Question

Assuming that 1.00 L of 4% PVA solution is spread out to form a thin sheet of thickness equal to the average length of a PVA strand, calculate the total area of the liquid sheet. Then calculate the average of the sheet of solution per strand of PVA. Assuming this area is a little square, the square root of this area gives the edge length of the square which is approximately the average distance between the PVA strands. Show that this distance is about ten times the estimated diameter of a PVA strand (0.2-0.3 nm).

Answer 1

One unit of PVA (monomer) looks like is -(C₄H₆O₂)_n-.

The degree of polymerization of polyvinyl acetate (PVA) is typically 100 to 5000.
4% PVA = 40g per litre
Molar mass C₄H₆O₂ = 86g/mol
40g = 40/86 = 0.465 mol
Number of molecules of un-polymerised PVA = 0.465x6.022x10²³ = 2.8x10²³

If n = 1 in the above formula, then there would be 2.8x10²³ particles or strands
If n = 933.3 then there would be (2.8x10²³)/933.3 = 3x10²⁰ particles or strands
Where n = the degree of polymerization, which is not given in the question, but it is quite reasonable to have 3x10²⁰ strands of PVA, n = 933 that fits neatly into the range of n = 100 to 5000.

Given the diameter of the PVA strand or particle, d = 0.3x10^-9 m

Therefore total length = no. of strands x d = 3x10²⁰x0.3x10^-9 = 9x10^-10 m

A square has 4 nos. of equal length sides. Therefore the length of the one side (edge length), a = 9x10^-10/4 = 2.25x10^-10 area

(total area), A = a²

A = (2.25x10^-10)² = 5x10^-20 m²

Therefore, area per strand is, a₁² = 5x10^-20/3x10²⁰ = 1.66x10^-40 m²