Molecular interpretation of T∥, the rubbery-viscous ‘transition’ temperature of amorphous polymers

Many physical and mechanical properties of amorphous polymers show anomalous behaviour at a temperature above T_g, designated T_∥, the ‘liquid-liquid transition temperature’. It is suggested here that T_∥ can be considered to be the rubbery-viscous ‘transition’ temperature of amorphous polymers, analogous to T_g, the glassy-rubbery transition temperature. At T_∥, the viscous dissipation goes through a maximum due to a shift in response of the molecules to stress from a coiling-uncoiling process (elastic rubbery region) to slippage between the molecules (viscous region). It is argued here that this maximum is responsible for the occurrence of a maximum in log(decrement) traces obtained by torsional braid analysis (t.b.a.) above T_g.     

N.m.r. study of cellulose-water systems: Water proton spin-lattice relaxation in the rotating reference frame

A pulsed n.m.r. study of relaxation in the rotating reference frame was performed on cellulose samples with moisture contents (MC) ranging from 20.5% to 218%. The dependence of the spin-lattice relaxation time (T_1ρ) in the rotating frame on temperature in a sample hydrated to approximately the fibre saturation point (FSP) indicates that in this case water exists in two different environments or phases. The first phase consists of a small number of water molecules (<1% of adsorbed water molecules in sample) tightly bonded to cellulose whereas the second phase consists of the remaining adsorbed water molecules which are more loosely attached. At room temperature exchange occurs between these phases at an intermediate exchange rate. For samples with MC >FSP a third water phase was identified. From the dependence of T_1ρ on the rotating field strength information about water molecule dynamics was deduced.     

Solid-state C NMR analyses of the structures of crystallized and quenched poly(lactide)s: Effects of crystallinity, water absorption, hydrolytic degradation, and tacticity

The effects of crystallinity, water absorption, hydrolytic degradation, and tacticity on the solid structure and chain mobility of poly(lactide)s were investigated by solid-state ¹³C NMR spectroscopy. The following results were obtained from the line shapes of the carbonyl and methine carbons in ¹³C NMR spectra and their spin-lattice relaxation behavior. The crystallized poly(l-lactide) (PLLA) specimens in the dried, hydrated, and hydrolyzed states had two components, rigid and mobile components which can be, respectively, assigned to the crystalline and non-crystalline components. Upon water absorption, the chain mobility in the non-crystalline component of PLLA-C remained unvaried, reflecting a very small effect of the incorporated water molecules at room temperature. In contrast, the elevated chain mobility in the crystalline component and unclear splitting of carbonyl carbon strongly suggest that the water molecules are incorporated in the crystalline lattice. Upon removal of the non-crystalline components by hydrolytic degradation of crystallized PLLA, the chain mobility was slightly elevated in both crystalline and non-crystalline components by the lowered crystalline thickness and shortened non-crystalline chains. The non-crystalline specimens, PLLA (PLLA-Q) and poly(dl-lactide) (PDLLA), could be analyzed to contain two components, rigid and soft components, with the similar conformation but different restricted states of chains which cause high and low chain mobility. The insignificant difference in the spectral shapes and T_1C values between PLLA-Q and PDLLA strongly suggests that the effects of difference in the chain regularity and interaction on the spectral shapes and T_1C values are very low.     

Glass transition behavior and dynamic fragility in polylactides containing mobile and rigid amorphous fractions

