Retention and transport of silica nanoparticles in saturated porous media: effect of concentration and particle size.

Abstract

Investigations on factors that affect the fate and transport of nanoparticles (NPs) remain incomplete to date. In the present study, we conducted column experiments using 8 and 52 nm silica NPs to examine the effects of NPs' concentration and size on their retention and transport in saturated porous media. Results showed that higher particle number concentration led to lower relative retention and greater surface coverage. Smaller NPs resulted in higher relative retention and lower surface coverage. Meanwhile, evaluation of size effect based on mass concentration (mg/L) vs particle number concentration (particles/mL) led to different conclusions. A set of equations for surface coverage calculation was developed and applied to explain the different results related to the size effects when a given mass concentration (mg/L) and a given particle number concentration were used. In addition, we found that the retained 8 nm NPs were released upon lowered solution ionic strength, contrary to the prediction by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The study herein highlights the importance of NPs' concentration and size on their behavior in porous media. To the best of our knowledge, it is the first report of an improved equation for surface coverage calculation using column breakthrough data.

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Retention and Transport of Silica Nanoparticles in Saturated Porous
Media: Effect of Concentration and Particle Size
Chao Wang,†Aparna Devi Bobba,†Ramesh Attinti,†Chongyang Shen,‡Volha Lazouskaya,†
Lian-Ping Wang,§,* and Yan Jin†,*
†Department of Plant and Soil Sciences, University of Delaware, Newark, Delaware 19716, United States
‡Department of Soil and Water Sciences, China Agricultural University, Beijing 100094, China
§Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716, United States
*
S Supporting Information
ABSTRACT: Investigations on factors that affect the fate and
transport of nanoparticles (NPs) remain incomplete to date. In
the present study, we conducted column experiments using 8
and 52 nm silica NPs to examine the effects of NPs’
concentration and size on their retention and transport in
saturated porous media. Results showed that higher particle
number concentration led to lower relative retention and
greater surface coverage. Smaller NPs resulted in higher
relative retention and lower surface coverage. Meanwhile,
evaluation of size effect based on mass concentration (mg/L)
vs particle number concentration (particles/mL) led to
different conclusions. A set of equations for surface coverage
calculation was developed and applied to explain the different
results related to the size effects when a given mass concentration (mg/L) and a given particle number concentration were used.
In addition, we found that the retained 8 nm NPs were released upon lowered solution ionic strength, contrary to the prediction
by the Derjaguin−Landau−Verwey−Overbeek (DLVO) theory. The study herein highlights the importance of NPs’
concentration and size on their behavior in porous media. To the best of our knowledge, it is the first report of an improved
equation for surface coverage calculation using column breakthrough data.
■INTRODUCTION
The rapid growth of nanotechnology is giving rise to mass
production and widespread application of NPs.1During their
production, application, and disposal, the NPs inevitably enter
the environment. Because of their potential toxicity as well as
their role as carriers for sorbed contaminants, the release of NPs
may lead to environmental contamination.
Retention and transport of NPs in subsurface environment,
especially in saturated porous media, has received considerable
attention. For example, the retention and transport of
manufactured C60,2−12carbon nanotubes,13−16and oxide
NPs2,17−25in saturated porous media have been intensively
studied. In these studies, factors that affect NPs’ retention and
transport have been evaluated, for example, flow velocity,2,18,20
NPs’ surface potential,23and presence of organic species.25,26
Nevertheless, the investigations to date are still largely
incomplete. For instance, while the uniqueness of NPs (e.g.,
small size, large surface to volume ratio, and high reactivity) has
been acknowledged,27systematic study on the effect of particle
size on NPs’ environmental fate remains limited.22,28−31A
general conclusion from previous investigations on size effect
using TiO2, aluminum, and Fe0NPs is that larger NPs have
higher retention.22,23,28,31Nonetheless, it is difficult to draw
definite conclusions because TiO2, aluminum, and Fe0NPs are
easily agglomerated, leading to size changes duringtransport27,32
and making it difficult to determine whether, how, and to what
extent particle size played a role in their transport. Further
investigation of NPs’ size effect that uses relatively stable NPs is
therefore necessary. On the other hand, Auffan et al.33reported
that inorganic NPs with sizes <30 nm show different properties
from those >30 nm and proposed that the definition of NPs be
modified from 1∼100 nm to 1∼30 nm, whereas studies on NPs’
environmental fate with stable sizes smaller than 30 nm are
almost nonexistent.
