Polymer glasses are one of the most widely used commercial and engineering materials today. Their unique properties, particularly their toughness, allow them to be used in many aspects of our everyday life. Understanding why these seemingly solid materials can yield and flow (see Figure 1) upon the application of stress (rather than break!) has been the main goal of our research. The Eyring model, proposed 70 years ago, has been used to attempt to understand how the energy barriers for molecular motion are lowered as a result of stress. From this perspective, the polymer glass is transformed into a very viscous liquid during the deformation. Many modeling efforts use this theory as a basis, yet they are unable to capture all of the behavior of the polymer glass during deformation. With the knowledge of the molecular motion during deformation, we have the information needed to help modeling efforts more accurately predict polymer behavior during different deformation protocols.
Figure 1. Deformed polycarbonate pieces. Polycarbonate is unique because it is remains ductile down to room temperature (100 K below Tg!). Deformation increases the segmental mobility thereby allowing the polycarbonate to flow into the deformed shape.
Figure 2. Cross-section schematic of our deformation apparatus. Using the linear actuator and the load cell, we can accomplish many different types of tensile deformation and relaxation experiments.
A photobleaching method using a confocal fluorescence microscope selectively creates an anisotropic distribution of dye molecules (about 10 ppm) in our sample. Allowing the reorientation of the unbleached dye molecules causes the regeneration of an isotropic distribution. The time dependent anisotropy decay can be measured using the fluorescence from a weak circularly polarized beam and with this information we calculate the rotational correlation function and the rotational correlation time (mobility). In creep deformations with conditions of 16 MPa and Tg-16 K, we see a hundred-fold enhancement of mobility occurring in polystyrene samples lightly cross-linked with 2 and 4 weight percent of divinylbenzene. Quantitatively greater mobility enhancement has been seen in lightly cross-linked poly(methyl methacrylate).
Figures 2 and 3 show the deformation apparatus that we use in our experiments. A thin polymer sample (containing a small concentration of dye molecules) is deformed in tension. The deformation apparatus sits atop a fluorescence microscope. We use photobleaching with linearly polarized light to selectively create an anisotropic distribution of dye molecules in our sample – see Figure 4. The reorientation of the unbleached dye molecules causes the regeneration of an isotropic distribution. The time dependent anisotropy decay can be measured using the fluorescence from a weak circularly polarized beam and with this information we calculate the rotational correlation function and the rotational correlation time (mobility).
Figure 5 shows creep deformation experiments on lightly cross-linked PMMA. During this experiment, mobility increased by more than a factor of 1000!
In other experiments, creep deformation on polystyrene samples lightly cross-linked with 2 and 4 weight percent of divinylbenzene (16 MPa at Tg-16 K), we see a hundred-fold enhancement of mobility. During the recovery portion of the deformation, all three systems show a mobility enhancement as the initial response. Data from all three systems can be plotted on a master plot of the mobility as a function of the local strain rate during creep. Additionally, in the flow regime we see a significant narrowing of the distribution of relaxation times for both the polystyrene and poly(methyl methacrylate) glasses. Because polystyrene lacks the prominent beta relaxation of poly(methyl methacrylate), we conclude that the changes in mobility during creep deformation are a result of changes in the alpha segmental relaxation time.
Our group has also developed an apparatus for increasing the scope of the types of deformations we can perform while observing molecular mobility – see Figure 2. Constant strain rate experiments show an increase of mobility (up to a factor of 160) as yield is approached and then constant mobility after yield. The experiments closely parallel the mobility seen in simulations done by Riggleman et al.
The mobility increases a factor of 500 times up until the softening regime after yield then remains constant during the continued constant strain rate experiment. In contrast to the constant engineering stress experiments above, the stress is increasing (as a result of strain-hardening) yet the mobility remains constant after yield. Stress relaxation experiments have been completed and have shown that the mobility approaches that of the undeformed aged sample. This increased flexibility in our experimental apparatus allows us to probe additional molecular factors of polymer glasses during deformation.
Figure 4. Schematic of the dye reorientation measurement. Initially the dye is randomly oriented (isotropic). A high intensity polarized bleaching beam bleaches the dyes in a particular orientation creating an anisotropic distribution (more horizontal transition dipoles in this schematic). Then we probe the fluorescence of the dyes using a weak, circularly polarized beam. The intensities perpendicular and parallel to the direction of the bleaching beam are measured. This allows us to observe the decay of the anisotropy during the experiment.
Figure 5. Simultaneous local measurements of strain and mobility in PMMA glass. (A) Strain during creep experiments at 375.7 K with an engineering stress of 16.0 MPa, followed by recovery. The initial and final shapes of the sample are shown. (B) Normalized anisotropy decays obtained during the creep experiment at times indicated by letters a to f. As the strain rate increased, higher mobility (faster anisotropy decay) was observed. The solid lines are KWW fits to the data. (C) Mobility shift factor during creep and recovery. Mobility increased by up to a factor of 1000. The solid lines are guides to the eye. (D) Correlation between the KWW b parameter and mobility for three different trials with stresses in the range of 15.5 to 16.0 MPa. Data were acquired as the mobility was both increasing (●) and decreasing (▾). The solid line is a fit to the data. Figure from Lee, H., & Paeng, K. (2009). Direct Measurement of Molecular Mobility in Actively Deformed Polymer Glasses. Science, 231(November), 1713–1727. doi:10.1126/science.1165995