pubs.acs.org/Macromolecules Published on Web 12/10/2009 r 2009 American Chemical Society Macromolecules 2010, 43, 29–32 29 DOI: 10.1021/ma902289k Influence of Fragility on Polymer Cold Crystallization Alejandro Sanz, Aurora Nogales, and Tiberio A. Ezquerra* Instituto de Estructura de la Materia, CSIC. Serrano 121, Madrid 28006, Spain Received October 16, 2009 Revised Manuscript Received November 18, 2009 The first-order phase transition by which a supercooled amorphous polymer material transforms into a semicrystalline one continues to be a challenging central problem of poly- mer physics affecting other fields including material properties and protein crystallization. Although substantial progress has been made in understanding polymer crystallization over the past four decades, several aspects of this process remain open. In particular, the influence of chain cooperativity, dynamic fragility, and correlated motions on polymer crystallization remain un- clear. Here we show the existence of a correlation between nucleation kinetics and dynamic fragility when the crystallization process takes place in the proximity of the glass transition temperature. In general, upon cooling liquids either crystallize or vitrify. Below the equilibrium melting temperature, T m , but above the glass transition temperature, T g , a liquid is in a supercooled state. When dealing with crystallizable materials, the supercooled liquid becomes unstable under these conditions due to its higher free energy as compared with that of the crystal. Consequently, there exists a probability that the supercooled liquid tends to reduce its free energy undergoing a first-order phase transition by which molecules self-assemble forming crystals. This transition is known as crystallization. 1-6 Supercooled crystallizable polymers can develop a characteristic folded chain crystalline lamellar morphology at the nanometer level by thermal treatment within the temperature range defined between T g and T m . The lamellar morphology consists of stacks of laminar crystals and amorphous regions intercalated between them. 6-8 Although extended chain crystals are thermodynamically more stable, a kinetic factor induces a polymer chain to fold several times building up thin crystal lamellae. During the isothermal crystallization of a poly- mer the relative amount of crystalline phase, referred to as crystallinity, evolves in a sigmoidal fashion. 6-11 As an example, Figure 1 shows the evolution with time of the crystallinity dur- ing isothermal treatment for three characteristic aromatic poly- esters. 10-13 In general, the crystallization rate depends strongly on temperature. To emphasize this, Figure 2a shows the induc- tion time of crystallization (t ind ), defined as the time at which crystallinity first becomes detectable, for some polymers as a function of the reciprocal temperature normalized by their corresponding glass transition temperatures. In general, upon cooling below T m crystallization rate first increases, then reaches a maximum, and finally decreases as T g is approached. This effect has been illustrated in Figure 2a by the dashed line. Customarily, one speaks about melt crystallization for the temperature range below T m but above the maximum in crystallization rate and about cold crystallization for the temperature range below the maximum and close to T g . In both regimes, after an initial induction time a primary crystallization process takes place where morphological units, typically spherulites, grow until they com- pletely fill in the material. 6-10 Subsequently, a secondary crystal- lization regime is achieved where the crystallization rate is strongly reduced. According to the thermodynamics, crystal- lization would be possible as soon as the energy difference, ΔG bulk , between the free energy of the crystal, G cryst , and that of the melt, G melt , is negative. 9 This process should start as soon as the system is below T m . Supercooling arises due to the fact that any crystal must start by a much smaller ordered entity with a certain specific surface area. In this case, the free enthalpy of crystallization ΔG (Gibbs free energy) becomes ΔG = ΔG bulk þ G s , where G s is the surface energy. 9 The surface term is, in general, always positive, leading to a free enthalpy barrier to crystal- lization. Therefore, for temperatures below T m , where ΔG bulk is negative, ΔG exhibits a maximum which corresponds to the critical size nucleus. 9 According to Boltzmann’s law, the prob- ability of the presence of a nucleus of given size at constant volume and temperature will be proportional to exp(-ΔG/kT). In classical nucleation ΔG corresponds to the difference between a crystal and a quiescent melt. 9 Experiments and theory indicate that in some polymer melts a coupling between density and chain conformation may induce the appearance of a spinodal texture previous to the nucleation step. 14 In this case ΔG would corre- spond to the difference between a crystal and a preordered melt. In this case one speaks about spinodal-assisted nucleation. 14 In both cases, the free enthalpy barrier to crystallization is overcome by thermal random local fluctuations of order in the melt. 3,9,14,15 In this situation, 9 the rate of nucleation, I*, can be described by I  µ exp½-ðΔG  þ ΔG η Þ=kT  ð1Þ where ΔG* corresponds to the free enthalpy for crystallization of a nucleus of critical size and ΔG η stands for the term which governs the short distance diffusion of the crystallizing element across the phase boundary. 9,15 In general, the ΔG* term reaches its higher values close to T m and decreases with temperature upon approaching T g . On the contrary, the term ΔG η adopts its higher values close to T g and decreases rapidly with increasing tempera- ture. 9 Considering the relation of the ΔG η term with diffusion, it was proposed it to follow a Vogel-Fulcher-Tammann behavior of the type 9 ΔG η =kT ¼ a þ½b=ðT -T 0 Þ ð2Þ where T 0 < T g is referred to as Vogel temperature and depends on the material. The combination of the two opposite effects in eq 1 makes the rate of nucleation to exhibit a maximum at tempera- tures in between T g and T m . While close to T m crystallization is thermodynamically driven, in the proximity of T g is kinetically controlled. Although polymer melt crystallization has been intensively studied in the past 50 years, cold crystallization did not receive similar attention. For polymer crystallization close to T g , i.e., kinetically driven crystallization (Figure 1a), one can, in a first approach, neglect the ΔG* term in eq 1 because its value is expected to be much smaller than that of ΔG η . Polymer crystal- lization experiments in this regime indicate a close relation between segmental relaxation and crystallization. 16-19 The influ- ence of the term ΔG η in eq 1 has been investigated applying to eq 2 either the concept of energy barriers or Williams-Landel-Ferry (WLF) expressions. 19 Considering that cold crystallization phe- nomena in polymers are essentially governed by short distance diffusion, then one may expect fragility to be relevant. Fragility is *To whom correspondence should be addressed.