The possibly trapped excess free volume

Excess free-volume trapping incurred by quenching has been quantified for atactic polystyrenes with different molecular weights. As the initial temperature (T₀) is elevated from the glass transition (T_g), the increment in excess free-volume trapping first responds sharply, then becomes sluggish, and finally levels off. Molecular weight increase shifts the isochronal curves to a higher temperature region, which coincides with the isochronal change in glass transition temperature (T_g ^t)- As the isochronal curves are superposed to form a master curve, the mechanism of excess free-volume trapping is essentially controlled by T₀, from which the conformational structures of molecules are determined prior to quenching, rather than by the final aging temperature. In order for this superposition to occur, conceivably, the content of excess free volume trapped in the glassy state has to be fairly constant throughout all temperatures below T_g. Consequently, this study does not support the existence of an underlying equilibrium extrapolated from the rubber state.     

Time-temperature superposition and relaxational behavior in polymeric glasses

It is shown that a free-volume treatment of the relaxational behavior of a polymer can be extended into the glassy region. A modified form of the WLF equation is derived in which the temperature is replaced by T_e, a parameter related to the “frozen” free volume in the glass and defined such that Te = T at equilibrium. Measurements of the isothermal volume contraction of polystyrene and poly(methyl methacrylate) between ?20 and + 95°C are used to estimate the “frozen” free volume and to calculate the temperature dependence of log(a_T) below Tg. The calculated shift factors are compared to experimental values for the glassy state, and good agreement is obtained by selecting an arbitrary, but reasonable, equilibrium glass volume-temperature curve. The slope of this equilibrium glass curve is smaller than the experimental volume curve at some finite cooling rate. The data indicate that the glass is not an “iso-free volume” state and that the relaxation mechanisms in the glass are controlled primarily by the free volume, at least in the vicinity of Tg. A quantitative definition of the role of free volume in the glassy state requires evaluation of the quantities ? log a_T/?V)_T,P and (? log a_T/?T)_v,p; sufficient data of this type are not presently available.     

Effects of thermal and mechanical history on the viscoelastic properties of rigid poly(vinyl Chloride)

The effects of processing variables on the solid state properties of rigid PVC were studied by evaluating dynamic mechanical and tensile properties for thin film specimens of two different resins. The dynamic measurements were performed over the temperature range ?1]60 to 85°C, encompassing both the low temperature β transition and above ambient a transition (T_g). Engineering tensile strengths and energies to fracture were obtained at ambient conditions for several rates of elongation. Test specimens were prepared by solvent casting and compression molding techniques and subsequently were subjected to various thermal-mechanical histories. The results obtained were similar for both types of specimens and are described below. The various thermal histories considered include: (1) quick quenching from 225°C (samples referred to as “untreated”); (2) very slow (equilibrium) cooling after annealing at T_g; (3) quick quenching from T_g. In addition, the effects of frozen stresses were examined by systematically varying the stresses imposed on samples during the cooling processes 2 and 3. Increasing the load level imposed on specimens during equilibrium cooling resulted in enhancements of the β transition loss dispersion and tensile yield strength. Changes in loading during process 3, however, had little effect on the cooled specimens. But process 3 does alter the relaxation spectrum below T_g so that additional molecular relaxation is induced between T_β and T_α as much as 45°C below the a transition. The anomalous tan δ dispersions thus produced are accompanied by diminished tensile yield strengths and greatly increased energies to fracture. The most extreme case was encountered for the “untreated” specimens which were rapidly quenched from 225°C. The loss tangent data indicate remarkable differences in the region between T_β and T_α. When comparing the dynamic mechanical data with the fracture energy results for the same samples we note that increases in the intensity of the T < T_g anomalous dispersion correlate with increasing energies to fracture. On the other hand, the β transition intensity does not directly correlate. One molecular model which is consistent with these observations assumes that elongation induces a dilation of the polymer. Since most polymers possess Poisson ratios less than 0.5, the dilation will create extra internal volume (including free volume) in the polymer network. The increase in internal volume as elongation proceeds has the net effect of shifting the conditions of testing toward higher temperatures on a molecular relaxation scale permitting a higher level of molecular mobility at ambient conditions. As a sample continues to elongate one of two consequences is encountered: the imposed deformation cannot be accommodated by the available molecular mobility and the specimen fractures; or the deformation results in dilation to the extent that the response properties are shifted into a region of the relaxation spectrum where molecular mobility is sufficient for the specimen to accommodate the imposed deformation and yielding occurs. Yielding is expected if the effective temperature shifts as far as T_g before the sample fractures. In a case where there are additional molecular relaxation possibilities prior to the a transition, such as those in the anomalous dispersion region between T_β and T_α, sufficient dilation for yielding will be encountered before the normal T_g is reached. The anomalous T < T_g relaxation process thus tends to promote increased elongation and higher energies to fracture in PVC.     

