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     

A relationship between macroradical decay kinetics and α-segmental dynamics in glassy amorphous polymers

For a series of five amorphous polymers with a broad range of T_g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T_tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T₀ of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for α-segmental dynamics. This parameter represents the onset of α-segmental mobility in glassy state below T_g. A nontraditional way of the estimation of T₀ values for α-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested. © 1996 John Wiley & Sons, Inc.     

The effect of crystallinity and crosslinking on the depression of the glass transition temperature in nylon 6 by water

The influence of crystallinity and crosslinking on the depression of the glass transition temperature in nylon 6 by water has been investigated by dynamic mechanical methods. Radiation crosslinking by high-energy electrons was effective in preventing morphological changes during the measurement of the incremental change in heat capacity (ΔC_p) at T_g, which was performed by differential scanning calorimetry. The experimentally determined value of ΔC_p, when normalized to account for the crystalline phase, was found to deviate from a linear two-phase relation and was reduced further than would be expected based on this model. It is proposed that nylon 6 is best described by a three-phase model which consists of a crystalline domain, a wholly amorphous domain, and an “intercrystalline” region. The importance of this in explaining the relatively large depression of T_g by small quantities of water is illustrated by applying equations derived to account for the compositional dependence of T_g in polymerdiluent mixtures, based on a classical thermodynamic interpretation of the glass transition phenomenon.     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

Non-enzymatic browning-induced water plasticization

An exotherm, observed in differential scanning calorimetry (DSC) scans of amorphous food materials above their glass transition temperature,T _g, may occur due to sugar crystallization, nonenzymatic browning, or both. In the present study, this exothermal phenomenon in initially anhydrous skim milk and lactose-hydrolyzed skim milk was considered to occur due to browning during isothermal holding at various temperatures above the initialT _g. The nonenzymatic, Maillard browning reaction produces water that in amorphous foods, may plasticize the material and reduceT _g. The assumption was that quantification of formation of water from theT _g depression, which should not be observed as a result of crystallization under anhydrous conditions, can be used to determine kinetics of the nonenzymatic browning reaction. The formation of water was found to be substantial, and the amount formed could be quantified from theT _g measured after isothermal treatment at various temperatures using DSC. The rate of water formation followed zero-order kinetics, and its temperature dependence well aboveT _g was Arrhenius-type. Although water plasticization of the material occurred during the reaction, and there was a dynamic change in the temperature differenceT–T _g, the browning reaction was probably diffusioncontrolled in anhydrous skim milk in the vicinity of theT _g of lactose. This could be observed from a significant increase in activation energy. The kinetics and temperature dependence of the Maillard reaction in skim milk and lactose-hydrolyzed skim milk were of similar type well above the initialT _g. The difference in temperature dependence in theT _g region of lactose, but above that of lactose-hydrolyzed skim milk, became significant, as the rate in skim milk, but not in lactose-hydrolyzed skim milk, became diffusion-controlled. The results showed that rates of diffusion-controlled reactions may follow the Williams-Landel-Ferry (WLF) equation, as kinetic restrictions become apparent within amorphous materials in reactions exhibiting high rates at the same temperature under non-diffusion-controlled conditions.     

Twinkling fractal theory of the glass transition: Rate dependence and time–temperature superposition

