Tll Transition Research Articles

A Dual-Phase Approach to Reveal the Presence and the Impact of the TLL Transition in Polymers Melts. Part I: Predicting the Existence of Boyer’s TLL Transition from the Vogel–Fulcher Equation

R.F. Boyer recognized the manifestations of a T > Tg transition-relaxation as early as 1963 and named it TLL, the liquid-liquid transition. He suggested that it was due to the melting of “local order”, a controversial issue conflicting with the dominant theories at the time, led by P. Flory, which asserted a structure-less liquid state for melts. At the same time as this controversy unrolled, de Gennes published his reptation model of polymer physics which, after some modifications and ramifications, quickly became the new paradigm to describe the dynamic properties of polymer flow. The new model of reptation has no theoretical arguments to account for a T > Tg transition occurring in the melt; hence, the current consensus about the existence of TLL is still what it was already in 1979, that it is probably an artifact only existing in the imagination of Boyer. In part I of this paper on the TLL transition we mathematically derive the existence and the characteristics of TLL from a dual-phase description of the free volume using a modification of the Vogel-Fulcher equation (VF), a well-known formulation of the temperature dependence of the viscosity of polymer melts. This new expression of the VF formula, that we call the TVF equation, permits to determine that TLL is in an iso-free volume and iso-enthalpic state when M, the molecular weight, varies. The data analyzed by the TVF equation are the dynamic rheological results for a series of monodispersed, un-entangled polystyrene samples taken from the work of Majesté. The new analysis also permits to put in evidence the existence of a new transition, which we call Mmc, approximately located at Mmc ≈ Mc/10, where Mc is the molecular weight for entanglement. A Dual-Phase interpretation of Mmc is proposed.

A Dual-Phase Approach to Reveal the Presence and Impact of the TLL Transition in Polymer Melts. Part II. The Theoretical and Practical Relevance of the TLL Existence and Characteristics on the Understanding of the Melt Thermal Analysis and Rheological Properties of Polymers: Duality and Cross-Duality of the Interactions

In Part I of these 2 parts article, we derived mathematically the existence of a unique state for polymeric melts, occurring at a specific temperature above Tg, which we recognized to be the liquid–liquid transition, TLL, observed and described by Boyer and others. TLL is the temperature at which the melt is in an iso-free-volume and iso-enthalpic state independent of the molecular weight. It is a fundamental property of the material. The purpose of part II is to examine and explain the following: 1) the elusive character of TLL (at the origin of the controversy about the existence of TLL in the past), 2) the increase of free volume at TLL, and 3) the endothermal change of heat capacity on heating across TLL. Finally, our objective is to provide an explanation of TLL and emphasize its importance as an example of a self-dissipative dynamic process that converts, at TLL, into a classical thermally activated process. In this article, the experimental evidence found in the literature for TLL is critically examined to point out the often biased reviews offered by the antagonistic authors of a controversy, here the pros and cons TLL. We propose a Dual-Phase origin of the interactions in polymers to explain the weak and elusive manifestations of TLL and show, by DSC, that the TLL manifestations are made much more visible and prominent when the samples’ state has been brought out of equilibrium. We analyze, in detail, the thermally activated depolarization of samples which have been submitted to a polarization stage by a voltage field. The experimental technique of thermal stimulated depolarization (TSD), and its sister derivative the thermal windowing deconvolution (TWD), are unique and powerful analytical tools that can experimentally characterize “interactive coupling”, the factor that we have assumed is quantitatively responsible for the behavior of polymers and in particular of TLL. The existence and the characteristics of TLL were understood and predicted in Part I from rheological results by the use of the Thermo–Vogel–Fulcher equation whose thermo-kinetic terms, ΔH, ΔS, and T∞, could be interpreted by the interactive coupling of the local free volume and the rotational isomeric conformational state of dual-conformers belonging to the macromolecules, themselves embedded in a collective dissipative system of interactions. The statistics controlling the interactive coupling parameters was described by the Dual-Phase and Cross-Dual-Phase models. In Part II, the same models are used to explain the interactive coupling manifestations specific to the TSD and TWD results. We show that certain characteristics of the TSD and TWD results are directly related to specific parameters of the Dual-Phase model. It is the case for the transitions visible by TSD, such as Tg,ρ related to space charges and local free volume (F-conformers), and TLL marking the end of the specific impact of the Dual-Phase statistics on the properties. It is also the case when interactive coupling is analyzed by TWD: the compensation of the enthalpy and entropy of activation of the relaxations taking place at various polarization temperatures only occurs below TLL, permitting its specific determination. We conclude pointing out the perhaps crucial importance of TLL in establishing the distinct role of thermal energy in structuring or modulating the dynamics of the interactions. The Dual-Phase view of the interactions in polymers suggests that the local density difference between the b-grains and the F-conformers is “time-averaged” by the constant wiping (above Tg) of an “elastic dissipative wave” having a frequency, ωo, i.e., a function of temperature and molecular weight, and thus is different from the Brownian dissipation, i.e., the thermal fluctuation characteristic of the Boltzmann’s mean field (the classical kT/h term). The elastic dissipative wave kinetically loses its collective modulation role and becomes the thermal wave at TLL.

