  The hot disk transient plane source (TPS) method is a widely used standard
technique (ISO 22007-2) for the characterization of thermal properties of
materials, especially the thermal conductivity, k. Despite its well-established
reliability for a wide variety of common materials, the hot disk TPS method is
also known to suffer from a substantial systematic errors when applied to low-k
thermal insulation materials. Here, we present a combined numerical and
experimental study on the influence of the geometry of hot disk sensor on
measured value of low-k materials. We demonstrate that the error is strongly
affected by the finite thickness and thermal mass of the sensor's insulation
layer was well as the corresponding increase of the effective heater size
beyond the radius of the embedded metal heater itself. We also numerically
investigate the dependence of the error on the sample thermal properties,
confirming that the errors are worse in low-k samples. A simple correction
function is also provided, which converts the apparent (erroneous) result from
a standard hot disk TPS measurement to a more accurate value. A standard
polyimide sensor was also optimized using both wet and dry etching to provide
more accurate measurement directly. Experimentally corrected value of k for
Airloy x56 aerogel and a commercial silica aerogel using the numerical
correction factor derived based on the standard TPS sensor is in excellent
agreement with the directly measured value from the TPS sensor using the
optimized polyimide sensor. Both of these methods can reduce the errors to less
than 4% as compared to around 40% error of overestimation from raw values
measured with the pristine sensor. Such results show that both the numerical
correction to a pristine senor or an optimized sensor are capable of providing
highly accurate value of thermal conductivity for such materials.
