Article
pubs.acs.org/est

Do Goethite Surfaces Really Control the Transport and Retention ofMulti-Walled Carbon Nanotubes in Chemically Heterogeneous
Porous Media?
Miaoyue Zhang,† Scott A. Bradford,*,‡ Jirka Šimůnek,§ Harry Vereecken,† and Erwin Klumpp††

Agrosphere Institute (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
Agricultural Research Service, U.S. Salinity Laboratory, United States Department of Agriculture, Riverside, California 92507, UnitedStates§Department of Environmental Sciences, University of California Riverside, Riverside, California 92521, United States‡

S Supporting Information*

ABSTRACT: Transport and retention behavior of multiwalled carbon nanotubes (MWCNTs) was studied in mixturesof negatively charged quartz sand (QS) and positively charged
goethite-coated sand (GQS) to assess the role of chemical
heterogeneity. The linear equilibrium sorption model provided
a good description of batch results, and the distribution
coeﬃcients (KD) drastically increased with the GQS fractionthat was electrostatically favorable for retention. Similarly,
retention of MWCNTs increased with the GQS fraction inpacked column experiments. However, calculated values of KD
on GQS were around 2 orders of magnitude smaller in batch
than packed column experiments due to diﬀerences in leverarms associated with hydrodynamic and adhesive torques at
microscopic roughness locations. Furthermore, the fraction of
the sand surface area that was favorable for retention (Sf) was much smaller than the GQS fraction because nanoscale roughness
produced shallow interactions that were susceptible to removal. These observations indicate that only a minor fraction of the
GQS was favorable for MWCNT retention. These same observations held for several diﬀerent sand sizes. Column breakthroughcurves were always well described using an advective-dispersive transport model that included retention and blocking. However,depth-dependent retention also needed to be included to accurately describe the retention proﬁle when the GQS fraction was
small. Results from this research indicate that roughness primarily controlled the retention of MWCNTs, although goethitesurfaces played an important secondary role.

■

INTRODUCTION
Carbon nanotubes (CNTs) are allotropes of carbon with aneedle-shaped nanostructure.1,2 Single-walled CNTs are individual graphene tubes, whereas multi-walled CNTs (MWCNTs)
consist of rolled layers (concentric tubes) of graphene. Carbon
nanotubes have unique electrical, chemical, and physicalproperties that have been utilized in numerous commercial
applications.3,4 Their wide use and lack of disposal regulations
are expected to ultimately lead to the release of CNTs into soil
and groundwater environments.5,6 Available literature indicatesthat CNTs are biologically nondegradable, and they are therefore
expected to be very persistent in the environment.7 Several
potential health risks of CNTs in environmental ecosystems havebeen identiﬁed.8,9 An understanding of factors that inﬂuence thetransport and fate of CNTs in soils and groundwater is therefore
needed to assess the potential risks that CNTs pose to humans
and ecosystems.
A number of studies have investigated the transport andretention behavior of CNTs in soils and sand.6,10−13 Most of this© 2016 American Chemical Society

research has been conducted with CNTs that were functionalized
to obtain a net negative surface charge in order to enhance thestability of the CNT suspension.11,14 This research has provided
valuable information on the inﬂuence of speciﬁc physicochemicalfactors on the fate of CNTs in the environment, including ionicstrength and pH, ionic composition, dissolved organic matterand surfactants, input concentration, grain size, and watervelocity.6,10,11,13,15−20 However, most of these studies have only
measured CNT breakthrough curves and have not determined
retention proﬁles that are needed to achieve mass balance and tobetter determine retention mechanisms.11,21 Furthermore, high
CNT concentrations have commonly been employed that are
not environmentally relevant.13,15,17,18,22 No research studies
have systematically examined the inﬂuence of soil chemical
Received: July 1, 2016
Revised: October 11, 2016
Accepted: October 27, 2016
Published: October 27, 2016
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advective and dispersive transport but diﬀer in their descriptionof retention processes.11,40,41 The simplest model employs
ﬁltration theory to describe ﬁrst-order irreversible colloid
retention.39,42,43 Further levels of model complexity are addedby considering other processes such as release, retention on
multiple kinetic sites, time-dependent blocking or ripening
behavior, and depth-dependent retention processes.11,12,40,41,44
Model analysis of experimental data provides valuable
information on processes that control colloid retention by
allowing various hypotheses to be tested.45 Additional modelingstudies are especially warranted in chemically heterogeneous
porous media (i.e., mixtures of quartz sand and iron oxide-coatedquartz sand). In this case, multiple kinetic retention sites are fully
justiﬁed, and it may be possible to separately study and predict
retention parameters for “favorable” and “unfavorable” sites.
The overall objective of this study was to investigate andsimulate the transport and retention of MWCNTs at anenvironmentally relevant concentration (1 mg L−1) in both
batch and column experiments in chemically heterogeneous
porous media with diﬀerent mass ratios of quartz sand (QS) andgoethite-coated quartz sand (GQS). Several diﬀerent sand grain
sizes were considered in these experiments. Measured breakthrough curves (BTCs) and retention proﬁles (RPs) were
simulated using models of increasing complexity. Our analysis
provides an improved understanding of the relative importanceof roughness and electrostatically “favorable” surfaces on
MWCNT retention in chemically heterogeneous porous media.

