Supporting information for:
Laser synthesis and size tailor of carbon quantum dots
1. Fluorescence Quantum Yield
The quantum yield was measured based on references (Lakowicz 1999; Liu et al. 2007; Xu et
al. 2004), i.e. comparing the integrated photoluminescence intensities and the absorbency values
of the samples with the reference quinine sulfate, and then the quantum yield was calculated
using the following equation:
Q  QR
I  AR  2
I R  A  R2
(1)
where Q is the quantum yield, I is the measured integrated emission intensity, η is the
refractive index, and A is the optical density. The subscript R refers to the reference fluorophore
of known quantum yield. To minimize re-absorption effects the optical densities in the 20 mm
fluorescence cuvette were kept under 0.1 at the excitation wavelength. An excitation slit width of
2.5 nm and an emission slit width of 2.5 nm were used to excite the samples of C-dots and to
record their photoluminescence spectra.
Table 1 Quantum yield of sample A
Integrated
Emission
Intensity (I)
183.2
Absorption
at 380 nm
(A)
0.057
Sample
Quinine
sulfate
Sample A
36.8
0.053
Table 2 Quantum yield of sample B
Refractive
Index of
solvent (η)
1.33
Quantum
yield (Q)
0.54 (known)
1.36
0.122 (calculated)
Integrated
Emission
Intensity (I)
234.7
Absorption
at 380 nm
(A)
0.071
Sample
Quinine
sulfate
Sample B
23.6
0.065
Table 3 Quantum yield of sample C
Sample
Quinine
sulfate
Sample C
Refractive
Index of
solvent (η)
1.33
Quantum
yield (Q)
0.54 (known)
1.36
0.062 (calculated)
Integrated
Emission
Intensity (I)
223.67
Absorption
at 380 nm
(A)
0.053
Refractive
Index of
solvent (η)
1.33
Quantum
yield (Q)
0.54 (known)
8. 72
0.097
1.36
0.012 (calculated)
2. Thermodynamic Model and Calculated Results
According to classical nucleation theory, the Gibbs free energy change of a spherical nucleus
of radius r formed by condensation from laser-induced bubbles can be expressed as (Hu et al.
2010; McDonald 1963)
4
G  r 3 g  4r 2 f
3
(1)
where f is the surface energy of the nuclei (3.27 J/m2). For graphite nanostructure, f can be
defined as f  ( f b Ab  f h Ah ) /( Ab  Ah ) , where the subscripts b and h denote the basal and highindex planes, respectively; A shows the corresponding area (Jiang and Chen 2006). ∆g is the
Gibbs free energy difference per unit volume from vapor to solid, which is given by (Hu et al.
2010; McDonald 1963; Ali and Winterer 2010),
g  RT ln( Ps / P) / Vm   RT ln( 1   ) / Vm
(2)
where P, T, R, Vm and σ are the pressure, the temperature, the gas constant, the mole volume of
the nuclei (5.398×106 m3/mol) (Jiang and Chen 2006), and the supersaturation, respectively. Ps is
the equilibrium vapor pressure of a particle of radius r and is given by (Ali and Winterer 2010)
 H V 
 2 fVm 
Ps  K exp  
 exp 

 RT 
 rRT 
(3)
where K is a constant and its value is equal to 7.245×105 Pa and ∆HV is the enthalpy of bulk
graphite evaporation (355.80 kJ/mol) (Zhao et al 2002; Ali and Winterer 2010)
The critical radius r* is obtained by differentitationg Eq. 1 with respect to r and follows as
r *  2 fVm / RT ln( 1   )
(4)
and the corresponding critical free energy ∆G* (i.e. the energy barrier of nucleation) is given
by
G *  16f 3Vm2 / 3[ RT ln( 1   )] 2
(5)
Assuming that the nuclei and the surrounding vapor have the same temperature and then the
nucleation time t can be expressed as (Feder et al. 1966; Wang et al. 2005)
t
(2mkT ) 0.5 kTf
Ps g / Vm N A 
2
(6)
where m, k and NA denote the mass of a single carbon atom, Boltzmann’s constant and
Avogadoro number.
The nucleation rate is defined as (Ali and Winterer 2010)
0.5
 2 f   P  Vm
 G  
  

J  
exp  
 kT 
 MN A   kT  N A
2
(7)
where M is the molar mass of carbon.
The general growth velocity V of the nuclei is given by (Wang et al. 2005)
 g 
 E 

V  h exp   a  1  exp  

RT
 RT  


(8)
where h, ν and Ea are the lattice constant of crystalline nuclei in the growth direction (0.336
nm), the thermal vibration frequency (about 2.3×1013 Hz) and the molar absorption energy of
adatoms attached at surface sites (about 2.4×105 J/mol) (Zhou et al. 2007; Mehandru and
Anderson 1990; Xie et al. 1999).
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