Expansion of monomer units in poly(ethylene terephthalate) molecules under conditions of thermal and zero-point atomic vibrations

The temperature dependence of the expansion ?_C of trans conformers of the carbon skeleton of macromolecules in crystallized and amorphous poly(ethylene terephthalate) (PET) due to zero-point and thermal atomic vibrations is investigated by IR spectroscopy. It is found that the thermal expansion coefficient β_C jumpwise increases at the characteristic temperatures T _t and T _b. This increase is associated with the crossover from the quantum to classical statistics of torsional and bending vibration modes. The quantum and classical contributions to the expansion ?_C are determined for each mode. The quantum and classical contributions of the torsional vibrational mode in the amorphous polymer are approximately 1.5 times larger than those in the crystallized polymer. This effect is caused by an increase in the anharmonicity of torsional vibrations in the amorphous polymer.     

Electron-level dynamics in the presence of impurities and the Ruijsenaars-Schneider model

The dynamic equations for the energy level of a finite system with impurities are shown to be equivalent to the rational Ruijsenaars-Schneider system. The action, which is simultaneously the generating function of the Bäcklund canonical transformation for this system, is calculated. Various variants of statistical averaging of the energy-level distribution are discussed.     

Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum

The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ ₀ and , where is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M ^−1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 57–60 (10 July 1996)     

Phase transitions in molecular crystals of the paraffin series: Heneicosane and docosane

Comparative analysis of phase transition in normal paraffins, heneicosane (C₂₁H₄₄) and docosane (C₂₂H₄₆), was performed using differential scanning calorimetry. Elimination of methodical inaccuracies allowed obtaining proper values of the thermodynamic parameters of the phase transitions and revealing their nature. Quantitative analysis of the heat capacity steps was made based on the theory of blurred first-order phase transitions and Landau’s theory for second-order phase transitions.

     

Evolution of the structure of near-surface ultrahigh molecular weight polyethylene nanolayers during orientational drawing

A comparative investigation of the surface structure of ultrahigh molecular weight polyethylene film filaments obtained with different draw ratios from xerogels prepared from 1.5 wt % polymer solutions in decaline and mineral oil has been performed using a SUPRA-55V scanning electron microscope and a nanoluminograph for recording thermoluminescence of ultrathin near-surface layers of solids. It has been found that, with an increase in the draw ratio, the luminescence intensity decreases, and the peaks responsible for the segmental mobility are shifted toward higher temperatures. It has been assumed that this is associated with the improvement of the structure of near-surface layers of the polymer (with a decrease in the number of microcavities and segments of molecules with a high degree of coiling). It has also been revealed that the peaks observed in glow curves of the oriented gel samples from polymer solutions in decaline are shifted more significantly than those of the gel samples from polymer solutions in mineral oil, and the extremely oriented films are characterized by a large discretization of kinetic units of motion.     

Size effect of nanostructured formations on scattering of optical phonons in poly(ethylene terephthalate)

The temperature dependence of the half-width of the infrared (IR) absorption band at a frequency of 971.5 cm^?1 in the spectra of poly(ethylene terephthalate) (PET) is investigated for crystallized and amorphous PET samples in which the lengths of trans sequences are approximately equal to 4–7 and 2–3 nm, respectively. The observed increase in the half-width with increasing temperature is explained by inelastic scattering of phonons of stretching vibrations of the macromolecular skeleton by other phonons. The half-width of the band at 971.5 cm^?1 in the IR spectra of the amorphous polymer is approximately 1.5 times larger than that in the spectra of the crystallized polymer. This is associated with the violation of the wave-vector selection rules due to a small length of the trans sequences in the amorphous sample.     

Specific features of the melting of poly(ethylene terephthalate) after its thermal and mechanical treatment

Specific features of the melting of PET samples with different molecular masses after their thermal and mechanical treatment (orientational drawing) are studied by the DSC method. Orientational drawing of the samples leads to the development of a supermolecular structure, which depends on the molecular mass and thermal prehistory of the initial samples.     

On a two-dimensional Schrödinger equation with a magnetic field with an additional quadratic integral of motion

The problem of commuting quadratic quantum operators with a magnetic field has been considered. It has been shown that any such pair can be reduced to the canonical form, which makes it possible to construct an almost complete classification of the solutions of equations that are necessary and sufficient for a pair of operators to commute with each other. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables; this change is similar to that in the theory of integrable tops. As an example, this procedure has been considered for the two-dimensional Schrödinger equation with the magnetic field; this equation has an additional quantum integral of motion.     

Phase transitions in molecular crystals of dicarboxylic acids

A comparative analysis of phase transitions in molecular crystals of saturated dicarboxylic acids with {COOH(CH₂) _n COOH} chains of different lengths has been performed by differential scanning calorimetry, which revealed a number of new effects related with specific features of the phase transitions. A quantitative analysis of temperature dependence of the heat capacity has been carried out in the context of the theory of smeared (Λ-shaped) first-order phase transitions.     

Solutions of two-dimensional Schrödinger-type equations in a magnetic field

We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation.