Page 37 - Engineering Plastics Handbook

Chemistry of Polymerization 11

The specific reaction rate is related to the Arrhenius activation energy
and temperature by [10]
 − E 
k = Aexp  
 RT 

where k = specific reaction rate
A = preexponential factor
−E = Arrhenius activation energy, kJ/mol
R = universal gas constant, 8.314 J/(mol⋅ K)
T = temperature, K

(Arrhenius activation energy and gas constant units differ by a factor
of 1000.)
The equation for k is expressed in a variety of ways, but they all have
the same parameters. Arrhenius is credited with defining this rela-
tionship (in 1899) and proposing the specific reaction rate model which
shows the reaction rate k is a function of E and T. Rate constants are
plotted at several temperatures. The ln k (natural log of k) [y axis] is plot-
ted at several temperatures as 1/T [x axis] to obtain the slope.
The degree of crystallinity (DC) is determined from a polymer’s heat
of fusion

 ∆H 
DC =  f  100
 ∆H µ 

where ∆H = heat of fusion of polymer, Kcal/mol
f
∆H = heat of fusion of perfectly crystalline polymer, Kcal/mol
µ
The ∆H is determined by differential scanning calorimetry (DSC), and
f
∆H is determined by differential thermal analysis (DTA) and from heat
µ
of fusion tables such as values obtained by Flory’s method.
The rate of crystallization is a function of temperature, free energy,
and activation energy. The rate of nucleation or crystal growth is asso-
ciated with chain folding (lamella growth), which is associated with the
three conditions of temperature, free energy, and activation energy.
Turnbull and Fischer equated the rate of nucleation or crystal growth
to the following parameters [10]:
 −∆ G   −∆ E 
I = I exp   kT   exp   kT  
0