The structural organization of liquid low-molecular-weight epoxy oligomers

The possibility of the existence and the behavior of molecular aggregates in low-molecular-weight epoxy resins were studied. The globular morphology of all liquid resins was determined using transmission electron microscopy. The lamellar morphology of crystallized ED24 was established by additionally using atomic-force microscopy. The thermal behavior of oligomeric epoxides was studied over the temperature range −100–100°C. The Tg and Tll transitions were recorded for liquid resins by differential scanning calorimetry. For solid ED24, the Tm peak of resin melting situated between Tg and Tll was observed. The existence of the Tll transition was substantiated by positron annihilation measurements. The morphological picture was thermally unstable and became completely degenerate at Tll. The morphology and thermophysical parameters of the resins changed substantially after their vibrational treatment. The morphology of oligomers was shown to be “hereditarily” (genetically) related to that of the corresponding network polymers.

Effect of miscibility and forced compatibility on damping properties of CIIR/PAc blend

AbstractIn this study, a kind of novel damping materials was prepared based on the blend of chlorinated butyl rubber (CIIR) and polyacrylate (PAc) synthesized by different molar ratio of butyl methacrylate and ethyl acrylate. Research results from experiments and analyses by employing DMA, TEM, and FTIR show that whether at a cocured system or noncocured system, it can be achieved to shift a loss peak of CIIR towards a higher temperature region and to keep the damping value from markedlly decreasing, which broadens the effective damping function area of CIIR to the vicinity of ambient temperature. In the former system, the thermodynamical miscibility of CIIR and PAc, to some extent, is predominated by the molecular design of PAc, while in the latter system, covulcanized networks play a more significant role in improving compatibility and abating the peak split, though the suppression effect of thermal stress on the transition of CIIR Tll transition still can not be neglected. Furthermore, transition state derived from the cocuring CIIR and PAc cannot make the phase separation completely take place, and consequently results in the deformation of phase morphology of the cocured CIIR/PAc blend. It is the influence of thermodynamics miscibility and forced compatibility in different size that makes the suppression effect of foreign PAc on CIIR Tll transition be controllable. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3127–3133, 2006

Regression analysis studies of polymer transitions II. TII from specific heat and other data for polyisobutylene