The segmental dynamics of polylactide chains covering the T_g − 30 °C to T_g + 30 °C range was studied in absence and presence of a crystalline phase by dynamic mechanical analysis (DMA) using the framework provided by the WLF theory and the Angell's dynamic fragility concept. An appropriate selection of stereoisomers combined with a thermal conditioning strategy to promote crystallization (above T_g) or relaxation of chains (below T_g) was revealed as an efficient method to tune the ratio of the rigid and mobile amorphous phases in polylactides. A single bulklike mobile amorphous phase was taken for poly(d,l-lactide) (PDLLA). In turn three phases, comprising a mobile amorphous fraction (MAF, X_MA), a rigid amorphous fraction (RAF, X_RA) and a crystalline fraction (X_c) were determined in poly(l-lactide) (PLLA) by modulated differential scanning calorimetry (MDSC) according to a three-phase model. The analysis of results confirms that crystallinity and RAF not only elevate the T_g and the breadth of the glass transition region but also yields an increase in dynamic fragility parameter (m) which entails the existence of a smaller length-scale of cooperativity of polylactide chains in confined environments. Consequently it is proposed that crystallinity is acting in polymeric systems as a topological constraint that, preventing longer range dynamics, provides a faster segmental dynamics by the temperature dependence of relaxation times according to the strong-fragile scheme.     

Solid state nuclear magnetic resonance study of highly oriented poly(glycolic acid)

The structure of isotropic and highly drawn poly(glycolic acid) (PGA) fibres is investigated using solid-state ¹H NMR spectroscopy. Relaxation times in the rotating frame (T1ρ) using a spin-lock method at 100 °C indicate that isotropic PGA can be adequately described by two phases, a rigid crystalline phase and an amorphous mobile phase with relaxation times of 16.6 and 0.9 ms, respectively. A crystallinity of 40% is obtained by this method and agrees well with previous calorimetric studies. In contrast, T1ρ measurements indicate that oriented PGA is 50% crystalline and can be adequately described by a three phase model consisting of: rigid crystalline material with long relaxation time, semi-rigid non-crystalline material with intermediate mobility and relaxation time and highly mobile non-crystalline material with the shortest relaxation time. It was found that the crystalline phase has a T1ρ=53 and T1ρ=39 ms when the fibre direction is at 0 and 90° relative to the external magnetic field, respectively. This difference in relaxation time is associated with higher spin interactions at 0°, reducing the effect on the mobility of the chains. The WAXS orientation averages P₂=0.99 and P₄=0.96 obtained from the azimuthal scans of the (020) and (002) reflections indicate a highly oriented crystalline structure. These results are used to contrast the structural information obtained from measurements and theoretical calculations of the rigid-lattice anisotropy of the second moment (M₂), from which the orientation averages P₂=0.96 and P₄=0.94 were obtained on the basis of a published crystal structure. The discrepancies found are associated with small differences between the published crystal structure and that required to explain the spin interactions among adjacent molecules.     

N.m.r. studies on the effect of water on the glass transition of polystyrene

These investigations are concerned with water-polymer interactions in polymer latices. It is known that water can act as a plasticizer for many solid polymers and cause a reduction in the glass transition temperature, T_g, of the amorphous regions. Experiments were carried out to determine whether pulsed n.m.r. techniques could be used to study the T_g of a polymer suspension and hence the influence of water and electrolyte on it. From T₁ and T₂ proton relaxation measurements as a function of temperature on polystyrene latex systems it was shown that the presence of water lowers the T_g of the polymer particles (by about 10°C), the effect being slightly greater in the presence of concentrated electrolyte. The extent of electrolyte penetration into the particles was deduced by studying relaxation as a function of particle diameter in latices containing paramagnetic Mn²⁺ ions. Using simple theories of relaxation and spin diffusion it was concluded that for all but the smallest particles electrolyte penetration is restricted to a very thin shell of the order of 1 nm. These conclusions were supported by the results of similar measurements on PTFE particles.     

Lindemann-like size-independent glass-transition criterion for polymers

It is well known that the intrinsic melting mechanism is independent of crystal size according to Lindemann's melting criterion. In order to probe whether the glass transition mechanism is also size-independent, segment dynamics of free-standing polystyrene (PS) films is determined by considering the temperature- and thickness-dependent number of styrene segments N_α(T,D) in the cooperative rearranging region (CRR). Under the help of Adams-Gibbs glass transition theory and molecular dynamics simulation, N_α(T,D) function is established and it decreases as D decreases or T increases. However, N_α[T_g(D),D] at the glass transition temperature T_g(D) is size-independent, which is consistent with the simulation results obtained by Donth's method. Meanwhile, its relative temperature function N_α{[T − T_g(D)]/T_g(D)} is also size-independent. Therefore, N_α[T_g(D),D] function as a criterion for glass transition, which describes the physical nature of the glass transition, is similar to the vibrational amplitude in Lindemann's melting criterion.     

