On the gas dependence of thermal transpiration and a critical appraisal of correction methods for capacitive diaphragm gauges

TL;DR

This paper investigates thermal transpiration effects in low pressure measurements with capacitance diaphragm gauges, proposing a simple calibration method and evaluating correction models, emphasizing the importance of gas viscosity and molecular speed over molecular size.

Contribution

It introduces a straightforward calibration approach and compares correction models, demonstrating the universal scaling of characteristic pressures based on gas viscosity and thermal speed, challenging existing formulas.

Findings

Characteristic pressures scale with gas viscosity and thermal speed.

Current correction formulas based on molecular size are unphysical.

Recommended correction schemes depend on the Knudsen number.

Abstract

Thermal transpiration effects are commonly encountered in low pressure measurements with capacitance diaphragm gauges. They arise from the temperature difference between the measurement volume and the temperature stabilised manometer. Several approaches have been proposed to correct for the pressure difference, but surface and geometric effects usually require that the correction is determined for each gas type and gauge individually. Common (semi) empirical corrections are based on studies of atoms or small molecules. We present a simple calibration method for diaphragm gauges and compare transpiration corrections for argon and styrene at pressures above 1 Pa. We find that characteristic pressures at which the pressure difference reaches half its maximum value, are compatible with the universal scaling p_{1/2} = 2 \{\eta} \cdot \{v_{th}} / d, thus essentially depending on gas viscosity \eta, thermal molecular speed v_{th} and gauge tubing diameter d. This contradicts current recommendations based on the Takaishi and Sensui formula, which show an unphysical scaling with molecular size. Our results support the Miller or \v{S}etina equations where the pressure dependency is basically determined by the Knudsen number. The use of these two schemes is therefore recommended, especially when thermal transpiration has to be predicted for new molecules. Implications for investigations on large polyatomics are discussed.