heterogeneities on the transport and fate of functionalized
CNTs.
Iron (Fe) and aluminum (Al) oxyhydroxides are the mostcommon source of surface charge heterogeneity in natural
aquatic environments. Both Fe and Al oxyhydroxides areamphoteric minerals that have relatively high points of zerocharge. The zero point of charge for Fe and Al oxyhydroxides isreported to be 7.5 and 9,23 respectively. These minerals adsorb
protons and acquire a net positive surface charge in aquatic
environments that are below their zero point of charge. In
contrast, common silica minerals exhibit a net negative surface
charge at ambient pH values because of their lower zero point ofcharge.24 Natural porous media therefore often exhibit surface
charge heterogeneity. If functionalized CNTs are negatively
charged, then the electrostatic interaction is expected to be“favorable” on positively charged Fe and Al hydroxyoxides and“unfavorable” on negatively charged silica minerals under neutral
pH conditions. The inﬂuence of chemical heterogeneity on thetransport and retention of colloids, microbes, and otherengineered nanoparticles has been previously studied by using
various combinations of untreated and iron oxide-coated quartz
sand.25−27 Results demonstrate that increasing the iron oxidecoated sand fraction (chemical heterogeneity) increases theamount of retention, presumably due to attachment onto ironoxide-coated sand. However, the potential confounding roles ofroughness have not been considered in these studies.
A number of experimental and theoretical studies havedemonstrated the important role of roughness on colloid andnanoparticle retention.28,29 Nanoscale roughness on macroscopically “unfavorable” surfaces locally reduces the energy
barrier height to create regions where particle interaction in a
primary minimum is “favorable”.28,30 The combination ofnanoscale roughness and Born repulsion on a macroscopically“favorable” surface also creates a shallow primary minimum
where interacting particles are susceptible to diﬀusive orhydrodynamic removal.30,31 Consequently, the question arises
whether iron oxide-coated surfaces are truly favorable to CNT
retention.
Batch and column experiments are common approaches tostudy colloid retention in porous media.32 Some researchers haveattempted to use batch experiments to predict the retention
behavior of colloids and nanoparticles in packed columns33,34
because batch studies are generally more simple, quick, and lesscostly than packed column experiments. However, distinct
diﬀerences in the amount of colloid retention on clean quartz
sand have been reported for various sized colloids and solution
chemistries.32 In particular, much greater amounts of colloid
retention occur in packed column than batch systems, especiallyfor larger colloids and lower ionic strength (IS) conditions, due
to diﬀerences in lever arms associated with applied hydrodynamic and resisting adhesive torques at microscopic roughness
locations and grain−grain contacts;32 for example, lever arms areconstant in column systems whereas they continuously change inmixed batch systems. It is still unclear whether diﬀerences incolloid retention in batch and column systems will decrease
under electrostatically favorable conditions that occur on ironoxide-coated surfaces. If so, then batch experiments could
potentially be employed to predict colloid transport andretention behavior at the column scale on electrostaticallyfavorable surfaces.
A number of mathematical models have been developed tosimulate the transport and retention of colloids and nanoparticles
in soils and groundwater.35−40 These models typically consider■

MATERIALS AND METHODS
Carbon Nanotubes. Radioactively (14C) labeled MWCNTs
were prepared by catalytic chemical vapor deposition using 14Cbenzene as feedstock gas (Bayer Technology Services GmbH,
Leverkusen, Germany). The synthesis, functionalization, andcharacterization of these functionalized MWCNTs werepreviously described.11,12 The MWCNTs have a median
diameter of 10−15 nm, a median length of 200−1000 nm,46
an average hydrodynamic diameter of approximately 180 nm(determined by dynamic light scattering, Malvern Instruments
GmbH, Herrenberg, USA), and a speciﬁc density of 1.641 g
cm−3.47 Well-dispersed stock suspensions of MWCNTs wereprepared in 1 mM KCl by ultrasonicating for 15 min at 65 W
using a cup horn sonicator (Branson Soniﬁer W-250, Danbury,
CT, U.S.A.). These stock suspensions were ultrasonicated (for10 min) a second time immediately before use in batch orcolumn studies. The concentration of 14C-labeled MWCNTs
was determined using a PerkinElmer (Rodgau, Germany) liquid
scintillation counter (LSC). LSC is the measurement of activity
associated with a radioactive sample. The unit of LSC is
Becquerel (Bq), and the speciﬁc radioactivity of the functionalized MWNTS was 3.2 MBq mg−1.
Preparation of Porous Media. Three highly uniform sandsieve size fractions of quartz sand (QS) were used in theexperiments. The median grain size of these sieved size fractions
was 240, 350, and 607 μm. These QS were puriﬁed following a
protocol in the literature.11 Stable, high density, goethite-coatedquartz sand (GQS) was prepared using the procedure of
Scheidegger et al.48 The surface roughness and distribution ofgoethite coating on the QS and GQS were imaged using ascanning electron microscope (SEM). The Brunauer−Emmett−Teller (BET) surface area49 and iron concentration of the QS
and GQS were also measured. Chemically heterogeneous porous
medium was prepared by combining a known mass fraction of
GQS (λ) with QS. Values of λ = 0, 0.1, and 0.3 were selected to be
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consistent with reported ranges in the literature.27,50 Section S1of the Supporting Information (SI) provides details.
Interaction Energy Calculations. The approach of
Bradford and Torkzaban30 was used to calculate the totalinteraction energy (Φ) of a spherical colloid with similar
properties to MWCNTs on QS and GQS in 1 mM KCl solution.
These calculations allowed consideration of selected roughness
properties on the sand surface and employed a Hamaker
constant of 9.8 × 10−21 J51 and a hydrodynamic diameter of 180
nm to be consistent with MWCNTs. Zeta potentials of
MWCNTs, crushed QS, and goethite particles in 1 mM KCl
solution were also determined using a Zetasizer Nano (Malvern
Instruments GmbH, Herrenberg, Germany. Details pertaining tothese calculations are given in Section S2 of the SI.
Batch Experiments. Batch experiments were conductedusing MWCNTs and two diﬀerent sizes (350 and 607 μm) of QS
and GQS. In accordance with the Organization for Economic
Cooperation and Development (OECD) Guideline 106,52 batch
sorption experiments were carried out under quasi-equilibrium
conditions33 by adding 20 mL of 14C-labeled functionalized
MWCNT suspensions of diﬀerent concentrations (0−1 mg L−1of MWCNT in 1 mM KCl) to 1 g of QS or GQS in a centrifuge
tube (50 mL). The tubes were continuously mixed using an
overhead shaker for 24 h. Preliminary experiments revealed that
this duration was suﬃcient for sorption equilibrium. Afterremoving the suspension of MWCNT, the sorbents (QS or
GQS) were dried in an oven at 50 °C and combusted by using a
biological oxidizer (OX 500, R.J. Harvey Instrumentation
Corporation, Tappan, NY, U.S.A.). The emerging 14CO2 was
dissolved in vials ﬁlled with a scintillation cocktail (Oxisolv,
MERCK KGAA, Darmstadt, Germany), and the 14C concentration of MWCNTs adsorbed to the sorbents was determinedusing the LSC. The concentration of MWCNTs in the
supernatant ﬁlled with the scintillation cocktail (5 mL, InstaGel Plus, PerkinElmer, Rodgau, Germany) before and after thesorption experiments was also measured with the LSC so that the
total mass balance of MWCNTs could be determined. All thesorption experiments were performed in triplicate. Blank
experiments were conducted to verify that minimal sorption of
14
C-labeled MWCNTs occurred to the wall of the centrifuge tube
and the air−water interface. Nearly complete mass balance wasachieved in the blank experiments (>99%).
Column Transport Experiments. Chemically heterogeneous porous media (QS and GQS mixtures) were incrementally
wet packed (deionized water) into stainless steel columns (3 cmin inner diameter and 12 cm in length) equipped with a stainlesssteel plate (1 mm openings) and a polytetraﬂuoroethylene(PTFE) mesh (100 or 200 μm openings) at the column bottom
to support the porous media. The column was connected to apump (MCP V 5.10, Ismatec SA, Glattbrugg, Switzerland) on theinlet side with the ﬂow direction from the bottom to the top of
the column at a Darcy velocity of 0.72−0.75 cm min−1. This
Darcy velocity is consistent with rapid sand ﬁltration studies, ﬂow
near injection/extraction wells, and other published column
studies examining colloid and nanoparticle transport andfate.11,53 Approximately 30 pore volumes (PV) of backgroundelectrolyte solution (1 mM KCl) were passed through thecolumn before conducting the transport experiments. A
nonreactive tracer (1 mM KBr, approximately 90 mL and 2.6
PVs) pulse was injected into the column to characterize thehydraulic conditions (porosity and dispersivity), followed byelution with the same particle-free electrolyte solution(approximately 3.2 PVs). Eﬄuent solutions of bromide werecollected using a fraction collector (FoxyJr., Teledyne Isco, Inc.,
Lincoln, NE, U.S.A.) every 30 s (e.g., approximately 2.5 mL pervial) and measured using a high-performance liquid chromatography (HPLC) (STH 585, Dionex, Sunnyvale, CA, U.S.A.)
equipped with a UV-detector (UV2075, Jasco, Essex, U.K.). The
same procedure was repeated when MWCNT suspensions wereapplied. A relatively low input concentration of MWCNT (1 mg
L−1) was selected for all column experiments to be consistent
with environmentally relevant scenarios.5,54 The eﬄuent
concentrations of MWCNTs were measured using the LSC.
After recovery of the breakthrough curve, the sand in the packed
column was excavated in approximately 0.5−1 cm thickincrements, dried, and then homogenized using a mill. Similar
to the sorption experiments, the crushed sands were combusted
by using a biological oxidizer and measured using the LSC todetermine the MWCNTs retained in the column packing. The
total mass balance of MWCNTs in the eﬄuent and retained in
the sand was determined from this information. All column
experiments were replicated and exhibited good reproducibility.

