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Kinetics of Cation and Oxyanion Adsorption and Desorption on Ferrihydrite: Roles of Ferrihydrite Binding Sites and a Unified Model Lei Tian, Zhenqing Shi, Yang Lu, Alice Dohnalkova, Zhang Lin, and Zhi Dang Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03249 • Publication Date (Web): 10 Aug 2017 Downloaded from http://pubs.acs.org on August 10, 2017

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Environmental Science & Technology

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Kinetics of Cation and Oxyanion Adsorption and Desorption on

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Ferrihydrite: Roles of Ferrihydrite Binding Sites and a Unified

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Model

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Lei Tian,†,‡ Zhenqing Shi,*,†,‡ Yang Lu,†,‡ Alice C. Dohnalkova,§ Zhang Lin,†,‡ Zhi

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Dang†,‡

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†

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Guangzhou, Guangdong 510006, People’s Republic of China

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‡

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Clusters, Ministry of Education, South China University of Technology,

School of Environment and Energy, South China University of Technology,

The Key Lab of Pollution Control and Ecosystem Restoration in Industry

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Guangzhou, Guangdong 510006, People’s Republic of China

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§

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Laboratory, Richland, WA 99354, USA

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Environmental Molecular Sciences Laboratory, Pacific Northwest National

*

Corresponding author: email: [email protected], phone: 86-20-39380503

Total Words: 4953+ 300 + 600 + 300 + 600 + 600 + 300 = 7653

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1

ACS Paragon Plus Environment


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Abstract Quantitative understanding the kinetics of toxic ion reactions with various heterogeneous

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ferrihydrite binding sites is crucial for accurately predicting the dynamic behavior of

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contaminants in environment. In this study, kinetics of As(V), Cr(VI), Cu(II), and Pb(II)

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adsorption and desorption on ferrihydrite was studied using a stirred-flow method, which showed

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that metal adsorption/desorption kinetics was highly dependent on the reaction conditions and

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varied significantly among four metals. High resolution scanning transmission electron

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microscopy coupled with energy-dispersive X-ray spectroscopy showed that all four metals were

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distributed within the ferrihydrite aggregates homogeneously after adsorption reactions. Based

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on the equilibrium model CD-MUSIC, we developed a novel unified kinetics model applicable

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for both cation and oxyanion adsorption and desorption on ferrihydrite, which is able to account

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for the heterogeneity of ferrihydrite binding sites, different binding properties of cations and

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oxyanions, and variations of solution chemistry. The model described the kinetic results well.

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We quantitatively elucidated how the equilibrium properties of the cation and oxyanion binding

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to various ferrihydrite sites and the formation of various surface complexes controlled the

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adsorption and desorption kinetics at different reaction conditions and time scales. Our study

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provided a unified modeling method for the kinetics of ion adsorption/desorption on ferrihydrite.

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TOC Art

35 36 2


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Introduction

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Ferrihydrite is one of the most important mineral adsorbents to control the fate of both cation and

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oxyanion contaminants in soil.1 Typical heavy metals (and metalloids), such as As(V), Cr(VI),

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Cu(II), and Pb(II), form strong complexes with ferrihydrite.2-10 Ferrihydrite has been considered

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to be meta-stable, but its transformation to more stable mineral phases may be slow in soils,

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possibly due to the impact of adsorption/co-precipitation of organic matter11 and incorporation of

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other cations.12 Therefore, understanding both cation and oxyanion adsorption and desorption on

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ferrihydrite is crucial for predicting the dynamic behavior of metal contaminants in soil.

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Extensive work has been done on ion adsorption on iron minerals with both surface

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complexation models (SCMs)13-21 to quantitatively describe the adsorption equilibrium and

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spectroscopic techniques to elucidate the adsorption mechanisms.5, 22-27 Among those SCMs, the

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CD-MUSIC (Charge Distribution Multi Site Complexation) model15, 28 is capable of describing

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ion binding to iron minerals.6 The CD-MUSIC model assumes that the surface complexes of

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cations or oxyanions have a spatial distribution of charges in the water-mineral interface regions,

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which has shown success on modeling the adsorption of various cations and oxyanions, such as

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As(V), Cr(VI), Cu(II), and Pb(II),3, 4, 8, 29, 30on iron minerals.

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Compared with the equilibrium studies, less progress has been made on the kinetics of

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cation and oxyanion adsorption/desorption on ferrihydrite.31-33 The adsorption of both Cu(II) and

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Pb(II) on ferrihydrite surface sites was considered to be fast, with most adsorption occurred

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within a few minutes.34 Cu(II) adsorption rates may be affected by both solution chemistry and

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reaction conditions.35 The adsorption of As(V) with iron minerals have been reported to show

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typical biphasic reaction kinetics, a fast reaction with a time scale of minutes followed by a slow

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reaction lasting for hours to days.10, 36 Based on the density functional theory modeling, the slow

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As(V) adsorption/desorption kinetics was attributed to the high Gibbs free energies of activation

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for forming and breaking bonds with the iron minerals.37

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Overall, previous kinetic studies only dealt with either cations or oxyanions, and there is

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still a lack of a unified modeling framework for the kinetic reactions of both cation and oxyanion

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contaminants with ferrihydrite, which requires a comprehensive consideration of different

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reactivity of various ions, ion binding to heterogeneous ferrihydrite sites, and the effect of 3



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solution chemistry. More importantly, how individual ferrihydrite binding sites and various

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surface complexes control the adsorption and desorption kinetics under various reaction

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conditions, to our knowledge, have never been explored. Cations and oxyanions may form

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various surface complexes on ferrihydrite binding sites, which have different thermodynamic

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equilibrium properties and different impact on the surface charge, and therefore may have

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significantly different kinetic behavior. In addition, ferrihydrite nanoparticles tend to

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agglomerate in solutions and form large aggregates, which complicates the modeling of the

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kinetic reactions. All those factors should be considered in order to accurately predict the

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kinetics of both cation and oxyanion adsorption and desorption reactions with ferrihydrite.

