thousand-fold larger than the thermal energy.9-12 The reorganization of particles to minimize the elastic distortions results in ordered structures with potential applications in preparing novel materials. In a liquid crystal (LC) exhibiting orientational order, particles are subjected to additional interactions due to (i) the elastic *To whom correspondence should be addressed. E-mail:
[email protected]. br. (1) Hiemenz, P. C.; Rajagopalan, R. Principles of colloid and surface chemistry, 3rd ed., Marcel Dekker, Inc., New York, 1997. (2) Israelachvili, J. Intermolecular and surface forces, 2nd ed., Academic Press, San Diego, 1991. (3) Suresh, S. Science 2001, 292, 29. (4) van der Kooji, F. M.; Kasspidou, K.; Lekkerkerker, H. N. W. Nature 2000, 406, 869. (5) Pham, A.; Puertas, J.; Bergenholtz, S; Egelhaag, U.; Moussaid, A; Pusey, P. N.; Schofield, A. B.; Cates, M. E; Fuchs, M.; Poon, W. C. K. Science 2002, 296, 104. (6) Rey, A. D. J. Chem. Phys. 1996, 104, 4334. (7) Wright, C. F.; Teichmann, S. A.; Clarke, J.; Dobson, C. M. Nature 2005, 438, 878. (8) San-Abria, H.; Kubota, Y.; Waxham, M. N. Biophys. J. 2007, 92, 313. (9) Musevic, I.; Skarabot, M.; Tkalec, U.; Ravnik, M.; Zumer, S. Science 2006, 313, 954. (10) Hung, F. R. Phys. Rev. E 2009, 79, 021705. (11) Ognysta, U.; Nych, A.; Nazrenko, V. Phys. Rev. Lett. 2008, 100, 217803. (12) Fukuda, J.; Zumer, S. Phys. Rev. E 2009, 79, 041703.
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deformations introduced into the medium by the particles, which depend on the relative orientation of the particles, on the distance between them, and on the anchoring of the LC on the particle surface,10-17 (ii) the nonuniformity of the order parameter in the vicinity of surface particles, due to the anchoring imposed on the particle surface,10,18,19 and (iii) the local suppression of fluctuation modes between two particles, where an ordering different from the bulk can be induced by the boundary conditions imposed on the particles.20-22 The elastic energy stored in the host LC is proportional to KR, where K is the elastic constant of the host liquid crystal and R is the radius of the particle. The surface energy, due to the anchoring, is proportional to WR2, where W is the anchoring strength on the particle surface.23,24 When the particles are large or the anchoring is strong, topological defects are generated, and the particular configuration depends on the specific anchoring conditions.10,17,25-28 For normal (or homeotropic) boundary conditions, a hedgehog radial configuration of the director is created (13) Kuksenok, O. V.; Ruhwandl, R. W.; Shiyanovskii, S. V.; Terentjev, E. M. Phys. Rev. E 1996, 54, 5198. (14) Stark, H. Eur. Phys. Lett. 1999, 10, 311. (15) Ruhwandl, R. W.; Terentjev, E. M. Phys. Rev. E 1997, 56, 5561. (16) Lubensky, T. C.; Pettey, D.; Currier, N.; Stark, H. Phys. Rev. E 1998, 57, 610. (17) Stark, H.; Fukuda, J.; Yokoyama, H. Phys. Rev. Lett. 2004, 92, 205502. (18) de Gennes, P. G. Langmuir 1990, 6, 1448. (19) Galatola, P.; Fournier, J.-B. Phys. Rev. Lett. 2001, 86, 3915. (20) Adjari, A.; Peliti, L.; Prost, J. Phys. Rev. Lett. 1991, 66, 1481. (21) Adjari, A.; Duplantier, B.; Hone, D.; Peliti, L.; Prost, J. J. Phys. (Paris) 1992, 2, 487. (22) Zhiherl, P.; Podgornik, R.; Zumer, S. Phys. Rev. Lett. 1999, 82, 5361. (23) de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals, Oxford Science Publishers, Oxford, U.K., 1993. (24) Sonin, A. A. Surface Physics of Liquid Crystals, Gordon and Breach Publishers, New York, 1995. (25) Poulin, P.; Stark, H.; Lubensky, T. C.; Weitz, D. A. Science 1997, 275, 1770. (26) Poulin, P.; Weitz, D. A. Phys. Rev. E 1998, 57, 626. (27) Loudet, J. C.; Barois, P.; Poulin, P. Nature 2000, 407, 611. (28) Gu, Y.; Abbott, N. L. Phys. Rev. Lett. 2000, 85, 4719.