■

NUMERICAL MODELINGThe HYDRUS-1D code55 was used to simulate the onedimensional transport of MWCNTs with the advectiondispersion equation (ADE) and two kinetic retention sites:56,57
θ

∂S
∂S
∂C
∂C
∂ 2C
+ ρ 1 + ρ 2 = θD 2 − q
∂t
∂t
∂t
∂x
∂x

(1)

3 −3

where θ is volumetric water content [L L , where L denotes
units of length], C is MWCNT concentration in liquid phase[NL−3, where N denotes number], t is the time [T, where T
denotes units of time], ρ is the bulk density of the porous matrix[ML−3, where M denotes units of mass], x is the spatial
coordinate [L], D is the hydrodynamic dispersion coeﬃcient[L2T−1], q is the Darcy velocity [LT−1], and S1 and S2 [NM−1]
are the solid-phase concentrations of MWCNTs on retention
sites 1 and 2, respectively. The solid phase mass balance on sites 1
and 2 are given asρ

∂S1= θψ1ksw1C − ρkrs1S1
∂t

(2)

ρ

∂S2
= θψ2ksw2C − ρkrs2S2∂t(3)

where subscripts 1 and 2 on parameters denote the site, ksw1 andksw2 [T−1] are the ﬁrst-order retention rate coeﬃcients, krs1 andkrs2 [T−1] are the ﬁrst-order release rate coeﬃcients, and ψ1 andψ2 [-] are dimensionless functions that account for time or depthdependent retention. The total solid-phase concentration (S;NM−1) is equal to the sum of S1 and S2.
Three model formulations for MWCNT retention wereconsidered in this work. The ﬁrst model (M1) considers
retention only on Site 1 (ksw2 = 0) and time-dependent
Langmuirian blocking by setting ψ1 equal toψ1 = 1 −

S1
Smax1

(4)

where Smax1 [NM−1] is the maximum solid phase concentrationon Site 1. This model accounts for retention of MWCNTs on
both QS and GQS using a single retention site. The percentage ofthe solid surface area that is favorable for MWCNT retention (Sf)can be determined from Smax1 as32
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Sf = 100 ×Ac ρSmax1(1 − γ )Asand out of these shallow primary minimum on the GQS as aresult of surface roughness.29,30 Consequently, these observations indicate that QS and GQS may not be completely“unfavorable” and “favorable”, respectively, as expected based on
only electrostatic considerations.
Batch Experiments. Batch experiments were conducted toquantify the sorption behavior of MWCNTs onto two grain sizes(350 and 607 μm) of QS and GQS. Replicate batch experiments
exhibited good reproducibility and mass balance. Figure 1 shows(5)

where γ [-] is the porosity of a monolayer packing of MWCNTs
on the solid surface that is equal to 0.5,58 Ac [L2N1−] is theeﬀective cross-section area per MWCNT, and As [L−1] is thesolid surface area per unit volume. Details on parameters are
given in Section S3 of the SI.
The M2 model separately accounts for retention and blockingof MWCNTs on QS (Site 1) and GQS (Site 2) sites using eqs 2
and 3, respectively, by deﬁning ψ2 in an analogous fashion to ψ1(e.g., S1 and Smax1 in eq 4 are replaced with S2 and Smax2,
respectively). The M3 model considers retention and timedependent blocking on Site 1 using eqs 2 and 4 and depthdependent retention on Site 2. In this case, the value of ψ2 wasdeﬁned as⎛ d50 + x ⎞−β
ψ2 = ⎜⎟⎝ d50 ⎠

(6)

where d50 [L] is the median grain size of the porous media, β [-] isa ﬁtting parameter which controls the shape of the retention
proﬁle. We set the value of β = 0.765 based on reported results for
MWCNTs.11,12■

RESULTS AND DISCUSSION
SEM Images. Figure S1 shows SEM images of QS and GQS
at several diﬀerent magniﬁcations. These images clearly show thecomplex surface topography of the sand grain surfaces. Diﬀerent
amounts and heights of roughness are found over the surface ofboth QS and GQS. EDX measurement was used to conﬁrm thepresence of goethite on the GQS. The SEM images indicate thatthe goethite coating exhibits a wide distribution of sizes, shapes,
and density on the surface of GQS. Consequently, quantitative
determination of the goethite surface coverage was not possible.
However, Wang et al.50 reported that a similar goethite coating
technique produced a 75% surface coverage on the sand.
Similarly, Duschl et al.59 reported that our goethite coating
technique produced a high goethite surface density of 6 to 27
particles per μm2. Collectively, the literature and Figure S1
indicate a high density of goethite particles coated the GQS. Thiswas further conﬁrmed by measurement of high iron concentrations following acid digestion of the GQS (Table S1).
Interaction Energies. The average zeta potentials of
MWCNTs, crushed quartz sand, and goethite particles in 1
mM KCl solution were measured to be −40.2, −63.6, and 10.2
mV, respectively. Consequently, the electrostatic interaction
between the MWCNTs and quartz is unfavorable, whereas thatbetween MWCNTs and goethite is favorable. However, Φ also
depends on van der Waals and Born interactions. Figure S2
presents plots of Φ as a function of separation distance (h) whena spherical colloid, with properties similar to MWCNTs,
approaches the surface of QS and GQS in 1 mM KCl when
the sand surface has a uniform roughness height of 50 nm androughness fraction of 0.5%, 1%, 2.5%, and 5%. The energy barrier
to the primary minimum is present and absent on QS and GQS,
respectively, as expected based on electrostatics. However, theheight of the energy barrier and the depth of the primary
minimum is a strong function of the roughness fraction. A
decrease in the roughness fraction produces a rapid decrease in
the energy barrier on the QS and the magnitude of the primary
minimum on the GQS. The kinetic energy model predicts thatcolloids could diﬀuse over these small energy barriers on the QS