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The objective of this study is to quantitatively investigate how the cation and oxyanion

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binding to various ferrihydrite binding sites controls the adsorption and desorption kinetics of

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cations and oxyanions under various reaction conditions and develop a unified model for both

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cations and oxyanions. The kinetics of As(V), Cr(VI), Cu(II), and Pb(II) adsorption and

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desorption on ferrihydrite under various reaction conditions was studied using a stirred-flow

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method. The high-resolution (HR) scanning transmission electron microscopy (STEM) coupled

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with energy-dispersive X-ray spectroscopy (EDS) was employed to investigate the elemental

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distribution within the ferrihydrite aggregates at nanometer scales after adsorption reactions.

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Based on the experimental results, we developed a novel unified kinetics model applicable for

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both cation and oxyanion adsorption and desorption on ferrihydrite by integrating the CD-

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MUSIC model.

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Materials and Experiments

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Synthesis of the Ferrihydrite. Two-line ferrihydrite was synthesized using the method

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described by Schwertmann and Cornell.38 The ferrihydrite suspension samples were kept in the

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refrigerator at 4 ℃ and used within 2 days after synthesis. Portion of ferrihydrite suspensions

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was freeze-dried and then analyzed with XRD for mineral compositions. All samples were two-

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line ferrihydrite according to their XRD results (Figure S1, Supporting Information).

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Batch Adsorption Equilibrium Experiments. Batch adsorption edge experiments were conducted to quantify the adsorption capacity of synthesized ferrihydrite for As(V), Cr(VI),

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Cu(II), and Pb(II) at various pH, and test the applicability of the CD-MUSIC model. Detailed

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experimental conditions are presented in the Supporting Information (S2 section).

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Stirred-flow Adsorption and Desorption Kinetic Experiments. The stirred-flow

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reactor used in this study (Figure S2, Supporting Information) was developed previously to study

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the kinetic reactions in soil in the short-term scales (e.g. a few hours) 39-41and had the advantages

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of controlling the experimental variables and for developing the kinetics models42-44. Compared

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with the traditional batch, miscible displacement or column techniques, the stirred-flow reactor

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minimized the diffusion limitation by well-mixing the diluted suspensions in the reactor and the

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continuous flow during the kinetic reactions.41, 42, 45 The continuous flow with heavy metals

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during the adsorption process enhanced the adsorption reactions and, during the desorption

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process, the desorbed metals were continuously removed from the reactor, in which further

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release of metals was not prohibited by the released metals. Therefore, the stirred-flow reactor

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was chosen to study the kinetics of As(V), Cr(VI), Cu(II), and Pb(II) adsorption and desorption

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on ferrihydrite under various reaction conditions.

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The background electrolytes were 10 mM NaNO3 for As(V) and Cr(VI) experiments and

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10 mM Ca(NO3)2 for Cu(II) and Pb(II) experiments since Ca(II) ions may compete with Cu(II)

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and Pb(II) for binding to ferrihydrite. Both solutions were buffered with 10 mM DEPP (N,N'-

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diethylpiperazine) (pH = 5.0) or MES ([2-(N-morpholino) ethane sulfonic acid]) (pH = 5.5 –

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6.5), which may result in different ionic strength of the solutions due to adding different amounts

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of NaOH to adjust pH for MES. Both MES and DEPP are non-complexing buffers that do not

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complex with metal ions.46 Metal stock solution was made with Na2HAsO4, K2CrO4, Cu(NO3)2

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or Pb(NO3)2 salts, which was added to the background electrolyte to prepare different

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concentrations of As(V), Cr(VI), Cu(II), or Pb(II) solutions.

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For kinetic experiments, an aliquot of the ferrihydrite suspension sample (0.5 - 1 mL) and

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a Teflon-coated magnetic stir bar were placed into the reaction cell (volume = 7.5 cm3), which

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was filled with the background electrolyte. The final ferrihydrite particle concentrations in the

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reaction cell varied from 0.065 to 1.3 g L-1 among different experiments. A 25 mm diameter

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filter membrane with a 0.22-µm pore size was used to retain the ferrihydrite in the reaction cell.

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To initiate the adsorption experiment, the metal solution was pumped through the reactor, and,

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after 4 h of adsorption, desorption was initiated by passing the background electrolyte through 5



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the reactor. The desorption continued for another 4 h. The flow rate for all experiments was 1

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mL min-1. The effluent samples were collected every 5 min. Blank experiments were conducted,

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which showed that the adsorption of metals by the reactor was minimal (Figure S3, Supporting

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Information). The release of ferrihydrite particles from the reactor was also negligible since the

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effluent Fe concentrations were below the detection limit for all experiments. Duplicate

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experiments were done, which showed good reproducibility of the kinetic experiments (Figure

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S4, Supporting Information). Considering the small volume of the ferrihydrite suspension

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samples used in each experiment, a few replicate samples were analyzed by acid digestion with

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concentrated HNO3 to obtain the ferrihydrite particle concentrations, which generally showed

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good repeatability. All experiments were conducted at 25 °C.

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To test the potential impact of diffusion limitation on the observed kinetics within the

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time scales of our experiments, we conducted kinetic experiments at various mixing rates in the

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stirred-flow reactor. When the mixing rates were above certain value, further increase in the

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mixing rates had little impact on metal adsorption kinetics (Figures S5 and S6, Supporting

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Information), an indicator of minimal impact of diffusion limitation due to the liquid and

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interparticle diffusion processes. Therefore, all kinetic experiments were conducted at the pre-

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determined mixing rate (450 r min-1) that minimized the impact of diffusion limitation.