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around the particle.17,25 The long-range interactions have dipolar symmetry, leading to the formation of chains of particles.25 For tangential boundary conditions, two boojums point defects result in long-range quadrupolar interactions between particles.16,17,28 Experimentally, both configurations have been observed in thermotropic LC with dispersion of water or silicon oil droplets25-28 and solid colloids9 and in a lyotropic host system.29,30 The elastic distortion can provide long-range attractive interaction leading to aggregation, whereas the topological defects provide shortrange repulsive interaction avoiding coalescence. Both effects can be used as additional resources for controlling colloid stability. For small particles or weak anchoring (WR/K , 1), distortions of the nematic order and elastic forces are minimal. In this regime, the interaction between two particles is anisotropic and can be either attractive or repulsive, depending on their relative orientation with respect to the LC director and their mutual distance. Attractive interactions have been observed between particles with a diameter of 60 nm dispersed in a lyotropic liquid crystal of uniaxial symmetry.29-31 The authors report particle agglomeration in the nematic phase and dissociation in the transition to the isotropic phase. However, an estimation of the interaction energy between the particles due to the elastic distortions in the medium shows that it is smaller than the thermal energy.30 The last contribution to the interaction between particles in an anisotropic medium is called the “pseudo Casimir” effect.20-22 When a nematic is confined between two flat parallel surfaces, the suppression of fluctuation modes of the director induces interactions between the surfaces, decaying with r-2, where r is the separation distance between the surfaces. Such interactions are attractive for symmetric boundary conditions. In this work, we experimentally investigate the behavior of latex spheres with a diameter of 100 nm dispersed in a lyotropic LC presenting three nematic phases, two uniaxial discotic (ND) and calamitic (NC) phases and the biaxial phase (NBX). We considered two different host systems, whose compositions were chosen so that the three different nematic phases would be around room temperature. In such ternary systems, the micelles have the shape of rounded, slightly biaxial platelets, with typical dimensions of 7 nm 5 nm 3 nm.32,36 In the biaxial phase, the orientational fluctuation modes have a small amplitude and there is orientational order around the three symmetry axes,35 whereas in the uniaxial calamitic and discotic phases, micelles freely rotate along their shortest and longest axis in the ND and NC phases, respectively (Figure 1). X-ray and light scattering studies31-36 have revealed that in all nematic phases micelles tend to stack along their shortest axis to form local pseudolamellar structures of period d comparable to the micelle size, extending over a distance ξ comparable to a few periods. The aim of this paper is to present experimental evidence of the reversible aggregation of latex particles in the lyotropic system. We discuss the possible mechanisms responsible for the formation (29) Ragunathan, V. A.; Richetti, P.; Roux, D. Langmuir 1996, 12, 3789. (30) Raghunathan, V. A.; Richetti, P.; Roux, D.; Nallet, F.; Sood, A. K. Langmuir 2000, 16, 4720. (31) Poulin, P.; Frances, N.; Mondain-Monval, O. Phys. Rev. E 1999, 59, 4384. (32) Galerne, Y.; Figueiredo Neto, A. M.; Liebert, L. J. Chem. Phys. 1987, 87, 1851. (33) Figueiredo, A. M.; Galerne, Y.; Levelut, A. M.; Liebert, L. J. Phys. Lett. 1985, 46, L-499. (34) Hendrikx, Y.; Charvolin, J.; Rawiso, M.; Liebert, L.; Holmes, M. C. J. Phys. Chem. 1983, 87, 3991. (35) Lacerda-Santos, M. B.; Galerne, Y.; Durand, G. Phys. Rev. Lett. 1984, 53, 787. (36) Oliveira, E. A.; Liebert, L.; Figueiredo Neto, A. M. Liq. Cryst. 1989, 5, 1669.
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Figure 1. (a) Symmetry axes of the biaxial micelles and fluctuation modes. In the biaxial phase, the orientational fluctuations around the three symmetry axes have a small amplitude and there are three orientational symmetry axes. In the discotic (ND) phase (b) and calamitic phases (NC) (c), the micelles freely rotate around the shortest and longest axis, respectively.
of latex aggregates and how such interactions are related to the particular symmetry of the surrounding nematic phase.
2. Materials and Methods Latex particles (from Rodhia Laboratory, Paulinı´ a, Brazil) with an average diameter of 100 nm with a Gaussian size distribution with a full width at half-maximum of ≈30 nm were dispersed in a water solution at a concentration of 50 wt % and pH 6.7. The particles prepared from polystyrene were negatively charged with a ζ potential at the surface of the particles equal to -5.4 mV, according to the characterization made by the fabricant (private comunication). Dilute solutions at a concentration of ∼5 wt % were prepared from the mother solution, and the proper quantity was added to the LC to yield the desired concentration (0.1-1 wt %). Lyotropic mixtures were prepared taking into account the water from the particle solution. For fluorescence observations, a small fraction of latex particles (4%) was substituted with fluorescent latex particles (T8872, Molecular Probes) with the same diameter. Two ternary lyotropic mixtures were used as host fluids (without particles): S1 and S2. Both systems exhibit two uniaxial phases, calamitic (NC) and discotic (ND), separated by a narrow domain in temperature (∼2 °C) corresponding to the biaxial phase (NBX). System S1 was composed of potassium laurate (35.3 wt %), decylammonium chloride (4 wt %), and water, with an NC T NBX T ND phase sequence, with an increasing temperature and an NBX T ND transition temperature equal to 39 °C.36 System S2 was composed of potassium laurate (27.6 wt %), decanol (6.8%), and water, with a NBX T ND transition temperature equal to 13 °C.32,33,37 The composition of both mixtures was chosen to create a large temperature domain of the nematic calamitic phase around room temperature.32,33,36 The biaxial and discotic phases were reached with an increasing temperature in S1 and a decreasing temperature in S2. From the optical observations, a phase diagram was built for a variable concentration of particles and a fixed composition of the host. We also investigated the influence of the LC composition (S1) on the aggregation dissociation process. Using polarizing and fluorescence microscopy, we observed, in the calamitic phase, the formation of latex aggregates that become larger in the vicinity of the transition to the ND phase, due to a coalescence process. Such aggregates also become elongated with a major axis, up to 50 μm long, tending to align parallel to the director field. The aggregation-dissociation process is reversible as particles reassociate coming back to the NC phase. The (37) Yu, L. J.; Saupe, A. Phys. Rev. Lett. 1980, 45, 1000.