Figure 1. Linear sorption isotherms for MWCNTs on QS or GQS
having grain sizes of 350 and 607 μm. The electrolyte solution was 1 mM
KCl.

the sorption isotherms. The linear equilibrium sorption model (S= KDC, where KD [L3 M−1] is the equilibrium partitioncoeﬃcient)52 provided an excellent description of all isotherm
data sets, with the coeﬃcient of linear regression (R2) always
greater than 0.97. The sorption behavior over this concentration
range was therefore completely characterized by values of KD, i.e.,the slope of the linear isotherm.
Values of KD were much larger on GQS (KD = 9.5 and 3.6 cm3
g−1 on 350 and 607 μm sand, respectively) than QS (KD = 0.3 and0.6 cm3 g−1 on 350 and 607 μm sand, respectively). This result is
expected because the electrostatic interaction between thenegatively charged MWCNTs (i.e., carboxylate groups,−COO−) and the positively charged GQS (Fe−OH2+) is
attractive, whereas it is repulsive for the negatively charged
QS.60,61 Figure S2 also conﬁrms that statement and demonstrates that the signiﬁcant amounts of roughness shown in Figure
S1 will decrease and increase the MWCNT adhesive interaction
between GQS and QS, respectively. The value of KD also
dramatically increased with a decrease in the grain size of the
GQS because of a corresponding increase in the speciﬁc surface
area (Table S1). This grain size eﬀect was not observed for QS. In
contrast to GQS, the value of KD on QS is controlled by small
amounts of nanoscale roughness and chemical heterogeneity that
locally reduces or eliminates the energy barrier (FigureS2).29,30,32 One plausible explanation for the slight increase in
KD with increasing grain size of QS is due to diﬀerences in theamount and distribution of these nanoscale heterogeneities(Figure S1 and Table S1).
Eﬀect of Goethite Coating on MWCNT Transport.
Figure 2a and b presents BTCs and RPs, respectively, for
MWCNTs in various mass ratios of uncoated and goethitecoated quartz sand (λ = 0, 0.1 and 0.3). The BTCs are plotted as
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to describe the BTCs shown in Figure 2a for the various sandmixtures. Table 2 provides a summary of ﬁtted M1 model
parameters (ksw1, krs1, and Smax1) and separate R2 values for BTCs
and RPs. Simulations for the M1 model are shown in Figure 2,
and R2 values for BTCs were always very good (R2> 0.96). Fitted
M1 model values of ksw1 and krs1 were subsequently employed toθkdetermine column values of KD = ρksw1 .32,42 Batch KD values for
rs1

these same sand mixtures were determined as a linear
combination of components equal to (1 − λ) KQS + λ KGQS,
where KQS and KGQS are batch KD values for QS and GQS (cf.
Figure 1), respectively. Column and batch values of KD are given
in Table 2. Note that column values of KD are always much larger
than batch values, and this diﬀerence increased with λ (nearly 2orders of magnitude higher when λ = 0.3). Clearly, the batch
results had little relevance in predicting column scale retention
even when the electrostatically favorable fraction was relatively
high (λ = 0.3).
Others have observed a similar inconsistency between batchand column retention parameters.29,32,62,63 Torkzaban and
Bradford29 provided a detailed explanation for diﬀerences incolloid retention parameters in batch and column studies. In
brief, the amount of retention in batch and column experiments
depends on the forces and torques that act on MWCNTs near
the porous medium surface.29,32 The torque balance between
applied hydrodynamic (TH) and resisting adhesive (TA) torques
is not continuously satisﬁed in a well-mixed batch system becausechanges in the ﬂow direction alter the lever arms. Conversely, thetorque balance in the column system is constantly satisﬁed (TH ≤TA) at microscopic roughness locations (Figure S1) and grain−
grain contacts that reduce the lever arm for TH and increase thelever arm for TA. Greater amounts of MWCNT retention are
therefore expected in the column than the batch system forsimilar values of adhesive, hydrodynamic, buoyancy, and diﬀusive
forces. In other words, diﬀerent mechanisms of MWCNT
retention occur in batch and column systems. Only attachment
processes contribute to MWCNT retention in the batch system,
whereas attachment and surface straining processes (dependent
on the grain surface topology) operate in the column system.
Note that this analysis does not consider the potential inﬂuenceof pore straining that may occur in column systems when the
porous medium has wider ranges in grain- and pore-size
distributions.
Fitted values of ksw1 showed a nonlinear dependency on λ. In
particular, ksw1 slightly increased as λ increased from 0 to 0.1 but
dramatically increased when λ increased from 0.1 to 0.3. This
result is consistent with bacteria transport studies in various
fractions of iron oxide-coated sands,25,26 but a linear increase in
ksw1 with λ has been reported for nanoparticles.27,64 This
discrepancy is likely related to diﬀerences in the size of the