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All filtered solution and effluent samples were acidified by HNO3 and then analyzed by

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atomic absorption spectroscopy (Shimadzu AA-6880) or inductively coupled plasma mass

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spectrometry (Agilent 7900) to determine the total As, Cu, Fe, and Pb concentrations. The

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concentrations of Cr(VI) were analyzed by the diphenylcarbohydrazide spectrophotometric

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method with a UV-Vis spectrophotometer (Shimadzu UV-2600).

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HR TEM and Particle Size Measurements. We collected freshly made ferrihydrite

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samples and ferrihydrite samples after 4 h adsorption experiments for HR TEM analysis to

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determine morphology and elemental distribution of ferrihydrite particles/aggregates. Metal

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adsorbed ferrihydrite samples were characterized with an FEI Titan Themis-200 instrument with

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a field emission gun operated at 200 kV in STEM mode. It is fitted with high angle annular dark

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field (HAADF) and backscattered electron (BSE) detectors, as well as EDS (Bruker). STEM-

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EDS spectrometer was used in this study as well as HAADF and BF detectors. Experimental

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conditions used in the preparation of samples and additional experimental details are described in 6


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the Supporting Information (S4 section). For the ferrihydrite suspensions, we also monitored the

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changes of particle size distribution during the kinetic experiments using an EyeTech particle

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size analyzer to evaluate its potential impact on the kinetic reactions.

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Model Description

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Since the diffusion limitation was minimized in our stirred-flow reactor, the rates of cation or

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oxyanion adsorption and desorption on specific ferrihydrite binding site and the change of the

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cation or oxyanion concentrations in solutions can be described as,

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dCpi = −kdi Cpi + kai Cion dt

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dCion = dt

(1)

∑ k i mC i − ∑ k i mC d

p

a

ion

−

Q(Cion − Cion,0 ) V

(2)

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where kai (L (g min)-1), kdi (min-1), and Cpi (µmol g-1) are adsorption and desorption rate

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coefficients and adsorbed metal concentration for specific ferrihydrite site i, respectively, Cion

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(µmol L-1) is the effluent concentration of the studied cation or oxyanion, m (g L-1) is the

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ferrihydrite particle concentration, Q (L min-1) is the flow rate, and V (L) is the reaction volume

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of the reactor. Subscript 0 denotes the influent cation or oxyanion concentration.

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In the kinetics model, we specifically considered the nonlinear cation and oxyanion

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binding to different ferrihydrite binding sites and the formation of different surface complexes

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during the kinetic reactions. Recently we have developed a mechanistically based modeling

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approach for the kinetics of cation binding to humic substances,43, 44, 47 and, in this study, we

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attempted to extend the similar modeling approach to the kinetic reactions of both cation and

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oxyanion with ferrihydrite and developed a unified model for both types of ions. The CD-

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MUSIC model was specifically integrated into the kinetics model to account for the variations of

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solution chemistry and heterogeneity of ferrihydrite binding sites. The key elements of the

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kinetics model include, (i) for each ferrihydrite binding site, the cation and oxyanion adsorption

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and desorption rate coefficients are constrained by the equilibrium distribution coefficients, Kpi

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(L g-1), that can be computed by the CD-MUSIC model at specific reaction conditions (equation

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3), and (ii) for one specific cation or oxyanion, the desorption rate coefficients of different 7



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ferrihydrite binding sites are constrained by their metal binding constants, KMi (equation 4). The

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detailed derivations of both equations are presented in the Supporting Information (S5 section).

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k ai = k di K pi

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logkdi − logkdj = 0.5(logK Mj − logK Mi ) (4)

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Note that in equation 3, Kpi is not a constant (in contrast to the linear isotherm model) but

(3)

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a function of Cpi, solution chemistry conditions, and the reaction time during the kinetic

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reactions. Equation 4 applies to different binding sites involving similar reactions, e.g. forming

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the bidentate surface complexes, indicating the slower desorption of metals (small kdi) from the

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stronger surface complexes (larger KMi). In the model calculations, the effect of solution

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chemistry is incorporated into the adsorption reaction, and the desorption rate coefficients are

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assumed to be constant irrespective of the reaction conditions,43, 44, 47 which suggests a

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disjunctive reaction pathway for the desorption reaction. Therefore, the effects of reaction

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chemistry and nonlinear binding on the reaction rates are accounted for by the CD-MUSIC

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model through equations 3 and 4 and no additional model fitting parameters are needed when

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reaction conditions vary.

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One key issue is to specifically consider each of the surface complexes formed on

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ferrihydrite binding sites in the kinetics model, which may vary in term of their reaction rates,

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and we used the surface complexation reactions built in the CD-MUSIC model for each metal.

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All four metals form different complexes with ferrihydrite (Table S2, Supporting Information).

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For As(V), it may form three types of complexes according to the CD-MUSIC model, two

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bidentate complexes and one monodentate complex, which differed in their complexation

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reactions and surface charges. We denoted these three As(V) binding sites as Fh-bi-np, Fh-bi-p

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and Fh-mono, in which Fh-bi-np and Fh-bi-p represent the non-protonated and protonated

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bidentate surface complexes, respectively. For Pb(II), there are three types of bidentate sites with

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weak, medium and strong binding strength, which differed in their metal binding constants and

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site density. We denoted these three bidentate complexes as Fh-bi-weak, Fh-bi-medium, and Fh-

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bi-strong, respectively. For Cr(VI) or Cu(II), all surface sites form one type of bidentate

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complexes with the same affinity, denoted as Fh-bi-weak. 8


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For CD-MUSIC calculations, the major input parameters include the solution parameters

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and ferrihydrite concentrations, and were entered as in experiments. We used the latest three-

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plane CD-MUSIC model with model parameters for ferrihydrite from Tiberg and Gustafsson.4, 48

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A detailed description of the CD-MUSIC model parameters is presented in the Supporting

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Information (S5 section).

