Effect of composition on the width of the calorimetric glass transition in polymer–solvent and solvent–solvent mixtures

The calorimetric glass‐transition temperature (T_g) and transition width were measured over the full composition range for solvent–solvent mixtures of o‐terphenyl with tricresyl phosphate and with dibutyl phthalate and for polymer–solvent mixtures of polystyrene with three dialkyl phthalates. T_g shifted smoothly to higher temperatures with the addition of the component with the higher T_g for both sets of solvent–solvent mixtures. The superposition of the differential scanning calorimetry traces showed almost no composition dependence for the width of the transition region. In contrast, the composition dependence of T_g in polymer–solvent mixtures was different at high and low polymer concentrations, and two distinct T_g's were observed at intermediate compositions. These results were interpreted in terms of the local length scale and associated local composition variations affecting T_g. The possible implications of these results for the dynamics of miscible polymer blends were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1155–1163, 2004     

Correlations with and prediction of activation energies of gas permeation and diffusion in glassy polymers

Three types of novel correlations for activation energies of gas permeation E_P and diffusion E_D in amorphous glassy polymers are considered and their application for prediction of the E_P and E_D values for different gases are examined. The first one is based on application of the group contribution method. Combined consideration of the equation of free volume and Arrhenius equation results in the correlation of E_P and E_D with free volume V_f and fractional free volume (FFV). At last, the correlations between E_P and the permeability coefficient at a certain reference temperature P(T_ref), as well as E_D versus D(T_ref), are based on the fulfilment of the so-called compensation effect between activation energies and preexponential factors in activated processes. Examples of applicability of the correlations considered and recommendations for their use in prediction of the E_P and E_D values are given for transport of various gases in glassy polymers and separately in amorphous glassy polyimides.     

Polymer diffusion in latex films at ambient temperature

Polymer diffusion across interfaces at room temperature (21°C) was analyzed by direct nonradiative energy transfer (DET) in labeled latex films. Two modellatex polymers were examined: poly(butyl methacrylate) [PBMA, M_w = 3.5 × 10⁴, T_g (dry) = 21°C] and a copolymer of 2-ethylhexyl methacrylate with 10 wt % (acetoacetoxy)-ethyl methacrylate [P(EHMA-co-AAEM), M_w = 4.8 × 10⁴, T_g (dry) = −7°C]. Little energy transfer due to polymer diffusion was detected for the P(EHMA-co-AAEM) latex samples in the dispersed state or dried to solids content below ca. 90%, but above 90% solids, diffusion occurs among particles. For PBMA, diffusion occurs only after the film is dried (>97% solids) and aged. In the dry PBMA films, it requires 4–5 days at 21°C to reach a significant extent of mixing (f_m = 0.3–0.4). This corresponds to an estimated penetration depth d_app of 30–40 nm and a mean apparent diffusion coefficient (D_app) of 5 × 10⁻⁴ nm²/s. The corresponding D_app value for the dry P(EHMA-co-AAEM) sample is 5 × 10⁻² nm²/s, and it takes about 25–40 min for this polymer to reach f_m of 0.3–0.4 with d_app of 20–30 nm. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1129–1139, 1998     

Glass transition kinetics of some Se-Te-Ag chalcogenide glasses

Summary The present paper reports the Differential Scanning Calorimetric (DSC) study of some Ag doped Se-Te chalcogenide glasses. DSC runs were taken at different heating rates. Well-defined endothermic and exothermic peaks were obtained at glass transition and crystallization temperatures. The variation of glass transition temperature T_gwith Ag concentration has been studied. It has been found that T_gdecreases with increase in Ag concentration. The heating rate dependence of T_gis used to evaluate the activation energy of glass transition (DE_t). The value of<span style='font-size:10.0pt; font-family:"SymbolProp BT";mso-bidi-font-family:"SymbolProp BT"'>DE_thas been found to increase with increase in Ag concentration followed by nearly constant value at higher concentrations of Ag.     

