Gregory B. McKenna

Effects of confinement on material behaviour at the nanometre size scale

In this article, the effects of size and confinement at the nanometre size scale on both the melting temperature, Tm, and the glass transition temperature, Tg, are reviewed. Although there is an accepted thermodynamic model (the Gibbs–Thomson equation) for explaining the shift in the first-order transition, Tm, for confined materials, the depression of the melting point is still not fully understood and clearly requires further investigation. However, the main thrust of the work is a review of the field of confinement and size effects on the glass transition temperature. We present in detail the dynamic, thermodynamic and pseudo-thermodynamic measurements reported for the glass transition in confined geometries for both small molecules confined in nanopores and for ultrathin polymer films. We survey the observations that show that the glass transition temperature decreases, increases, remains the same or even disappears depending upon details of the experimental (or molecular simulation) conditions. Indeed, different behaviours have been observed for the same material depending on the experimental methods used. It seems that the existing theories of Tg are unable to explain the range of behaviours seen at the nanometre size scale, in part because the glass transition phenomenon itself is not fully understood. Importantly, here we conclude that the vast majority of the experiments have been carried out carefully and the results are reproducible. What is currently lacking appears to be an overall view, which accounts for the range of observations. The field seems to be experimentally and empirically driven rather than responding to major theoretical developments.

The melting behavior of organic materials confined in porous solids

The solid–liquidphase transition temperatures and heats of fusion ΔH f of nonpolar organic solids confined in the pores of controlled pore glasses were measured by differential scanning calorimetry. The pore diameters d were in the range of 40–730 A and the organics studied were cis‐decalin, trans‐decalin, cyclohexane, benzene, chlorobenzene, naphthalene, and heptane. In accordance with previous reports on studies of primarily inorganic materials, the melting point of the pore solidT(d) decreased with decreasing pore diameter. In addition, a large reduction in the bulk enthalpy of fusion ΔH f of the pore solid was measured, which apparently has not been studied in detail by other workers. A linear correlation was found between the melting point depression (ΔT m ) and the reciprocal diameter, as predicted by theories of solidification in a capillary. The calculated values of the solid–liquid interfacial energy σsl were in reasonable agreement with values reported in the literature based on other methods of measurement.

The glass transition of organic liquids confined to small pores

Abstract The glass-transition temperatures, T g , of organic liquids confined to small pores were studied by differential scanning calorimetry (DSC). The T g was measured as a function of pore size in controlled pore glasses (CPG) having pore diameters in the range of 40–730 A. The surface of the glass was treated with hexamethyldisilazane to promote wetting by the organic liquids studied ( o -terphenyl and benzyl alcohol). Glasses formed in the pores had a lower T g than in the bulk and the reduction in T g increased as the pore size decreased. For example, the depression of the glass transition temperature, ΔT g , of benzyl alcohol in 40 A and 85 A pores was 7.2 K and 3.1 K, respectively. The magnitude of ΔT g also depends on the material; e.g. for o -terphenyl in the 85 A pores, ΔT g was 8.8 K versus 3.1 K for benzyl alcohol. In general, it was noted that ΔT g was considerably less than for the depression of the crystalline melting point, ΔT m , studied in related work. For example, for benzyl alcohol in the 85 A pores, ΔT m was ∼ 25 K and ΔT g was ∼ 3 K.

New insights into the fragility dilemma in liquids

A compilation of data for small molecule organic, polymeric, and inorganic glass-forming liquids shows that the original expectation, that there be a positive correlation between the thermodynamic measure of fragility Cpl/Cpg (or Cpl/Cpc) and the dynamic fragility index m, is not generally true. The results are consistent with three classes of behavior: (1) a decrease in m with increasing Cpl/Cpg for the polymeric glass formers; (2) a nearly constant value of m independent of Cpl/Cpc for small molecule organics and hydrogen bonding small molecules; (3) an increasing value of m with increasing Cpl/Cpc for inorganic glass formers as originally considered by Angell.

Arrhenius-type temperature dependence of the segmental relaxation below Tg

In a recent paper DiMarzio and Yang [J. Res. Natl. Inst. Stand. Technol. 102, 135 (1997)] predicted that transport properties such as viscosity and diffusion coefficient do not follow the typical Williams, Landel, and Ferry (WLF) [J. Am. Chem. Soc. 77, 3701 (1955)] or Vogel–Fulcher-type of temperature dependence as the glass transition is approached. Rather, a transition to an Arrhenius-type of temperature dependence is predicted. Here we describe long term aging experiments that explore the temperature dependence of the viscoelastic response of polycarbonate in the vicinity of the glass transition. Aging the material for long times below the nominal glass transition temperature, assures that equilibrium is attained and we can directly test the DiMarzio–Yang prediction. In tests in which glassy samples of polycarbonate were aged into equilibrium at temperatures up to 17 °C below the conventionally measured glass transition temperature, we find that the results are consistent with a transition from Vogel–F...

Modeling the evolution of the dynamic mechanical properties of a commercial epoxy during cure after gelation

ABSTRACT: The cure kinetics for a commercial epoxy have been established and theinfluence of the degree of cure on the glass transition determined. Time-temperatureand time-conversion superposition principles have been built into a model that success-fully predicts the development of the viscoelastic properties of the epoxy during iso-thermal cure from gelation to after vitrification.

