MW Avg. Calculations Flashcards
number avg. MW
M sub n
dependent on the abundance of various chain lengths in mixture
the # of chains w/ a specific mass
independent of molecular size
how is number avg. MW measured?
osmometry, gel permeation (count molecules)
Mn = (sum of NiMi / Ni)
weight/mass avg.
weighted average of molar mass
dependent on size (mass) of a polymer chain in a mixture
larger molecules have greater contribution (higher % of sample)
how is wight/mass avg. measured?
light-scattering, gel permeation
weight fraction of molecules with molar mass Mi divided by total weight
Mw = ((sum of Ni(Mi)^2) / sum of NiMi)
polydispersity index (PDI)
PDI = Mw / Mn
Mw based on size
Mn based on #
condensation rxns
PDI ~ 2
more heterogeneous mixture variety of chain lengths present; polydisperse
if PDI = 1
then Mw = Mn
monodisperse homogeneous mixture (chains all same length)
never happens synthetically, but does happen in nature
viscosity avg. molar mass (Mv)
dependent on solvent
Mv = (((sum of NiMi^(1+a)) / sum of NiMi))^(1/a)
if a = 1 Mv = Mw
if a = 0 Mv = Mn
what is “a” in Mv
constant that varies with polymer, solvent, and Temp
in general between .6 - .8
empirically derived using known polymers
affects the shape/size of molecule
Mark-Hovwink-Sakurada equation
finds intrinsic viscosity
[n] = kM^a
k is a constant
a & k evaluated by
measure viscosities
molecular weight –> absolute value MW
light scattering or osmotic pressure
over a series of polymers of a wide range of MWs
good/bad “a”
good is ~ .8 where polymer “coils”
very good is 1 where polymer chain is expanded in a rod interacting fully w/ solvent
bad is less than or equal to ~.8 where polymer is a sphere
