A Unified Surface Complexation Modeling Approach for Chromate

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Environmental Modeling

A unified surface complexation modeling approach for chromate adsorption on iron oxides Nefeli Bompoti, Maria Chrysochoou, and Michael L. Machesky Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.9b01183 • Publication Date (Web): 07 May 2019 Downloaded from http://pubs.acs.org on May 8, 2019

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Environmental Science & Technology

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A unified surface complexation modeling approach for chromate adsorption on iron oxides

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Nefeli Maria Bompoti*,†, Maria Chrysochoou† and Michael L Machesky‡

3 4

†Department

of Civil and Environmental Engineering, University of Connecticut, Storrs, CT USA

5 6

‡Illinois

State Water Survey, Prairie Research Institute, Champaign, IL USA

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ABSTRACT

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A Multi–start optimization algorithm for

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surface complexation equilibrium parameters

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(MUSE) was applied to a large and diverse

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dataset for chromate adsorption on iron

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(oxy)hydroxides (ferrihydrite and goethite).

13

Within the Basic Stern and the charge-

14

distribution multisite complexation (CD-MUSIC) framework, chromate binding constants and the

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Stern Layer capacitance were optimized simultaneously to develop a consistent parameter set for

16

surface complexation models. This analysis resulted in three main conclusions regarding the model

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parameters: a) there is no single set of parameter values that describe such diverse datasets when

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modeled independently, b) parameter differences among the datasets are mainly due to different

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amounts of total sites, i.e. surface area and surface coverages, rather than structural differences

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between the iron (oxy)hydroxides, and c) unified equilibrium constants can be extracted if total

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site dependencies are taken into account. Implementing the MUSE algorithm automated the

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process of optimizing the parameters in an objective and consistent manner, and facilitated the

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extraction of predictive relationships for unified equilibrium constants. The extracted unified

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parameters can be implemented in reactive transport modeling in the field by either adopting the

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appropriate values for each surface coverage or by estimating error bounds for different conditions.

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An evaluation of a forward model with unified parameters successfully predicted chromate

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adsorption for a range of capacitance values.

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Keywords: Adsorption, Chromate, Surface complexation modeling, MUSE, CD-MUSIC, Iron

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oxides, Ferrihydrite, Goethite.

30 31

INTRODUCTION

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Surface complexation models (SCMs) have been proven superior tools compared to traditional

33

distribution factors (Kd), to describe adsorption processes and estimate the partitioning of ions at

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the solid-solution interface.1 In the component additivity (CA) approach, the modeler assumes that

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adsorption on a mineral assemblage can be predicted accounting for each individual mineral

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surface when surface properties and surface complexation reactions are known.2 Although SCMs

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are mechanistic and thus can theoretically describe environmental conditions, they have been used

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mostly for the description of laboratory adsorption data. Their transferability to real systems is

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hindered by the high degree of parametrization required, and subsurface transport modeling is

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usually performed by empirical relationships or by generalized component (GC) models, which

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treat all soil components as one generic surface.1–3 Reducing the number of parameters to be

42

determined or estimated in a natural system could be accomplished by considering various classes

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of surfaces, instead of individual minerals, as in the Particle Assemblage Model of Lofts and

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Tipping,4 adopted later by Bonten et al.5 and Serrano et al.6 These studies utilized either non-


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electrostatic models or only a diffuse layer, in order to simplify the approach and reduce the

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number of fitted parameters. Surface types included organic matter, iron oxides, aluminum oxides,

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manganese oxides, silicates and clay minerals.4 The success of this approach is difficult to judge

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on the basis of these studies, which utilized real soils with highly variable properties,7 and not

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laboratory data on pure mineral phases.

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The objective of this study is to adopt a hybridized approach utilizing characteristics of the particle

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assemblage model in our effort to scale up the component additivity approach for one surface class

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(iron (oxy)hydroxides, and specifically goethite (GH) and ferrihydrite (FH)), and one contaminant

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(chromate, CrO42-), and investigate whether a unified model can capture a variety of experimental

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conditions. The parameters required can be obtained from crystallographic studies (site densities,

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mineral face distribution), binding geometries (CD values), estimated by the properties in each

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individual system (specific surface area (SSA), solid concentration (Gs)), or optimized by fitting

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experimental data (capacitance, proton, electrolyte, and ligand binding constants).

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The Rossendorf Expert System for Surface and Sorption Thermodynamics (RES3T)8 database is

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useful for retrieving and summarizing literature parameters for many mineral-ligand systems. Thus

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far, the parameters reported are highly variable even for one system and one particular type of

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model.