The phase composition and molecular motions of plasticized wheat gluten-based biodegradable polymer materials studied by solid-state NMR spectroscopy

The water plasticized wheat gluten (WG) materials were prepared by thermal processing and studied by dynamic mechanical analysis and solid-state NMR spectroscopy. The results indicate that the materials displayed a broad distribution of molecular motions and could be divided into different phases in terms of their mobility above the T_g. The rigid phase mainly consisted of proteins and starch with enhanced interactions between the two components via hydrogen bonding with water molecules. Lipid and water formed the mobile phase, however, lipid molecules were always more mobile than water. The intermediate phase consisted of plasticized starch and proteins (mainly proline and glutamine segments). The whole plasticized WG materials were heterogeneous at a scale of 20-30 nm, but the miscibility between proteins and starch was enhanced via increasing hydrogen bonding interactions with water molecules. Such strong hydrogen bonding acted as adhesion among these multi-components/phases over a wide range of temperature thus resulting in good mechanical properties of the materials. The results demonstrated that solid-state NMR techniques can provide valuable information of quantitative composition of phase structures with different mobility in a multi-component system and the chemical nature of each phase along with the interactions among these components/phases.     

Moisture absorption by cyanate ester modified epoxy resin matrices. Part I. Effect of spiking parameters

The moisture absorption of cyanate ester modified epoxy resin matrices has been studied under thermal spiking conditions. Enhanced moisture absorption has been observed at spike-temperatures above 120 °C. The results of the desorption studies on both control specimens and the spiked specimens showed that some of the water molecules remained entrained in the polymer. It is postulated that this water could be associated with that which is hydrogen bonded or from the hydrolysis of isolated residual cyanate ester groups because the concentration of entrained water remains constant at spike-temperatures below 180 °C. Above 180 °C a thermally activated process, leading to chain scission as indicated by a reduced recoverability of the glass transition temperature (T_g) on drying.On isothermal resorption, the moisture concentration was found to be similar to that achieved through thermal spiking, showing that the entrained water at the lower spike-temperatures can also be achieved under mild conditions. The T_g is reversibly recovered to within 5 °C, which indicates a degree of relaxation rather than degradation. The moisture diffusion coefficient estimated from the resorption curves is lower than those estimated from the absorption and desorption curves. The isothermal resorption diffusion coefficient also decreased with increasing spike temperature. It is proposed that thermal spiking induced a relaxation of the network but as the spike-temperature approaches the transition region of the wet polymer, further hydrolytically induced relaxation events become feasible.     

Evaluation of local polarity of polymer solids by a rigid fluorescent probe of carbazole-terephthalate cyclophane

A novel rigid fluorescent probe, carbazole-terephthalate cyclophane (Cz-TP) was applied to evaluate local dielectric constants (ε) of various polymer solids in a wide range of temperatures. For poly(vinylidene fluoride), the ε increased above the glass transition temperature (T_g), due to relaxations of the polar segment -(CH₂CF₂)- of the main chain. For poly(alkyl methacrylate)s, the ε increased above the T_g or the melting temperature of the side chain, where motions of the polar ester groups are activated. For cyanoethylated polymers, the ε increased owing to motions of the polar cyano groups at the end of the side chain and the ε corresponded to the dielectric constant evaluated by dielectric relaxation measurement at a high frequency, because the Cz-TP exciplex has a lifetime of tens of nanoseconds. For a cyanoethylated polymer with a high content of cyano groups, the ε was larger at low temperatures than the dielectric constant obtained by the macroscopic dielectric relaxation measurement. These results show that the Cz-TP molecule is a useful probe for evaluation of the local polarity in polymer solids over a wide temperature range and can detect even a small change in ε at transition temperatures such as glass transition, side-chain melting, and side-chain relaxation.     