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Figure 2. Textures observed via polarization microscopy for a sample introduced in a 200 μm glass flat capillary by flow where the director orients parallel to the longest axis of the capillary. P and A indicate the orientation of the polarizer and analyzer, respectively: (a) in the NC phase, (b) 2 °C below the transition to the ND phase, and (c) higher magnification of an aggregate with enhanced contrast. characterization of the nematic phases was complemented with X-ray scattering experiments on doped and nondoped liquid crystals, allowing the determination of the mean repetition distance in the discotic and calamitic phases. X-ray diffraction experiments were performed, using a laboratory rotatory anode (Rigaku, 0.8 kW), with the samples encapsulated in glass cylindrical capillaries (1.5 mm diameter). Measurements were taken on nondoped and doped S1 samples, with 0.4 wt % latex particles. The temperature of the sample was controlled within 0.5 °C. We measured normal forces between two curved mica surfaces confining the lyotropic liquid crystal in the discotic and calamitic phases by means of a surface force apparatus (SFA). A periodic layered structure parallel to the surfaces was observed in both nematic phases, resulting in oscillating forces of increasing amplitude as the confinement thickness was decreased. Such measurements provide key experimental evidence for justifying capillary condensation. A detailed description of the SFA can be found in ref 38. Two back-silvered mica sheets were glued onto cylindrical glass lenses with radii (R) of ≈2 cm and assembled at a distance D in a crossed configuration. When D , R, this geometry can be approximated as a sphere of radius R at a distance D from a plane. D is determined with a multiple-beam interferometric technique based on fringes of equal chromatic order (FECO),39 giving a resolution of a few angstroms in the D range from 0 to 100 nm. The lower surface is attached to a horizontal double cantilever spring with an elastic constant k of 260 N/m, which is displaced vertically toward or away from the fixed upper surface using a piezoelectric actuator. As the surfaces are approached or retracted from each other, the presence of an attractive or repulsive force causes the spring to deflect by an amount l = F/k that is directly measurable with subnanometer resolution. The resulting force sensitivity is better than 0.1 μN. The sealed inox chamber of the SFA was filled with ∼40 mL of S1 lyotropic solution in the NC phase, completely immersing the surfaces. The temperature was controlled within 0.1 °C, and the SFA measurements were first taken in the ND phase, well above the NBX T ND transition temperature, and then in the NC phase.
3. Experimental Results 3.1. Phase Diagram and Optical Observations. Samples of nondoped S1 and S2 mixtures were quite transparent at room temperature, whereas doped mixtures had a turbid appearance that changed to transparent and slightly blue going toward the ND phase (i.e., by heating S1 mixtures or cooling S2 mixtures). The change from turbid to transparent occurs when T ≈ 40 °C for system S1 and when T ≈ 12 °C for system S2 ((0.5 °C), corresponding approximately to the transition temperatures to the ND phase of the nondoped mixtures. (38) Israelachvili, J. N.; McGuiggan, P. M. J. Mater. Res. 1990, 5, 2223. (39) Israelachvili, J. N. J. Colloid Interface Sci. 1973, 44, 259–272.
