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Retention and Transport of Silica Nanoparticles in Saturated Porous Media: Effect 1
of Concentration and Particle Size 2
3
4
Chao Wang,† Aparna Devi Bobba,† Ramesh Attinti,† Chongyang Shen,‡ Volha 5
Lazouskaya,† Lian-Ping Wang,§ * Yan Jin† * 6
7
8
9
†Department of Plant and Soil Sciences, University of Delaware, Newark, Delaware 10
19716, USA 11
‡Department of Soil and Water Sciences, China Agricultural University, Beijing 100094, 12
China 13
§Department of Mechanical Engineering, University of Delaware, Newark, Delaware 14
19716, USA 15
16
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18
*Address correspondence to either author. Phone: (302)831-6962 (YJ); (302)831-8160 19
(LPW). Fax: (302)831-0605 (YJ); (302)831-3619 (LPW). E-mail: [email protected] (YJ); 20
[email protected] (LPW). 21
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Abstract 22
Investigations on factors that affect the fate and transport of nanoparticles (NPs) 23
remain incomplete to date. As such, we conducted column experiments using 8- and 24
52-nm silica NPs to examine the effects of NPs’ concentration and size on their retention 25
and transport in saturated porous media. Results showed that higher particle number 26
concentration led to lower relative retention and greater surface coverage. Smaller NPs 27
resulted in higher relative retention and lower surface coverage. Evaluation of size effect 28
based on mass concentration (mg/L) vs. particle number concentration (particles/mL) led 29
to opposite conclusions. An improved equation for surface coverage calculation was 30
developed to explain the different results related to the size effects when a given mass 31
concentration (mg/L) and a given particle number concentration were used. In addition, 32
we found that the retained 8-nm NPs were released upon lowered solution ionic strength, 33
contrary to the prediction by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. 34
This report highlights the importance of NPs’ concentration and size on their behavior in 35
porous media. To the best of our knowledge, it is the first report to present an improved 36
method for a previously well accepted equation for surface coverage calculation. 37
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Introduction 38
The rapid growth of nanotechnology is giving rise to mass production and widespread 39
application of NPs.1 During their production, application, and disposal, these 40
nanomaterials will inevitably enter the environment. Because of their potential toxicity as 41
well as their role as carriers for sorbed contaminants, the release of NPs may lead to 42
environmental contamination. 43
Retention and transport of NPs in the subsurface environment, especially in 44
saturated porous media, has received considerable attention. For example, the retention 45
and transport of manufactured C60,2-12 carbon nanotubes,13-16 and oxide NPs2,17-25 in 46
saturated porous media have been intensively studied. In these studies, factors that affect 47
NPs’ retention and transport have been evaluated, e.g., flow velocity,2,18,20 NPs’ surface 48
potential,23 and presence of organic species.25,26 However, the investigations to date are 49
still largely incomplete. For instance, while the uniqueness of NPs (e.g., small size, large 50
surface to volume ratio, and high reactivity) has been acknowledged,27 systematic study 51
on the effect of particle size on NPs’ environmental fate remains limited.22,28-31 A general 52
conclusion from previous investigations on particle size effect using TiO2, aluminum, and 53
Fe0 NPs is that larger NPs have higher retention.22,23,28,31 However, it is difficult to draw 54
definite conclusions from those studies because TiO2, aluminum, and Fe0 NPs are easily 55
agglomerated leading to size changes during transport.27,32 Further investigation of NPs’ 56
size effect that employs relatively stable NPs is thereby essential. Moreover, Auffan et 57
al.33 reported that inorganic NPs with sizes < 30-nm show different properties from 58
those > 30-nm and proposed that the definition of NPs be modified from 1 ~ 100 nm to 1 59
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~ 30 nm. However, studies on NPs’ environmental fate with stable particle sizes smaller 60
than 30-nm are almost non-existent. 61