The Slow Molecular Mobility in Semicrystalline Poly(Ethylene Oxide)

The thermally stimulated depolarization current (TSDC) technique has been used to study the slow molecular mobility in the amorphous part of the semicrystalline polymer, poly(ethylene oxide) (PEO). Experiments were carried out in the temperature range that includes the glassy state, the glass transformation region and the rubber state. The dipole moments in the polymeric main chain originated a broad and low intensity secondary relaxation in the temperature region from ?130°C up to the glass transition region; the activation energy of the motional modes of this secondary relaxation was in the range between 35 and 100 kJ mol^?1. The glass transition temperature of the PEO, provided by the TSDC technique, was T_g = ?53°C, and the fragility index was found to be m = 43. A strong relaxation above T_g was observed, whose molecular origin was discussed. The thermal behavior of the PEO was also characterized by differential scanning calorimetry.     

Nanostructured morphology of polymer films prepared by matrix assisted pulsed laser evaporation

As recently illustrated, nanostructured glassy polymer films with exceptional thermal and kinetic stability can be formed via Matrix Assisted Pulsed Laser Evaporation (MAPLE) (Guo et al. in Nat. Mater. 11:337, 2012). Relative to the standard poly(methyl methacrylate) glass formed on cooling at standard rates, glasses prepared by MAPLE can be 40 % less dense and have a 40 K higher glass transition temperature (T _g ). Furthermore, the kinetic stability in the glassy state can be enhanced by 2 orders-of-magnitude. Here, we examine the stability of the structured morphology. We show that nanostructured glasses may be formed even when the substrate is held at temperatures greater than the polymer T _g during deposition. In addition, we discuss the origin of the enhanced stability and the mechanism of nanostructured film formation within the framework of the Zhigilei model. Finally, we compare the nanostructured morphology to the surface morphology of other MAPLE-deposited films in the literature.     

Is the glass transition in some super-cooled polyphenyls preceded by molecular cluster formation?

A recently reported anomalous behaviour of the positronium annihilation rate with temperature in certain super-cooled organic liquids is explained in terms of a simple free-volume model modified in the presence of molecular cluster formation. This model apart from showing the entropic origin of the phenomenon accounts for the existence of the transition temperature “T_r” much above the glass-transition temperature T_g. It also predicts for the threshold temperature “T_r” fo clusters to commence formation a value of 310_-7.0^+8.0 K as against the experimental value of 304 K for ortho-terphenyl.     

Correlation between glass transition temperature and thermal expansion coefficients of polymers: Its interpretation and implication

A new approach pertaining to the hole and lattice theories of polymeric systems is developed to interpret the universal inverse relationship between the glass transition temperature (T_g) and the difference in thermal expansion coefficients for liquid and glassy polymers (δ α). The success of this particular theoretical consideration rests upon the familiar hypothesis of the iso-free volume state at T_g and the entropy contribution to the hole-polymer segment interaction energy. Based on the experimental data available, we have established the free volume fraction at T_g, v_g = 0.025, which is identical with the assessment of the empirical Williams-Landel-Ferry (WLF) equation for the temperature-dependence shift factor a_T. However, appreciably higher values of v_g are reported by other contemporary models. The present findings justify an alternative form of the WLF equation with the product T_g, δ α playing the role of δ α. The universality of this novel expression is demonstrated, by means of statistical analysis, to be remarkably more warrantable than its original version.     

Metal-induced effects on the glass transition kinetics of glassy Se70Te30 alloy

The calorimetric measurements have been made in glassy Se₇₀Te₃₀ and Se₇₀Te₂₈M₂ (M?=?Ag, Cd, and Zn) alloys using non-isothermal differential scanning calorimetry technique to see the effects of Ag, Cd, and Zn additives on the glass transition kinetics of binary Se₇₀Te₃₀. From the heating rate dependence of glass transition temperature, T _g, different kinetic parameters of glass transition have been evaluated. The composition dependence of glass transition temperature T _g and the related activation energy (E_t ) is also discussed.     