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Optical microscopy observations showed that the turbidity was due to the formation of latex aggregates. The nematic director became aligned along the direction of fluid flow during filling of flat glass capillaries with a thickness of 200 μm (Vitrocom) with doped mixtures in the NC phase. The overall texture was uniform and birefringent, indicating that the anchoring of the NC director was parallel (planar) on the capillary glass boundaries. Anisotropic aggregates were visible in this nematic phase (Figure 2). This was a slow process that stabilized after approximately 15 min for a fixed temperature, resulting in larger aggregates with a length of up to 50 μm. The large aggregates had a shape of prolate (calamitic) ellipsoid (like a lemon) with an ∼1.3 anisotropy and with the long axis oriented parallel to the director. The length of an aggregate varied from a few micrometers to 50 μm. When the sample was heated, their size remained almost constant up to 2 °C below the transition to the ND phase, when they started to coalesce. Larger aggregates formed by coalescence of small ones (Figure 3), in the temperature domain corresponding to the NBX phase of the nondoped system. Continuing to heat the sample, at 39 °C we observed the transition to the ND phase as a sudden change in anchoring conditions.40 Such a transition is easily identified by polarizing microscopy due to the change in the texture, planar to homeotropic, with respect to the capillary walls. In the NC phase, the micelles tend to lie with their largest surface parallel to the boundary surfaces, resulting in a planar texture, which can be homogeneous or degenerated. In our experiments, when the sample is introduced into the capillary in the NC phase, a uniform planar alignment is obtained, with the director parallel to the flow direction. At the transition to the ND phase, the director tends to be oriented perpendicular to the boundary surfaces, resulting in a homeotropic texture that develops very quickly in the whole sample, and we observed also that the aggregates quickly disappeared during this transition: the dynamics of particle dissociation was therefore much faster than the coalescence. Particles dissociated in the ND phase and reassociated at the transition to the NC (or NBX) phase: aggregation and dissociation are therefore reversible processes. However, when the sample was cooled from the ND phase back to the NC phase, the anchoring on the capillary walls changed from uniform homeotropic to planar degenerated (see the Supporting Information). The texture becomes inhomogeneous, and the shape and orientation of the aggregates vary from one domain to another. We observed a similar behavior also for doped S2 mixtures: aggregation in the NC phase, slow coalescence in the temperature range of the NBX phase of the nondoped mixture, and alignment of the lemon-shaped aggregates with the director (40) Bechtold, I. H.; Bonvent, J. J.; Oliveira, E. A. Phys. Rev. E 2002, 65, 011704.
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Figure 3. Observations via polarization (left) and fluorescence microscopy (right) with a small fraction of latex particles marked with a fluorescence probe, appearing in white. The sequence of photos illustrates the coalescence of aggregates on a time scale of approximately 15 min, at a fixed temperature T of 37.5 °C, corresponding to the NC phase (system S1).
Figure 4. Reorientation of the aggregates, following the reorientation of the medium, at 38 °C. (a) Initial orientation, with n oriented by flow, and parallel to the longest axis of the capillary. (b) Final orientation, with n making an angle of approximately 45° with respect to the initial orientation. The director is then parallel to the polarizer, and the texture is planar, with a minimum of transmittance between crossed polarizers. The aggregates reorient to follow the orientation of the director.
(see the Supporting Information). The latter aspect was further investigated by applying an intense magnetic field at an angle of 45° with the initial uniform orientation of the director (Figure 4), for sample S1. After ∼10 h, the director becomes oriented with the magnetic field and the anisotropic aggregates follow the same orientation of the director. The effect of sample thickness on aggregate length was also investigated using capillaries with different thicknesses: 50, 100, 200, and 400 μm. Small aggregates, varying from 10 to 20 μm, were observed for the two thinner capillaries. For the thicker ones, it seems that the limiting length of the aggregates is ≈50 μm. Different types of latex particles were used in our experiments: different compositions (styrene and butadiene), different surface chemistries (other surfactants and dialyzed), and different diameters (40 nm). In all these assays, a similar behavior was observed, namely a reversible aggregation-dissociation process related to the NBX-ND transition (see the Supporting Information). Therefore, the aggregation process is quite reproducible and is not related to a particular composition of the latex particles or to their surface chemistry. In the presence of latex particles, we determined the phase diagram using sample S1 as the host fluid for a fixed composition of the host nematic and variable particle concentration. Comparing the phase diagram of the nondoped system (Figure 5a) with the phase diagram presented in Figure 5b, we see that the 11852 DOI: 10.1021/la901520r
Figure 5. (a) Phase diagrams for system S1, adapted from ref 36. (b) Phase diagram for a fixed composition of the host system and varying concentrations of latex particles. The composition of the host fluid corresponds to the vertical dashed line in panel a. We have tried to determine the NBX-NC transition temperature in the doped system, by measuring the birefringence using a Berek compensator; however, it was not possible to observe the interference fringes. Both phases present a planar texture, although with a weak birefringence in the biaxial phase. ISO represents an isotropic phase. S represents the formation of a solid phase of latex that precipitates to the bottom of the tube.
transition temperature to the ND phase remains almost the same for a small fraction of latex particles added to the system, up to ≈0.5 wt %, but its range of temperature becomes narrower. It is also seen that the high-temperature isotropic phase (T > 60 °C) is Langmuir 2009, 25(19), 11849–11856
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Figure 6. (a) X-ray scattering patterns obtained in the calamitic phase for LC mixture S1 not doped (a) and doped with latex particles, at 0.4 wt % (b) The scattering curves were fitted by Gaussians.
