Page 38 - Engineering Plastics Handbook

12 Introduction

where I = rate of nucleation or crystal growth
0
I = temperature-independent constant
−∆G = free-energy change for the formation of a nucleus of
critical size
k = thermodynamic function (Boltzmann’s constant)
T = thermodynamic absolute temperature, K
−∆E = viscosity factor

Knowledge of the variation and complexity of crystalline shapes opens
a universe of new polymers and properties. H. D. Keith and F. J. Padden,
Jr., observed that crystalline characteristics are a function of crystal
growth rate, and crystalline transformation occurs when a single crys-
tal grows to predictable size. To calculate a predictable crystal size from
melt for homopolymers [10],

δ= D
G r
where δ= single crystal size when transformation occurs
D = diffusion coefficient in crystalline medium (coefficient of
self-diffusion)
G = crystalline growth rate
r
2
Spherulite and lamella characteristics vary from polymer to polymer.
Many semicrystalline polymers have an optimum crystallization tem-
perature. Above the optimum crystallization temperature, the nucle-
ation rate slows, limiting crystallization; below the optimum
crystallization temperature, viscosity increases, which also limits crys-
tallization. The rate of crystallization is affected by several methods,
such as adding a nucleating agent to increase crystallization. Quick-
quenching polymers such as PET produce amorphous PET, as noted
earlier. To calculate the crystallization rate for a given polymer as a func-
tion of temperature [10],

  2  
 4 E  (  DT m) 
p 
K = B −     ( T − T ) 2 

c
m
 KT c   T c    

  
where K = crystallization rate constant
B = constant for a given polymer
2
See H. D. Keith and F. J. Padden, Jr., “A Phenomenological Theory of Spherulite
Crystallization,” Bell Telephone Labs Inc., Murray Hill, N.J., USA, published by The
American Institute of Physics in 1963; and other reports on the crystallization phenom-
enon from the 1950s to 2004.