Another factor that deserves more attention is the effect of
particle concentration onNPs’retentionandtransport inporous
media. The previous studies have demonstrated significant
influence of input concentration on rates and retention
mechanisms of micrometer-size particles (e.g., bacteria, latex,
and aggregated TiO2particles).20,34−37Concentration effect of
NPs,however,hasnotbeenfullyevaluated.38,39Studiesthathave
Received:
Revised:
Accepted:
Published: May 29, 2012
February 3, 2012
May 23, 2012
May 29, 2012
Article
pubs.acs.org/est
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investigated effects of size used the same mass concentrations
whencomparingthebehaviorofdifferentlysizedNPs.22,28,31Itis
not clear whether the comparison is conclusive because at the
same mass concentration (mg/L), particle number concen-
tration (particles/mL) can be orders of magnitude different
when particles being compared span a wide size range. To date
the potential implications of using mass or particle number
concentrationsinthistypeofstudiesoninterpretationofparticle
size effect have not been adequately investigated. Similarly,
standardprotocolshavenotbeendevelopedtoguidestudiesthat
examine the size-dependent toxicological behavior. For example,
Simon-Deckers et al.40evaluated NPs’ size effect on the toxicity
using the same mass concentration, but Jones et al.41and Nair et
al.42performed the evaluation using the same particle number
concentration. This makes comparison between different studies
and interpretation of results difficult. Therefore, potential effect
of concentrations, in terms of mass concentration and particle
number concentration or namely appropriate concentration
expression, needs to be systematically evaluated. Such
information would be useful in the development and
implementation of standard protocols for future investigations
of NPs’ environmental fate and toxicity.
Besides,mostcurrenttheoreticaldescriptionofNPs’retention
and transport is limited to the classical filtration theory (CFT)43
supplemented by the DLVO44,45force representa-
tions.3,5,7,9,15,22,46−50Forexample,Lietal.7investigatedfullerene
depositionandtransportandobservedthattheeffectivecollision
efficiency was more than 1 order of magnitude larger than the
value predicted by the DLVO theory. Conventional DLVO
theory uses approximate expressions, for example, Derjaguin
approximation51to represent electric double layer interaction.
The assumptions under which the approximations hold,52for
example, h ≪ ap(i.e., separation distance is much less than NPs’
radius) and κh ≫ 1 (i.e., separation distance is much larger than
theDebyelength), however, maynotbeapplicable to smallNPs.
Because NPs, especially those with sizes <20∼30 nm, may have
unique properties (e.g., large specific surface area, exponentially
increased surface atoms, and high interfacial reactivity)33or are
smaller than the thickness of electrical double layer,53the
applicability of the DLVO theory for describing their
agglomeration, retention, and transport behavior has been
questioned.30
The objectives of this study were to (1) investigate effects of
concentration and particle size on NPs’ retention and transport
in saturated porous media, and (2) examine the applicability of
the DLVO theory to describe deposition of small NPs on sand
surfaces. Because silica NPs are stable in suspension54,55and
thereby can be more easily controlled to have constant
concentration and particle size, they were selected as
representative NPs in the present study. In addition, the
equations developed by Guzman et al.23were used in order to
calculate the DLVO interaction, considering that the equations
exclude the Derjaguin approximation and thus do not need the
assumptions of h ≪ apand κh ≫ 1.
■MATERIALS AND METHODS
Porous Media. A mixture of Accusands that is composed of
96.9% SiO2and 3.1% CaCO3with a mean diameter of 0.22 mm
(Unimin, Le Sueur, MN) was used in this study. Before use, the
sands were treated to remove metal oxides and other
impurities,56,57following the treatment procedure given in the
Supporting Information (SI).
