CALCULATION OF THE PAIR POTENTIAL INTERACTION

IN ELECTRIC DOUBLE LAYERED MAGNETIC FLUIDS :

A QUANTITATIVE ANALYSIS OF THE pH - DEPENDENT PHASE DIAGRAM.

A. F. C. Campos ¹ , F. A. Tourinho ¹ , G. J. Da Silva ² , J. Depeyrot ² .

1. Complex Fluids Group, Instituto de Quimica, Universidade de Brasilia, Brazil.

2. Complex Fluids Group, Instituto de Fisica, Universidade de Brasilia, Brazil.

One of the major challenges in the research of electrostatic stabilized colloidal dispersions is to predict the stability conditions of the system from theoretical data coupled with experimental measurements. In the case of electric double layered magnetic fluids (EDL-MF), besides the balance between the Van Der Waals attraction and the screened electrostatic repulsion (DLVO potential), the attractive magnetic dipolar interaction has to be included to control the thermodynamical stability of the dispersion. The interplay between these three contributions leads to a pair potential interaction function which exhibits a primary minimum at short distances, a positive energy barrier at intermediate distances and a secondary minimum at large distances. At constant temperature and in absence of external magnetic field, modifications of the ionic strength and particle charge may induce phase transitions [1]. If the energy barrier is sufficient low or inexistent, the particles aggregate in the primary minimum of their potential energy (coagulation). In this irreversible phase transition, the particles are held together by strong Van Der Waals forces and do not break apart without strong external forces. When both an energy barrier and a secondary attractive minimum energy exist, the particles may aggregate at this minimum and the system become kinetically stable. Nevertheless, it as a weaker effect and a reversible transition (flocculation).

Simultaneous potentiometric and conductometric titrations have been used as a powerful tool to determine the particle charge in EDL-MF [1, 2]. It has been evidenced that the EDL-MF systems inductive as a mixture of strong acid and weak diprotic, corresponding to the bulk dispersion and particle surface, respectively. The particle superficial density of charge is generated through the equation reactions of superficial metal ions which undergo hydrolysis, leading to three kind of superficial sites: positively (negatively) charged in acidic (basic) medium and discharged in neutral one. The analysis of equilibrium involved between the particle surface and the bulk dispersion allows to determine the pH dependence of the surface charge density. As the hydrogen ionic concentration of the EDL-MF dispersion controls the particle charge [1], the interactions between nanoparticles also may be tuned varying the pH. Recently, the stability of EDL-MF based on 7.1 nm mean sized maghemite particles has been investigated as function of pH at constant ionic strength and at room temperature [4]. It has been observed a thixotropic gel phase between the sol one and the coagulation zone in pH regions between 3.9 and 4.9 in acidic medium and 9.6 and 10.8 in basic one. In the present work two fundamental targets are focused. The first one is to establish the experimental pH-dependent phase diagram of an acid EDL-MF sample based on manganese ferrite nanoparticles of mean size around 7.5 nm. The later is to calculate the pair potential interaction of the nanosized particles in the framwork of the extended DLVO theory in order to improve the understanding of the pH-dependent phase diagram.

The EDL-MF sample was synthesized by following the procedures described elsewhere [4]. In a first step, it has been performed a hydrothermal coprecipitation of aqueous solutions of MnCl₂ – FeCl₃ in alkaline medium. Then the particles were conveniently peptized in acidic medium by adjustment of the ionic strength. The resulting dispersions are stable sols of high quality. The phase diagram was built up as follows: for a volume fractions j = 1.8 %, many samples of the precursor ferrofluid dispersion at different pH (2.0 £ pH £ 7.5) were prepared, pH being adjusted by addition of varying quantities of tetramethylammonium hydroxide (TAMOH). In order to determine the pH dependence of the surface charge density, simultaneous potentiometric titration of 40 ml of the ferrofluid sample (volume fraction j = 1.5 % corresponding to approximately 6.8 x 10²¹ particles per m³) were performed using titrant solutions of sodium hydroxide 0.099 mol x l ^{– 1} with an electronic burette Metrohm 715 DOSIMAT. The potentiometric readings were carried out with a pH – meter Metrohm 713 using a pH glass double-junction electrode, which includes a salt bright in order to avoid the direct contact of the colloidal solution with the glass membrane. The conductivity k was measured with a conductometer Metrohm 712 using an imersion-type measuring cell. All reagents used in this work are of analytical grade from Aldrich or Merck. The saturation value of the surface charge density was found equal to 0.25 Cm ^{– 2} which approximately corresponds to one charge per 0.64 nm² or about 276 sites per particle. This value is in excellent agreement with the the reported ones [5]. Figure 1 exhibits the pH-dependent phase diagram of the EDL-MF sample and the pH ranges of the phase transitions observed are similar to the reference [4].

Moreover, the height of the energy barrier (W) obtained from the pair potential calculation as the variation of the surface charge density (s₀) are plotted as a function of pH. The electrostatic contribution to the interaction potential is achieved by the expansion of the Poisson-Boltsmann equation up to cubic terms [6]. In low pH medium, the sol state is ensured by a high energy barrier (22 k_BT £ W £ 18 k_BT) related to the saturation value of the surface charge density. With increasing pH, it is observed a reduction of the energy barrier and a superficial density of charge decrease about 50 % of its saturation value. These conditions leads to a reversible place transition (flocculation) generating a thixotropic gel state of kinetic stability. For pH ³ 5.2 it acidic medium, W and s₀ fall drastically so that the thermal fluctuations are sufficient to include primary minimum aggregation (coagulation).

Figure 1.

The pH-dependent phase diagram of the EDL-MF sample, the height

of the energy barrier (W) and the variation of the surface charge density s₀ with pH.

References:

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4. E. Hasmonay, A. Bee, J. – C. Bacri, R. Perzynski. // J.. Phys. Chem. B 103 (1999) 6421.

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