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An implicit finite difference numerical method was used to solve the model equations in

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Excel spreadsheets. Visual MINTEQ 3.1,49 which adopts surface mole fraction based activity for

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surface species in calculating mass action equations,50 was used to execute the CD-MUSIC

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simulation. For each cation and oxyanion, Visual MINTEQ calculated the adsorption isotherms

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and the resulting equilibrium partition coefficients Kpi for all surface complexes at various metal

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concentrations and reaction pH, which were then tabulated as the adsorption isotherm database in

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Excel spreadsheets. At each reaction time during the numerical calculations, the Kpi values of all

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binding site were obtained by searching the adsorption isotherm database and doing linear

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interpolation according to the specific reaction conditions and the correspondent Cpi values. The

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detailed method to obtain Kpi value is explained in the Supporting Information (S5 section).

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For each observation time, the difference between measured and model calculated total

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dissolved metal concentrations was divided by the influent metal concentrations, which was

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squared and summed as the squared errors (SE). For each cation or oxyanion, the sum of the SE

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for all data sets was calculated to obtain the total squared error (TSE). For each metal, there is

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one global model fitting parameter, the kdi value for the Fh-bi-weak sites, kd-bi-weak, for Cr(VI),

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Cu(II) and Pb(II), and the kdi value for the non-protonated As(V) bidentate sites, kd-bi-np. For both

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As(V) and Pb(II), the kdi values for other bidentate complexes can be calculated from kd-bi-weak or

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kd-bi-np according to equation 4, with the metal binding constants in the CD-MUSIC model (Table

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S2, Supporting Information). For As(V), there was another group of monodentate complexes, but

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the formation of the As(V) monodentate complexes was minor in our kinetic experiments as

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shown later, which precludes from obtaining its kd value based on model fitting. Therefore, we

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still used equation 4 to calculate the kd value for the As(V) monodentate complexes, which had

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little impact on the overall model calculations. The SOLVER program in EXCEL was used to

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obtain kd-bi-weak or kd-bi-np for each cation and oxyanion by minimizing the TSE.

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Results and Discussion 9



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Metal Adsorption Edges. The adsorption edge results of As(V), Cr(VI), Cu(II) and Pb(II) are

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presented in Figure 1. For both As(V) and Cr(VI), adsorption decreased with the increase in pH

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at various initial metal concentrations, a typical behavior for oxyanion adsorption on iron

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mineral, while for both Cu(II) and Pb(II), adsorption increased significantly with pH. Overall,

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the CD-MUSIC model calculations with the model parameters presented in S5 section of the

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Supporting Information matched the experimental results well for most experimental conditions,

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indicating a good applicability of the CD-MUISC model for predicting both cation and oxyanion

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adsorption equilibrium across a wide range of reaction pH, metal concentrations and ferrihydrite

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particle concentrations. Therefore, the CD-MUSIC model provided a solid basis for the

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development of the kinetics model for both cations and oxyanions.

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Ferrihydrite Particle Aggregates and Distribution of Metal Ions. High-resolution

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TEM images of the ferrihydrite samples showed a typical amorphous morphology and the

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ferrihydrite particles formed large aggregates (Figure S10, Supporting Information). The small

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two-line ferrihydrite nanoparticles usually had a size of a few nm,51 which agglomerated to form

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larger aggregates during the synthesis process. During the kinetic processes, it appeared that, the

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particle size distribution of the ferrihydrite aggregates did not change significantly under two

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typical ferrihydrite concentrations and most aggregates had a size of a few micrometer (Figures

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S11 and S12, Supporting Information).

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EDS mapping results indicated that all four cations and oxyanions distributed

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homogeneously on the ferrihydrite aggregates after adsorption (Figure 2, Figure S13, Supporting

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Information). The EDS mapping of Fe, O and each metal correlated with each other well, except

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for the O mapping of the Cr(VI) adsorbed samples, in which Cr(VI) signal interfered with O

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signal. Even for the tiny pore space in the aggregates (e.g. < 10 nm), all four metal ions can

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adsorb onto the edges of the pore space as shown in the EDS mapping results. This suggests that

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all four metal ions can effectively diffuse and access the binding sites of the ferrihydrite

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aggregates within the time scale in our experiments (a few hours).

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Previous study on Cu(II) and Pb(II) adsorption kinetics showed that the effect of surface

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diffusion on metal adsorption, which limited the access to the reactive sites, was small for the

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freshly synthesized ferrihydrite particles/aggregates.34 This is in line with both the results of the

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kinetic experiments with varying mixing rates and the EDS mapping results for all four cations 10


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and oxyanions in this study. Similarly, although the slow interparticle diffusion was proposed to

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account for the long-term slow As(V) adsorption on ferrihydrite,36 adding additional surface sites

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to account for the surface diffusion did not significantly improve the CD-MUSIC model

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performance on predicting As(V) adsorption on ferrihydrite.52 This is consistent with the CD-

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MUSIC modeling results of the adsorption edge data, and suggests that, for the fresh ferrihydrite

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particle aggregates, most of the surface sites were accessible for ion binding within short time

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scales when the ferrihydrite suspensions were well mixed. If the liquid/interparticle diffusion

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controls the observed kinetics, increase in the mixing rates will enhance the overall reaction

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rates, which was only observed when the mixing rates were low. Therefore, the stirred-flow

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experiments at various mixing rates, TEM results, and particle size analysis, collectively,

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indicate that the diffusion limitation was minimal under our well-controlled experimental

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conditions with high mixing rates.

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Metal Adsorption and Desorption Kinetics. The kinetics of As(V), Cr(VI), Cu(II), and

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Pb(II) adsorption and desorption on ferrihydrite under various reaction pH, initial metal

282

concentrations, and ferrihydrite particle concentrations are presented in Figure 3 and Figure S14

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(Supporting Information). Note that, during the adsorption or desorption processes in the stirred-

284

flow reactor, the overall reaction rates were governed by adsorption rates, desorption rates and

285

flow effects (equation 2), which was shown by the effluent concentration data. Generally,

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decrease in pH enhanced both As(V) and Cr(VI) adsorption while increase pH increased both

287

Cu(II) and Pb(II) adsorption during the adsorption process. Both Cu(II) and Pb(II) adsorption

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kinetics showed strong dependence on pH while the pH effect was less pronounced for both

289

As(V) and Cr(VI) adsorption kinetics. Under similar experimental conditions, higher ferrihydrite

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particle concentrations resulted in faster metal uptake from the solution due to more ferrihydrite

291

binding sites.