Silica NPs. Two monodispersed stock suspensions that
contained surfactant-free silica NPs were purchased from the
Nissan Chemical Industries, Ltd. (Tarrytown, NY). The mean
diameters of silica NPs in the two suspensions are 8 ± 2 nm and
52 ± 1 nm, respectively, based on measurements from
transmission electron microscopy (TEM) images (see SI Figure
S1 and experimental procedure for TEM imaging in the SI). The
manufacturer reporteddensitiesof8nmand52nmNPsare1.14
g/mL and 1.30 g/mL, respectively. The silica NPs under the
experimental conditions of the present study were stable, which
was confirmed by dynamic light scattering (DLS) measurements
of influent and effluents samples (Zetasizer Nano ZS, Malvern
Instruments) and is consistent with literature reports.54,55
Electrophoretic mobilities of silica NPs were measured using a
Zetasizer Nano ZS (Malvern Instruments) at 25 ± 0.5 °C, pH =
10, and with 50−2000 mg/L suspensions, which were then
converted tozetapotentials(TableS1intheSI)usingtheHenry
Equation58(eq S1 in the SI).
Solution Chemistry. Deionized (DI) water and ACS grade
NaCl were used for the preparation of background solutions at
desired ionic strength (IS). Input NPs’ suspensions were
prepared by spiking the background solutions with NPs’ stock
suspensions and degassed thoroughly. Solution pH was there-
Table 1. Experimental Conditions, Deposition Rate Coefficients (kd), Attachment Efficiencies (α), and Mass Recoveries of the
Column Transport Experimentsa
exp.
no.
particle size
(nm)
input concentration
(particles/mL)
2.7 × 1011
2.7 × 1011
1.4 × 1012
1.3 × 1012
1.3 × 1013
1.2 × 1013
0.9 × 1013
1.7 × 1013
3.5 × 1014
3.5 × 1014
1.3 × 1013
ionic strength
(mM)
water approach velocity
(m/s)
1.46 × 10−5
1.46 × 10−5
1.48 × 10−5
1.47 × 10−5
1.48 × 10−5
1.47 × 10−5
1.51 × 10−5
1.51 × 10−5
1.48 × 10−5
1.45 × 10−5
1.47 × 10−5
deposition rate
coefficientb(h−1)
(1.5 ± 2.5) × 10−2
(1.4 ± 0.3) × 10−1
(5.1 ± 2.6) × 10−2
(1.4 ± 0.3) × 10−1
(3.2 ± 2.4) × 10−2
(9.0 ± 2.6) × 10−2
(1.5 ± 0.3) × 10−1
(3.2 ± 0.3) × 10−1
(4.1 ± 27) × 10−3
(1.5 ± 0.2) × 10−1
(5.8 ± 0.3) × 10−1
attachment
efficiencyb(α)
(2.5 ± 4.1) × 10−4
(2.3 ± 0.4) × 10−3
(8.5 ± 4.4) × 10−4
(2.3 ± 0.4) × 10−3
(5.3 ± 4.0) × 10−4
(1.5 ± 0.4) × 10−3
(5.8 ± 1.0) × 10−4
(1.2 ± 0.1) × 10−3
(1.6 ± 10) × 10−5
(5.6 ± 1.0) × 10−4
(2.3 ± 0.1) × 10−3
mass recoveryc
(%)
1
2
3
4
5
6
7
8
9
52
52
52
52
52
52
8
8
8
8
8
1 98%
90%
95%
91%
98%
93%
89%
85%
100%
92%
57%
100
1
100
1
100
1
100
1
10
11
100
200
aSands (210 g) were packed in each column with column porosity at ∼0.340; solution pH was maintained at 10.b“ ± ” represents the uncertainty of
the value, based on >9 steady-state data points.cMass recovery was calculated as ratio of the number of NPs in effluent (phases 1 and 2) and the
number of NPs in influent.