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We hypothesize that there are four possible reasons for parameter variability:

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1. Optimization inconsistencies: SCM fitting algorithms are often trapped in local minima

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resulting in an inability to find the global optimum parameters. In addition, adoption of

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subjective judgement on the goodness of fit instead of quantitative criteria may also lead

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to selection of non-optimal parameters. Better optimization tools can facilitate the



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extraction of parameters towards an internally consistent thermodynamic database. In

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previous work, we developed a MUlti–start optimization algorithm for Surface

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complexation Equilibrium parameters (MUSE) for that purpose.9

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2. Interdependency of SCM parameters: Thermodynamic constants for surface complexation

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depend on other parameters (i.e. capacitance, site density, surface area).10–14 Optimizing

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certain parameters implies fixing others, quite often arbitrarily, which renders the

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comparison of log K values from different studies problematic. Also, the structural and

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adopted proton binding model for a surface can differ among studies, influencing other

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parameters.

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3. Poor representation of surface interactions: SCMs are approximations of the

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physicochemical properties of the solid-solution interface. Even though considerable effort

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has been made to refine the mathematical description of bonding mechanisms and the

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electrostatic gradient near the surface, there is still uncertainty as to whether a certain

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formulation accurately captures those interfacial properties.

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4. Experimental or analytical error: Errors in pH, solid, and ligand concentration

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measurements increase the uncertainty of extracted parameters. However, quantifying

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these errors is rarely attempted.

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Fundamentally, this is a problem with contradictory challenges: greater complexity is needed to

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have a more accurate representation of interfacial properties, while less complexity is needed to

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reduce the number of required parameters and characterization demands for scaling up purposes.

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Both the GC and the Particle Assemblage Models are promising approaches to bridge these

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contradicting demands. This study builds on the particle assemblage approach, which offers the


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advantage of adopting insights from mechanistic studies on pure mineral surfaces. Specifically,

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we build on previous studies that attempted to unify the description of iron oxide surface behavior.

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Dzombak and Morel (1990) described ion adsorption on FH by combining datasets from different

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studies using a generic 2-pK protonation formulation in combination with the Gouy-Chapman

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diffuse layer model. Although the FH structure was not yet known, the authors used mean and

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median values of site densities estimated from experimental data. Later studies employed the

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goethite surface structure and adjusted the proportion of crystallographic faces to describe the FH

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surface, such as the CD-MUSIC approach for adsorption of uranyl and carbonate,15 and a 2-pK

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triple-layer model (TLM) for proton and arsenate adsorption.16 Ponthieu et al.17 used the CD–

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MUSIC formalism to describe cation binding on both ferrihydrite and goethite using the goethite

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surface structure as a proxy and adjusted the crystallographic faces and inner-layer capacitance

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values to describe FH behavior. Similarly, Han and Katz14 rationalized the variable reactivity of

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goethites using a CD-MUSIC model in which crystallographic face distributions, inner-layer

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capacitance values, and protonation constants were correlated to differences in specific surface

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area.

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This study will build upon these previous approaches by addressing two fundamental questions:

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

two iron (oxy)hydroxides or other factors?

106 107

Is the variability in specific adsorption log Ks driven by structural differences between the



Can a unified model capture chromate adsorption on iron (oxy)hydroxides?

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MATERIALS AND METHODS

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Cr adsorption datasets. Batch adsorption pH envelopes from the literature were utilized in this

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study (Table S1), covering a broad range of surface coverages, background electrolyte types and

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concentrations, and sorbent surface areas. For all FH studies, a freshly precipitated suspension was



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either explicitly noted or assumed in order to adopt the corresponding proton charge model

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discussed by Bompoti et al18. The measured Brunauer, Emmett, and Teller (BET) surface area was

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used for modeling GH datasets, while for FH studies the theoretical value of 600 m2/g was

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commonly adopted, which relies on the empirical estimate of particle size.19

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A challenge in modeling diverse literature datasets was the inclusion of CO2, which is an important

117

competitive ligand for chromate20 and other anions. Two of the studies (Honeyman21 and Ajouyed

118

et al.22), did not explicitly mention experimental measures to minimize CO2. We have discussed

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in previous work how consideration of carbonate adsorption affects fitted results.9 Although all

120

studies were included in the modeling exercise, the parameters extracted by studies with non-

121

quantified CO2 (Honeyman21 and Ajouyed et al.22) were excluded from the statistical analysis. The

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datasets of Weerassoriya and Tobschall23 were also excluded from the statistical analysis, as the

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average extracted equilibrium constant were much lower than for the other goethite studies (Table

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S5).

