Design of high pressure differential volumetric adsorption measurements with increased accuracy

High pressure adsorption measurements for light gases on volumetric equipment are prone to error. Differential units reduce the sensitivity to leakage, gas compressibility, and temperature gradients, but remain highly sensitive to volume uncertainties, the calibration of which is difficult in the presence of low-density, microporous samples. Calibration error can be reduced using a high initial pressure differential and large calibration volume; however, systematic error is prevalent in the literature. Using both analytical and multivariate error analysis, we demonstrate that calibration of the differential unit with the differential pressure transducer significantly decreases volume sensitivity. We show that hydrogen adsorption to GX-31 superactivated carbon at 298 K and 80 bar can be measured with a 7 % error in measurement (i.e. within 0.05 wt% for a 100 mg sample), even when experimental volume calibration is determined only within similar to 1 %. This represents approximately a 2-7 fold increase in sensitivity relative to previous reports using differential measurements. We also provide a framework for optimizing the design of a volumetric adsorption unit. For virtually any system design, the improved differential methods offer a significant increase in precision relative to the conventional volumetric measurement (from 10- to over 250-fold, depending on the precision of the pressure transducer). This improvement further enhances advantages of the differential unit, in addition to advantages that arise for treating gas compressibility and temperature fluctuations.