Foam Planck

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We want the foam to absorb as much of the mid-IR energy as possible to reduce the radiative fraction of overall thermal conductivity (see Foam-Conductivity). Why mid-IR? Because at temperatures normal for thermal insulation the Planck equation tells us that that's where the thermal energy is. At each wavelength λ we need to know the Spectral Radiance, L at temperature T (in Kelvin) using Planck's constant, h, Boltzmann's constant k, the speed of light c and the frequency of the radiation ν:

`L=(2hc^2)/(λ^5(e^((hν)/(kT))-1))`

We then need to know the absorption A of the foam material at these wavelengths. This is known from the standard FT-IR spectrum of CB (Carbon Black), PE (Polyethylene), PS (Polystyrene), PU (Polyurethane) and Silica. Confusingly we tend to plot the Planck graph in terms of wavelength μm and the FT-IR spectrum in terms of cm^-1, very often from high to low (an option you can choose) rather than the more conventional graph of low to high.

The app plots the graphs for both the μm and cm^-1 conventions. The FT-IR plots are stylised in this version but will use proper spectra when the datasets become available. Each is normalized to 1 as we are interested in getting a feel for the relative merits of different foam materials. The "1" for the spectra is defined as the largest peak in the classic FT-IR spectrum from 4000 to 400cm^-1 to make the comparisons somewhat fair. Eventually the spectra must be normalized for constant sample thickness.

Finally, the app multiplies each pair of radiance and absorption numbers and sums the result to get an integrated absorption. As is immediately obvious, and as is well known, PE and PS foams have low absorption of mid-IR radiation while PU and Silica both show significant absorption.

Your own data files

If you have your own spectrum as simple pairs of comma-separated or tab-separated values then you can load it directly to get the same analysis. For example, a Bruker .dpt file can be loaded directly. Be aware that you need smart background correction to your dataset, especially given the well-known fact that foams tend to give an upward-moving baseline towards the low cm^-1 region. The app makes no attempt to do any correction other than remove negative values.