w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Available online at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/watres

Transport and retention of multi-walled carbon nanotubes insaturated porous media: Effects of input concentration andgrain size 
Daniela Kasel a,*, Scott A. Bradford b, Jirı́ Sim
unek c, Marc Heggen d,e, Harry Vereecken a,aErwin Klumppa

Agrosphere Institute (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
US Salinity Laboratory, Agricultural Research Service, United States Department of Agriculture, Riverside, CA 92507, USAc
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USAdPeter Grünberg Institute (PGI-5), Forschungszentrum Jülich GmbH, 52425 Jülich, GermanyeErnst Ruska-Centre (ER-C), Forschungszentrum Jülich GmbH, 52425 Jülich, Germanyb

article info

abstract

Article history:

Water-saturated column experiments were conducted to investigate the effect of input

Received 1 August 2012

concentration (Co) and sand grain size on the transport and retention of low concentrations

Received in revised form

(1, 0.01, and 0.005 mg L1) of functionalized 14C-labeled multi-walled carbon nanotubes

9 November 2012

(MWCNT) under repulsive electrostatic conditions that were unfavorable for attachment.

Accepted 13 November 2012

The breakthrough curves (BTCs) for MWCNT typically did not reach a plateau, but had an

Available online 23 November 2012

asymmetric shape that slowly increased during breakthrough. The retention profiles (RPs)
were not exponential with distance, but rather exhibited a hyper-exponential shape with

Keywords:

greater retention near the column inlet. The collected BTCs and RPs were simulated using

Carbon nanotubes

a numerical model that accounted for both time- and depth-dependent blocking functions

Column experimentson the retention coefficient. For a given Co, the depth-dependent retention coefficient andQuartz sandthe maximum solid phase concentration of MWCNT were both found to increase with

Breakthrough curves

decreasing grain size. These trends reflect greater MWCNT retention rates and a greater

Retention profiles

number of retention locations in the finer textured sand. The fraction of the injectedTransport modeling

MWCNT mass that was recovered in the effluent increased and the RPs became less hyperexponential in shape with higher Co due to enhanced blocking/filling of retention locations.
This concentration dependency of MWCNT transport increased with smaller grain size
because of the effect of pore structure and MWCNT shape on MWCNT retention. In
particular, MWCNT have a high aspect ratio and we hypothesize that solid phase MWCNT
may create a porous network with enhanced ability to retain particles in smaller grain
sized sand, especially at higher Co. Results demonstrate that model simulations of MWCNT
transport and fate need to accurately account for observed behavior of both BTCs and RPs.
ª 2012 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: þ49 2461 61 3521; fax: þ49 2461 61 2518.
 unek),
E-mail addresses: d.kasel@fz-juelich.de (D. Kasel), scott.bradford@ars.usda.gov (S.A. Bradford), jiri.simunek@ucr.edu (J. Sim
m.heggen@fz-juelich.de (M. Heggen), h.vereecken@fz-juelich.de (H. Vereecken), e.klumpp@fz-juelich.de (E. Klumpp).
0043-1354/$ e see front matter ª 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.watres.2012.11.019

934

1.

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Introduction

Carbon nanotubes (CNT) are needle-shaped particles with
nano-scale diameters and micro-scale lengths (Iijima, 1991;
Mauter and Elimelech, 2008). In principle, CNT are rolled up
sheets of graphene forming individual tubes (single-walledcarbon nanotubes, SWCNT) or tubes within tubes (multiwalled carbon nanotubes, MWCNT) (Sinnott, 2002). Carbon
nanotubes exhibit unique electronic, chemical, and physicalproperties that have been exploited in numerous commercial
applications (Liu et al., 2009; Mattison et al., 2011). The widespread use and a lack of regulations for CNT disposal willundoubtedly result in their release into the environment,
especially into soils and groundwater (Nowack and Bucheli,
2007; Klaine et al., 2008; Köhler et al., 2008; Jaisi andElimelech, 2009). However, the fate and effects of CNT in theenvironment are still not yet well understood (Saleh et al.,2008). Previous studies have revealed a potential health riskof CNT to several organisms, e.g., rainbow trout and rats (Lamet al., 2006; Handy et al., 2008; Farré et al., 2009). Furthermore,
CNT are one of the most biologically non-degradable manmade materials (Lam et al., 2004). The transport of CNT
through porous media is therefore of considerable interest
regarding potential risks to organisms and human health(Mattison et al., 2011). This is especially true for CNT that havebeen functionalized to increase their stability in aqueous
suspensions because this modification will also increase theirmobility in the environment (Mattison et al., 2011).
To date, several studies have investigated CNT transport inpacked sand columns under water-saturated conditions. The
transport and retention of CNT has been found to be sensitive
to a diversity of experimental conditions including ionicstrength (IS), pore water velocity, and collector grain size (Jaisi
et al., 2008; Jaisi and Elimelech, 2009; Liu et al., 2009; Tian et al.,2010; Mattison et al., 2011; Tian et al., 2012). Despite thisresearch, transport and retention processes for MWCNT are
still not completely understood (Mattison et al., 2011). For
example, the effect of CNT input concentration on theirtransport behavior has not yet been reported, and the selected
input CNT concentrations for previous studies were morethan nine orders of magnitude higher than is expected formost environmentally relevant scenarios (Gottschalk et al.,2009). This is an important aspect to consider because theinput concentration has been demonstrated to significantly
influence colloid deposition (Bradford and Bettahar, 2006;
Bradford et al., 2009), and this concentration effect was also
found to depend on the grain size (Bradford and Bettahar,2006). In general, transport studies at low CNT concentrations are of interest for fundamental research but recent
studies only considered input concentration significantly
higher than 1 mg L1 (Jaisi et al., 2008; Jaisi and Elimelech,
2009; Liu et al., 2009; Tian et al., 2010; Mattison et al., 2011;
Tian et al., 2012). Environmental concentrations of MWCNT
will depend on their source and on hydro-geochemical
conditions. However, initial model estimates predict very
low CNT concentrations in soils in the range of several ng kg1
(Mueller and Nowack, 2008; Gottschalk et al., 2009). In addition, information on retention profiles for CNT is very scarce(Wang et al., 2012b). Retention profiles provide needed

information for mass balance and useful insight on controlling mechanisms of retention (Bradford and Bettahar, 2005).
Furthermore, breakthrough curves and retention profiles needto both be accurately simulated by numerical models in orderto reliably predict environmental fate and risk (Bradford et al.,2003).
The aim of this study was to investigate the transport andretention of MWCNT in saturated porous media for different
input concentrations and sand grain sizes. Three sand grain
sizes (607, 350, and 240 mm) were considered in these studies.
The input MWCNT concentrations were 1, 0.01, and
0.005 mg L1. In addition to breakthrough curves, retention
profiles were measured and numerically modeled in order toobtain information on MWCNT mass balance, retention
mechanisms, and to more accurately predict environmental
fate.

2.

Materials and methods

2.1.