Another factor that deserves more focused attention is the effect of particle 62
concentration on NPs’ retention and transport in porous media. A number of previous 63
studies have demonstrated significant influence of input concentration on rates and 64
retention mechanisms of micron-size particles (e.g., bacteria, latex, and aggregated TiO2 65
particles). 20,34-37 Concentration effect of NPs, however, has not been well evaluated.38,39 66
Studies that have investigated effects of NPs’ size used the same mass concentrations 67
when comparing the behavior of differently sized particles.22,28,31 It is not clear whether 68
such comparison is conclusive because at the same mass concentration (mass/volume), 69
particle number concentration (number/volume) can be orders of magnitude different 70
when particles being compared span a wide size range. The potential implications of 71
using mass or particle number concentrations in this type of studies on interpretation of 72
particle size effect have not been adequately investigated to date. Similarly, no standard 73
protocols have been developed to guide studies that examine the size-dependent 74
toxicological behavior of NPs. For example, Simon-Deckers et al.40 evaluated effect of 75
oxide NPs’ size on their toxicity using the same mass concentration, whereas Jones et 76
al.41 and Nair et al.42 performed the evaluation using the same particle number 77
concentration. This makes comparison between different studies and meaningful 78
interpretation of results difficult. Therefore, potential effects of concentration, in terms of 79
both mass and numbers, need to be evaluated. Such information will be useful in the 80
development and implementation of standard protocols for future investigations of NPs’ 81
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environmental fate and toxicity. 82
Current theoretical description of NPs’ retention and transport is mostly limited to 83
the classical filtration theory (CFT)43 supplemented by the DLVO44,45 force 84
representations.3,5,7,9,15,22,46-50 For example, in a study of fullerene deposition and transport, 85
Li et al.7 reported that the effective collision efficiency needed to match their observation 86
was more than one order of magnitude larger than the value predicted by the DLVO 87
theory. Conventional DLVO theory uses approximate expressions, e.g., Derjaguin 88
approximation51 to represent electric double layer interaction. However, the assumptions 89
under which the approximations hold,53 e.g., h << ap (i.e., separation distance is much less 90
than NPs’ radius) and κh >> 1 (i.e., separation distance is much larger than the Debye 91
length), may not be applicable to small NPs. Because NPs, especially those with sizes < 92
20 ~ 30 nm, may have unique properties (e.g., large specific surface area, exponentially 93
increased surface atoms, and high interfacial reactivity)33 or are smaller than the thickness 94
of electrical double layer,54 the applicability of the DLVO theory for describing their 95
agglomeration, retention, and transport behavior has been questioned.30 96
Thus, the objectives of this study were to 1) quantify effects of concentration and 97
particle size on NPs’ retention and transport in saturated porous media, and 2) examine 98
the applicability of the DLVO theory to describe deposition of small NPs on grain 99
surfaces. We selected silica particles as representative NPs because they are largely stable 100
in suspension55,56 and thereby can be more easily controlled to have constant 101
concentration and particle size. Besides, we used the recently developed equations by 102
Guzman et al. to calculate the DLVO interaction.23 These equations exclude the 103
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Derjaguin approximation and thus do not need the assumptions of h << ap and κh >> 1. 104
Materials and Methods 105
Porous Media. A mixture of Accusands that is composed of 96.89% SiO2 and 106
3.11% CaCO3 with a mean diameter of 0.22 mm (Unimin, Le Sueur, MN) was used in 107
this study. Before use, the sands were treated to remove metal oxides and other 108
impurities, following the treatment procedure given in the Supporting Information. 109
Silica NPs. Two mono-dispersed stock suspensions that contained surfactant-free 110
silica NPs were purchased from the Nissan Chemical Industries, Ltd. (Tarrytown, NY). 111
