Theory and observations of polymer crystal thickening

Abstract

The thickening of polymer crystals during isothermal annealing is usually observed to be an irreversible process. Phenomenological laws that govern such processes take the form of simple proportionalities-flux being proportional to force. For polymer crystals, a thermodynamic force capable of driving the thickening phenomenon arises from the unequal free energies of the fold and lateral surfaces. By analogy with other irreversible phenomena, the rate of crystal thickening is taken to be proportional to the derivative of the surface free energy with respect to crystal thickness. After certain assumptions, integration yields an equation in which three parameters characterize the system: an initial thickness 1 0 , an equilibrium thickness I *, and a relaxation time T which is a function of the "undercooling". The theory provides a basis for considering the effects of parameters such as time, temperature, thermal history, pressure, and liquids on the thickening rate. In particular, the theory adequately describes the time and temperature dependence of crystal thickening in random copolymers of tetrafluoroethylene and hexafluoropropylene which exhibit thickening behavior completely analogous to that of homopolymers. During thickening, the unit cell dimensions of these quenched-crystallized copolymers decrease in a manner that is consistent with the concept of complete comonomer inclusion upon crystallization.

Thickening process of polyethylene single crystals at an early stage of annealing

“…The log t law well explains the thickening process at low temperatures but not that at high temperatures. Apparently the theory based on irreversible thermodynamics seems to cover the whole process over all the temperature range [12,13]. Leveling-off of long period on high temperature annealing (stage II) can be explained by this theory.…”

“…Annealing process is essentially irreversible. From this point N 753 of view, the process was theoretically treated later in terms of the irreversible thermodynamics of nonequilibrium state [12,13]. However, some aspects of this thickening process, for example, a sudden increase in lamellar thickness at an extremely early stage of annealing, are not thoroughly studied either experimentally or theoretically.…”

Crystallization of random copolymers

“…Comparison of eq (6) with eq (2b) shows that they are identical in form except that RTm has replaced IlHd in eq (2b) -a manifestation of the different effects considered (entropy versus enthalpy). Although Flory did not consider the effect of crystal size on the melting temperature, such an effect is obtainable from his theory [see eq (14) of ref. [1]].…”

“…For the tetrafluoroethylene-hexafluoropropylene random copolymers, annealing studies [14] have shown that the rate of annealing is determined by the under· cooling (T~" (X) -Tanneal); i.e., the crystal thickness of copolymers with different concentrations will thicken approximately at the same rate at equal undercoolings. The rate of annealing decreases exponentially as (T~" (X) -Tannea l) inc reases.…”

Polarity of the transformation processes in thermal measuring systems

“…Near T ~ leq increases exponentially against a baseline expressed by the l0 value, and the period z may be considered as T ~ R Ctransf ~ A I (7) where Al -(l,q(T)-lo) or (/~q(T) -IBL(T)) if the baseline has a slope different from zero. Figure 4 gives the values (E, K) determined for HDPE [17,18], LDPE with CF3 [19] and CH3 [20] as side-groups, and PET [21]. It results that the polarity of the crystallization process given by E, n > 0 remains the same as for crystallization from the melt.…”