125

Surface Complexation Modeling with the MUSE algorithm. A Basic Stern CD-MUSIC SCM

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is our model of choice. It offers the advantages of a Stern Layer capacitance value being the only

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unknown electrostatic parameter, while the CD-MUSIC formalism allows for both incorporating

128

spectroscopic data via the CD value, and multisite protonation reactions via the MUSIC approach.

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A complete description of surface reactions involves two consecutive steps: a) developing a unified

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model for proton adsorption, and b) developing a unified model for specific ion adsorption. In this

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paper, we adopted proton affinities specific to the surface structure of each mineral. Table S2

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summarizes the surface properties adopted for the two minerals. Ferrihydrite surface charge was

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simulated by a 3–site model discussed in previous work.18 Surface properties for goethite were

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based on Venema et al.24 and included three surface sites: one singly coordinated hydroxyl (SC)


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and one triply coordinated hydroxyl (TC) located on the (1-10) face, and one SC on the (021)

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face.24 For goethite, the dominant faces were taken to be the (1-10) at 90% and the (021) at 10%

137

of the total surface area. Other studies have shown the effect of different mineral face coordination

138

on the adsorption of ions.25–27 To simplify the surface model, sites of the same type located on the

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same face were merged into one by summing their site densities. The protonation log Ks for

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goethite were adopted from Venema et al.24 For the merged sites, the log KH+ values were fit to

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titration curves. The fitted surface charge curves are shown in Figure S1. The Stern Layer

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capacitance values fit to several surface charge datasets for both minerals ranged from 0.7 to 1.36

143

F/m2 for FH (shown in previous work)18, and from 0.7 to 1 F/m2 for GH (given in the respective

144

section of the SI).

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Using this proton affinity model, we developed a single model for chromate adsorption. This relies

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on the hypothesis that proton affinity is different for each mineral as reflected by the charging

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curves, while specific ion affinity is similar, at least for chromate. Once the differences in surface

148

structure are taken into account, the interaction energy for sorption of an ion is approximately the

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same for all iron oxides.28 The hypothesis is also supported by spectroscopy, which shows that

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both monodentate and bidentate complexes form on FH29,30 and GH.31 Table S3 summarizes the

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surface complexation reactions, CD factors, and equilibrium constants. The CD values were fixed

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at the commonly accepted values for monodentate and bidentate species.32 Fixing the CD values

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also enabled us to better constrain the capacitance value range, since the CD values describe the

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charge allocation of the adsorbing ion between the Stern and surface planes, and hence are highly

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correlated with the Stern Layer capacitance.

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The optimization was performed using the MUSE algorithm, a fitting algorithm built in

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MathematicaTM notebooks that can be combined with any type of SCM.9 MUSE offers an unbiased



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optimization of multiple parameters utilizing a multistart-algorithm to create a matrix of random

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initial guesses, and a local optimizer that performs a local optimization for all initial parameters.

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Each of the solutions are then sorted based on the mean squared error (MSE). However, the process

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depends on the number of initial guesses. In a previous study, we have shown that 500 initial points

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are sufficient to find the global optimum,9 and therefore the same approach was adopted in this

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study. The optimization was performed by constraining the two log K values (log KMD and log KBD

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for the monodentate and bidentate species, respectively), within the following ranges: log KMD [0,

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25], log KBD [10, 30]. This was facilitated by fitting the multivariate curve resolution with

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alternating least-squares (MCR-ALS) profiles, as shown in a previous study.9

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An important consideration for any optimization problem is choosing the fixed and definable

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parameters. We have chosen the parameters for optimization from the perspective of an end user,

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who will typically adopt an SCM for forward modeling purposes: that is, they will adopt the site

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densities, surface structure and all binding constants (proton, electrolyte, ion densities) as an

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internally consistent set of parameters and then utilize experimental values for solid and ion

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concentrations and specific surface area. The SSA effect will be discussed later on, here we address

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the problem of capacitance. In the overwhelming majority of modeling studies, the capacitance is

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taken as a constant value from the literature, usually in the vicinity of 1 F/m2 for the inner Stern

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Layer. Stern Layer capacitance is defined as 𝐶𝑆𝑡𝑒𝑟𝑛 =

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which depends on the radius or binding distance of the adsorbing ion, and εStern is the permittivity

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of the Stern Layer, which depends both on the surface charge and the charge located within the

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Stern Layer, including charge oriented water molecules.33 Clearly, capacitance is not a constant

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but is variable for different faces of a crystal and possibly also varies with charge or surface

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coverage. Boily34 developed the Variable Capacitance Model in order to address the variability

𝜀0𝜀𝑆𝑡𝑒𝑟𝑛 𝛿

where δ is the Stern Layer thickness,


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imposed by different crystal faces and the presence of ions with different radii. Machesky et al.35

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postulated that Stern Layer capacitance values may depend on surface charge. However, it is not

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practical to incorporate such detail into SCMs designed to fit a wide variety of adsorption data.

