In this paper ( http://pubs.acs.org/doi/suppl/10.1021/cm902516f/suppl_file/cm902516f_si_001.pdf ) the calculation of the amount of Zn/S precursor for the first layer ZnS growth on CdS core was as following:
- The size of CdS core: D0=3.7 nm R0=3.7/2=1.85nm
- The amount of CdS particles: n1=1.2×10-7 mol
- The average thickness of one monolayer of ZnS zinc blende (d): d=0.312 nm
- The amount of Zn and S precursor of the first layer ZnS (1ML):
- The volume of the first ZnS monolayer: V1= 4/3*pi*(R13 - R03) = 1.5684E-26 m3
- The density of ZnS: For Zinc blende: D=4.10E-3 kg/cm3 = 4.10E+6 g/m3
- The mass of the 1st ML ZnS shell in one core/shell particle: m=Volume * Density; m=1.5684 E-26 m3 *4.1E6 g/m3= 6.43044 E-20 g
- M.W. (Molecular weight) of ZnS = 97.474 g/mol
- The amount of ZnS in one core/shell particle: n2=m/M.W = 6.43044 E-20 g/97.474 g/mol=6.597 E-22 mol/particle
- Avogadro's constant (N) = 6.025*10E23 particle/mol
In paper the amount of Zn/S precursor for the first layer ZnS growth (A1) was calculated by this method: A1=n1* N *n2
A1=1.2E-7 mol*(6.025*10E23 particle/mol) *(6.597 E-22 mol/particle) = 0.0477 mmol
But I could not understand why Avogadro's constant (N) was used here. I calculated the amount of Zn/S precursor for the first layer ZnS growth (A1) by different method simply by multiplying the amount of ZnS in one core/shell particle (n2) by the number of CdS core particle (A0): A1 = n2*A0
And here how I calculated A0:
- The volume of the CdS core: V0= 4/3*pi*(R03) = 2.6522E-26 m3
- The density of CdS: D=4.87E-3 kg/cm3 = 4.87E+6 g/m3
- The mass of the CdS core in one core/shell particle: m=Volume * Density; m=2.6522 E-26 m3 *4.87E6 g/m3= 1.2916 E-19 g
- M.W. (Molecular weight) of CdS = 144.46 g/mol
- The number of moles per one CdS core particle (n0)= 8.9410E-22 mol/particle
- the number of CdS core particles (A0) in solution: A0= n1/n0 = 1.2×10-7 mol / 8.9410E-22 mol/particle = 1.3421E14 particles
Then; A1 = n2*A0 = 6.597 E-22 mol/particle * 1.3421E14 particles = 0.000089 mmol
If my method is correct, how can measure in lab this very small number?
The Avogadro constant is used for converting weight in grams to mol; or going by the vol. method of the reference, to convert number of Zn and S molecules to be added into mol. This is necessary because precursor solutions are usually prepared based on concentration expressed in mols (or Molar).
I don't understand your method, because for calculating the amount of shell precursors, we don't need to do any calculation of the core.
In simple terms: (i) find the volume of shell and divided by unit cell volume and you will get -> number of unit cells in the shell
(ii) Multiply with number of atoms per unit cell and you will get -> number of atoms needed for shell layer on each core QDs
(iii) Multiply with the number of Core QDs and you will get -> total number of Zn and S atoms needed to grow shell on ALL the cores.
(iv) convert this large number into mol (or Molar) by using the Avogadro constant.
Dr. Abhilash, thank you for your reply.
In the step three of your answer you said that we multiply with the core number and my method was to calculate the core number in solution (Please check if my calculation procedure is correct?). Then I multiply the number of core (A0) by the number of moles of ZnS molecule for each core particle to get the total number of Zn/S precursor in mole?
Is the amount of CdS particles: n1=1.2×10-7 mol in the paper related to the total number of CdS core particles or to the mole number of CdS molecule in solution?
Hi Abu,
The amount of CdS (n1) is the 'concentration' of CdS particles (NOT molecules). Essentially it is the number of CdS particles divided by Avogadro number. I guess they found that value from the absorption spectra. So finding the number of core particles has to be experimentally determined, and not by calculation. There are papers where the extinction coefficient of CdSe, CdS and CdTe has been empirically determined. From these values, finding the concentration (hence the number) of core QDs can be done from absorption spectra. You can find the references in either my PhD thesis or in one of my papers (Microwave mediated synthesis of semiconductor quantum dots).
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