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Supporting Information
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Effects of humic acid and solution chemistry on the retention and transport of cerium
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dioxide nanoparticles in saturated porous media
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Xueyan Lv1, Bin Gao2, Yuanyuan Sun1*, Xiaoqing Shi1, Hongxia Xu1, Jichun Wu1*
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1. Key Laboratory of Surficial Geochemisty, Ministry of Education, School of Earth Sciences
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and Engineering, Hydrosciences Department, Nanjing University, Nanjing 210093, China
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2. Department of Agricultural and Biological Engineering, University of Florida, Gainesville, FL
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*
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E-mail address: sunyy@nju.edu.cn (Y.Y. Sun), jcwu@nju.edu.cn (J.C. Wu).
Corresponding authors. Tel.: +86 25 89680835; fax: +86 25 83686016.
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S1. XDLVO theory
The distinct effect of HA on the transport of CeO2 NPs cannot be neglected due to the
adsorption density of HA to the particles. Additional steric repulsive interactions were provided
by the adsorbed HA on CeO2 NPs (G. X. Chen et al. 2012). In our study, XDLVO theory was
utilized to investigate the interaction energy between the CeO2 NPs and sand grain by combining
the retarded van der Waals attraction, electrical double layer repulsion and steric
repulsion(osmotic repulsion (Vosm) and elastic-steric repulsion (Velas)). However, the DLVO
theory was originally developed to estimate the interaction energy for spherical particles and no
theory has been developed for a rod-shaped particle. Tian et al. (2011) used either the length or
diameter as an effective size to explore the interactions between carbon nanotubes and porous
media. In this study, XDLVO energy was estimated by treating the NPs–NPs system as a
sphere–sphere interaction and the NPs–collector system as a sphere–plate interaction.
The retarded van der forces (𝑉𝑣𝑑𝑤 ) and electrical double layer forces (𝑉𝑒𝑙 ) for a spheresphere and sphere-plate system can be written as (Hogg et al. 1966):
𝐴131 𝑎𝑝 𝑎𝑝2
𝑉𝑣𝑑𝑤 = − 6ℎ2 (𝑎
𝑝1 +𝑎𝑝1 )
[1 −
5.32ℎ
𝜆
𝜆
ln(1 + 5.32)]−1
(1)
𝑉𝑣𝑑𝑤 = −
𝐴132 𝑎𝑝
6ℎ
[1 + (1 +
14ℎ
𝜆
)]
−1
(2)
Where 𝑎𝑝1 and 𝑎𝑝2 refer to the radii of the two interacting spherical CeO2 NPs (Eq. (1)), and
𝑎𝑝 refers to the radius of the NPs (Eq. (2)); h is the separation distance between the two CeO2
NPs (Eq. (1)) or between CeO2 NPs and plate surface (Eq. (2)); 𝜆 is the characteristic wavelength
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of interaction (100 nm) (Jiang et al. 2012); 𝐴131 is the Hamaker constant for substances ‘‘1’ in
the presence of medium ‘‘3’’, and 𝐴132 is the Hamaker constant for substances ‘‘1’’and ‘‘2’’ in
the presence of medium ‘‘3’’, which can be determined from the Hamaker constant of individual
material (K. L. Chen and Elimelech 2007; Bergendahl and Grasso 1999):
𝐴131 = (√𝐴11 − √𝐴33 )
2
(3)
𝐴132 = (√𝐴11 − √𝐴33 )(√𝐴22 − √𝐴33 )
(4)
where A11 is the Hamaker constant for CeO2 NPs. The value of Hamaker constant for CeO2
NPs in the absence of HA is 5.57·10 -20J (Karimian and Babaluo 2007). Adsorption of HA to the
CeO2 NPs would occur when HA is present in the aqueous solutions, thus the Hamaker constant
for HA (4.85·10-20J) is employed to represent the Hamaker constant for CeO2 NPs when HA is
present in the solutions (Hu et al. 2010). A22 is the Hamaker constant for sand grains and is taken
from Bergstrom as 8.86 × 10-20J (Bergstrom 1997). A33 is the Hamaker constant for water and is
taken from Israelachvili as 3.7 × 10-20J (Israelachvili 2011).
