Europhysics Letters. Manuscript ref. number G8637. Revised version

LYOTROPIC FERRONEMATICS:

MAGNETIC ORIENTATIONAL TRANSITION IN THE DISCOTIC PHASE

V. Berejnov ^1,2 , Yu. Raikher ², V. Cabuil ¹, J.-C. Bacri ³, R. Perzynski ³

1. Laboratoire de Physicochimie Inorganique, Université Pierre et Marie Curie, Bat. F, case 63, 4 place Jussieu, 75252 Paris Cedex 05, France.

2. Laboratory of Kinetics of Complex Fluids, Institute of Continuous Media Mechanics, Urals Branch of the Russian Academy of Sciences, Perm, 614013, Russia.

3. Laboratoire des Milieux Désordonnés et Hétérogènes, Université Pierre et Marie Curie, Tour 13, case 78, 4 place Jussieu, 75252 Paris Cedex 05, France

Corresponding author: Dr. Valerie Cabuil, Laboratoire de Physicochimie Inorganique, Université Pierre et Marie Curie, Bat. F, case 63,4 place Jussieu, 75252 Paris Cedex 05, FRANCE

E-mail: cabuil@ccr.jussieu.fr

Telephone: 33 – 1 – 44 – 27 – 31 – 74

Telefax: 33 – 1 – 44 – 27 – 36 – 75

Abstract.

We report synthesis of lyotropic ferronematics with the content of magnetic nanoparticles (~ 6 nm) up to 1 vol.%. In the ferrodiscotic phase we observe a magnetic Frederiks transition with critical fields about two orders of magnitude lower than that for an undoped lyotropic system. A model accounting for the magnetic polarization behavior of the studied ferronematic is presented.

Key words: liquid crystals, lyotropic nematics, ferrofluids, orientational transitions

Running title: Synthesis of lyotropic ferronematics

Introduction.

Complex magnetic media which integrate nanoscopic magnetic particles into self-organizing assemblies of surfactant molecules are raising growing interest. Synthesis of such smart materials evidently opens new technical prospects. Nowadays emulsions, lamellar phases and vesicles have been successfully modified yielding, respectively, ferroemulsions [1], ferrosmectics [2] and ferrovesicles [3]. But up to now micellar phases have been hardly touched [4]. Though tiny quantities of agglomerated ferroparticles are used since more than 15 years to help to align lyotropic nematic liquid crystals, it is only very recently that lyotropic ferronematics, i.e., true colloidal dispersions of magnetic nanoparticles in a ternary surfactant matrix, stable over periods of months, have been successfully synthesized.

In the pioneering paper [5], F. Brochard and P. de Gennes have proposed a theoretical description for ferronematics assuming that the particles are coupled to the LC matrix by a strong surface anchoring. More recently, the model was extended [6] for the case of soft anchoring as well. However, in both works the authors supposed that the particles are magnetically rigid. We argue that lyotropic ferronematics fall out of the scope of the theory [5,6]. The main difference is that in the studied systems the particles are superparamagnetic. As a direct consequence of this magnetic softness, we observe an orientational transition that has a symmetry of a conventional Frederiks one but whose thresold is orders of magnitude lower than that in pure lyotropic nematics.

The systems under study consist of maghemite g-Fe₂O₃ nanoparticles, synthesized according to the Massart method [7], which are dispersed in a well-known [8,9] lyotropic micellar system: potassium laurate / 1-decanol / water (PLDW). We first specify our complex magnetic fluid, then report the observed 2D-textures and the measurements of the Frederiks thresholds, and end up by proposing a model to explain the orientational transition.

As a ternary system, PLDW has been investigated in [8–10]. Under concentration variations, two kinds of uniaxial nematic structures (built of either calamitic or discotic micelles) as well as a biaxial phase, have been reported. According to [10], the characteristic size of discotic micelles is: diameter 7 nm and thickness 4 nm. Since PL is not commercially available, we have synthesized and purified it by ourselves. The phase diagrams of the prepared PLDW solutions proved to be well reproducible, the nematic phase domain being located (in wt.%) at 25–32 in PL, 7–11 in 1-D, and 62–68 in water [11]. With both birefringence and conoscopy techniques we observe the above-mentioned nematic micellar phases. In the discotic phase, our system near a glass wall acquires a homeotropic orientation. (Conventionally, the director n is chosen along the symmetry axis of the micelles thermally-averaged.)

Experimental

Maghemite particles of typical size 6 nm are single domains with a bulk magnetization I=470 G. Due to the method of preparation, the grains are positively charged with the surface density 20 m C/cm². They are thus macroions with mutual electrostatic repulsions. Being dispersed in a liquid carrier, such particles infer to the solution a giant paramagnetic behavior with a saturation magnetization proportional to the particle volume fraction F . From the shape of the magnetization curve, a particle size distribution may be deduced in good agreement with SANS and electron microscopy observations [12]. The magnetic anisotropy of the particles is found [13] to be of the surface origin and uniaxial, its energy density being K_{s »} 2.8 erg/cm².

