Study of the glass transition in the amorphous interlamellar phase of highly crystallized poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) is a semi--crystalline polymer that can be crystallized to different degrees heating from the amorphous state. Even when primary crystallization has been completed, secondary crystallization can take place with further annealing and modify the characteristics of the amorphous interlamellar phase. In this work we study the glass transition of highly crystallized PET and in which way it is modified by secondary crystallization. Amorphous PET samples were annealed for 4 hours at temperatures between 140C and 180C. The secondary crystallization process was monitored by differential scanning calorimetry and the glass transition of the remaining interllamelar amorphous phase was studied by Thermally Stimulated Depolarization Currents measurements. Non--isothermal window polarization is employed to resolve the relaxation in modes with a well--defined relaxation time that are subsequently adjusted to several standard models. Analysis of experimental results, show that cooperativity is reduced to a great extend in the interlamellar amorphous regions. The evolution of the modes on crystallization temperature reveals that large scale movements are progressively replaced by more localized ones, with higher frequency, as crystallization takes place at higher temperatures. As a consequence, the glass transition temperature of the amorphous interlamellar phase tends to lower values for higher annealing temperatures. Evolution of calorimetric scans of the glass transition are simulated from the obtained results and show the same behaviour. The interpretation of these results in terms of current views about secondary crystallization is discussed.Comment: 30 pages, 5 tables, 12 figures; figure 5 modifie

Dielectric study of the glass transition of PET/PEN blends

An analysis of the glass transition of four materials with similar chemical structures is performed: PET, PEN and two PET/PEN blends (90/10 and 70/30 w/w). During the melt processing of the blends transesterification reactions yield block and random PET/PEN copolymers that act as compatibilizers. The blends obtained in this way have been characterized by 1H-NMR and DSC. A degree of randomness of 0.38 and 0.26 has been found for the 90/10 and 70/30 copolymers. It is shown by DSC that this copolimerization is enough to compatibilize the blends. The alpha relaxation, the dielectric manifestation of the glass transition, has been studied by thermally stimulated depolarization currents (TSDC). The relaxation has been analyzed into its elementary modes by means of a relaxation map analysis. The activation energies of the modes of the glass transition do not change significantly between the four materials: in all cases the modes with a larger contribution have around 3 eV and modes with less than 1 eV are not detected. The change in the pre-exponential factor accounts entirely for the relaxation time change from material to material, that is larger as the PEN content increases. The compensation law is fulfilled and compensation plots converge for high-frequency modes. The polarizability decreases as the PEN content increases due to the increased stiffness of the polymer backbone. An analysis of the cooperativity shows that the central modes of the distribution are the most cooperative while high-frequency modes tend to behave more as Arrhenius. The low-frequency modes are difficult to study due to the asymmetry of the distribution of relaxation times. PEN turns out to be the less cooperative material. It is demonstrated how the parameters obtained from the dielectric study are able to reproduce calorimetric data from DSC scans and are, therefore, a valid description of the glass transition.Comment: 22 pages, 13 figure

Dielectric study of the glass transition: correlation with calorimetric data

The glass transition in amorphous poly(ethylene terephthalate) is studied by thermally stimulated depolarization currents (TSDC) and differential scanning calorimetry (DSC). The ability of TSDC to decompose a distributed relaxation, as the glass transition, into its elementary components is demonstrated. Two polarization techniques, windows polarization (WP) and non-isothermal windows polarization (NIW), are employed to assess the influence of thermal history in the results. The Tool-Narayanaswami-Moynihan (TNM) model has been used to fit the TSDC spectra. The most important contributions to the relaxation comes from modes with non-linearity (x) around 0.7. Activation energies yield by this model are located around 1eV for polarization temperature (Tp) below 50C and they raise up to values higher than 8eV as Tp increases (up to 80C). There are few differences between results obtained with WP and NIW but, nonetheless, these are discussed. The obtained kinetic parameters are tested against DSC results in several conditions. Calculated DSC curves at several cooling and heating rates can reproduce qualitatively experimental DSC results. These results also demonstrate that modelization of the non-equilibrium kinetics involved in TSDC spectroscopy is a useful experimental tool for glass transition studies in polar polymers.Comment: 13 pages, 2 tables, 10 figures; minor change

Double glass transition in polyethylene naphthalate structural relaxation by MDSC, BDS and TSDC

We present the experimental study of the primary, $\alpha$, and secondary, $\beta^*$, relaxations of the glassy polymer polyethylene naphthalate (PEN), by Modulated Differential Scanning Calorimetry (MDSC), Thermally Stimulated Discharge Currents (TSDC) and Broadband Dielectric Spectroscopy (BDS). Results show how the $\alpha$ and $\beta^*$ relaxations can be considered part of a very broad and distributed relaxation. The $\beta^*$ relaxation is composed of a main contribution ($\beta_3^*$) and two additional ones ($\beta_1^*$ and $\beta_2^*$) and each elementary mode of the relaxation has its own glass transition temperature. This scenario gives rise to an extended glass transition mainly centered in $T_{g\beta^*} \sim 305$ K and $T_{g\alpha} \sim 387$ K

Efficient Computation of Location Depth Contours by Methods of Computational Geometry

The concept of location depth was introduced as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. The depth contours form a collection of nested polygons, and the center of the deepest contour is called the Tukey median. The only available implemented algorithms for the depth contours and the Tukey median are slow, which limits their usefulness. In this paper we describe an optimal algorithm which computes all bivariate depth contours in O(n 2) time and space, using topological sweep of the dual arrangement of lines. Once these contours are known, the location depth of any point can be computed in O(log 2 n) time with no additional preprocessing or in O(log n) time after O(n 2) preprocessing. We provide fast implementations of these algorithms to allow their use in everyday statistical practice