Hexadecyltrimethylammonium bromide has a long hydrophobic chain and a polar head group.

The molecule does not dissolve well in either aqueous or organic solvents.  In an organic solvent containing a small amount of water the hexadecyltrimethylammonium bromide traps the aqueous portion in a micelle sphere with the polar heads facing in and the non-polar tails facing out. The relative amount of pentanol cosurfactant controls the size of the micelle.

A water-in-oil microemulsion droplet. This static picture
does not properly convey "the dynamic reality of the aggregates."
Figure based on J. Phys. Chem. 100, 3190-3198 (1996).
Mixing hexadecyltrimethylammonium bromide pentanol micelles of CdCl

2 with similar micelles containing Na2S produces nanoparticle CdS since the aqueous solution serves as a nanoreactor and the particles cannot grow bigger than the micelle. The pentanol also acts as a capping agent to stabilize the CdS particles. The formation of CdS nanoparticles can be detected by spectroscopy since quantum size effects make the visible absorption spectra different than that of bulk CdS

Test the reagents by adding a drop of aqueous Cd+2 to a drop of aqueous S-2. A yellow color should appear if the Na2S solution is good. If the mixture remains clear, remake the Na2S solution.
In a cuvet, add an equal amount of aqueous 0.012 M Cd+2 and aqueous 0.012 M S-2. Record your observations and immediately obtain the visible absorption spectrum (before the solution becomes too opaque.)
Add 0.20 g hexadecyltrimethylammonium bromide to a test tube. Add a stir bar. Clamp over a magnetic stirrer.
Add 4.0 mL heptane and 1.0 mL pentanol to the hexadecyltrimethylammonium bromide. Stir to give a suspension.
Transfer half the suspension to a second tube. Stir both solutions to maintain the suspension.
To one test tube, add 0.1 mL (3 drops) of 0.012 M CdCl2. The solution will clear as hexadecyltrimethylammonium bromide micelles containing CdCl2 form.
To the second test tube, add 0.1 mL (3 drops) of 0.012 M Na2S. The solution will clear as hexadecyltrimethylammonium bromide micelles containing Na2S form.
Join the two solutions and mix. Record the visible absorption spectrum in a glass cuvet.

Materials

CAUTION: Avoid physical contact with cadmium chloride and cadmium sulfide as both are carcinogens.
    Stock Solutions for hundreds of batches
  • 0.012 M CdCl2: Dissolve 0.110 g in 50 mL distilled water. This solution keeps for months.
  • 0.012 M Na2S.9H2O: Dissolve 0.144 g in 50 mL distilled water. This solution does not keep well.
  • hexadecyltrimethylammonium bromide (Aldrich 855820 Cetyltrimethylammonium bromide)
  • heptane
  • pentanol

    • Equipment
  • Test tubes, ring stand, test tube clamps
  • plastic dropper
  • 1/4" magnetic stir bar, magnetic stirrer
  • Cuvet and absorption spectrometer

Calculations

The x-intercept of the linear portion of the absorbance as a function of wavelength graph is a measure of Eg.

Eg = h c / λ
h = 6.626x10-34 J s
c = 2.998x108 m/s
e = 1.602x10-19 C
ε0 = 8.854x10-12 C2/N/m2
m0 = 9.110x10-31 kg

CdS
λbulk = 512 nm
ε = 5.7
me* = 0.19
mh* = 0.80

CdSe
λbulk = 709 nm
ε = 10.6
me* = 0.13
mh* = 0.45

ZnO
λbulk = 365 nm
ε = 8.66
me* = 0.24
mh* = 0.59

The effective mass model suggests

where r is the radius of the nanoparticle. The second term is the particle-in-a-box confinement energy for an electron-hole pair in a spherical quantum dot and the third term is the Coulomb attraction between an electron and hole modified by the screening of charges by the crystal.

After multiplying by r2, rearranging, and using the quadratic formula,

What is the diameter of the nanoparticles?