J. Phys. Chem. B 1999, 103, 6421-6428
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pH Effect on an Ionic Ferrofluid: Evidence of a Thixotropic Magnetic Phase E. Hasmonay,† A. Bee,‡ J.-C. Bacri,†,§ and R. Perzynski*,† Laboratoire des Milieux De´ sordonne´ s et He´ te´ roge` nes (associated with the Centre National de la Recherche Scientifique, U.M.R. 7603), UniVersite´ Pierre et Marie Curie (Paris 6), Tour 13, Case 78, 4 place Jussieu, 75252 Paris Cedex 05, France, and Laboratoire des Liquides Ioniques et Interfaces Charge´ es (associated with the Centre National de la Recherche Scientifique, U.M.R. 7612), UniVersite´ Pierre et Marie Curie (Paris 6), Baˆ timent F, Case 63, 4 place Jussieu, 75252 Paris Cedex 05, France ReceiVed: January 4, 1999; In Final Form: May 17, 1999
We investigate the stability of aqueous colloidal dispersions of ionic magnetic nanoparticules as a function of pH. The charge of the γ-Fe2O3 particles is modified, and as a consequence, the interparticle interactions may be tuned through pH variations. Scanning the whole pH scale from acidic to alkaline medium, different states are observed for the dispersion: sol, thixotropic gel, and floc (around the point of zero charge). Using the dynamic magnetooptical properties of the magnetic grains, we locally probe the sols and the thixotropic gels. A steep increase of the characteristic time of birefringence relaxation, in the sol phase close to pHGel, marks a divergence of the macroscopic viscosity at the gel point, compatible with a percolation theory. A temporal study of the regeneration of shaken gels reveals that, in these thixotropic systems, the process is dominated by a cluster aggregation on a sample-spanning one, with an energy barrier to overcome, compatible with chemical measurements.
1. Introduction We study here ionic magnetic fluids (MF or ferrofluids) constituted of nanoparticles of iron oxide chemically synthesized1 and dispersed into water. The numerous industrial applications of such aqueous colloidal dispersions are appealing for studies of their limits of colloidal stability in order to preserve the ferrofluid from any flocculation of the magnetic particles. The interparticle attractions, such as van der Waals interactions or averaged magnetic-dipolar interactions, have to be balanced by some interparticle repulsions that depend on the nature of the solvent. Hence, in a nonpolar medium, the particles are coated by surfactant chains; steric hindrance is at the origin of the repulsions. In contrast in an aqueous medium, the magnetic particles are macroions and bear surface charges all of the same sign; they repel each other. The stability of the ferrofluid is then due to electrostatic repulsions. The influence of an ionic strength increase2 or of a temperature decrease3 on ionic ferrofluids has already been studied. In the present work we investigate the consequences of pH variations on ionic ferrofluids samples, on the basis of maghemite particles (γ-Fe2O3), in the dilute regime. The pH controls the superficial density of charges of the magnetic particles and thus the stability of the solutions. This paper presents how, at room temperature, the system evolves by modification of the pH from a sol state (acid or alkaline) toward flocculation (close to the point of zero charge (PZC) of the particles), going through a thixotropic gel state. A thixotropic fluid4 has the property of being in a gel state at equilibrium. If it is mechanically sheared or shaken above a given threshold, it becomes a flowing liquid. The gel regenerates * Corresponding author. Fax: +(33) 1.44.27.45.35. E-mail: rperz@ ccr.jussieu.fr. † Laboratoire des Milieux De ´ sordonne´s et He´te´roge`nes. ‡ Laboratoire des Liquides Ioniques et Interfaces Charge ´ es. § Also at Universite ´ Denis Diderot (Paris 7), UFR de Physique, 2 place Jussieu, 75251 Paris Cedex 05.
