Sorption and diffusion of organic acid ions in anion exchange membranes: Acetate and lactate ions as a case study

Highlights

• Solubility and conductivity of lactate and acetic anions measured in anion exchange membranes.

• Less acid dissociation in the membrane phase than in the external solution.

• Diffusion coefficients of each anion within the membrane change little with concentration.

• Diffusion coefficient of acetic anion falls with pH, possibly due to dimer formation.

• The Manning model fits the lactate data well, but not that for the acetate anion.

Abstract

In this study, the sorption behaviour and conductivity of two anion exchange membranes (AR103 and AR204) equilibrated with sodium acetate and sodium lactate solutions are studied across a range of concentrations and pH values. The results indicate that the dissociation equilibria of the organic acids differ between the membrane phase and the external solution. There are significant concentrations of the neutral organic acid in the membranes at pH 6.5 even though the dissociation is virtually complete in the external solution. The concentration of this neutral acid increases as the pH is lowered, leading to a reduction in membrane conductivity. The diffusion coefficients of acetate and lactate ions in these membranes are determined from conductivity data. The results show that these diffusion coefficients are relatively constant but decrease slightly with an increase of external solution concentration due to osmotic deswelling. The diffusion coefficient of the acetate anion decreases as the pH falls, possibly due to dimer formation. Models extended from Manning's condensation theory have been utilized in the prediction of the co-ion concentrations within the membrane and the diffusion coefficients of the lactate and acetate anions. There is an excellent agreement between the experimental values of these parameters and the model predictions for the sodium lactate system but the model is unable to accurately fit the sodium acetate data.

Introduction

Organic acids such as acetic acid and lactic acid are used broadly within the food and pharmaceutical industries as preservatives [1], chemical intermediates [2] and buffer media. In addition, due to their biodegradable properties, there is a growing demand for these compounds in the production of polymeric materials [3]. Generally, organic acids are produced commercially either by fermentation or chemical synthesis. The former approach is preferred in the food industry as many food regulations stipulate that acids used in foods must be of biological origin [4]. The development of effective separation steps for organic acid recovery plays an important role in many biochemical industries since the conventional fermentation processes produce a mixture of organic acids as well as calcium, ammonium, or sodium salts [5]. Membrane processes, especially diffusion dialysis (DD), conventional electrodialysis (ED) and electrodialysis with bipolar membranes (EDBM), are widely used in the production and recovery of these organic acids [[4], [5], [6], [7], [8]] as they operate continuously and virtually eliminate the waste produced by other processes. However, commercial applications of these processes are often affected by the ion selectivity, electrical resistance and manufacturing costs of the ion exchange membranes (IEMs). Thus, to obtain a process with high efficiency and low energy consumption, a fundamental understanding of ion sorption and transport in IEMs is necessary. A better knowledge of the influence of polymer structure on transport properties could further facilitate rational development of ion exchange membranes with improved properties.

Ion transport in ion-exchange dense polymer membranes is normally quantified by ion diffusion coefficients. A variety of experimental techniques based on the Nernst-Planck equation have been employed to measure the diffusion coefficients of inorganic ions in these membranes, including a Donnan dialysis method [[9], [10], [11], [12]], radiotracer method [13,14] and conductivity method [[15], [16], [17], [18]]. The conductivity method is the most often used as diffusion coefficients measured in the presence of an external driving force are closer to the real operation of the membrane process.

For one-dimensional ion transport in a membrane, the molar flux of ion $i$ through a membrane, $J_i^m$, can be described by the Nernst-Plank equation as Eq. (1):

$$J_i^m=-D_i^m\left[\frac{d{C}_i^m}{dx}+\frac{z_{i}F{C}_i^m}{RT}\frac{d\psi }{dx}\right]$$

where $D_i^m$ and $C_i^m$ are the ion diffusion coefficient and concentration in the membrane, respectively; $z_i$ is the valence of the ion; $T$ is absolute temperature, R and F are the ideal gas constant and Faraday's constant, respectively. $\psi$ is the electric potential and $x$ is the thickness of the membrane.