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Overall, the kinetics model was able to reproduce most of the experimental results in a

293

wide range of ferrihydrite concentrations, reaction pH, and influent metal concentrations, which

294

supports the validity of our kinetic modeling approach based on the CD-MUSIC model. The

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ranges of the root-mean-square errors (RMSE) (µmol L-1) of model fits for all data are presented

296

in the figure captions. Note that the effects of reaction chemistry conditions on kinetic reactions

297

were accounted for by the CD-MUSIC model as explained in the modeling section. 11



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The Roles of Different Ferrihydrite Binding Sites. One novel feature of our kinetics

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model is the ability to quantitatively describe metal binding to various ferrihydrite binding sites

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with reaction time and how the formation of various surface complexes control the overall

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adsorption and desorption kinetics.

302

For As(V), it may form three different types of surface complexes during the adsorption

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process with varying charges (Table S2, Supporting Information). The changes of the

304

concentrations for all three As(V) surface complexes during the adsorption and desorption

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kinetic processes are shown in Figures 4a-4d under typical reaction conditions. Overall, both

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total As(V) concentrations on ferrihydrite (surface coverage) and reaction pH controlled the

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kinetics of the formation of surface As(V) complexes. For all reaction pHs, the quick formation

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of the non-protonated bidentate complexes on ferrihydrite, (FeO)2AsO22-, accounted for the

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observed fast As(V) uptake in the beginning stage of the adsorption process, in which the

310

effluent As(V) concentrations were almost close to zero (Figures 4a-4c). With the increase of the

311

As(V) surface coverage on ferrihydrite, the non-protonated bidentate complexes were close to

312

saturation and the effluent As(V) concentrations increased steadily. Then the protonated

313

bidentate complexes, (FeO)2AsOOH-, started to dominate the adsorption process. At pH 5.0,

314

more protonated bidentate complexes were formed at the end of the adsorption process than the

315

non-protonated bidentate complexes (Figures 4c-4d). Under our experimental conditions,

316

formation of the monodentate complexes, FeOH2AsO31/2-, was minor.

317

The effects of As(V) concentrations and pH on the formation of different surface

318

complexes reflected two important factors during the As(V) kinetic reactions, the ferrihydrite

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surface charge after As(V) adsorption and the competition of different surface complexes on the

320

ferrihydrite binding sites. During adsorption process, the non-protonated bidentate As(V)

321

complexes predominated at low As(V) surface coverage on ferrihydrite but will build up excess

322

surface charge at high As(V) surface coverage. Therefore, the protonated bidentate As(V)

323

complexes, with less surface charge, will be more favorable when the adsorbed As(V) was high.

324

It may be expected that, at very high As(V) surface coverage, the formation of monodentate

325

complexes will be significant due to both the less surface charge than the bidentate complexes

326

and the complexation reaction with only one surface site (Table S2, Supporting Information).

327

Interestingly, there was little difference for the desorption behavior of As(V) in most conditions, 12


Page 12 of 25

Page 13 of 25


328

with the effluent As(V) concentrations quickly dropped to very low concentrations (Figures 3a-

329

3c). This suggests that the overall desorption of As(V) was slow from both bidentate sites as

330

shown in Figures 4a-4d.

331

For Pb(II), there are three types of bidentate complexes with the same surface

332

complexation reaction but different metal binding constants and site abundance (Table S2,

333

Supporting Information). The weak binding sites dominated the overall adsorption and

334

desorption reactions at pH 5.5 and 6.0 and high Pb(II) concentrations since the weak sites consist

335

of 99% of the total binding site. However, the medium and strong binding sites may play

336

important roles at pH 5.0 when Pb(II) concentrations were low (Figures 4e-4h). These small

337

amount of the medium and strong Pb(II) binding sites has been overlooked previously in most

338

surface complexation modeling,6 and our results have quantitatively demonstrated the

339

importance of considering these sites during the kinetic reactions when the environmental

340

conditions favor the formation of the medium/strong Pb(II) complexes. Considering the small kd

341

values for these two binding sites (Table 1), we expect that these medium and strong Pb(II)

342

binding sites may play a key role to control the kinetic behavior of Pb(II) in long time scales (e.g.,

343

days to month).

344

Since there is only one type of bidentate complexes for both Cr(VI) and Cu(II), the

345

changes of adsorbed Cr(VI) or Cu(II) concentrations during the kinetic processes (Figure S15,

346

Supporting Information) basically mirrored the changes of the effluent Cr(VI) or Cu(II)

347

concentrations during the kinetic experiments (Figure 3). Compared with As(V), the adsorbed

348

Cr(VI) concentrations may quickly approach steady status, consistent with the much weaker

349

adsorption ability of Cr(VI) than As(V) (Table S2, Supporting Information). The desorption of

350

Cr(VI) appeared to be faster than As(V). For Cu(II), the adsorption was relatively fast with the

351

adsorbed Cu(II) steadily increased with time, similar to that of Pb(II), but desorption of Cu(II)

352

appeared to be faster than Pb(II) as Cu(II) was quickly released from ferrihydrite.

353

Adsorption and Desorption Rate Coefficients of Various Ferrihydrite Binding Sites.

354

Table 1 showed the kd values of various ferrihydrite binding sites obtained in this study for all

355

four metals. The kd values of the weak bidentate complexes or the non-protonated As(V)

356

complexes are relatively large, indicating the reaction of these complexes may be fast. The kd

357

values of the other bidentate complexes for As(V) and Pb(II), however, are much smaller due to 13



358

the large metal binding constants (equation 4), so that our model would predict those sites to

359

control the kinetic behavior of As(V) and Pb(II) at much longer time scales.