if the sample is left to stand. Many thixotropic products are used in industrial applications such as paints, oils, and drilling muds, and in the food industry. A recent extensive review on this topic is presented by H. A. Barnes in ref 4. Thixotropic gels are encountered in systems as different as liquid crystals, micellar solutions, clay suspensions, and silica-based adhesives. The thixotropy of nonmagnetic colloids has been known since the pioneering studies indicated in ref 5. However, the magnetic aspects of our γ-Fe2O3 colloids strongly help their characterization. To our knowledge, the present work is the first detailed study of a thixotropic magnetic fluid. In such a thixotropic MF, the magnetooptical properties of the particles allow us to probe the gel without external mechanical forces, using an applied magnetic field either static or pulsed. The paper is presented as follows: section 2 is the Experimental Section, section 3 is the Results, and section 4 is the Discussion. 2. Experimental Section A. Samples. i. Synthesis of the MF Precursors (FFA and FFB). The ionic aqueous ferrofluids used in the present work are synthesized according to the Massart’s method,6 by alkalizing an aqueous mixture of iron(II) chloride and iron(III) chloride. The magnetite (Fe3O4), so obtained, is then acidified, oxidized in maghemite, and dispersed into water, leading to an acidic ferrofluid (FFA). Particles of the FFA ferrofluid are positively charged with nitrate counterions (NO3-). To obtain an alkaline ferrofluid (FFB), the FFA is alkalized with tetramethylammonium hydroxide (TMAOH) under an inert atmosphere of argon. The particles of the FFB ferrofluid bear a negative superficial charge with low polarizing counterions TMA+. Both ferrofluids, FFA and FFB, are stable colloidal solutions (Sol). ii. Samples at Different pH. In the experiments FFA and FFB precursors are diluted at various volume fractions Φ of magnetic
10.1021/jp9900180 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/16/1999
6422 J. Phys. Chem. B, Vol. 103, No. 31, 1999 material (10-4 e Φ e 3.5 × 10-2). Φ is deduced from the chemical titration of iron in the ferrofluid.7 For a given volume fraction, many samples at different pH are prepared, pH being adjusted either by addition of varying quantities of TMAOH to the dilute ferrofluids FFA or by addition of nitric acid to the dilute FFB. The ionic strength variations always remain smaller than 5 × 10-2 mol L-1. All experiments are carried out at room temperature. To check any pH evolution of the samples, the pH values are periodically measured with a Hanna Instrument pH meter until equilibrium is reached, which is generally observed after 3 days. We use a calomel reference and a glass electrode that is calibrated at a pH value of 4, 7, or 10, depending on the explored pH range. iii. Magnetic Particles Characterization. Particle Size Distribution. Magnetic fluids are composed of roughly spherical particles, the distribution of their diameters d is rather polydisperse and is usually approximated by a log-normal law.8 The parameters of this law, diameter d0 (ln d0 ) 〈ln d〉) and standard deviation s, can be determined by magnetization measurements.9 All ferrofluids (FFA and FFB) used in this study have the same particle size distribution of parameters d0 ) 7.1 nm and s ) 0.4. The mean crystallite size, as deduced from Debye-Scherrer X-rays diffraction, is dRX ) 8 nm. Charge of the Particles. As the pH of the ionic ferrofluid suspension is modified, the superficial charge density of the particles varies. The PZC of ferrofluids based on maghemite particles is located at pHPZC ≈ 7.3. The superficial charge density is positive for pH > pHPZC and negative for pH < pHPZC. B. Qualitative Experimental Observations. Some modifications of the macroscopic aspect of the samples come with the particle charge variations. Three situations can be encountered. At low pH values, the ferrofluid is a stable sol (Sol). It has a dark-brown color, and it flows. When the pH is increased, the surface charge is progressively neutralized and the solution becomes more viscous. At pH g 3.9, the formation of a thixotropic gel (Gel) is observed. The solution does not flow at equilibrium. It has sufficient rigidity to sustain its own weight in an inverted test tube. Its color is now less dark. It becomes liquid under gentle shaking. If the pH is still increased (4.9 e pH e 9.8), the solution flocculates (Floc). There is a macroscopic phase separation with a clear aqueous supernatant. The flocculation is reversible because a further increase of the pH allows recovery, in alkaline medium, first of the Gel state and then of the Sol state. A pH decrease of FFB from alkaline toward the acidic area leads to similar observations. If the Gel/Floc limits are the same in the two experiments, the Sol/Gel limits are shifted. Therefore, we only compare experiments performed in the following sequence: Sol f Gel f Floc; i.e., FFA from pH ) 2 up to pH ≈ pHPZC and FFB from pH ≈ 12 down to pH ≈ pHPZC. This macroscopic approach is completed by optical microscopy in glass cells of thickness 10 or 100 µm. The initial state of a gel, which has been shaken to become a flowing liquid, closely depends on the applied shear rate during shaking. In the present work, we limit our investigations to samples all prepared in the same reproducible way. In the following, we qualify “shaken Gels” as samples with pH ranging in the Gel area, mechanically agitated for 1 min using a Janke & Kunkel VF2 device set on maximum speed. We shall investigate more precisely in a forthcoming study the effect of applied shear rate on the rheological properties of the shaken gels. Note that those samples are out of equilibrium; they evolve with time from a flowing state toward a totally frozen one. C. Experimental Methods. i. Density of the Flocculate. To
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Figure 1. Static birefringence ∆n as a function of applied magnetic field H for a Sol. The full gray line is the best fit of the experimental data with a Langevin formalism (second Langevin function coupled to a log-normal distribution of diameters; see ref 12). Inset: static birefringence ∆n(H) of a sample experiencing a gelation process during the birefringence measurement. The arrows distinguish the measurements performed under an increasing magnetic field and a decreasing one.