replaced with a viscous gel phase that is optically isotropic, but with birefringence induced by flow. For latex particle fractions higher than 0.5 wt %, precipitates of latex particles (S) coexist with the dispersion (Figure 6). The low-temperature hexagonal phase (T < 12 °C), observed for the nondoped system, is replaced with an isotropic phase, in the doped system. The destabilization of the ND phase can be interpreted as being due to a perturbation introduced in the ordering of the micelles due to the latex particles that are dispersed in the discotic phase; however, by flow, close to the walls of the tube the micelles can be oriented by surface effects, resulting in the induced birefringence. In the lowtemperature domain, the growing of the micelles in one direction and their positional order would be inhibited by the latex aggregates. We also investigated the influence of the composition of the host system on the aggregation of the latex particles. Using mixture S1, we varied the ratio between the surfactants, with a [DaCl]/[LK] ratio between 0.12 and 0.16. The relative concentration of the surfactants plays an important role in the shape of micellar aggregates,32-34 and it is known that the addition of the surfactant with a shorter carbonic chain favors the flattening of the micelles. For nondoped system S1, the range of the biaxial phase is slightly increased when the ratio of surfactants ([DaCl]/[LK]) is increased from 0.12 and 0.16, and we observed that this also corresponds to the increasing anisotropy of the latex aggregates in the doped system. In summary, in our experiments we observed that the presence of dispersed latex particles in lyotropic LC solutions does not visibly affect the alignment anchoring of the bulk nematic phase. In the NC phase, the director is uniform between the aggregates and oriented along the direction of flow produced during filling. In the ND phase of doped and nondoped samples, the director is always uniform and normal to the glass capillary walls, and we did not notice any particular defect in the texture. Close to the transition to the discotic phase (in the NBX phase of the nondoped system), the aggregates appear “pinched” at the extremities in the shape of a lemon, suggesting the presence of a pair of defects of the “boojum” type.16,17 Our results share more analogies with a typical phase separation than an emulsion stabilized by elastic forces and defects of the nematic continuous phase. We did not observe a nematic birefringent texture connecting the aggregates in a lattice, even irregular, and we did not clearly identify defects between aggregates. The interaction between particles due to the elastic distortion introduced into medium can be either attractive or repulsive, Langmuir 2009, 25(19), 11849–11856
depending on their relative orientation with respect to the director field, and decays with their separation distance r-5.12,14,15 One of the authors has studied anchoring of lyotropic LCs, and the estimation of anchoring energy in the nematic calamitic phase (W) was on the order of ≈10-6 J.41 Then, considering typical values of W, and K for the lyotropic systems, and assuming that the particles are in contact (r = 2R, K ≈ 10-12 J/m, W ≈ 10-6 J,41 and R = 5 10-8 m), we evaluate the pair potential to be U ≈ W2R8/(Kr5) ≈ 10-24 J15 (see the Supporting Information), which is much smaller than the thermal energy of the particles (U , kBT ≈ 10-21 J). The anchoring strengh should be at least 2 orders of magnitude to make U larger than the thermal energy. 3.2. X-ray Diffraction Experiments. We performed X-ray experiments in the NC and ND phases, for the doped and nondoped system (S1). The samples were placed in glass cylindrical capillaries at room temperature (NC phase), and the director tends to orient, in average, parallel to the cylinder walls. We observed an anisotropic diffusion band (Figure 6) due to the pseudolamellar, short-scale positional ordering of the micelles in the nondoped system. The diffusion band had a peak at a scattering vector for q = 1.38 ( 0.21 nm-1 and a width Δq = 0.6 nm-1, in both NC and ND phases. The corresponding intermicellar distance is d = 2π/q = 4.7 ( 0.7 nm. The orientation of the sample induced only by surface effects was very poor, and it was not possible to determine the correlation length. Within the accuracy of our experiments, we measured the same peak position and bandwidth in mixtures containing latex particles, both in the NC phase and in the ND phase. 3.3. SFA Force Measurements. After injecting a droplet of nondoped S1 mixture between the mica surfaces in the NC phase, we observed a nonuniform birefringent texture that became uniform and nonbirefringent upon heating corresponding to the homeotropic alignment that develops at the transition to the ND phase. Figure 7 shows the force, F, measured in the NC phase and plotted as a function of the distance D between the cylindrical surfaces of the SFA. F was normalized by the average radius of curvature (R ≈ 2 cm) of the surfaces at the position of contact. F periodically oscillated between attractive (F < 0) and repulsive (F > 0) and rapidly decayed with D. This is the typical appearance of structural forces due to layering of micelles at the surfaces: micelles tend to lie flat on the surface and stack on top of each other. This type of ordering has been studied in detail, both (41) Ribas, A. M.; Evangelista, L. R.; Palangana, A. J.; Oliveira, E. A. Phys. Rev. E 1995, 51, R5204.
