Do Goethite Surfaces Really Control the Transport and Retention of

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Do Goethite Surfaces Really Control the Transport and Retention of MultiWalled Carbon Nanotubes in Chemically Heterogeneous Porous Media? Miaoyue Zhang, Scott A. Bradford, Jiri Simunek, Harry Vereecken, and Erwin Klumpp Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b03285 • Publication Date (Web): 27 Oct 2016 Downloaded from http://pubs.acs.org on November 1, 2016

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Environmental Science & Technology

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Do Goethite Surfaces Really Control the Transport and Retention

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of Multi-Walled Carbon Nanotubes in Chemically Heterogeneous Porous Media?

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Miaoyue Zhang†, Scott A. Bradford‡*, Jirka Šimůnek§, Harry Vereecken†, and Erwin Klumpp†

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†

Agrosphere Institute (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

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‡

United States Department of Agriculture, Agricultural Research Service, U. S. Salinity

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Laboratory, Riverside, CA 92507, USA

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§

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92521, USA

Department of Environmental Sciences, University of California Riverside, Riverside, CA

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Revised Manuscript Submitted to

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October 11, 2016

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*

Corresponding Author: [email protected]; 951-369-4857.

ACS Paragon Plus Environment


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ABSTRACT – Transport and retention behavior of multi-walled carbon nanotubes

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(MWCNTs) was studied in mixtures of negatively charged quartz sand (QS) and positively

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charged goethite-coated sand (GQS) to assess the role of chemical heterogeneity. The linear

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equilibrium sorption model provided a good description of batch results, and the distribution

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coefficients (KD) drastically increased with the GQS fraction that was electrostatically

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favorable for retention. Similarly, retention of MWCNTs increased with the GQS fraction in

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packed column experiments. However, calculated values of KD on GQS were around two

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orders of magnitude smaller in batch than packed column experiments due to differences in

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lever arms associated with hydrodynamic and adhesive torques at microscopic roughness

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locations. Furthermore, the fraction of the sand surface area that was favorable for retention

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(Sf) was much smaller than the GQS fraction, because nanoscale roughness produced shallow

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interactions that were susceptible to removal. These observations indicate that only a minor

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fraction of the GQS was favorable for MWCNT retention. These same observations held for

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several different sand sizes. Column breakthrough curves were always well described using

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an advective-dispersive transport model that included retention and blocking. However,

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depth-dependent retention also needed to be included to accurately describe the retention

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profile when the GQS fraction was small. Results from this research indicate that roughness

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primarily controlled the retention of MWCNTs, although goethite surfaces played an

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important secondary role.


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INTRODUCTION Carbon nanotubes (CNTs) are allotropes of carbon with a needle-shaped

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nanostructure.1, 2 Single-walled CNTs are individual graphene tubes, whereas multi-walled

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CNTs (MWCNTs) consist of rolled layers (concentric tubes) of graphene. Carbon nanotubes

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have unique electric, chemical, and physical properties that have been utilized in numerous

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commercial applications.3, 4 Their wide use and lack of disposal regulations are expected to

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ultimately lead to the release of CNTs into soil and groundwater environments.5, 6 Available

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literature indicates that CNTs are biologically non-degradable, and they are therefore

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expected to be very persistent in the environment.7 Several potential health risks of CNTs in

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environmental ecosystems have been identified.8, 9 An understanding of factors that influence

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the transport and fate of CNTs in soils and groundwater is therefore needed to assess the

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potential risks that CNTs pose to humans and ecosystems.

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A number of studies have investigated the transport and retention behavior of CNTs in

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soils and sand.6, 10-13 Most of this research has been conducted with CNTs that were

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functionalized to obtain a net negative surface charge in order to enhance the stability of the

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CNT suspension.11, 14 This research has provided valuable information on the influence of

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specific physicochemical factors on the fate of CNTs in the environment, including: ionic

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strength and pH, ionic composition, dissolved organic matter and surfactants, input

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concentration, grain size, and water velocity.6, 10, 11, 13, 15-20 However, most of these studies

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have only measured CNT breakthrough curves, but have not determined retention profiles that

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are needed to achieve mass balance and to better determine retention mechanisms.11, 21

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Furthermore, high CNT concentrations have commonly been employed that are not

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environmentally relevant.13, 15, 17, 18, 22 No research studies have systematically examined the

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influence of soil chemical heterogeneities on the transport and fate of functionalized CNTs.