Carbon nanotubes

Radioactively (14C) labeled MWCNT were prepared by catalytic
chemical vapor deposition (Bayer Technology Services GmbH,
51368 Leverkusen, Germany) using 14C-benzene as feedstockgas. The synthesis procedure was a lab-scale setup of the
Baytubes production process with slight modifications(Bierdel et al., 2007). After synthesis, the MWCNT were boiled
in 70% nitric acid (SigmaeAldrich Chemie GmbH, 89555
Steinheim, Germany) for 4 h under reflux to remove residual
metal catalysts and to enhance their stability in the aqueous
phase by addition of oxygen containing functional groups (e.g.
carboxylic groups) to their surfaces (Nagasawa et al., 2000;
Pumera, 2007; Xia et al., 2007; Smith et al., 2009). Afterwards,
the MWCNT were removed from the acid by filtering througha 0.45 mm polytetrafluoroethylene (PTFE) membrane andrinsing with deionized water until a neutral pH-value wasachieved in the filtrate (Mattison et al., 2011). Finally, functionalized MWCNT were dried in an oven at 45  C and stored atroom temperature until needed.
Morphological properties of MWCNT were characterizedusing a transmission electron microscope (TEM, Philips CM20
FEG, FEI Company, 5651 GG Eindhoven, The Netherlands). The
amountofmetalcatalystsbeforeandaftertheacidtreatmentwas
determined using inductively coupled plasma-mass spectrometry (ICP-MS, Agilent 7500ce, Agilent Technologies, Inc., 71034
Böblingen, Germany). Oxygen containing functional groups on
the MWCNT induced by the functionalization procedure wereidentified using X-ray photoelectron spectroscopy (XPS, Phi 5600,
Physical Electronics Inc., Chanhassen, MN 55317, USA).
For preparation of nanoparticle suspensions, 1 mg of 14Clabeled functionalized MWCNT were added to 1 L of 1 mM KCl
solution and ultrasonicated for approximately 10 min at 65 W
using a cup horn sonicator (Branson Sonifier W-250, Danbury, CT 06813-1961, USA) until no aggregates were visible. To
obtain suspensions with lower MWCNT concentrations (0.01
and 0.005 mg L1), the stock suspensions (1 mg MWCNT L1)
were diluted with 1 mM KCl to achieve the desired concentrations. The concentration of the MWCNT suspensions wasassessed by measuring the radioactivity of five 2.5 ml aliquots.

935

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Each aliquot was added to 5 mL of scintillation cocktail (InstaGel Plus, Perkin Elmer, 63110 Rodgau, Germany), shaken, andthe radioactivity was measured using a liquid scintillation
counter (LSC, Perkin Elmer, 63110 Rodgau, Germany). The
standard deviation of the radioactivity measured in the five
replicates was low, indicating that the MWCNT suspensions
were homogeneous. The specific radioactivity of the functionalized MWCNT was approximately 3.2 MBq mg1.
The stability and electrophoretic mobility of suspensions
were determined using unlabeled functionalized MWCNT.
The critical coagulation concentration of 10 mg L1 MWCNT in
KCl (1e100 mM) solution was determined by visual observations over a 24 h period. The hydrodynamic radius and theelectrophoretic mobility of MWCNT suspensions (1 mg L1,
1 mM KCl, pH 8.5) were determined using a Zetasizer Nano
(Malvern Instruments GmbH, 71083 Herrenberg, Germany).
The hydrodynamic radius of MWCNT was measured immediately after suspension preparation, after 1 h, and after 24 h.

2.2.

Porous media

Three quartz sands with different median grain sizes were
utilized in the experiments. In particular, we employed twohigh purity quartz sands (Quarzwerke GmbH, 50226 Frechen,
Germany) with an average grain size of 350 mm and 240 mm,
and a sterile fused silica sand (Teco-Sil, C-E Minerals, King ofPrussia, PA, 19406, USA) with an average grain size of 607 mm.
The sands were sequentially treated for 2 h with 65% nitricacid to remove metal oxides, and then 10% peroxide to eliminate organic material (Mattison et al., 2011). The organiccarbon content of the sands was below 0.01 wt%. The sands
were repeatedly rinsed with deionized water following bothacid and peroxide treatments until a neutral pH was achievedin the rinse water. Electrophoretic mobilities of milled sandsamples were determined in 1 mM KCl solution using thepreviously described Zetasizer Nano.

2.3.

Column transport experiments

Stainless steel columns with an inner diameter of 3 cm anda length of 12 cm were used for all experiments. The column
ends were fitted with a stainless steel plate (1 mm openings)
and a PTFE mesh (200 mm openings) to support the sand andto ensure uniform flow. The columns were incrementally
filled with porous medium by trickling sand and deionizedwater into the column, and then tapping the column witha rubber mallet. The packed column was connected toa pump (MCP V 5.10, Ismatec SA, 8152 Glattbrugg,
Switzerland) on the inlet side and a fraction collector (FoxyJr., Teledyne Isco Inc., Lincoln, NE 68504, USA) on the outlet
side. A Darcy velocity of 0.62e0.66 cm min1 (Table 1) wasapplied for all experiments; equivalent to a pore watervelocity of 1.39e1.66 cm min1. The flow direction was fromthe column bottom to the top. Preliminary transport studies
were conducted using an empty column to determine losses
of MWCNT due to the experimental setup. The initial
MWCNT concentration (Co) that was applied to the column
was corrected for these losses.
The wet-packed column was rinsed with around 30 porevolumes of the 1 mM KCl solution before starting a transport
experiment. A pulse of approximately 3 pore volumes ofa conservative tracer (1 mM KBr) was applied to determine thecolumn porosity and dispersivity. Afterwards, this tracer was
flushed to background levels using 1 mM KCl solution. Effluent
solutions were collected using the fraction collector every 30 s(e.g., 2.3 mL per vial). The effluent bromide concentrations
were determined using a high performance liquid chromatograph (STH 585, Dionex, Sunnyvale, CA, USA) equipped witha UV-detector (UV2075, Jasco, Essex, UK).
The same procedure was repeated using the MWCNT
suspensions. In this case, the effluent concentrations of
MWCNT were measured using the previously discussed liquid
scintillation counter method. Retention profiles for MWCNT
were also determined after recovery of the breakthroughcurves. In this case, the packed column was excavated in
0.5e1 cm thick increments. The sand from each layer wasdried and then homogenized using a mill. The crushed sandwas then divided into five 500 mg replicates and combusted at
900  C using a biological oxidizer (OX 500, R.J. Harvey Instrumentation Corporation, Tappan, NY 10983, USA). The
emerging 14CO2 was dissolved in vials filled with scintillation
cocktail (Oxisolv, MERCK KGAA, 64293 Darmstadt, Germany)and the radioactivity was measured using the liquid scintillation counter. Table 1 summarizes measured column properties determined from the conservative tracer experiments
and mass balance information for MWCNT.