The mean diameters of silica NPs in the two suspensions are 8 ± 2 nm and 52 ± 1 nm, 112
respectively, based on measurements from transmission electron microscopy (TEM) 113
images (see Figure S1 and experimental procedure for TEM imaging in the Supporting 114
Information). The manufacturer reported densities of 8-nm and 52-nm NPs are 1.14 g/mL 115
and 1.30 g/mL, respectively. The silica NPs under the experimental conditions of the 116
present study were stable, which was confirmed by dynamic light scattering (DLS) 117
measurements of influent and effluents samples (Zetasizer Nano ZS, Malvern 118
Instruments) and is consistent with literature reports.55,56 Electrophoretic mobilities of 119
silica NPs were measured using a Zetasizer Nano ZS (Malvern Instruments) at 25 ± 0.5 120
°C, pH = 10, and with 50 ~ 2000 mg/L suspensions, which were then converted to zeta 121
potentials (Table S1 in the Supporting Information) using the Henry Equation57 (Equation 122
S1 in the Supporting Information). 123
Solution Chemistry. Deionized (DI) water and ACS grade NaCl were used for the 124
preparation of background solutions at desired ionic strength (IS). Input NPs’ suspensions 125
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were prepared by spiking the background solutions with NPs’ stock suspensions and 126
degassed thoroughly. Solution pH was thereafter adjusted to 10 with 0.1 mM NaHCO3 127
and 0.1 mM Na2CO3 and subsequently using 0.01 M HCl/NaOH. We used pH as high as 128
10 to minimize surface charge heterogeneity and to ensure attachment of silica NPs under 129
unfavorable conditions.34,37 130
Column Transport Experiments. Column experiments were performed in a 131
10-cm long acrylic column (id = 3.85 cm) with similar column setups described 132
elsewhere.58,59 A summary of experimental conditions is presented in Table 2. Briefly, 133
during each experiment, ~ 20 PVs (pore volumes) of particle-free background solution 134
was introduced upward to the column with a peristaltic pump, to leach tiny impurities and 135
to establish chemical equilibrium and steady-state flow condition.59 Experiments were run 136
following a 3-phase procedure to differentiate primary- and secondary-minimum 137
deposition.60 Input solution was then switched successively to silica NPs suspension (10 138
PVs, phase 1), background solution (4 PVs, phase 2), and DI water (6 PVs, phase 3). 139
Samples of the effluent were collected from top of the column with a fraction collector. 140
Column dissection was not performed because the size ratios of silica particles to media 141
grains were an order of magnitude smaller than the reported 0.0017 threshold for straining 142
to occur.61 In addition, DLS measurements showed that the sizes of silica NPs in effluent 143
and influent samples were the same, indicating that the NPs were stable and did not 144
aggregate during the experiments. 145
Sample Analysis. Silica concentrations were measured by inductively coupled 146
plasma - optical emission spectrometer (ICP - OES, Varian VISTA - MPX). Samples 147
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were diluted with acidified (2% HNO3) background solution (see Figures S2a and S2b of 148
representative calibration curves in Supporting Information). The measured 149
concentrations were corrected for background silica concentrations in controls (i.e., 150
effluent samples of background buffer before introduction of silica NPs). 151
Theoretical Consideration 152
Deposition Rate Coefficient (kd) and Attachment Efficiency (α). The deposition rate 153
coefficient (kd, h-1) is determined by the equation:43,59,62 154
⎟⎠
⎞⎜⎝
⎛=
CC
Lv
k pd
0ln (1) 155
where vp is pore water velocity (cm/min), L is column length (cm), C0 is input NPs’ 156
number concentration (particles/mL), and C is effluent NPs’ concentration (particles/mL) 157
which was represented by steady-state concentration, CS (particles/mL), in the present 158
study.8,9,22 159
The estimated kd was then used to calculate the attachment efficiency (α) using the 160
equation:59,62 161
( ) Op
cd
vakηε
α−
=134 (2) 162
where ac is mean collector radius (mm), ε is column porosity, ηO is single collector 163
efficiency, which is determined by the correlation equation:62 164
053.011.124.0125.0125.055.1052.0715.0081.03/1 22.055.04.2 vdWGRvdWPeRSvdWPeRSO NNNNNNANNNA −−−− ++=η (3) 165