360

The adsorption rate coefficients for all ferrihydrite binding sites are presented in Figure 5

361

for all four metals, which was shown as a function of reaction pH and adsorbed metal

362

concentrations in each surface binding site. The ka values decreased with the increase of the total

363

adsorbed metal concentrations in specific binding sites, and, with the increase of pH, the ka

364

values increased for Cu(II) and Pb(II) but decreased for As(V) and Cr(VI). For each metal, the ka

365

values may vary a few orders of magnitude for different ferrihydrite sites, indicating the

366

importance to consider the nonlinear binding behavior of metal reactions with ferrihydrite for

367

both cations and oxyanions.

368

Model Assessment and Environmental Implications. In this study, the CD-MUSIC

369

model was integrated into the cation and oxyanion adsorption/desorption kinetics model through

370

the relationships between the reaction rate coefficients and the equilibrium binding properties for

371

ferrihydrite bindings sites. The current model had only one fitting parameter for each metal, and

372

has shown good applicability to both cations and oxyanions under various reaction conditions. It

373

should also be recognized that, in the kinetics model, the number of surface complexes may vary

374

significantly among different metals as formulated in the CD-MUSIC model, and, in theory, each

375

specific binding mechanism will require one additional fitting parameter (equation 4). It can also

376

be coupled with the transport processes and incorporated into reactive transport models using the

377

component additivity approach.53, 54 In natural environments, other competing ions or ligands

378

may be present, and it is thus desired to incorporate the effects of other important ligands in the

379

future study.55-58 In addition, ferrihydrite minerals in natural environment may differ from the

380

synthetic ferrihydrite suspensions, and the solution conditions, e.g. ionic strength and pH, may

381

vary significantly from the conditions tested in this study. Our model, in principle, can be applied

382

to various other environmental conditions and future work is desired to test its applicability.

383

In natural environment, due to the frequent changes of solution chemistry conditions and

384

the dynamic behavior of iron mineral formation/transformation,59, 60 the adsorption and

385

desorption kinetics of metals on ferrihydrite plays an essential role controlling the dynamic

386

speciation of both cations and oxyanions. Based on the rate coefficients obtained in this study,

387

the rates of cations and oxyanions adsorption to the weak bidentate sites of ferrihydrite are 14


Page 14 of 25

Page 15 of 25


388

relatively rapid. However, for those medium and/or strong binding sites, they may account for

389

the long-term slow metal adsorption and desorption kinetics. For Pb(II), those medium and

390

strong binding sites have small quantity, which likely is important in uncontaminated or mildly

391

contaminated sites. For As(V), the formation of the non-protonated or protonated bidentate

392

complexes may play a dominant role at different contaminated sites. For both Cu(II) and Cr(VI),

393

it appears that the kinetic behavior of all surface complexes is similar and a simple model would

394

be appropriate. All these factors should be specifically considered when studying the fate of

395

cation and oxyanion contaminants in the environment. Our work has provided a unified

396

theoretical framework to predict the adsorption and desorption kinetics of both cations and

397

oxyanions, and have implications for predicting the bioavailability, fate and transport of both

398

cations and oxyanions, especially under environmental conditions favoring the reactions with

399

those strong binding sites of ferrihydrite.

400

Acknowledgments

401

We thank Dr. Jon Petter Gustafsson for his comments on Visual MINTEQ calculations. Funding

402

was provided by the National Science Foundation of China (Project number: 41573090),

403

Guangdong Innovative and Entrepreneurial Research Team Program (No. 2016ZT06N569), and

404

the Thousand Talent Program for Young Outstanding Scientists of China.

405

Supporting Information

406

The Supporting Information is available free of charge on the ACS Publications website,

407

including additional details of the batch, stirred-flow and TEM experiments, details of the model,

408

and additional figures.

