# Temperature Estimation during Pulsed Laser Sintering of Silver Nanoparticles
## 1 Introduction
Constant thermal conductivity of bulk Ag (429 W/m\(\cdot\)K) was adopted in the study for the Ag NPs [25]. The calculations in the study suggested that the melting temperature of about 50 nm Ag NPs was 440 \({}^{\circ}\)C. [PERSON] et al. studied the thermal effects of a nanosecond pulsed laser sintering using a constant thermal conductivity of 140 W/(m\(\cdot\)K) for the Ag NPs ink. They studied a case with a maximum of 10 laser pulses and discussed the accumulative thermal effects on the underlying polyethylene napthalate (PEN) substrate [24]. More recently, lateral and longitudinal thermal diffusion within the copper NPs layer were elaborated during nanosecond pulsed laser sintering at different laser scanning speeds [26]. These studies considered constant thermal conductivities instead of using temperature-dependent thermal conductivity relations [26]. [PERSON] et al. examined the pulse shaping effect on the heat transfer process during microsecond pulsed laser sintering of Ag NPs (50 nm) [20]. In their numerical model, to address the change in the material properties during the pulse excitation and relaxation periods of pulsed laser operation they considered a solid-liquid phase transition for the metal NPs at an estimated phase change temperature of 255 \({}^{\circ}\)C to simulate the real-time sintering effects. However, the melting behavior of Ag NPs (5-50 nm) has been known to be close to bulk Ag melting temperatures in multiple studies [10; 27; 28; 29; 30]. Nanoparticles tend to coalesce in an attempt to reduce their surface energy and the coalescence happen at low temperatures via solid state diffusion process. Due to the thermodynamic size effect, metal nanoparticles exhibit large melting point depression [29], e.g., 2 nm-sized nanoparticles are reported to melt at around 130-140 \({}^{\circ}\)C [31]. Therefore, all these limitations need to be addressed with a novel numerical model to accurately estimate the scanning pulsed laser sintering process while considering the pulsed excitation and relaxation periods with temperature-dependent thermal conductivity of Ag NPs. In this work, we developed a numerical model that can precisely monitor the temperature field by regulating the temperature-dependent material properties (thermal conductivity and reflectivity) during the pulsed laser sintering. During a scanning pulsed laser operation each pulse induces maximum temperature within the pulse-excited location and subsequently this heating sinters the NPs. Hence maximum thermal conductivity is induced at each location where the laser pulse is incident as the NPs get sintered. Based on our developed algorithm, the attained maximum thermal conductivity value does not decrease with the decrease in the temperature during the pulse relaxation period. Subsequently, the attained maximum thermal conductivity of the sintered NPs by a previous pulse acts as an initial condition for the laser pulse to follow. In this way, a real-time sintering process distinguishing between the sintered and unsintered NPs is simulated providing an improvement in the temperature field estimation. The presented temperature estimation method overcomes the limitations of the reported methods so far.