How stress imparts mobility to glasses is an ongoing subject of debate in soft matter. Many experiments and simulations have shown that stress or strain applied to polymers, colloids, granular materials, etc. in the glassy state leads to enhanced mobility. In some cases, such deformation can even appear to erase past physical aging as if “rejuvenating” the glass. How deformation imparts mobility to glasses is a process often described by an potential energy landscape ‘tilting’ mechanism, where the applied stress is thought to reduce energy barriers, allowing the system to transition to a higher energy state.
Upon vitrification (e.g., glass formation by a temperature quench), the material transitions from an equilibrium liquid to a non-equilibrium glass at the glass transition temperature T_g. Structural relaxation of the non-equilibrium glassy state leads to a decrease in free volume of the material over logarithmic time scales. The stability of the glassy state is quantified by measuring the physical aging rate β, characterizing this decrease in volume with logarithmic time.
Although these volume contractions are minuscule (<1%), the resulting property changes termed physical aging (e.g., changes in mechanical properties and failure modes in particular) can be substantial and often adverse. As an example, the permeability of gas-separation membranes is exceedingly sensitive to the free volume in the polymer gas-sieving layer. Decreases in permeability of nearly 50% have been observed as a result of physical aging.
Importance of Quench Conditions on the Subsequent Physical Aging Rate of Glassy Polymer Films
Laura A. G. Gray, Suk W. Yoon, William A. Pahner, James E. Davidheiser, and Connie B. Roth, Macromolecules 2012, 45, 1701-1709.
Dating back to the mid-1990s, the gas separation membranes community have reported anomalous “accelerated” (faster) physical aging of free-standing polymer films with decreasing film thickness for a range of different polymers. What was surprising was that these deviations in the aging rate from bulk behavior began at enormous film thicknesses of several microns, much larger than the ~100 nm thicknesses where most thin film interfacial effects occur.
Using a streamlined ellipsometry technique we developed to measure the physical aging rate of polymer films, we have systematically addressed various possible causes of this phenomenon from differences in molecular structure, quench depth below T_g, experimental technique, sample preparation, and stresses on the film. We demonstrated that the physical aging rate of the material is strongly dependent on conditions during the formation of the glassy state. Although supported films do not display any film thickness dependence to their aging rate at this large micron length scale, films quenched in a free-standing state exhibit a strong thickness dependence. We suggested that differing quench conditions may impose unintended stresses trapping the glassy films into different states (potential energy minima), dictating the subsequent physical aging rate. We then followed this up with studies that demonstrated this correlation conclusively by vitrifying films under different controlled stress conditions.
Physical Aging of Polymer Films Quenched and Measured Free-Standing via Ellipsometry: Controlling Stress Imparted by Thermal Expansion Mismatch between Film and Support
Justin E. Pye and Connie B. Roth,
Macromolecules 2013, 46, 9455-9463.
We have demonstrated that stress effects on cooling can lead to changes in physical aging rate β even when the stress imparted arises inherently from how the film is supported. By cooling films on different holders, we conclusively demonstrated that stress imparted during vitrification caused by thermal expansion mismatch Δα between the film and sample support was controlling the subsequent physical aging rate β of the film.
The stress imparted to the free-standing polystyrene (PS) films on cooling when supported on rigid frames of different materials can be directly quantified by calculating the thermal expansion mismatch Δα between the film and rigid frame. This stress is independent of film thickness, but depends on the thermal expansion mismatch between the film and rigid frame. We demonstrated that the physical aging rate is independent of film thickness, but correlates with the difference in thermal expansion between the PS film and frame material, and hence the stress imparted to the film on cooling.
Stability of Polymer Glasses Vitrified Under Stress
Laura A. G. Gray and Connie B. Roth,
Soft Matter 2014, 10, 1572-1578.
In addition, we designed a simple jig that allowed us to apply a known stress to a free-standing polymer film during vitrification in order to quantify how the physical aging rate β changes with increasing stress. This enabled us to investigate the impact of applying different stresses during vitrification, i.e., formation of a glass during thermal cooling, on the subsequent physical aging. We found that the subsequent stability of the glassy system is affected by the stress applied on cooling, even after the stress has been removed. The data showed an initial plateau in aging rate at low stresses that quickly transitions to a much higher aging rate at high stresses. Above a minimum threshold in stress, the aging rate appeared to plateau at a higher value indicative of a less stable glass. These effects could be understood in terms of the potential energy landscape (PEL) ‘tilting’ mechanisms from theoretical efforts in the field. We proposed that a glassy system formed under high stress is left trapped in a higher, shallower energy minimum with a corresponding faster physical aging rate.