Macromolecular conformational volume and thermodynamics of crystal melting (original) (raw)
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Physical Review E, 2007
We present results from constant pressure molecular-dynamics simulations for a bead-spring model of a crystallizable polymer melt. Our model has two main features, a chemically realistic intrachain rigidity and a purely repulsive interaction between nonbonded monomers. By means of intrachain and interchain structure factors we explore polymer conformation and melt structure above and below the temperature T crys hom of homogeneous crystallization. Here, we do not only determine average spatial correlations, but also site-specific correlations which depend on the position of the monomers along the polymer backbone. In the liquid phase above T crys hom we find that this site dependence can be well-accounted for by known theoretical approximations, the Koyama distribution for the intrachain structure and the polymer reference interaction site model ͑PRISM͒ for the interchain structure. This is no longer true in the semicrystalline phase. Below T crys hom short chains fully extend upon crystallization, whereas sufficiently long chains form chain-folded lamellae which coexist with amorphous regions. The structural features of these polymer crystals lead to violations of premises of the Koyama approximation or PRISM theory so that both theoretical approaches cannot be applied simultaneously. Furthermore, we find a violation of the Hansen-Verlet freezing criterion; our polymer melt crystallizes more easily than a simple liquid. This hints at the importance of the coupling between conformation ͑backbone rigidity͒ and density ͑packing constraints͒ for polymer crystallization.
Macromolecules, 1975
The three methacrylate polymers and melts of low and high density polyethylenes investigated in the preceding paper are discussed in terms of theory. Corresponding literature data on n-paraffins and hevea rubbers are also considered. The good agreement between experimental and predicted PVT relations obtained for the high polymers is similar to that found earlier in several instances. The extensive results available a t present make possible comparisons of the characteristic scaling parameters for different systems, with a variation of the characteristic temperatures by a factor of 2. A relationship between the characteristic compressibility factor or entropy per unit mass and the temperature scaling factor ensues, which results in a correlation between the characteristic segmental energy factor and the two-thirds power of the segmental'mass. Proceeding to the pressure dependence of the thermodynamic functions, we find again good agreement between experimental and theoretical energies andentropies. The results once more illustrate the inadequacy of a van der Waals form for the configurational internal energy. The analysis of the liquid-glass transition line in the methacrylate systems yields the variation of the hole fraction
The enthalpy of fusion and degree of crystallinity of polymers as measured by DSC
European Polymer Journal, 2003
Crystalline polymers are not in thermal equilibrium and thermodynamic parameters such as enthalpy of fusion as determined by differential scanning calorimetry from the area under the melting endotherm over a wide temperature range have not been measured under equilibrium conditions. Accordingly measurements of the degree of crystallinity based on the enthalpy of fusion reflect experimental conditions, are incorrect in that they do not usually agree with those determined by other analytical procedures, such as density and WAX scattering, particularly when measured at ambient temperatures. While this has been repeatedly pointed out procedures used to determine the fractional crystallinity of polymers based on the enthalpy of fusion continue to be widely used.
Thermodynamic properties of poly(trans-1,4-butadiene) crystals. Relationship to molecular structure
Heat capacity measurements of melt crystallized poly( trans-1,4-butadiene) (PTBD) were carried out in the 50-130" region and the entropy change from 73" to the melting point, 139", was calculated. A value of the entropy change obtained using the rotational isomeric state approximation is found to underestimate the experimental entropy change. Theoretical energy calculations were carried out using empirical potential energy functions for a single PTBD chain, a unit cell and a lattice of cells. Minimization of the lattice energy with respect to two of the monoclinic cell constants for the low-temperature crystal form gave results in good agreement with X-ray diffraction data. The energy of transition from the low-temperature form was calculated and a theoretical heat capacity curve was obtained.
Macromolecules, 1990
Molecular dynamics is used to study the melting on the surface of a polyethylene-like crystal. The rate constant for melting of a crystalline molecule without and with one to four folds is determined at several different temperatures and molecular lengths. The results show a strong dependence of the transition rate on the number of folds. For a constant lamellar thickness, the transition rate decreases with increasing number of folds for temperatures near the equilibrium melting temperature, as expected from analogy with experimental melting temperatures. In contrast, the transition rate increases with increasing number of folds for temperaturesthat exceed the equilibrium melting temperature by more than 100 K. Two melting paths are suggested to explain the simulation data. One pathway involves a competition between melting and crystallization. This pathway leads to a decreasing transition rate as a function of increasing folding. The second pathway exhibits dominating melting. In this case, the rate of transition tends to increase with increasing number of folds. Diffusion coefficients of segments at different locations along the chain show that motion of the ends of a polymer chain or of the folds is faster than in the center of the stem. The overall effect of increasing temperature is to increase the diffusion coefficients.
Study on the Thermodynamics of Polymer Crystallization Based on Twin-Lattice Model
The Journal of Physical Chemistry B, 2018
Polymer crystallization is the most important part in determining the performance of polymeric materials. The twin-lattice model originally provided by Lennard-Jones and Devonshire, developed by Pople and Karazs and other researchers, is extended for describing the thermodynamics of polymer crystallization. The positional order of segments and the orientational order of bonds are considered in this model. The free energy of polymers is obtained by further introducing the conformational energy and entropy, and thus a new parameter is defined, which is the ratio of conformational energy and positional diffusion energy. We studied two kinds of processes in polymer crystallization, including the process with plastic crystal phase and without any mesophases. The choice of crystallizing process is determined by the magnitude of lattice energy and conformational energy. The solid-solid transition from crystal to plastic crystal shows a significant dependence on the conformational energy. Considering data reliability, N-paraffins are chosen as the representation of polymers to compare the predictions of the model with experimental observations. We predict the number of carbons beyond which the rotator phase disappears, which is quite agreement with the experiments. These calculations and results show this model can provide a new understanding to the crystallization of polymers.
Phenomenological study of the isotope effect on the equilibrium melting point of polymer crystal
a b s t r a c t The equilibrium melting point ðT o m Þ or the ultimate melting point of a polymer crystal is different between the hydrogeneous (H) and dueterated (D) species, as exemplified for the various cases of polyethylene, isotactic polypropylene, polyoxymethylene and so on. The present study has focused on the specific case of the blend samples of hydrogeneous and deuterated polyoxymethylenes (POM-H [e(CH 2 O) n e] and POM-D [e(CD 2 O) n e]) and the random copolymers between the CH 2 O and CD 2 O monomeric units. As the POM-H samples, the homopolymers composed of H-trioxane monomeric units and the copolymer containing a small amount of ethylene oxide (EO-POM copolymer) were used since these two samples were different in the melting point. The T o m of the blend samples was found to change continuously depending on the D/H content, although the content dependence was different between the blend samples of POM-D with POM-H homopolymer and those of POM-D with EO-POM copolymer. The T o m of the D/H random copolymers was found to change also remarkably. Such an isotopic effect on T o m has been interpreted reasonably on the basis of the thermodynamic equations derived with the statistical probabilities of the D and H component distributions taken into account. The agreement between the experimentally-evaluated values and the theoretically-estimated values is good for the T o m in both the cases of D/H blends and D/H random copolymers.