Table 1 e Experimental conditions, hydraulic parameters, and mass balance information (as fractions of the total applied
mass; eff e effluent, soil e soil profile) for all column experiments. The electrolyte was 1 mM KCl.
MWCNT input
Pore waterdc [mm] q [cm min1]
Porosity Disp.a [cm] CNT effb CNT soilc Total massconcentration [mg L1]
velocity [cm min1]
balance
0.01
0.01
0.01
0.005
1
1
1

240
350
607
350
240
350
607

0.64
0.63
0.62
0.64
0.64
0.66
0.66

1.39
1.66
1.51
1.45
1.42
1.53
1.43

0.46
0.38
0.41
0.44
0.45
0.43
0.46

a Disp. is the longitudinal dispersivity estimated on basis of the conservative tracer BTC.
b CNT eff is the total amount of CNT in the liquid phase.
c CNT soil is the total amount of CNT in the solid phase.

0.029
0.043
0.090
0.051
0.038
0.052
0.069

0.05
0.27
0.51
0.13
0.04
0.33
0.73

0.91
0.72
0.46
0.95
0.82
0.56
0.21

0.96
0.99
0.98
1.07
0.85
0.88
0.94

936

2.4.

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Mathematical modelingTransport experiments were analyzed using the HYDRUS-1D
code, a finite element model for simulating one-dimensional
movement of water, heat, and multiple solutes in (variably) saturated media (Simunek et al., 2008). The code includes
a nonlinear least squares optimization routine (Marquardt,
1963) that allows model parameters to be inversely fitted toexperimental breakthrough curves (BTC) and retention
profiles (RP). Weights to data points were adjusted so that thecontributions to the minimized objective function by the sumof squared deviations between measured and fitted values
were approximately the same for BTC and RP. The conservative tracer BTC for each column was simulated using
the advective dispersive equation (ADE) and the column
porosity and dispersivity was obtained by inverse optimization (Table 1).
The transport of MWCNT was simulated using the ADEwith terms for one site kinetic retention. The total massbalance equation is written as (Gargiulo et al., 2007):


vqC
vS
v
vC vqC
þr ¼
qD

vt
vt vx
vx
vx

(1)

where q [] is the volumetric water content, r is the bulk
density of the porous media [ML3, where M and L denoteunits of mass and length, respectively], t is the time [T; T
denotes units of time], x is the spatial coordinate [L], q is theflow rate [LT1], C is the particle concentration in the aqueous
phase [NcL3, where Nc is the number of MWCNT], S is thesolid phase particle concentration [NcM1], and D is thehydrodynamic dispersion coefficient [L2T1]. The corresponding solid phase particle mass balance equation is given
as:
r

vS
¼ qk1 jC  k2 rS
vt(2)

where k1 [T1] is the first-order retention coefficient [T1], k2 is
the first-order detachment coefficient [T1], and j [] isa dimensionless function to account for time and depthdependent retention. The parameter j is given as:

j¼

1

S
Smax



b
dc þ xdc(3)

where Smax [Nc M1] is the maximum solid phase particle
concentration, dc [L] is the median diameter of the sandgrains, and b [] is an empirical variable that controls theshape of the retention profile.
The above model formulation is very flexible and canaccount for time-dependent breakthrough curves and retention profiles that are exponential, uniform, and/or hyperexponential with depth. The first term on the right side ofEq. (3) accounts for time-dependent blocking/filling of retention sites using a Langmuirian approach (Gargiulo et al., 2007).
This blocking term implies that retention decreases with time
and that the retention profile becomes uniform with depth as
S approaches Smax. The second term on the right side of Eq. (3)describes depth-dependent retention (e.g., a decreasing
retention rate with depth). When b ¼ 0 this term equals 1 andan exponential distribution of retained MWCNT is predictedwith depth similar to conventional filtration theory.
Conversely, when b > 0 is employed then the retention profile
of MWCNT exhibits a hyper-exponential shape (e.g., a higher
deposition rate close to the column inlet). Bradford et al. (2003)
found an optimal value of b ¼ 0.432 for different sized
spherical latex microspheres and sand grains. However,this value of b did not adequately describe the observed
depth-dependency in retention profile shape for the nonspherical MWCNT. This parameter was therefore reestimated by simultaneously fitting b and k1 to BTC and RP
from the three sized sands. Based on this information a valueof b for MWCNT was estimated from the average value fromthese experiments as 0.765 (standard deviation ¼ 0.1). A
similar value for b (0.8) was employed by Wang et al. (2012b) in
MWCNT transport studies.
Four model formulations based on Eqs. (1)e(3) will beconsidered in this work. The conventional attachment anddetachment model (M1) is obtained by setting j ¼ 1. A modelthat includes attachment, detachment, and Langmuirian
blocking (M2) is achieved when b ¼ 0. A depth-dependent
retention model (M3) is acquired by setting b ¼ 0.765 andsetting Smax to a large value so that the first term on the rightside of Eq. (3) goes to 1. Finally, a time and depth-dependent
retention model (M4) is given when b ¼ 0.765 and Smax is set
equal to a value resulting in the first term on the right side ofEq. (3) being smaller than 1.

3.

Results and discussion

3.1.

Characterization of MWCNT

Results of the ICP-MS measurements indicated that catalyst
impurities were significantly removed after the functionalization process. The acid treatment reduced the amount of Mg,
Mn, Co, and Al from 3.26 wt% to less than 0.07 wt%. Thus,
metal impurities were almost completely removed and were
not expected to influence interaction of MWCNT with theporous media.
Fig. 1 shows XPS spectra of as-received and functionalized
MWCNT. The intensity of the binding energy of the O 1s
spectra (Fig. 1a) was significantly higher after the acid treatment, indicating that functionalization produced an increased
amount of groups containing oxygen. The two materials also
show differences in their C 1s spectra (Fig. 1b). The peak at
285 eV, representing the sp2 carbon atoms of the graphenesheets, was dominant for both samples (Xia et al., 2007).
Between 287 and 293 eV the spectra of the functionalized
MWCNT showed a shoulder that is attributable to carbon
atoms exhibiting bonds to oxygen atoms (Xia et al., 2007).
Hence, the XPS spectra demonstrate that acid treatment of
MWCNT produced functional groups that carried oxygen.
Transmission electron microscope (TEM) images (Fig. 2)
show that MWCNT were tortuous particles with a high aspectratio. At higher magnification, the multiple walls of carbon
were visible (Fig. 2b). The size distribution of MWCNT is very
heterogeneous. Pauluhn (2010) reported that MWCNT had
a median diameter of 10e15 nm and a median length of
200e1000 nm. Qualitative analysis of Fig. 2 yielded similar
results. The hydrodynamic radius of MWCNT dispersed inw a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4937

Fig. 1 e High resolution O 1s (a) and C 1s (b) spectra of untreated (blue line) and functionalized (red line) multiwalled carbon
nanotubes obtained using X-ray photoelectron spectroscopy.