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after adjusted to 10 with 0.1 mM NaHCO3and 0.1 mM Na2CO3
andsubsequentlyusing0.01MHCl/NaOH.WeusedpHashigh
as 10 in order to minimize surface charge heterogeneity and also
to ensure attachment of silica NPs under unfavorable
conditions.34,37
Column Transport Experiments. Column experiments
were performed in a 10 cm long acrylic column (i.d. = 3.85 cm)
with similar column setups described elsewhere.56,59A summary
of experimental conditions are presented in Table 1. Briefly,
duringeachexperiment,∼20PVs(porevolumes)ofparticle-free
background solution was introduced upward to the column with
a peristaltic pump. Background solution amended with bromide
tracer (KBr)wasafterthat pumpedtoproducethebreakthrough
curves for the confirmation of consistency and reproducibility of
the column packing (SI Figure S2).56Experiments were
thereafter run following a 3-phase procedure to differentiate
primary- and secondary-minimum deposition.60Successively,
input solution was switched to silica NPs suspension (10 PVs,
phase 1), background solution (4 PVs, phase 2), andDI water (6
PVs, phase 3). Samples of the effluent were collected from top of
the column with a fraction collector. Column dissection was not
performed, considering that the size ratios of silica NPs to media
grains were an order of magnitude smaller than the reported
0.0017 threshold for straining to occur.61
Sample Analysis. Silica concentrations were measured by
inductively coupled plasma−optical emission spectrometer
(ICP−OES, Varian VISTA−MPX). Samples were diluted with
acidified (2% HNO3) background solution and the measured
concentrations were corrected for background silica concen-
trations in controls (i.e., effluent samples of background buffer
before introduction of silica NPs). The method detection limits
were estimated 6.3 × 1011particles/mL for 8 nm silica NPs and
2.0 × 109particles/mL for 52 nm silica NPs, respectively.
■THEORETICAL CONSIDERATION
Deposition Rate Coefficient (kd) and Attachment
Efficiency (α). The deposition rate coefficient (kd, h−1) is
determined by the following equation:43,56,62
⎛
⎝
LC
=
⎜⎟
⎠
⎞
k
v
C
ln
d
p
0
(1)
where vpis pore water velocity (cm/min), L is column length
(cm), C0is input NPs’ number concentration (particles/mL),
and C is effluent NPs’ concentration (particles/mL) which was
represented by steady-state concentration, Cs(particles/mL), in
the present study.9,22,63
The obtained kdwas then used to calculate the attachment
efficiency (α) using the following equation:56,62
α
εη
=
−
k a
4
v
3(1)
d c
p 0
(2)
where acis mean collector radius (mm), ε is column porosity, η0
issinglecollectorefficiency,whichisdeterminedbythefollowing
correlation equation:62
η =
0
+
+
−
R
−
Pe
0.24
−
Pe
−
R
ANNNA N
S
N
NNNN
2.40.55
0.22
S
1/3 0.0810.715
vdW
0.052
R
1.550.125
vdW
0.125
G
1.11
vdW
0.053
(3)
where ASis a porosity-dependent parameter, NRis aspect ratio,
NPeis Peclet number, NvdWis van der Waals number, and NGis
gravitational number.
SurfaceCoverage(θ).Surfacecoverage wascomputedfrom
a breakthrough curve, using the following equation:64−66
()
L
3 (1)
∫
θ
π
ε
=
−
−
a Ua C
p
t
1d
t
C
C
2
c0
0
0
(4a)
where apis particle radius (nm), U is water approach (Darcy)
velocity (cm/min), and t is duration of time for phase 1
breakthrough experiment (min).