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Iron (Fe) and aluminum (Al) oxyhydroxides are the most common source of surface

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charge heterogeneity in natural aquatic environments. Both Fe and Al oxyhydroxides are ACS Paragon Plus Environment


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amphoteric minerals that have relatively high points of zero charge. The zero point of charge

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for Fe and Al oxyhydroxides is reported to be 7.5 and 9,23 respectively. These minerals

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adsorb protons and acquire a net positive surface charge in aquatic environments that are

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below their zero point of charge. In contrast, common silica minerals exhibit a net negative

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surface charge at ambient pH values because of their lower zero point of charge.24 Natural

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porous media therefore often exhibit surface charge heterogeneity. If functionalized CNTs are

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negatively charged then the electrostatic interaction is expected to be “favorable” on

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positively charged Fe and Al hydroxyoxides and “unfavorable” on negatively charged silica

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minerals under neutral pH conditions. The influence of chemical heterogeneity on the

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transport and retention of colloids, microbes, and other engineered nanoparticles has been

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previously studied by using various combinations of untreated and iron oxide coated quartz

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sand.25-27 Results demonstrate that increasing the iron oxide coated sand fraction (chemical

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heterogeneity) increases the amount of retention, presumably due to attachment onto iron

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oxide coated sand. However, the potential confounding roles of roughness have not been

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considered in these studies.

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A number of experimental and theoretical studies have demonstrated the important

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role of roughness on colloid and nanoparticle retention.28, 29 Nanoscale roughness on

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macroscopically “unfavorable” surfaces locally reduces the energy barrier height to create

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regions where particle interaction in a primary minimum is “favorable”.28, 30 The combination

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of nanoscale roughness and Born repulsion on a macroscopically “favorable” surface also

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creates a shallow primary minimum where interacting particles are susceptible to diffusive or

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hydrodynamic removal.30, 31 Consequently, the question arises whether iron oxide coated

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surfaces are truly favorable to CNT retention.

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Batch and column experiments are common approaches to study colloid retention in

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porous media.32 Some researchers have attempted to use batch experiments to predict the

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retention behavior of colloids and nanoparticles in packed columns,33, 34 because batch studies ACS Paragon Plus Environment

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are generally more simple, quick, and less costly than packed column experiments. However,

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distinct differences in the amount of colloid retention on clean quartz sand have been reported

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for various sized colloids and solution chemistries.32 In particular, much greater amounts of

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colloid retention occur in packed column than batch systems, especially for larger colloids

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and lower ionic strength (IS) conditions, due to differences in lever arms associated with

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applied hydrodynamic and resisting adhesive torques at microscopic roughness locations and

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grain-grain contacts;32 e.g., lever arms are constant in column systems whereas they

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continuously change in mixed batch systems. It is still unclear whether differences in colloid

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retention in batch and column systems will decrease under electrostatically favorable

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conditions that occur on iron oxide coated surfaces. If so, then batch experiments could

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potentially be employed to predict colloid transport and retention behavior at the column-

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scale on electrostatically favorable surfaces.

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A number of mathematical models have been developed to simulate the transport and

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retention of colloids and nanoparticles in soils and groundwater.35-40 These models typically

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consider advective and dispersive transport, but differ in their description of retention

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processes.11, 40, 41 The simplest model employs filtration theory to describe first-order

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irreversible colloid retention.39, 42, 43 Further levels of model complexity are added by

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considering other processes such as release, retention on multiple kinetic sites, time-

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dependent blocking or ripening behavior, and depth-dependent retention processes.11, 12, 40, 41,

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44

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control colloid retention by allowing various hypotheses to be tested.45 Additional modeling

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studies are especially warranted in chemically heterogeneous porous media (i.e., mixtures of

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quartz sand and iron oxide coated quartz sand). In this case, multiple kinetic retention sites are

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fully justified, and it may be possible to separately study and predict retention parameters for

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“favorable” and “unfavorable” sites.

