Sensitivity Optimization in Continuous-Flow FTNMR

Abstract

Equations simulating the steady-state magnetization of liquids in continuous-flow FTNMR are derived using a classical vector model, assuming plug flow. These equations are applied to calculation of (S/N)t, the relative signal/noise per unit time of any nucleus undergoing any degree of Overhauser enhancement either in the detection cell or upstream, or both, and to optimization of experimental conditions, including pulse repetition timeTrep, pulse angle β, and flow rate. Ideal parameters include a pulse angle of 90° and aTrepvalue equal to sample residence time in the NMR detection cell. Optimal flow rates are directly proportional to the premagnetization volume (the portion of sample equilibrated with the magnetic field prior to detection) and inversely proportional to spin–lattice relaxation timesT1. Optimal premagnetization times are smaller than previously assumed, varying from about 1.1 to 1.9T1values. (S/N)tfor static FTNMR is discussed in some detail, and a new graphical method is presented for its optimization. Flow advantage, the (S/N)tof optimized flow FTNMR experiments compared to that of static FTNMR in a given detection cell, is proportional to the square root of the ratio of premagnetization to detection cell volumes, and virtually independent of[formula]where[formula]is the apparent transverse-relaxation time. The theory is applied to examples from recent literature, including dynamic electron–nuclear polarization, and the literature is critically reviewed. The analysis shows that claims by previous authors of recycled flow FTNMR by itself leading to increased (S/N)tfor slowly relaxing resonances are misleading, owing to underdetermination of (S/N)tin static measurements and failure to account for greater sample sizes required in flow experiments. For monitoring and control of chemical processes, the theory presented here enables the first rational basis for the design of a flow FTNMR apparatus and for the selection of acquisition parameters.