Parametric analysis on the growth of colloidal ZnO nanoparticles generated in alcoholic medium

A.S. Fonseca1, P. A. Figueira2, A. S. Pereira2, R. J. Santos4, T. Trindade2, M. I. Nunes3*

1 Institute of Environmental Assessment and Water Research (IDAEA-CSIC), Barcelona, Spain

2 Departamento de Química-CICECO, Universidade de Aveiro, Portugal

3Centre for Environmental and Marine Studies (CESAM), Dep. de Ambiente e Ordenamento, Universidade de Aveiro, Aveiro, Portugal4 Laboratory of Separation and Reaction Engineering - Laboratory of Catalysis and Materials (LSRE-LCM), Universidade do Porto, Faculdade de Engenharia, Porto, Portugal

*Corresponding author: isanunes@ua.pt, phone: +351 234 370 200; fax: +351 234 370 309

Supplementary material

0.0 0.4 0.8 1.21.0

2.0

3.0

4.0

5.0

6.0Ethanol1-Bu-tanol

t [hours]

d [n

m]

Fig. S1 Influence of alcohol chain-length on ZnO NP diameter obtained in experiments carried out in a

semi-batch reactor. T = 20ºC, [Zn2+] = 2 mM and Zn/OH = 0.625.

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Fig. S2 Sensitivity analysis for the parameters of the empirical Eq. S3.

2

Fig. S3 Sensitivity analysis for the parameters of the simultaneous coarsening oriented aggregation model.

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Annex 1: Rate constant for coarsening

The rate constant for coarsening (kL) can be obtained from the slopes of the linear regions of the plots of r3

versus t and is given by:

k L=8 γ D V m

2 cr=∞

9 RT (A1)

where is the diffusion coefficient at temperature T(K), given by D0exp (−Ea /k BT ) (D0 is the maximum

diffusion coefficient, Ea is the activation energy for diffusion and kB is the Boltzmann constant), cr=∞ is the

equilibrium concentration at a flat surface (i.e., the bulk solubility), γ is the surface energy, is the molar

volume of the solid (mol cm-3).

The temperature and solvent dependence of the rate constant can be considered by eliminating the diffusion

coefficient from Eq. (A1) using the Stokes-Einstein equation:

D=k BT

6 πμa (A2)

where μ is the solvent viscosity, and a is the solvated ion radius. Substituting into Eq. A2, one obtains(Lifshitz

and Slyozov 1961; Wagner 1961):

k L=8 γ D V m

2 cr=∞

54 πηaN A (A3)

where, NA is Avogadro’s number.

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