determine the particle density of the flocculate, the volume of the sediment VSed, reduced to the total volume VTot of the sample, is measured either as a function of the pH for a given volume fraction Φ or as a function of the volume fraction at pH ≈ 7. These measurements are performed at equilibrium. Typically, after 1 day the sedimentation process is over. ii. Optical Birefringence Measurements. In the ferrofluid solution each magnetic particle bears a magnetic moment µ typically on the order of 104 µB (µB: Bohr’s magneton) and is optically uniaxial.10 For simplicity, we suppose here that the magnetic moment is rigidly linked to the optical axis of the particle. In the absence of a magnetic field, the particles are randomly orientated because of Brownian motion; the ferrofluid solution is optically isotropic. As a magnetic field is applied, the particles tend to align along the field direction and the solution becomes macroscopically uniaxial. The medium is probed by a laser beam of wavelength λ0. The sample behaves as a birefringent plate characterized by a phase lag φ related to its birefringence ∆n. ∆n is defined as ∆n ) n| - n⊥, n| being the optical index in the direction of the magnetic field and n⊥ the optical index in the perpendicular direction. For a sample of thickness e, the phase lag is φ ) 2πe∆n/λ0. The ferrofluid solutions are also weakly dichroic. We neglect this effect, since for our particles it is of second order with respect to birefringence. Static Birefringence. The birefringence ∆n(H) of the solutions as a function of the applied static magnetic field H is determined, using an optical setup described elsewhere (see ref 11, for example). In the Sol state, the birefringence ∆n(H) of a dilute monodisperse sample (Φ < 2%), where the particle interactions are negligible, is that of a paramagnetic material. It may be described by the second Langevin law L2(ξ) ) 1 - 3L(ξ)/ξ where L(ξ) ) coth ξ - 1/ξ is the first Langevin law and ξ ) µH/(kBT), the Langevin parameter (T is temperature; kB is Boltzmann’s constant). Taking into account the polydispersity of the sample through a log-normal distribution of the roughly spherical particles, it is possible to determine the two parameters of the distribution: an optical diameter dbir 0 and the standard deviation sbir.12 Figure 1 shows the experimental variations of ∆n(H) and its
pH Effect of Ferrofluid
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Figure 3. Experimental phase diagram volume fraction Φ as a function of pH. Three different states are observed for the ionic maghemite ferrofluid: Sol (thixotropic), Gel, and Floc. Figure 2. Experimental setup used for the pulsed birefringence measurements (for details see the text). Part a presents the orientation of the different optical axes. Part b shows the principle of the experiment: the pulse of magnetic field and the corresponding pulse of light intensity I(t). Part c presents the experimental relaxation of the transmitted intensity I(t), in a semilogarithmic representation, as a function of the time; t ) 0 corresponds to the field cutoff. The full line is a stretched exponential fit. bir ) 0.21) for a best fit by a log-normal law (dbir 0 ) 11.6 nm, s Sol FFA sample of Φ ) 0.8% and pH ) 1.8. In the Gel state at equilibrium no birefringence is detected. If the thixotropic Gel sample is shaken and the birefringence measurement performed during the gelation process, the experimental curve ∆n(H) presents a hysteresis (see inset of Figure 1). It is evidence of dynamic processes on the same time scale as that of the experiment; some of the magnetic particles that have been aligned along the applied field are trapped in the Gel structure and then unable to relax to random directions in zero field. Dynamic Birefringence. To probe those dynamic effects during gelation, a second experiment is performed using a pulsed magnetic field. It allows one to study the solutions by macroscopically nondestructive means, both in the Sol and in the Gel state. If a magnetic field is applied, the particles align along its direction. As the field is cut off, the particles relax toward random directions in the carrier liquid. As a consequence, the birefringence decays and the transmitted light intensity I goes to zero. The temporal dependence of I is directly related to the dynamics of the medium. An analysis of the polarization of the light transmitted by the ferrofluid sample is possible with the optical setup of Figure 2. A He-Ne laser (L) of weak power (∼5 mW) and of wavelength λ0 ) 632.8 nm goes through an optical system consisting of a polarizer (P), the sample (S), a quarter-wave plate (λ/4), an analyzer (A), and a photodetector (PD). The MF sample is put in a nonbirefringent glass cell (thickness e on the order of 200 µm) and submitted to a pulsed vertical magnetic field (HP ) 12 kA m-1) produced by Helmholtz’s coils (HC). A crossed polarizer and an analyzer are first put at 45° of the direction of the pulsed magnetic field HP (see inset a of Figure 2). The λ/4 plate is introduced with its optical axis parallel to the polarizer and analyzer directions between the sample and the analyzer. It is then turned by an angle of 45° to increase the detected signal. As the field is on, the medium presents a phase lag I0, as defined before. The maximum light intensity
I(t)/I0 detected by the photodetector is then proportional to φ, and consequently, I0 ∝ ∆n. Inset c of Figure 2 shows in a semilogarithmic representation the relaxation I(t)/I0 of the signal for the sol phase FFA at Φ ) 1.75% and pH ) 3.3. Owing to the particle size distribution, the relaxation is not a single exponential. It is here approximated either by the initial slope of ln[I(t)/I0] ) f(t) to determine a typical relaxation time τE 13 or by a stretched exponential law I(t) ) I0 exp(-(t/τSE)R), τSE being a characteristic time and R an exponent characteristic of the width of the relaxation time distribution; R ) 1 for a monodisperse Sol. The two characteristic times τE and τSE are slightly different but close to each other. A comparison between the two different fittings is given further on. In the following text, if the conclusions do not depend on the way the characteristic time is determined, we just note it as τ. With this experimental setup, we obtain either for a Sol sample or for a “shaken Gel” sample, the relaxation time τ, the exponent R that is a characterization of the width of the relaxation time distribution, and the value of the maximum transmitted light intensity I0. For a thixotropic Gel initially shaken, the same experiment may be periodically performed during the Gel regeneration until no light is transmitted through the sample. It allows us to probe the gelation process. To be able to perform such relaxation experiments, it is necessary to have tFrozen . tExp . τ, tExp being the time necessary to record the birefringence relaxation; here, tExp is on the order of 1 min and tFrozen is the time necessary for the sample to be completely frozen. 3. Results A. Phase Diagrams and Microscopic Observations. Figure 3 presents the phase diagram of the system. Many samples (about 300) coming from different chemical syntheses are used to build up this phase diagram. The forthcoming analysis (see part 4.C) of the dynamic birefringence measurements confirms the macroscopic observations of the pH limits of the three states of the system (Sol, Gel, and Floc). Observations by optical microscopy of these three states are presented in Figure 4 for Φ ) 1.6%. The Sol phase (Figure 4a) is homogeneous on the scale of the optical microscope. It appears red with a cell thickness e of 100 µm and yellow with e ) 10 µm. In the Floc state there is a macroscopic phase separation between the supernatant, which is made of solvent and is free of magnetic particles, and the sediment collecting
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Figure 5. (a) Maximum transmitted intensity I0 and (b) relaxation time τE, both as a function of pH (FFA and FFB samples, Φ ) 1.6%). In both figures the vertical line shows respectively in part a the decrease of I0 and in part b τE as a function of time, for a shaken Gel (FFA sample at Φ ) 1.6%).
Figure 4. Microscopic observation of FFA samples at Φ ) 1.6% (full horizontal scale is 300 µm), from top to bottom: (a) Sol at pH ≈ 2 (cell thickness of 100 µm); (b) Gel at pH ≈ 4.5 (cell thickness of 10 µm); (c) Floc sediment at pH ≈ 7 (cell thickness of 10 µm).