Model analysis of experimental data provides valuable information on processes that



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The overall objective of this study was to investigate and simulate the transport and

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retention of MWCNTs at an environmentally relevant concentration (1 mg L-1) in both batch

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and column experiments in chemically heterogeneous porous media with different mass ratios

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of quartz sand (QS) and goethite coated quartz sand (GQS). Several different sand grain sizes

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were considered in these experiments. Measured breakthrough curves (BTCs) and retention

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profiles (RPs) were simulated using models of increasing complexity. Our analysis provides

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an improved understanding of the relative importance of roughness and electrostatically

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“favourable” surfaces on MWCNT retention in chemically heterogeneous porous media.

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MATERIALS AND METHODS

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Carbon Nanotubes

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Radioactively (14C) labeled MWCNTs were prepared by catalytic chemical vapor

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deposition using 14C-benzene as feedstock gas (Bayer Technology Services GmbH,

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Leverkusen, Germany). The synthesis, functionalization, and characterization of these

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functionalized MWCNTs were previously described.11, 12 The MWCNTs have a median

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diameter of 10-15 nm and a median length of 200-1000 nm,46 an average hydrodynamic

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diameter of approximately 180 nm (determined by dynamic light scattering, Malvern

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Instruments GmbH, Herrenberg, USA ), and a specific density of 1.641 g cm-3.47 Well-

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dispersed stock suspensions of MWCNTs were prepared in 1 mM KCl by ultrasonicating for

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15 min at 65 W using a cup horn sonicator (Branson Sonifier ® W-250, Danbury, USA).

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These stock suspensions were ultrasonicated (for 10 min) a second time immediately before

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use in batch or column studies. The concentration of 14C-labeled MWCNTs was determined

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using a Perkin Elmer (Rodgau, USA) liquid scintillation counter (LSC). LSC is the

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measurement of activity associated with a radioactive sample. The unit of LSC is Becquerel

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(Bq), and the specific radioactivity of the functionalized MWNTS was 3.2 MBq mg-1.

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Preparation of Porous Media Three highly uniform sand sieve size fractions of quartz sand (QS) were used in

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experiments. The median grain size of these sieved size fractions was 240, 350, and 607 µm.

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These QS were purified following a protocol in the literature.11 Stable, high density, goethite-

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coated quartz sand (GQS) was prepared using the procedure of Scheidegger et al.48. The

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surface roughness and distribution of goethite coating on the QS and GQS was imaged using a

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scanning electron microscope (SEM). The Brunauer–Emmett–Teller (BET) surface area49 and

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iron concentration of the QS and GQS were also measured. Chemically heterogeneous

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porous medium was prepared by combining a known mass fraction of GQS (λ) with QS.

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Values of λ=0, 0.1, and 0.3 were selected to be consistent with reported ranges in the

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literature.27, 50 Section S1 of the Supporting Information (SI) provides details.

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Interaction Energy Calculations The approach of Bradford and Torkzaban30 was used to calculate the total interaction

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energy (Φ) of a spherical colloid with similar properties to MWCNTs on QS and GQS in 1

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mM KCl solution. These calculations allowed the consideration of selected roughness

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properties on the sand surface, and employed a Hamaker constant of 9.8E-21 J51 and a

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hydrodynamic diameter of 180 nm to be consistent with MWCNTs, and measured zeta

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potentials of MWCNTs, crushed QS, and goethite particles in 1 mM KCl solution that were

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determined using a Zetasizer Nano (Malvern Instruments GmbH, Herrenberg, USA). Details

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pertaining to these calculations are given in the section S2 of the SI.