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This discussion only serves to illustrate the following premise: the capacitance value is an average

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parameter for any SCM and is not “attached” to a particular dataset. Rather than taking a constant

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value, we believe an end user will be better served by optimizing the capacitance depending on

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experimental conditions, within a realistic range of values.

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In this study, the capacitance range was calculated using the Stern layer capacitance formula 𝐶𝑠𝑡𝑒𝑟𝑛

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=

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Å34 for Cl-) and range of dielectric constants for mineral/water interfacial properties, εstern [35,

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53],34,37 resulting in lower (0.62 F/m2) and upper (1.8 F/m2) capacitance values. Clearly, the range

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of calculated capacitance values is wider than the range of optimized (from surface charge data)

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for FH (0.7-1.36 F/m2) and GH (0.7-1 F/m2). Since the majority of the studies do not provide

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surface charge titration data, it is uncertain what range of capacitance values to adopt. To better

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account for that uncertainty, we decided to perform the optimizations using the C [0.62, 1.8] F/m2

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range of capacitance values.

𝜀0𝜀𝑠𝑡𝑒𝑟𝑛 𝛿

accounting for the plane thickness for different adsorbing ions (5 Å36 for CrO42- or 2.6

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RESULTS AND DISCUSSION

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Effect of variable capacitance. A sensitivity analysis was conducted for two goethite studies with

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6 datasets each (Measure and Fish38 and Xie et al.39), to evaluate the effect of capacitance range

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on the optimized parameters (C and log Ks). One additional range of capacitance values was

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evaluated (0.3 to 3 F/m2) as well as the scenario of constant capacitance at 1.1 F/m2. The effect of

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choosing different capacitance ranges or a constant value was generally small across the 12



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datasets (Figure S2), with standard deviations less than one log K unit. The largest discrepancies

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of 3-4 log K units were observed in datasets that tended to optimize toward large or very low

206

capacitance values, so that a broader range resulted in the capacitance shifting towards the upper

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or lower extreme, i.e. a capacitance value of 0.3 or 3 F/m2. The two datasets of Xie et al.39 with

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the highest standard deviations for monodentate species in the sensitivity analysis (X1 and X3 in

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Figure S2) also yielded the lowest log KMDs. Because of the extreme values that the optimized

210

capacitance had in these datasets, the constant capacitance scenario in this case yielded a very

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different result compared to the three “floating” scenarios, causing the high standard deviation.

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Another feature of these datasets is that their optimal solutions are uncertain; for example, for the

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dataset X3 in Figure S3, the log KMD values varied from 2.7 (best solution) to 7.7 in the 15th best

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solution in the constant capacitance scenario, while the MSE was the same up to 6 significant

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digits. The log KBD variability for these six solutions was in the second significant digit. The

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standard deviation across the four different capacitance scenarios was very low for that parameter,

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which further supports the observation that the instability of a parameter renders it susceptible to

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large changes when another parameter is varied. This analysis yields the following overall

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observations: a) the chosen range of capacitance has a small effect on the optimal log K, except

220

for datasets that yield extreme values; and, b) because it is unclear why some datasets yield extreme

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values (potentially due to experimental errors), the statistical approach adopted here is a much

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better way for determining global log K values for a particular surface-ligand pair. Finally,

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evaluating the output of the algorithm in terms of several optimal solutions is worthwhile to assess

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the stability of the top solution with the best MSE.


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Extracted parameters. Optimized parameters and fitted data using the [0.62, 1.8 F/m2]

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capacitance range are given in Table S4 and S5, and Figures S3 – S6. The boxplots of the extracted

227

parameters for each mineral are shown in Figure 1 and the corresponding values are in Table S6.

228

A comparison between the log Ks as extracted by the MUSE algorithm and the values reported in

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the literature was performed. The literature values were adopted from the RES3T database for

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chromate adsorption on ferrihydrite and goethite. Figure S7 and Figure 1 also shows a comparison

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between the MUSE extracted parameters and the respective RES3T values, given as boxplots.