all the particles. Figure 4c (cell thickness of 10 µm) shows that the sediment is inhomogeneous and diphasic. There is coexistence of a dilute MF phase (yellow) and solid aggregates (brownred). If a “shaken Gel” is optically homogeneous as a Sol, a Gel appears at rest as if in an intermediate state between a Sol and a Floc. Observed in an optical cell 10 µm thick, it presents (Figure 4b) local spatial inhomogeneities and is presumably triphasic; yellow areas, dilute in magnetic particles, coexist with red areas more concentrated in particles, and several disconnected pockets of pure solvent appear white in Figure 4b. The phase separation, corresponding to an ejection of the solvent from the MF material, happens here on the scale of a few 10 micrometers. As the pH becomes closer to pHPZC, the size of the solvent pockets increases and the microscopic phase separation evolves toward a macroscopic phase separation. If the frozen Gel is observed in thicker optical cells (thickness of
500 µm), the spatial inhomogeneities are embedded in 3D and they are more difficult to detect optically, since they are not numerous. With such sample thicknesses, we do not observe any diffraction pattern by an He-Ne laser beam. B. Floc State: Density of the Solution. In the whole sequence Sol f Gel f Floc f Gel f Sol, the macroscopic volume V, in which the particles are collected, is measured. In Sol and Gel states, V remains equal to VTot. In the Floc state, V is equal to VSed, the sediment volume, and is smaller than VTot. If the variations of V/VTot as a function of pH are steep, close to the Gel/Floc limit, the minimum located around the PZC is rather flat and is Φ-dependent. Typically for Φ ) 1.6% and 6 e pH e 8, we measure VSed/VTot ) 0.60 ( 0.05, corresponding to an average concentration of particles in the sediment ΦSed ) ΦVTot/ VSed ) 2.7%. A large amount of water remains present in the flocculate. This is why it is possible to reversibly recover a Sol state from the Floc state either by an increase or by a decrease of the pH. C. Dynamic Birefringence: Sol and Shaken Gels. The relaxation of the magnetooptical birefringence is analyzed at different volume fractions Φ in the following range of pH values: pH < 4.9 for FFA samples and pH > 9.8 for FFB samples. The maximum intensity I0 (as defined in inset b of Figure 2), presented in Figure 5a for Φ ) 1.6%, is more or less constant in the Sol state and decreases abruptly in the Gel area. We note in Figure 5b that the relaxation time τE, obtained for the same samples, slightly increases in the Sol phase as the pH is approaches the Sol/Gel limit. It denotes some pretransitionnal effect in the Sol state. Shaken Gels give a clearly distinct characteristic time τE; it is on the order of a few milliseconds, which is 3 orders of magnitude larger than in the Sol state. This wide jump of the relaxation time does not depend on the way the data are analyzed. Figure 6 compares τE and τSE (the corresponding exponent R is displayed in the inset of the Figure 6) for FFA samples (Φ ) 1.75%) at different pH. τE and τSE are close to each other and present similar variations with pH. The progressive decrease of the R exponent as pH increases
pH Effect of Ferrofluid
Figure 6. τE and τSE as a function of pH (FFA sample, Φ ) 1.75%). The inset displays the corresponding variations of the exponent R.
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Figure 8. Linear representation of I0/I0(θ) as a function of (t - θ)/ tGel. The full line corresponds to I0/I0(θ) ) exp[-(t - θ)/tGel]. Inset: semilog representation of I0/I0(θ).
Figure 7. Evolution of tFrozen as a function of pH. The inset is a sketch of the interparticle potential V(r).
denotes a progressive broadening of the relaxation time distribution.14 Note that in the Sol phase those measurements are performed at equilibrium. In contrast, shaken Gels for which τ and I0 are here determined just after shaking are by essence out of equilibrium samples; they afterward evolve with time. Below, we study this time evolution. D. Regeneration of a Thixotropic Gel. To study the gelation process, a rough evaluation of the gelation time of different samples is first made. Different FFA samples are shaken, and the time tFrozen necessary for the sample to be completely frozen is estimated in tubes of section of 1 cm2. The regeneration time depends on the particle volume fraction Φ and on the pH value of the solution. It runs from a few minutes to several days. As an example, the Figure 7 presents tFrozen as a function of the pH in a semilogarithmic representation for different samples at Φ ) 1.75% (the black dot corresponds to a sample at pH ≈ 4.1 and Φ ) 1.6%). Birefringence relaxation experiments are performed in optical cells of thickness of 100 µm. The complete preparation of a cell (shaking time and filling up) takes less than 2 min. Measurements are then recorded periodically during the gelation process. The maximum intensity I0 is a decreasing function of time t. A stretched exponential fit of the relaxation of the birefringence intensity leads to a relaxation time τSE going through a maximum at t ) θ. The corresponding exponent R
Figure 9. Relaxation time τSE normalized by its initial value τ0 at t ) 0, as a function of (t - θ)/tGel. Inset: corresponding variations of the stretched exponent R. The full line corresponds to R ) 0.35.
TABLE 1: Comparison of the Various Characteristic Times of Gelation for Two FFA Samples Φ (%)
pH
tFrozen (min)
tGel (min)
θ (min)
1.75 1.6
4.2 4.1
60 360
20 106
13 70
first diminishes and at t ) θ reaches a constant value on the order of 0.35. Table 1 gives values of θ for two FFA samples. For t > θ, I0 decreases exponentially with a characteristic time tGel (see Figure 8). For both samples, tGel, tFrozen, and θ are proportional. We obtain tGel ≈ tFrozen/3 (which is a natural order of magnitude for an exponential relaxation) and θ ≈ tGel/1.5 ≈ tFrozen/4.5. Figure 9 shows in a reduced representation the relaxation time τSE normalized by its value τ0 at t ) 0 as a function of (t - θ)/tGel; the corresponding evolution of the exponent R is given in the inset. The decrease of I0 of the sample (Φ ) 1.6% and pH ) 4.1) during the gelation is reported in Figure 5a as a vertical line for comparison, the corresponding variations of τSE being reported in Figure 5b. These strong variations of I0 during the gelation process are associated with weaker variations of τSE.