The above equation (see derivation of eq 4a in the SI)
calculates surface coverage using the total loaded particles in the
column at any given time, which includes both the suspended
particlesinporewaterandtheattachedonesoncollectorsurfaces
and thereby overestimates surface coverage. The overestimation
wouldbesignificantwhenC0ishighandespeciallythesuspended
particles in pore water account for a significant portion of all the
particles inthecolumn.Tocorrectsuchanoverestimation, eq4b
is developed (see derivation of eq 4b in the SI) to calculate the
corrected surface coverage:
⎧
⎪
⎪
⎪
⎪
⎪⎪
⎪
⎪
⎪
⎪
⎪
⎪
k
d
∫
∫
θ
π
3 (1
ε
)
ε
π
3 (1
ε
)
ε
=
−
1
−
−−
<
−
1
−
⎞
⎠⎟
−−
≥
−
−
⎨
⎩
⎡
⎣
⎢
⎢
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝⎜
⎞
⎠⎟
⎤
⎦
⎥
⎥
⎡
⎣
⎢
⎢
⎛
⎝
k L
v
p
⎜
⎞
⎠
⎟
⎛
⎝⎜
⎤
⎦
⎥
⎥
a aC v
L
C
C
t
k
e
a a C v
L
C
C
t
e
1d
1,
for PV1
1d
1,
for PV1
c
t
k
v
t
p
2
0 p
0
0
d
PV
L
p
p
2
c0 p
0
0
d
d
(4b)
wherePV isporevolume. FigureS3in theSI showsthat afterthe
correction the surface coverage was significantly reduced in the
present study.
Equation 4b can be further written as follows with several
approximations (see Derivation of eqs 4c and 4d in the SI):
⎧
⎪
⎪
⎪
⎪
()
v
3(1)
p
θ
π
ε
−ε
π
ε
−ε
=
<
−≥
⎜
⎝
⎟
⎠
⎨
⎩
⎛⎞
()
a k C
p
a
L
v
a k C
p
a
L
3(1)
PV
2
,for PV1
PV
1
2
, for PV1
2
d0
c
p
2
2
d0
c
(4c)
or
θ
ε
ε
ε
ε
ρ
ρ
=
−
<
−
−≥
⎜
⎝
⎟
⎠
⎧
⎪
⎪
⎪
⎪
⎨
⎩
⎛⎞
m
a
a
k L
v
p
m
a
a
k L
v
p
4(1)
PV
2
,for PV1
4(1)
PV
1
2
, for PV1
0
c
p
d
2
0
c
p
d
(4d)
where m0[= (4/3)πap
and ρ is NP’s density (g/mL). Equation 4c states that θ is
proportionaltoπap
to (kd/ap) for a given mass concentration (m0).
Additionally, when using the concept of surface coverage,
assumptions (1) particles form monolayer coverage on collector
surfacesand(2)noparticledetachmentoccursduringdeposition
processes, are generally made.11,67These assumptions are likely
valid in the present study for the following reasons. First, silica
NPsusedinthisstudyhadsameparticle-size distributionsbefore
and after experiments, as indicated by DLS measurements,
3ρC0] is input mass concentration (mg/L)
2kpC0andeq4dindicatesthatθisproportional
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consistent with reports in the literature that silica NPs are stable
in suspension.54,55Second, breakthrough curves reached stable
plateau concentrations, suggesting the lack of ripening effects
(Figure 1a−d). Third, there was little particle detachment as
indicated by the negligible tailing during flushing with particle-
free solution (phase 2)50,68(Figure 1a−d).
DLVO Interactions. The DLVO interaction energy (ΦDLVO,
J) between NPs and collectors, which is regarded as sphere-plate
interaction, is a sum of the double-layer repulsion (Φel, J) and
retarded van der Waals attraction (ΦvdW, J):23
Φ
DLVOel vdW
where
= Φ + Φ
(5)
∫
πε ε κ ψ
r
0
ψ
κ
κ
ψψ
+
ψψ
κ
ψψ
+
ψψ
κ
Φ =
el
+
−+−−
+++−
++
−−
−+
+−
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟⎟
⎠
haar a
( / ) )]
p
haar a
( / ) )]
p
hha
a r a
( / ) )]
p
hha
ar a
( / ) )]
p
()
coth[ (1
coth[ (1
(2
2
)
( )csc [ (
1
(2
2
)
()csc [ (
1
rdr
a
s
2
p
2
0
pp
2
pp
2
s p
sp
2
p
p
2
s p
sp
2
p
p
2
p
(6)
+Φ = −+
++
⎡
⎣
⎢
⎢
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎤
⎦
⎥
⎥
A a
6
h
a
ha
h
ha
2
ln
2
vdW
pp
pp
(7)
where ε0 is free space permittivity (F/m), εr is relative
permittivity, κ is inverse of Debye length (nm−1) (see eq S2 in
the SI), ψsand ψpare surface potentials of sphere and plate,
respectively, and are usually approximated as zeta-potentials,52h
isminimumsurface-to-surfaceseparationdistance(nm),andAis
nonretarded Hamaker constant (=6.3 × 10−21J).69,70Equations
6 and 7 were developed by Guzman et al.23with surface element
integration technique,71which exclude Derjaguin approximation
and thus do not need the assumptions of h ≪ apand κh ≫ 1.
