Thermodynamic Quantities Governing Melting

Although a collection of regularly structured, flexible chains will crystallize, they never do so completely. Depending on the molecular constitution, the chemical nature of the chain and the crystallization conditions the level of crystallinity attained can range from 90% to just a few percentage. In order for the crystallization of polymers from the melt to be carried out at finite rates, it must be 

The kinetic restraints that are placed on the crystallization of polymers make it difficult, if not impossible to directly determine their equilibrium melting temperatures. The directly observed melting temperatures are primarily a reflection of the structure and morphology of the actual crystalline systems. The primary factors involved are the crystallite thickness, the interfacial free energy, and the influence, if any, of the noncrystalline region. There are, however, indirect methods by which to estimate the value of T. One of these is a theoretical method. The others are based on extrapolative procedures. To properly use the T values that are tabulated, and to understand their limitations, the basic assumption involved and the problems in execution need to be recognized. 

Both of the extrapolative methods are based on the Gibbs-Thomson equation for the melting of crystallites of finite size [3]. For a lamellar crystallite, whose length is very much greater than its thickness, this equation can be expressed as  

FIGURE 11.1. Melting temperature, in degrees Celsius, as a function of reciprocal crystallite thickness in Angstroms for poly(tetrafluoroethylene) [5]. 

There are also other matters of concern that need to be taken into account when using this method. It is very rare to develop a uniform crystallite thickness distribution. In particular, the distribution becomes very broad after high-temperature crystallization. The question then arises as to what portion of the distribution curve corresponds to the observed melting temperature. Usually some average crystallite thickness is measured. The use of this method with polymer systems where a large proportion of the crystallinity develops during the quenching process, after isothermal crystallization, would introduce major uncertainties if the crystallite thickness (/) is measured at room temperature. 

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Mandelkem L and Alamo RG, "Thermodynamic Quantities Governing Melting", in Mark, JE (Ed), "Physical Properties of Polymers Handbook", Chapter 11, AIP Press, Woodbury, NY, 1996. 

PVT data for polymers are important both from the academic and practical points of view. On the scientific side, PVT data are frequently needed for model considerations on polymer solutions and melts. On the industrial side, these data are needed for process design. An equally important thermodynamic quantity is the surface tension of polymer melts, due to their relevance in wetting, adsorption, and adhesion. It may strongly govern such surface processes as film formation or coating. Here we report on PVT data and surface tensions of different random copolymers. We also relate thermodynamic quantities describing bulk properties to surface tension of polymer melts. 

The ordered structures of some polymers are governed by the influence of specific diluents. This involves a specific type of polymorphism, the more general aspects of which will be discussed in the chapter concerning thermodynamic quantities. Syndiotactic poly(styrene) is a polymer that is rich in compound formation with solvent mediated polymorphic behavior.( 126-130) The polymer can crystallize in four major crystalline modifications that involve two different chain conformations. In the a and p modifications the chains adopt an all trans planar zigzag conformation. These two modifications are formed by crystallization from the melt and, under special conditions, from solution. In contrast the y and 5 modifications are characterized by a helical conformation. The 5 polymorph can only be prepared in the presence of solvent. Its exact crystal structure depends on the nature of the solvent. Compound formation between the 5 form of the polymer and the solvent has been demonstrated. Complete elimination of the solvent results in the pure, helical y form. 

It is a matter of interest to assess how of a homopolymer depends on the chemical nature and structure of its chain repeating unit. The melting temperature is uniquely described by the ratio of the heat of fusion to entropy of fusion, per repeating unit. Therefore, attention should be focused on how these two independent quantities depend on structure. The enthalpies of fusion per chain repeating unit are experimentally accessible for many polymers. From these data, and T, it is possible to develop an understanding of the molecular and structural basis of the thermodynamic quantities that govern fusion. 

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