End-surface free energy

Where Ug is the side surface free energy, Ug is the end surface free energy, I is the thickness of the crystal, a and b are the width and thickness of the stem (as marked in Fig. 14), and AF is the bulk free energy of crystallization per imit volume. The term 26Zag is due to the formation of the side surfaces, (u — l)(2a6(re) is due to the end surfaces, and the terms in AF are due to the reduction in free energy because of the lower energy of the bulk crystal compared to the bulk melt. In all cases it is assumed that the known macroscopic energies can be simply used. Four rate constants are defined ... 

Fig. 5 Chain deposition on the side surface of a polymer crystal, a and ae are side-surface and end- (fold-) surface free energies, and b is the width of the chain (after [16])...

Tt is often desirable to increase the surface free energy of a synthetic polymer to alleviate such processing or end-use problems as static buildup, poor wettability, dyability, printability, or adherability, and poor stain-release or soil redeposition properties in textile applications. One method for accomplishing this is to graft copolymerize hydrophilic monomers onto the polymer molecules in the surface using ionizing radia-... 

AHu is the heat associated with the melting of one mole of monomer units, T0 is the melting temperature of the pure isotactic polymer 6m is the value of 6 when T = Tm and Tm is the melting temperature of partially isotactic polymer D is a function of the surface free energy per unit surface associated with the end surfaces of the crystallite. 

Here AFu is the standard free energy change per repeat unit on melting, and ae is the surface free energy change per chain at the ends of the crystallite. It can be shown that the surface free energy associated with lateral surfaces may be ignored in the present case. 

It should be noted that with increasing molecular weight there is a transition from extended-chain to folded-chain crystals. This transition must dramatically affect the surface free energy of the crystals. As pointed out by Buckley Kovacs (1976) and Balta Calleja et al. (1969), when the crystals have extended chains there is a high proportion of hydrogen bond formation between the -OH groups at adjacent chain ends. 

For high molecular weight (M — °o) binary blends, the Helfand and Tagami theory predicts that in binary blends (i) the interfacial thickness, A/ is inversely proportional to the interfacial tension coefficient,v , the product, A/ v being independent of the thermodynamic interaction parameter, X, (ii) the surface free energy is proportional to (iii) the chain-ends of both polymers concentrate at the interface (iv) any low molecular... 

---