Adsorption equilibria of di(2-ethylhexyl)phosphoric acid at the water-dodecane-interface. Effects of additional electrolytes

Adsorption equilibria of di(2-ethylhexyl)phosphoric acid at the water- dodecane-interface: Effects of additional electrolytes

Keywords: Di(2-ethylhexyl)phosphoric acid, interfacial activity, adsorption equilibrium, counterion adsorption, pseudo-nonionic modelling, liquid-liquid-interface, interfacial tension

Abstract

Based on the adsorption of both derivatives of di(2-ethylhexyl)phosphoric acid - monomer and anion - a new modelling strategy is presented for the adsorption equilibria and the interfacial tension as the consecutive physical value. The starting point is a description of the adsorption equilibrium of these two interfacial active substances using the Langmuir isotherm. Because of the accumulation of the counterions, which is reproduced by the Stern isotherm, the Gibbs adsorption equation, unlike with the nonionic modelling strategy normally used for this material system, has to be supplemented by the quantity of the importance of counterions. A simple model integrating micelle formation makes it possible to simulate the equilibrium interfacial tension even at high concentrations of interfacially active agents.

1 Introduction

The adsorption of surfactants significantly determines the properties of the interface. In liquid- liquid systems the accumulation of substances at the interface mainly modifies the interfacial tension, the interfacial charge and the interfacial rheology [1,2]. These adsorptive interface modifications have far-reaching consequences on the process design in fluid engineering. For example, phase formations such as the mechanisms of breakage and coalescence, the droplet velocity and the mass transport over the interface are influenced by interfacial adsorption in disperse multiphase systems. If the adsorbed substances are the transition components in the physical extraction or if the interfacially active substances are reactants in the reactive extraction, the description of the adsorption equilibria is very important, because in these cases the processes at the interface and in the interfacial layer guide the extraction process.

The adsorption isotherms characterize the equilibrium composition of the interface by linking the concentrations in the interface with those in the volume phases. These isotherms are fundamental for the formulation of unrestricted adsorption processes, because the enrichment step is performed by the local equilibrium between the interface and the adjacent bulk phase, known as the subsurface. The mass transfer from the separate bulk phases to the subsurface is performed by the kinetics of convection and diffusion and, in aqueous regimes, with electrolytes additional by migration. If the adsorption is delayed by interactions in the interface and in the subsurface, the sorptive mechanism must be described using a kinetic approach instead of the isotherms[3]. This kinetic formulation can be derived from the adsorption isotherms, since the isotherms define the steady state of the sorption kinetics.

The suitability of specific isotherms is verified by adjusting measured profiles of the equilibrium interfacial tension. Their change is related with the interfacial concentration and activity changes in the volume phase by means of the Gibbs adsorption equation[3]. The different modelling strategies are the result of assumptions made about additional interface-active agents as a consequence of previously independent adsorbed components[4].

Despite the industrial use of the cation exchanger di(2-ethylhexyl)phosphoric acid - D2EHPA for short - in metal salt extraction[5]and its known interfacial activity[6], it is still common practice to describe the adsorption as a spontaneous chemical reaction [7,8]. Even if the adsorption takes place without sorptive inhibition, the limited enrichment capacity of the interface is suppressed in these methods. In the subsequent metal salt formation reactions this fact results in a stagnation of the mass transfer as the turbulence intensity in the phase from which is adsorbed is increased. At this phase side transport limitations arise from the limited interfacial concentration.

Even the works which deal with the adsorption of D2EHPA at water-oil interfaces reveal large differences. Miyake et al.[9]and Szymanowski et al.[10]describe the equilibrium interfacial tension during the adsorption of the cation exchanger by the Langmuir isotherm for multicomponent adsorption. They base their description on the same minimal area per adsorbed monomer and anion of the cation exchanger. Even Vandegrift et al.[11]and Shen et al.[12] neglect the influence of anion adsorption at the interface and postulate the adsorption of only one component. None of these authors consider the influence of counterions, as demonstrated by Goanker et al.[6]on the basis of experimental curves of the equilibrium interfacial tension.

2 Experimental

The measurements of the equilibrium interfacial tension at the liquid-liquid interface were carried out at 20°C based on a pendant drop using drop shape analysis. In this method, the profile of a rotationally symmetric drop is recorded as a silhouette and is described by the force balance of interfacial tension, buoyancy and gravity[13]. Since there is a density difference between the droplet and bulk phase, the curvature radii of the drop change due to the adsorption and every drop shape change is definitely assigned an interfacial tension. The equilibrium interfacial tension is obtained as the stationary value of the measured curve of the dynamic interfacial tension.

The measurement setup used is shown in Figure 1: a dosing system consisting of a gas-tight glass syringe whose stroke is controlled by a stepper motor is used to generate the aqueous pendant drop on a Teflon capillary which is inserted into a glass cuvette filled with organic phase. This cuvette is embedded in a temperature-measuring cell.

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Figure 1: Schematic experimental setup of the pendant-drop tensiometer

The temperature of the cell is stabilized using a cryostat to measure and regulate the temperature in a stirred cooling water (or heating water). The drop is illuminated by a light source whose light is parallelized by a diffuser and lens. The silhouette of the drop is transmitted through the lens with an attached CCD camera to the computer. There it is digitized using a frame grabber [14]. The PAT 1 software, produced by SINTERFACE, allows the digital drop profile to be saved automatically at any time. This software controls the dosing unit via an interface. In this way, the surface or the volume of the drop can optionally either be held constant or modified during the experiment by means of permanent controlling in accordance with the test program. The time profiles of the experimental program are implemented by entering the corresponding mathematical functions.