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Batch Experiments Batch experiments were conducted using MWCNTs and two different sizes (350 and

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607 µm) of QS and GQS. In accordance with Organization for Economic Cooperation and

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Development (OECD) -guideline 106,52 batch sorption experiments were carried out under ACS Paragon Plus Environment


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quasi-equilibrium conditions33 by adding 20 ml of 14C-labeled functionalized MWCNT

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suspensions of different concentrations (0-1 mg L-1 of MWCNT in 1 mM KCl) to 1 g of QS

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or GQS in a centrifuge tube (50 ml). The tubes were continuously mixed using an over-head

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shaker for 24 h. Preliminary experiments revealed that this duration was sufficient for

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sorption equilibrium. After removing the suspension of MWCNT, the sorbents (QS or GQS)

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were dried in an oven at 50 0C and combusted by using a biological oxidizer (OX 500, R.J.

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Harvey Instrumentation Corporation, Tappan, USA). The emerging 14CO2 was dissolved in

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vials filled with scintillation cocktail (Oxisolv, MERCK KGAA, Darmstadt, Germany) and

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the 14C concentration of MWCNTs adsorbed to the sorbents was determined using the LSC.

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The concentration of MWCNTs in the supernatant filled with scintillation cocktail (5 mL,

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Insta-Gel Plus, PerkinElmer, Rodgau, USA) before and after the sorption experiments was

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also measured with the LSC so that the total mass balance of MWCNTs could be determined.

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All the sorption experiments were performed in triplicate. Blank experiments were conducted

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to verify that minimal sorption of 14C-labeled MWCNTs occurred to the wall of the centrifuge

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tube and the air-water interface. Nearly complete mass balance was achieved in the blank

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experiments (>99%).

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Column Transport Experiments

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Chemically heterogeneous porous media (QS and GQS mixtures) were incrementally

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wet packed (deionized water) into stainless steel columns (3 cm in inner diameter and 12 cm

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in length) equipped with a stainless steel plate (1 mm openings) and a polytetrafluoroethylene

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(PTFE) mesh (100 or 200 µm openings) at the column bottom to support the porous media.

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The column was connected to a pump (MCP V 5.10, Ismatec SA, Glattbrugg, Switzerland) on

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the inlet side with the flow direction from the bottom to the top of the column at a Darcy

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velocity of 0.72-0.75 cm min-1. This Darcy velocity is consistent with rapid sand filtration

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studies, flow near injection/extraction wells, and other published column studies examining ACS Paragon Plus Environment

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colloid and nanoparticle transport and fate.11, 53 Approximately 30 pore volumes (PV) of

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background electrolyte solution (1 mM KCl) were passed through the column before

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conducting the transport experiments. A non-reactive tracer (1 mM KBr, approx. 90 mL and

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2.6 PVs) pulse was injected into the column to characterize the hydraulic conditions (porosity

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and dispersivity), followed by elution with the same particle-free electrolyte solution (approx.

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3.2 PVs). Effluent solutions of bromide were collected using a fraction collector (FoxyJr.®,

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Teledyne Isco Inc., Lincoln, USA) every 30 s (e.g., approximately 2.5 mL per vial) and

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measured using a high performance liquid chromatography (HPLC) (STH 585, Dionex,

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Sunnyvale, CA, USA) equipped with a UV-detector (UV2075, Jasco, Essex, UK). The same

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procedure was repeated when MWCNT suspensions were applied. A relatively low input

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concentration of MWCNT (1 mg L-1) was selected for all column experiments to be consistent

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with environmentally relevant scenarios.5, 54 The effluent concentrations of MWCNTs were

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measured using the LSC. After recovery of the breakthrough curve the sand in the packed

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column was excavated in approximately 0.5-1 cm thick increments, dried and then

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homogenized using a mill. Similar to the sorption experiments, the crushed sands were

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combusted by using a biological oxidizer and measured using the LSC to determine the

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MWCNTs retained in the column packing. The total mass balance of MWCNTs in the

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effluent and retained in the sand was determined from this information. All column

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experiments were replicated and exhibited good reproducibility.

