The use of "thermal-windowing" methods to decouple molecular motions in polymeric materials was in the nineties a very popular method to characterize polymers, as a result of the introduction of the automated TSC/RMA spectrometer from Solomat Instruments on the thermal analysis market [282]. The decoupling of the relaxation modes responsible for internal motion leads to a better understanding of their coupling characteristics which often relate to the state of the material itself.
Originally, thermal stimulated current depolarization techniques were used to measure charge detrapping in low-molecular-weight organic and inorganic compounds. Ever since 1967 they have been applied to the study of structural transitions in polymers.
The credit for the initial development must be given to Professor C. Lacabanne and her co-workers at the University of Toulouse, France. She pioneered the use of the technique of " thermal-windowing polarization" as early as 1974, and has applied it to the study of a wide variety of macromolecular materials.
Several techniques exist to analyze the molecular response of materials to physical or chemical inputs, in order to determine their specific performance. Differential Scanning Calorimetry (DSC), and Differential Thermal Analysis (DTA) are among the most popular in laboratories and on production sites. Other techniques include Thermal Mechanical Analyzers (TMA), Dynamic Mechanical Analyzers (DMA), stress relaxation or creep analyzers, thermal expansion coefficient devices, and dielectric analyzers (DEA). The method of thermo-stimulated current (TSC) consists in putting the specimen rapidly at high temperature (above the transition temperature at which the relaxation phenomena is expected), orient the dipoles at that temperature and freeze-in the orientation thus produced by quenching at low temperature (Fig. 0-1).
Fig. 0-1The voltage field applied is then removed and the temperature is ramped linearly back up to reveal the polarization induced at high temperature. TSC is therefore a thermally stimulated recovery experiment. An electrometer is connected to the sample to record the short-circuit current while heating . A current is created when the material depolarizes. This thermally stimulated current reveals the molecular mobility of the material's structure. The rate of depolarization is related to the relaxation times of the internal motions providing a new opportunity to study the physical and morphological structure of materials.
The depolarization current, J, flowing through the external circuit is measured by a very sensitive electrometer (capable of measuring currents 10 million times smaller than those measured by a tunnelling microscope), and allows determination of the "dipole conductivity".
The current peaks recorded this way (Figs. 0-2a and 0-2b) are found to correlate well with the transition temperatures measured by mechanical relaxation (DMA), by DSC or by conventional (a.c.) dielectric spectroscopy (DETA). A TSC output looks like a tan δ versus temperature plot, showing maxima at the transitions occurring inside the material. In fact, TSC provides very similar results to those obtained from other analytical instruments operating at the same low frequency equivalent (10-4 Hz), with the addition of an accrued sensitivity, and a separating power unseen in other technologies.
Fig. 0-2a
Fig. 0-2b
The concept of "thermal-windowing" gives the TSC another dimension. Windowing consists of polarizing only a fragment of the full spectrum of relaxation and depolarizing it partially to isolate or "window" a single relaxation process. There are two types of possible windowing techniques: the first method, which can be called "partial isothermal recovery" or "isothermal windowing", consists of the following: first, polarize the sample at temperature Tp for a time tp adjusted to allow orientation only of a certain fragment of the dipoles. At the same temperature Tp, cut off the polarizing voltage and stay at Tp for a time td. This allows the depolarization of a fragment of the oriented dipoles. Finally, quench the sample to To << Tp. Reheat at constant rate and measure the current of depolarization. Δt = (tp - td) is the "time-window" and can vary between 1 min and about 1 hour.
The most practical and commonly used thermal deconvolution method is the "thermal-windowing" experiment (Fig. 0-3), because it essentially gives identical results and it is the fastest.
Fig. 0-3
In this option, a constant voltage is applied at Tp for a time tp, commonly of the order of 2 minutes. The temperature is then lowered to Td at which the voltage is removed and the specimen allowed to recover partially for a time td, usually equal to tp. ΔT = (Tp - Td) is the temperature window and can vary between 1 oC and about 10 oC. The specimen is then quenched by 50 to 100 oC to a sub-temperature To where the amount of polarization induced in the material is frozen. A linear heating-up is then performed, and the variation of current due to thermally induced depolarization or other current discharges is observed as a function of time (i.e. temperature). Since the current J(t) is the derivative of polarization, the ratio P(t) divided by J(t) is a quantity with the dimension of time and represents, according to Bucci [56], the elementary relaxation time τi typical of the relaxing system. Figure 0-4 shows the result of thermal-windowing on the TSC output.