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233 234

Figure 1. Comparison of average Log KMD and Log KBD log Ks in the RES3T database and

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values optimized with MUSE: (a) RES3T – MD, (b) MUSE – MD, (c) RES3T – BD, and (d)

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MUSE – BD.

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The extracted log KMD had mean values of 10.18 ± 0.74 and 11.58 ± 0.80 for ferrihydrite and

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goethite, respectively, while log KBD was 18.20 ± 1.34 and 19.95 ± 2.64 (Table S6). The mean



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capacitance values (Table S6) were 1.18 ± 0.44 for ferrihydrite and 1.56 ± 0.37 for goethite. The

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variability of the exacted parameters was reduced in terms of interquartile range between the

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MUSE optimized parameters and the RES3T values, with the exception of the bidentate constant

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of ferrihydrite that increased by 0.7 log K units. The bidentate constant of goethite exhibited an

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interquartile range of 2.79 log K units in RES3T database while the MUSE reduced that range to

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1.14 log K units. This was achieved despite the higher number of datasets analyzed (9 datasets for

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ferrihydrite and 25 for goethite compared to 4 and 9 in RES3T).

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Effect of Specific Surface area. A sensitivity analysis on the surface area was performed for two

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FH adsorption datasets (Dataset 1 from Zachara et al.40 and Dataset 3 from Hsia et al.),41, and three

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GH datasets (Dataset 1 from Villalobos and Pérez-Gallegos,42 Dataset 4 form Xie et al.,39 and

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Dataset 5 from Mesuere and Fish).38 The results are shown in Figure 2 and values given in Table

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S7. The sensitivity analysis was expanded to a wider than plausible range of surface area for

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goethite only to better illustrate the common trends between the two minerals.

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253


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Figure 2. Surface area effect on (a) monodentate and (b) bidentate thermodynamic constants,

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and (c) capacitance values for FH and GH. Data adopted from Zachara et al. (1987) (blue

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diamonds) and Hsia et al. (1993) (cyan circles) for FH, and from Villalobos et al. (2008) (red,

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open triangles), Xie et al. (2015) (red, open squares), and Mesuere and Fish (1992) (green, open

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circles) for GH.

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An immediate observation is that most datasets converge to a single value for both Log KMD and

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Log KBD, when tested with the lowest SSA of 50 m2/g. This is approximately 11.8 for log KMD and

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~21 for log KBD. Both equilibrium constants follow an inverse logarithmic trend with SSA, even

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though “denticity effects” are taken into account in the model formulation. An important outcome

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of this analysis is that the SSA effect can account for up to two log units of variability for SSAs

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ranging between 50 and 600 m2/g. The slopes of the linearized logarithmic trends ranged from -

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0.29 to -0.88 for log KMD, and from -0.41 to -0.89 for log KBD (Table S7). The slope values are in

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turn, linearly related to surface coverage (Figure S8), i.e. the higher the surface coverage, the

268

higher the slope, and the log Ks are more dependent on the value of the surface area. As such,

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surface coverage emerged as an additional factor that affects log K values. Capacitance values are

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also dependent on surface area (Figure 2c). Although, the trend cannot be described by a

271

mathematical equation, we observe that, in most datasets, the higher the surface area, the lower the

272

capacitance values. Datasets with lower surface coverages (GH Dataset 1 from Villalobos and



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Pérez-Gallegos42 and FH Dataset 1 from Zachara et al.)40 exhibited the lowest variability with

274

respect to surface area, for all three parameters. This implies that the uncertainty associated with

275

surface area has a smaller impact on SCM parameters and adsorption prediction at lower surface

276

loadings compared to higher ones.

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Effect of surface coverage. To evaluate the effect of surface coverage, the fitted thermodynamic

278

constants are plotted against surface coverage in Figure 3. The monodentate constant shows a

279

slight surface coverage dependence, while the bidentate constant increases significantly with

280

decreasing surface coverage. In general, the capacitance values increased with increasing surface

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coverage, with the exception of few datasets with very low surface coverage (Figure S9). This

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trend agrees with previous findings that linked double layer capacitance to salt concentration.37,43

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The trend lines for goethite and ferrihydrite have similar slope but the intercepts are offset by 1.1

284

log units for log KMD and 1.5 log units for log KBD. As seen in Figure 2, this is the average

285

difference in log K between low and high SSA values; most ferrihydrite datasets were modeled

286

with SSA 600 m2/g, while for goethite the SSA ranged from 11.6 to 95 m2/g. To illustrate this

287

point further, a SSA normalization was performed using the average slope of the Log K-SSA

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relationships extracted via the sensitivity analysis (Table S7), i.e. 𝐿𝑜𝑔 𝐾𝑛𝑜𝑟𝑚 = 𝐿𝑜𝑔 𝐾 + 0.7 × ln

289

(𝑆𝑆𝐴). As shown in Figure 3c and d, this results in a single relationship for log Knorm dependence

290

on surface coverage for both ferrihydrite and goethite. The normalized log K is an indicator that

291

when the large differences in SSA between the two minerals are accounted for, the log Ks vary in

292

the same way for both FH and GH.