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Figure 7. (a) Normal forces, F, between two mica surfaces, measured with the SFA in the NC phase of a nondoped S1 mixture. R ≈ 2 cm is the radius of curvature of the cylindrical mica surfaces, and D is their mutual distance. Empty (O) and filled (b) circles indicate approach and retraction of the surfaces, respectively. Blank regions are due to mechanical instability of the SFA for dF/dD > K, where K is the elastic constant of the force measuring spring. Data from two different experiments are shown. The rank n is shown for the first two force oscillations. The dotted curve is the best fit to the theoretical eq 1 with the following parameters: d = 4.1 nm, D0 = 5.6 nm, ξ = 10 nm, and A = 0.95 mJ/m2. The inset illustrates the layer deformation and removal. (b) Normal forces, F, measured with the SFA in the ND phase of a nondoped S1 mixture. F is normalized by the radius of curvature R of the cylindrical surfaces, as a function of the mica-mica separation Di. Empty (O) and filled (b) circles indicate approach and retraction of the surfaces, respectively. The rank n is shown for the first two force oscillations. The inset shows the attractive force.
theoretically and experimentally18,42-44 in the framework of a phenomenological description of the positional micellar order near the surfaces. It was calculated that, when the positional order at the surfaces does not depend on surface separation D, the force curve, F(D), is given by the following equation: F 1 -cos½φ 0 ¼ 2πAξ tanhðD =2ξÞ þ -1 R sinhðD0 =2ξÞ D0 ¼ D - D0
ð1Þ
½φ ¼ 2πðD0 =d -nÞ In eq 1, n is the “rank” (see Figure 7) or the number of micelle layers between the surface that can be completely removed from the confinement by compression, d is the thickness of a layer of (42) Moreau, L.; Richetti, P.; Barois, P. Phys. Rev. Lett. 1994, 73, 3556. (43) Richetti, P.; Moreau, L.; Barois, P.; Kekicheff, P. Phys. Rev. E 1996, 54, 1749. (44) Schopohl, N.; Sluckin, T. J. Phys. Rev. Lett. 1987, 59, 2587.
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micelles (including the liquid between them), ξ is the correlation length of the positional order, A is proportional to the order at the surface, and D0 is the thickness of one or more layers that are trapped between the surfaces and cannot be removed. The force profile of eq 1 shows minima at distances D0 equal to an integral number of layers ([φ] = 0). Equation 1 can be fitted to the data of Figure 7a to yield the following parameter values: d = 4.15 ( 0.10 nm, ξ = 10 ( 1 nm, A = 0.95 mJ/m2, and D0 = 5.6 ( 0.2 nm. Note that we were not able to bring the mica surfaces into direct contact (D = 0) upon compression due to the presence of residual layers, whose undeformed total thickness was similar to D0. After the sample had been heated to ND phase, the overall appearance of the force curves showed only small changes. (a) An additional long-range attraction appeared that rendered the oscillation completely negative in the D range of 40-80 nm. (b) Oscillations were not symmetrical around the maxima, as the force measured upon approach increased more steeply toward the maxima than in the NC phase. Equation 1 was fitted to the data of Figure 7b to yield the following parameter values: d = 4.18 ( 0.10 nm, ξ = 10 ( 1 nm, A = 1.60 mJ/m2, and D0 = 11.0 ( 0.2 nm. The fit is precise for d and D0, whereas the long-range attraction in the ND phase affected the precision of A and ξ. Long-range nematic order appears in solutions of micelles because it is associated with a reduction in the excluded volume between micelles and an increase in entropy.23 Excluded volume effects also give discotic and biaxial micelles a tendency to stack or pile on top of each other, creating a pseudolamellar positional order over a short length scale comparable to the size of a few micelles.32,33,35 In the proximity of a smooth, extended solid surface of mica, glass, or latex, such short-scale positional ordering is preserved when the direction of the stack (i.e., of the short axes of the micelles) is normal to the surfaces. This boundary condition appears to be sufficiently strong to align the director of the ND phase (i.e., the average orientation of the shortest micelle axes) along the surface normal of glass and mica surfaces. SFA measurements (Figure 7) show that micelles are indeed structured in layers of with a thickness d of ≈4 nm with a correlation length of the positional order, ξ, comparable to the thickness of a few layers. The layering of micelles in the NC phase is remarkable, as it restricts rotation of the micelle around the long axis and is therefore incompatible with the structure of the phase. This conflict is reflected in the value of parameter A determined from SFA measurements, which is related to the positional order at the surfaces (eq 1): A is lower in the NC phase than in the (fully compatible) ND phase. We point out here that we did not observe a strengthened attraction in the NC phase (Figure 7a) compared to the ND phase (Figure 7b). Therefore, attraction and aggregation of particles in the NC phase are not driven by changes in structural forces related to the surface layering of micelles. In conclusion, both the thickness d of a layer of micelles and the correlation length ξ of the positional order were basically constant in the NC and ND phases, and similar to the values obtained by X-ray scattering on bulk, because d and ξ are mainly due to micelle-micelle interaction rather than to micelle-surface interaction. On the other hand, both D0 and A were larger in the ND phase than in the NC phase. This shows that micelles have a stronger tendency to bind to the surface in the ND phase, resulting in a larger thickness D0 of the “residual” layers, and to form layered structures with higher order at the surface and larger values of A. Nevertheless, we notice that our latex particles had a curvature radius R of ≈50 μm, only 1 order of magnitude larger than the micelle size. Under these circumstances, the Derjaguin formula Langmuir 2009, 25(19), 11849–11856