Figure 2. Experimental and estimated breakthrough curves (a) andretention proﬁles (b) for MWCNTs under diﬀerent mixing mass ratios(λ). The Darcy velocity was 0.72−0.75 cm min−1. The grain size of thesand was 350 μm.

the normalized eﬄuent concentration (C/C0, where C0 is theinﬂuent suspension concentration) of MWCNTs versus porevolumes. The RPs are given as normalized solid-phase
concentration (S/C0) against column depth. The experimental
conditions and mass balance information are presented in Table
1. The total mass balance (Mtotal) for MWCNTs in theseexperiments was very good (>90.7%). The MWCNT eﬄuent
mass balance (Mef f) strongly decreased from 79.6% to 9.7%
(Table 1) as λ increased from 0 to 0.3. Similarly, the MWCNT
solid-phase mass balance (Msolid) increased from 16.3% to 82.8%
as λ increased from 0 to 0.3. As expected from batch experiments,
these observations reﬂect the increasing amounts of favorable
electrostatic interactions between negatively charged MWCNTs
and positively charged goethite as λ increases.
Mathematical model studies were conducted to investigate therelationship between column retention and batch sorption
parameters for MWCNTs. The M1 model was initially employed

Table 1. Experimental Conditions, Hydraulic Parameters, and Mass Balance Information for All Column Experimentsa
λd50 [μm]

ρ [g cm−3]q [cm min−1]

Disp. [cm]Porosity

Mef f [%]

Msolid [%]Mtotal [%]

0
0.1
0.3
0.1
0.1
0.1

350
350
350
240
350
607

1.69
1.7
1.71
1.63
1.7
1.29

0.73
0.72
0.75
0.75
0.72
0.73

0.025
0.033
0.036
0.036
0.033
0.033

0.41
0.4
0.43
0.43
0.4
0.47

79.6
60.6
9.7
2.4
60.6
76.0

16.3
30.1
82.8
94.2
30.1
17.7

95.9
90.7
92.5
96.6
90.7
93.7

a
IS was 1 mM KCl. The input concentration of MWCNT was 1 mg L−1. ρ is the bulk density. Disp. is the estimated longitudinal dispersivity. Mef f is
the eﬄuent percentage of MWCNTs recovered from the column experiment. Msolid is the retained percentage of MWCNTs recovered from thecolumn experiment. Mtotal is the total percentage of MWCNTs recovered from the column experiment.

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Table 2. Fitted Model Parameters Using Diﬀerent Model Formulationsa
Model

λ

M1
M1
M1
M1
M1

0
0.1
0.3
0.1
0.1

Model

λ

d50
[μm]
350
350
350
240
607
d50
[μm]

ksw1
[min−1]

0
0.1
0.3
0.1
0.1

Smax1/C0[cm3 g−1]

SE Smax/Co−03

Column KD[cm3 g−1]−02

Batch KD
[cm3 g−1]

0.053
3 × 100.186
6.10 × 10
4.29
0.079
1 × 10−03
0.634
0.13
18.59
0.34
4 × 10−04
12.17
1.93
213.740.551
3 × 10−04
4.342
0.46
NF
0.059
5 × 10−03
0.289
4.20 × 10−02
NF
ksw1
Smax1/C0kQS
SmaxQS/C0
ksw2[min−1][cm3 g−1][min−1][cm3 g−1][min−1]

M2
0
350
0.053
M2
0.1
350
0.047
M2
0.3
350
0.037
Model
λ
d50 [μm]
M3
M3
M3
M3
M3

krs1 [min−1]

350
350
350
240
607

0.186
0.167
0.13
ksw1 [min−1]

0.053
0.053
0.053
krs1 [min−1]

0.059
0.061
0.309
0.513
0.032

NF
NF
NF
NF
NF

Geometric Sf
[%]

R2BTC

R2RP

0.32 ± 0.21
0.05 ± 0.03
0.968
1.08 ± 0.46
0.17 ± 0.07
0.991
22.03 ± 7.07
2.92 ± 0.94
0.993
5.14 ± 1.09
0.48 ± 0.10
0.976
0.74 ± 0.21
0.52 ± 0.15
0.987
Smax2/C0
kGQS
SmaxGQS/C0[cm3 g−1][min−1][cm3 g−1]

0.621
0.732
0.985
0.994
0.726
R2

BET Sf [%]

0.3
1.22
3.06
NF
NF

0.186
0
0
0.32
0.186
0.032
0.47
0.32
0.186
0.096
1.40
0.32
Smax1/C0 [cm3 g−1]
ksw2 [min−1]
krs2 [min−1]
0.039
0.151
3.862
4.665
0.044

0.491
0.817
1.066
0.907
0.516

NF
NF
NF
NF
NF

BTC+RP

β

4.67
4.67
4.67
R2 BTC

0.917
0.867
0.466
R2RP

0.765
0.765
0.765
0.765
0.765

0.971
0.99
0.991
0.974
0.987

0.986
0.906
0.958
0.999
0.995

a 2
R BTC, R2RP, and R2 BTC+RP reﬂect the correlation of observed and ﬁtted data for BTC, RP, and Total (BTC+PR), respectively. NF denotes not ﬁtted.
In M2 model, krs1 = krs2 = 1 E−5 min−1; ksw1 = (1 − λ) kQS, ksw2 = λ kGQS, Smax1 = (1 − λ) SmaxQS, Smax2 = λ SmaxGQS, where kQS and kGQS are ksw values for
QS and GQS, respectively. SmaxQS and SmaxGQS are Smax values for QS and GQS, respectively.

