Thermodynamics of Crystallization

The free energy change of a polymer from liquid to crystal is ∆F=∆H-T∆S At the melting point Tm the crystals and the liquid polymer are at equilibrium. The change in free energy, therefore, ∆F = 0. That means that at the melting point: Tm =∆H/∆s If the heat of fusion is large, then the melting temperature of the polymer crystals will be high (due to high intermolecular attraction) or if the entropy of fusion is small. Mendel kern [42] noted that there are three different interfacial free energies that are characteristic of crystallites. One, se, is for the equilibrium extended chain crystallite, a second one sec represents the mature, but non-equilibrium crystallite, and the third one is σ_en is the interfacial free energy involved in forming a nucleus. These quantities cannot be identified with one another. Because only portions of the polymeric chains participate in the formations of crystallites, the section or sections of the chains of x length that participate in crystallite formation can be designated as ze0 and the sections of the chains that remain in disorder and amorphous, as x ze. The dependence of the melting temperature of such a system upon chain length is [42]:

where, ∆Hu is the enthalpy of fusion per repeat unit and ze is the equilibrium crystalline length. The effective interfacial free energy associated with the basal plane of an equilibrium crystalline length ze designated as se is [42]:

where T⁰_m is the equilibrium melting temperature for an infinite molecular weight chain and T_me is the corresponding melting temperature for a fraction that contains x repeat units. From the stand point of thermodynamics, T_me is a first-order transition temperature [15]. The melting points, when measured very carefully, can in many cases be sharp. On the other hand, melting points of ordinary crystals may melt over a range (Table 2.3). Table 1.2 shows some first-order transition temperatures, commonly designated as Tm. For systems that are polydisperse, with a most probable chain-length distribution, the melting temperature molecular weight relation is expressed as [42]:

Where Xn is the number average degree of polymerization. In this equation, the quantity 2⁄ Xn represents the mole fraction of non-crystallizing units. This equation is based on the stipulation for conditions for phase equilibrium. It is specific to and valid only for polymers that have a most probable molecular weight distribution. This relationship for the melting temperature of each polydisperse system has to be treated individually [42]. By applying the Clapeyron equation and from measurements of applied hydrostatic pressure the value of ∆Hu can be determined. This equation, Tm = ∆H_m/∆S_m applies to very high molecular weight polymers. For polymers that are medium or low in molecular weight, the degree of polymerization (X) has to be included:

Mandelkern points out [38] that the experimental data shows that there is no correlation between the melting temperature of a polymeric crystal and the enthalpy of fusion, as is found in many small molecules. The DH values of polymers generally fall into two classes. They are ether within a few thousand calories per more or about 10,000 cal/mole. Polymers that fall into the category of elastomers have low melting temperatures and high entropies of fusion. This reflects the compacted highly flexible nature of the chains. At the other extreme are the rigid engineering plastics. These materials possess high melting points and correspondingly lower entropies of fusion .

اخر الاخبار

اخبار العتبة العباسية المقدسة

قسم التطوير يبحث آفاق التعاون المشترك مع المعهد العالي لإعداد وتأهيل القادة

إدارة العتبة العباسية المقدسة تطلع على آليات تطوير المهارات الحِرَفية بقسم صناعة الشبابيك

سماحة السيد الصافي يؤكد أهمية التدريب المستمر وتطوير قدرات الملاكات الطبية للارتقاء بالخدمات الصحية

العتبة العباسية المقدسة تقيم مجلسًا عزائيًا لإحياء ذكرى شهادة الإمام الكاظم (عليه السلام)

المزيد

الآخبار الصحية

6 فواكة تساعدك على الشعور بتحسّن عند المرض

حفاظا على صحة العين.. هذا أفضل وقت لتناول فيتامين أ

الاستخدام اليومي لسماعات الأذن.. أخطر مما تتصور !

هل توقيت نشاطك اليومي يؤثر على صحة دماغك؟.. العلماء يجيبون

المزيد

الآخبار التكنلوجية

ابتكار ألماني قد يغيّر مستقبل صناعة البلاستيك

تحديثات وأرباح عبر المشاهدات.. ما الذي تخطط له "لينكد إن"؟

"الكوكايين الوردي".. مخدر جديد يثير قلق السلطات الأميركية

دراسة: تغيّرات في أسلوب القيادة قد تكشف مبكرا عن الخرف !

المزيد

مواضيع ذات صلة

Methods for Measuring Molecular Weights of Polymers

Radius of Gyration

Solutions of Polymers

Orientation of Polymers

The Mesomorphic State, Liquid Crystal Polymers

Kinetics of Crystallization

Autoacceleration

Ceiling Temperature

Effect of Reaction Medium

Steric, Polar, and Resonance Effects in the Propagation Reaction

Propagation

Capture of Free Radicals by Monomers