■RESULTS AND DISCUSSION
Concentration Effect. Concentration effect of silica NPs on
theirtransport insaturated porous mediawasevaluated atISof1
mM and 100 mM over a concentration range from 1011to 1014
particles/mL (Table 1),which arewithin colloidal concentration
range used in relevant studies.72Breakthrough curves (BTCs) of
silica NPs, that is, relative effluent concentration (C/C0) as a
function of PV, are plotted in Figure 1a−d. The BTCs of 8 nm
NPs (Figure 1b and d) show that the values of steady-state
effluent concentrations (Cs/C0) increased with C0at both IS
values, suggesting that higher C0gave rise to lower relative
retention. On the other hand, the values of Cs/C0in the BTCs of
52 nm NPs reached close to 1.0 (Figure 1a and c), implying that
the retention capacity of the porous media for 52 nm NPs was
low. Because the differences in the breakthrough curves with
respect to 52 nm NPs are so small, which was caused by the
limited retention capacity of the porous media for the 52 nm
silica NPs, a definite evaluation of concentration effect on the
BTCs was not allowed in this case.
Additionally, we evaluated concentration effect on surface
coverage(θ)ofsilicaNPsusingeq4b.Figure2a−ddemonstrates
thathigherC0contributedtolargerθatbothISof1and100mM.
This observation is supported by eq 4c, which shows that surface
coverage is proportional to C0. To further evaluate the
concentrationeffect,wecalculatedthedepositionratecoefficient
(kd) and attachment efficiency (α) using measured Cs/C0values
and eqs 1 and 2. Table 1 shows that a definite trend of the
dependenceofkdandαonC0isnotavailabletothepresentcases.
Figure 1. Concentration (C0) effect on retention of 52 nm and 8 nm
silica NPs: (a) 52 nm and IS = 1 mM, (b) 8 nm and IS = 1 mM, (c) 52
nm and IS = 100 mM, and (d) 8 nm and IS = 100 mM.
Figure 2. Concentration (C0) effect on surface coverage (θ) of 52 nm
and8nmsilicaNPs:(a)52nmandIS=1mM,(b)8nmandIS=1mM,
(c) 52 nm and IS = 100 mM, and (d) 8 nm and IS = 100 mM.
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Results from this study are generally consistent with literature
reports based on studies with micrometer-sized particles (e.g.,
latex microspheres, bacteria cells, and aggregated TiO2
particles).18,35−37Bradford and colleagues36,37hypothesized
that the concentration-dependent colloid retention and trans-
port are due to (i) concentration-dependent filling of retention
sites and (ii) concentration-dependent mass transfer of colloids
to retention sites. At present, studies of concentration effect on
retention and transport of NPs are very limited.38,39Our study
indicates that these proposed mechanisms may also apply to
explain the behavior of very small NPs. Additionally, it was once
reported that greater input concentrations resulted in increased
relative colloidal retention atIS>0.1mM,34whichisopposite to
the present results, attributing to the ripening effect.34Since the
silica NPs used in the present study were stable, ripening should
be insignificant in the present cases.
The above discussion suggests that it is important to pay
attention to the concentration effects when comparing results
from different studies. Moreover, interpretation of experimental
results involving different concentrations becomes more
complex when the key focus of the studies is to identify
differences between NPs and their larger counterparts. The
additional complexity may arise from inconsistent use of mass or
particle number concentrations. We address the interplay
between particle size and concentration effects in detail in Size
Effect section below.