15



Page 16 of 25

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References

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19. Lofts, S.; Tipping, E., An assemblage model for cation binding by natural particulate matter. Geochim. Cosmochim. Acta 1998, 62, (15), 2609-2625. 20. Subramaniam, K.; Vithayaveroj, V.; Yiacoumi, S.; Tsouris, C., Copper uptake by silica and iron oxide under high surface coverage conditions: surface charge and sorption equilibrium modeling. J. Colloid Interface Sci. 2003, 268, (1), 12-22. 21. Wang, Z.; Ulrich, K.-U.; Pan, C.; Giammar, D. E., Measurement and modeling of U(IV) adsorption to metal oxide minerals. Environmental Science & Technology Letters 2015, 2, (8), 227-232. 22. Johnston, C. P.; Chrysochoou, M., Investigation of chromate coordination on ferrihydrite by in situ ATR-FTIR spectroscopy and theoretical frequency calculations. Environ. Sci. Technol. 2012, 46, (11), 5851-5858. 23. Waychunas, G. A.; Fuller, C. C.; Rea, B. A.; Davis, J. A., Wide angle X-ray scattering (WAXS) study of “two-line” ferrihydrite structure: Effect of arsenate sorption and counterion variation and comparison with EXAFS results. Geochim. Cosmochim. Acta 1996, 60, (10), 17651781. 24. Waychunas, G. A.; Rea, B. A.; Fuller, C. C.; Davis, J. A., Surface chemistry of ferrihydrite: Part 1. EXAFS studies of the geometry of coprecipitated and adsorbed arsenate. Geochim. Cosmochim. Acta 1993, 57, (10), 2251-2269. 25. Moon, E. M.; Peacock, C. L., Adsorption of Cu(II) to ferrihydrite and ferrihydritebacteria composites: Importance of the carboxyl group for Cu mobility in natural environments. Geochim. Cosmochim. Acta 2012, 92, 203-219. 26. Wang, X.; Li, W.; Harrington, R.; Liu, F.; Parise, J. B.; Feng, X.; Sparks, D. L., Effect of ferrihydrite crystallite size on phosphate adsorption reactivity. Environ. Sci. Technol. 2013, 47, (18), 10322-10331. 27. Gu, C.; Wang, Z.; Kubicki, J. D.; Wang, X.; Zhu, M., X-ray absorption apectroscopic quantification and speciation modeling of sulfate adsorption on ferrihydrite surfaces. Environ. Sci. Technol. 2016, 50, (15), 8067-8076. 28. Hiemstra, T.; Van Riemsdijk, W. H., A surface structural model for ferrihydrite I: Sites related to primary charge, molar mass, and mass density. Geochim. Cosmochim. Acta 2009, 73, (15), 4423-4436. 29. Hiemstra, T.; Zhao, W., Reactivity of ferrihydrite and ferritin in relation to surface structure, size, and nanoparticle formation studied for phosphate and arsenate. Environmental Science-Nano 2016, 3, (6), 1265-1279. 30. Ponthieu, M.; Juillot, F.; Hiemstra, T.; van Riemsdijk, W. H.; Benedetti, M. F., Metal ion binding to iron oxides. Geochim. Cosmochim. Acta 2006, 70, (11), 2679-2698. 31. Yiacoumi, S.; Tien, C., Modeling adsorption of metal ions from aqueous solutions: II. transport-controlled cases. J. Colloid Interface Sci. 1995, 175, (2), 347-357. 32. Yiacoumi, S.; Tien, C., Modeling adsorption of metal ions from aqueous solutions: I. reaction-controlled cases. J. Colloid Interface Sci. 1995, 175, (2), 333-346. 33. Yiacoumi, S.; Tien, C., Kinetics of Metal Ion Adsorption from Aqueous Solutions: Models, Algorithms, and Applications. Kluwer Academic Publishers: Norwell, MA, 1995. 34. Scheinost, A. C.; Abend, S.; Pandya, K. I.; Sparks, D. L., Kinetic controls on Cu and Pb sorption by ferrihydrite. Environ. Sci. Technol. 2001, 35, (6), 1090-1096. 35. Subramaniam, K.; Yiacoumi, S., Modeling kinetics of copper uptake by inorganic colloids under high surface coverage conditions. Colloids and Surfaces A: Physicochemical and Engineering Aspects 2001, 191, (1), 145-159. 17



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36. Swedlund, P. J.; Holtkamp, H.; Song, Y.; Daughney, C. J., Arsenate–Ferrihydrite systems from minutes to months: A macroscopic and IR spectroscopic study of an elusive equilibrium. Environ. Sci. Technol. 2014, 48, (5), 2759-2765. 37. Farrell, J.; Chaudhary, B. K., Understanding arsenate reaction kinetics with ferric hydroxides. Environ. Sci. Technol. 2013, 47, (15), 8342-8347. 38. Schwertmann, U.; Cornell, R. M., Iron oxides in the laboratory: preparation and characterization. 2nd ed. ed.; Wiley-VCH: Weinheim, 2000. 39. Carski, T. H.; Sparks, D. L., A modified miscible displacement technique for investigating adsorption-desorption kinetics in soils. Soil Science Society of America Journal 1985, 49, (5), 1114-1116. 40. Seyfried, M. S.; Sparks, D. L.; Bar-Tal, A.; Feigenbaum, S., Kinetics of calciummagnesium exchange on soil using a stirred-flow reaction chamber. Soil Science Society of America Journal 1989, 53, (2), 406-410. 41. Yin, Y.; Allen, H. E.; Huang, C. P.; Sparks, D. L.; Sanders, P. F., Kinetics of mercury(II) adsorption and desorption on soil. Environ. Sci. Technol. 1997, 31, (2), 496-503. 42. Shi, Z.; Di Toro, D. M.; Allen, H. E.; Ponizovsky, A. A., Modeling kinetics of Cu and Zn release from soils. Environ. Sci. Technol. 2005, 39, 4562-4568. 43. Shi, Z.; Di Toro, D. M.; Allen, H. E.; Sparks, D. L., A WHAM-based kinetics model for Zn adsorption and desorption to soils. Environ. Sci. Technol. 2008, 42 5630-5636. 44. Shi, Z.; Di Toro, D. M.; Allen, H. E.; Sparks, D. L., A general model for kinetics of heavy metal adsorption and desorption on soils. Environ. Sci. Technol. 2013, 47, (8), 3761. 45. Amacher, M. C., Methods of Obtaining and Analyzing Kinetic Data. In Rates of Soil Chemical Processes, Sparks, D. L.; Suarez, D. L., Eds. Soil Science Society of America: Madison, WI, 1991; pp 19-59. 46. Kandegedara, A.; Rorabacher, D. B., Noncomplexing tertiary amines as “better” buffers covering the range of pH 3−11. temperature dependence of their acid dissociation constants. Anal. Chem. 1999, 71, (15), 3140-3144. 47. Shi, Z.; Wang, P.; Peng, L.; Lin, Z.; Dang, Z., Kinetics of heavy metal dissociation from natural organic matter: roles of the carboxylic and phenolic Sites. Environ. Sci. Technol. 2016, 50, (19), 10476–10484. 48. Tiberg, C.; Gustafsson, J. P., Phosphate effects on cadmium(II) sorption to ferrihydrite. J. Colloid Interface Sci. 2016, 471, 103-111. 49. Gustafsson, J. P., Visual MINTEQ ver. 3.1. Available at http://vminteq.lwr.kth.se/download/ [Verified 5 September 2016]. 2015. 50. Wang, Z.; Giammar, D. E., Mass action expressions for bidentate adsorption in surface complexation modeling: Theory and practice. Environ. Sci. Technol. 2013, 47, (9), 3982-3996. 51. Wang, X.; Zhu, M.; Koopal, L. K.; Li, W.; Xu, W.; Liu, F.; Zhang, J.; Liu, Q.; Feng, X.; Sparks, D. L., Effects of crystallite size on the structure and magnetism of ferrihydrite. Environmental Science: Nano 2016, 3, (1), 190-202. 52. Gustafsson, J. P.; Sjöstedt, C., Revised best-fit parameters for arsenate adsorption to ferrihydrite. In Arsenic Research and Global Sustainability, CRC Press: 2016; pp 139-140. 53. Davis, J. A.; Coston, J. A.; Kent, D. B.; Fuller, C. C., Application of the surface complexation concept to complex mineral assemblages. Environ. Sci. Technol. 1998, 32, (19), 2820-2828. 54. Alessi, D. S.; Fein, J. B., Cadmium adsorption to mixtures of soil components: Testing the component additivity approach. Chem. Geol. 2010, 270, (1–4), 186-195. 18


