Science of the Total Environment 656 (2019) 70–79

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Science of the Total Environment
journal homepage: www.elsevier.com/locate/scitotenv

Mechanisms of graphene oxide aggregation, retention, and release inquartz sandYan Liang a, Scott A. Bradford b,⁎, Jiří Šimůnek c, Erwin Klumpp daSchool of Resources, Environment and Materials, Guangxi University, Nanning, China
US Salinity Laboratory, USDA, ARS, Riverside, CA, United States
Department of Environmental Sciences, University of California, Riverside, CA, United Statesd
Agrosphere Institute, IBG-3, Forschungszentrum Jülich GmbH, Jülich, Germanybc

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T• GO interaction depended on GO geometry and orientation, roughness, andadsorbed Ca2+.
• GO interacted in a shallow primary minimum under low ionic strength conditions.
• Level arms from roughness and graingrain contacts were important for GO
retention.
• A mathematical model interpreted theaggregation, retention, and release ofGO.

a r t i c l e

i n f oArticle history:
Received 12 October 2018
Received in revised form 15 November 2018
Accepted 17 November 2018
Available online 22 November 2018
Editor: Kevin V. Thomas
Keywords:
Graphene oxide
Aggregation
ReleaseBlocking
Ripening

a b s t r a c t
The roles of graphene oxide (GO) particle geometry, GO surface orientation, surface roughness, and nanoscalechemical heterogeneity on interaction energies, aggregation, retention, and release of GO in porous media
were not fully considered in previous studies. Consequently, mechanisms controlling the environmental fate of
GO were incompletely or inaccurately quantiﬁed. To overcome this limitation, plate-plate interaction energies
were modiﬁed to account for these factors and used in conjunction with a mathematical model to interpretthe results of GO aggregation, retention, and release studies. Calculations revealed that these factors had alarge inﬂuence on the predicted interaction energy parameters. Similar to previous literature, the secondary minimum was predicted to dominate on smooth, chemically homogeneous surfaces that were oriented parallel toeach other, especially at higher ionic strength (IS). Conversely, shallow primary minimum interactions weresometimes predicted to occur on surfaces with nanoscale roughness and chemical heterogeneity due to adsorbed
Ca2+ ions, especially when the GO particles were oriented perpendicular to the interacting surface. Experimental
results were generally consistent with these predictions and indicated that the primary minimum played a majorrole in GO retention and the secondary minimum contributed to GO release with IS reduction. Cation exchange(Na+ replacing Ca2+) enhanced GO release with IS reduction when particles were initially deposited in the presence of Ca2+ ions. However, retained GO were always completely recovered into the excess deionized water
when the sand pore structure was destroyed during excavation, and this indicates that primary minima wereshallow and that the pore structure also played an important role in GO retention. Further evidence for the⁎ Corresponding author.
E-mail address: scott.bradford@ars.usda.gov (S.A. Bradford).

https://doi.org/10.1016/j.scitotenv.2018.11.258
0048-9697/© 2018 Elsevier B.V. All rights reserved.

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

71

role of pore structure on GO retention was obtained by conducting experiments in ﬁner textured sand and at
higher input concentrations that induced greater aggregation. In both cases, greater GO retention occurred,
and retention proﬁles became more hyperexponential in shape.
© 2018 Elsevier B.V. All rights reserved.