Effect of methoxy position on dynamic mechanical and shape memory properties of methoxyphenol-based polybenzoxazines

Abstract

Two series of benzoxazines were synthesized from o-, m-, and p-methoxyphenols, two polyetheramines with different molecular weights, and formaldehyde. The glass transition temperatures (T _gs) of m-methoxyphenol-based polybenzoxazines are respectively higher than those of o- and p-methoxyphenol-based counterparts. The polybenzoxazines exhibit thermally induced one-way dual-shape memory behavior based on T _g, and the o- and p-methoxyphenol-based polybenzoxazines exhibit higher shape memory performance than m-methoxyphenol-based counterparts under motion constraints.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

EFFECT OF EXCESS ENTHALPY RELAXATION ON PERMEATION OF CO_2 AND TOLUENE THROUGH PET FILM

Structural change in an unoriented, amorphous PET film annealed at temperatures below T_gand the effect of excess enthalpy relaxation on permeation rates of CO_2 gas and toluene liquid intreated samples have been studied. The results suggest that the amount of excess enthalpy relaxa-tion as determined from the endothermic peak in T_g interval, the T_g and density all increase withannealing time, but the trans-conformation component of samples decreases. No change of struc-ture in the amorphous phase was found other than the normal densification of the molecular chainpacking or a reduction in free volume had occurred during the annealing regimes. Therefore, thepermeation rate of CO_2 gas in treated samples reduced. While the apparent permeation rate oftoluene liquid increased with annealing time because of a creation of extensive cracks at film surfacearising from both the increase in embrittlement of polymer and the swelling action of toluene liquidon treated samples.     

Small molecule diffusion in a rubbery polymer near Tg: Effects of probe size,shape, and flexibility

A novel experimental approach involving fluorescence nonradiative energy transfer (NRET) is employed to study the Fickian diffusion of small molecules in rubbery poly(isobutyl methacrylate) (PiBMA) films near the glass transition, using a formalism that directly relates the small molecule translational diffusion coefficient, D, to changes in the normalized nonradiative energy transfer efficiency, E_N. Values of D for pyrene, 1,3-bis-(1-pyrene) propane (BPP), 1,3-bis-(1-pyrene) decane (BPD), 9,10-bis-phenyl ethynyl anthracene (BPEA), diphenyl Disperse Red 4 (DPDR4), and decacyclene in PiBMA are measured over temperatures ranging from approximately T_g to T_g + 25°C. Among these chromophores, significant differences in both the magnitude and temperature dependence of D are observed which are attributed to differences in molecule shape and flexibility, as well as molar volume. Other factors being equal, chromophore flexibility was shown both to increase the magnitude of D and to decrease its dependence on temperature, as does an increase in aspect ratio. For BPD, these effects are attributed to the ability of the flexible molecule to diffuse in a piecewise manner, requiring the cooperative mobility of fewer polymer chain segments than a rigid molecule of the same molar volume. For BPEA and DPDR4, this deviation from D being dominated by molar volume effects is attributed the to high aspect ratio of these elongated molecules. © 1996 John Wiley & Sons, Inc.     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Thermoanalytical evaluation of readily available reference polymers

A commercial set of polymers has been characterized by TG-DTA, DSC, TMA, FTIR spectroscopy and X-ray diffraction analysis (XRD). Thermal and mechanical stability, as well as the polymer glass transition temperature,T _g, and melt temperature,T _m, have been documented. There is a good correlation between measuredT _g andT _m values and published data. The degree of polymer crystallinity for polyethylene has been verified by XRD. The credibility and stability of these reference polymers is based on a comparison of their thermal properties, over a wide range of temperatures from two versions of a reference set, published in 1979 (A) and 1994 (B). The thermal properties and crystallinity of these polymers have stood the test of time and are reliable, readily available and consistent.     

Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory

A previously developed model of simple penetrant diffusion is extended to encompass complex penetrants of idealized molecular shape, characterized by dimensions of length, width, and thickness. Expressions are obtained for D(0,T), the diffusion coefficient at zero penetrant concentration (c), and the fractional increase in D(0,T) as a function of c and temperature (T). The model predicts that D(0,T) will exhibit Arrhenius behavior at temperatures well above T_g and gives the limiting activation energy as a function of penetrant thickness and the polymer energy/distance constants used previously. For T_g < T ? T_g + 150 K the model requires two new disposable parameters, in addition to the jump-length parameter of the simple penetrant theory. These parameters, however, have precise physical meanings (all are lengths) and together with the penetrant dimensions and polymer constants determine the absolute magnitude of the diffusion coefficient as well as its relative dependence on c and T. For T ? T_g + 40 the relative concentration dependence may be calculated in terms of the penetrant dimensions and polymer constants only.     

Gas transport properties of annealed polyimide films

Sorption and permeation of CO₂ in various annealed polyimide (PI) films were investigated. Dual-mode sorption and partial immobilization models were used to analyze the data. Sorption of CO₂ in PI film quenched from above the glass transition temperature (T_g) is greater than in film as received. In fact, sorption is decreased over the entire pressure range by cooling the film slowly. These changes in sorption of CO₂ can be attributed to a change in the Langmuir sorption capacity C′_H by annealing, since the other dual-mode sorption parameters, k_D and b, are almost independent of annealing. The value of C′_H is increased by quenching, and decreased by slow cooling from above T_g. The two diffusion coefficients D_D and D_H according to the Henry and Langmuir modes, respectively, for CO₂ also depend markedly on annealing. Diffusion coefficients of quenched PI films are increased and those of film cooled slowly are decreased compared with values for PI film as received. The change in D_H is larger than that in D_D. The permeability coefficient of quenched PI films at 100 cmH_g is about 1.7 times that of PI film as received. The film structure formed by quenching can enhance permselectivity.     