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Figure 3. Equilibrium constants for monodentate: (a) optimized and (c) normalized values, and

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bidentate: (b) optimized and (d) normalized values with respect to surface coverage, for

296

ferrihydrite (FH) and goethite (GH).

297

These results agree with other studies that have shown a dependence of sorption affinity on surface

298

coverage. Dzombak and Morel44 reported a decrease in the chromate affinity constant from 10.85

299

to 10.29, for estimated surface coverages of 0.001 µmol/m2 and 1.48 µmol/m2, respectively. Their

300

interpretation was that at high adsorption densities, the affinity of the surface for the ion becomes

301

too low to compete with the adsorbing protons, thus lowering the sorption constants. Fundamental

302

calorimetric and molecular modeling studies have indicated that the change in log Ks is related to

303

a real change in adsorption energetics. Machesky et al.45 showed that adsorption enthalpies for

304

several ions (salicylate, phosphate, iodate, and fluoride) decreased with increasing surface

305

coverage on goethite at pH 4. Similarly, Kabengi et al.46 measured decreasing enthalpies for

306

chromate adsorption on both ferrihydrite and hematite with increasing surface coverage. Our



307

modeling results suggest the following trends (slopes and R2 values in Figure 3a, 3b): the bidentate

308

constant decreases significantly with surface coverage while the monodentate constant decreases

309

to a smaller, if not negligible, extent. The modeling results and the previous calorimetric studies

310

suggest that as the surface coverage of chromate increases, it is more difficult for the bidentate

311

complex to form due to limited binding sites. Therefore, the relative distribution between the two

312

complexes is different in high/low surface coverage regimes. Differences in surface species with

313

respect to surface coverage were also shown in recent IR spectra for chromate adsorption on FH.47

314

The presence of outer-sphere surface species could also be suspected at high surface coverages,

315

however this scenario is contradicted by recent DFT studies that show prevalence of bidentate

316

species at higher surface coverages.47

317

Forward modeling. The main objective of this approach is to ultimately use a single set of

318

constants to model a complex system. A prerequisite for this is to have an experimental measure

319

of the amount of iron oxide in the solid matrix and the available SSA for the iron oxide fraction.

320

As illustrated above, it is also necessary to have an initial guess for the anticipated surface

321

coverage, which is proportional to the ratio of the initial aqueous concentration to the available

322

sorption sites (Figure S10). The choice of method to estimate the two input parameters (solid

323

concentration and mineral-specific SSA) influences the result and thus the adopted log Ks.

324

The amount of Fe and Al oxides available for surface reactions is commonly measured using

325

selective extraction methods, such as the hot HCl method employed by Davis et al.3, or the

326

dithionite-citrate-bicarbonate (DCB) method48. This approach requires the assumption of a

327

molecular weight to convert Fe mass to a solid concentration. The most recent methods to

328

determine the SSA of Fe/Al oxides in soils are by Hiemstra et al.48,49 and Dong and Wan50, which

329

utilize probe ions to relate sorption capacity to mineral SSA. With phosphate as the probe ion, a


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330

CD-MUSIC model is calibrated for goethite to back-fit the SSA of the oxide fraction, with the

331

total Fe and Al oxide mass determined from a DCB extraction. For the soils studied in Hiemstra

332

et al.48, this approach resulted in very high SSAs, ranging from 200 to 1200 m2/g which the authors

333

interpreted as the presence of nanoparticles in the soils. The humic acid method of Dong and Wan50

334

also requires a comparison with the maximum sorption capacity of a pure goethite obtained under

335

controlled conditions.

336

Clearly, all these parameters (solid concentration, SSA, site densities) ultimately relate to the total

337

amount of surface sites available and refer to the intrinsic properties of the solid. This is in

338

accordance with recent findings suggesting a method to predict goethite crystal face distribution,

339

capacitance, and protonation constants based on BET-SSA.14 Because the surface area (and most

340

likely, the choice of site densities that were not varied in this study) influences the log K value

341

adopted for forward modeling, we propose that both be kept constant based on the mineral choice,

342

and only the solid concentration and the capacitance varied. The effective available solid

343

concentration may be determined using the probe ion method, i.e. either the phosphate51 or the

344

humic acid50 method may be adapted to determine site densities and mineral SSA assuming a

345

representative mineral (FH or GH) and the solid concentration can be fit. Extraction methods may

346

be used for comparison to gauge whether the available SSA is comparable to the one adopted by

347

the model.

