# Mixture nonideality: investigation by IR spectroscopy

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Currently, I’m working on topics related to thermal radiation in a fire safety science research group. One thing that is under study is the capability of flammable liquids and solid polymers to absorb infrared radiation produced by flaming combustion. This capability is important, as in a situation of an accidental fire, most of the heat transfer happens by radiation and a combustible material that absorbs thermal radiation very effectively will heat up quickly at its surface and catch fire.

Related to this topic, I measured near-infrared absorbance spectra of several flammable liquids and their mixtures, trying to find out how well the IR spectrum of a mixture can be approximated with a weighted average of the spectra of the components. It was expected that this kind of averaging will work with nonpolar liquids but not with all polar liquids. Data of the infrared absorbance of organic compounds at wavelengths of less than 2500 nm is quite limited, and even more so for mixtures.

An example spectrum, of n-octane, toluene (both nonpolar) and a mixture of them (with 31 mass % of toluene) is shown in the following image.

As can be seen, the graph for the mixture is between the graphs for the pure components at every point in the whole range, so it could be a weighted mean of them.

If we denote the wavelength dependent absorption coefficient of toluene by $\kappa_{C_7 H_8}(\lambda)$ and that of n-octane by $\kappa_{C_8 H_{18}}(\lambda)$, and determine coefficients $a$ and $b$ so that the sum $a\kappa_{C_8 H_{18}} + b\kappa_{C_7 H_8}(\lambda)$ has the least possible average deviation from the actual mixture spectrum $\kappa_{mix}(\lambda)$ on the whole interval from 1400 to 2000 nanometers, the result is $a=0.78$ and $b=0.22$. Drawing the weighted average spectrum in the same image with the actual one, we see that they are practically the same.

Measuring a same kind of infrared spectrum for a mixture of acetone and isopropyl alcohol, of which both are polar and the isopropyl alcohol also hydrogen bonding, the graph is like this:

Now it’s quite clear that the mixture spectrum can not be approximated very precisely by a weighted mean, as the blue curve denoting a mixture with 36 mass-% acetone isn’t always even between the curves for the pure components. This is more apparent when zooming to around 1425 nm.

Initially, I had an expectation that any mixtures with least one polar component would have this kind of deviations from ideality, but doing a same kind of measurement for n-heptane and acetone shows that this is not the case.

The graph for the mixture is between the other graphs at every wavelength, and doing a least squares fitting of a weighted mean spectrum to the measured mixture datapoints reveals that it is quite a good fit at least for near-infrared wavelengths.

Overall, these measurements and the related literature search gave me some good insights about the ways how nonideality of liquid mixtures manifests itself. I hope these data also contain something interesting for others.

Nice summer for everyone (on the northern hemisphere),

-Teemu