1 mM KCl was determined using dynamic light scattering(DLS) to range between 170 and 210 nm. DLS measurements
and TEM images did not reveal significant changes in size anddiameter after the acid treatment.
Reliable determination of MWCNT stability and interactionenergies using conventional approaches (DLS and DLVO
calculations) is not trivial because of their complex size
distribution and configuration (Fig. 2). However, the criticalcoagulation concentration for unlabeled, functionalized
MWCNTs was found to be 40 mM KCl in simple aggregation
experiments. The electrolyte concentration used in thetransport experiments (1 mM KCl) was significantly below thisvalue. Furthermore, no visual MWCNT aggregates wereobserved after 4 h in 1 mM KCl solution and the hydrodynamic
radius at three measurement times (t ¼ 0 h, t ¼ 1 h, andt ¼ 24 h) was in the same range. Thus, it was assumed that all
MWCNT suspensions were stable for the duration of thetransport experiments (approximately 1 h). The electrophoretic mobility for MWCNT in 1 mM KCl solution (pH 8.5) was

measured to be 2.85  108 m2 V1 s1. The electrophoretic
mobility values for the sands were 3.90  108 (240 mm),
4.47  108 (350 mm), and 3.15  108 m2 V1 s1 (607 mm).
The negative charge on both MWCNT and sand, and the low IS
conditions, suggests that repulsive electrostatic conditions,that were unfavorable for attachment, existed for MWCNT
during the transport experiments.

3.2.

Effect of grain size

Column experiments were conducted to assess the effect of
the collector grain size on MWCNT transport and retention.
Fig. 3 presents observed and simulated BTCs for MWCNT inthree different sized sands (240, 350, and 607 mm) whenq ¼ 0.62e0.66 cm min1, IS ¼ 1 mM, and Co ¼ 0.01 mg L1. The
BTCs are plotted as the normalized effluent concentration (C/Co) as a function of pore volumes that have been flushed
through the column. The corresponding observed and simulated RPs for the MWCNT are shown in Fig. 4. The RPs are

Fig. 2 e Transmission electron micrographs of multiwalled carbon nanotubes at different magnifications.

938

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Improved agreement with the BTCs was obtained for models
that included the Langmuirian blocking term (M2 and M4).
The Akaike information criterion (AIC) (Akaike, 1974) wasused to assess the relative ability of the four model formulations to describe the BTC and RP data. The AIC value isa measure of the goodness of a fit that penalizes for adding
fitting parameters; i.e., the model with the lowest value of AIC
is preferred. The AIC decreases from M1 to M4, indicating that
M4 provides the best agreement with the observed data. For
a particular model, k1 and Smax increased with decreasing
grain size. Previous studies on the transport and deposition offullerene (C60) nanoparticles reported similar trends (Li et al.,2008). These trends reflect an increasing rate of retention
and more retention locations in the finer textured sand.
MWCNT retention shown in Fig. 4 was highest close to thecolumn inlet and then rapidly decreased with distance.
Consistent with the BTCs shown in Fig. 3, greater MWCNT
retention occurred with decreasing sand size. Large deviations
were observed between experimental and simulated RPs formodels M1 and M2. The Pearson’s correlation coefficient for
the RP ðR2soil Þ was less than 0.58. Models M1 and M2 tended tounderestimate the high concentrations near the column inlet
and overestimated the concentrations at greater distances,
especially for finer textured sand. Thus, RPs were notconsidered for fitting model parameters using models M1 andM2. These observations indicate that the experimental RPs

plotted as normalized solid phase concentration (S/Co) as
a function of distance. The total mass balance information
presented in Table 1 ranged from 0.85 to 1.07.
The MWCNT breakthrough curves (Fig. 3) reached thecolumn outlet only slightly after the conservative tracer (datanot shown), indicating that size exclusion was negligible for
MWCNT (Bradford et al., 2003). A clear decrease in the
maximum MWCNT effluent concentration occurred withdecreasing grain size. This can partially be explained by anincreasing rate of mass transfer to the solid surface witha decrease in sand grain size as predicted by filtration theory(Yao et al., 1971; Tufenkji and Elimelech, 2004). The MWCNT
BTCs in the 240 and 350 mm sands also exhibited some timedependent blocking behavior (increasing breakthroughconcentrations with time), suggesting that retention locations
were being filled over time. The observed concentration tailing
was negligible after recovery of the BTC. The value of k2 wastherefore set equal to zero for all of these simulations.
The fitted model parameters to the BTCs (M1 and M2) aswell as to BTCs and RPs (M3 and M4) are provided in Table 2, as
well as the Pearson’s correlation coefficient for the BTC ðR2eff Þ.
A direct comparison between k1 values for the four model
formulations is not meaningful since models M1 and M2 do
not account for a depth-dependency, whereas models M3 andM4 do. All four model formulations (M1, M2, M3, and M4)
described the MWCNT BTCs quite well with ðR2eff Þ>0.85.

0.08

0.4

a

b

240 µmfit M1
fit M20.06

350 µmfit M1
fit M20.3

fit M3fit M3fit M4

C/Co

C/Co

fit M4
0.04

0.02

0.2

0.1

0.00
0

1

2

3

4

0.0

5

0

1

2

Pore volume

3

4

5

Pore volume

0.6c

607 µmfit M1
fit M2fit M30.4

C/Co

fit M4

0.2

0.0
0

1

2

3

4

5

Pore volume

Fig. 3 e Observed and simulated breakthrough curves for MWCNT in three different sized quartz sands: 240 mm (a), 350 mm(b), and 607 mm (c). Experimental data were fitted with four different models including: attachment and detachment (M1);
attachment, detachment, and blocking (M2); depth-dependent retention (M3); and blocking combined with depthdependent retention (M4). The flow rate was 0.62e0.66 cm minL1, the electrolyte was 1 mM KCl, and the MWCNT input
concentration was 0.01 mg LL1. Note different vertical scales in the figures.

939

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4
0

a

-2

-2

-4

-4

Depth [cm]Depth [cm]0-6240 µmfit M1-8b-6
350 µmfit M1-8

fit M2fit M2fit M3-10

fit M3-10

fit M4fit M4

-12
0

1

2

3

4

5

-12

6

0

1

2

3

S/Co [mL g-1]
0

4

5

6

S/Co [mL g-1]cDepth [cm]

-2
-4
-6
607 µmfit M1-8

fit M2fit M3-10

fit M4
-12
0

1

2

3

4

S/Co [mL g-1]

Fig. 4 e Observed and simulated retention profiles for MWCNT in three different sized quartz sands: 240 mm (a), 350 mm (b),and 607 mm (c). Experimental data were simulated with four different models including: attachment and detachment (M1);
attachment, detachment, and blocking (M2); depth-dependent retention (M3); and blocking combined with depthdependent retention (M4). The flow rate was 0.62e0.66 cm minL1, the electrolyte was 1 mM KCl, and the MWCNT input
concentration was 0.01 mg LL1.

