A dispersion of spherical polymer particles contains Np = 4•1013 particles/dm3. The total surface of the particles in 1 dm3 is Asp = 820 m2.

a) What kind of average diameter can we calculate. Calculate this average diameter.

b) If we know that the dispersion contains 60 vol% water, we can calculate another type of average diameter. Which? Find it!

a) Surface average.

\(\bar{d_s} = \sqrt{\frac{\Sigma n_i d_i^2}{\Sigma n_i}}\)

b) Volume average.

\(\bar{d_s} = \sqrt{\frac{\Sigma n_i d_i^3}{\Sigma n_i}}\)

I don't know how to incorporate the data into the formulas.

 

That's because these formulae are too complicated.

In both a and b consider unit volume = 1 cubic dm.

a)

Total area = average area x number of particles

b)

Since 60% is disperse medium 40% is disperse phase

Total Volume x 0.40 = average volume x number of particles

I presume you can substitute suitable formulae for area and volume of a sphere.

 

OK, thanks! I found the answers 2.55 μm and 2.67 μm, which means that this is a polydisperse system.