When discussing the reproducibility of measurement results in general, what is known as the “reproducibility conditions” must always be taken into account. Measuring exactly the same specimen several times with exactly the same measuring device is usually not considered to be a reproducibility test, but a repeatability test. In order to draw conclusions about the reproducibility, one requires – at a minimum – measurements of multiple specimens of the same type and additionally, if possible, measurements using different devices. Such a reproducibility study is described in the following (download this article as pdf).
NETZSCH-Gerätebau GmbH has recently qualified its own factory standard for calibration and validation of heat flow meter (HFM) instruments in the temperature range between 8°C and 40°C: NETZSCH EPS which is made of expanded polystyrene (see figure 1). Numerous NETZSCH EPS specimens with the dimensions 600 mm x 600 mm x 25 mm, 300 mm x 300 mm x 25 mm and 200 mm x 200 mm x 25 mm were investigated using five different NETZSCH Heat Flow Meter devices of the HFM 446 type (one HFM 446 Large, two HFM 446 Medium and two HFM 446 Small instruments). The NETZSCH EPS specimens had mean densities in the range 24.5 to 28 kg/m³. The HFM measurements were carried out at mean temperatures of 8°C, 16°C, 24°C, 32°C and 40°C using a temperature gradient of 20 K and a load of 2 kPa. In order to calibrate the HFM devices, three different, certified reference samples (one specimen 600 mm x 600 mm x 25 mm, one specimen 300 mm x 300 mm x 25 mm and one specimen 200 mm x 200 mm x 25 mm) of the NIST SRM 1450d type were used, which are fiber boards.
Fig. 1: Photo of a 300 mm x 300 mm x 25 mm NETZSCH EPS specimen.
Figure 2 shows the thermal conductivity values of 30 different NETZSCH EPS specimens:
- 10 specimens of the size 600 mm x 600 mm x 25 mm were measured with an HFM 446 Large
- 10 specimens of the size 300 mm x 300 mm x 25 mm were measured with an HFM 446 Medium
- 10 specimens of the size 200 mm x 200 mm x 25 mm were measured with an HFM 446 Small
Fig. 2: Temperature- and density-dependent thermal conductivity of 30 different NETZSCH EPS specimens.
These measurements resulted in three main observations: Firstly, the thermal conductivity values are higher for higher mean sample temperatures; this finding was, of course, expected. Secondly, the thermal conductivity values do not depend – within about ±0.5% standard deviation – on the specimen size or measuring device, which demonstrates a reproducibility of the results of about ±0.5%. Thirdly, the relatively low scatter of the data even allows for identification and quantification of a slight dependence of the thermal conductivity on the density of the specimens. The lower thermal conductivity at higher density is a known property of such EPS materials; it can be explained by the fact that less radiation is contributed to the thermal conductivity .
Based on data such as shown in figure 2, the mean thermal conductivity of NETZSCH EPS can be described as a function of two parameters, the mean sample temperature and density. This allows for calculating the “nominal” thermal conductivity for each individual specimen in future measurements. Figure 3 displays the temperature-dependent part which exhibits the typical linear behavior.
Fig. 3: Mean thermal conductivity of NETZSCH EPS for a density of 26 kg/m³ as a function of temperature.
Another reproducibility test is depicted in figure 4. Over a period of about 2 to 3 weeks, 100 different NETZSCH EPS specimens of the size 300 mm x 300 mm x 25 mm were measured with the same HFM 446 Medium device at a mean sample temperature of 40°C. The calibration of the HFM was validated from time to time using the same specimen of NIST SRM 1450d with which the device had originally been calibrated. The thermal conductivity values obtained are compared with the nominal values, which refer to the the certified reference value at 40°C in case of NIST SRM 1450d, and the expected density-dependent value at 40°C (see above) in case of NETZSCH EPS. The thermal conductivity values for NETZSCH EPS shown in figure 4 are within ±0.5% in agreement with the nominal values – in particular, if the individual sample density is taken intoconsideration, because this clearly reduces the standard deviation. These results again demonstrate the excellent reproducibility of measurements carried out with the NETZSCH HFM 446 in general – and furthermore confirm a correct and representative description of the thermal conductivity values of NETZSCH EPS.
Fig. 4: Relative deviation of the thermal conductivity λ from nominal values of 100 different NETZSCH EPS specimens of the size 300 mm x 300 mm x 25 mm measured with the same HFM 446 Medium device at 40°C mean sample temperature. In case of the solid green full symbols, the density for each individual NETZSCH EPS specimen was considered for calculating its nominal λ value, whereas a constant density of 26 kg/m³ was assumed for all specimens in case of the green outline symbols. The black triangles reflect calibration checks done with a NIST SRM 1450d specimen.
Regarding the qualification of NETZSCH EPS, it should be noted that the thermal conductivity values determined via HFM measurements were reproduced for an exemplary pair of 300x300x25 mm samples using two different Guarded Hot Plates devices – one of the NETZSCH GHP 456 type and another of the NETZSCH GHP 456 HT type – with an absolute accuracy of about ±1.5%. Furthermore, two exemplary 500 mm x 500 mm x 25 mm EPS samples were investigated at the FIW Munich institute, D-82166 Gräfelfing, Germany, also using HFM and GHP instruments; the results were in agreement with the thermal conductivity values obtained by NETZSCH within about ±1.0 (GHP) / ±0.5% (HFM). In addition, an investigation was conducted regarding the long-term stability of the NETZSCH EPS thermal conductivity values; over the course of several dozens of HFM and GHP measurements at 40°C, no significant change in thermal conductivity was observed.
A total of more than 300 different NETZSCH EPS specimens of the sizes 600 mm x 600 mm x 25 mm, 300 mm x 300 mm x 25 mm and 200 mm x 200 mm x 25 mm were measured with five different NETZSCH heat flow meter devices of the types HFM 446 Large, HFM 446 Medium and HFM 446 446 Small. These HFM devices were calibrated using three different, certified reference samples of the type NIST SRM 1450d. Measurements were carried out in the temperature range between 8°C and 40°C. Reproducibility of the thermal conductivity values was observed at about ±0.5%, thus fulfilling the requirements set forth by HFM standards [2, 3]. These results allowed for the qualification of NETZSCH EPS as a new standard material for calibration and validation of HFM instruments.
 J. Schellenberg and M. Wallis, Dependence of Thermal Properties of Expandable Polystyrene Particle Foam on Cell Size and Density, Journal of Cellular Plastics, Volume 46, 2010, p.209-222.
 ASTM C518: Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus.
 ISO 8301: Thermal Insulation – Determination of steady-state thermal resistance and related properties – Heat flow meter apparatus.
Dr. Alexander Schindler has worked in the fields of experimental physics, thermal analysis and thermophysical properties for over 20 years. At NETZSCH, he has been employed in the Applications Laboratory as well in the Hardware and Software Development. He is a known expert in thermal characterization methods and applications.