were hyper-exponential with distance, and that the retention
coefficient exhibited a depth-dependency. Models M3 and M4
include a depth-dependency in the retention coefficient, andtherefore provided a much better description of the MWCNT
RPs than either M1 or M2. The value of ðR2soil Þ for the M3 and M4models was >0.98. Model M4 provided the best overall
description of the data when both BTCs and RPs wereconsidered.
Hyper-exponential RPs have frequently been reported in
the literature for colloids, microorganisms, and nanoparticles
under unfavorable attachment conditions (Bradford andBettahar, 2006; Bradford and Toride, 2007; Gargiulo et al.,2007, 2008; Wang et al., 2011; Wang et al., 2012a). A variety ofreasons for hyper-exponential RPs have been identified,including: straining at grainegrain contacts and surface
roughness locations (Shellenberger and Logan, 2001; Bradford
et al., 2002 ,2003; Yoon et al., 2006), particle aggregation (Chenand Elimelech, 2006, 2007; Chatterjee and Gupta, 2009;
Chatterjee et al., 2010), hydrodynamic factors (Li et al., 2005;
Bradford et al., 2009; Wang et al., 2011), and chemical
heterogeneity on the sand and colloid (Bolster et al., 1999; Liet al., 2004; Tufenkji and Elimelech, 2005; Tong and Johnson,2006). The relative contribution of each of these factors to
the observed RP data is difficult to ascertain without additional information. However, our data does clearly indicate
a strong dependency of the RP shape on the grain size under

low IS conditions. The contribution of physical processes tothe observed hyper-exponential RPs has to be proven.
However, other results in the literature indicate that straining
played a dominant role in the CNT retention under low IS
conditions (Jaisi et al., 2008; Wang et al., 2012b).
Previous transport studies with CNT measured and simulated only BTCs (Jaisi et al., 2008; Jaisi and Elimelech, 2009; Liuet al., 2009; Mattison et al., 2011). Determination and modelingof retention profile are scarce (Wang et al., 2012b). Accurate
simulation of both BTCs and RPs is needed in order to assess
the fate and risks associated with MWCNT migration. To
illustrate this point, Fig. 5 presents the simulated RPs of
MWCNT in the three different sized sands over a distance of
500 cm when using the various model formulations that were
calibrated to the column BTC (M1 and M2) or BTC and RP (M3and M4) data, respectively (Fig. 3). In Fig. 5 and the discussion
below we set the lower limit of the predicted S/Co to 1E5 mL g1. Increasing deviations in the model predictions
occurred with transport distance and grain size. The M1 andM2 predictions were quite similar for a given grain size, withno breakthrough at a depth of 500 cm. The maximum transport distance predicted by the M1 and M2 models was around200 cm in the coarsest textured 607 mm sand. In contrast,
models M3 and M4 predict similar low levels of MWCNT
breakthrough at 500 cm for the two largest grain sizes (350 and
607 mm). Consequently, using M1 and M2 to predict MWCNT

940

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4Table 2 e Fitted model parameters using different model formulations. Correlation of observed and fitted data is reflectedby R2effDsoil for BTC and RP, by R2eff for BTC, and by R2soil for RP.
Co [mg L1] dc [mm] Model R2effþsoil R2eff R2soil
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
1
1
1
00.005

240
350
607
240
350
607
240
350
607
240
350
607
240
350
607
240
350
607
350

M1
M1
M1
M2
M2
M2
M3
M3
M3
M4
M4
M4
M4
M4
M4
M4
M4
M4
M4

0.57
0.45
0.32
0.54
0.43
0.30
0.98
0.96
0.99
0.98
0.98
0.98
0.98
0.97
0.98
0.95
0.97
0.98
0.97

0.88
0.98
0.98
0.96
0.99
0.98
0.86
0.98
0.98
0.91
0.99
0.98
0.74
0.95
0.97
0.98
0.98
0.97
0.78

0.44
0.53
0.49
0.54
0.50
0.47
0.99
0.99
0.99
0.99
0.99
1.00
0.99
0.98
0.99
0.93
0.97
0.81
0.98

b

k1 [min1] Standard k2 [min1] Standard Smax [Bq g1] Standard
error k1
error k2
error Smax
0.34
0.17
0.08
0.35
0.19
0.09
11.47
4.70
1.64
11.97
5.14
1.72
11.75
4.73
1.60
22.94
7.27
1.69
6.75

0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765
0.765

0.47Eþ1
1.75E-1
2.90E-1
0.43Eþ1
0.24Eþ1
0.34E-2
0.25E-2
0.47Eþ1
0.43E-1
2.37E-1
0.69E-1
0.57E-1
2.52E-3
1.22E-1
0.57E-1
4.26E-1
2.64E-1
1.09E-1
3.61E-1

0.5E-30.3E-2
0.3E-2NF
0.17E-2
0.22E-2

289
68
49

0.15
5.40
14.40

2760
338
303
11,9674659
1516
11,967
4659
1516
4659

717
45
129
NF
NF
NF
1419
283
129
NF

NF e denotes not fitted.

0

a

-100

-100

-200

-200

Depth [cm]Depth [cm]0-300
240 µm M1
240 µmM2

-400

b

-300
350 µm M1
350 µm M2-400

240 µm M3

350 µm M3
350 µm M4

240 µm M4
-500
1E-5

1E-4

1E-3

1E-2

S/Co

1E-1

1E+0

1E+1

-500
1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

S/Co [mL g-1]

[mL g-1]0cDepth [cm]

-100

-200

-300
607 µm M1
607 µm M2-400

607 µm M3
607 µm M4

-500
1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

S/Co [mL g-1]

Fig. 5 e Predicted retention profiles for MWCNT in 500 cm long columns packed with 240 mm (a), 350 mm (b), and 607 mm (c)sand. Here the normalized solid phase concentration (S/Co) is plotted on a log-scale as a function of distance. Simulations
employed model parameters determined in Figs. 3 and 4. Four different model formulations were considered, namely:attachment and detachment (M1); attachment, detachment, and blocking (M2); depth-dependent retention (M3); andblocking combined with depth-dependent retention (M4).

941

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4fate would lead to the conclusion that MWCNT will be
retained in the various sands before reaching a depth ofaround 200 cm. In contrast, M3 and M4 would predicta transport of MWCNT to depths greater than 500 cm. Sincemodels M3 and M4 provided the best description of the BTCs
and RPs at the column scale (Figs. 3 and 4), the predictions ofthese models are more reliable than the predictions obtained
from the other two models (M1 and M2).

3.3.

Effect of MWCNT input concentration

Additional column experiments were performed to investigate the influence of MWCNT input concentrations. Fig. 6
presents observed and simulated BTCs (Fig. 6a) and RPs(Fig. 6b) for MWCNT in 350 mm sand whenq ¼ 0.62e0.66 cm min1, IS ¼ 1 mM, and Co ¼ 1, 0.01, and
0.005 mg L1. Based on the findings of the previous section,
only simulation results from model M4 were considered inFig. 6. Simulation fits to BTCs and RPs were very good, witha ðR2eff Þ>0.97 and ðR2soil Þ>0.96. Tables 1 and 2 provide
a summary of the associated experimental, mass balance, andmodel parameters.
Inspection of Fig. 6a indicates that the fraction of theinjected mass of MWCNT that was recovered in the effluent
increased with Co. In addition, the shape of the BTC was muchsteeper for the highest Co ¼ 1 mg L1 condition. These trends
may be explained by blocking behavior as retention locations
fill up over time and produce increasing effluent concentrations (Bradford and Bettahar, 2006). Consistent with observations in Fig. 6a, a higher Co is expected to fill a given Smax more
rapidly. The value of Smax was fitted for the highest Co andthen kept constant for the lower input concentrations. The
fitted retention rate parameter k1 was similar for all Co. After
recovery of the BTC, concentration tailing tended to be low,
but was most pronounced for the highest Co ¼ 1 mg L1
condition. This indicates that some of the MWCNT retention
was reversible at higher Co when Smax was filled to a greater
extent (Kretzschmar et al., 1995).
Similar to the BTCs (Fig. 6a), the shape of the RPs was also
sensitive to Co (Fig. 6b). In particular, the fraction of MWCNT
0.6

retained close to the column inlet increased with decreasing
Co. Conversely, the RPs became less hyper-exponential (moreuniform) with increasing Co. Blocking provides an explanation
for changes in the RPs shape with Co (Bradford and Bettahar,
2006; Bradford et al., 2009; Zhang et al., 2010; Kim et al.,2011). As MWCNT retention approaches Smax the overall rateof retention decreases and the RPs become uniform withdepth (Bradford et al., 2009).
Results from Fig. 6 demonstrate that Co can have a large
impact on the transport and retention behavior of MWCNT.
Enhanced retention and limited mobility of MWCNTs is expected for lower, more environmentally relevant concentrations of MWCNT. These Co effects need to be considered inmodels that are used to predict MWCNT fate and risks,
otherwise they may overestimate their transport potential
and groundwater concentrations.