1. Introduction
Graphene oxide (GO) is an oxidized form of graphene-based
nanomaterial that contains reactive oxygen functional groups, such ashydroxyl, carbonyl, carboxyl and phenol (Dreyer et al., 2010). GO has
found widespread use in industrial applications because of its excellent
electrochemical properties (Zhu et al., 2010). A number of studies havealso investigated the use of GO for pollutant removal in groundwater,
surface water, and wastewater (Wang et al., 2013; He et al., 2018).
However, there is concern about the inevitable release of GO into theenvironment due to its potential to adversely inﬂuence organisms,
cells, and ecosystems (Guo and Mei, 2014; Liu et al., 2011).
A number of physicochemical factors are known to inﬂuence the aggregation, transport, retention, and release of GO in porous media (Heet al., 2017). Commonly examined effects of solution chemistry on GO
environmental fate include the ionic strength (IS) (Dong et al., 2016;
Dong et al., 2017; Fan et al., 2015a; Lanphere et al., 2013; Lanphereet al., 2014; Liu et al., 2013; Qi et al., 2014; Wang et al., 2017a; Wanget al., 2018; Wu et al., 2013b; Xia et al., 2015) and cation type (Fanet al., 2015b; Wang et al., 2017a; Wang et al., 2018; Xia et al., 2015).
An increase in solution IS has been reported to increase GO aggregation
and retention in porous media due to the compression of the double
layer thickness and charge screening which increases the depth of thesecondary minimum (Dong et al., 2016; Lanphere et al., 2013; Liuet al., 2013; Wang et al., 2017a; Wang et al., 2018; Xia et al., 2015). Divalent cations have been reported to increase GO aggregation and retention due to cation bridging (Fan et al., 2015b; Wang et al., 2018;
Wu et al., 2013a; Xia et al., 2015).
Previous GO transport studies that have conducted interaction energy calculations assumed smooth and chemically homogeneous surfaces to interpret their results (Chowdhury et al., 2014; Dong et al.,2016; Feriancikova and Xu, 2012; Liu et al., 2013; Wang et al., 2017a;
Wang et al., 2018; Wu et al., 2013b; Xia et al., 2015). In this case, GO interactions were mainly attributed to secondary minimum interactions(Dong et al., 2016; Liu et al., 2013; Wang et al., 2017a; Wang et al.,2018; Xia et al., 2015). A decrease in the solution IS to deionized (DI)water should eliminate the secondary minimum and induce disaggregation or release of retained particles (Shen et al., 2018; Torkzaban
and Bradford, 2016; Wang et al., 2017a). Indeed, release pulses of previously retained GO have been observed in column studies when the IS
was reduced to DI water (Dong et al., 2016; Lanphere et al., 2014;
Wang et al., 2017a). However, only a fraction of the retained GO particles was released when the IS was reduced to DI water, especiallywhen GO particles were deposited in the presence of divalent cations(Dong et al., 2016; Wang et al., 2017a). Interaction energy calculations
on smooth, chemically homogeneous surfaces also cannot explain theenhanced GO aggregation and retention in the presence of divalent cations at low IS (Fan et al., 2015b; Wang et al., 2018; Wu et al., 2013a; Xiaet al., 2015), or complete recovery of retained GO following sand excavation (Lanphere et al., 2014; Sun et al., 2015; Wang et al., 2017a).
These observations indicate that other factors were contributing to the
GO retention and release besides the secondary minimum.
One potential explanation for these deviations between conventional interaction energy predictions and experimental observations isdue to violation of assumptions in these calculations. In particular,
nanoscale surface roughness and chemical heterogeneity have beenshown to have a large inﬂuence on interaction energy parameters(Bendersky and Davis, 2011; Bhattacharjee et al., 1998; Bradford et al.,2017; Bradford and Torkzaban, 2012). For example, the presence ofnanoscale roughness and/or chemical heterogeneity can locally reduce
and/or eliminate the energy barrier on electrostatically unfavorable surfaces (Bendersky and Davis, 2011; Bhattacharjee et al., 1998; Bradford
and Torkzaban, 2013; Henry et al., 2011; Hoek and Agarwal, 2006;
Suresh and Walz, 1996), and nanoscale roughness can dramatically reduce the depths of the secondary and primary minima, especiallywhen roughness occurs on both surfaces (Bradford et al., 2017;
Bradford et al., 2018). Shen et al. (2018) demonstrated that sphericalcolloids could attach in a primary minimum on concave and/or convex
surfaces under unfavorable electrostatic conditions, with convex locations being more hydrodynamically favorable. Furthermore, GO requires additional modiﬁcation to conventional interaction energy
calculations to account for its ﬁnite plate geometry and orientation
with the surface. Wu et al. (2013a) demonstrated that the interactionenergy for multi-walled carbon nanotubes was sensitive to its orientation with the interacting surface. Wang et al. (2017a) showed how theplate structure of GO could be accounted for in interaction energy calculations but did not consider the inﬂuence of this structure during aggregation or the orientation of the plate with the surface. No studies haveconsidered the role of surface roughness and chemical heterogeneity
in conjunction with GO plate geometry and surface orientation. This information is needed to accurately predict the adhesive interactions that
contribute to GO aggregation, retention, and release.
The GO input concentration (Co) can also potentially inﬂuence GO
aggregation and retention through several different processes that are
not fully understood or quantiﬁed. For example, an increase in the suspension concentration is expected to increase the frequency of collisions and aggregation (Lee, 1983), although this effect has not yet
been examined for GO suspensions. Conversely, an increase in Co has
also been reported to decrease the retention rate coefﬁcient and enhance GO transport because of more rapid ﬁlling/blocking of available
retention sites (Sun et al., 2015). Blocking has commonly been observedin GO transport studies (Lanphere et al., 2014; Sun et al., 2015; Wanget al., 2017a). Aggregating GO suspensions have been associated withincreased straining, ripening behavior (a decrease in efﬂuent concentration with continued GO injection), and changes in the particle size distribution during transport. For example, straining is expected toincrease with increasing aggregate size, decreasing grain size, and to
produce retention proﬁles with a more hyperexponential shape(Bradford et al., 2003). Ripening of GO has sometimes been observed
to occur under higher IS conditions and in the presence of divalent cations (Lanphere et al., 2014). The average particle size of GO has beenfound to increase during transport through porous media, although asmaller GO particle size and more retention was observed in ﬁner textured sand due to an increase in the GO mass transfer to the solid
phase (Sun et al., 2015). However, decreasing GO retention with a decreasing sand size has also been reported and attributed to an increasein hydrodynamic shear force (Wang et al., 2017b). These conﬂicting
ﬁndings indicate that further research is needed to clarify the roles of
Co and grain size on GO retention.
The objective of this study is to clarify the mechanisms of aggregation, retention, and release of GO in porous media under various physicochemical conditions, including IS, cation type, Co, and grain size. Thisdata was interpreted using novel interaction energy calculations andan advanced model that considered advection and dispersion transport,
ﬁrst-order retention, blocking or ripening, and transient (IS reduction
and cation exchange) release. The interaction energy calculations for
GO-GO and GO-sand accounted for the plate geometry of GO, horizontal
and vertical orientations of the GO plate with a surface, and nanoscale

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Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

roughness and chemical heterogeneity on both the solid water interface
and GO. These interaction energy calculations, retention and transient
release experiments, and retention proﬁles were used to better infer
the mechanisms of GO retention and release. Additional aggregationand transport studies were conducted at different Co and grain sizes to improve our understanding of the inﬂuence of concurrent aggregation on
time- (blocking or ripening) and depth-dependent (hyperexponential retention proﬁles) retention, and straining processes. The collected data
provides valuable insight into the mechanisms of aggregation, retention,and release of GO and other particles (e.g., clays) with plate structure.
This information is important for the assessment of the fate of GO in soil
and groundwater environments.
2. Materials and methods
2.1. Solution chemistry and porous media
Electrolyte solutions were made using DI water and NaCl or CaCl2(analytical reagent) with various solution IS, i.e., different concentrations of 1, 10, 20, 50, 75, 100, 150, and 200 mM NaCl or 0.10, 0.20,
0.33, 0.40, 0.50, 0.60, 0.70, 0.83, 1.67, 2.50, and 3.33 mM CaCl2. These solutions were unbuffered and the pH ranged from around 7 to 8.
Three sizes of analytically pure quartz sand (Sinopharm Chemical
Reagent CO., Ltd., China) were employed in column experiments, withmedian grain sizes of 1090, 519, or 330 μm. To minimize the trace
amount of metal oxides and organic impurities that can occur in quartz
sand, puriﬁcation procedures were conducted before sand column
packing (Fan et al., 2015a). The surface charge characteristics of the puriﬁed sand were determined using a ZetaSizer Nano ZS90 (Malvern Instruments, Worcestershire, U.K.) after it had been milled into powders
and placed in selected NaCl or CaCl2 solutions.
2.2. GO suspensions
The raw GO suspension (2 g L−1) was purchased from Carmery Materials Technology Co. Ltd., Shanxi, China. Information on the surface
characterization of these GO particles (e.g., AFM, FT-IR, Raman spectra,
and XPS) is already provided in the literature (Xia et al., 2017). The suspension for each experiment was freshly prepared by diluting the raw
concentrated GO suspension into a selected NaCl or CaCl2 solution toachieve an approximate concentration of 5, 10, 50, or 100 mg L−1 GO.
The GO suspension was shaken by hand and then sonicated for
15 min in a sonication bath. The ZetaSizer apparatus was used tomeasure the hydrodynamic diameter and the zeta potential of GO
suspensions.
Aggregation experiments were conducted by measuring the hydrodynamic diameter of GO in the suspension every 5 s over a 50 min
duration with the ZetaSizer. The aggregation rate and attachment efﬁciency were calculated using Eqs. (S1)–(S3).
Concentrations of GO were determined using a UV–Vis spectrophotometer (Thermo ScientiﬁcTM Evolution 300, U.S.) at a wavelength of
230 nm. GO concentrations were evaluated using a calibration curve between the absorbance and standard solutions (R2 N 0.9995).