All chemicals except the used cation exchanger (D2EHPA, 95 weight-%, technical quality, Sigma) were checked for possible contamination using tensiometric measurements. Only in the case of the diluent (n-dodecane, 99 weight-%, for synthesis, Merck) was preparation necessary. This was done by washing with deionised water. All other chemicals were used in analytical quality without any preparation, because no interfacially active impurities were detected.

To study the influence of the two interfacially active variants of the cation exchanger - the monomer and anion - by shifting the dissociation equilibrium and to understand the effect of the counterions on the interfacial tension, sulphuric acid, sodium sulphate or sodium hydroxide were added to the aqueous phase in various concentrations. In the organic dodecane phase the D2EHPA concentration was varied based on the concentration of classical surfactants added at different levels, up to those used in technical applications. Before the interfacial tension was measured of aqueous droplets and an organic volume phase, the two phases were mixed for 24 hours in a shaker with a constant volume ratio. As this completed the mass transfer between the phases, this excluded the possibility of errors resulting from different volumes because of the different shape of drops and the inaccurate filling of the cuvette. So that not all variable concentration values had to be calculated using balance equations, the pH value was additionally measured in the aqueous solution.

3 Modelling

The Gibbs adsorption equation provides the change of interfacial tension in the case of the joint adsorption of the monomer and the cation exchanger anion including the counterion adsorption of protons and sodium ions, if the concentration shift in the electrochemical double layer is neglected:

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(1)

Because electrostatic effects are left out, the following modelling strategy is called pseudononionic. In Eq. (1) the Langmuir isotherms are introduced with the simplification that the maximum interfacial concentrations of the multicomponent adsorption are the same as in the adsorption of only one component.

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(2)

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(3)

The interfacial concentrations of the counterions are coupled via the Stern isotherm - neglecting the electrostatic interfacial potential - with their bulk phase activities and the interfacial concentration of adsorbed cation exchanger anions.

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(4)

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(5)

Since the monomer concentration of the organic phase is connected with the activities of the proton and the anion of the cation exchanger by the distribution of the monomers in the aqueous phase and the following dissociation, any concentration value of the one component is always defined by the concentration values of the other two components. Therefore, changes to activities of these reactive coupled substances in the Gibbs adsorption equation, Eq. (1), are expressed by the remaining independent variables. The partition equilibrium between monomers in the two phases

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(6)

and by the mass action law of dissociation

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(7)

are used to find the relationship between the different activities:

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(8)

From this the total differential of the anion activity is formed:

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(9)

After the isotherms are introduced and the dependent activities are linked, the calculation formula of the equilibrium interfacial tension is obtained by integrating the Gibbs adsorption equation, Eq. (1).

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Initially this relation applies only to the submicellar concentration range, but the equation can easily be modified to include the micellar range. The modification makes use of the fact that the micelle formation is not a chemical reaction in the classical sense but rather a self-assembly of surfactant molecules. Because of this, the micelle formation has no effects on chemical reaction equilibria processes. Its importance results from its effect on the adsorption isotherms. The disaggregated quantity of the interfacially active component is crucial for the adsorption isotherms. Because of the known micelle formation of the cation exchanger anion[15]and the discussed micellar influences the linkages between the activities are also valid in the micellar concentration range and the anion activity simply has to be replaced in the calculation formula of the equilibrium interfacial tension, Eq. (10), with that of the unbound anion.

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(11)

The fraction of the unbound anion is defined by means of a micelle formation reaction, which is technically similar to a chemical reaction. Neglecting the importance of the counterions on the micelle formation, the micelle formation can be described using the reaction scheme:

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(12)

In this reaction scheme, there are additionally assumed to be monodisperse micelles with the same aggregation number. The corresponding mass action law leads to:

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(13)

Since the micelle formation does not affect the chemical reaction equilibria, the micelle activity is formulated from the equilibria of the partition and the dissociation using the fraction of the unbound anion.

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(14)

By introducing this equation, Eq. (14), together with the relation in Eq. (11), into the mass action law, Eq. (13), the fraction of the unbound anion is defined by an implicit equation:

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(15)

While the activity of the proton was measured, the other activities have to be calculated. Since sodium is not extracted by D2EHPA to any noticeable degree, the concentration of the sodium ion is known. The other, unknown concentration values have to be determined using mass balances and reaction equilibria. The unknown activity coefficient is described involving the radius of the hydrated ion as the only ion-specific parameters according to the extended Debye- Hückel law. For the activity coefficients of an arbitrary z-valent ion, this produces[16]:

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(16)

The Debye-Hückel length this includes is defined by means of the ionic strength.

(17)

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Because of the dependence of the electrolyte activity coefficients on the ionic strength, all the ion concentrations have to be determined. Since these values are derived from the different reaction-specific equations of mass action law, knowledge is required of the activity coefficients of all the ions present. The hydrated ion radii (see Tab. 1) are calculated from the average electrolyte activities[17]using a numerical regression procedure.

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Table 1: Used hydrated ionic radii rhyd

The radius of the hydrated cation exchanger anion is estimated as the average of other values. The determination of the concentration values, which are necessary for the calculation of the ionic strength, requires only the presence of the dissociated forms of the sulphuric acid. The equilibrium between the sulphate and hydrogen sulphate ions is formulated via the mass action law

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(18)

and it is calculated by assessing the total amount of sulphate. The concentration of hydroxide, which is also unknown, is defined thus:

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(19)

The required dissociation constants are taken from the standard references [18,19] describing the equilibria of inorganic electrolytes.

The activity of the cation exchanger anion is explained by Eq. (8). From this the corresponding concentration is calculated by linking:

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(20)

At first the activity of the monomer has to be determined. Taking account of the equilibrium of the dimerization

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