3.4.

Effect of grain size and MWCNT input concentration

Fig. 7 presents observed and simulated BTCs (Fig. 7a) and RPs(Fig. 7b) for MWCNT in three different sized sands (240, 350,
and 607 mm) when q ¼ 0.62e0.66 cm min1, IS ¼ 1 mM, andCo ¼ 1.0 mg L1. Simulation results from model M4 wereconsidered in Fig. 7. Simulation fits to BTCs and RPs weregood, with a ðR2eff Þ>0.97 and ðR2soil Þ>0.81. Tables 1 and 2 provide
a summary of the associated experimental, mass balance, andmodel parameters. Similar to Figs. 3 and 4, Fig. 7 examines theinfluence of grain size on MWCNT transport and retention.
However, the experiments shown in Fig. 7 were conducted at
a Co that was two orders of magnitude higher than in Figs. 3
and 4.
Comparison of Figs. 3 and 4 and 7 reveals a similar trend ofincreasing MWCNT retention (decreasing breakthrough) withdecreasing grain size at both Co levels. In contrast, the timedependent blocking behavior shown in the BTCs (e.g.,increase in the normalized effluent concentrations shown in
Figs. 3 and 7a) was much steeper for experiments conductedat the higher Co. The RPs were also more hyper-exponential at
the lower Co (see Figs. 4 and 7b). As explained in the lastsection, these trends occur because retention locations were

0

a

b

1 mg/L0.01 mg/L-20.005 mg/L
1 mg/L M4-4

Depth [cm]

0.4

C/Co

0.01 mg/L M4
0.005 mg/L M4

0.2

-6

1 mg/L0.01 mg/L-80.005 mg/L
1 mg/L M4-100.01 mg/L M4
0.005 mg/L M4

0.0
0

1

2

3

Pore volume

4

5

-12
0

1

2

3

4

5

6

7

8

9

S/Co [mL g-1]

Fig. 6 e Observed and simulated breakthrough curves (a) and retention profiles (b) for MWCNT at input concentrations (Co)equal to 1, 0.01, and 0.005 mg LL1. The flow rate was 0.62e0.66 cm minL1, the electrolyte was 1 mM KCl, and the grain sizeof the quartz sand was 350 mm. The data was simulated using a model combining depth- and time-dependent retention
(M4).

942

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4

1.0

a

0

607 µm350 µm

0.8

240 µm
607 µm M4

C/Co

Depth [cm]350 µm M4

0.6

b

-2

240 µm M4
0.4

-4
-6

607 µm350 µm-8

240 µm

607 µm M4

0.2

-10

350 µm M4

240 µm M4
0.0
0

1

2

3

4

-12

5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S/Co [mL g-1]

Pore volume

Fig. 7 e Observed and simulated breakthrough curves (a) and retention profiles (b) for MWCNT in three different sized quartz
sands: 240 mm (a), 350 mm (b), and 607 mm (c). The flow rate was 0.62e0.66 cm minL1, the electrolyte was 1 mM KCl, and the
MWCNT input concentration was 1 mg LL1. The data was simulated using a model combining depth- and time-dependent
retention (M4).

25

12000

a

Co=1 mg/L
Co=0.01 mg/L

20b

Co=1mg/L

10000

Co=0.01 mg/L

Smax (Bq mL-1)

k1(min-1)

8000
15

10

5

6000
4000
2000

0
240

350

0

607

240

grain size [µm]

350

607

grain size [µm]Fig. 8 e Plots of the depth-dependent (model M4) retention coefficient (k1) (a) and the maximum solid phase particle
concentration (Smax) (b) as a function of sand grain size for input MWCNT concentrations (Co) of 1 and 0.01 mg LL1.

filled more rapidly at a higher Co. However, close inspection of
Figs. 3, 4 and 7 indicates that this concentration-dependenttransport behavior was also a function of the sand grain size.
Examination of parameters k1 (Fig. 8a) and Smax (Fig. 8b) as
a function of grain size for the two Co levels revealed that thevalues of k1 and Smax both increased with decreasing grain
size. As mentioned above, this reflects greater MWCNT
retention rates and number of retention locations in the finer
textured sand. However, higher Co values accentuated thistrend with k1 and this rate of enhancement increased withdecreasing grain size. Hence, the observed concentration
dependency of MWCNT transport became more importantwith increasing Co and decreasing grain size. In contrast to ourobservations with MWCNT, Bradford and Bettahar (2006)
observedforspherical
latex
microspheres
that
concentration-dependent colloid transport behavior became
more important with increasing grain size. These trends canbe explained by the effect of porous media’s pore structure on
MWCNT retention (Tan et al., 1994). The non-spherical
MWCNT have a high aspect ratio and we hypothesize thatsolid phase MWCNT may create a porous network with theability to retain particles (Sumanasekera et al., 2010; Xin et al.,2012). It is logical to anticipate that the retained MWCNT
network will become more significant at higher Co and insmaller grain sized sand. This finding suggests that theparticle shape will have a strong influence on concentrationdependent colloid transport.

4.

Conclusions

This study highlights the importance of considering input
concentration and retention profiles to allow reliable predictions of MWCNT transport and fate. The work provides new
information on the mobility of multi-walled carbon nanotubes
because both breakthrough curves and retention profiles wereconsidered. Additionally, experiments were performed using
more environmentally relevant MWCNT concentrations.
Results demonstrate that normalized MWCNT transport
increased with higher input concentrations and in coarser
textured sand. The retention profiles showed that the majorityof MWCNT retention occurred near the surface of the porous
medium, especially for lower input concentrations and smaller
sand sizes. Simulations that considered a combination of time-w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4

and depth-dependent retention provided a good description of
the experimental data. Analysis of model parameters demonstrated that concentration dependent transport behavior
became more important for smaller grain sizes and higher
input concentrations. These trends were attributed to thecomplex shape and deposition morphology of MWCNT insmaller pore spaces at higher input concentrations. The resultsof this study suggest that functionalized MWCNT tend to be
mobile in sandy subsurface environments, and may be transported to depths greater than 500 cm. Thus, aquifer contamination cannot be excluded. Further work is needed to assess
the mobility of MWCNT in natural porous media, such as
undisturbed soils.