In typical electric field driven ion transport, the Fickian component of the driving force in Eq. (1) is minimal and the electric potential difference becomes the dominant driving force for ion transportation. Under this electric potential difference, cations migrate toward the cathode and anions move toward the anode. The electric current density (I) is related to the ionic fluxes in the membrane via Eq. (2).

$$I=F\sum _i{z}_i{J}_i^m$$

Combining Eq (1) and Eq (2) yields Eq. (3).

$$I=-\frac{F^2}{RT}\sum _i{z}_i^2{C}_i^m{D}_i^m\frac{d\psi }{dx}$$

The membrane ion conductivity ($\kappa$) is defined by Eq. (4):

$$\kappa =\raisebox{1ex}{$-I$}\!\left/ \!\raisebox{-1ex}{$\frac{d\psi }{dx}$}\right.$$

Combining Eq (3) and Eq (4) then yields

$$\kappa =\frac{F^2}{RT}\sum _i{z}_i^2{C}_i^m{D}_i^m=\frac{F^2}{RT}(z_{+}^2{C}_{+}^m{D}_{+}^m+z_{-}^2{C}_{-}^m{D}_{-}^m)$$

Eq (5) gives the relationship between the individual ion diffusion coefficients ($D_{+}^{m}and$ $D_{-}^m$) and the ionic conductivity of the membrane but this expression cannot be solved to yield the individual diffusion coefficients. Some researchers assume that the co-ion concentration ($C_{+}^m$) approaches zero [9,[18], [19], [20]], as the Donnan potential repels these ions from the ion exchange membrane and this prevents the internal co-ion concentration from rising beyond an equilibrium value [21]. This allows the diffusion coefficients of the counter-ions ($C_{-}^m$) to be determined by Eq (5).

The strength of the Donnan potential depends on the counter-ion/co-ion concentration difference between the membrane and the external salt solution. For conventional membrane processes, the counter-ion concentration difference between the membrane and solution decreases with the increase of external solution concentration as the counter-ion concentrations in the membrane itself are relatively constant [22]. This results in a weaker Donnan potential and greater co-ion sorption in the membrane. Thus, for ion exchange membranes equilibrated with concentrated solutions, the co-ions in the membrane must also be considered. To solve this problem, Kamcev et al. (2018) developed a new procedure in which the individual ion diffusion coefficients are obtained from experimental ion sorption and membrane ionic conductivity results [16]. They also modified Manning's counter-ion condensation theory [23,24], originally developed as a ‘‘limiting law’’ for polyelectrolyte solutions, by relaxing the assumption of immobile condensed counter-ions, then used this as a model for the prediction of counter-ion diffusion coefficients in the membrane [16]. The central parameter in the modified Manning model is the dimensionless linear charge density of a polyelectrolyte, $\xi$, which depends on the average distance between fixed charge groups on the polymer chain. For monovalent ions, condensation occurs if ξ is greater unity (see Supporting Information).

With only one additional adjustable parameter, the modified Manning condensation theory offers excellent agreement with counter-ion/co-ion diffusion coefficients calculated from experimental results in NaCl systems. It is also predicted that this model will be suitable for similar 1:1 inorganic salt systems. However, it is less clear whether it would suitable for organic acid systems as the dissociation equilibria of the organic acid and its ions may affect their transport behaviour.

As there is a growing demand for organic acid production by electro-membrane processes, a fundamental understanding of organic ion transport in IEMs is necessary, especially the influence of polymer structure on the transport properties. To date, most research on ion transport in ion exchange membranes relates to inorganic ions, with very little information about organic acids. These are generally weak acids that at neutral and low pH are only partly dissociated, which makes their sorption equilibria more complex. In this study, the sorption behaviour of acetic acid (pKa 4.76) and lactic acid (pKa 3.86) in anion exchange membranes are experimentally studied and compared with the sodium chloride system. The individual diffusion coefficients for the acetate and lactate ions in the same anion exchange membranes are then measured by a conductivity method and fitted to the modified Manning model proposed by Kamcev et al. [16] to verify whether it is applicable to organic acid systems.