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Numerical Modeling The HYDRUS-1D code55 was used to simulate the one-dimensional transport of MWCNTs with the advection-dispersion equation (ADE) and two kinetic retention sites:56, 57

+

+

= −

(1)

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where is volumetric water content [L3L-3; where L denotes units of length], is MWCNT

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concentration in liquid phase [NL-3; where N denotes number], t is the time [T; where T ACS Paragon Plus Environment


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denotes units of time], is the bulk density of the porous matrix [ML-3; where M denotes

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units of mass], x is the spatial coordinate [L], is the hydrodynamic dispersion coefficient

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[L2T-1], is the Darcy velocity [LT-1], and and [NM-1] are the solid phase

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concentrations of MWCNTs on retention sites 1 and 2, respectively. The solid phase mass

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balance on sites 1 and 2 are given as:

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= −

(2)

= −

(3)

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where subscripts 1 and 2 on parameters denote the site, and [T-1] are the first-order

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retention rate coefficients, and [T-1] are the first-order release rate coefficients, and

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and [-] are dimensionless functions that account for time or depth-dependent retention.

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The total solid phase concentration (S; NM-1) is equal to the sum of S1 and S2.

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Three model formulations for MWCNT retention were considered in this work. The

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first model (M1) considers retention only on Site 1 (ksw2 = 0), and time-dependent

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Langmuirian blocking by setting equal to: = 1 −

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(4)

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where [NM-1] is the maximum solid phase concentration on Site 1. This model

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accounts for retention of MWCNTs on both QS and GQS using a single retention site. The

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percentage of the solid surface area that is favorable for MWCNT retention (Sf) can be

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determined from Smax1 as:32

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= 100 ∗

"# $ (&')")

(5)

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where * [-] is the porosity of a monolayer packing of MWCNTs on the solid surface that is

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equal to 0.5,58 Ac [L2N-1] is the effective cross section area per MWCNT, and As [L-1] is the

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solid surface area per unit volume. Details on parameters are given in section S3 of the SI.


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The M2 model separately accounts for retention and blocking of MWCNTs on QS

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(Site 1) and GQS (Site 2) sites using Eqs. (2) and (3), respectively, by defining in an

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analogous fashion to (e.g., and in Eq. (4) are replaced with and ,

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respectively). The M3 model considers retention and time-dependent blocking on Site 1 using

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Eqs. (2) and (4), and depth-dependent retention on Site 2. In this case, the value of was

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defined as: +,- . &/ ) +,-

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= (

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where 012 [L] is the median grain size of the porous media, 3 [-] is a fitting parameter which

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controls the shape of the retention profile. We set the value of 3 = 0.765 based on reported

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results for MWCNTs.11, 12

(6)

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RESULTS AND DISCUSSION

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SEM Images

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Figure S1 shows SEM images of QS and GQS at several different magnifications.

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These images clearly show the complex surface topography of the sand grain surfaces.

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Different amounts and heights of roughness are found over the surface of both QS and GQS.

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EDX measurement was used to confirm the presence of goethite on the GQS. The SEM

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images indicate that the goethite coating exhibits a wide distribution of sizes, shapes, and

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density on the surface of GQS. Consequently, quantitative determination of the goethite

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surface coverage was not possible. However, Wang et al.50 reported that a similar goethite

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coating technique produced a 75% surface coverage on the sand. Similarly, Duschl et al.59

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reported that our goethite coating technique produced a high goethite surface density of 6 to

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27 particles per µm2. Collectively, the literature and Figure S1 indicate a high density of

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goethite particles coated the GQS. This was further confirmed by measurement of high iron

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concentrations following acid digestion of the GQS (Table S1). ACS Paragon Plus Environment


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Interaction Energies The average zeta potential of MWCNTs, crushed quartz sand, and goethite particles in

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1 mM KCl solution was measured to be -40.2, -63.6 and 10.2 mV, respectively. Consequently,

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the electrostatic interaction between the MWCNTs and quartz is unfavorable, whereas that

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between MWCNTs and goethite is favorable. However, Φ also depends on van der Waals and

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Born interactions. Figure S2 presents plots of Φ as a function of separation distance (h) when

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a spherical colloid, with properties similar to MWCNTs, approaches the surface of QS and

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GQS in 1 mM KCl when the sand surface has a uniform roughness height of 50 nm and

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roughness fraction of 0.5, 1, 2.5, and 5%. The energy barrier to the primary minimum is

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present and absent on QS and GQS, respectively, as expected based on electrostatics.