Crystallization of polycarbonate from the glassy state. part II. Thin films melted and quenched

The crystallization of glassy amorphous thin polycarbonate films quenched from the melt has been followed. Structures similar to those observed during the crystallization of films containing small amount of adsorbed solvent are formed. However, crystallization, at the same temperatures, is much slower and more irregular. Preannealing of the samples below T_g affects the crystallization process, increasing the nucleation rate. Annealing above T_g does not destroy all order gained by annealing below T_g.     

The effect of Bi content on the thermal stability and crystallization of Se–Te chalcogenide glass

Glass formation and devitrification of intermediate alloys in the Se–Te–Bi system were studied by differential scanning calorimetry. A comparison of various simple quantitative methods to assess the level of stability of the glassy materials in the above-mentioned system is presented. All of these methods are based on characteristic temperatures, such as the glass transition temperature, T _g, the onset temperature of crystallization, T _in, the temperature corresponding to the maximum crystallization rate, T _p, or the melting temperature, T _m. In this work, a kinetic parameter, K _r(T), is added to the stability criteria. The thermal stability of several compositions of Se–Te–Bi was evaluated experimentally and correlated with the activation energies of crystallization by this kinetic criterion and compared with those evaluated by other criteria. All the results confirm that the thermal stability decreases with increasing Bi content in this glassy system. The crystallization results are analysed and the activation energy and mechanism of crystallization characterized.     

Application of a new structural theory to polymers. ii. transition states for amorphous polymers and copolymers

A recently developed nonequilibrium thermodynamic theory of continuum rheology is combined with a generalized definition of thermomechanical transitions, to produce a single equation for interrelating the basic variables (stress o, strain rate ε, pressure p, temperature T, and structure ?) at a transition. Specialization of ? to represent uncrosslinked polymers leads to incorporation of molecular weight M as a variable. New predictions are thus made for the glass transition [T_g(M), T_g(p), T_g(ε) and others] and compared successfully with data. Particularly remarkable are the results that 1/T_g is a piecewise linear function of In M, and T is piecewise linear with p. Comparable results and confirmation with data arise when applying the theory to the liquid-liquid transition, T _ll (M). For random copolymers, application of a single mixing rule to the transition equation leads to a prediction of T_g as a function of composition and the T_gi for the homopolymers (components i). This relationship reduces, in various cases, to several familiar equations in which the parameters were simply empirical, thus providing an interpretation of those parameters and defining restrictions applicable to each case. Finally, an alternative interpretation of ? in terms of free volume allows the theory to be extended to other systems, including those with small molecules.     

Structural changes in glassy poly(ethylene terephthalate)

Structural changes in glassy poly(ethylene terephtbalate) and their effects on its crystallization, melting, and various properties were studied. Quenched, annealed below T_g, crystallized, and drawn samples were studied using calorimetry, wide-and small-angle X-ray diffraction, mechanical spectroscopy, and stress-strain analysis. All results indicate some level of order in the glassy polymer which can be increased by annealing below T_g. This order still exists at tempertures above T_g and affects the properties of the polymer.     

Glass and β transitions of atactic polystyrenes monitored by volume dilatometry

Volume recovery in the temperature range of above T_g to below T _β has been studied for two atactic polystyrene specimens (M _w = 210,000 and 300,000 g/mol). Observations clearly disclose the collapse of free volume even at temperatures well below T_β. In an excess free volume sufficient environment, as the aging temperature is lowered through T_β, the retardation of the initial volume recovery becomes progressively longer, forming a variation in the nonlinearity of the isotherms. Indeed, it is this variation that leads to the observation of the β transition in the V-T plot. The β transition is time dependent, but molecular weight independent. On the other hand, in addition to well-known molecular weight and time dependence, the glass transition has another important feature: The difference in thermal expansion coefficients above and below T_g increases slightly with aging time. Thus, time cannot alter the existence of Tg. Consequently, this study favors thermodynamic theories for the formation of T_g.     