AbstractLinear regression analysis studies with residuals of heat capacity vs. temperature (Cp vs. T) data above the glass transition temperature (Tg) for polyisobutylene (PIB) of molecular weights M¯v = 1,350,000 and M = 4900 show that the data points can be represented by three straight lines in each case. The lower intersection temperature represents the intermolecular Tll transition (relaxation); the upper one an intramolecular Tlp process. Both processes are confirmed by ultrasonic velocity data in vulcanized butyl rubber, by zero shear melt viscosity data in PIB (M = 4900); and by isothermal specific volume vs. pressure data in PIB (M¯v = 36,000). Tll is confirmed by thermal diffusivity, differential scanning calorimetry (DSC), 13C nuclear magnetic resonance (NMR) spectroscopy and the T* temperature of Lobanov and Frenkel based on Arrhenius‐type plots log frequency vs. 1/Tg. A comparison of dynamic mechanical loss data, both old and new, reveal that Tll follows a Vogel‐WLF type relation; log f vs. 1/(T0 −1/To). PIB samples with number average molecular weights between 7100 to 860,000 have been measured on three types of support systems: glass braid (0.3 Hz), filter paper (11 Hz), brass shim stock (14–16 Hz), and give similar values of Tu. A considerable amount of literature data long neglected from the viewpoint of its bearing on Tll is reviewed. Tll has been observed in the same way as Tg by both relaxational and quasi‐static methods. Some instructive cross comparisons between these two types of methods emerge. With so many diverse methods yielding evidence for Tll in PIB, it cannot be dismissed as an artifact. A molecular origin for Tll is plausible in terms of the Frenkel‐Baranov phase dualism mechanism. A complete relaxation map (log f vs. 1/T) has been assembled with frequencies from 10−2 to 1010 Hz and temperatures from 150 to 500 K. It shows Tβ, Tg, Tll and methyl group rotation, all based on data in the literature. The molecular weight dependence to Tg and Tll and the low resiliency of butyl rubber as it relates to Tll are discussed in the appendices.

Influence of tacticity on Tβ, Tg, and TLL in poly(methyl methacrylate)s by the method of thermally stimulated current (TSC)

AbstractThe thermally stimulated‐current method (TSC) has been employed to determine the temperatures and intensities of Tβ, Tg, and T > Tg for pure isotactic, pure syndiotactic, and five atactic specimens with syndiotactic triad content from 49.5 to 75%; Tg was found to increase linearly with syndiotactic triad content as Tg (°C) = 48.0 + 0.856 (% syn), with R2 = 0.970 standard error 5.6°C; Tg for the syndiotactic specimen is 136.6°C measured, 133.6°C calculated. Several atactic specimens exhibit a second glass temperature 15 to 35 K above the regression line ascribed to some pure syndio content, and/or some isotactic–syndiotactic stereocomplexes. All specimens exhibited the liquid–liquid or TLL transition (relaxation) which increases linearly with 100‐% isotactic triad content. Isotactic PMMA shows a T′LL relaxation 50 K above TLL. The Tg and TLL values obtained correlate extremely well with values from differential scanning calorimetry (DSC) determined in a separate study, as well as with most literature data. Intensities of Tg and TLL by TSC are greatest for isotactic, next for syndiotactic, with a broad, low minimum for atactic materials. The intensity of a β relaxation increases slowly from isotactic to syndiotactic. The TLL found by TSC compares well with literature values for isotactic PMMA obtained by several methods, and TLL in the atactic region compares well with literature values for atactic material. The ratio TLL/Tg ranges from 1.09 to 1.20 with no dependence on tacticity. Tg follows simple Arrhenius behavior with enthalpies of activation about one‐half of the values normally calculated from dielectric and mechanical loss. The frequency dependences of TLL and T′LL follow a Vogel–WLF relationship with temperature. The origin of TLL is discussed in terms of the Frenkel hypothesis of segment–segment interaction. Evidence for TLL and TLL from a variety of methods indicates that these two temperatures are not artifacts of the TSC method.

Some evidence against the existence of the liquid‐liquid transition. III. The evaluation of the Tll event by differential scanning calorimetry

AbstractThe liquid‐liquid transition Tll has been examined by using differential scanning calorimetry as the tool of measurement. The results presented show that for the case of polystyrene, the Tll event appears to be an artifact caused by the presence of volatile components. Purified samples of polystyrene, polydienes, and poly(1‐butene) do not show the Tll transition.