Size Effect. The breakthrough curves in Figure 3a and b
shows that the relative retention was higher for 8 nm NPs than
for 52 nm NPs at both 1 and 100 mM IS. On the other hand,
Table1 indicatesthat8nmNPshave largerkdvaluesthan 52nm
NPs at both 1 and 100 mM IS (exp. 7 vs exp. 5 and exp. 8 vs exp.
6, respectively). These results suggest that, at the same particle
number concentration, the smaller 8 nm NPs would deposit
faster. There are likely two mechanisms that are responsible for
the observed size effect. First, size affects directly the interaction
energiesbetweenNPsandsandsurfaces,asshownbyeqs6and7.
Second, size affects NPs physical and/or chemical properties, for
example, zeta-potential as shown in SI Table S1, and thereby
indirectly and further affects the interaction energies. In both
mechanisms, size is the origin to the observed different retention
and transport behaviors.
Table1alsoshowsthattheattachmentefficiencies(α)of8nm
NPswerealmostsimilartothatof52nmNPsatthetwoISvalues
(exp. 7 vs exp. 5 and exp. 8 vs exp. 6). The results indicate that
faster deposition rate is not a guarantee for higher attachment
efficiency, because attachment efficiency is determined by both
the deposition rate coefficient (kd) and collector contact
efficiency (η0), not by kdalone (see eq 2). In addition, Figure
3c and d demonstrates that, at both IS values, the smaller 8 nm
NPs had lower surface coverages. This is reasonable because, at
the same particle number concentration (C0), smaller particles
have much smaller total projection area (πap
ones (see eq 4c).
Analyses of the results from this study also reveal that,
interpretation of size effect on NPs’ retention and transport
would lead to different conclusions, depending on whether the
interpretation was based on mass concentration (mg/L) or
particle number concentration (particles/mL). For example,
undersimilarparticlenumberconcentrations, thelargerNPs(52
nm) had lower relative retention, but higher surface coverage
(Figure 3a−d) than the smaller NPs, whereas under similar mass
concentrations, relative retention of both 52 nm and 8 nm NPs
was similar but the smaller NPs had higher surface coverage
(Figure S4a−d in the SI). The discrepancy suggests that, when
studies are conducted with the goal to reveal potential behavior
of NPs relative to their larger counterparts (both on environ-
mental fate and toxicity), special attention should be paid to the
potentialeffectofconcentrations,intermsofmassconcentration
and particle number concentration or namely appropriate
concentration expression. In fact, the apparent discrepancy can
beexplainedbyeqs4cand4d.Equation4cshowsthat,foragiven
particle number concentration (C0), θ can be higher for larger
NPsbecauseitisproportionaltoπap
decrease alotincomparison tothatoftheincreaseinap
true according to Table 1. Meanwhile, eq 4d indicates that, for a
given mass concentration (m0), θ is higher for smaller NPs,
where the kdvalue is similar according to eq 1 because of the
nearly identical Cs/C0. We believe that using particle number
concentration as the basis for comparisons of NPs’ fate and
toxicity may provide additional insights. In aerosol research, it
has been reported that surface area and particle number
concentrations are better predictors than mass concentrations
of risks associated with NPs’ exposure and toxicity in air.38,39
The above results demonstrate that the smaller NPs (8 nm vs
52 nm) corresponded to higher relative retention, faster
deposition, and lower surface coverage. These results are
contrary to the previous reports that the smaller NPs (e.g.,
TiO2, aluminum, and Fe0NPs) had less relative reten-
tion.22,23,28,31This could be because the comparison was made
previously based on the same NPs’ mass concentration. In
addition, it is likely that particle size was not well controlled due
to agglomeration, leading to particle size and particle number
concentration change during the experiments. As such, it is
difficultto make a definite evaluation on the effect of NPs’size in
those studies.
ApplicabilityofDLVOTheory.TheresultsinFigure4aand
b show that both 8 nm and 52 nm silica NPs were released upon
introduction of DI water during phase 3 (from 14 to 20 PVs).