(PV) of a selected background electrolyte solution. A D2O tracer pulse(100 mL) was injected into the column followed by at least 5 PV of
the background solution. A 100 mL pulse of the GO suspension was
injected into the column, followed by ﬂushing with several PV of theparticle-free background solution until the efﬂuent concentration was
b0.5% of the input concentration (Phase I). The inﬂuent GO suspension
was continuously mixed with a magnetic stirrer during GO injection.
The column efﬂuent was collected continuously in glass tubes using afraction collector with 4 mL for each sample. Efﬂuent concentrationsof the tracer were quantiﬁed by a high-performance liquid chromatography (D-7000 HPLC, High-Technologies Corporation, Japan) with a refractive index detector, whereas the GO concentration was determinedusing the UV–Vis spectrophotometer. Tracer and GO breakthroughcurves (BTCs) were obtained from these efﬂuent concentrations. After
recovery of the BTCs, the porous medium in the packed column was
carefully excavated in 1 cm increments (12 layers in total) and placedin DI water to release and resuspend GO for concentration measurements. The GO retention proﬁle (RP) was subsequently determinedfrom this information and the measured dry mass of sand in eachincrement.
2.3.2. Release experiments
Additional experiments were conducted to study the inﬂuence of IS
reduction and cation exchange on the release of GO following the recovery of the BTC. Determination of the GO BTC followed the same protocol
as for the transport experiment (Phase I). After recovery of the GO BTC
in various NaCl and CaCl2 solutions, different solution chemistry elution
sequences were applied to deduce the effects of the IS reduction andcation exchange on the release of the retained GO. The GO release by
the IS reduction was studied by ﬂushing columns with DI water(Phase II). This is the only release phase that was considered when GO
was retained in the presence of the NaCl solution. Conversely, when
GO was retained in the presence of CaCl2 (Phase I) then a series of solution chemistry elution steps was employed in the release phase,namely: DI water (Phase II); NaCl at the same IS as in the retention experiment (Phase III); DI water (Phase IV); 100 mM NaCl (Phase V); andDI water (Phase VI). After completion of the release experiment, the GO
RP was determined following the same protocol as for the transport
experiments.
2.4. Interaction energy calculations
Interaction energy calculations were conducted to better understand mechanisms contributing to GO aggregation, retention, and release under various solution chemistry conditions. In this work, theGO geometry, GO orientation, surface roughness, and nanoscale chemical heterogeneity were considered for interaction energy calculations.
Section S2 of the Supporting information (SI) provides details
pertaining to these calculations. The dimensionless depths of the primary (Φ1min) and secondary (Φ2min) minima, and the energy barrierheight (Φbar) were obtained by analyzing the interaction energy
proﬁles.
2.5. Mathematical modeling2.3. Column experiments
2.3.1. Transport experiments
Saturated transport experiments were performed following similar
procedures to our previous study (Liang et al., 2013). In brief, astainless-steel column with a 3 cm inner diameter and a 12 cm length
was wet-packed with quartz sand. The background electrolyte solution(NaCl or CaCl2) and velocity were kept constant in a given transport experiment. The steady-state Darcy velocity of approximately 0.7 cm/min
was applied to the column in an up-ﬂow mode using a peristaltic pump.
The transport experiment was conducted using the following sequence.
The packed column was preconditioned with around 50 pore volumes

Numerical simulations of GO transport experiments were conductedusing HYDRUS-1D (Šimůnek et al., 2016) to quantify mechanisms of retention (Phase I), blocking or ripening (Phase I), and transient release(Phases II–VI). Section S3 of the Supporting information describes themodeling approach in detail. Values of the Darcy velocity (q), porosity(θ), bulk density (ρ), and dispersivity (λ) were determined from available experimental information and the D2O tracer. Other model parameters were determined by optimization to GO BTCs, RPs, and/or release
pulses using the nonlinear least squares ﬁtting routine in HYDRUS-1D(Šimůnek et al., 2016). The retention rate coefﬁcient (ksw) was optimized during Phase I, along with the normalized maximum solid