Acknowledgements
This research was performed within the framework of the‘NanoFlow’-project supported by the German Federal Ministryof Education and Research. Analysis of bromide in the liquidsamples by Stephan Köppchen is highly appreciated. The
technical assistance of Herbert Philipp is gratefully acknowledged. We also thank Wolfgang Schierenberg for the determination of the critical coagulation concentration.

references

Akaike, H., 1974. A new look at the statistical model identification.
Automatic Control, IEEE Transactions on 19 (6), 716e723.
Bierdel, M., Buchholz, S., Michele, V., Mleczko, L., Rudolf, R.,
Voetz, M., Wolf, A., 2007. Industrial production of multiwalledcarbon nanotubes. Physica Status Solidi (B) 244 (11),3939e3943.
Bolster, C.H., Mills, A.L., Hornberger, G.M., Herman, J.S., 1999.
Spatial distribution of deposited bacteria following miscible
displacement experiments in intact cores. Water Resources
Research 35 (6), 1797e1807.
Bradford, S.A., Bettahar, M., 2005. Straining, attachment, anddetachment of oocysts in saturated porous media. Journal ofEnvironmental Quality 34 (2), 469e478.
Bradford, S.A., Bettahar, M., 2006. Concentration dependenttransport of colloids in saturated porous media. Journal ofContaminant Hydrology 82 (1e2), 99e117.
Bradford, S.A., Toride, N., 2007. A Stochastic Model for colloidtransport and deposition all rights reserved. No part of thisperiodical may be reproduced or transmitted in any form or by
any means, electronic or mechanical, including photocopying,recording, or any information storage and retrieval system,without permission in writing from the publisher. Journal ofEnvironmental Quality 36 (5), 1346e1356.
Bradford, S.A., Yates, S.R., Bettahar, M., Simunek, J., 2002. Physicalfactors affecting the transport and fate of colloids in saturated
porous media. Water Resources Research 38 (12), 12.
Bradford, S.A., Simunek, J., Bettahar, M., van Genuchten, M.T.,
Yates, S.R., 2003. Modeling colloid attachment, straining, andexclusion in saturated porous media. Environmental Science& Technology 37 (10), 2242e2250.
Bradford, S.A., Kim, H.N., Haznedaroglu, B.Z., Torkzaban, S.,
Walker, S.L., 2009. Coupled factors influencing concentrationdependent colloid transport and retention in saturated porous

943

media. Environmental Science & Technology 43 (18),6996e7002.
Chatterjee, J., Gupta, S.K., 2009. An agglomeration-based model
for colloid filtration. Environmental Science & Technology 43(10), 3694e3699.
Chatterjee, J., Abdulkareem, S., Gupta, S.K., 2010. Estimation ofcolloidal deposition from heterogeneous populations. Water
Research 44 (11), 3365e3374.
Chen, K.L., Elimelech, M., 2006. Aggregation and deposition kinetics
of fullerene (C60) nanoparticles. Langmuir 22 (26), 10994.
Chen, K.L., Elimelech, M., 2007. Influence of humic acid on theaggregation kinetics of fullerene (C60) nanoparticles inmonovalent and divalent electrolyte solutions. Journal of
Colloid & Interface Science 309 (1), 126e134.
Farré, M., Gajda-Schrantz, K., Kantiani, L., Barceló, D., 2009.
Ecotoxicity and analysis of nanomaterials in the aquatic
environment. Analytical and Bioanalytical Chemistry 393 (1),81e95.
 
Gargiulo, G., Bradford, S., Sim
unek, J., Ustohal, P., Vereecken, H.,
Klumpp, E., 2007. Bacteria transport and deposition underunsaturated conditions: the role of the matrix grain size andthe bacteria surface protein. Journal of ContaminantHydrology 92 (3e4), 255e273.
Gargiulo, G., Bradford, S.A., Simunek, J., Ustohal, P.,
Vereecken, H., Klumpp, E., 2008. Bacteria transport anddeposition under unsaturated flow conditions: the role ofwater content and bacteria surface hydrophobicity. Vadose
Zone Journal 7 (2), 406e419.
Gottschalk, F., Sonderer, T., Scholz, R.W., Nowack, B., 2009.
Modeled environmental concentrations of engineered
nanomaterials (TiO2, ZnO, Ag, CNT, fullerenes) for different
regions. Environmental Science & Technology 43 (24),9216e9222.
Handy, R., von der Kammer, F., Lead, J., Hassellöv, M., Owen, R.,
Crane, M., 2008. The ecotoxicology and chemistry of
manufactured nanoparticles. Ecotoxicology 17 (4), 287e314.
Iijima, S., 1991. Helical microtubules of graphitic carbon. Nature
354 (6348), 56e58.
Jaisi, D.P., Elimelech, M., 2009. Single-walled carbon nanotubes
exhibit limited transport in soil columns. Environmental
Science & Technology 43 (24), 9161e9166.
Jaisi, D.P., Saleh, N.B., Blake, R.E., Elimelech, M., 2008. Transport ofsingle-walled carbon nanotubes in porous media: filtration
mechanisms and reversibility. Environmental Science &Technology 42 (22), 8317e8323.
Kim, H., Lee, M., Chae, W., Ezeh, T.D., Walker, S.L., 2011. Coupledeffect of input concentration and solution ionic strength on
colloid transport in saturated porous media. International
Proceedings of Chemical, Biological, and Environmental
Engineering 17, 195e198.
Klaine, S.J., Alvarez, P.J.J., Batley, G.E., Fernandes, T.F.,
Handy, R.D., Lyon, D.Y., Mahendra, S., McLaughlin, M.J.,
Lead, J.R., 2008. Nanomaterials in the environment: behavior,fate, bioavailability, and effects. Environmental Toxicology
and Chemistry 27 (9), 1825e1851.
Köhler, A.R., Som, C., Helland, A., Gottschalk, F., 2008. Studying
the potential release of carbon nanotubes throughout theapplication life cycle. Journal of Cleaner Production 16 (8e9),927e937.
Kretzschmar, R., Robarge, W.P., Amoozegar, A., 1995. Influence of
natural organic matter on colloid transport through saprolite.
Water Resources Research 31 (3), 435e445.
Lam, C.W., James, J.T., McCluskey, R., Hunter, R.L., 2004.
Pulmonary toxicity of single-wall carbon nanotubes in mice 7
and 90 days after intratracheal instillation. Toxicological
Sciences 77 (1), 126e134.
Lam, C.-W., James, J.T., McCluskey, R., Arepalli, S., Hunter, R.L.,
2006. A review of carbon nanotube toxicity and assessment of