The twinkling fractal theory (TFT) of the glass transition temperature T_g provides a new method of analyzing rate effects and time–temperature superposition in amorphous materials. The rate dependence of T_g was examined in the light of new experimental and theoretical evidence for the nature of the dynamic heterogeneity near T_g. As T_g is approached from above, dynamic solid fractal clusters begin to form and eventually percolate rigidity at T_g. The percolation cluster is a solid fractal and to the observer, appears to “twinkle” as solid and liquid clusters interchange in dynamic equilibrium with a vibrational density of states g(ω) ∼ ω. The solid-to-liquid twinkling frequencies ω_TF are controlled by the Boltzmann population of intermolecular oscillators in excited energy levels of their anharmonic potential energy functions U(x) such that ω_TF = ω exp −B(T*² − T²)/kT in which T* ≈ 1.2T_g. An oscillator changes from a solid to a liquid when a thermal fluctuation causes it to expand beyond its inflection point in the anharmonic potential. This leads to a continuous solid fraction P_s near T_g given by P_S ≈ 1−[(1 − p_c) T/T_g] where p_c ≈ 1/2 is the rigidity percolation threshold. Since g(ω) is continuous from very low to very high frequencies, the complex twinkling dynamics existing near T_g produces a continuous relaxation spectrum with many different length scales and times associated with the fractal clusters. The twinkling frequencies control the kinetics of T_g such that for a given observation time t when the rate γ > 1/t, only those parts of the twinkling spectrum with ω > γ can contribute to relaxation or percolation upto time t. The most important results in this article are as follows: The TFT describes the rate dependence of T_g, both for DSC thermal heating/cooling rates and DMA frequencies as the classic T_g − lnγ law as T_g(γ) = T_go + (k/2B) ln γ/γ_o in which the constant B = 0.3 cal/mol K². The constant B appears quite universal for the 17 thermoset polymers investigated in this study and 18 linear polymers investigated by others. Many other amorphous metal and ceramic glass materials exhibited the same rate law but required a new B value approximately half that for polymers. The same B = 0.3 value was also used to successfully describe the TTS shift factors using the twinkling fractal frequencies ω_TF = ωexp −B(T*² − T²)/kT, as ln a_T(TFT) = exp B(T_R² − T²)/kT, which gave comparable results with the classical WLF equation, log a_T = [−C₁(T − T_R)]/[C₂ + (T − T_R)]. The advantage of the TFT over the WLF is that C₁ and C₂ are not universal constants and must be determined for every material, whereas the TFT uses one known constant B which appears to be the same for all polymers. The TFT has also been found to describe the strong and fragile nature of the viscosity behavior of liquids and the rate and temperature dependence of the yield stress in polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2578–2590, 2009     

Glass transition and miscibility in blends of two semicrystalline polymers: Poly(aryl ether ketone) and poly(ether ether ketone)

Binary melt‐blended mixtures of two aryl ether ketone polymers (i.e., a new poly(aryl ether ketone) (code name PK99) and poly(ether ether ketone) (PEEK), have been studied. Polymer miscibility in glassy amorphous (or melt) domains has been demonstrated for the binary blend comprising of two aryl‐ether‐ketone‐type semicrystalline polymers. Composition‐dependent, single T_g was observed within full composition range in the PK99/PEEK blends, and the narrow T_g breadth also suggests that the scale of mixing was fine and uniform. To better resolve any possible overlapping T_g's, physical aging was imposed on a comparison set of blend samples for the purpose of improving detectability of overlapped multiple transitions if existing. The result still showed one single T_g. The relative sharp T_g and lack of cloud point transition suggest that the scale of molecular intermixing is good. Phase homogeneity was further confirmed using optical and scanning electron microscopy. The X‐ray diffractograms suggest that isomorphism does not exist in the PK99/PEEK blends and that the crystal forms of the respective polymers remain distinct and unchanged by the miscibility in the amorphous region. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1485–1494, 1999     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

---

Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

On the predictability of the high-frequency elastic modulus of semicrystalline polymers as function of crystallinity

The relation of the high-frequency elastic moduli of semicrystalline polymers to volume fraction crystallinity is correctly described by the Hashin-Shtrikman theory, without any disposable constants, as a function of the ratio of the modulus of the amorphous to that of the crystalline phase. Hence the (high-frequency) reduced modulus of semicrystalline polymers is largely a function of the temperature T/T_g. The importance of T/T_m for the modulus of the crystalline phase precludes the existence of a single universal reduced modulus versus temperature curve.     

Experimental free volume aspects of the polymer rheology as obtained by positron annihilation lifetime spectroscopy

The ortho‐positronium (o‐Ps) annihilation parameters, i.e. the mean o‐Ps lifetime, τ₃, and the o‐Ps relative intensity, I₃, in cis‐1,4‐polybutadiene (cis‐1,4‐PBD) and polyisobutylene (PIB) over a wide temperature range including the glass‐liquid transition have been measured by means of positron annihilation lifetime Spectroscopy (PALS). From them the free volume microstructural characteristics, i.e. the mean free volume hole size, V_h, and the free volume hole fraction, f_h, have been determined via a semiempirical quantum‐mechanical model of o‐Ps in a spherical hole or a phenomenological model of volumetric and free volume hole properties, respectively. Consequently, the literature rheological data for both the above‐mentioned polymers have been related to the free volume hole fractions via the WLF‐Doolittle type equation. It has been found that i) in the case of PIB this equation holds over 130K above the glass transition temperature T_g and ii) in the case of cis‐PBD the WLF‐Doolitle equation is valid in the temperature range over 60K above 1.3T_g, but below 1.3T_g down to T_g the modified WLF‐Doolittle‐Macedo‐Litovitz equation with the additional activation‐energy term describes the shift factor data better.     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