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

phase concentration of deposited GO (Smax/Co) for blocking or the empirical parameter (γ) for ripening. The transient release rate coefﬁcient(krs) and the equilibrium release fraction (Feq) were optimized during
Phases II–VI, whereas the fraction of retained GO that was not released(fnr) was determined from mass balance calculations.
3. Results and discussion
3.1. GO-sand and GO-GO interactions
Table S1 presents a summary of zeta potentials and hydrodynamic
diameters (dp) for various NaCl (1 to 200 mM) and CaCl2 (0.10 to
1.67 mM) solution chemistry conditions considered in this work. This
information on zeta potential and hydrodynamic diameter is also
shown as a function of the solution chemistry in Figs. S1 and S2, respectively. The zeta potential increased from −49.7 to −27.2 mV for sand as
the IS increased from 1 to 200 mM NaCl due to the compression of the
double layer thickness and charge screening (Torkzaban et al., 2010).
Similarly, the zeta potential of GO increased from −29.3 to −18.7 mVover the IS range of 0 to 200 mM NaCl when the GO concentration
was 10 mg L−1. Although the change in GO zeta potentials was rather
small, it was sufﬁcient to signiﬁcantly alter values of dp, which increased
from around 600 nm to almost 2000 nm (Fig. S2a).
Small changes in the IS produced much larger changes in zeta potential and dp for CaCl2 than NaCl (Table S1, Figs. S1 and S2). In particular,
the value of dp increased from 600 to 8000 nm as the CaCl2 concentration increased from 0.10 to 1.67 mM. In addition to compression of
the double layer and charge screening, adsorbed Ca2+ ions can also produce nanoscale chemical heterogeneity due to charge neutralization orreversal (Grosberg et al., 2002; Roy and Dzombak, 1996) and/or cation
bridging (Torkzaban et al., 2012). These factors can explain the enhanced sensitivity of dp to CaCl2 than NaCl.
Interaction energy parameters provide additional insight into factorsthat contribute to GO retention and aggregation. Table S2 summarizes
interaction energy parameters for GO with sand or another GO particle
for all solution chemistries when GO is oriented parallel to theinteracting surface. The energy barrier height (Φbar) and the magnitudeof the secondary minimum (Φ2min) tend to increase with increasing IS.
Note that the probability of GO interaction in a primary minimum(Φ1min) rapidly goes to 0 as Φbar becomes greater than around 5.7(Bradford et al., 2015). The GO aggregation is therefore only predicted
to occur in a strong Φ1min under low IS conditions (1 mM NaCl and ≤0.4 mM CaCl2) because Φbar is smaller than 5.7, whereas no aggregation
is predicted for a higher IS because Φ2min is zero. This behavior is clearly
not consistent with the experimental observations (Figs. S1 and S2). GOinteraction with sand is predicted to be dominated by Φ2min with an increasing IS. Similar conclusions have been reported by other investigators for the parallel orientation of GO (Wu et al., 2013b). However,these calculations do not consider the potentially signiﬁcant inﬂuenceof other GO orientations, GO thickness, nanoscale roughness, and chemical heterogeneity on GO interactions that will be discussed below.
Table S3 shows an illustrative example of the inﬂuence of the GO
thickness (i.e., the GO thickness of 1 or 10 nm) and orientation (paralleland perpendicular) on GO-GO and GO-sand interactions when the IS =20 mM NaCl. Thicker (layered) GO particles increased the magnitudes ofΦbar and Φ2min, and the importance of secondary minimum interactions.
Conversely, the perpendicular orientation of GO particles withinteracting surfaces drastically decreases the magnitudes of Φbar,
Φ2min, and Φ1min in comparison to the parallel orientation, and therefore
increases the probability of primary in comparison to secondary minimum interactions.
The role of nanoscale roughness on interaction energy calculations
was subsequently investigated. Nanoscale roughness is ubiquitous onsand surfaces (Konopinski et al., 2012; Shellenberger and Logan, 2002;
Shen et al., 2011). Table S4 presents interaction energy parameters for
GO with sand or another GO particle for all solution chemistries when73

GO is oriented perpendicular to the interacting surface that has a nanoscale roughness height of 30 nm and a fraction of 0.05 on the sand surface. Table S5 shows similar calculations when the nanoscale roughnessof height of 30 nm and a fraction of 0.05 occurs on both surfaces. A perpendicular orientation of GO in conjunction with small amounts ofnanoscale roughness drastically decreases the magnitudes of Φbar,
Φ2min, and Φ1min and creates primary minimum interactions under all
solution chemistry conditions. However, Φ1min is very shallow and susceptible to diffusive and/or hydrodynamic release only when roughness
occurs on both surfaces. It should be mentioned that the perpendicularorientation is the optimum scenario for primary minimum interactions,but that nanoscale roughness will similarly inﬂuence Φbar, Φ2min, andΦ1min in the parallel orientation. Furthermore, adsorbed Ca2+ ions tosurfaces can produce nanoscale chemical heterogeneity due to charge
neutralization or reversal (Grosberg et al., 2002; Roy and Dzombak,
1996) and/or cation bridging (Torkzaban et al., 2012). Such nanoscalecharge heterogeneity has been demonstrated to produce primary minimum interactions by lowering Φbar and increasing the depth of Φ1min
on a relatively smooth surface, but its relative importance decreases
on surfaces with small amounts of nanoscale roughness (Bradford
et al., 2017; Bradford et al., 2018).
The above information indicates that GO retention and aggregation
will be a strong function of the solution IS, the GO orientation and thickness, the nanoscale roughness on the sand and GO, and the amount ofchemical heterogeneity induced by the presence of Ca2+ ions. Variability in these parameters is expected to produce different strengths andmodes of interaction (e.g., a secondary in comparison to the primary
minimum) that contribute to GO aggregation, retention, and release.
Primary minimum interactions due to nanoscale roughness and perpendicular orientation are expected to be more important at a lower
IS and for CaCl2 experiments. Conversely, both primary and secondary
minimum interactions are expected for the NaCl experiments, with secondary minimum playing a larger role at a higher IS.

3.2. Aggregation of GO
The GO aggregation behavior was investigated over a 50 min period
under different IS and compositions (NaCl and CaCl2 solutions). Fig. 1aand b present values of dp as a function of the concentration of NaCl
and CaCl2 solutions, respectively. GO suspensions were relatively stable
only under 1 mM, 10 mM, and 20 mM NaCl, and 0.10 and 0.20 mM CaCl2
conditions. Conversely, values of dp gradually increased with time andexhibited ﬂuctuations when concentrations were N20 mM NaCl or
0.2 mM CaCl2 and became larger with increasing IS and in the presenceof CaCl2 than NaCl.
The GO aggregation behavior presented in Fig. 1a and b was described with the attachment efﬁciency (α) (Eq. (S3)). The attachment
efﬁciency as a function of the concentration of NaCl and CaCl2 is alsopresented graphically in Fig. S3. It was determined by normalizing theaggregation rate constant (ka) (Eq. (S2)) obtained in a speciﬁc background solution chemistry to the rate constant that was the most favorable for aggregation (ka, fast) (Chen and Elimelech, 2006; Wu et al.,2013b). Variations in dp with the solution chemistry in Fig. 1a and b
can be attributed to differences in the attachment efﬁciency, which increases with the IS at a lower concentration for CaCl2 than NaCl
(Fig. S3). These trends can be explained by interaction energy parameters shown in Tables S2–S5. In particular, the potential for secondaryand primary minimum interactions increases with increasing IS due tocompression of the double layer and charge screening. Secondary minimum interactions are expected to be more pronounced for parallel GO
conﬁgurations, whereas strong primary minimum interactions may
sometimes occur for perpendicular GO conﬁgurations. These contributions occur at a lower IS in the presence of Ca2+ ions which induce
nanoscale chemical heterogeneity (e.g., local charge neutralization orreversal, and/or cation bridging).