Properties of low-temperature spectral relaxation of eosin phosphorescence in a glycerol-water mixture

The low-temperature dynamics of the Stokes shift of the instantaneous phosphorescence spectra of eosin in 94% glycerol-water solution is studied upon pulsed excitation. At temperatures T<T _tg , where T _g =183–187 K is the glass transition temperature of the solution, the blue shift of the instantaneous phosphorescence spectra is observed. In the vicinity of T _g , the spectral dynamics undergoes inversion, and the red shift of the instantaneous spectra is observed at temperatures between 188 and 210 K, which is caused by freezing out the orientation mobility of the solvent molecules in the first solvate shells of the chromophore molecule. In the temperature range from 230 to 273 K, the enhancement effect was observed at the initial parts of phosphorescence kinetic curves, which is probably explained by cooperative phenomena in the solvent.     

Thermal characterization of Se78Ge22 and Se68Ge22M10 (M=Cd,In, Pb) chalcogenide glasses

The paper reports studies on the glass transition kinetics of Se₇₈Ge₂₂ and Se₆₈Ge₂₂M₁₀ (M?=?Cd, In, Pb) chalcogenide glasses. Differential scanning calorimetry (DSC) was performed at different heating rates under non-isothermal conditions. Different kinetic parameters, such as glass transition temperature (T _g) and the activation energy of the glass transition (E _t) have been calculated to investigate the effects of Cd, In and Pb additives on the glass transition kinetics of glassy Se₇₈Ge₂₂ alloy.     

The effect of compositional variations on the glass-transition and crystallisation temperatures in Ge-Se-In glasses

The glass-transition (T_g) and crystallisation (T_x) temperatures of glassy Ge_xSe_yIn₁₂ (7≤x≤28) have been determined from differential scanning calorimetry measurements. The variations of T_g and T_x with composition have been specified. It has been found that T_g reaches a maximum at 614 K for the composition Ge_23.33 Se_64.67 In₁₂ while T_x passes through a minimum at 740 K for the same composition. The values of the cohesive energies of the studied compositions have also been estimated using the chemical bond approach method. It is found that the composition Ge_23.33Se_64.67In₁₂ possesses the maximum cohesive energy. These results are explained in terms of the structure of Ge-Se-In glasses. Received: 12 March 2001 / Accepted: 29 March 2001 / Published online: 23 May 2001     

Effect of annealing cold-drawn polystyrene and polymethylmethacrylate below Tg

Annealing of both cold-drawn atactic polystyrene and cold-drawn poly-methylmethacrylate at temperatures ranging from 50°C to their respective T_g's and for times ranging from 1 to 6 days gradually but completely eliminates the orientation arcing from the wide-angle X-ray diffraction pattern but induces only ～25% recovery of the cold-drawn deformation (as calculated from dimensional shrinkage). Analogous studies show that the birefringence of cold-drawn polystyrene is reduced by 57% during the annealing treatment. The results are evidence for segmental molecular motion below T_g and suggest that the molecular alignment responsible for the wide-angle X-ray diffraction arcing is not necessarily the same molecular orientation required for dimensional recovery. We have tentatively interpreted these results in terms of our recently proposed structural model consisting of both ordered domains and connecting disordered regions in the amorphous polymeric solid state. Annealing below T_g can produce chain backbone motion within the disordered regions and cause disorientation of the aligned ordered domains brought about by the initial cold-draw process.     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Doping effect of copper in germanium tellurium semiconducting glass system

Addition of copper to the semiconducting glassy system Ge₁₅Te_85−xCu_x (x=2, 4, 5, 6, 8, and 10) at the tellurium site is seen to produce considerable changes in the glass transition temperature (T_g) of the system. For a particular value of copper percentage, the T_g shows a minimum critical value. We have made an attempt to explain the observed variation of T_g with Cu content on the basis of various models like the chemically ordered network model, the constraints theory, the covalent bond approach of Tichy and Ticha and former valence shell (FVS) model proposed by Liu and Taylor.     

The effect of microtacticity on the glass temperature of poly[α-methyl styrene]

The effect of micrestructure on the glass temperature Tg of poly (α-methyl styrene) has been investigated. It has been observed that T_g increases as the syndiotacticity of the molecule increases-thus T_g = 446 ± 2°K for polymer with 67% syndiotactic placements, while a value of T_g = 453 ± 2°K is found for a sample with 95% syndiotactic placements. Coefficients of expansion for the liquid and glassy states have been calculated and from these a chain stiffness parameter δε/k has been estimated using the Gibbs-DiMarzio theory. The result indicates that the flex energy of the α-methyl styrene chain is 20% larger than for the polystyrene chain.