where AS is a porosity-dependent parameter, NR is aspect ratio, NPe is Peclet number, NvdW 166
is van der Waals number, and NG is gravitational number. 167
Surface Coverage (θ). Surface coverage was computed from a breakthrough curve, 168
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using the following equation previously by Ko et al.:63,64 169
( )ε
π
θ−
⎟⎟⎠
⎞⎜⎜⎝
⎛−
=∫13
10
00
2
L
dtCCCUaa
t
cp
(4a) 170
where ap is particle radius (nm), U is water approach (Darcy) velocity (cm/min), and t is 171
time duration for phase 1 breakthrough experiment (min). 172
The above equation (see Derivation of Equation 4a in the Supporting Information) 173
calculates surface coverage using the total concentration in the column at any given time, 174
which includes both suspended particles in pore water and attached particles on collector 175
surfaces and thereby it overestimates surface coverage. The overestimation could be 176
significant especially when C0 is high and the suspended particles in pore water account 177
for a significant portion of all the particles in the column. To correct for this 178
overestimation, Equation 4b was developed (see Derivation of Equation 4b in the 179
Supporting Information) and used to calculate the corrected surface coverage: 180
( )
( )⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
≥⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−=
−
⋅−
∫
∫
1for ,11113
1<for , 11113
00
02
00
02
PVek
dtCC
LvCaa
PVek
dtCC
LvCaa
p
d
p
d
vLk
d
tpcp
vLk
PV
d
tpcp
ε
επ
ε
επ
θ (4b) 181
where PV is the pore volume. Figure S3 in the Supporting Information shows that after 182
the above correction the surface coverage was significantly reduced. 183
Equation 4b can be further written as follows after several approximations (see 184
Derivation of Equations 4c and 4d in the Supporting Information): 185
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( )( )
( )( )⎪
⎪
⎩
⎪⎪
⎨
⎧
≥⎟⎠
⎞⎜⎝
⎛ −−
−=
1for ,21
v13
1<for , 2v13
p0
2
2
p0
2
PVPVLaCka
PVPVLaCka
cdp
cdp
εε
π
εε
π
θ (4c) 186
or
187
( )
( )⎪⎪
⎩
⎪⎪
⎨
⎧
≥⎟⎠
⎞⎜⎝
⎛ −−
−=
1for ,21
v14
1<for , 2v14
p0
2
p0
PVPVLk
aa
m
PVPVLka
am
d
p
c
d
p
c
ρεε
ρεε
θ (4d) 188
where 03
0 34 Cam pρπ= is input mass concentration of NPs (mg/L) and ρ is NP’s density 189
(g/mL). Equation 4c states that θ is proportional to 02 Cka dpπ and Equation 4d indicates 190
that θ is inversely proportional to ap for a given mass concentration (m0). 191
In addition, it is important to note that, when using the concept of surface coverage, 192
assumptions 1) particles form monolayer coverage on collector surfaces and 2) no particle 193
detachment occurs during deposition processes, are generally made.11,65 These 194
assumptions are likely valid in the present study for the following reasons. First, silica 195
NPs suspensions used in this study had similar particle-size distributions before and after 196
experiments, as indicated by DLS measurements. This is consistent with reports in the 197
literature that silica NPs are stable in suspension,55,56 indicating strong repulsive 198
particle-particle interactions. Second, breakthrough curves reached stable constant plateau 199
concentrations, indicating the lack of ripening effects. Third, there was little particle 200
detachment as indicated by the negligible tailing during flushing with particle-free 201
solution (phase 2)50,66 (see Figures 1a ~ 1d). 202
DLVO Interactions. The DLVO interaction energy (ΦDLVO, J) between NPs and 203
collectors, which is regarded as sphere-plate interaction, is a sum of the double-layer 204
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repulsion (Φel, J) and retarded van der Waals attraction (ΦvdW, J):23 205
vdWelDLVO ΦΦΦ += (5) 206
where 207
( )
( )
( )( )( ) ( )
( )( ) ( )
∫
⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ −++
+−
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ −−+
++
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ −+++
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ −−+−
+=pa
pppps
ps
pppps
ps
ppp
ppp
psr rdr
araahh
araahh
araah
araah
0
222
222
2
2
220el
/1csc2
/1csc2
/1coth
/1coth
Φ
κψψ
ψψ
κψψ
ψψ
κ
κ
ψψκεπε (6) 208
209
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛
++
++−=
pp
pp
ahh
aha
haA
2ln
26Φ vdW (7) 210
ε0 is free space permittivity (F/m), εr is relative permittivity, κ is inverse of Debye length 211