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Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

3.3. Transport, retention, and release of GO
This section discusses BTCs and RPs for GO under different IS, cation
types, inﬂuent GO concentrations, and sand grain sizes. The BTCs areplotted as normalized efﬂuent concentrations (C/Co) versus pore volumes. The RPs are plotted as normalized solid phase concentrations(S/Co) as a function of the distance from the column inlet. Some of theﬁgures which present BTCs also include release curves (RCs) undertransient solution chemistry conditions. Experimental conditions andthe mass balance for each column experiment are summarized inTable 1. Simulated BTCs, RPs, and RCs are also shown in the ﬁgures.
Table 2 presents a summary of the ﬁtted model parameters as well as
statistical measures of the goodness of ﬁt.

3.3.1. Ionic strength
Fig. 2 presents observed and simulated BTCs and RCs for GO whenusing 1090 μm quartz sand, Co = 10 mg L−1, and the IS equal to 1, 20,
and 100 mM NaCl during Phase I. An increase in the solution IS led toa signiﬁcant decrease of GO mobility (the efﬂuent mass balance, Meff,in Table 1) and enhanced retention (ksw in Table 2) due to the compression of the double layer thickness and charge screening (Dong et al.,2016; Liu et al., 2013; Wang et al., 2017a; Wang et al., 2018; Xia et al.,2015). Interaction energy parameters reveal that increasing the solution
IS increases the depth of the secondary minimum (Table S2) and the frequency of primary minimum interactions that may sometimes occur
depending on local scale variations in sand surface roughness and the
GO orientation (Tables S4 and S5). In addition, the value of dp for GO
also increased with the solution IS (Fig. 1) and ﬁltration theory indicatesthat this will alter the rate of mass transfer to the sand surface; e.g., theminimum in the mass transfer is expected to occur around dp =1500 nm (Messina et al., 2015).

Table 1
Experimental parameters and the mass recoveries of graphene oxide transport and release
experiments.
d50

Fig. 2

Fig. 3Fig. S5

Fig. 4
Fig. 1. Aggregation of graphene oxide over 50 min as a function of the ionic strength in
NaCl (a), CaCl2 (b), and initial GO suspension concentration in 50 mM NaCl solution (c).

Additional experiments were conducted to investigate the inﬂuence of the initial GO suspension concentration on the aggregation
behavior. Fig. 1c presents values of dp over a 50 min period as a function of the initial GO suspension concentration in the 50 mM NaCl solution. The value of d p increases with time and the initial GO
suspension concentration. Fig. 1c indicates that aggregation rapidly
increased with the initial GO suspension concentration. In particular,
the average distance between GO particles decreases with increasingsuspension concentration and this produces an increased frequency
of GO collisions. Consequently, this concentration dependency of aggregation occurs because of differences in the aggregation rate
(Baalousha, 2009; Lee, 1983).

Fig. 5abFig. 5cd

Fig. S4Co

Cation
−1

μm

mg L

1090
1090
1090
1090
1090
1090
1090
1090

10
10
10
10
10
10
10
10

Recovery, %

mM

MI

MII

1 Na+
20 Na+
100 Na+0.33 Ca2+
0.40 Ca2+
0.83 Ca2+
1.67 Ca2+
100 Na+

95.6
76.3
24.8
91.2
28.7
11.8
0.7
16.3

1.2
3.9
24.4
0.6
0.1
1.6
0.5
11.9

MIII

MIV

MV

MVI

1.1
0.0
2.1
0.1

3.8
0.1
2.3
0.4

1.6
0.5
3.0
0.0

8.1
11.2
9.7
2.5

d50

Co

CationRecovery, %μmmg L−1

mM

Meff

Msand

Mtotal

68.7
65.2
38.4
29.7
65.2
50.7
39.9
29.7
19.0
12.5
96.0
65.2
20.7

33.5
36.9
59.8
67.6
36.9
48.8
65.1
67.6
76.8
86.1
8.6
36.9
86.1

101.2
102.1
98.2
97.3
102.1
99.5
105.0
97.3
95.8
98.6
104.6
102.1
106.8

1090
1090
1090
1090
1090
519
330
1090
519
330
1090
1090
1090

5
10
50
100
10
10
10
100
100
100
10
10
10

+

50 Na
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
1 Na+
50 Na+
100 Na+Fig. 2: release of graphene oxide (GO) by ionic strength reduction; Fig. 3: release ofretained GO by cation exchange and ionic strength reduction; Fig. 4: concentration effect;
Fig. 5ab: grain size effect (Co = 10 mg L−1); Fig. 5cd: grain size effect (Co = 100 mg L−1);
Fig. S4: ionic strength effect; Fig. S5: GO release was initiated by reversing the ﬂow direction; Co, input concentration of GO; MI – MVI are the mass percentages recovered from
Phase I–VI in release experiments; Meff, Msand, and Mtotal are mass percentages recoveredfrom efﬂuent, sand, and total in transport experiments, respectively.

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

75

Table 2Fitted parameter values of graphene oxide retention (Smax/Co, ksw) and release (Feq, krs, and fnr) experiments.

Fig. 2

Fig. 3Fig. 4

Fig. 5abFig. 5cd

Fig. S4Co

CationSmax/Co,ksw,

μm

mg L−1mM

cm3 g−1

min−1

1090
1090
1090
1090
1090
1090
1090
1090
1090
1090
1090
1090
519
330
1090
519
330
1090
1090
1090

10
10
10
10
10
10
10
5
10
50
100
10
10
10
100
100
100
10
10
10

1 Na+
20 Na+
100 Na+0.33 Ca2+
0.40 Ca2+
0.83 Ca2+
1.67 Ca2+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
50 Na+
1 Na+
50 Na+
100 Na+

0.043
0.216
1.493
0.076
0.442
0.334
148.6400.619
0.444
1398.200
0.353
0.444
0.552
0.649
2.319
162,500.000
7.383
0.045
0.444
2.370

0.031
0.114
0.162
0.046
0.096
0.191
3.633
0.066
0.068
0.145
0.087
0.068
0.167
0.269
0.186
0.219
0.246
0.052
0.068
0.187

Cationfnr (II)fnr (III)fnr (IV)fnr (V)fnr (VI)

0.84
0.84
0.68
0.93
1
0.98
0.99

0.81
1
0.96
0.99

0.38
1
0.93
0.99

0.19
0.99
0.90
0.99

0.00
0.83
0.79
0.96

d50

Fig. 2

Fig. 3

R2

d50

Co
−1

μm

mg L

1090
1090
1090
1090
1090
1090
1090

10
10
10
10
10
10
10

Feq,

krs,
min−1

0.101
0.141
0.455

0.080
0.820
0.393
0.207
0.566
0.159
0.116

0.999
0.997
0.915
0.958
0.651
0.808
0.985
0.977
0.979
0.892
0.962
0.979
0.956
0.937
0.891
0.850
0.844
0.998
0.979
0.780

mM
1 Na+
20 Na+
100 Na+0.33 Ca2+
0.40 Ca2+
0.83 Ca2+
1.67 Ca2+

Smax/Co, the normalized maximum solid phase concentration of deposited nanoparticles; ksw, the retention rate coefﬁcient; Feq, equilibrium release fraction; krs, the transient release rate
coefﬁcient; fnr, the fraction of retained GO that is not released in Phases II to VI; R2, Pearson's correlation coefﬁcient.