𝑎𝑝1 𝑎𝑝2
𝑉𝑒𝑙 = 𝜋𝜀𝑟 𝜀0 (𝑎
𝑝1 +𝑎𝑝2 )
1+exp(−𝜅ℎ)
{2𝜁𝑝1 𝜁𝑝2 𝑙𝑛 [1−exp(−𝜅ℎ)] + (𝜁𝑝1 2 + 𝜁𝑝2 2 )𝑙𝑛[1 − exp(−2𝜅ℎ)]}
𝑉𝑒𝑙 = 𝜋𝜀𝑟 𝜀0 𝑎𝑝 {2𝜁𝑝 𝜁𝑐 𝑙𝑛 [
1+exp(−𝜅ℎ)
1−exp(−𝜅ℎ)
] + (𝜁𝑝 2 + 𝜁𝑐 2 )𝑙𝑛[1 − exp(−2𝜅ℎ)]}
𝜀 𝜀 𝑘 𝑇
𝑟 0 𝐵
𝜅 −1 = √ 2𝑁
𝐼𝑒 2
𝐴
(5)
(6)
(7)
Where 𝜀𝑟 is the dielectric constant of the medium; 𝜀0 is the vacuum permittivity; 𝑒 is the
electron charge; 𝜁𝑝1 and 𝜁𝑝2 (Eq. (5)), and 𝜁𝑝 and are 𝜁𝑐 (Eq. (6)) are the Zeta potentials of
particles and sand grains, respectively; 𝜅 is the reciprocal of the Debye length; 𝑁𝐴 is the
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Avogadro constant; 𝐼 is the ionic strength; 𝑘𝐵 is the Boltzmann’s constant; T is the absolute
temperature; e is the electron charge.
For HA absorbed CeO2 NPs, steric repulsion including osmotic repulsion (Vosm) and elasticsteric repulsion (Velas) must be considered. Overlap of the HA layer on two segment
concentration and thus increases the local osmotic pressure in the overlap region (Vosm). Vosm can
be written as below (Fritz et al. 2002; Phenrat et al. 2008):
𝑉𝑜𝑠𝑚
𝐾𝐵 𝑇
𝑉𝑜𝑠𝑚
𝑘𝐵 𝑇
𝑉𝑜𝑠𝑚
𝑘𝐵 𝑇
=0
=
=
𝑎𝑝 4𝜋
𝜐1
𝑎𝑝 4𝜋
𝜐1
2𝑑 ≤ ℎ
ℎ 2
1
𝜙𝑝2 (2 − 𝜒) (𝑑 − 2)
1
ℎ
𝑑 ≤ ℎ < 2𝑑
1
ℎ
𝜙𝑝2 (2 − 𝜒) 𝑑 2 (2𝑑 − 4 − 𝑙𝑛 (𝑑))
ℎ<𝑑
(8)
where χ is the Flory-Huggins solvency parameter, which is assumed to be 0.45 for HA/water
interaction; 𝜐1 is the volume of a solvent molecule (0.03 nm3) (Wang et al. 2012). 𝜙𝑝 is fractional
HA surface coverage (Li and Chen 2012); d is the thickness of the adsorbed HA layer (Li and
Chen 2012).
Any compression of the adsorbed HA layer below the thickness of the unperturbed layer (d)
leads to a loss of entropy and gives rise to the elastic repulsion (Velas). Velas can be expressed as
(Fritz et al. 2002):
𝑉𝑒𝑙𝑎𝑠
𝑘𝐵 𝑇
𝑉𝑒𝑙𝑎𝑠
𝑘𝐵 𝑇
=0
=
2𝜋𝑎𝑝
𝑀𝑊
𝑑≤ℎ
2
ℎ
ℎ
3−
𝜙𝑝 𝑑 𝜌𝑝 [𝑑 𝑙𝑛 (𝑑 (
2
ℎ
𝑑
2
) ) − 6 𝑙𝑛 (
3−
2
ℎ
𝑑
ℎ 2
) + 3 (1 + 𝑑) ]
𝑑>ℎ
(9)
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where MW is the molecular weight of the HA (Hong and Elimelech 1997), and 𝜌𝑝 is its
density.
