Reply on CC1

Abstract

<strong class="journal-contentHeaderColor">Abstract.</strong> Monitoring the build-up or decay of hyperpolarization in nuclear magnetic resonance requires radio-frequency (RF) pulses to generate observable nuclear magnetization. However, the pulses also lead to a depletion of the polarization and, thus, alter the spin dynamics. To simulate the effects of RF pulses on the polarization build-up and decay, we propose a first-order rate-equation model describing the dynamics of the hyperpolarization process through a single source and a relaxation term. The model offers a direct interpretation of the measured steady-state polarization and build-up time constant. Furthermore, the rate-equation model is used to study three different methods to correct for the errors introduced by RF pulses: (i) a 1/ cos^<em>n</em> &theta; correction, which is only applicable to decays, (ii) an analytic formula to correct for the build-up and decay times and (iii) a newly proposed iterative, self-consistent correction. The corrections are first tested in low signal-to-noise ratio (SNR) simulations (SNR around 40 for 2.5&deg; pulses), predicting accurate results (&plusmn;10 % error) up to 25&deg; pulses. The correction methods are then tested on experimental data obtained with dynamic nuclear polarization (DNP) using 4-oxo-TEMPO in ¹H glassy matrices, resulting in high SNR acquisitions (around 1000 for 2.4&deg; pulses). It is experimentally demonstrated that the rate-equation model allows to obtain build-up times and steady-state polarization (enhancement) even for large RF flip angles (25&deg;) during build-up yielding results within &plusmn;10 % error when compared to data acquired with small RF flip angles (&lt; 3&deg;). For decay experiments, corrections are shown to be accurate for up to 12&deg; RF flip angles with discrepancies to the simulations attributed to the low experimental acquisition SNR. In conclusion, corrections based on a rate-equation description offer fast and accurate estimations of achievable polarization levels and build-up time constants in hyperpolarization experiments for a wide range of samples.