Blocking was observed and captured by the model when the IS was 1
and 20 mM NaCl. Fitted values of Smax/Co (Table 2) increase with IS, indicating that more of the solid surface area contributed to GO retention.
Conversely, continued injection of GO produced a slight decrease in the
efﬂuent concentration of GO when the IS was 100 mM. This behavior
was accurately captured (Table 2) by the ripening model (Eq. (S19)), although aggregation of GO may also produce this result due to a decreasein the total number of GO particles (Bradford and Leij, 2018). Table 1
and Fig. 1 clearly demonstrate that GO-GO interactions and aggregation,

Fig. 2. Transport, retention and release behavior of graphene oxide in quartz sand.
Retention occurred at an ionic strength of 1, 20, and 100 mM NaCl, respectively,
whereas release was initiated by eluting with DI water. Other experimental conditions
were the same: input concentration, 10 mg L−1; grain size, 1090 μm; Darcy velocity,
0.7 cm/min.

respectively, occurred in the aqueous phase when the IS = 100 mM.
However, aggregation and ripening are related processes that reﬂect
GO-GO interactions in the aqueous phase and the solid phase, respectively. It was not possible to separate these effects from the collected information, but it is logical to anticipate that both aggregation andripening may be occurring simultaneously.
Fig. 2 also shows observed and simulated RCs when the IS during
Phase I (1, 20, and 100 mM) was reduced to DI water during Phase II.
The efﬂuent mass of GO during Phase II was equal to 1.2, 3.9, and24.4% when the Phase I IS equaled 1, 20, and 100 mM NaCl, respectively(Table 1). This trend of increasing efﬂuent mass with the IS during PhaseI reﬂects differences in the amount of GO retention. Around 16 to 32% of
the retained GO was released when the IS was decreased to DI water.
The GO release with IS reduction was adequately modeled (Table 2)
using a release model that considered both equilibrium and kinetic
sites (Eqs. S20–S22). GO release with IS reduction may occur due to either elimination of the secondary minimum, and/or a decrease in theenergy barrier to detachment from a primary minimum to less thanaround 5.7 on a nanoscale rough surface (Shen et al., 2018). Releasefrom a secondary minimum with IS reduction is expected to approach
equilibrium conditions (Feq), whereas release from a primary minimum
is expected to be a slower diffusion-controlled process (krs would become small for deeper minima). Fitted values of Feq and krs tended to increase and decrease, respectively, with an increase in IS during Phase I.
This increase in Feq with IS likely reﬂects an increasing contribution of
secondary minimum interactions (Table S2). However, the releasefrom both primary and secondary minima apparently occurred during
Phase II due to differences in the GO orientation with the surface andthe roughness conditions which produced different interaction
strengths (Tables S2–S5).
Fig. S4a presents observed and simulated GO BTCs when the IS = 1,
50, and 100 mM NaCl and other conditions were the same as in Fig. 2.

76

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

Tables 1 and 2 provide mass balance results and model parameters forthese experiments. The BTCs and trends with IS were fully consistent
with those shown in Fig. 2 and demonstrated the reproducibility of
the results. Fig. S4b presents observed and simulated RPs for GO following completion of Phase I when the IS = 1, 50, and 100 mM NaCl. Consistent with the BTC information (Fig. 2), the retained mass of GO in thesand increased with IS (Table 1). The RPs for the IS = 1 and 50 mM NaCl
were generally well described by the blocking model (Fig. S4b andTable 2). Similarly, the ripening model provided a reasonable description of the IS = 100 mM data (Fig. S4b and Table 2), and consistent
with experimental observations exhibited greater retention near thesand surface than for the low IS conditions. Table 1 indicates that nearly
all of the retained GOs were recovered when determining the RP (thetotal recovered mass ranged from 102.1 to 106.8%). In contrast, only
16 to 32% of the retained GO were recovered with the RC in Fig. 2 during
Phase II. This observation indicates that most of the retained GO following IS reduction were associated with a shallow primary minimum on arough sand surface (Tables S4 and S5), and that level arms from microscopic roughness and grain-grain contacts played an important role in
the GO retention (Torkzaban and Bradford, 2016; Zhang et al., 2016);
e.g., the lever arms are constant during Phases I and II, whereas theyrandomly vary during determination of the RP. An additional experiment was conducted to further demonstrate the role of pore structureon the GO retention. Fig. S5 shows a replicate of the 100 mM experiment. In this case, the GO release was initiated by reversing the ﬂow direction and keeping the IS = 100 mM. A very large release pulse wasobserved when the ﬂow was reversed that accounted for 11.9% of theinjected GO mass, which conﬁrms the importance of surface straining
processes for GO.
3.3.2. Cation type and exchange
Additional experiments were conducted to study the inﬂuence of amultivalent cation and cation exchange on GO transport and release, respectively. Fig. 3a presents observed and simulated BTCs for GO in thepresence of 0.33, 0.40, 0.83, and 1.67 mM CaCl2 when using 1090 μm
quartz sand, and Co = 10 mg L−1. Similar to NaCl (Fig. 2), increasing
the CaCl2 concentration produced an increase in the GO retention due
to the compression of the double layer thickness and charge screening.
However, CaCl2 had a much larger inﬂuence on the GO retention than
NaCl (Fig. 2), even though its IS was much lower (b5 mM). This can be
explained by the greater inﬂuence of Ca2+ than Na+ on the zeta potentials of the sand and GO (Fig. S1), as well as the interaction energies(Tables S2–S5). Furthermore, Ca2+ also enhances aggregation (Fig. 1)
and retention (Figs. 2 and 3a) in comparison to Na+ due to cation bridging and/or charge neutralization or reversals, which reﬂect a form ofnanoscale chemical heterogeneity (Grosberg et al., 2002; Roy andDzombak, 1996; Torkzaban et al., 2012). In comparison to the NaCl experiments (Fig. 2), the retention of GO in the presence of CaCl2 is expected to be more dependent on primary minimum interactions(e.g., the depth of the secondary minimum is much smaller at thelower IS b 5 mM) which may occur on rough surfaces and in the presence of nanoscale chemical heterogeneity (Tables S4 and S5), and on
surface straining processes because of larger aggregate sizes (Fig. 1).
The blocking (Eq. (S18)) or ripening (Eq. (S19)) model accurately
described the measured GO BTCs (Table 2). Blocking was only observedin Fig. 3a when the CaCl2 concentration was 0.33 mM. Conversely, theripening behavior was observed when the CaCl2 concentration was
0.40 and 0.83 mM. Furthermore, almost no breakthrough of GO occurred when the CaCl2 concentration was 1.67 mM. This ripening andcomplete retention behavior reﬂect the potential for increasing GO-GO
interactions in the liquid phase (Fig. 1 and S3) and on the solid phasewith increasing CaCl2 concentrations.
The RCs shown in Fig. 3a provide additional insight into the mechanisms of GO retention and release. For example, injection of DI water
following completion of Phase I (recovery of the BTC), produced avery minor amount of GO release (b1.6%) and this further conﬁrms