Syntheses and properties of novel fluorinated polyamides based on a bis(ether‐carboxylic acid) or a bis(ether amine) extended from bis(4‐hydroxyphenyl)phenyl‐2,2,2‐trifluoroethane

Two series of novel fluorinated aromatic polyamides were prepared from 1,1‐bis[4‐(4‐carboxyphenoxy)phenyl]‐1‐phenyl‐2,2,2‐trifluoroethane with various aromatic diamines or from 1,1‐bis[4‐(4‐aminophenoxy)phenyl]‐1‐phenyl‐2,2,2‐trifluoroethane with various aromatic dicarboxylic acids with the phosphorylation polyamidation technique. These polyamides had inherent viscosities ranging from 0.51 to 1.54 dL/g that corresponded to weight‐average and number‐average molecular weights (by gel permeation chromatography) of 36,200–80,000 and 17,200–64,300, respectively. All polymers were highly soluble in aprotic polar solvents, such as N‐methyl‐2‐pyrrolidone and N,N‐dimethylacetamide, and some could even be dissolved in less‐polar solvents like tetrahydrofuran. The flexible and tough films cast from the polymer solutions possessed tensile strengths of 76–94 MPa and initial moduli of 1.70–2.22 GPa. Glass‐transition temperatures (T_g's) and softening temperatures of these polyamides were observed in the range of 185–268 °C by differential scanning calorimetry or thermomechanical analysis. Decomposition temperatures (T_d's) for 10% weight loss all occurred above 500 °C in both nitrogen and air atmospheres. Almost all the fluorinated polyamides displayed relatively higher T_g and T_d values than the corresponding nonfluorinated analogues. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 420–431, 2003     

Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4

The dissociation energies of MH₄ (M =  La, Hf–Hg) were computed using full optimized reaction space (FORS) multi-configuration self-consistent field (MCSCF) and second-order multi-reference Møller–Plesset perturbation methods with the SBKJC basis sets augmented by a set of polarization functions (SBKJC(f,p)). It was shown that of the molecules examined, only four tetra-hydrides HfH₄, TaH₄, WH₄, and OsH₄ with T_d symmetry are lower in energy than the corresponding dissociation limits. For WH₄ and OsH₄, the potential energy surfaces from the D_4h to the T_d structure were explored from both theoretical calculations and symmetry arguments based on the pseudo-Jahn- Teller effect. As for WH₄, it is found that the ground state could be ³E_g, ³A_2g, or ³B_2g at the D_4h structure. The present calculations suggest that the ground state is ³E_g, and that this state is stabilized by the e_u deformation into a C_2v structure (³B₁) and then sequentially to the most stable T_d structure (³A₂). If the molecular system is promoted to the lowest ³B_2g state, the D_4h structure can directly deform into the most stable T_d structure along the b_2u vibrational mode. For OsH₄, the ground state (⁵B_1g) at the D_4h structure deforms into a D_2d structure and the resulting ⁵B₂ state strongly interacts with the lowest ³E and ¹A₁ states due to the spin-orbit couplings (SOCs). As a result, it was shown that the relativistic potential energy of the lowest spin-mixed state (ground state) monotonically decreases along the D_2d deformation path from the D_4h to the T_d structure.     

Analysis of packing factors of crystalline polymers in terms of the glass transition to melting temperature radio

An expression for the ratio of the glass transition temperature to the melting temperature, T _g/T _m, was derived with allowance for fluctuations of the packing factor in the amorphous state. This relationship made it possible to describe the actual range of variation in T _g/T _m depending on a change in the packing factor in the crystalline state k _{o, cr}. The proposed approach forms the basis for the method of determination of increments in the packing ratio k _{o, cr} and formulation of the principles of selection of experimental data for calculations. The glass transition temperatures in polyethylene depending on the type of unit cell were calculated.     