(nm-1) (see Equation S2 in the Supporting Information), ψs and ψp are the surface 212
potentials of the sphere and plate and are usually approximated as the zeta-potentials,53 h 213
is minimum surface-to-surface separation distance (nm), and A is non-retarded Hamaker 214
constant (= 6.3×10-21 J).67,68 Equations 6 and 7 were developed by Guzman et al.23 with 215
the technique of surface element integration,69 which excludes the Derjaguin 216
approximation and thus do not need the assumptions of h << ap and κh >> 1. 217
Results and Discussion 218
Concentration Effect. Concentration effect of silica NPs on their transport in 219
saturated porous media was evaluated at IS of 1 mM and 100 mM over a concentration 220
range from 1011 to 1014 particles/mL (see Table 2), which are within colloid concentration 221
range used in relevant studies.70 Breakthrough curves (BTCs) of silica NPs, i.e., relative 222
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effluent concentration ( 0/CC ) as a function of PV, are plotted in Figures 1a ~ 1d. The 223
BTCs of 52-nm NPs reached steady-state effluent concentrations ( 0/CCS ) close to 1.0 224
(Figures 1a and 1c), suggesting that the porous media used in this study had low retention 225
capacity for the NPs. DLVO calculations indicate lack of both primary minimum 226
deposition (due to the presence of high energy barriers) and secondary minimum 227
deposition (because of the very shallow depth secondary energy minimum) (Table 1). The 228
small differences in breakthrough concentrations measured at different particle 229
concentrations did not allow definite evaluation of concentration effect for the 52-nm NPs 230
under the experimental conditions employed in this study. However, a clear trend of 231
concentration effect is reflected in Figures 1b and 1d with respect to the 8-nm NPs, 232
showing that the values of 0/CCs increased with C0 at both IS values, which indicates 233
that higher C0 gave rise to lower relative retention of the smaller silica NPs. 234
To further evaluate the concentration effect, we calculated the deposition rate 235
coefficient (kd) and attachment efficiency (α) using measured 0/CCs values and 236
Equations 1 and 2. Table 2 shows that a clear trend of the dependence of kd and α on C0 237
cannot be ascertained under the experimental conditions. In addition, we evaluated 238
concentration effect on surface coverage (θ) of silica NPs using Equation 4b. Figures 2a ~ 239
2d demonstrate that higher C0 contributed to larger θ at both IS of 1 and 100 mM. This 240
observation is supported by Equation 4c, which shows that surface coverage is 241
proportional to C0. It should be noted that in some cases the θ values might still be higher 242
than the actual, which is likely because the overestimated surface coverage was not 243
completely corrected by Equation 4b, a point that will be further discussed in the 244
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Dynamics of Surface Coverage section. 245
Results from this study are consistent with literature reports based on studies with 246
micron-sized particles (e.g., latex microspheres, bacteria cells, and aggregated TiO2 247
NPs).18,35-37 Bradford and colleagues36,37 hypothesized that the concentration-dependent 248
colloid retention and transport are due to (i) concentration-dependent filling of retention 249
sites and (ii) concentration-dependent mass transfer of colloids to retention sites. To date, 250
studies of concentration effect on retention and transport of NPs are very limited.38,39 Our 251
study indicates that these proposed mechanisms may also apply to explain the behavior of 252
very small silica NPs. Additionally, Zhang et al.34 did observe that greater input 253
concentrations resulted in increased relative colloid retention at IS > 0.1 mM, which is 254
opposite to the present results. Zhang et al.34 attributed that the retained colloids acted as 255
new retention sites for other suspended colloids (i.e., ripening effect). Since the silica NPs 256
used in the present study were stable, ripening should be insignificant in the present cases. 257
The above discussion suggests that it is important to pay due attention to the 258
concentration effects when comparing results from different studies. Interpretation of 259
experimental results involving different input concentrations becomes more complex 260