Ferronematic phases are synthesized by admixing a cationic maghemite ferrofluid to PLDW solutions. The process has several steps including removal of particle coagulates by a gradient magnetic field. The resulting system is four-component, and so is its concentration chart. A detailed account on it will be published elsewhere [11]. Here we just remark that from the succession of its ternary cross-sections (volume fraction F of magnetic particles being the parameter) one finds that at room temperature the ferronematic domain survives until F >1%, though shrinking considerably against its size at F ® 0 (pure ternary solution). All our preparations are macroscopically homogeneous and of red-brown color which deepens with the amount of the suspended ferrite. Oriented under gravity in 1 cm-diameter tubes, the samples are strongly birefringent. The data reported in what follows were obtained for ferrodiscotics with the characteristic weight content of the lyotropic matrix PL=26.5%, 1-D=7.25%, W=66.3%; and F ranging from 0.044 to 1.1%.

Magnetization M of the samples is measured in vertical cylindrical cells (height 5 cm, cross-section 1 cm²) with a vibrating-sample set-up at 120 Hz. Note that in the cells that thick, the orienting influence of the walls, i.e., the magnetic anisotropy of the ferronematic with respect to n, is negligible. The recorded dependences—see the example in Fig. 1—fairly well obey the scaling law M(H) µ M₀(H), where M₀(H) is the magnetization curve of the parent ferrofluid. This affinity means that dilution does not spoil the uniformity of the particle spatial distribution.

At high fields, M tends to M_s =F I, whereas in the low-field limit M=c ₀H, see the inset in Fig. 1. For dilute suspensions one has c ₀=F I ²<V ²>/3<V>k_BT, where angular brackets denote averaging over polydispersity, so that <V> is the mean volume. In our case the particle size distribution is log-normal (see the caption to Fig.1), and at room temperature the susceptibility formula yields c₀=0.7F. The latter relation ship was used to determine the particle volume fraction in the ferrodiscotic samples.

Magneto-orientational effects are measured in flat glass capillaries of thickness 30 £ D £ 500 m m, other dimensions being orders of magnitude greater. The samples look homogeneous on the spatial scale down to 1 m m. Polarized-light microscopy reveals the following facts.

1. In the absence of magnetic field, all the samples (whatever the particle content F , including the bare matrix with F =0) have the same homeotropic texture with the director normal to the walls. The recorded defect patterns are typical for the usual nematic phase, see Fig. 2.

2. In the bare matrix, a field up to 400 Oe applied either normally to or along the capillary plane has no effect.

3. For a ferrodiscoic sample, the same field has no effect if applied in the cell plane but strongly distorts the Schlieren patterns if imposed normally to the layer, i.e., parallel to the initial director. An example of such a texture is given in Fig. 3 for F =0.044%. The local orientation is planar with a lot of defects at the spatial scale of 100 m m. These distortions are reversible: if the field is turned off, the homeotropic orientation restores in about 15 min.

Results and discussion

Comparing these observations, we conclude that in the ferrodiscotics under study, a sufficiently strong coupling between the nanoparticles and the nematic matrix is achieved. Moreover, in our samples the equilibrium (easy axes) directions for the nematic and magnetic subsystems are perpendicular to each other.

With a field normal to the cell plane, we observe the Frederiks transition, i.e., the onset of distortions that takes place only after some threshold H_c is exceeded. When in experiment, trying to obtain H_c, we diminish the supercriticality H – H_c , the time of the distortion development seems to increase unboundedly. This compelled us to introduce a reference cut-off of the observation time; we set it to 15 min. The results of so done evaluation of H_c are presented in Fig. 4.

The threshold field H_c is found to be a function of the reduced variable D ^{–1F –1/2} with a linear initial behavior. This admits a simple qualitative explanation. In a cell, the actual director orientation results from an interplay between the wall-imposed and field-induced alignments. The transition occurs when the magnetic energy density gain F_{m~ c a}H ², where c _a is the susceptibility anisotropy, exceeds the elastic energy density increment F_{el~ p} ²K_B /D ², where K_B~ 10^–6 dynes is a bend modulus. The balance condition F_m » F_el yields H_{c ~} that scales as D ^{–1F –1/2}, if one sets c _a µ F . We remark that by its form the expression for H_c does not differ from that in a customary nematic. However, for ferronematics at D=100 m m and F =0.1%. we measure H_c » 30 Oe that leads to c _a ~ 10^–4. Comparing that to pure systems, with their diamagnetic anisotropies c _a ~ 10^–7 [14,15], one sees that, the presence of magnetic particles effectively enhances the magnetic susceptibility of a liquid-crystalline system several orders of magnitude.

To account for the occurring c _a, we propose a model that one may call the trapped grain approximation. Its basic assumptions are: (i) ferroparticles possess a magnetic anisotropy of a uniaxial type; (ii) ferroparticles are individually adsorbed by micelles and are not aggregated; (iii) due to the positive superficial charge density of the particles, they stick to the array of negative polar heads of the surfactant chains at the micelle surface in such a way that the anisotropy axis of the particle falls in plane with a discotic micelle; (iv) this adsorption of particles is strong enough (>> k_BT).

