Crystallization of Polymers Under 1D Confinement
233
data set permitted us to build up the bases of a physical framework capable to explain
the increase in crystallization time at molecular level.
Working at constant sample surface, the scaling t cry ~h
−1 implies that the crystal
growth rate (~t cry
−1 ) is directly proportional to the sample volume. This condition is
in agreement with the trend observed in nanodroplets of PEO, where the nucleation
time linearly scales with the volume of the drop [3, 17]. This implies that for films
of PET down to 20 nm, the slowing down in the crystallization kinetics is merely
related to nucleation issues. To understand how this reasoning implies the scaling
t cry ~h
−1 , let us consider a polymer melt with homogenous nuclei density. Reduction
of the thickness, achievable by considering thinner and thinner slabs of the abovementioned melt, yields lower and lower probabilities to find active nuclei within a
given portion of the slab of constant surface. The scaling is finally obtained assuming
that crystallization is limited by nucleation; that is, the timescale of the process is
proportional to the probability of finding a nucleus in a slab of given surface and
thickness h.
The continuous and unperturbed reduction of β, in line with the prediction of the
finite size corrections proposed by Schultz to the Avrami model [57], further supports
the reasoning. In the case of a finite volume, in fact, the presence of interfaces does
not permit a full development of the crystals as in bulk and contribution of trunked
crystals and lost nuclei (belonging to region outside the volume considered) results
in a lower effective transformation rate and smaller values of β.
As observed for other systems, crystallization does not take place in the thinnest
films. For films thinner than ~20–25 nm, no substantial reduction in dielectric strength
imputable to crystallization was observed. In such films, only the logarithmic drop in
ε is present. Based on these results, we may conclude that either the crystallization
rate decreased by more than three orders of magnitude or that crystallization was
definitely inhibited. Because of the importance of this condition, further experiments
were performed at higher temperatures, where the crystallization kinetics is sped up
by the larger diffusion coefficients, and in repeated temperature scans up to T m + 20 K.
No crystallization was observed (Fig. 7).
Considering the increase in δ upon reduction of the thickness, it was proposed
that adsorption could be responsible for the tremendous increase (eventually to an
infinite value) in t cry of films thinner than 20 nm. Adsorbed chains would have a
lower (or zero) crystallization rate and thus act as a retarding agent on the formation
of ordered structures. To test this hypothesis, it was necessary to verify that adsorption takes place before crystallization. In line with evidence from other polymers,
thermal annealing in the liquid state promotes the adsorption of PET chains onto Al.
Vanroy et al. monitored the irreversible adsorption kinetics by isolating irreversibly
adsorbed layer from 40-nm-thick films held at 373 K for different annealing times.
The thickness of such layer, h ads , is an operational parameter to determine the amount
of chains irreversibly adsorbed onto a unit surface [52, 58]. At 40 nm, the onset of
crystallization is observed after 10 h of annealing at this temperature, while after
already 10 min the adsorbed amount reached a constant value. Further tests at 363 K,
where the kinetics of adsorption is much slower, permitted to better study the kinetics
of adsorption and confirmed the same saturating value. These results clearly show
233
data set permitted us to build up the bases of a physical framework capable to explain
the increase in crystallization time at molecular level.
Working at constant sample surface, the scaling t cry ~h
−1 implies that the crystal
growth rate (~t cry
−1 ) is directly proportional to the sample volume. This condition is
in agreement with the trend observed in nanodroplets of PEO, where the nucleation
time linearly scales with the volume of the drop [3, 17]. This implies that for films
of PET down to 20 nm, the slowing down in the crystallization kinetics is merely
related to nucleation issues. To understand how this reasoning implies the scaling
t cry ~h
−1 , let us consider a polymer melt with homogenous nuclei density. Reduction
of the thickness, achievable by considering thinner and thinner slabs of the abovementioned melt, yields lower and lower probabilities to find active nuclei within a
given portion of the slab of constant surface. The scaling is finally obtained assuming
that crystallization is limited by nucleation; that is, the timescale of the process is
proportional to the probability of finding a nucleus in a slab of given surface and
thickness h.
The continuous and unperturbed reduction of β, in line with the prediction of the
finite size corrections proposed by Schultz to the Avrami model [57], further supports
the reasoning. In the case of a finite volume, in fact, the presence of interfaces does
not permit a full development of the crystals as in bulk and contribution of trunked
crystals and lost nuclei (belonging to region outside the volume considered) results
in a lower effective transformation rate and smaller values of β.
As observed for other systems, crystallization does not take place in the thinnest
films. For films thinner than ~20–25 nm, no substantial reduction in dielectric strength
imputable to crystallization was observed. In such films, only the logarithmic drop in
ε is present. Based on these results, we may conclude that either the crystallization
rate decreased by more than three orders of magnitude or that crystallization was
definitely inhibited. Because of the importance of this condition, further experiments
were performed at higher temperatures, where the crystallization kinetics is sped up
by the larger diffusion coefficients, and in repeated temperature scans up to T m + 20 K.
No crystallization was observed (Fig. 7).
Considering the increase in δ upon reduction of the thickness, it was proposed
that adsorption could be responsible for the tremendous increase (eventually to an
infinite value) in t cry of films thinner than 20 nm. Adsorbed chains would have a
lower (or zero) crystallization rate and thus act as a retarding agent on the formation
of ordered structures. To test this hypothesis, it was necessary to verify that adsorption takes place before crystallization. In line with evidence from other polymers,
thermal annealing in the liquid state promotes the adsorption of PET chains onto Al.
Vanroy et al. monitored the irreversible adsorption kinetics by isolating irreversibly
adsorbed layer from 40-nm-thick films held at 373 K for different annealing times.
The thickness of such layer, h ads , is an operational parameter to determine the amount
of chains irreversibly adsorbed onto a unit surface [52, 58]. At 40 nm, the onset of
crystallization is observed after 10 h of annealing at this temperature, while after
already 10 min the adsorbed amount reached a constant value. Further tests at 363 K,
where the kinetics of adsorption is much slower, permitted to better study the kinetics
of adsorption and confirmed the same saturating value. These results clearly show