Supporting Information for: Measuring the Time-Dependent Monomer
Concentration during the Hot-Injection Synthesis of
Colloidal Nanocrystals.
Natalia Razgoniaeva, 1,2 Amit Acharya,1,2 Narayan Sharma,1,2 Prakash Adhikari1,2, Martin
Shaughnessy3, Pavel Moroz,1,2 Dmitry Khon3, Mikhail Zamkov1,2,*.
The Center for Photochemical Sciences1, Department of Physics2, Bowling Green State University,
Bowling Green, Ohio 43403. Department of Chemistry and Biochemistry3, St. Mary’s University, San
Antonio, Texas, 78228.
Corresponding author: [email protected]; Tel: 419-372-0264; Fax: 419-372-9938
S1
Figure SF1. The expected relation between the spectral position of the Au/Ag core/shell plasmon
resonance and the thickness of the Ag shell, calculated from Eq. SI1 (dAu = 5 nm). For small values
of the Ag shell thickness, the spectral shift of the plasmon resonance is roughly linear.
S2
Blue-shift of the plasmon resonance in Au/Ag core/shell nanoparticles. According to previous
works,1,2 the spectral position of the Au/Ag NP plasmon resonance can be approximately expressed
as a simple function of the Au volume fraction, νAu:

plasmon
Au / Ag
  Au 
plasmon
Au
 (1   Au )
plasmon
Ag
 R
 525   Au
R
 Au / Ag
3
 

  420  1   R Au

  R Au / Ag






3




(SI1)
For small values of the Ag shell thickness, ΔRAu/Ag, the shift of the plasmon resonance can be
approximated using a linear relationship:
plasmon
 Au
/ Ag ( nm)    R Au / Ag ( nm);   88.
S3
(SI2)
Figure SF2. Evolution of the plasmon resonance in Au/Ag core/shell nanoparticles corresponding to
(a) - growth of the shell in the presence of AgNO3 precursor (T = 110 C°). (b), - thermal dissolution
of the Ag shell (T = 110 C°). The process of dissolution appears to be much slower.
S4
Calculation of the nanoparticle growth rate. The total flux of monomers toward the particle
surface is given by3:
J  (4r 2 / Vm )
dr
dt
where dr/dt is a particle growth rate and Vm is the molar volume. According to the nucleation
framework proposed by Talapin et al.,4 the nanoparticle growth rare can be express as:
 2Vm 
[ M 1 ]  C 0 exp 

rRT 
dr

 Vm D
dt
 2Vm 
r  D k  exp 

 rRT 
(SI3)
where D is the monomer diffusion coefficient, [M1] is a monomer concentration in the bulk of the
solutions, γ is the surface energy per unit area, C0 is the solubility of the monomer, k is the growth
rate constant, α and β are transfer coefficients.
Prior to nucleation, the monomer concentration is relatively high, such that the negative term in
the numerator of Eq. SI3, which reflects the particle dissolution process, can be neglected (see Fig.
SF2). This will allow simplifying the expression for nanoparticle growth rate:
dr
 D  [M 1 ]  L
dt
where L 
(SI4)
Vm
 2Vm 
r  D k  exp 

 rRT 
Evolution of the monomer concentration [M1] at a constant temperature. The amount of
precursor molecules, dN, which is thermally converted into a monomer during dt time of the
reaction is: dN = -kNdt, or dN/N = -kdt, where k is the temperature dependent rate of the precursor
decomposition. By integrating both sides of this equation, we obtain the number of precursor
molecules, remaining in the flask as a function of time: N = N(t=0)e-kt. Assuming that prior to the
onset of nucleation the monomer is not being consumed, we can express the monomer concentration
in the reaction mixture:
S5
[ M1 (T )]  [ P](1  e k (T )t )
(SI5)
where [P] is the initial concentration of the precursor in the flask. In reactions where the nucleation
is achieved with only a small fraction of the converted precursor (high [P]), the rise in the monomer
concentration can be expressed as a linear function of time:
[M1 ]M1P  [ P](1  e  kt )  [ P](1  (1  kt))  [ P]kt
(SI6)
Figure SF2. Evolution of the monomer concentration in the flask prior to the onset of nucleation (T
= const). The linearity of [M1] at early times ( see Eq. SI6) is highlighted.
S6
References.
1
Shore, M. S.; Wang, J.; Johnston-Peck, A. C.; Oldenburg, A. L.; Tracy, J. B. Synthesis of
Au(Core)/Ag(Shell) Nanoparticles and their Conversion to AuAg Alloy. Nanoparticles 2011, 7,
230–234
2
Mingzhao, Guyot-Sionnest, P. Synthesis and Optical Characterization of Au/Ag Core/Shell
Nanorods. J. Phys. Chem. B, 2004, 108, 5882-5288.
3
Sugimoto, T. Preparation of monodispersed colloidal particles. Adv. Colloid Interfac. Sci. 1987,
28, 65-108.
4
Talapin, D. V.; Rogach, A. L.; Haase, M.; Weller, H. Evolution of an Ensemble of
Nanoparticles in a Colloidal Solution: Theoretical Study. J. Phys. Chem. B 2001, 105, 1227812285 S7