# Ultrahigh-Strain-Rate Mechanical Properties of Polystyrene near the Glass Transition Temperature
## 1 Introduction  
Amorphous polymers exhibit a continuous transition in their mechanical behaviors near their glass transition temperatures (\(T_{\text{g}}\)), at which their molecular mobility becomes exponentially altered without phase transition. Below \(T_{\text{g}}\), the configurational rearrangement of polymer chains occurs substantially slowly, resulting in elastic and brittle characteristics (the glassy state). In contrast, above \(T_{\text{g}}\), the increased molecular mobility renders extensive plasticity (the rubbery state). Consequently, the temperature-sensitive configurational rearrangement rate causes a second-order transition in their free volume [1]. Although the typical conditions are where the free volume is thermodynamically determined [2; 3; 4], polymers can also be subjected to extreme mechanical conditions, where the free volume can be altered on a short time scale to that of the molecular reconfiguration time scale (ns-\(\upmu\)s). Consequently, the shot-time-scale modification of the free volume can result in mechanical properties that deviate considerably from conventional expectations. Thesetime-scale-dependent extraordinary behaviors of polymers have gained increasing importance with the recent progress in additive manufacturing (AM), where the AM process inherently requires the rapid volumetric consolidation of small mass elements [5]. For example, cold spray, a subclass of additive manufacturing, utilizes a supersonic stream of feedstock powder or microparticles (\(\upmu\)Ps). The CS process uses pressurized gas to accelerate the desired \(\upmu\)Ps to high velocities through a de Laval converging-diverging nozzle. When the high-velocity gas stream containing these \(\upmu\)Ps is directed toward a stationary target substrate, the impacting \(\upmu\)Ps undergo severe plastic deformations and deposit to form a uniform, non-porous coating [6; 7; 8]. Consequently, as heating-free and solvent-free AM can be realized for polymers using the CS approach, understanding polymers' extreme behaviors is more critical than ever [9; 10; 11]. Since its inception as a material coating technique, CS has been used in various industries to spray various feedstock powders, including metals, composites, ceramics, and polymers [7; 12]. The bond between the deposited \(\upmu\)Ps and the substrate during this high-velocity collision event can be metallurgical, chemical, and/or mechanical [6]. CS has been extensively studied for metallic powder particles sprayed onto metallic surfaces, reaching deposition efficiencies near 99%, but studies on the CS of polymer powder have been sparse [13]. The inherent differences between polymers and metals, such as the size of molecules, transition temperatures, degree of crystallinity, primary bond availability, and thermal conductivity, result in drastically different behavior for polymeric powders from metallic powders during the CS process [14]. [PERSON] and [PERSON] studied the CS deposition of polyolefin powder on polyethylene and aluminum substrates. Through their CS study elevating temperature above the melting temperatures of feedstock polymer microparticles (\(\sim\)110 \({}^{\circ}\)C), the formation of a layer of polymer melt formed on the substrate surface aided in the CS deposition of the polyolefin \(\upmu\)Ps [15]. [PERSON] et al. studied the CS feasibility of thermoplastic polymers (nylon-6 microparticles) on fiber-reinforced plastics. A deposition efficiency above 30% was demonstrated without damaging the substrates [16]. In the authors' extended research studying the effects of CS operating temperature and gas pressure, the CS operating temperature from 150 \({}^{\circ}\)C to 175 \({}^{\circ}\)C significantly improved nylon-6 deposition due to the concurrent extreme plastic deformation of impacting microparticles and the epoxy polymer matrix substrate [10]. [PERSON] et al. studied the CS deposition of high-density polyethylene (HDPE) on various polymer substrates to develop a deposition window for the polymer powder-substrate pair [14]. [PERSON] et al.