Predicted BTCs and RPs for the M2 model provided a muchpoorer description of the data than the ﬁtted M1 model. Thisoccurs because ﬁtted M1 model parameters exhibited a nonlinear
dependence on λ (Table 2). Consequently, information on thetransport and retention parameters for the individual components is not suﬃcient to predict behavior of the sand mixture.
However, M2 model parameters may still be ﬁtted to BTCs for
MWCNTs to give an equal or superior description of this data
than the M1 model because of the increased number of ﬁtting
parameters.
Although the M1 model always described the BTCs very well,
the RPs were poorly described when λ = 0 or 0.1 (cf., Figure 2b
and Table 2). In these cases, the RPs exhibited a hyperexponential shape, with MWCNT mass removal under predicted
near the column inlet and overestimated at the column outlet.
Interestingly, the BTC and RP were both well described when λ= 0.3. A number of potential explanations for hyper-exponential
RPs have been provided in the literature, including straining,40,68
chemical and/or size heterogeneity of the colloid suspension,69,70 and pore-scale ﬂuid distribution.57,71 The relative
importance of all of these factors on MWCNT retention cannot
be conclusively deduced from the collected information.
However, dramatic diﬀerences in batch and column scaleretention indicate that surface straining played an importantrole in retention.
Additional terms need to be considered in the model toaccount for the observed depth-dependent retention shown in(Figure 2b). In particular, we employed a two-site retention
model with time-dependent blocking on Site 1 and depthdependent retention on Site 2 (M3 model). Simulated BTCs andRPs for the M3 model are also shown in Figure 2 and provide an
excellent description of BTCs and RPs. The ﬁtted model
parameters and R2 values are given in Table 2. As expected, thevalues of ksw1, ksw2, and Smax1 increased with increasing λ. It shouldbe mentioned that the relative importance of Sites 1 and 2 cannot
be determined by comparison of the values of ksw1 and ksw2
because of the depth dependency on Site 2. However, model
mass balance information can be used to determine the total
amount and the fraction of retained MWCNTs that waselectrostatic zone of inﬂuence, which is proportional to thecolloid size.65 In particular, the inﬂuence of nanoscale chemical
heterogeneity is less pronounced for larger colloids because theseeﬀects are averaged over a larger zone of inﬂuence.66,67
MWCNT BTCs shown in Figure 2a exhibited time-dependent
blocking behavior (increasing breakthrough concentrations with
injection) as retention locations ﬁlled over time. Fitted values of
Smax1 increased with λ (Table 2) because of the presence of more
electrostatically favorable goethite-coated retention locations.
Time-dependent blocking behavior is less apparent in Figure 2afor higher values of Smax1 because they take a long time to ﬁll.
Consequently, ﬁtted values of Smax1 exhibited a greater standard
error at high values of λ = 0.3.
Table 2 shows ﬁtted values of Smax1 and the standard error thatwas used to calculate its 95% conﬁdence interval. Table S1provides geometric estimates and BET measurements for As.
This information was used to calculate corresponding values of Sf
with eq 5. Calculated values of Sf were very small. For example,
when λ = 0.1, the 95% conﬁdence interval for Sf was always<1.6%, even when goethite coated 10% of the sand surface.
Equation 5 indicates that the value of Sf is inversely related to As.
The BET value of As was much higher than the geometric value of
As. Consequently, BET values of Sf were around 1 order ofmagnitude smaller than those based on geometric estimates of As.
These low Sf values suggested that highly unfavorable attachment
conditions occurred even on goethite-coated surfaces that areelectrostatically favorable for attachment. An explanation for thisobservation is due to nanoscale roughness (Figures S1). The
combined inﬂuence of nanoscale roughness and Born repulsion
produces shallow primary minima (Figure S2),30 and colloids
that interact in these minima are susceptible to diﬀusive orhydrodynamic removal.28,29
The M2 model may be used to separately quantify thetransport and retention of MWCNTs on QS and GQS sites. In
this case, ﬁtted values of ksw1 and Smax1 from the M1 model wereused to predict QS and GQS parameters for the M2 model byassuming a linear dependence on λ (Table 2). A summary ofthese calculated M2 model parameters is given in Table 2, as wellas the R2 values between observed and predicted BTCs and RPs.
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Environmental Science & Technology

