# Ultrahigh-Strain-Rate Mechanical Properties of Polystyrene near the Glass Transition Temperature
## 3 Results and Discussion  
As reference data for angled LIPIT, the PS \(\upmu\)Ps were perpendicularly impacted on a silicon wafer target substrate having a native oxide layer with controlled velocities of \(200\pm 25\) m/s while \(T_{\text{exp}}\) was systematically varied from room temperature to 130 \({}^{\circ}\)C. A minimum of five impact events were performed at each temperature. The \(CoR\) was measured from the perpendicular impact experiments to demonstrate the typical UHSR behavior of the PS \(\upmu\)Ps (Figure 3). The error bars represent the standard deviation of \(CoR\) values measured at respective temperatures. A common source of these errors was the error in \(v_{i}\) (\(\pm 25\) m/s); however, additional fluctuation arose from the unstable interfacial dynamics of PS \(\upmu\)Ps with the substrate during the rebound stage [22]. Therefore, the trend in the error bars can provide valuable insight into understanding the UHSR characteristics of PS. Generally, the mean \(CoR\) displayed negative slopes as the temperature increased. This decreasing trend can be understood as the higher energy loss at impact due to the increased plasticity of the PS particles resulting from the softening of the \(\upmu\)Ps at elevated temperatures. The high rigidity of the silicon substrate resulted in more pronounced plastic deformation, as the plastic deformation was confined within the PS \(\upmu\)Ps. This led to a lower \(CoR\) trend compared to the more compliant polymeric substrate [22]. Below \(T_{\text{g}}\), \(CoR\) was linearly decreased at the rate of \(-6.1\times 10^{-4}\) according to the linear fitting of the \(CoR\) values from the four lowest temperatures. At the lower edge of \(T_{g}\), \(CoR\) started to decrease with a five times higher rate of \(-3.4\times 10^{-3}\). The larger reduction was attributed to the accelerated molecular motion of PS chains in the rubbery state that shortened the average time of polymer chains escaping from the local configuration traps. Although the representative strain rate estimated by \(\dot{\epsilon}\equiv\frac{v_{i}}{D_{p}}\) was extraordinarily high (\(4.7\times 10^{6}\) s\({}^{-1}\)), the bilinear \(CoR\) trend showed that the \(T_{g}\) defined from the first heating cycle under the static condition still can serve as a valid reference temperature predicting the plasticity of PS. Itshould be noted that the represented strain rate is an approximate estimate, intended to reflect the order of the actual strain rates, which may vary localized strain variations. As the perpendicular collision geometry primarily produces the volumetric deformation driven primarily by compressive stresses, the 45-deg tilted LIPIT was performed to elucidate the shear-dominant and interfacial deformation characteristics. Three representative collision regimes were conceived to exhibit the low-, intermediate-, and high-\(\upsilon_{1}\) cases based on the previous LIPIT study using 83 kDa PS uPs, which showed the onset of a rheological transition around 400 m/s [26]. These three velocities were chosen to capture the characteristic responses below and above the activation threshold for interfacial rheological dynamics. Figure 4 shows the spectra of \(CoR_{n}\) and \(CoR_{t}\), defined by Equations (2) and (3). Compared to \(CoR\) in Figure 3, \(CoR_{n}\) (Figure 4a) was greater than the \(CoR\) under the angled impact of 200 m/s, which could be attributed to the slower normal impact velocity, \(v_{i,n}\simeq 0.7v_{i}\). Notably, \(CoR_{n}\) exhibited a transition near 60 \({}^{\circ}\)C, significantly lower than that observed in \(CoR\) under the perpendicular impact of 200 m/s. This transition of \(CoR_{n}\) was also observed from the previous 45-degree impact study of PS uPs (\(D_{\text{p}}\sim\) 14.4 \(\upmu\)m) at room temperature [26]. Thus, this inelastic deformation mechanism could be promoted through crazing at a temperature substantially lower than \(T_{\text{g}}\).