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(F/R = 2πE) may incorrectly accounted for curvature effects used to compare SFA results. The formula relates the force F between a sphere and a plane to the energy per unit area E between parallel walls and is valid only when the range of the interactions is much smaller than R. Therefore, SFA experiments conducted with macroscopic surfaces and theoretical models derived for parallel plates may neglect curvature effects,42,43 an interesting point that deserves further investigation. A related example is the interaction force between layers of polymers end-grafted to solid surface (polymer “brushes”). The distribution of monomers near the surface can be described with a mean field order parameter (or local concentration), as in the case of micelles.42,45 It has been shown that the force between two parallel plates coated with layers of grafted polymers45 is markedly different from the force between two particles having a radius comparable to the layer thickness.46
4. Discussion In this section, we will discuss the possible mechanisms responsible for the reversible aggregation of latex particles, presenting arguments supported by our experimental observations. We have seen that the particles or aggregates do not introduce defects in the nematic texture and that the contribution of interaction between particles due to the elastic distortion introduced in medium is very weak. The profiles of force obtained from SFA experiments gave evidence of the layering of the micelles induced by confinement between mica surfaces; however, the results obtained do not support the hypothesis of structural forces of layering as being responsible for aggregation. Another possible contribution is due to the suppression of fluctuation modes of the director between the latex particles. For a nematic confined between two flat parallel plates, the excess free energy density is given by20 kB T ζð3Þ K3 K3 δF ¼ - 2 þ h 16π K1 K2
ð2Þ
where K1, K2, and K3 are the elastic constants related to the splay, twist, and bend distortions, respectively, h is the thickness of the nematic separating the surfaces, and ζ(3) is the Riemann’s ζ function [ζ(3) = 1.202].19 Assuming a separation distance h of 40 nm and one constant approximation (K1 ≈ K2 ≈ K3), the excess of energy density is ≈1.2 10-7 J/m2, which normalized by the radius of the particles gives an F/R value of ≈10-7 N/m. This is 3 orders of magnitude lower than that reported in SFA measurements, for the same separation distance. The anisotropy of the LC host determines the elongated shape and alignment of the aggregates along the asymptotic orientation of the director. Droplets of water and oil in thermotropic liquid crystals maintain a spherical shape and carry visible topological defects,25-28 because the surface tension γ at the LC-liquid interface is high. Therefore, γ appears to be particularly low at the LC-aggregate interface in the NBX phase. The pinching would remove the defects, thereby reducing the local distortion of the LC director. These observations indicate that the anchoring of the LC director at the interface with the aggregates is planar and that the aggregates in the NBX phase are deformable (fluidlike). On the basis of the experimental results presented above, we can suppose that the positional and nematic orders become somehow coupled a distance from a surface comparable to the (45) de Gennes, P. G. Macromolecules 1982, 15, 492. (46) Lin, E. K.; Gast, A. Macromolecules 1996, 29, 390.
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micelle size. Since layering is incompatible with the NC order, the latter is forced to become more discotic as the distance z from the surface decreases, possibly becoming biaxial at some finite value of z near the surface. Therefore, gradients of nematic order around latex particles are expected to be much more pronounced in the NC phase than in the ND phase. In our experiments, gradients were not optically resolved and the LC appeared uniformly ordered (NC) and aligned (planar anchoring) near a solid surface. Therefore, the distortion of the NC structure occurred at a scale smaller than a few micrometers. This is the scenario of order reconstruction found around disclinations in uniaxial nematics47,48 and defects in nematics subject to high strain.49-51 Latex particles would behave like defect structures in the NC phase, which require a high surface energy to remain dispersed in the bulk, whereas particles do not significantly perturb the order in the ND phase. Gradients of nematic order are associated with positive terms of the free energy expansion in the (tensor order) Landau-De Gennes description of the nematic order, and processes that reduce gradients between surfaces are associated with attractive forces. Then, the aggregation of latex particles observed in the NC and NBX phases would be due to this type of attraction. In a previous work,52 it was shown that confining the LC sample in the NC phase to small thickness between two parallel plates produces a bulk transition to the NBX phase. The two principal directions are normal to the plates and parallel to the direction of planar anchoring common to both plates, respectively. This phenomenon is similar to confined-induced capillary condensation common for liquids possessing a first-order transition between an ordered and an isotropic phase (refs 44, 52, and 53 and references cited therein). Inside the latex aggregates observed in our samples, the LC is confined between particles, inducing planar anchoring conditions with different anchoring directions at the surface of each particle. Capillary condensation from the NC phase could produce a ND phase where gradients are reduced or removed. In the