Fig. 3. (a) Retention and release behavior of graphene in quartz sand. Retention (PhaseI) occurred at a CaCl2 concentration of 0.33, 0.40, 0.83 and 1.67 mM (IS = 1.0 1.2, 2.5,
and 5.0 mM) respectively, whereas release was initiated by eluting with DI water(Phases II, IV, and VI) and cation exchange (Phases III and V) as summarized in Table 1.
(b) Retention proﬁles after completion of release experiments. Other experimental
conditions were the same: input concentration, 10 mg L−1; grain size, 1090 μm; Darcy
velocity, 0.7 cm/min.

the lack of secondary and the dominance of primary minimum interactions (Tables S2–S5). Two sequences of cation exchange and expansionof the double layer were subsequently initiated by injecting various
strengths of the NaCl solution followed by DI water, respectively. The
exchange of Ca2+ on the solid phase increases with increasing injected
NaCl concentrations (Bradford and Kim, 2010). Very little GO release occurred during the injection of the NaCl (1 to 100 mM) solutions (b3%).
However, much larger amounts of the GO release occurred following
cation exchange in the presence of DI water when the double layer
was expanded (as high as 11.2%). This GO release depended on the
CaCl2 concentration during Phase I and the NaCl concentration during
the cation exchange phase; e.g., higher CaCl2 concentrations tended to
produce less GO release and higher NaCl concentrations enhanced release. These observations indicate that the strength of the primary minimum interactions, caused in part by Ca2+adsorption, can sometimes bereversed by cation exchange and expansion of the double layer. Consistent with primary minimum interactions, the release model indicates aslower release behavior for GO in the presence of CaCl2 than in NaCl
(Fig. 2) that was adequately described using the one-site kinetic releasemodel (Eqs. S20–S22 with Feq = 0).
Observed and simulated GO RPs in the CaCl2 experiments are shownin Fig. 3b following completion of Phase VI. Only limited GO retention
occurred when the CaCl2 concentration during Phase I equaled
0.33 mM, and the RP distribution with depth was nearly uniform. In
contrast, the vast majority of the GO retention occurred near the column
inlet when the CaCl2 during Phase I equaled 0.40, 0.83, and 1.67 mM.

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

This hyper-exponential retention was only partially captured by the ripening model (Eq. (S19)) (Table 2), and this non-exponential behavior
reﬂects the combined inﬂuence of enhanced aggregation (Fig. 1) andsurface straining (Fig. S5) in the presence of CaCl2 (Lanphere et al.,2014). The GO mass balance was nearly complete after recovery of the
BTCs, RCs, and RPs (Table 1). Similar to the NaCl experiments (Fig. 2),
this indicates that GO was interacting in the presence of a shallow primary minimum and/or the signiﬁcant inﬂuence of lever arms on GO retention (Torkzaban and Bradford, 2016; Zhang et al., 2016).
3.3.3. Input concentration
Column experiments were conducted to explore the inﬂuence of Co
on GO transport and retention. Fig. 4 presents observed and simulated
BTCs and RPs for Co = 5, 10, 50, and 100 mg L−1 when the IS =50 mM NaCl and the sand size was 1090 μm. Some evidence of blocking
is apparent in the BTCs when Co = 5, 10, and 100 mg L−1; e.g., an increasing efﬂuent concentration during GO injection. Furthermore, theblocking model provided a satisfactory description of the BTCs
(Table 2), although the model under-predicted the RP concentrationnear the inlet with increasing Co. Blocking is also expected to be a function of Co. In particular, larger values of Co should ﬁll up a ﬁxed numberof retention sites more rapidly and produce a higher efﬂuent concentration when a stable, monodispersed suspension is considered (e.g., Leijet al., 2015). Conversely to this expected behavior for blocking, Fig. 4
shows that the GO efﬂuent mass decreased with increasing Co(Table 1). This observation was therefore attributed to the faster aggregation and larger aggregate sizes that occur with increasing Co (Fig. 1c).
An increase in the aggregate size will alter the rate of mass transfer tothe solid surface (Messina et al., 2015), increase the energy barrier