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4. Discussion Our experimental observations indicate that, as a function of pH, the present MF may exist under three different colloidal states: Sol, Gel, and Floc. From a thermodynamic point of view, the colloidal equilibrium of the MF is determined by a balance in the free energy of the system15 among van der Waals interparticle interactions, magnetic dipolar interactions that tend to form chains of dipoles, electrostatic repulsions, and an entropic term. For pH < 2 and pH > 12, the particles bear a maximum superficial density of structural charges |Σ| on the order of 20 µC/cm2. SANS measurements have demonstrated that the interparticle electrostatic repulsions are then strongly efficient.16-18 To destabilize such a ferrofluid Sol by a lowering of the temperature or by an applied magnetic field, it is first necessary to screen the electrostatic interactions2,17 with a large ionic strength cS (cS ≈ 0.5 mol L-1 for the present size distribution of nanoparticles). With low polarizing counterions, it is then possible to obtain “liquid-gas-like” separation of the sample in two liquid phases. Here, a pH variation, which modifies the charges on the surface of the particles, decreases the interparticle repulsions. In particular, an experimental determination19 of the interparticle potential V(r) shows that it presents at short interparticle distance an energy barrier WM (see inset of Figure 7). This barrier is about (20-40)kBT far from pHPZC; it linearly decreases toward pHPZC and becomes equal to 2kBT for |pH - pHPZC| of about 2 units of pH. Hence, it is natural to observe a destabilization of the colloid for pH values close to the PZC. Our experiment shows that the process of destabilization occurring here is not the one observed with a large ionic strength screening; we obtain here a thixotropic gel or a flocculation depending on the pH value. We note that other physical systems such as, for example, silica spheres stabilized by coating stearyl alcohol in benzene20 present in addition to a gas-liquid transition a Gel state in which the Brownian particles form an interconnected static structure. A. Phase Diagram and Microscopic Observations. Our observations tend to show that Gels and Flocs are both triphasic; magnetic phases eject pure solvent first as microscopic pockets in the Gel state and then at the macroscopic level. As the pH reaches the threshold value, the solvent pockets become connected together and a macroscopic phase separation (Floc) occurs. The sediment part contains two coexisting phases: a solid phase and a liquid phase dilute in magnetic particles. The threshold is Φ-independent; it is equal to pHFloc ) 4.9 in an acidic medium and pHFloc ) 9.8 in an alkaline one. The same threshold values pHFloc are obtained by alkalizing a FFA ferrofluid or by acidifying a FFB sample. On the other hand, the thresholds of the transitions (Sol/Gel) strongly depend on the way the transition is crossed; it is the signature of the existence of metastabilities in the system. Moreover, the pH thresholds of the Sol f Gel transition (pHGel) is, in a first approximation, a linear function of the volume fraction Φ. The Gel observation range is almost nonexistent at low volume fraction and enlarges with Φ. B. Dynamic Birefringence Measurements in the Sol Phase. In the Sol state, far from pHGel, the relaxation time of the birefringence corresponds to the diffusion of rotation of the particles toward random directions. This Brownian time can be written as τ ) ηπdh3/(6kBT) where η is the viscosity of the suspending carrier liquid and dh is the mean hydrodynamic diameter of the particles. Since the measurement is performed with a low magnetic field, it gives a “high moment” average on the time distribution. The deduced hydrodynamic diameter dh lies between (〈d3〉)1/3 and (〈d9〉/〈d6〉)1/3.9 It corresponds to a
Figure 10. Semilogarithmic representation of τE as a function of ∆pH for both acidic (full symbols) and alkaline (open symbols) samples at various volume fractions Φ. All the measurements scale as a single master curve. The full line is the power function: τE ∝ |pH pHGel|-0.78(0.02 corresponding to the best fit of the experimental results obtained for Φ ) 0.65% and Φ ) 1.75%. The inset displays these results and the fit in a logarithmic representation.