944

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 9 3 3 e9 4 4potential occupational and environmental health risks.
Critical Reviews in Toxicology 36 (3), 189e217.
Li, X., Scheibe, T.D., Johnson, W.P., 2004. Apparent decreases incolloid deposition rate coefficients with distance of transport
under unfavorable deposition conditions: a general
phenomenon. Environmental Science & Technology 38 (21),5616e5625.
Li, X., Zhang, P., Lin, C.L., Johnson, W.P., 2005. Role ofhydrodynamic drag on microsphere deposition and reentrainment in porous media under unfavorable conditions.
Environmental Science & Technology 39 (11), 4012e4020.
Li, Y., Wang, Y., Pennell, K.D., Abriola, L.M., 2008. Investigation of
the transport and deposition of fullerene (C60) nanoparticles inquartz sands under varying flow conditions. Environmental
Science & Technology 42 (19), 7174e7180.
Liu, X., O’Carroll, D.M., Petersen, E.J., Huang, Q., Anderson, C.L.,
2009. Mobility of multiwalled carbon nanotubes in porous
media. Environmental Science & Technology 43 (21),8153e8158.
Marquardt, D., 1963. An algorithm for least-squares estimation of
nonlinear parameters. Journal of the Society for Industrial andApplied Mathematics 11 (2), 431e441.
Mattison, N.T., O’Carroll, D.M., Kerry Rowe, R., Petersen, E.J., 2011.
Impact of porous media grain size on the transport of multiwalled carbon nanotubes. Environmental Science &Technology 45 (22), 9765e9775.
Mauter, M.S., Elimelech, M., 2008. Environmental applications ofcarbon-based nanomaterials. Environmental Science &Technology 42 (16), 5843e5859.
Mueller, N.C., Nowack, B., 2008. Exposure modeling of engineered
nanoparticles in the environment. Environmental Science &Technology 42 (12), 4447e4453.
Nagasawa, S., Yudasaka, M., Hirahara, K., Ichihashi, T., Iijima, S.,
2000. Effect of oxidation on single-wall carbon nanotubes.
Chemical Physics Letters 328 (4e6), 374e380.
Nowack, B., Bucheli, T.D., 2007. Occurrence, behavior and effects
of nanoparticles in the environment. Environmental Pollution
150 (1), 5e22.
Pauluhn, J., 2010. Multi-walled carbon nanotubes (Baytubes):
approach for derivation of occupational exposure limit.
Regulatory Toxicology and Pharmacology: RTP 57 (1), 78e89.
Pumera, M., 2007. Carbon nanotubes contain residual metal
catalyst nanoparticles even after washing with nitric acid atelevated temperature because these metal nanoparticles are
Sheathed by several graphene sheets. Langmuir 23 (11),6453e6458.
Saleh, N.B., Pfefferle, L.D., Elimelech, M., 2008. Aggregation
kinetics of multiwalled carbon nanotubes in aquatic systems:
measurements and environmental implications.
Environmental Science & Technology 42 (21), 7963e7969.
Shellenberger, K., Logan, B.E., 2001. Effect of molecular scaleroughness of glass beads on colloidal and bacterial deposition.
Environmental Science & Technology 36 (2), 184e189.
Sinnott, S.B., 2002. Chemical functionalization of carbon nanotubes.
Journal of Nanoscience and Nanotechnology 2 (2), 113e123.
 

Sim
unek, J., van Genuchten, M.T., Sejna,M., 2008. Development
and applications of the HYDRUS and STANMOD software
packages and related codes. Vadose Zone Journal 7 (2),587e600.
Smith, B., Wepasnick, K., Schrote, K.E., Cho, H.-H., Ball, W.P.,
Fairbrother, D.H., 2009. Influence of surface oxides on thecolloidal stability of multi-walled carbon nanotubes:
a structure-property relationship. Langmuir 25 (17), 9767e9776.
Sumanasekera, G.U., Chen, G., Takai, K., Joly, J., Kobayashi, N.,
Enoki, T., Eklund, P.C., 2010. Charge transfer and weakchemisorption of oxygen molecules in nanoporous carbon
consisting of a disordered network of nanographene sheets.
Journal of Physics: Condensed Matter 22 (33), 334208.
Tan, Y., Gannon, J.T., Baveye, P., Alexander, M., 1994. Transport ofbacteria in an aquifer sand: experiments and model
simulations. Water Resources Research 30 (12), 3243e3252.
Tian, Y., Gao, B., Silvera-Batista, C., Ziegler, K., 2010. Transport ofengineered nanoparticles in saturated porous media. Journalof Nanoparticle Research 12 (7), 2371e2380.
Tian, Y., Gao, B., Wang, Y., Morales, V.L., Carpena, R.M.,
Huang, Q., Yang, L., 2012. Deposition and transport offunctionalized carbon nanotubes in water-saturated sandcolumns. Journal of Hazardous Materials 213e214 (0), 265e272.
Tong, M., Johnson, W.P., 2006. Colloid population heterogeneity
drives hyperexponential deviation from classic filtration
theory. Environmental Science & Technology 41 (2), 493e499.
Tufenkji, N., Elimelech, M., 2004. Deviation from the classicalcolloid filtration theory in the presence of repulsive DLVO
interactions. Langmuir 20 (25), 10818e10828.
Tufenkji, N., Elimelech, M., 2005. Spatial distributions ofcryptosporidium oocysts in porous media: evidence for dual
mode deposition. Environmental Science & Technology 39(10), 3620e3629.
Wang, D., Paradelo, M., Bradford, S.A., Peijnenburg, W.J.G.M.,
Chu, L., Zhou, D., 2011. Facilitated transport of Cu withhydroxyapatite nanoparticles in saturated sand: effects ofsolution ionic strength and composition. Water Research 45(18), 5905e5915.
Wang, D., Bradford, S.A., Harvey, R.W., Hao, X., Zhou, D., 2012a.
Transport of ARS-labeled hydroxyapatite nanoparticles insaturated granular media is influenced by surface charge
variability even in the presence of humic acid. Journal ofHazardous Materials 229e230 (0), 170e176.
Wang, Y., Kim, J.H., Baek, J.B., Miller, G.W., Pennell, K.D., 2012b.
Transport behavior of functionalized multi-wall carbon
nanotubes in water-saturated quartz sand as a function of
tube length. Water Research 46 (14), 4521e4531.
Xia, W., Wang, Y., Bergsträßer, R., Kundu, S., Muhler, M., 2007.
Surface characterization of oxygen-functionalized multiwalled carbon nanotubes by high-resolution X-ray
photoelectron spectroscopy and temperature-programmed
desorption. Applied Surface Science 254 (1), 247e250.
Xin, S., Guo, Y.-G., Wan, L.-J., 2012. Nanocarbon networks foradvanced rechargeable lithium batteries. Accounts ofChemical Research 45 (10), 1759e1769.
Yao, K.M., Habibian, M.T., O’Melia, C.R., 1971. Water and waste
water filtration. concepts and applications. Environmental
Science & Technology 5 (11), 1105e1112.
Yoon, J.S., Germaine, J.T., Culligan, P.J., 2006. Visualization ofparticle behavior within a porous medium: mechanisms forparticle filtration and retardation during downward transport.
Water Resources Research 42 (6), W06417.
Zhang, W., Morales, V.N.L., Cakmak, M.E., Salvucci, A.E.,
Geohring, L.D., Hay, A.G., Parlange, J.Y., Steenhuis, T.S., 2010.
Colloid transport and retention in unsaturated porous media:
effect of colloid input concentration. Environmental Science &Technology 44 (13), 4965e4972.