Ultrafast temperature jump in polymers: Phonons and vibrations heat up at different rates

Optical calorimetry is used to study the dynamics of a polymer, poly-(methyl methylacrylate), (PMMA), subjected to a temperature jump which is faster than the time required for Boltzmann equilibrium. The temperature jump is produced by exciting a near-infrared dye embedded in the polymer with a 23 ps duration optical pulse. The magnitude of the temperature jump ΔT was as large as 125 degrees. To attain such a large temperature jump with good spatial uniformity requires optical heating pulses which strongly saturate the heater dye absorption. A formalism is developed to quantitatively treat optical heating with saturation. The heat capacity of the polymer, C_pol, can be determined to an accuracy of 8% using this method. The temperature jump data could not be fit by assuming the polymer heats up in a single stage. A quasitemperature model with two-stage heating, where the dye first excites polymer phonons and then the phonons excite polymer vibrations by multiphonon up pumping, gave quantitative agreement. The data at several values of ΔT were simultaneously fit using three adjustable parameters: κ_vc, the molecular thermal conductivity for vibrational cooling of the heater dye; κ_up, the molecular thermal conductivity for multiphonon up pumping; and C_pol. The value of κ_vc was the same magnitude as k_th, the thermal conductivity of the polymer, despite the fact that the vibrational cooling process occurs on the 1 nm length scale. The value of κ_up was 2 orders of magnitude smaller than κ_th.