348

Based on this study, it is possible to adopt either a goethite-based or ferrihydrite-based model for

349

chromate adsorption, depending on the estimated SSAs (Table 1). The chromate log Ks are

350

equivalent, adjusting for differences in surface area. However, each of the minerals was modeled

351

using a different set of site densities and protonation log Ks. The log Ks to be adopted for forward

352

modeling have to account for the effect of surface coverage, either by directly employing the



Page 18 of 35

353

correlation functions in Figure 3, or by taking average values for low and high coverages, as shown

354

in Table 1. If surface coverage is unknown, then different model scenarios can be created to

355

account for variable conditions. The capacitance may be treated as an adjustable parameter within

356

a narrow range that can “absorb” some of the uncertainty related to surface coverage and surface

357

area.

358

Table 1. Proposed methodology for utilizing SCM parameters for reactive transport modeling. Estimate/ Adjust to fit

Database values Mineral structure, site densities and SSA

Solid concentration

Protonation Log Ks Specific adsorption Log Ks Surface FH GH Coverage MD BD MD BD (umol/ m2) Low (< 1.5) 10.60 19.20 11.70 21.00 High (> 1.5)

10.15

18.00

11.25

Measure in the field

Capacitance (range 0.6-1.8 F/m2)

Solution composition (pH, solutes, ionic strength)

19.80

359

To illustrate this approach, we applied it to all batch adsorption studies. Each dataset was modeled

360

with the respective mineral model, and log Ks chosen on the basis of surface coverage as shown

361

in Table 1; the capacitance was kept constant at two values; the upper (1.8 F/m2) and lower

362

boundary (0.62 F/m2). Selected results are shown in Figure 4 and the remaining results in Figures

363

S11-S14. The shaded areas in Figure 4 represent the range of predicted chromate adsorbed for

364

capacitance values within the range of 0.62-1.8 F/m2. For the majority of the studies, the results

365

are satisfactory and the data fall within the range covered by varying the capacitance alone. Two

366

of the studies that were excluded from the statistics (the studies of Ajouyed et al.22 and

367

Weerasooriya and Tobschall)23 were considered outliers (Table S5), and the study of Honeyman21


Page 19 of 35


368

had several data points that were within the predicted range. Adsorption data collected in high

369

surface coverage regimes show a higher dependence on the capacitance value, which is reflected

370

in a wider range of predicted values (shaded area in Figure 4). The capacitance value has a higher

371

impact when the surface loading is higher (Figure 4b, 4d), compared to a low surface loading

372

(Figure 4a, 4c).

373

374 375

Figure 4. Forward modeling for FH: (a) at low surface coverage (Zachara et al.40, Davis and

376

Leckie52), (b) at high surface coverage (1 mM Cr(VI) and 0.5 g/L FH), and GH: (c) at low

377

surface coverage (Mesuere and Fish38), and (d) high surface coverage (Grossl et al.53).

378

Shaded areas represent the predicted chromate adsorbed within the lower/ upper capacitance

379

boundaries (0.62-1.8 F/m2), similar to figure (b).



380

To assess the overall ability of the capacitance to capture the uncertainty in forward modeling, a

381

plot of actual versus predicted adsorbed chromate concentrations was created for all experimental

382

values included in the statistical analysis (Figure 5a). The black line in Figure 5 represents the

383

fitted model, where three parameters were optimized for each dataset (log Ks and capacitance).

384

The blue and red line represent the forward model for a lower and upper capacitance boundary,

385

respectively. Both forward models adopted the log K values suggested in Table 1 without fitting

386

any parameters. A linear regression was performed for the fitted model: y=0.98x + 0.002, R2: 0.99,

387

and the forward model with capacitance of 1.8 F/m2 and 0.62 F/m2: y=1.23x + 0.03, R2: 0.89 and

388

y=0.82x + 0.02, R2: 0.92, respectively. The fitted model exhibited a slope close to one, giving the

389

best fit to the actual values, as expected. The forward models included the fitted model predictions,

390

indicating a good range of upper and lower boundaries for capacitance values. Optimal capacitance

391

values are tailored to each dataset and can be identified only when capacitance values are treated

392

a fit parameter. Interpolation of regression slopes also indicates that a single capacitance value of

393

about 0.93 F/m2, could provide adequate predictions.