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55. Weng, L. P.; Van Riemsdijk, W. H.; Hiemstra, T., Effects of fulvic and humic acids on arsenate adsorption to goethite: Experiments and modeling. Environ. Sci. Technol. 2009, 43, (19), 7198-7204. 56. Weng, L. P.; Van Riemsdijk, W. H.; Koopal, L. K.; Hiemstra, T., Adsorption of humic substances on goethite: Comparison between humic acids and fulvic acids. Environ. Sci. Technol. 2006, 40, (24), 7494-7500. 57. Weng, L. P.; Van Riemsdijk, W. H.; Koopal, L. K.; Hiemstra, T., Ligand and Charge Distribution (LCD) model for the description of fulvic acid adsorption to goethite. J. Colloid Interface Sci. 2006, 302, (2), 442-457. 58. Hinkle, M. A. G.; Wang, Z.; Giammar, D. E.; Catalano, J. G., Interaction of Fe(II) with phosphate and sulfate on iron oxide surfaces. Geochim. Cosmochim. Acta 2015, 158, 130-146. 59. Tishchenko, V.; Meile, C.; Scherer, M. M.; Pasakarnis, T. S.; Thompson, A., Fe2+ catalyzed iron atom exchange and re-crystallization in a tropical soil. Geochim. Cosmochim. Acta 2015, 148, 191-202. 60. Wang, Z.; Schenkeveld, W. D. C.; Kraemer, S. M.; Giammar, D. E., Synergistic effect of reductive and ligand-promoted dissolution of goethite. Environ. Sci. Technol. 2015, 49, (12), 7236-7244.

563

19



564

Page 20 of 25

Table 1. Desorption rate coefficients (kdi) of four cations and oxyanions Bidentate complexes (min-1)

Monodentate complexes (min-1)

As(V)

565

1.29×10-2

Non-protonated

Protonated

1.51×10-1

4.46×10-4

Weak

Medium

Strong

Cr(VI)

--

7.14×10-2

--

--

Cu(II)

--

1.07×10-1

--

--

Pb(II)

--

1.69×10-1

7.81×10-3

7.90×10-4

-- Not applicable

566

20


Page 21 of 25

567 568 569 570


Figure 1. Adsorption edges of (a) As(V), (b) Cr(VI), (c) Pb(II) and (d) Cu(II) and CD-MUSIC modeling results. Solid lines are CD-MUSIC model predictions. The initial metal concentrations (C0) and the ferrihydrite concentrations ([Fh]) are presented in the legends. The background electrolyte was 10 mM NaNO3.

571

21



Page 22 of 25

572

573 574 575 576 577

Figure 2. STEM-EDS mappings of As(V), Cr(VI), Cu(II), and Pb(II) after 4 h adsorption to ferrihydrite: (1-5) As(V) adsorption samples; (6-10) Cr(VI) adsorption samples; (11-15) Cu adsorption samples; (16-20) Pb adsorption samples. (2, 7, 12, 17) O mapping; (3, 8, 13, 18) Fe mapping; (4, 9, 14, 19) metal mapping (5, 10, 15, 20); Fe+O+Metal color overlays.

578

22


Page 23 of 25

579 580 581 582 583 584 585 586 587


Figure 3. Kinetics of As(V), Cr(VI), Pb(II), and Cu(II) adsorption and desorption with different ferrihydrite concentrations, reaction pH, and influent metal concentrations. As(V): (a) (RMSE = 0.26, 0.53, 0.36), (b) (RMSE = 0.25, 0.20, 0.09 ) and (c) (RMSE =0.78, 0.69, 0.46); Cr(VI): (d) (RMSE = 0.30, 0.26, 0.32), (e) (RMSE = 1.11, 0.80, 0.79, 0.43) and (f) (RMSE = 1.47, 0.80); Pb(II): (g) (RMSE =0.43, 0.38, 0.28), (h) (RMSE =0.94, 0.82, 0.73, 0.50) and (i) (RMSE = 2.25, 4.07, 2.27 ); Cu(II): (j) (RMSE = 3.77, 1.35, 0.57), (k) (RMSE = 0.65, 0.91, 0.34) and (l) (RMSE = 4.91, 5.89, 2.17, 0.82). The symbols represent the experimental data, and the solid lines are model calculations.

588

23



589 590 591 592 593

Figure 4. Distribution of (a)-(d) As(V) ([Fh] = 0.13 g L-1), and (e)-(h) Pb(II) ([Fh] = 1.3 g L-1) among different ferrihydrite binding sites during the adsorption and desorption kinetic processes. The reaction conditions are presented in the legend. [Fh]: ferrihydrite concentrations in the experiments. 24


Page 24 of 25

Page 25 of 25


594 595 596 597 598

Figure 5. The variations of adsorption rate coefficients (kai) of cation/oxyanion for various ferrihydrite binding sites under different reaction conditions. The ranges of Cpi values of each binding site are determined by the kinetic modeling results under the experimental conditions. Refer to the text for the definition of each binding site.

599

25


Kinetics of Cation and Oxyanion Adsorption and Desorption on

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