Effects of high-pressure CO2 on the glass transition temperature and mechanical properties of polystyrene

Hydrostatic pressure usually increases the glass transition temperature T_g of a polymer glass by decreasing its free volume; if the pressurizing environment is soluble in the polymer, however, one might expect an initial decrease in T_g with pressure as the polymer is plasticized by the environment. Just such a minimum in the T_g of polystyrene (PS) is observed as the pressure of CO₂ gas is increased over the range 0.1–105 MPa from both ultrasonic (1 MHz) measurements of Young's modulus E and static measurements of the creep compliance J. A time-temperature-pressure superposition law is obeyed by PS which allows a master curve for the compliance to be constructed and shift factors to be determined. A master curve for E is then obtained by using the Boltzmann superposition principle. The compliance J reaches a maximum, and E and T_g reach minima, at a CO₂ pressure of ca. 20 MPa at both 34 and 45°C, which are above the critical temperature (31°C) of CO₂. At the minimum, T_g is 41 at 45°C and 36 at 34°C, the larger depression at 34°C evidently corresponding to the higher solubility of CO₂ at the lower temperature. The plasticization effect due to CO₂ can be isolated by subtracting the effect of hydrostatic pressure alone from the experimental data. The results leave no doubt that at high pressures CO₂ gas is a severe plasticizer for polystyrene.     

Low-frequency dielectric behavior of poly(vinylidene fluoride)

An explicit mechanism is described for the anomalous increase in dielectric constant and dielectric loss at low frequencies and high temperatures for poly(vinylidene fluoride) containing ionic impurities. Relations are proposed for the ionic contributions, ε_i″ and ε_i″, to the dielectric constant and dielectric loss: where v₀ and D₀ are the concentration and the diffusion coefficient of the mobile ions at infinite temperature, q is the charge of an ion (in cgs electrostatic units), l is the distance between electrodes, k is the Boltzmann constant, T is the absolute temperature, E_d is the apparent activation energy for diffusion of the ions, and W is the dissociation energy of the ionic impurities. From the slopes of curves of log εT′ versus 1/T and log ε″T versus 1/T for poly(vinylidene fluoride), energies E_d = 34 kcal/mole and W = 342 kcal/mole were obtained.     

The effect of masked isocyanates on the moisture absorption of MY 720/DDS epoxy resin

Several masked isocyanates were prepared with variations in both the type of isocyanate and masking group. They were characterized by elemental analysis and NMR spectroscopy, and their unblocking temperatures were determined. In general, higher unblocking temperatures were obtained using acyclic and cyclic aliphatic isocyanates and fluorinated phenols. Those with unblocking temperatures in the range of 120–180°C were incorporated into MY 720/DDS epoxy resin prior to cure. Highly fluorinated variations were incompatible with the resin. IR and DSC analyses showed that residual functional groups in the epoxy resin reacted with the masked isocyanates. Reductions in moisture absorption as high as 65% were obtained depending on the masked isocyanate. DMA studies showed that the T_g of the epoxy resin is lowered by incorporation of the masked isocyanate but the elastic modulus (E′) is relatively unchanged at temperatures below T_g.     

Diffusion mechanisms in solid and molten polyethylene

The diffusion coefficient D and solubility coefficient k of small molecules [C₃H₆, C₄H₁₀, (CH₃)₄C] are determined at very low solute concentrations in annealed linear polyethylene over a wide range of temperature above and below the melting point T_m. For measurements above T_m the specimen was lightly crosslinked by irradiation from a ⁶⁰Co source. The diffusion data fit equations of the form D = D₀ exp {–ΔH_D/RT}. An abrupt change in ΔH_D occurs at T_m: representative values (for C₄H₁₀) are 4.53 and 14.9 kcal/mole above and below T_m. At T_m, D₀ also changes abruptly: representative values (for C₄H₁₀) are log D₀ = ?2.65 above T_m and log D₀ = +2.70 below T_m. The mechanism of diffusion therefore changes at the melting point. The melt exhibits typical liquidlike characteristics (negative values of activation entropy ΔS_D). The ratio ΔS_D/ΔH_D = 4β (β denoting the isobaric coefficient of volume expansion) holds below but not above T_m. Equations of the form k = k₀ exp {–ΔH_k/RT} fit the solubility data. The log k versus T^?1 plots above and below T_m are parallel but separated by a step at T_m. If crystallization followed by annealing is assumed to leave a weight fraction of polymer α_k (the amorphous fraction) in which the solute can absorb and if the specific solubility coefficient of the amorphous fraction is identical to that of the melt, then log α_k Equals the magnitude of the step at T_m. Values of α_k determined from the observed step are very close to values of amorphous fraction determined by measurement of density. The solubility experiments support the concept of polyethylene as a two-phase solid with the amorphous fraction of specific volume equal to the extrapholated specific volume of the melt. The passage of a solute molecule from one potential well to another, however, occurs by processes in the melt and the amorphous fraction which are entirely different.