ies involving isothermal (8) and no

ies involving isothermal (8) and nonisothermal (15) TP crystallization in sesame oil. This cooling rate is in line with the
slow cooling rate achieved by industrial crystallizers.
Microscopy studies. Crystal morphology of the PS/sesame
oil solution was obtained under the same isothermal conditions
utilized in the DSC studies using a polarized microscope with
camera (model BX60F/PMC35; Olympus Optical Co., Ltd.,
Tokyo, Japan). The experimental setup has been described previously (8). After induction of nucleation, pictures of the crystals were taken as a function of time.
Calculation of kinetic parameters.The isothermal DSC data
were utilized to evaluate the kinetics of TP crystallization in
the PS/sesame oil solutions using the Avrami equation (18):
−ln(1 −F) = zt
n
[2]
where Fis the fraction of crystal transformed at timet, nis the
index of the crystallization reaction or Avrami exponent, and z
is the rate constant of crystallization, which depends on the
magnitude of n,the nucleation rate, and the linear growth rate
of the spherulite (19). The value of Fwas calculated by integration of the isothermal DSC crystallization curves as described by Henderson (20) utilizing Equation 3 and according
to Figure 1:
F= ∆Ht
/∆Htot
[3]
where ∆Ht is the area under the DSC crystallization curve from
t= T
i
to t= t, and ∆Htot
is the total area under the crystallization
curve. The values of ∆Ht
and ∆Htot
were calculated with the
DSC software library. In fact, Fis a reduced crystallinity since
it associates an instant crystallinity to the total one achieved
under the experimental conditions. Then, Fvaries from 0 to 1.
The value of nwas calculated from the slope of the linear
regression of the plot of ln[−ln(1 −F)] vs. ln(t) using values of
fractional crystallization between 0.25 and 0.75 (18). The n
value describes the crystal growth mechanism. Thus, a crystallization process with a n= 4 follows a polyhedral crystal
growth mechanism, a value of n= 3 represents a plate-like
crystal growth mechanism, and a n= 2 indicates a linear crystal growth (19).
When nucleation occurs from the melt the rate of nucleation,
J, depends on the activation free energy to develop a stable nucleus, ∆Gc,
and the activation free energy for molecular diffusion, ∆Gd.
The Fisher-Turnbull equation (Eq. 4) describes this
situation and was utilized, according to Ng (21) and Herrera et
al.(22), to evaluate the magnitude of ∆Gc
J= (NkT/h)exp(−∆Gc
/kT)exp (−∆Gd
/kT) [4]
where Jis the rate of nucleation that is inversely proportional
to T
i
, Nis the number of molecules per mole, kis the Boltzman
constant, Tis absolute temperature, and his Planck’s constant.
In a spherical nucleus, ∆Gc
is associated with the effective supercooling, ∆T, and the surface free energy at the crystal/melt
interface, σ, through the following equation:
∆Gc
= (16/3)πσ
3
(TM
o
)
2
/(∆H)
2
(∆T)
2
[5]
where (16/3)πresults from the spherical shape attributed to the
nucleus and ∆H is the heat of fusion. The effective supercooling, (T
M
o
−T), is the difference between the equilibrium melting temperature, T
M
o
, and the isothermal temperature of crystallization, T. The magnitude of T
M
o
was established following