394 395

Figure 5. Predicted versus actual chromate adsorbed (in umol/m2): (a) for three models: fitted (3

396

parameters), forward for lower (C 0.62 F/m2) and upper (C 1.8 F/m2) boundary, and (b) 95 %

397

confidence and prediction intervals for the fitted model.


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398

The 95% confidence and prediction intervals were calculated for the fitted model (Figure 5b). The

399

prediction interval is approximately constant over the entire range of surface coverage, and is ±0.15

400

umol/m2. This implies that the error associated with prediction is inversely proportional to the

401

surface coverage; at surface coverages less than 0.3 umol/m2, the error exceeds 100% of the actual

402

surface coverage. At the highest surface coverages, the prediction error is a minimum of 10% of

403

the actual surface coverage value.

404

The performance of the forward model is evaluated with respect to the fitted model, accounting

405

for a 5% significance level. The range of results for lower and upper capacitance boundaries were

406

compared with the 95% prediction intervals of the fitted values (Figure S15). For a 5% significance

407

level, only 8.4% of the predicted values plot outside the capacitance range. If we increase the

408

significance level to 10%, the outliers account for the 9.9% of the total data. Since capacitance

409

boundaries define the range of predicted values, there is a single capacitance value that plots on

410

the regression line, and consequently gives the best prediction for each data point. This value can

411

be either fitted or left as range of possible values. The variability in capacitance values has more

412

effect at higher than lower surface loadings (Figure S15b). The majority of outliers are observed

413

at lower surface coverages (1 umol/m2), the range of

414

capacitance values out performs the range of the 95% prediction intervals, and therefore most data

415

are predicted by the forward model. Since the uncertainty related to the capacitance value is more

416

evident at higher surface coverages, it is suggested that capacitance values be fit only when high

417

surface loadings (>1 umol/m2) are expected, whereas a range of capacitance values can give

418

reliable results for low loadings.

419

Our results show that although there is considerable variability across the different studies, the

420

forward model with unified parameters can capture most of the data values. We showed that when



421

adsorption datasets are optimized in a consistent manner using the MUSE algorithm, unified

422

equilibrium constants can be identified, when accounting for different surface areas and surface

423

occupancies. The results demonstrate that the hybridized approach for iron (oxy)hydroxides could

424

be implemented in natural systems if the mineral surface composition is identified. The unified

425

parameters extracted for chromate adsorption can be applied to SCMs using the CD-MUSIC

426

framework and a Basic Stern model. However, since the MUSE algorithm can accommodate any

427

type of SCM, the same modeling approach can be utilized for other model formulations. An

428

overarching future goal would be to improve and extend the approach with the aim of developing

429

a database containing unified surface complexation parameters for a variety of ions for use in

430

complex media reactive transport modeling.

431

ASSOCIATED CONTENT

432

Supporting Information. Reported thermodynamic constants from RES3T database, chromate

433

studies used in the analysis. Detailed description of the Surface Complexation model, including

434

the FH and GH surface structure, surface complexation reactions, and surface charge modeling.

435

Effect of capacitance, and optimization results, graphs and statistics. Surface area and surface

436

coverage dependency. Results and evaluation of the forward model.

437

AUTHOR INFORMATION

438

Corresponding Author

439

*Phone: +1860-771-8519, E-mail: [email protected]

440

Notes

441

The authors declare no competing financial interest.

442

FUNDING SOURCES


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443

This work was supported by the National Science Foundation Environmental Chemical Sciences

444

program under Award Number CHE-1404643 entitled “Collaborative Research: Toward a unified

445

model for ferrihydrite nanoparticles behavior in the environment: a multipronged investigation of

446

surface structure and reactivity.”

447

ACKNOWLEDGMENTS

448

The authors would like to thank Dr. Mavrik Zavarin for insightful discussion.

449

REFERENCES

450

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Figure 2. Surface area effect on (a) monodentate and (b) bidentate thermodynamic constants, and (c) capacitance values for FH and GH. Data adopted from Zachara et al. (1987) (blue diamonds) and Hsia et al. (1993) (cyan circles) for FH, and from Villalobos et al. (2008) (red, open triangles), Xie et al. (2015) (red, open squares), and Mesuere and Fish (1992) (green, open circles) for GH. 81x50mm (300 x 300 DPI)


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84x47mm (300 x 300 DPI)


A Unified Surface Complexation Modeling Approach for Chromate

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