Supplementary Material
Aggregation behaviour of TiO2 nanoparticles in natural
river water
Journal of Nanoparticle Research
Véronique Adam, Stéphanie Loyaux-Lawniczak, Jérôme Labille, Catherine Galindo, Mireille del Nero, Sophie
Gangloff, Tiphaine Weber, Gaetana Quaranta*
*corresponding author: [email protected]
Laboratoire d’Hydrologie et de Géochimie de Strasbourg / EOST / UDS, 1 rue Blessig, 67084 Strasbourg
Cedex, France.
Characterization of TiO2 NPs
Fig. S1: X-Ray diffraction pattern of TiO2 NPs studied
1
(a)
(b)
Fig. S2: Transmission Electronic Microscopy micrograph of (a) an aggregate of TiO2 NPs (b) a zoom
of an aggregate border with the nanoparticle sizes (Jeol JEM 2100)
2
Illite Puy en Velay <2µm
570
560
550
540
Characterization
of illite
530
520
(a)
510
500
490
480
470
d=9,99
460
450
440
430
420
410
400
390
380
370
360
350
340
330
Lin (Counts)
320
310
300
290
d=3,32
280
270
260
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
d=4,98
80
70
60
50
40
30
20
10
0
30
20
10
9
8
7
6
d - Scale
3
5
4
3
(b)
Fig. S3: (a) X-Ray Diffraction pattern of studied illite (b) Reference illite pattern. The comparison
between (a) and (b) shows that it is pure illite
40
30
zeta potential (mV)
20
10
0
1
2
3
4
5
6
7
8
9
10
11
-10
-20
-30
-40
pH
Fig. S4: Zeta potential of TiO2 NPs in deionized water ([NaCl] = 10mM) as a function of pH
4
Interaction energy calculations according to the DLVO theory
The interaction energy between two particles can be calculated by summing the attractive (Van der
Waals - vdW) and repulsive (electrical double layer - edl) forces (Equation 1).
(1)
The Van der Waals attraction between two spheres is given by Gregory:2
( )
(
*
)+
(2)
Where AH [J] is the Hamaker constant, accounting for materials properties, d [m] is the shortest
distance between the spheres of radii R1 and R2 (m), b1 = 5.32, b2 = 14.02 and λd = 100 nm.
The Hamaker constant between two materials 1 and 2 immersed in a medium 3 can be calculated by:
√
(3)
(√
√
)(√
√
)
(4)
Where Aii is the Hamaker constant of a material in vacuum, Aij is the Hamaker constant related to the
interaction between materials i and j in vacuum.
The electrical double layer repulsion between two spheres is given by:3
( )
,
*
+
(
)
[
]- (5)
Where d is the shortest distance between two spheres of radii R1 and R2 [m], ε0 is the free space
permittivity [F.m-1], εr the liquid permittivity [-], ζ1 and ζ2 are the zeta potentials of the particles [V],
and κ is the inverse of the Debye length [m-1].
The Debye length, which is the thickness of the double layer, is given by:
(
)
(6)
With kB is the Boltzmann constant [J.K-1], T is the temperature [K], e is the electron charge [C], NAv is
the Avogadro number [-], and I is the ionic strength of the suspension [mol.m-3].
5
200
0
0
10
20
30
40
50
W/kT
-200
60
EDL; river water
vdW; river water
DLVO; river water
-400
EDL; river water +
2.75 mM CaCl2
-600
vdW; river water
+ 2.75 mM CaCl2
DLVO; river water
+ 2.75 mM CaCl2
-800
-1 000
d (nm)
Fig. S5: Interaction energies between TiO2 NPs aggregates in the river water and in the river water
with added CaCl2 (pH 8)
200
0
0
10
20
30
40
50
EDL; river water
vdW; river water
-200
W/kT
60
DLVO; river water
-400
EDL; river water +
2.75 mM CaCl2
-600
vdW; river water +
2.75 mM CaCl2
DLVO; river water +
2.75 mM CaCl2
-800
-1 000
d (nm)
Fig. S6: Interaction energies between TiO2 NPs and illite aggregates in the river water and in the river
water with added CaCl2 (pH 8)
6
SmoluCalc model approach
In this model the Smoluchowski equations are solved numerically using a size gridding procedure to
divide the particle population into different size classes and thus controlling the number of differential
equations to be solved. On one hand, the sticking efficiency α is an open parameter that is adjusted to
fit the measured aggregation kinetics data. On the other hand, the collision frequency β is generated by
the model, accounting for the particle properties (size, density, concentration, fractal dimension), the
solvent properties (velocity gradient, viscosity, density, temperature) and the type of interparticle
collision resulting from the aggregate permeability to the streamlines.4 In the present work, the
aggregate permeability was calculated from Gmachowski model, as derived by Thill et al., 20014.