Let us recall the expression for the orientation-dependent part of the particle magnetic energy and write it down as U/k_BT = –(x e)–s (en )², where x =(IV/k_BT)H, s = (K_sS/k_BT) and e and n are unit vectors of the magnetic moment and anisotropy axis, respectively. The partition integral for a particle with a fixed n is , that for the free-energy density of an assembly of identical particles yields F = – (F k_BT/V) ln Z. Then for the susceptibility tensor one has c _ik = – ¶ ²F / ¶ H_{i ¶} H_k= – 3c ₀ ¶ ²ln Z/¶ x _{i ¶ x k}), where c ₀=F I ²V/3k_BT is the initial susceptibility for an assembly of identical superparamagnetic particles. Substituting, taking the derivatives and tending x ® 0, we get, with , (1) with Q being the particle internal orientation order parameter, see [16]. From Eq.(1) the anisotropic part of c _ik is, that for s <1 reduces to (2).

When transforming Eq.(2) into the magnetic term in the ferronematic free-energy density, we recall that in the adopted notations vector n is perpendicular to what we define as n—the director of the micellar texture. Then the direction of poorer magnetization (smaller c ) lies along n, and that of enhanced magnetization (higher c ) is normal to n. Because of that, with c _a from Eq.(1), the magnetic term of the trapped grain model takes the form F_m = c _a(nH)². To get the Frederiks transition threshold, the decrement d F_{m »} c ₀ Q H² (d n)² must be compared to the increment of the elastic energy d F_el » p ²(K_B/D²)(d n)². This yields H_{c »} (p /D) ´ . For maghemite particles with the size about 6 nm and K_s =2.8´ 10 ^–2 erg/cm ², one finds s » 0.8. This allows to use the expansion given in Eq.(2) and yields the expression (3).

Since by definition c ₀ is linear in F , Eq.(3) supports the scaling law H_{c µ} D ^{–1F –1/2} . Using the latter quantity as a coordinate and adjusting the elastic modulus in order to fit the experimental data in Fig.4, one finds K_B =5.1´ 10 ⁶ dyn in fairly good agreement with the measurements on a comparable pure system [15,16]. The achieved consistence verifies the proposed model. Indeed, one could hardly expect that a small amount of solid admixture might drastically change the elasticity of the matrix. Had we found any considerable deviation in the K_B values, it would have gravely compromised the theory.

Conclusions

In conclusion. We report synthesis of highly stable lyotropic systems containing up to 1 vol.% of magnetic nanoparticles. This doping does not suppress the ability of the matrix to liquid-crystalline ordering, and as well does not significantly affect its orientational elasticity. On the other hand, the embedded superparamagnetic grains enhance the magnetic susceptibility of the system several orders of magnitude as compared to pure lyotropics. Due to that, the orientation texture of a discotic ferronematic becomes controllable by means of weak magnetic fields. In particular, it yields a Frederiks transition in a classic geometry but with the critical field 30–50 times lower than that for pure lyotropic LC. The assumed particle–micelle coupling allows to explain the scaling law of the threshold field and gives a reasonable estimation for its measured values. We remark that in our model, as in the Brochard–de Gennes description [5], the orientation of the anisotropy axes of nanoparticles is imposed by the liquid-crystalline carrier. However, the magnetic term is changed from the rigid dipole approximation to the soft one.

The presented experimental tests are macroscopic ones. To get a detailed notion of the internal structure of a ferronematic system, one has to explore it on the mesoscopic scale. These studies employing both electron microscopy of freeze-fractured preparations and SANS are now under way.

Acknowledgements

This work was supported by “Le Réseau Formation – Recherche” 90R0933 of MENESRIP, by the grant 96–1149 of the French Direction of Armament (DGA) and from the Russian side by the grant 95–02–03953 of RFBR.

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Figure Captions

Figure 1. Reduced magnetization curve: M/Ms versus H in a log-log representation for a ferrodicotic sample with the particle volume fraction F =0.05%. Full line: best fit of the Langevin law averaged over the log-normal size distribution with the most probable diameter 6 nm and standard deviation 0.3. Inset: initial susceptibility c 0 measurements (dots), the line corresponds to the relation c0 =0.7F
Figure 2. Optical polarized microscopy: typical homeotropic texture of a ferrodicotic nematic sample in a flat glass cell inthe absence of magnetic field; particle content F =1.1%, cell thickness D=100 m m
Figure 3. Optical polarized microscopy: texture of a ferrodicotic nematic sample of F =0.044% in a glass cell of thickness 100 m m and under 400 Oe magnetic field perpendicular to the cell plane
Figure 4. Field threshold Hc as a function of the reduced variable D^–1^F^–1/2 for different samples; the slope of the drawn straight line is 150 Oe/m m