Question

Calculate crystalline density Sample A of an unknown polymer has 33 volume percent crystallinity and a density of 0.856 g/cm3 and sample B of the same polymer has 74 volume percent crystallinity and a density of 0.918 g/cm3 . What is the density of the pure crystalline form of the polymer?

Answer 1

We know that

% crystallinity = ρc(ρs-ρa) X 100 / ρs(ρc-ρa)

Where

ρs =sample density

ρc = the density of the 100% crystalline polymer

ρa = the density of the 100% amorphous polymer

For sample A

0.33 = ρc(0.856-ρa) / 0.856(ρc-ρa) ............(1)

For sample B

0.74 = ρc(0.918-ρa) / 0.918(ρc-ρa) .....(2)

Divide equation (1) by (2)

0.33 / 0.74 = [ρc(0.856-ρa) / 0.856(ρc-ρa)] / [ρc(0.918-ρa) / 0.918(ρc-ρa)]

0.446 = 1.072 (0.856-ρa) / (0.918-ρa)

0.409 - ρa0.446 = 0.918 - 1.072ρa

ρa0.626 = 0.509

ρa = 0.813 ( density of amorphous polymer) ....(3)

the density of pure crystalline polymer will be calculated as

Put 3 in 1

0.33 = ρc(0.856-0.813) / 0.856(ρc-0.813)

0.282ρc - 0.268 = ρc0.037

0.245ρc = 0.268

ρc = 1.0938 g / cm^3