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However, the height of the energy barrier and the depth of the primary minimum is a strong

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function of the roughness fraction. A decrease in the roughness fraction produces a rapid

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decrease in the energy barrier on the QS and the magnitude of the primary minimum on the

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GQS. The kinetic energy model predicts that colloids could diffuse over these small energy

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barriers on the QS and out of these shallow primary minimum on the GQS as a result of

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surface roughness.29, 30 Consequently, these observations indicate that QS and GQS may not

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be completely “unfavorable” and “favorable”, respectively, as expected based on only

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electrostatic considerations.

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Batch Experiments Batch experiments were conducted to quantify the sorption behavior of MWCNTs

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onto two grain sizes (350 and 607 µm) of QS and GQS. Replicate batch experiments

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exhibited good reproducibility and mass balance. Figure 1 shows the sorption isotherms. The

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linear equilibrium sorption model (S=KDC; where KD [L3M-1] is the equilibrium partition

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coefficient)52 provided an excellent description of all isotherm datasets, with the coefficient of

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linear regression (R2) always greater than 0.97. The sorption behavior over this concentration ACS Paragon Plus Environment

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range was therefore completely characterized by values of KD; i.e., the slope of the linear

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isotherm.

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Values of KD were much larger on GQS (KD =9.5 and 3.6 cm3g-1 on 350 and 607 µm

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sand, respectively) than QS (KD =0.3 and 0.6 cm3g-1 on 350 and 607 µm sand, respectively).

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This result is expected because the electrostatic interaction between the negatively charged

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MWCNTs (i.e., carboxylate groups, -COO-) and the positively charged GQS (Fe-OH2+) is

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attractive, whereas it is repulsive for the negatively charged QS.60, 61 Figure S2 also confirms

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that statement, and demonstrates that the significant amounts of roughness shown in Figure

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S1 will decrease and increase the MWCNT adhesive interaction between GQS and QS,

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respectively. The value of KD also dramatically increased with a decrease in the grain size of

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the GQS because of a corresponding increase in the specific surface area (Table S1). This

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grain size effect was not observed for QS. In contrast to GQS, the value of KD on QS is

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controlled by small amounts of nanoscale roughness and chemical heterogeneity that locally

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reduces or eliminates the energy barrier (Figure S2).29, 30, 32 One plausible explanation for the

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slight increase in KD with increasing grain size of QS is due to differences in the amount and

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distribution of these nanoscale heterogeneities (Figure S1 and Table S1).

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Effect of Goethite Coating on MWCNT Transport

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Figures 2a and 2b present BTCs and RPs, respectively, for MWCNTs in various mass

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ratios of uncoated and goethite-coated quartz sand (λ = 0, 0.1 and 0.3). The BTCs are plotted

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as the normalized effluent concentration (C/Co; where Co is the influent suspension

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concentration) of MWCNTs versus pore volumes. The RPs are given as normalized solid-

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phase concentration (S/Co) against column depth. The experimental conditions and mass

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balance information are presented in Table 1. The total mass balance (Mtotal) for MWCNTs in

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these experiments was very good (>90.7%). The MWCNT effluent mass balance (Meff)

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strongly decreased from 79.6% to 9.7 % (Table 1) as λ increased from 0 to 0.3. Similarly, the ACS Paragon Plus Environment


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MWCNT solid phase mass balance (Msolid) increased from 16.3% to 82.8% as λ increased

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from 0 to 0.3. As expected from batch experiments, these observations reflect the increasing

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amounts of favorable electrostatic interactions between negatively charged MWCNTs and

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positively charged goethite as λ increases.