Both mechanical agitation and Brownian motion are accounted for in the β simulation, while
sedimentation is considered negligible due to the permanent agitation. The mechanical agitation was
also responsible for aggregate fractionation effect competing with the aggregation forces.
Nevertheless, although it was fitted here by a maximum aggregate size in the model, this effect is not
discussed in the present work as our attention is more focused on the very first steps of the aggregation
process to determine the driving α while fragmentation remains negligible.
Because the SmoluCalc model only deals with homoaggregation of spherical units, and clay gives the
major signal by laser diffraction on the clay / NP mixture, we used the clay characteristics to constrain
this unique type of particle input. This latter consists of the clay homoaggregates, 45 µm in average
size, preliminary formed in Thur water + CaCl2 (2.75 mM), before NP injection. For a valid estimation
of the collision frequency by these clay units, an appropriate estimation of the initial number
concentration and density of the clay units in the system was required. It was calculated from the
fractal dimension 2.18 measured for the clay units, using the Verapaneni approach. The structural
characteristics of the initial clay unit are given in Table S1.
Table S1: Structural characteristics of the initial clay units used in the SmoluCalc modeling
Clay characteristic
Mean particle diameter Dv50 of the primary particles
Volumic mass of the primary particles
Interparticle collision type
Fractal dimension of the primary particles
Fractal dimension of the forming aggregates
Surface of a primary particle
Primary particle number
Total surface of primary particles
Total volume of primary particles
7
Value
45 µm
54.7 kg/m3
Gmachowski
2.18
2.3
6.39x10-9 m2
1.94x106
1.23x10-2 m2
9.25x10-8 m3
Table S2: SmoluCalc results
NP
NP
total projected
concentration
number
area (m2)
(mg/L)
10
6.11E+10
1.20E-02
20
1.22E+11
2.40E-02
30
1.83E+11
3.60E-02
40
2.44E+11
4.80E-02
50
3.06E+11
6.00E-02
100
6.11E+11
1.20E-01
total NP
volume (m3)
number
ratio
surface
ratio
volume
ratio
alpha
global
4.00E-09
8.00E-09
1.20E-08
1.60E-08
2.00E-08
4.00E-08
3.15E+04
6.31E+04
9.46E+04
1.26E+05
1.58E+05
3.15E+05
9.73E-01
1.95E+00
2.92E+00
3.89E+00
4.87E+00
9.73E+00
4.33E-02
8.65E-02
1.30E-01
1.73E-01
2.16E-01
4.33E-01
0.11
0.17
0.27
0.8
1
References
(1)
UGA Clay Science website: http://clay.uga.edu/courses/8550/CM11.html. Consulted on 22
June 2015.
(2)
Gregory, J. Approximate expressions for retarded van der Waals interaction. J. Coll. Interface
Sci. 1981, 83 (1), 138-145.
(3)
Hogg, R.; Healy, T.; Fuerstenau, D. Mutual coagulation of colloidal dispersions. Transactions
of the Faraday Society 1966, 62, 1638-1651.
(4)
Thill, A.; Moustier, S.; Aziz, J.; Wiesner, M.; Bottero, J.Y. Flocs Restructuring during
Aggregation: Experimental Evidence and Numerical Simulation. J. Coll. Interface Sci. 2001, 243,
171-182; Doi: 10.1006/jcis.2001.7801.
8