Fig. 0-4
When tp, td, and (Tp - Td) are conveniently chosen, the depolarization current is supposed to represent the relaxation of a single Debye relaxation mode isolated from the spectrum of relaxation modes. By varying the value of the temperature of polarization Tp, and repeating the above thermal-windowing process, one can isolate the elementary modes one by one (Fig. 0-5).
Fig. 0-5
The computer in the TSC/RMA spectrometer integrates the current vs temperature peak for each temperature, and calculates the value of the relaxation time at each temperature. The analysis, according to the Bucci's equation, of each resolved Debye peak obtained at various polarization temperature gives a temperature dependent retardation time τi(T) which often follows an Arrhenius dependence (Fig. 0-6).
Fig. 0-6
The relaxation time is the inverse of the frequency of jump between two activated states. According to Eyring, the intercept of the Arrhenius equation is proportional to the Entropy of activation for the activated process involved, and the slope is proportional to the Enthalpy of activation. If a structure is "loose" the contrary of "ordered" or "compact", i.e. when molecular mobility is less hindered by the interactive intra-intermolecular surrounding, the Entropy of activation will be "larger". Conversely, any parameter which acts to "organize" the structure and create a tighter environment for the bonds will cause a decrease of the Entropy of activation. So, the activated Entropy calculated from the intercept of Figure 0-6 gives an indication of "the degree of disorder" (DOD) of the structure.
The technique of TSC/RMA is used to determine the degree of cooperativeness between the relaxation modes responsible for internal motions at the main transitions occurring in non-conductive materials, revealing the state of the structure and the morphology.
Fig. 0-7
A relaxation map (Fig. 0-7) is the collection of relaxation lines obtained for each deconvoluted Debye peak, and analyzed according to Bucci's equation. Relaxation maps can be looked at as "fingerprints" of the material, being representative of its chemical structure, morphology, and non-equilibrium structure (Fig. 0-8).
Fig. 0-8
Relaxation Map Analysis (RMA) determines the elementary Enthalpies of activation, and the pre-exponential factors (related to the Entropy of activation) for all the relaxation modes obtained by varying the temperature of polarization Tp.
In summary, the relaxation observed during the recovery stage of TSC reveals the kinetics, and the powerful method of "thermal-windowing" deconvolutes the individual relaxation modes. This allows the study of their coupling characteristics, reflecting the structure and the physical state of the material. Constitutive equations can be used thereafter to reconstruct the material dielectric behavior (Fig. 0-9) by calculation of the fundamental physical parameters from the spectrum of relaxation (dielectric permittivity, etc) .
Fig. 0-9
The various Arrhenius lines obtained by thermal-windowing at different polarization temperature Tp often converge to a common point, the compensation point (Fig. 0-10).
Fig. 0-10
The essential focus of interest in the work of thermal stimulated process analysis seems to lie around this phenomenon of compensation, the determination of its coordinates, the interpretation of its origin, its practical use to characterize the degree of coupling in the amorphous phase of polymeric matter, and its relationship with the state of (non) equilibrium.
In a certain sense, one could say that a new type of thermal analysis is born with the understanding of "thermal-windowing", since compensation phenomena apparently reflect the coupling between relaxation motions occurring cooperatively, and also because this new thermal analysis technique can describe WLF type of behavior susceptible to comparison with results observed in rheological experiments (upper temperature curve, T > Tg, in Fig. 0-8).
In subsequent blogs, we concentrate on many aspects of the depolarization phenomena. We compare the TSC results with those obtained by other techniques. We cover theoretical topics, such as the origin of the polarization, or the possible interpretations for the effect of voltage field. We use computer modelling to curvefit the depolarization curves, and give the equations which describe the effect of voltage, temperature of polarization or depolarization, etc.
Most importantly, We explore in depth the technique of thermal-windowing and use it to deconvolute the cooperative response of polymers at their main transitions, mainly the glass transition. We provide a new method to characterize the glass transition, and determine the respective contribution to the Entropy of the electronic and atomic vibrations.
The presence of multi-compensations in a material might be linked to the existence of multi-phases, and we dedicate a full blog to analyze blends, block copolymers and the other applications of RMA to which the concept of DOD (degree of disorder) applies its full force. But the presence of multi-compensations also occurs in cases where the material is known to be monophasic. The comparison of the multiple compensation RMA spectra for brittle and ductile polymers, or between annealed and quenched liquid crystal polymers is intriguing and will be explored in depth, because, we believe, it expresses the heart of "interactive coupling between conformers".