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Mathematical model studies were conducted to investigate the relationship between

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column retention and batch sorption parameters for MWCNTs. The M1 model was initially

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employed to describe the BTCs shown in Figure 2a for the various sand mixtures. Table 2

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provides a summary of fitted M1 model parameters (ksw1, krs1, and Smax1) and separate R2

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values for BTCs and RPs. Simulations for the M1 model are shown in Figure 2, and R2 values

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for BTCs were always very good (R2> 0.96). Fitted M1 model values of ksw1 and krs1 were

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subsequently employed to determine column values of 45 =

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these same sand mixtures were determined as a linear combination of components equal to (1-

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:) KQS + : KGQS; where KQS and KGQS are batch KD values for QS and GQS (cf. Figure 1),

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respectively. Column and batch values of KD are given in Table 2. Note that column values of

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KD were always much larger than batch values, and this difference increased with λ (nearly

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two orders of magnitude higher when λ=0.3). Clearly, the batch results had little relevance in

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predicting column scale retention even when the electrostatically favorable fraction was

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relatively high (λ=0.3).

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67)8 32, 42 . $79)

Batch KD values for

Others have observed a similar inconsistence between batch and column retention

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parameters.29, 32, 62, 63 Torkzaban and Bradford29 provided a detailed explanation for

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differences in colloid retention parameters in batch and column studies. In brief, the amount

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of retention in batch and column experiments depends on the forces and torques that act on

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MWCNTs near the porous medium surface.29, 32 The torque balance between applied

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hydrodynamic (TH) and resisting adhesive (TA) torques is not continuously satisfied in a well-

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mixed batch system because changes in the flow direction alter the lever arms. Conversely,

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the torque balance in the column system is constantly satisfied (TH ≤ TA) at microscopic ACS Paragon Plus Environment

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roughness locations (Figure S1) and grain-grain contacts that reduce the lever arm for TH and

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increase the lever arm for TA. Greater amounts of MWCNT retention are therefore expected in

353

the column than the batch system for similar values of adhesive, hydrodynamic, buoyancy,

354

and diffusive forces. In other words, different mechanisms of MWCNT retention occur in

355

batch and column systems. Only attachment processes contribute to MWCNT retention in the

356

batch system, whereas attachment and surface straining processes (dependent on the grain

357

surface topology) operate in the column system. Note that this analysis does not consider the

358

potential influence of pore straining that may occur in column systems when the porous

359

medium has wider ranges in grain- and pore-size distributions.

360

Fitted values of ksw1 showed a nonlinear dependency on λ. In particular, ksw1 slightly

361

increased as λ increased from 0 to 0.1, but dramatically increased when λ increased from 0.1

362

to 0.3. This result is consistent with bacteria transport studies in various fractions of iron

363

oxide coated sands25, 26, but a linear increase in ksw1 with λ has been reported for

364

nanoparticles.27, 64 This discrepancy is likely related to differences in the size of the

365

electrostatic zone of influence, which is proportional to the colloid size.65 In particular, the

366

influence of nanoscale chemical heterogeneity is less pronounced for larger colloids because

367

these effects are averaged over a larger zone of influence.66, 67

368

MWCNT BTCs shown in Figure 2a exhibited time-dependent blocking behavior

369

(increasing breakthrough concentrations with injection) as retention locations filled over time.

370

Fitted values of Smax1 increased with λ (Table 2) because of the presence of more

371

electrostatically favorable goethite coated retention locations. Time-dependent blocking

372

behavior is less apparent in Figure 2a for higher values of Smax1 because they take a long time

373

to fill. Consequently, fitted values of Smax1 exhibited a greater standard error at high values of

374

λ = 0.3.

375

Table 2 shows fitted values of Smax1 and the standard error that was used to calculate

376

its 95% confidence interval. Table S1 provides geometric estimates and BET measurements ACS Paragon Plus Environment


377

for As. This information was used to calculate corresponding values of Sf with Equation (5).

378

Calculated values of Sf were very small. For example, when λ=0.1 the 95% confidence

379

interval for Sf was always

Do Goethite Surfaces Really Control the Transport and Retention of

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