Fitted values of Smax1 from the M1 model also increased withdecreasing grain size. This trend is expected because the surface
area of the sand increases with decreasing grain size (Table S1),and this produces more electrostatically favorable sites forretention on the goethite-coated sand. The MWCNT BTCs
exhibited some time-dependent blocking behavior in Figure 3.
These blocking eﬀects were more pronounced for increasingcollector grain size because of smaller values of Smax1. As
explained previously, corresponding values of Sf values were verysmall; for example, the 95% conﬁdence interval on Sf was always
less than 6.3% and 0.68% (Table 2) when using geometricestimates and BET measurement for As, respectively. Thisobservation further supports the conclusion that only a small
portion of the goethite coatings on the sand surface werefavorable for retention.
The RPs shown in Figure 3b again exhibited a hyperexponential distribution with depth that was not well describedusing the one-site retention and blocking model (M1). The twosite model with time- (Site 1) and depth- (Site 2) dependent
retention (M3) was used to simulate this behavior. Simulation
results are shown in Figure 3, and ﬁtted model parameters are
given in Table 2. Values of ksw1, ksw2, and Smax1 increased withdecreasing grain size. The value of ksw1 was more sensitive tograin size than ksw2, especially when the grain size decreased from
350 to 240 μm. In general, the value of ksw2 was relatively
insensitive to λ because this parameter was mainly controlled bysystem hydrodynamics such as ﬂow velocity and grain size
distribution.50
Environmental Implications. Chemical heterogeneity ofporous media surfaces is commonly assumed to control colloidtransport and retention. Our results demonstrate that MWCNT
retention in chemically heterogeneous porous media wascontrolled mainly by roughness but that the mass fraction andsurface area (inversely related to the sand size) of chemical
heterogeneity also played an important secondary role. Roughness and Born repulsion can diminish colloid retention onelectrostatically favorable surfaces by creating shallow primary
minimum interactions that are susceptible to removal by
diﬀusion and hydrodynamic forces. Conversely, roughness canenhance retention on electrostatically unfavorable surfaces by
locally reducing the energy barrier and increasing and decreasing
the lever arms associated with adhesive and hydrodynamic
torques, respectively, in column systems. Measured breakthrough curves and retentions proﬁles for MWCNTs exhibited
time- and depth-dependent retention behavior even in thepresence of signiﬁcant fractions of goethite. This implies that
simple, irreversible retention models to describe colloid
retention in chemically heterogeneous soils may frequently beinadequate and that transport of colloids may be greater than
expected.

associated with Sites 1 and 2. This information is shown in Table
S2. The total amount associated with the depth-dependent site
was relatively constant with λ (11.2%−18.9%). However, thefraction of retained MWCNTs that was associated with thedepth-dependent site was much more important for lower valuesof λ, whereas the time-dependent site was dominant when λ =0.3. Note that surface straining processes have been demonstrated to be more important under highly unfavorable
attachment conditions.28 This implies an association between
the depth-dependent site and surface straining.
Eﬀect of Grain Size on MWCNT Transport. Additional
column experiments were conducted to investigate the transportand retention behavior of MWCNTs in porous media having thesame value of λ = 0.1 but diﬀerent grain sizes (240, 350, and 607
μm). Figure 3a and b shows the observed and simulated BTCs

Figure 3. Observed and simulated breakthrough curves (a) andretention proﬁles (b) for MWCNTs in goethite-coated quartz sand withthree diﬀerent grain sizes (240, 350, and 607 μm) but the same λ (0.1).
The Darcy velocity was 0.72−0.75 cm min−1.

and RPs, respectively. The experimental conditions and massbalance information are summarized in Table 1. Fitted M1 andM3 model parameters and R2 values for BTCs and RPs are shownin Table 2. The Mtotal was always greater than 90.7%. Values ofMef f and Msolid increased (2.4% to 76.0%) and decreased (94.2%
to 17.7%), respectively, as the grain size increased from 240 to607 μm. Similarly, ﬁtted values of ksw1 when using the one site
retention and blocking model (M1) increase in a nonlinear
fashion with decreasing grain size. Colloid ﬁltration theory
predicts that this trend of increasing ksw1 and Msolid withdecreasing grain size occurs because of an increasing rate of masstransfer to the solid surface.11,53,72 Direct comparison of ﬁtted
and ﬁltration theory predictions for ksw1 are hampered by theneedle-like shape of the MWCNTs and the need toindependently estimate the sticking eﬃciency.

■

ASSOCIATED CONTENT

S Supporting Information*

The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.est.6b03285.
Details pertaining to porous media preparation andcharacterization (S1), interaction energy calculations(S2), and determination of Sf (S3). Figure S1 shows
SEM images of QS and GQS. Figure S2 presents plots of
Φ(h) when a spherical colloid approaches the surface of
QS and GQS with diﬀerent roughness properties in 1 mM
KCl. Table S1 provides information on the sand surface
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Article

Environmental Science & Technology■

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area and iron content. Table S2 provides mass balance
information for the M3 model. (PDF)

AUTHOR INFORMATION

Corresponding Author*Phone: +1 951 369-4857. Fax: +1 951 342-4964. E-mail: scott.
bradford@ars.usda.gov.
Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
M.Z. thanks the China Scholarship Council (CSC) for ﬁnancial
support. The authors also acknowledge the technical assistancefrom Stephan Köppchen, Brendan Headd, Claudia Walraf,
Volker Nischwitz, Markus Duschl, and Herbert Philipp.

■

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DOI: 10.1021/acs.est.6b03285
Environ. Sci. Technol. 2016, 50, 12713−12721