probing either of the largest particles or of the clusters made of a few particles. Here, the hydrodynamic diameter far from pHGel is about 30-40 nm, associated with an initial polydispersity of the particles and clusters of a few particles. This point is confirmed by the exponent R ≈ 0.8 deduced from the stretched exponential fit (see inset of Figure 6). In the Sol phase, τ increases as the pH tends toward pHGel (see Figure 6). If we first assume that the effective viscosity of the sample is the viscosity of the liquid carrier η, this increase of τ could correspond to a progressive augmentation of the cluster mean size. Let us note that, because of the magnetic dipolar interparticle interactions, the clusters may adopt elongated shapes because of chaining of the particles. Simultaneously, in the Sol state, the exponent R progressively decreases from a value R ) 0.8 to 0.6 at pHGel (see inset of Figure 6). This decrease of R confirms the image of an enlargement of the time distribution in the sample14 corresponding to the growth of heterogeneous clusters. The cluster formation can be explained by the progressive neutralization of the particle surface charges as pH tends toward pHPZC. Owing to the thermal agitation in the solution, the particles collide, and since their structural surface charge is low, they stick together.21 This aggregate formation correlatively induces an augmentation of the macroscopic viscosity of the medium, which hinders the rotation of the probing objects (particles and small clusters). The drastic increase of τE close to pHGel is thus related both to an increase of the size of the probing objects and to an increase of the macroscopic viscosity. In the Sol phase, this pretransitionnal effect scales as a function of the pH distance to pHGel. All the curves obtained for different volume fractions can be superimposed (see Figure 10) if they are plotted either as a function of (pH - pHGel) for an acidic sample or as a function of (pHGel - pH) for an alkaline sample, the quantity |pH pHGel| being related to a surface charge variation ∆Q close to the gel threshold. In the Sol phase, in our experimental range of pH values, the relaxation time τ follows a power law: τ ∝ |pH -
pH Effect of Ferrofluid pHGel|-0.78(0.02, as is illustrated by the inset of Figure 10 for two volume fractions Φ ) 0.65% and Φ ) 1.75%. A subsidiary concentration dependence seems to remain. Note, however, that the critical exponent s ) 0.78, which governs the viscosity divergence of a gelating system at the Gel point in the framework of percolation theory22-24 is very close to our experimental observations. It suggests that in our τ measurements the divergence of the viscosity dominates close to the Gel point. C. Regeneration of a Thixotropic Gel. In a shaken Gel, the relaxation time is typically 3 orders of magnitude larger than in the Sol phase. The time evolution of the shaken samples gives insight to the gelation process. a. Gelation Time. First of all, at a given pH, the gelation is an exponential process (see Figure 8) of characteristic time tGel. Moreover, taking into account that tFrozen ∝ tGel (see Figure 7), the characteristic time tGel is itself a decreasing exponential function of pH. These two points can be explained in the framework of particle aggregation on a macroscopic cluster with an energy barrier WM to overcome. The kinetics is then ruled25 by a characteristic time proportional to exp[WM/(kBT)]. In the narrow experimental pH domain of Figure 7 and at the volume fractions of the experiment, the energy barrier WM is a decreasing function of pH that can be linearized19 as WM/(kBT) ) a - (b)(pH). In this framework, it leads to tFrozen ) 3tGel ∝ exp[-(b)(pH)], which corresponds to the observation in Figure 7 with b ≈ 12.5. This b value is coherent with the direct determinations of WM 19 leading to ∆[WM/(kBT)]/∆pH ≈ - 12 ( 1 at Φ ) 1.3%. b. Birefringence Measurements. The characteristic time of the birefringence relaxation goes through a maximum during the Gel regeneration at t ) θ. It is the signature of the competition of two antagonistic processes contributing to the measurements. First, a progressive growing of the size of the clusters makes the relaxation time τ increase. After a given time θ, about a fraction of tGel, the biggest clusters begin to be trapped on the macroscopic cluster. They do not contribute anymore to the birefringence. As a consequence, the global intensity decreases progressively to zero until all the clusters are blocked. During this time, the average size of the probed clusters diminishes. It is marked by the final decrease of the relaxation time τ. In our experiments, during the second phase of the gelation process, the exponent R remains almost constant. It has a very low value of about 0.35. This small value of R marks the existence in the Gel state of an extremely large distribution of characteristic times. This distribution may explain the metastabilities encountered at the “reversed” transition, from a Gel to a Sol. Stretched exponential functions with a low value of the exponent R fit well the birefringence relaxation. Such functions are commonly used to describe widely distributed systems,14 such as spins glasses,26 polymeric gels,27 and ripening foams.28 As a last remark, in Figure 11 is plotted the relaxation time τSE normalized by its Sol value 〈τSol〉 at pH ) 2 as a function of the stretched exponent R. From the Sol state to the frozen Gel state, R decreases typically from 0.85 to 0.35, and simultaneously, the characteristic relaxation time increases by a factor 103. For a comparison, the results obtained from another totally different experiment29 are presented in the same figure. Similar maghemite nanoparticles were used as local birefringent probes of a medium (aluminosilica in a mixture of water and isopropyl alcohol) encountering a gelation process as a function of time.29 The nanoparticles initially free to rotate were progressively trapped in bigger and bigger aggregates and
J. Phys. Chem. B, Vol. 103, No. 31, 1999 6427
Figure 11. Comparison of the relative variations of the stretched exponential parameters for a FFA sample (full symbols) at a volume fraction Φ ) 1.75% and a magnetic gel from ref 29.
