In this paper, we present a study on the adsorption of calcium (Ca 2+ ) onto polyacrylic acid-functionalized iron-oxide magnetic nanoparticles (PAA-MNPs) to gain an insight into the adsorption behavior of alkaline earth elements at conditions typical of produced water from hydraulic fracturing. An aqueous co-precipitation method was employed to fabricate iron oxide magnetic nanoparticles, whose surface was first coated with amine and then by PAA. To evaluate the Ca 2+ adsorption capacity by

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... MNPs, the Ca 2+ adsorption isotherm was measured in batch as a function of pH and sodium chlorite (electrolyte) concentration. A surface complexation model accounting for the coulombic forces in the diffuse double layer was developed to describe the competitive adsorption of protons (H + ) and Ca 2+ onto the anionic carboxyl ligands of the PAA-MNPs. Measurements show that Ca 2+ adsorption is significant above pH 5 and decreases with the electrolyte concentration. Upon adsorption, the nanoparticle suspension destabilizes and creates large clusters, which favor an efficient magnetic separation of the PAA-MNPs, therefore, helping their recovery and recycle. The model agrees well with the experiments and predicts that the maximum adsorption capacity can be achieved within the pH range of the produced water, although that maximum declines with the electrolyte concentration. Energies 2017, 10, 223 2 of 15 becoming an attractive alternative to the current practice [5] . However, produced water for external reuse requires desalination and current techniques face significant engineering challenges because of the large volume, hyper-salinity, and complicated composition of the water. Results show that crystallization is a feasible process for the removal of the major metal cations in the produced water, but due to the low supersaturation ratios precipitation of co-crystals might be favored [2] . Therefore, it would be envisaged to create a concentrated supersaturated brine of selected cations to allow fast precipitation of homogenous crystals. Nano-scale adsorbents are considered as an ideal candidate for the removal of selected ions because of their large surface area per mass and a great number of selectively active sites that can be generated on the surface. Among these nano-adsorbents, the iron-oxide based magnetic nanoparticles have been extensively investigated to remove multi-valent cations, such as copper, lead, zinc, nickel [6-8], as they have a number of advantages, including easy control, fast separation of the spent nanoparticles from the cleaned water with the application of magnetic field gradient, and the potential for the spent nanoparticles to be regenerated and reused. However, their ion selectivity and adsorption capacity reported to date are unsatisfactory [7, [9] [10] [11] [12] . With the aim to improve the adsorption capacity and ion selectivity, and the nanoparticle dispersion stability, the iron-oxide magnetic nanoparticles are conjugated on the surface with functional groups like carboxylate, hydroxyl and amino groups which have high affinity for cations to form metal complexes or chelates [13] [14] [15] . Selecting an appropriate functional material to modify the iron-oxide nanoparticles is of great importance in developing a high-performance magnetic nano-adsorbent. Polyacrylic acid (PAA) is used as an emulsifier and thickening agent for aqueous solutions and dispersions. In the recent years, it has been employed to make polymer-based hybrid adsorbents to effectively remove organic and inorganic pollutants [16, 17] . Recently, several authors have studied the use of PAA and modified-PAA to remove heavy metals, such as cadmium, chromium, copper, lead, mercury, nickel, and zinc [18] [19] [20] from waste water. In all cases, high removal efficiency under broad interval of pH and temperature has been observed. However, few studies have been dedicated to the adsorption of alkaline earth elements onto PAA [21, 22] . The work by Bartós and Bilewicz [22] shows significant adsorption of Ba 2+ , Ra 2+ , and Sr 2+ by PAA, but the effect of pH and ionic strength was not investigated extensively, in particular under the conditions of interest of this work. Here, we propose a technique to selectively separate ions from produced water and, then, create a highly supersaturated brine. It consists in using functionalized magnetic nanoparticles which can selectively adsorb targeted cations from produced water and be separated with a magnet from the treated water. They can be therefore regenerated for reuse producing a concentrated brine [12] . This paper presents the results from the study of the adsorption of Ca 2+ , a representative alkaline earth element and a congener of Ba 2+ , Ra 2+ , and Sr 2+ , by iron-oxide magnetic nanoparticles (MNPs) functionalized with PAA. An aqueous co-precipitation method was employed to fabricate iron-oxide magnetic nanoparticles, which was followed by the surface modification with the amine group [23] [24] [25] [26] . PAA was then conjugated on the surface of the amine-MNPs. The effect of pH and salinity on the removal of Ca 2+ was investigated in batch experiments as a function of solution pH and electrolyte (NaCl) concentration to understand the effect of pH and salinity on adsorption. A surface complexation model accounting for the electrostatic forces was implemented to describe the competitive adsorption between protons (H + ) and Ca 2+ onto an anionic adsorption site available on the surface of PAA-MNPs. The model well describes the pH-dependent adsorption of Ca 2+ onto the PAA-MNPs as a function of electrolyte concentration and it is used to make prediction on the adsorption of a general alkaline-Earth element from produced water. The paper is divided into four sections. Section 2 reports and discusses the results of nanoparticle synthesis and characterization, of the adsorption experiments and optimization, and of the simulations of adsorption. Section 3 describes the materials and the methods used in this work, including the developed surface complexation model. Finally, Section 4 draws the conclusions. Energies 2017, 10, 223 3 of 15