when the key focus of the studies is to identify differences between NPs and their larger 261
counterparts in terms of their environmental fate and transport behaviors. The additional 262
complexity may arise from inconsistent use of mass or particle number concentrations. 263
We address the interplay between particle size and concentration effects in detail in Size 264
Effect Section below. 265
Dynamics of Surface Coverage. The dynamics of particle deposition is illustrated 266
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in Figures 2a ~ 2d where surface coverage as a function of PV exhibited apparently two 267
distinct rates, fast at the beginning of the transport experiments then slow after ~ 2 PVs, 268
where the surface coverage either stayed constant or increased slowly. 269
A careful examination of our results, however, indicates that the apparent fast 270
increase of surface coverage before 2 PVs may not reflect the real dynamics of θ. First, 271
although Equation 4b largely improves the calculation of θ values, the correction to the 272
overestimated θ was not complete. This is because the initial deposition rate coefficient kd 273
could be larger than the steady-state deposition rate coefficient that was used in our 274
correction calculation, leading to possible underestimation of the correction and thus still 275
some overestimation of the surface coverage. This, in consideration of the significant 276
impact of correction (Figure S3), implies that the calculated θ before 2 PVs may still be 277
subject to large errors. Second, the change in the slope occurred suddenly at ~ 2 PVs, 278
which is comparable to the travel time of a suspended particle through the column. Such a 279
sudden change in slope is very likely a reflection of inadequate treatment of the correction 280
for suspended particles. Third, when applying Equation 4b, the effect of Brownian 281
diffusion was not considered and therefore there might be a significant error at the initial 282
stages caused by diffusion. These factors mean that the apparent trend of two-rate surface 283
coverage dynamics before and after 2 PVs might not be physically based. 284
While a complete correction of θ is pending, scrutiny on the θ dynamics (i.e., slopes 285
of θ curves) does show that in some cases (e.g., exp. 5 in Figure 2a) the slopes were 286
decreasing at the late stages after ~ 2 PVs, where the correction became less important 287
and Brownian diffusion was usually not predominant. Such an observation is attributed to 288
the blocking effect,65,71 referring to the reduced availability of deposition sites on 289
collector grains, because the deposited particles excluded the immediate vicinity region of 290
the collector surfaces from the subsequent deposition. 291
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Size Effect. The breakthrough curves in Figures 3a and 3b show that the relative 292
retention was higher for 8-nm NPs than for 52-nm NPs at both 1 and 100 mM IS. On the 293
other hand, the 8-nm NPs have larger kd values than the 52-nm NPs at both 1 and 100 294
mM IS (exp. 7 vs exp. 5 and exp. 8 vs exp. 6, respectively, in Table 2). These results 295
indicate that, at the same particle number concentration, the smaller 8-nm NPs would 296
deposit faster. 297
Table 2 also shows that the attachment efficiencies α of 8-nm NPs at the two IS 298
values are almost similar to that of 52-nm NPs at IS of 1 mM (exp. 7 vs exp. 5 and exp. 299
8 vs exp. 6). The results suggest that faster deposition rate is not a guarantee for higher 300
attachment efficiency, because α is determined by the deposition rate coefficient (kd) and 301
collector contact efficiency (η0), not by kd alone (see Equation 2). In addition, Figures 3c 302
and 3d demonstrate that, at both IS values, the smaller 8-nm NPs had lower surface 303
coverages. This is not surprising because, at the same particle number concentration, 304
smaller colloids have much smaller total projection area ( 2paπ ) than the larger ones (see 305
Equation 4c). 306
Analyses of the results from this study also reveal that, interpretation of size effect 307
on NPs’ retention and transport would lead to different conclusions, depending on 308
whether the interpretation was based on mass concentration (mg/L) or particle number 309
concentration (particles/mL). For example, under similar particle number concentrations, 310