The total extended DLVO interaction energy (𝑉𝑇 ) is:
𝑉𝑇 = 𝑉𝑣𝑑𝑤 + 𝑉𝑒𝑙 + 𝑉𝑜𝑠𝑚 + 𝑉𝑒𝑙𝑎𝑠
(10)
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References
Bergendahl, J., & Grasso, D. (1999). Prediction of colloid detachment in a model porous media:
Thermodynamics. Aiche Journal, 45(3), 475-484.
Bergstrom, L. (1997). Hamaker constants of inorganic materials. Advances In Colloid And
Interface Science, 70, 125-169.
Chen, G. X., Liu, X. Y., & Su, C. M. (2012). Distinct Effects of Humic Acid on Transport and
Retention of TiO2 Rutile Nanoparticles in Saturated Sand Columns. Environmental
Science & Technology, 46(13), 7142-7150.
Chen, K. L., & Elimelech, M. (2007). Influence of humic acid on the aggregation kinetics of
fullerene (C-60) nanoparticles in monovalent and divalent electrolyte solutions. Journal
Of Colloid And Interface Science, 309(1), 126-134.
Fritz, G., Schadler, V., Willenbacher, N., & Wagner, N. J. (2002). Electrosteric stabilization of
colloidal dispersions. Langmuir, 18(16), 6381-6390.
Hogg, R., Healy, T. W., & Fuersten.Dw (1966). Mutual Coagulation of Colloidal Dispersions.
Transactions of the Faraday Society, 62(522P), 1638-&.
Hong, S. K., & Elimelech, M. (1997). Chemical and physical aspects of natural organic matter
(NOM) fouling of nanofiltration membranes. Journal Of Membrane Science, 132(2),
159-181.
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Hu, J. D., Zevi, Y., Kou, X. M., Xiao, J., Wang, X. J., & Jin, Y. (2010). Effect of dissolved
organic matter on the stability of magnetite nanoparticles under different pH and ionic
strength conditions. Science Of The Total Environment, 408(16), 3477-3489.
Israelachvili, J. N. (2011). Intermolecular and surface forces. San Diego, Calif.: Elsevier Science
Publ.
Jiang, X. J., Tong, M. P., & Kim, H. (2012). Influence of natural organic matter on the transport
and deposition of zinc oxide nanoparticles in saturated porous media. Journal Of Colloid
And Interface Science, 386, 34-43, doi:DOI 10.1016/j.jcis.2012.07.002.
Karimian, H., & Babaluo, A. A. (2007). Halos mechanism in stabilizing of colloidal suspensions:
Nanoparticle weight fraction and pH effects. Journal Of The European Ceramic Society,
27(1), 19-25.
Li, K. G., & Chen, Y. S. (2012). Effect of natural organic matter on the aggregation kinetics of
CeO2 nanoparticles in KCl and CaCl2 solutions: Measurements and modeling. Journal
Of Hazardous Materials, 209, 264-270.
Phenrat, T., Saleh, N., Sirk, K., Kim, H. J., Tilton, R. D., & Lowry, G. V. (2008). Stabilization of
aqueous nanoscale zerovalent iron dispersions by anionic polyelectrolytes: adsorbed
anionic polyelectrolyte layer properties and their effect on aggregation and
sedimentation. Journal of Nanoparticle Research, 10(5), 795-814, doi:DOI
10.1007/s11051-007-9315-6.
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Tian, Y. A., Gao, B., & Ziegler, K. J. (2011). High mobility of SDBS-dispersed single-walled
carbon nanotubes in saturated and unsaturated porous media. Journal Of Hazardous
Materials, 186(2-3), 1766-1772, doi:DOI 10.1016/j.jhazmat.2010.12.072.
Wang, D. J., Bradford, S. A., Harvey, R. W., Gao, B., Cang, L., & Zhou, D. M. (2012). Humic
Acid Facilitates the Transport of ARS-Labeled Hydroxyapatite Nanoparticles in Iron
Oxyhydroxide-Coated Sand. Environmental Science & Technology, 46(5), 2738-2745,
doi:Doi 10.1021/Es203784u.
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