Dynamic mechanical behavior of a side-chain liquid crystalline polyacrylate

The phenomenology of the α- and β-relaxation processes in an amorphous and a crystallized specimen of a side-chain LC polyacrylate, based on the azobenzene mesogenic unit, was investigated by thermal and dynamic mechanical methods. The activation energy of the β relaxation of the crystallized sample is equal to that of the amorphous sample. The α-transition process of the amorphous sample was described by the WLF equation. In contrast, the α-relaxation behavior of the amorphous part of the semicrystalline sample was described by a double Arrhenius law broken at T = T_g. This peculiar behavior has been tentatively related to the decrease of the motion characteristic length of the macromolecules confined in the multidomain structure of the semicrystalline state. © 1996 John Wiley & Sons, Inc.     

Glass transition temperature versus conversion relationships for thermosetting polymers

Owing to enthalpy relaxation, values of the glass transition temperature (T_g) for partially reacted polymers may depend on the thermal history of samples and the heating rate used for measurements. Use of theoretical relations between T_g and the extent of reaction (x) of a thermoset must take this fact into account. The original DiBenedetto equation has been reevaluated as a convenient constitutive equation for expressing T_g versus x. An extension of Couchman's approach for the expression of the compositional variation of T_g enabled us to derive the same functionality as given by the DiBenedetto equation. Thus, the DiBenedetto equation may be regarded as based on entropic considerations applied to a model of the thermosetting polymer consisting of a random mixture of a fully reacted network with the initial monomers in an amount which depends on the particular conversion level. These two equations have been applied with success to different diepoxy-diamine copolymers.     

New amorphous perfluoro polymers: perfluorodioxolane polymers for use as plastic optical fibers and gas separation membranes

To address the need for perfluoro polymers with higher T_g, we have prepared and characterized various perfluorodioxolane monomers via direct fluorination of the hydrocarbon precursors. These monomers were readily polymerized in bulk or in solution initiated by perfluorodibenzoyl peroxide. The polymers obtained have relatively high T_g(~160°C) and exhibited low material dispersion. These polymers are completely amorphous and soluble in fluorinated solvents. The polymers are also chemically and thermally stable (T_g > 300°C). Thus, these perfluorodioxolane polymers may be used as plastic optical fiber material where high T_g is required, such as in automobile and aircraft application. These perfluorodioxolane polymers were also investigated for use as gas separation membrane. Among these polymers, the copolymer of perfluoro (2‐methylene‐1,3‐dioxolane) and perfluoro (2‐methylene‐4,5‐dimethyl dioxolane) showed superior gas separation performance compared with the commercial perfluoro polymers for a number of gas pair, including CO₂/CH₄, H_e/CH₄, H₂/CH₄, and N₂/CH₄. Copyright © 2015 John Wiley & Sons, Ltd.     

Dependence of cooperative relaxation of amorphous polymers on diluent concentration

The Adam–Gibbs molecular theory, which describes the temperature dependence of relaxation phenomena in the main transition region in terms of the configurational entropy of a system, has been extended to include the effect of concentration of a low-molecular-weight compound on the viscoelastic behavior of concentrated polymer solutions. The concentration dependence of relaxation times in the polymer–diluent mixture leads to an expression of the concentration dependence both of the shift factor in the Williams–Landel–Ferry (WLF) equation and of the glass transition temperature T_g of the mixture. The constants of the WLF equation and the concentration dependence of T_g are given in terms of a difference between the specific heats of the liquid and glass ΔC_p of the equilibrium temperature T₂ of the second-order transition, and of the parameter Δμs/k, which includes the chemical potential Δμ and the configurational entropy s of the smallest cooperatively rearranging region. The resulting relationships also predict the temperature dependence of the constants of the concentration WLF equation. Good agreement was found between theory and the viscoelastic and T_g data on the systems poly(vinyl acetate) + diethyl phthalate, poly(methyl methacrylate) + diethyl phthalate and polystyrene + dibutyl phthalate. This finding indicates that the configurational entropy, at least in the first approximation, is responsible for the concentration dependence of relaxation phenomena in concentrated polymer solutions.