the larger NPs (52-nm) had lower relative retention, but higher surface coverage (Figures 311
3a ~ 3d) than the smaller NPs, whereas under similar mass concentrations, relative 312
retention of both 52-nm and 8-nm NPs was similar but the smaller NPs had higher surface 313
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coverage (Figures S4a ~ S4d in the Supporting Information). The discrepancy suggests 314
that, when studies are conducted with the goal to reveal potential unique behavior of NPs 315
relative to their larger counterparts (both on environmental fate and toxicity), special 316
attention should be paid to the potential concentration effects, whether it is based on the 317
same mass or the same particle number concentration, while interpreting results from 318
different studies. In fact, the apparent discrepancy is well explained by Equations 4c and 319
4d. Equation 4c shows that, for a given particle number concentration (C0) and at higher 320
kd [corresponding to lower relative retention (i.e., higher 0/CCS ) according to Equation 321
1a], θ is lower for smaller NPs because it is proportional to 2pa . Meanwhile, Equation 4d 322
indicates that, for a given mass concentration (m0) and at similar kd, θ is higher for smaller 323
NPs because the surface coverage is inversely proportional to ap. We believe that using 324
particle number concentration as the basis for comparisons of NPs’ fate and toxicity may 325
provide additional insights. In aerosol research, it has been reported that surface area and 326
particle number concentrations are better predictors than mass concentrations of risks 327
associated with NPs’ exposure and toxicity in air.38,39 328
The above results demonstrate that the smaller NPs (8-nm vs 52-nm) corresponded 329
to higher relative retention, faster deposition, and lower surface coverage. These results 330
are contrary to the previous reports that the smaller NPs (e.g., TiO2, aluminum, and Fe0 331
NPs) had less relative retention.22,23,28,31 This could be because the comparison was made 332
based on the same NPs’ mass concentration in these studies. In addition, it is likely that 333
particle size was not well controlled due to agglomeration, leading to particle size change 334
during these experiments. As such, it is difficult to definitely evaluate the effect of NPs’ 335
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size on their transport behavior. 336
Applicability of DLVO Theory. The results in Figures 4a and 4b show that both 337
8-nm and 52-nm silica NPs were released upon introduction of DI water during phase 3 338
(from 14 to 20 PVs). However, the release of 8-nm silica NPs was much more 339
pronounced than 52-nm particles. Mass balance analysis indicated that ~ 100% of the 340
deposited 8-nm silica NPs at IS = 100 mM was released, whereas the release of the 52-nm 341
NPs was ~ 2%. 342
The limited release of 52-nm silica NPs is perhaps because there were not many 343
NPs retained in the columns since the mass recoveries of those experiments were high 344
(exp. no. 5 and 6 in Table 2). As such, it is hard for a definite evaluation whether the 345
behavior of 52-nm silica NPs was consistent with the DLVO prediction at this point. On 346
the other hand, the mass recoveries of the 8-nm silica NPs in those experiments were 347
sufficiently large (exp. no. 7, 8, and 11 in Table 2) and thereby allow the assessment of 348
the DLVO applicability subsequently. According to the DLVO prediction, the release of 349
8-nm silica NPs due to the change of solution IS in phase 3 should be negligible because 350
there do not exist secondary energy minima (Table 1). However, it is observed that the 351
8-nm silica NPs released significantly. The above results clearly indicate that the DLVO 352
theory is not applicable to describe the behavior of the 8-nm NPs. The reason may be that, 353
in addition to the double layer repulsion and van der Waals attraction, other short-range 354
interactions (e.g., hydration and solvation) may also play an important role. Hahn and 355
O’Melia77 have pointed out that the release of deposited particles can occur at separation 356
distances of a few nanometers where the DLVO theory usually is not able to provide a 357
Page 18
18
quantitative description due to significant contribution of other types of interactions. On 358