Effect of dispersity on the Tll (>Tg) transition in polystyrene

AbstractThe presence of a high temperature (>Tg) relaxation in amorphous polystyrene has been investigated further. In the previous work,1 the techniques of differential thermal analysis (DTA) and torsional braid analysis (TBA) were employed to study polystyrene as a function of “monodisperse” molecular weight. The occurrence of the Tll transition appeared to be associated with the attainment of a critical viscosity level with also corresponded with a free volume level. An entanglement network developed at a critical value of molecular weight, Mc, giving a break in the Tll‐versus‐M plots. The present work deals with the influence of dispersity on the Tll transition, below and above Mc. A series of binary blends of “monodisperse” anionically polymerized polystyrenes with systematic changes in M̄n and heterogeneity index (M̄w/M̄n) was tested by TBA. The results show that when both components have molecular weights below Mc, single and average values of Tg and Tll are observed which are linearly related to M̄n−1, as predicted by free volume arguments. Although a single Tg is observed when one component has a molecular weight above and the other has a molecular weight below Mc, the components appear to undergo the Tll relaxation independently. The results indicate that both the glass transition and the Tll transition are basically governed by the same type of molecular motion but at different length ranges.

The Tll (>Tg) transition of atactic polystyrene

AbstractTorsional braid analysis (TBA) (∼0.3 Hz) and differential thermal analysis (DTA) data are presented for the temperature for the region 0–200°C for two series of atactic polystyrenes with narrow molecular weight distributions: (a) anionic series, M̄n = 600–2×106, M̄w/M̄n ≃ 1.1; (b) fractionated thermal series, M̄n = 2,000–1.1×105, M̄w/M̄n < 1.25. Preliminary results on bimodal blends are also reported. Heating and cooling cycles were employed with TBA; only the heating mode was used with DTA. In addition to a dynamic mechanical loss peak at Tg, a higher temperature loss peak was also found. Designated the Tll or liquid–liquid transition (relaxation), its temperature is 1.1 to 1.2 Tg (°K) for polymers with molecular weight below the critical molecular weight (Mc) for chain entanglements. Above Mc ≃ 35,000, it rises steeply, being ≃200°C for M̄n = 110,000. The common dependence of Tg and Tll on M̄n−1 below Mc suggests a common molecular origin. The two facts, (a) that Tll > Tg and (b) that Tll reflects chain entanglements, further suggest that Tll involves a longer chain segment length and possibly the entire molecule. Comparison of Tll versus log M plots with T versus log M isoviscous state plots based on zero‐shear melt viscosity data from the literature implies that Tll measured by the TBA technique corresponds to an isoviscous state of 104–105 poises. The employment of narrow molecular weight polymers is presumably responsible for both the linear variation of the Tll transition with M̄n−1 (which suggests a free volume basis for the relaxation) and the form of the variation of the Tll transition with log M (which suggests an isoviscous basis for the relaxation). The sharpness of the Tll loss peak by TBA decreases with increasing molecular weight and dispersity. The DTA endothermic event corresponding to Tll is clearly related to the occurrence of flow since the fused films which result from heating granules to 200°C and cooling to R.T. do not reveal a Tll on reheating. If a fused film is crushed, a Tll event is observed on heating. For bimodal blends with M̄n < Mc for both components, the Tll transition was averaged; with one component less than and one greater than Mc, the Tll transitions of the components appeared to occur independently at temperatures corresponding to those of the isolated components. In accordance with Ueberreiter and Orthmann, Tg appears to separate a glassy state from a fixed liquid state, whereas Tll separates the fixed liquid from a true liquid state. Possible molecular interpretations for the Tll process are discussed. Systematic bodies of data from the literature which indicate the presence of the Tll process in other polymers are summarized.