NBX phase, a transition to the ND phase would remove twist deformations between the particles and associated gradients of order. As the phase of the LC host changes following the sequence of phases NC f NBX f ND, the state of aggregation of latex particles is observed to change from solidlike (noncoalescing aggregates with an irregular shape and sharp edges) to liquidlike (coalescing, deformable aggregates with a smooth and rounded shape) to gaslike (no aggregation). This suggests that the attraction between latex particles becomes weaker going from the NC phase to the NBX phase, probably because the latter is intermediate between the NC and ND phases. The attraction disappears in the ND phase where gradients of order are not necessary. The rather polydisperse distribution of aggregate sizes and separations (Figures 2 and 3) appears to be due to the dynamical processes of growth and coalescence of phase domains at the transition from the calamitic to the biaxial phase. At the transition, the dispersion of latex particles would be destabilized by attractive capillary forces, resulting in the growth of anisotropic aggregates. Since the overall concentration (47) Palffy-Muhoray, P.; Garland, E. C.; Kelly, J. R. Liq. Cryst. 1994, 16, 713. (48) Toledano, P.; Figueiredo Neto, A. M. Phys. Rev. Lett. 1994, 73, 2216. (49) Barberi, R.; Ciuchi, F.; Lombardo, G.; Durand, G. E. Phys. Rev. Lett. 2004, 93, 137801. (50) Zappone, B.; Richetti, Barberi, P. R.; Bartolino, R.; Nguyen, H. T. Phys. Rev. E 2005, 71, 041703. (51) Bechtold, I. H.; Gomez, S. L.; Bonvent, J. J.; Oliveira, E. A.; Hohlfed, J.; Rasing, Th. Phys. Rev. E 2004, 69, 061707. (52) Antelmi, D. A.; Kekicheff, P.; Richetti, P. Langmuir 1999, 15, 7774. (53) Kocevar, K.; Musevic, I. ChemPhysChem 2003, 4, 1049.
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of particles is low, the growth quickly slows, possibly reaching an equilibrium size, as particles are depleted from the continuous phase. In the biaxial phase, growth at a fixed temperature would continue by diffusion and coalescence of aggregates (Figure 3). The question of why SFA experiments did not detect a confinement-induced NC f ND capillary condensation arises. Attractive capillary forces, F, are generated during confinement to separations h smaller than a critical value h* and typically increase linearly with d if h < h*.45,53 The slope dF/dh is proportional to the difference in chemical potential μ between the two phases, which is probably small between different nematic phases in our system. The SFA is not able to directly detect a constant or a slowly varying linear force, unless the surfaces can be separated well beyond h*. The NC f NBX confinementinduced transition observed between parallel plates occurs at separations as large as 80 μm.51 Therefore, it is possible that SFA experiments failed to detect a capillary attraction in the NC phase simply because it occurred at a separation h* much larger than the maximum value of ≈150 nm considered in our experiments. In systems possessing a second-order transition between two ordered phases (such as NC and ND), a reduction of order gradients is usually obtained upon approaching the surfaces without producing a bulk capillary condensation. The attractive force between the surfaces has a typical tanh(h/σ) dependence on separation h, where σ is the correlation length of the order induced by the surface. An example is the attractive background of the oscillatory forces observed by the SFA in our system (eq 1, where σ = ξ and [φ] = 0), due to gradients of positional order. Again, such attraction would be linearly and slowly growing and, therefore, practically undetectable by the SFA if h , σ, as previous works52 appear to indicate.
with the phase transitions in the medium. We observed that the aggregates formed in the calamitic phase become larger and anisotropic in the temperature domain corresponding to the nematic phase in the pure liquid crystal, whereas the particles completely disperse in the medium in the discotic phase. SFA measurements with the liquid crystal confined between mica surfaces have shown a layered structure of the micelles, with oscillating forces between surfaces. The different contributions to the interactions between the particles arising from the anisotropy of the medium were evaluated, and we found that the more relevant contribution to the interaction between particles is due to the nonuniformity of the order parameter close to the surface; nevertheless, SFA measurements do not show any strengthened attraction in the calamitic phase that could be responsible for the aggregation of nanoparticles. We propose that capillary condensation of the NC phase, induced by the confinement between the particles, can take place for a separation distance smaller than a critical value, resulting in attractive forces. The capillary condensation could reduce or remove the gradient of order parameter, driving the transition of aggregates from solidlike to liquidlike and gaslike. In general, our experiments were not able to determine the precise nature of the attractive forces driving the aggregation of latex particles in the NC and NBX phases, and other explanations based on the presence of order gradients are possible. A tensorial theoretical model is beyond the scope of this work, and we are not able to conduct this task at the moment. This work will be presented in a future publication.
5. Conclusions We present experimental evidence of a reversible aggregation of nanoparticles in a lyotropic liquid crystal colloid, associated
Supporting Information Available: Additional experimental results. This material is available free of charge via the Internet at http://pubs.acs.org.
11856 DOI: 10.1021/la901520r
Acknowledgment. We acknowledge the Brazilian scientific agencies FAPESP, CAPES, and CNPQ for financial support.
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