Understanding the effect of chain entanglement on the glass transition of a hydrophilic polymer

In this article, we report an interesting phenomenon of the glass transition temperature (T_g) deviation of a hydrophilic polymer. Polyacrylamide (PAL) samples with different extents of chain entanglement were prepared by spray drying and solution casting. We found that the glass transition temperature increases as the extent of chain entanglement decreases upon the sub‐T_g annealing. The water content in the PAL matrix is found with no direct correlation to T_g. However, the observation of a faster diffusion process of water in the disentangled PAL matrix offers an evidence of a faster relaxation process of disentangled PAL molecules. The T_g increase of the disentangled PAL samples is believed to be associated with the increased molecular interaction during the chain relaxation process upon the sub‐T_g annealing. A macroscopic evidence is the fact that the density of the hot‐laminated samples increases as the extent of chain entanglement decreases. A thermodynamic analysis suggests that enthalpy more than entropy favors an elevated T_g of a disentangled hydrophilic polymer upon the sub‐T_g annealing. We believe that this research provides new understanding of T_g of the hydrophilic polymers, which are being extensively used in bio‐related studies. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Transitions from solid to liquid in isotactic polystyrene studied by thermal analysis and X-ray scattering

A three-phase model, comprising mobile amorphous fraction (MAF), rigid amorphous fraction (RAF) and crystalline fraction (C), has been applied to interpret the thermal transitions and structure of cold-crystallized isotactic polystyrene (iPS) from below the glass transition temperature, T_g, to above the melting point. Quenched amorphous iPS films were isothermally crystallized at different temperatures for 12 h. The fraction of crystalline phase, ?_c, was measured by differential scanning calorimetry (DSC), wide angle X-ray scattering and Fourier Transform infrared spectroscopy. The fraction of the mobile amorphous phase, ?_MAF, was obtained from the heat capacity increment at the glass transition temperature. In the three-phase model, the fraction of the rigid amorphous phase, ?_RAF, was found from 1−?_MAF−?_c. Specific heat capacity measurements by standard DSC confirm that the experimental baseline heat capacity conforms to a three-phase model for temperatures ranging from below T_g, up to the relaxation of RAF. The relaxation of RAF appears as a sigmoidal change in heat capacity accompanied by excess enthalpy, in which solid-like RAF is converted to an identical amount of liquid-like MAF.At temperatures above the relaxation of RAF, either one or two major crystal melting endotherms are observed in standard DSC, dependent upon crystallization temperature. However, using quasi-isothermal temperature modulated DSC, we always observed two reversing melting endotherms. The effects of annealing on iPS structure during the quasi-isothermal measurement were assessed using small angle X-ray scattering (SAXS). Combining the DSC and SAXS results, a model for the melting of iPS lamellae at low heating rates is presented.     

The mechanical enhancement of physical aging

The effect of physical aging on the tensile creep properties of rigid PVC and PMMA was investigated at three temperatures between the glass transition temperature T_g and room temperature. The results confirm Sternstein's claim that mechanical stresses may enhance aging, but also our previous conclusion that such effects occur only at strains larger than 0.3–0.5%. It is further shown that the term ‘enhancement’ should, preferably, be avoided.     

Temperature dependence of molecular motions in the polyurethane-based membranes studied with paramagnetic spin probe

This third paper in this series regarding structure and dynamics of the polyurethane-based membranes studied with TEMPO spin probe presents the results of the ESR measurements performed to characterise mobility of segments in the permeable regions of the membranes. The variations of the spin probe motions with temperature have been analysed for the series of polyurethanes (PU) differing in molecular structure and compared with the results of the DSC studies. Along with T_50 G, the other temperatures, T_n, T_i, T_τ, at which the significant change in dynamics occurs have been determined and correlated with the length of the PU soft and hard segments, and then discussed with regard to the respective relationships of T_g. The results have demonstrated the sensitivity of the ESR method to the segmental motions, which have not been detected by the DSC technique. From the DSC and ESR data the size of the motional chain segment in various PUs has been estimated, which has been found to follow the trend that polymers with higher T_g have bulkier segments. Two unusual observations have been made, concerning the deviation from the Arrhenius relation at high temperature for some PUs, and the increased mobility of the TEMPO molecules in some poly(urethane-urea)s after their thermal treatment. These results have been interpreted so far either in terms of the possible translational diffusion of the TEMPO molecules for those PUs showing lesser amount of the hard segments, or in terms of the increased free volume resulting from the temperature induced structural changes within the permeable regions of poly(urethane-urea)s.     