However, the release of 8 nm silica NPs was much more
2) than the larger
2kdC0,ifthekdvaluedoesnot
2,which is
Figure3.SizeeffectonretentionofsilicaNPs:(a)IS=1mMand(b)IS
=100 mMandon surfacecoverage (θ)ofsilica NPs:(c) IS=1mMand
(d) IS = 100 mM. Comparisons are performed under the same particle
number concentrations.
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pronounced than 52 nm particles. Mass balance analysis
indicated that ∼100% of the deposited 8 nm silica NPs at IS =
100 mM was released, whereas the release of 52 nm NPs was
∼2%.
Thelimitedreleaseof52nmsilicaNPscanbeexplainedbythe
DLVOtheory.AccordingtotheDLVOcalculation,thedepthsof
secondary energy minima (Φsec) are in the range of 0−1.4 kT
(Table 2). These Φsecvalues are smaller than the average kinetic
energy (1.5 kT) associated with particles’ Brownian motion,60,73
therefore, limited retention in and release from the secondary
energy minima is expected for 52 nm NPs. On the other hand,
the significant release of 8 nm silica NPs is inconsistent with the
DLVO prediction. This is because the DLVO calculation
suggests likelihood of primary minimum deposition (due to
low energy barrier heights) rather than retention in secondary
minima (due to minimal Φsecvalues) (Table 2), whereas the
experimental observation of the significant release indicates that
there was large deposition of 8 nm NPs in the secondary energy
minima.
The above results clearly indicate that theDLVO theory isnot
applicable to describe the behavior of 8 nm NPs. This might be
that, in addition to the double layer repulsion and van der Waals
attraction, other short-range interactions (e.g., hydration and
solvation)mayalsoplayanimportantrole,resultinginthefailure
of the DLVO prediction. Hahn and O’Melia73have pointed out
that the release of deposited particles can occur at separation
distances of a few nanometers where the DLVO theory usually is
not able to provide a quantitative description due to significant
contribution of other types of interactions. On the other hand,
when NPs are very small so that the overlap of diffuse double
layers is complete, DLVO theory may not be valid; rather, the
Brønsted concept based on the Transitional State theory of
interacting ions has been applied.53In addition, our recent
study74indicated that surface roughness, mainly in the form of
largevalleysonsandgrains,canlocallyincreasetheenergybarrier
as well as depth of the secondary energy minima, which would
allow additional retention of particles in the secondary energy
minima. Moreover, we found that the asperities on sand surfaces
would shield depositing particles from hydrodynamic shear from
beingdetached.Bothroughnesseffectsmightbealsoresponsible
for the significant reversible release of 8 nm NPs as was observed
during the phase 3 experiments.
While mechanisms for the failure of the DLVO theory to very
small NPs may need to be systematically studied further, the
aboveresultsinFigure4aandbsuggestthatcarefulexperimental
scrutinyonNPsreleasefromtheporousmediaisquitenecessary,
especially whenthe size reduces to verysmall value (e.g., 8 nm in
thiscase).PronouncedreleaseofdepositedNPsinporousmedia
may occur upon lowering of pore water IS (e.g., in the event of
rainfall), which is not predicted by the DLVO theory but could
exert severe environmental consequences.
■ASSOCIATED CONTENT
*
Additional material as noted in the text. This information is
available free of charge via the Internet at http://pubs.acs.org/.
■AUTHOR INFORMATION
Corresponding Author
*Phone: (302)831-6962 (Y. J.); (302)831-8160 (L. P. W.). Fax:
(302)831-0605 (Y. J.); (302)831-3619 (L. P. W.). E-mail: yjin@
udel.edu (Y. J.); lwang@udel.edu (L. P. W.).
Notes
The authors declare no competing financial interest.
■ACKNOWLEDGMENTS
This research was supported by the National Research Initiative
Competitive Grant (No. 2001-35107-01235) from the USDA
Cooperative State Research, Education, and Extension Services,
the Star Project (R833318) from the U.S. EPA, the National
Science Foundation under grants CBET-0932686 and EAR-
0207788(C.S.W.),andtheNationalNaturalScienceFoundation
of China (No. 40901109).
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