Effect of crosslink density on physical ageing of epoxy networks

Abstract Physical ageing of polypropylene oxide/DGEBA networks with different crosslink densities was investigated using the small-strain stress relaxation technique in simple extension. The effects of crosslink density on the glass transition temperature, Tg, and the change in specific heat ΔCp at Tg were measured using a differential scanning calorimeter (d.s.c.) in heating. Although we observed an increase in Tg as crosslink density increased, contrary to other studies of crosslinked polymers, the ΔCp did not change as the crosslink density changed. Ageing was studied at several temperatures below Tg after quenching from above Tg. It was possible to superimpose the stress relaxation curves at different ageing times, temperatures and crosslink densities to form a single master curve, demonstrating the applicability of a time-ageing time-temperature-crosslink density superposition principle to this type of network. Under all ageing conditions, the double logarithmic shift rate was found to decrease with increasing crosslink density while being independent of temperature for a given network. Furthermore, at temperatures of 10 and 5°C below Tg, we were able to age the network glasses into structural equilibrium, thus obtaining t∗ , the time required to reach structural equilibrium. At a constant temperature ΔT below Tg, we observed increases in t∗ as the crosslink density increased.

The physical ageing response of an epoxy glass subjected to large stresses

Physical ageing studies were made using model epoxy network glasses. Non-linear viscoelastic responses were measured after quenching the glasses from above Tg to the temperature of interest. The physical ageing responses at different magnitudes of applied load, for different duration times of the load application and at different temperatures were studied. The creep compliance curves at different ageing times were able to be superimposed to form a single master curve, demonstrating the validity of a time-ageing time superposition principle for this epoxy network. Similar to many other physical ageing studies, we observed that the double-logarithmic shift rate μ decreases as the stress amplitude increases. However, this study differs from others in that the glasses were aged close to Tg and it was possible to age them into structural equilibrium, i.e. the glasses cease to age. Thus, t∗, the time required to reach structural equilibrium, was obtained. Results showed that t∗ did not change with the magnitude of applied stress; therefore, it will be argued that ageing is not ‘erased’ by large mechanical stimuli. Furthermore, the creep response after reaching equilibrium for the glass that had been subjected to the repeated stresses as it aged into equilibrium was compared with that of the same glass that was aged thermally into equilibrium without any stress application. There was no significant difference between the responses in these two conditions. This demonstrates that, in spite of the mechanical stimulus, the response of the glass in the equilibrium state has not changed. All these results support the argument that the volume recovery that occurs during ageing impacts the small-deformation response differently than it does the large-deformation response.

Volume recovery in epoxy glasses subjected to torsional deformations : the question of rejuvenation

Abstract Torsional dilatometry was used to examine the mechanical properties of an epoxy glass during physical ageing, i.e. after a quench from above to slightly below the glass transition temperature. Volume changes in the sample were measured simultaneously with the viscoelastic responses in stress relaxation experiments as functions of the deformation magnitude. The torque relaxation obeys time-ageing time superposition where the shift factor, ate, increases with ageing time until the sample reaches mechanical equilibrium at t∗ ≈ 10 4 s , independent of the magnitude of the strain. In this epoxy, the torsional deformations induce volume expansions which relax on a time-scale similar to those of the torque relaxation. However, the volume recovery responses cannot be superposed at different ageing times by a simple shift along the time axis. Mechanical stimuli only momentarily disrupt the volume evolution following a quench. The underlying volume recovery kinetics, which are much slower than the mechanical torque or volume relaxation, remain unaltered. The facts that t∗ is independent of the magnitude of the strain and that the volume recovery after a quench remains unaltered, in spite of the imposition of mechanical deformations, support the argument that mechanical stimuli neither alter the underlying (non-equilibrium) thermodynamic state of the glass nor erase physical ageing.

Influence of physical ageing on the yield response of model DGEBA/poly (propylene oxide) epoxy glasses

Abstract Cylindrical specimens were prepared from two diglycidyl ether of bisphenol A (DGEBA) amine-terminated poly(propylene oxide) (PPO) networks of different crosslink density and subjected to quenching and isothermal ageing treatments at different temperatures and ageing times of between 0.1 and 1000 h. The changes in the structure of the glasses during the ageing towards equilibrium was subsequently assessed by measurement of the yield stress in uniaxial compression at the same temperature as the ageing. It was found that for both resins, the yield stress increases by as much as 1.8 times over the range of ageing times investigated. It was found for each system that the evolution of the yield stress virtually ceases after a critical ageing time t∗ which increases as temperature decreases. Also, it was observed that the lower yield stress corresponding to the onset of generalized plastic flow exhibits only a very small increase with the ageing time. From the influence of temperature and strain rate on the above phenomena, the kinetics of physical ageing were examined quantitatively in terms of the time-ageing time-temperature equivalence principle. The results suggest that the increase in yield stress on ageing is correlated to volume recovery and to the induced increase of the relaxation times as the polymeric glass evolves towards its equilibrium state.