Crystallization and vitrification effect in a poly(styrene)-g-poly(ethylene oxide) graft copolymer

Crystallization and solid state structure of a poly(styrene)-graft-poly(ethylene oxide) (PS-g-PEO) graft copolymer with crystallizable side chains were studied using simultaneous small angle X-ray scattering/wide angle X-ray scattering/differential scanning calorimetry (SAXS/WAXS/DSC). It is found that the glass transition temperature (T_g) of PS main chain is remarkably higher than that of PS homopolymer. The start cooling temperature (T_o) has a great influence on crystallization of the PEO side-chain. When the graft copolymer is cooled from the temperature above T_g, phase separation is suppressed due to the low mobility of the PS main chain and the homogeneous melt is vitrified. The unfavorable conformation of the rigid main chain results in a single crystallization peak and lower crystallinity. When PS-g-PEO is only heated to a temperature lower than the T_g and then cooled, phase separation is retained. Both the PEO side chains with high and low crystallizability can crystallize in the phase-separated state, leading to double crystallization peaks and higher crystallinity. The effect of solvent on crystallization of the graft copolymer was also examined. It is observed that addition of toluene reduces the T_g of the PS main chain and leads to the disappearance of the vitrification effect.     

Effect of chain rigidity on block copolymer micelle formation and dissolution as observed by 1H-NMR spectroscopy

Amphiphilic copolymers poly(methyl methacrylate-b-acrylic acid), poly(methyl methacrylate-b-methacrylic acid), poly(methyl acrylate-b-acrylic acid) and poly(methyl acrylate-b-methacrylic acid) were prepared by reversible addition fragmentation chain-transfer (RAFT) polymerization. The hydrophilic polyacid blocks were either synthesized directly or formed by the hydrolysis of poly(tert-butyl acrylate) or poly(tert-butyl methacrylate) blocks. The hydrophobic blocks consisted of either the more rigid, high glass transition temperature (T _g ) poly(methyl methacrylate) or more flexible, low T _g poly(methyl acrylate) material. The hydrophilic blocks were either poly(methacrylic acid) (rigid, high T _g ) or poly(acrylic acid) (flexible, low T _g ). The micellization behavior of the polymers was studied by proton nuclear magnetic resonance (¹H-NMR) spectroscopy in mixtures of 1,4-dioxane-d₈ and D₂O. All four polymers were soluble in neat dioxane. In solutions of higher water content, the polymers with the more rigid hydrophobic blocks formed into micelles as was evidenced by broadening of the resonances resulting from the protons in those blocks. At moderate water concentration (25–50%), dissolution of the micelles was observed upon heating the solution. No micellization was observed in polymers containing the less rigid poly(methyl acrylate) hydrophobic block regardless of the identity of the hydrophilic block. As further evidence of micellization formation and dissolution, the spin-lattice (T ₁) and spin-spin (T ₂) relaxation times of protons in the hydrophobic and hydrophilic blocks were measured. Significant differences in the relaxation times as functions of temperature and solvent concentration were observed between the hydrophilic and hydrophobic blocks of the micelle-forming polymers.     

