Chapter 2 Polymer Crystallization – Literature review

1 Chapter 229 Chapter 2 Polymer Crystallization Literature IntroductionWhile it is not possible to cover the subject of Polymer Crystallization in a reviewof this size, it is important in light of author s research to review the fundamental featuresthat are essential to the study of Polymer Crystallization . The topic itself is central to thepresent research work, which deals in large part with the Crystallization behavior ofsemicrystalline polyimides. This section thus attempts to cover the important topics inpolymer Crystallization , the understanding of which is directly or indirectly connected tothe present research work.

2 It is also important to look at the fundamental Lauritzen-Hoffman Polymer Crystallization theory, which was derived originally for flexiblepolymers like polyethylene. The topics covered in this review encompass severalconcepts that make the essential foundation on which a significant part of the subsequentresearch investigation Lauritzen-Hoffman theory and its conclusions serve more to establish thegeneral framework for explaining several important observations regarding thecrystallization behavior of flexible polymers.

3 While the theory is not readily applicableto more rigid chain polymers like PEEK and aromatic polyimides, it has been used manytimes without sufficient justification for explaining the Crystallization behavior of suchrigid chain systems1. It can only be said that in future, this theory may serve as a goodstarting point for better explaining the Crystallization behavior of rigid chain systems Thermodynamics of Crystallization and meltingFrom thermodynamic considerations alone, a crystal is in a lower free energy state thanthe liquid when the temperature is below the melting point (Te ) for a large crystal of avery high molecular weight Polymer .

4 Figure shows schematically the changes in theGibbs free energy of liquid and a crystal with temperature. The necessary (but notsufficient) criterion for any spontaneous phase transformation (for a constant temperatureand constant pressure process) is a negative value of G. Hence the process of crystalformation is spontaneous below the equilibrium melting point(Tm ) while the reverseprocess, crystal melting to form liquid is spontaneous above Tm . At Tm , a condit ionof equilibrium exists between the crystal and liquid as both phases have the same value ofG and G= the case of constant temperature process such as fusion at Tm , Gf = 0 and G = H - T S = 0 at T = Tm { }Thus:crlcrlffmSSHHSHT = = { }Thus both enthalpic and entropic effects will determine the equilibrium melting point forany Polymer crystal .

5 While a higher value of Hf leads to a higher Tm , the entropiceffects cannot be ignored and are often dominant in deciding the value of Tm . Table the values of Tm , Hf and Sf for a series of polymers and illustrates the effect of While Te represents the melting point of an infinitely long crystal of an infinite molecular weightpolymer, Tm represents the melting point of an infinitely long crystal of finite molecular weight. In thecase M , Tm Te.

6 Chapter 231 Table of Tm, Hf and Sf for various ( C) Hf (J/mol) Sf (J/( )) , (1,4-cis-isoprene)284, (decamethylene sebacatePoly(decamethylene azetate)806950,20041, (decamethylenesebacamide)Poly(decamethyl eneAzelamide)21621434,70036, General behavior of thermodynamic variables at the equilibriummelting temperature Tm (a) gibbs free energy (b) entropy Tm (a)(b) Chapter 232varying Hf and Sf. In this regard, it is especially important to visualize the importanceof the term Sl , the entropy of the liquid state.)

7 As shown in the table, while the values of Hf are lesser for the polyamides, the melting points are higher due to lower Sf. Thislower value of Sf is in part due to lower value of entropy (Sl) for the amide in the liquidstate. The value of Sl is lower due to presence of hydrogen bonding and increased chainstiffness. Similar effects of lower Sl and hence lower Sf could also be important forthe class of high melting semicrystalline polyimides, the topic of this proposal.

8 Althoughcomprehensive calculations of these fundamental thermodynamic parameters forsemicrystalline polyimides is still lacking in Literature , it is widely known (as discussed inChapter 1) that strong intermolecular forces due to CTC formation exist in inherent stiffness of the chain also contributes to a lower value of Sl .Gibbs free energy change for a particular phase is expressed asdG = V dP S dT{ }where V and S are the volume and entropy of the phase respectively.

9 Taking the partialderivatives of G with respect to P & T in the above equation, we obtain:( G/ T)p = -S&( G/ P)T = V{ }Figure (b) shows the idealized response of these variables as a function of temperatureand at the transition temperature Tm . These first derivatives of G show a step changeat the transition temperature Tm and the transition is called a first-order the above discussion addresses purely thermodynamic considerations, the kineticissues do not favor formation of an infinitely large crystal in polymers, which arecharacterized, by the formation of finite sized crystals.

10 The exact nature and morphologyof these crystals however, has been one of the most heavily debated topics in Crystallization in polymers: structure, models & relationshipsThe Crystallization of polymers can be broadly classified under three groups:(A) Crystallization during polymerization (B) Crystallization induced by orientation and(C) Crystallization under quiescent condition. While this discussion will only brieflyCHAPTER 233address type (A) and (B), the last category (C), will be covered in greater detail as it ismore pertinent to the present discussion.