Supporting Information
Effect of thermodiffusion on pH regulated surface charge properties of
nanoparticle
Pradipta Kr. Das
Global R&D Tata Steel, Jamshedpur-831001, India
Email: pradipta.iitk@gmail.com
S1.
Derivation of expression for surface charge density
 w  enM

  w  e
K A nMH
C1s
Now nT  nM  nMH . So, incorporating that expression of surface charge density becomes

  w  enT
  w  enT
  w  enT
  w  enT
K AnMH
C1s  nMH  nM  

KA
n
M
C1s 1  nMH
KA

C1s 1  CK1As
KA
C1s  K A



S2.
Effect of thermodiffusion on surface charge density for different
nanoparticle size.
Fig. S1 shows effect of nanoparticle size on surface charge density for different nanoparticle
temperature considering KCl solution only. Since both KCl and NaCl solutions show similar
trend in surface charge density, explanations for KCl solution will also applicable for that of
NaCl solution. It is observed from Fig. S1 that the effect of nanoparticle size is significant at
lower salt concentration. However, the effect decreases with increasing salt concentration. The
results also show the effect of nanoparticle size increases with its temperature and pH. Due to
increasing curvature effect, electrostatic attraction on counterions increases near solid surface
and hence smaller nanoparticle shows higher surface charge density (  W ) than larger
nanoparticle as long as both the sizes are below critical size. Above critical size, curvature effect
becomes negligible and the surface charge density attains a constant value (to that of a flat plate).
However, critical size depends on solution pH, salt concentration and nanoparticle temperature.
With increasing solution pH, critical size decreases which is attributed to the fact that with
increasing pH the dissociation of the functional group increases at the surface and hence, a larger
nanoparticle is required to reach the surface charge density (  W ) to that of flat plate. With
increasing salt concentration, on the other hand, an increasing trend observed for surface K+ ions
concentration which excludes the H+ ions leading to an increase in surface charge density
magnitude and this increasing K+ ion concentration at the surface reaches a maximum
corresponding to the flat plate at relatively lower nanoparticle size. Hence, critical size decreases
with increasing salt concentration. It is interesting from the present results that with increasing
temperature, the increasing thermodiffusion of ions leads to an increase in the surface
concentration of K+ ions and it reaches its saturation limit at relatively small sized nanoparticle
as compared to that for isothermal condition. This essentially indicates a decrease in critical size
with increasing temperature.
Figure S1. Effect of temperature on surface charge density for different nanoparticle size.
Solid and dashed lines represent Rp =1 and 50nm respectively. The results are shown for KCl
concentration C0=1mM (a) and 100mM (b).
S3.
Effect of thermodiffusion on surface concentrations of ions.
Figure S2. Effect of temperature on surface concentration of OH- and Cl- ions is shown for different
nanoparticle size, salt concentration and pH. Solid and dashed line represents C0=1 and 100mM
respectively. The results are shown for Rp=1nm (a-b) and Rp=50nm (c-d).