77

and the depth of the secondary minimum (Shen et al., 2007), and produce more surface straining (Lanphere et al., 2013). These factors likely
explain the deviations between blocking model for experimental RPs athigher values of Co.
3.3.4. Grain size
A sand grain size is another important factor that inﬂuences GOtransport and retention due to its inﬂuence on GO mass transfer to thesolid and pore structure geometry. Fig. 5a and b show observed and predicted BTCs and RPs, respectively, for GO when the median sand size
equaled 330, 519, and 1090 μm, the IS = 50 mM NaCl, and Co was
10 mg L−1. Fig. 5c and d show similar information when Co =100 mg L−1. The aggregation rate is much slower and the aggregate
size is smaller when Co is 10 than 100 mg L−1 (Fig. 1c). Differences in
BTCs and RPs shown in Fig. 5a and b are therefore mainly due to the inﬂuence of the GO mass transfer. In particular, the ﬁltration theory predicts that the mass transfer rate to the solid surface increases with adecrease in the median grain size and this produces a higher value ofksw (Table 2) and more retention (Table 1). The ﬁtted value of Smax/Co
also increases with decreasing grain size (Table 2), and this suggests
the presence of more retention sites. The nearly complete mass balancefrom BTCs and RPs (Table 1) indicates that retained GO was weakly associated with the solid phase either due to shallow secondary or primary minima, and alteration of the lever arms during recovery of theRPs liberated them.
There are similarities and differences in the GO BTCs and RPs in various sands when Co equals 10 (Fig. 5ab) and 100 (Fig. 5cd) mg L−1. Similar to Fig. 5ab, Fig. 5cd show an increase in retention with a decrease in
the median sand size due to differences in the GO mass transfer rate. In
contrast to Fig. 5ab, Fig. 5cd show a greater amount of retention andmore hyper-exponential RPs when Co = 100 mg L−1. Similar to Fig. 4
these observations were attributed to an increase in the aggregation
rate and size with an increase in Co (Fig. 1c). It is interesting to notethat these effects of Co did not have a large inﬂuence on the RP shapefor the largest 1090 μm median grain size, but had a pronounced inﬂuence on the RP shape for smaller 519 and 330 μm grain sizes. This clearly
demonstrates that hyper-exponential RPs were more pronounced insmaller sands and at a higher Co. Both of these factors are consistent
with physical retention mechanisms, such as surface straining, in producing hyper-exponential RPs.
4. Conclusions

Fig. 4. Effect of input concentration on the transport and retention of graphene oxide (GO)in quartz sand: breakthrough curves (a) and retention proﬁles (b) of GO under input
concentrations of 5, 10, 50, and 100 mg L−1, respectively. Other experimental conditions
were the same: electrolyte, 50 mM NaCl; grain size, 1090 μm; Darcy velocity, 0.7 cm/min.

The aggregation, retention, and release behaviors of GO were investigated under different physicochemical conditions (IS, cation type, Co,
and d50). Results indicate that greater GO transport occurred at alower IS, monovalent in comparison to divalent cations, lower Co, andin the coarser textured sand. Furthermore, reversible GO retention occurred with decreases in IS as a result of the expansion of the double
layer and/or cation exchange. Novel interaction energy calculations indicated that GO retention and aggregation would be a strong functionof the solution IS, the GO orientation, the roughness of the sand andGO, and the amount of chemical heterogeneity induced by the presenceof adsorbed multivalent cations. Secondary minimum interactions increased with an IS, whereas primary minimum interactions occurred
at a low IS, especially on rough surfaces and for a perpendicular orientation of GO with the surface. Aggregation and retention of GO were muchstronger in the presence of CaCl2 at a low IS than NaCl at a higher IS, due
to cation bridging and/or charge neutralization or reversals which reﬂect a form of nanoscale chemical heterogeneity. Only a fraction of GO
was released when the IS was reduced to DI water. This released fraction
decreased when GO was initially deposited in the presence of CaCl2 but
could be enhanced by later cation exchange (Na+ displaced Ca2+ on thesolid). This observation indicates that the primary minimum also contributed to GO retention and release and that cation exchange and the
IS reduction could alter the strength of this interaction. However, the78

Y. Liang et al. / Science of the Total Environment 656 (2019) 70–79

Fig. 5. Effect of grain size on the transport and retention of graphene oxide (GO) in quartz sand: breakthrough curves and retention proﬁles of GO under input concentrations of 10 mg L−1(ab) and 100 mg L−1(cd). Other experimental conditions were the same: electrolyte, 50 mM NaCl; Darcy velocity, 0.7 cm/min.

GO mass was completely recovered in the BTCs, RCs, and RPs. Theseﬁndings indicate that retained GO was mainly captured in a shallow primary minimum on a rough sand surface and that level arms from microscopic roughness and grain-grain contacts played an important role in
GO retention, e.g., the level arms acting on retained GO randomly varied
when the sand was excavated from the column and then placed in DI
water. In addition, the coupled effects of aggregation and straining
were shown to be inﬂuenced by Co and d50, and these processes also altered blocking, ripening, and RP shapes. The main features of theseobservations were well described by a mathematical model that
accounted for blocking, ripening, and release of GO during transient solution chemistry conditions. This information is needed to better understand and predict the interactions, retention, and release of colloids/
nanoparticles, especially particles with plate structure, in natural andengineering applications.
Acknowledgments
This research was funded by the National Natural Science Foundationof China (Grant No. 21507015; 170101), Guangxi Natural Science Foundation, China (Grant No. 2015GXNSFCA139015; 2017GXNSFBA198076).
The authors would like to acknowledge Dr. Dengjun Wang for his valuable suggestions.
Appendix A. Supplementary data
The supplementary information provides a brief description and discussion of: (i) determination of aggregation kinetics (S1); (ii) interaction energy calculations (S2); (iii) mathematical modeling (S3); (iv)zeta potentials of graphene oxide (GO) and quartz sand as a functionof the ionic strength (Fig. S1); (v) hydrodynamic diameters of GO as afunction of the IS (Fig. S2); (vi) calculated attachment efﬁciencies for
GO aggregation as a function of the IS (Fig. S3); (vii) effect of IS (1, 50,

and 100 mM NaCl) on the transport and retention of GO (Fig. S4);
(viii) the retention of GO and the GO release in the background electrolyte solution after the column was turned upside down (Fig. S5); (ix) parameters for interaction energy calculations (Table S1); (x) interactionenergy parameters for GO-GO and GO-sand for all solution chemistries
when GO is oriented parallel to the interacting surface (Table S2); (xi)interaction energy parameters for GO-GO and GO-sand for various GO
thicknesses (1 and 10 nm) and orientations (parallel and perpendicular)
with the surface when the IS = 20 mM NaCl (Table S3); (xii) interactionenergy parameters for GO-GO and GO-sand for all solution chemistries
when GO is oriented perpendicular to the interacting surface and oneof the surfaces has a roughness fraction of 0.05 and roughness of heightof 30 nm (Table S4); and (xiii) interaction energy parameters for GO-GO
and GO-sand for all solution chemistries when GO is oriented perpendicular to the interacting surface and both surfaces have a roughness
fraction of 0.05 and roughness of height of 30 nm (Table S5). This information is available free of charge via the Internet. Supplementary data tothis article can be found online at https://doi.org/10.1016/j.scitotenv.
2018.11.258.
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