Average degree of folding of macromolecules of flexible-chain, fibre-forming, oriented polymers in the crystalline phase

Abstract

678.01:548The problem of fabricating high-strength and high-modulus fibres from flexible-chain crystalline polymers was investigated. These polymers include polyethylene, polypropylene, and polyacrylonitrile, used to fabricate high-strength fibres with gel technology.Many mechanical and physical properties of fibres fabricated from crystallizable polymers, for example, the modulus of elasticity, strength, thermal stability, and others, are greatly determined by the degree of folding of the macromolecules in the crystalline phase --the less folding there is, the better these indexes are. We can intuitively predict that stretching of macromolecules during crystallization should suppress folding and it should disappear with a high enough degree of stretching of the macromolecules. However, experiments show that even with a high degree of stretching of the macromolecules, folding cannot be totally suppressed. In order to explain the causes of the appearance of folds in even strongly oriented polymers, let us consider the change in the free energy of an oriented melt of a polymer during its crystallization.Let all of the polymer molecules be in a force field, that is, let each macromolecule be stretched the same with respect to the direction and magnitude of forces f applied to its ends. We will only consider crystals whose formation is most thermodynamically advantageous, i.e., crystals with the axes of the molecules directed along the direction of stretching.Using the data in [I, 2], we can show that the change in the free energy of the system in formation of one such crystal will be determined with the equationfor AFIc = 2Ao~ef -2Ao(o~f -o) I t o -AolZ3d-/~(l -T I T~) -k/~b I t o I I T s = I I T o + k In(shb / b) / (Aolz~r'l) b = fl / (kT),where F, F are the free energy of a system without and with a crystal; I is the length of the static fold of the molecule; A 0 is the area of the cross section of a segment with the plane perpendicular to its axis; t is the total number of segments in the cross section of the crystal (tA o is the area of the cross section of the crystal); AFlk is the average change in the free energy of the system when t increases by 1; t o is the average number of segments in the cross section of the crystal belonging to one molecule; t 0-1 is the average number of folds belonging to one molecule in the crystal (t0A 0 is the average area of the end face of the cross section of the crystal per molecule in the crystal); AH is the specific heat of fusion of the crystal; T O is its equilibrium melting point in the absence of forces that stretch the macromolecules; T is the crystallization temperature; ~ is the number of segments over the thickness of the crystal (~l is the thickness of the crystal); k is the Boltzmann constant;Oef is the end face energy of a crystal from a folded chain on conversion to the unit of surface area; o is the free surface energy at the interface of crystalline and amorphous phases, also on conversion to the unit of surface area; in a first approximation, can be set equal ...