ultimately blocked at the end of the experiment. The stretched exponential relaxation of the birefringence in that medium leads to a shape very similar to the curve of Figure 11, the characteristic relaxation time τSE being normalized by 〈τSol〉, its initial Sol value. During the gelation process, the behavior of the maximum birefringence intensity and of the relaxation time τSE was also very similar to what is presented here in Figures 8 and 9. All these points comfort us in the description of the regeneration of the shaken thixotropic gels given above. Conclusion In ionic ferrofluids, pH modifications lead to a reversible colloidal destabilization of the Sol state: around the PZC of the nanoparticles, for 4.9 e pH e 9.7, a flocculation is observed; for intermediate pH values, between those for which a Sol or a Floc are observed, a macroscopically homogeneous Gel with thixotropic characteristics is obtained. The pH range for a Gel observation is larger the higher the volume fraction of nanoparticles. Under an optical microscope, a shaken Gel appears as homogeneous as a Sol. Being regenerated, it presents spatial inhomogeneities of concentration due to a cluster aggregation and locally ejects pockets of pure solvent. In the Floc, those pockets are connected and a part of the solvent is then macroscopically ejected. In the future we can imagine testing this picture by monitoring, in the ferrofluid gel, the self-diffusion of nanoparticles marked with fluorescent probes. The results of the study of regeneration of the shaken Gels indicate a wide distribution of relaxation times in the system, related to the spatial inhomogeneities and responsible for metastabilities in the Sol/Gel transition. The thixotropic characteristic times of Gel regeneration determined here, all scale together and are compatible with an aggregation on an infinite cluster with an energy barrier WM to overcome. The dynamics of regeneration of the Gel state in those thixotropic systems is here studied by birefringence relaxation. It is a local technique of rheological probing that should be completed in the future, first, by macroscopic rheological measurements in order to confirm the observed divergence of viscosity with pH in the Sol phase close to pHGel (τ ) η ) |pH - pHGel|-0.78(0.02) and, second, by microscopic probing of the cluster structure using, for example, small angle neutron scattering in order to measure an eventual fractal exponent characteristic of the thixotropic Gel.
6428 J. Phys. Chem. B, Vol. 103, No. 31, 1999 Acknowledgment. We thank Mme Carpentier for the preparation of samples, P. Lepert and J. Servais for their technical assistance, and L. Loiseau and F. Mazzella for their contribution to the measurements. This work was supported by Grant 96-1149 of the French Direction of Armament. References and Notes (1) Massart, R. IEEE Trans. Magn. 1981, 17, 1247. (2) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Colloid Interface Sci. 1989, 132, 43. (3) Dubois, E.; Cabuil, V.; Boue´, F.; Bacri, J.-C.; Perzynski, R. Prog. Colloid Polym. Sci. 1997, 104, 173. (4) Barnes, H. A. J. Non-Newtonian Fluid Mech. 1997, 70, 1. (5) Schalek, E.; Szegvari, A. Kolloid Z. 1923, 32, 318; 1923, 33, 326. English translation in the following. Bauer, W. H.; Collins, E. A. Rheology Theory and Applications; Eirich, F. K., Ed.; Academic Press: New York, 1967; p 423. (6) Bee, A.; Massart, R.; Neveu, S. J. Magn. Magn. Mater. 1995, 149, 6. (7) Charlot, G. In Les Me´ thodes de la Chimie Analytique; Masson & Cie, Eds.; 1966; p 737. (8) Bacri, J.-C.; Perzynski, R.; Salin, D.; Cabuil, V.; Massart, R. J. Magn. Magn. Mater. 1986, 62, 36. (9) Cabuil, V.; Perzynski, R. Magnetic Fluids and Applications Handbook; Berkovski, B., Ed.; Begell House Inc.: New York, 1996; p 22. (10) Gazeau, F.; Bacri, J.-C.; Gendron, F.; Perzynski, R.; Raikher, Yu. L.; Stepanov, V. I.; Dubois, E. J. Magn. Magn. Mater. 1998, 186, 175. (11) Neveu-Prin, S.; Tourinho, F. A.; Bacri, J.-C.; Perzynski, R. Colloids Surf. A 1993, 80, 1. (12) Hasmonay, E.; Dubois, E.; Bacri, J.-C.; Perzynski, R.; Raikher, Yu. L. Eur. Phys. J. B 1998, 5, 859.
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