the other hand, when NPs are sufficiently small so that the overlap of diffuse double 359
layers is complete, DLVO theory may be not valid; rather, the Brønsted concept based on 360
the Transitional State theory of interacting ions has been applied.54 361
While mechanisms responsible for the failure of the DLVO theory to very small 362
NPs might need to be systematically studied further, the above results in Figures 4a and 363
4b suggest that careful experimental scrutiny on NPs release from the porous media is 364
quite necessary, especially when the size reduces to very small value (e.g., 8-nm in this 365
case). Pronounced release of deposited NPs in porous media may occur upon lowering of 366
pore water IS (e.g., in the event of rainfall), which is not predicted by the DLVO theory 367
but could exert severe environmental consequences. 368
369
Acknowledgments 370
This research was supported by the National Research Initiative Competitive Grant 371
(No. 2001-35107-01235) from the USDA Cooperative State Research, Education, and 372
Extension Services, the Star Project (R833318) from the US EPA, and the National 373
Science Foundation under grants CBET-0932686 and EAR-0207788 (C.S.W.). 374
375
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Figure Captions 591
FIGURE 1. Concentration (C0) effect on retention of 52-nm and 8-nm silica NPs: (a) 592
52-nm and IS = 1 mM, (b) 8-nm and IS = 1 mM, (c) 52-nm and IS = 100 mM, and (d) 593
8-nm and IS = 100 mM. 594
FIGURE 2. Concentration (C0) effect on surface coverage (θ) of 52-nm and 8-nm silica 595
NPs: (a) 52-nm and IS = 1 mM, (b) 8-nm and IS = 1 mM, (c) 52-nm and IS = 100 mM, 596
and (d) 8-nm and IS = 100 mM. 597
FIGURE 3. Size effect on retention of silica NPs: (a) IS = 1 mM and (b) IS = 100 mM 598
and on surface coverage (θ) of silica NPs: (c) IS = 1 mM and (d) IS = 100 mM. 599
Comparisons are performed under the same particle number concentrations. 600
FIGURE 4. Reversibility of deposition of (a) 8-nm and (b) 52-nm silica NPs under 601
various IS. 602
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FIGURE 1 603
604
605
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31
FIGURE 2 606
607
608
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32
FIGURE 3 609
610
611
612
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33
FIGURE 4 613
614
615
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34
TABLE 1. Calculated maximum energy barriers (Φmax), secondary energy 616 minimum depths (Φsec), and their respective separation distances of DLVO 617 interaction profiles between silica NPs and sandsa. 618
619
IS Φmax Φsec height (kT) distance (nm) depth (kT) distance (nm)
(mM) 8 nm 52 nm 8 nm 52 nm 8 nm 52 nm 8 nm 52 nm 1 0.3 101.4 5.3 1.6 0 0 /b /b
100 1.8 30.8 0.6 0.5 0 1.4 /b 5.6 200 1.1 N/Ac 0.6 N/Ac 0 N/Ac /b N/Ac
620
aHamaker constant is 6.3×10-21 J 67,68 and pH = 10; 621 bΦsec does not exist; 622 cNone available623
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TABLE 2. Experimental conditions, deposition rate coefficients (kd), attachment efficiencies (α), and mass recoveries of the column transport 624 experimentsa 625
626
exp. no.
particle size (nm)
input concentration (particles/mL)
ionic strength (mM)
water approach velocity
(m/s)
deposition rate coefficientb
(h-1)
attachment efficiencyb (α)
mass recoveryc
(%) 1 52 2.7×1011 1 1.46×10-5 (1.5±2.5)×10-2 (2.5±4.1)×10-4 98% 2 52 2.7×1011 100 1.46×10-5 (1.4±0.3)×10-1 (2.3±0.4)×10-3 90% 3 52 1.4×1012 1 1.48×10-5 (5.1±2.6)×10-2 (8.5±4.4)×10-4 95% 4 52 1.3×1012 100 1.47×10-5 (1.4±0.3)×10-1 (2.3±0.4)×10-3 91% 5 52 1.3×1013 1 1.48×10-5 (3.2±2.4)×10-2 (5.3±4.0)×10-4 98% 6 52 1.2×1013 100 1.47×10-5 (9.0±2.6)×10-2 (1.5±0.4)×10-3 93% 7 8 0.9×1013 1 1.51×10-5 (1.5±0.3)×10-1 (5.8±1.0)×10-4 89% 8 8 1.7×1013 100 1.51×10-5 (3.2±0.3)×10-1 (1.2±0.1)×10-3 85% 9 8 3.5×1014 1 1.48×10-5 (4.1±27)×10-3 (1.6±10)×10-5 100% 10 8 3.5×1014 100 1.45×10-5 (1.5±0.2)×10-1 (5.6±1.0)×10-4 92% 11 8 1.3×1013 200 1.47×10-5 (5.8±0.3)×10-1 (2.3±0.1)×10-3 57%
627 aSands (210 g) were packed in each column with column porosity at about 0.340; solution pH was maintained 628 at 10; b“±” represents the uncertainty of the value, based on > 9 steady-state data points; cMass recovery was 629 calculated as ratio of the number of NPs in effluent (phases 1 and 2) and the number of NPs in influent. 630