A Study of the Interphase Region in Carbon Fibre/Epoxy Composites using Dynamic Mechanical Thermal Analysis

We have examined the effect of fibre addition on the glass transition temperature (T _g ) of two epoxy resin systems (an amine cured and an anhydride cured epoxy system) using dynamic mechanical thermal analysis (DMTA) and differential scanning calorimetry (DSC). The presence of fibres changes the glass transition temperature (T _g ) of an anhydride cured epoxy resin but does not affect that of an amine cured epoxy. The data suggest that two counteracting mechanisms are responsible for these changes: firstly, the presence of fibres causes a restriction of the molecular motion in the resin system, and secondly, the presence of carboxyi and keto-enol groups on the fibre surface inhibit curing of the resin close to the fibre, i.e. in the interphase region. The former increases the T _g and is a long range effect whereas the latter decreases the T _g and is a localised phenomenon. Changes in the dynamic properties of the interphase region are only detected when the samples are loaded in the longitudinal direction and not in the transverse direction where bulk matrix properties dominate. Sizing the fibres before their incorporation into the epoxy resin eliminates the variation in interfacial properties arising from differences in fibre surface chemistry.     

Oxygen solubility and specific volume of rigid amorphous fraction in semicrystalline poly(ethylene terephthalate)

The existence of rigid amorphous fraction (RAF) in semicrystalline poly(ethylene terephthalate) (PET) is associated with the lamellar stack crystalline morphology of this polymer, the regions where several crystalline lamellas are separated by very thin (20-40 Å) amorphous layers. In contrast, regular or mobile amorphous fraction is associated with much thicker interstack regions. The oxygen transport properties of PET isothermally crystallized from the melt (melt-crystallization) or quenched to the glassy state and then isothermally crystallized by heating above T_g (cold-crystallization) were examined at 25 °C. Explanation of unexpectedly high solubility of crystalline PET was attributed to the formation of RAF, which in comparison with mobile amorphous phase is constrained and vitrifies at much higher than T_g temperature thus developing an additional excess-hole free volume upon cooling. Measurements of crystallinity and jump in the heat capacity at T_g were used to determine the amount of mobile and rigid amorphous fractions. Overall oxygen solubility was associated with the solubility of mobile and rigid amorphous fractions. The oxygen solubility of the RAF was determined and related to the specific volume of this fraction. The specific volume of the RAF showed a direct correlation with the crystallization temperature. It was shown that upon crystallization from either melt or glassy state, the constrained between crystalline lamellas PET chains consisting of the RAF, vitrify at the crystallization temperature and resemble the glassy behavior despite high temperature. When cooled to room temperature, the RAF preserves a memory about the melt state of polymer, which is uniquely defined by the crystallization temperature.     

Influence of molecular weight on dynamic crossover temperature in linear polymers

Dielectric and light scattering spectra of two linear polymers, polyisoprene (PIP) and polystyrene (PS), were analyzed in broad temperature and frequency range above the glass transition temperature, T_g. The crossover temperature, T_C, was estimated using two approaches: (i) derivative analysis of relaxation times proposed by Stickel and (ii) Mode-Coupling Theory approach. Both estimates provide consistent values. T_C varies with molecular weight (MW) in both polymers, while the ratio T_C/T_g changes significantly with MW in PS only. It appears that the segmental relaxation time at T_C has value τ(T_C) ∼ 10⁻⁷ s for both polymers independent of MW and similar to the value reported for many non-polymeric glass-forming systems. No sign of the dynamic crossover has been observed in the chain relaxation around T_C of the segmental dynamics.     

Segmented copolymers of uniform tetra-amide units and poly(phenylene oxide): 1. Synthesis and thermal-mechanical properties

Copolymers of telechelic poly(2,6-dimethyl-1,4-phenylene ether) segments with terephthalic methyl ester endgroups (PPE-2T), 13 wt% crystallisable tetra-amide segments of uniform length (two-and-a-half repeating unit of nylon-6,T) and dodecanediol (C12) as an extender were made via a polycondensation reaction in the melt. The maximum reaction temperature was 280 °C. The PPE-2T/C12/T6T6T copolymers are semi-crystalline materials with a T_g around 170 °C, a melting temperature of 264-270 °C and a T_g/T_m ratio of above 0.8. The modulus is high up to the T_g, which is not achievable in a blend of PPE and polyamide. The most probable morphology is that of long crystalline nano-ribbons in the amorphous matrix. The materials are slightly transparent and have good solvent resistance, low water absorption and good processability.