Equations that allow determining the melting point, change in volume, and other thermodynamic parameters of melting of polymers at high pressure are proposed based on the statistical-thermodynamic theory of melting of polymers. The good agreement of the predictions of the theory and the experimental data for polyethylene is demonstrated.Determining the thermodynamic parameters of melting of polymers at high pressure is now a very pressing problem. Actually, the pressure is one of the fundamental parameters that determine the possibility of processing polymers to make articles from polymers in the solid state, including fibre-forming and composite materials in which one of the components is a fibre [1, 2], etc. The lack of data on the effect of the pressure on the melting point could, for example, lead to creation of inoperative equipment. There are many theoretical approaches to solving this problem, but the problem is so complex that there is still no definitive theory that will predict the thermodynamics of melting of polymers at high pressures.The results of predictions of the statistical-thermodynamic theory of melting of polymers [3,4] with the effect of the hydrostatic pressure p on the melting point T m , change in the enthalpy ∆H m , entropy ∆S f , and volume ∆V m in melting are examined here. A lattice model of the bulk polymer phase is used in this theory, where the total number of lattice points is equal to N = xn x + n 0 , where n x is the number of polymer molecules, each occupying x lattice points; n 0 is the number of vacant points (holes). Each lattice point is considered the center of a unit cell of volume C, the volume of the polymer melt is equal to V l = CN = C(xn x + n 0 ), and the volume of the polymer in the crystalline state is equal to V cr = Cxn x . V l can change with a change in the temperature and pressure only as a result of a change in the number of holes, and the volume of the crystalline phase will not change with a change in the temperature and pressure. To account for the effect of the conformations of the macromolecules, the rotational isomeric approximation is used, where each bond in the macromolecule can be either in one trans state with energy ε or in z -2 gauche states with high energy ε g, where z is the valence of the backbone atoms.The internal energy of the polymer melt is equal to U l = E l + Φ l , where E l = (x -e)n x [ƒε g + (1 -ƒ)ε l ] is the intramolecular (conformational) energy of the melt; ƒ is the proportion of flexible bonds (bonds in the gauche state); Φ l = Z c αn 0 S x /2 = E h n 0 S x is the intermolecular energy of the melt. In these ratios, z c is the lattice coordination number, -α is the segmentsegment bond energy;is the surface proportion of occupied points; E h = z c α/2 is the hole energy. The isobaric-isothermal statistical sum of the melt is calculated by statistical methods using the HugginsGuggenheim mean-field theory, and quantities ƒ and n 0 are determined from the condition of minimization of the free energy of the melt.The internal energy ...
The melting point and glass transition temperature of polymers is estimated with the lattice model of the bulk polymer phase. The good agreement of the predictions of the theory and the experimental findings on melting of polyethylene is demonstrated. The dependence between the melting point and glass transition temperature of polymers is obtained with the statistical thermodynamic theory and is in good agreement with the experimental data.Polymeric materials, including fibre-forming polymers, are partially crystalline, where the amorphous phase can represent ten percent or more. The question of not only their melting point T m but also the glass transition temperature T g inevitably arises. In addition to the purely scientific aspect, these temperatures are also of interest as extremely important performance characteristics of polymeric materials that determine their heat and cold resistance, crystallization conditions, compatibility of polymer composites, etc. However, there are still no theories that explain the glass transition and melting of polymers from a unified position.We estimated the glass transition temperature and melting point of polymers using the lattice model of the bulk polymer phase.Melting. We will use the lattice model of the bulk polymer phase in the statistical thermodynamic theory one of us developed [1,2], where the total number of lattice points is , 0 n xn N x + =where n x is the number of polymer molecules, each occupying x lattice points; n 0 is the number of vacant points (holes). Each lattice point is considered as the center of a unit cell of volume C, so that the total volume of the polymer melt is equal to ( ).l 0 n xn C Vx + = It is hypothesized that C is constant, and the volume of the system can change with a change in temperature T and pressure p only as a result of a change in the number of holes n 0 . To account for the conformations of the macromolecules, we use the rotational isomeric approximation, in which each bond in the macromolecule can be in one trans state with energy ε t (rigid bond) or in z -2 gauche states with high energy ε g (flexible bond), and z is the value of the backbone atoms in the chain.According to the theory in [1,2], in the crystalline state the macromolecules are absolutely ordered (proportion of flexible bonds ƒ = 0) and are stacked parallel to each other with no vacancies in the lattice (number of holes n 0 = 0), so that the volume of the system in the crystalline state is equal to . cr x Cxn V = It is hypothesized that the crystalline state is unique and can be realized uniquely so that the number of configurations in the crystalline state is equal to one and the configurational entropy is equal to zero.
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