Dealing with inaccuracies in the analysis on solvent‐induced swelling of transparent thin films using in situ spectroscopic ellipsometry in the visible wavelength range

Abstract

The accuracy of spectroscopic ellipsometry studies of transparent polymer films in the visible wavelength range is greatly reduced in the presence of a liquid ambient. The relatively high refractive index of a liquid ambient strongly amplifies the effects of experimental non-idealities, such as window birefringence and an unknowingly inaccurate description of the optical properties of the ambient. In particular for thin films (approximately <100 nm), the implications of even small non-idealities are substantial, and large deviations in the thickness and refractive index are found. The concurrent low root mean square error (MSE) values show that a good MSE does not show that the optical model is correct; it just shows a good agreement between the experimental and fitted data. This implies that quantitative in situ ellipsometry studies for thin films are intricate, and derived properties like sorption behaviour should be treated with caution. Here, we show that quantitative in situ ellipsometry swelling measurements in solvents require a very accurate solvent dispersion relation, a high-quality temperature control, especially to prevent temperature differences between the cell, its content and exterior ambient, and accurate quantification of window effects, in particular for polymer films with thicknesses of approximately below 100 nm, depending on the optical contrast of the polymer-solvent system.

Swelling of 9 polymers commonly employed for solvent-resistant nanofiltration membranes: A comprehensive dataset

“…Those values deviate slightly from the dilation values found in this study (0.6% and 3.8%, respectively). The difference is smaller than the inherent inaccuracy of the solvent massuptake technique and the error bars on our data [62].…”

“…Therefore, a further improvement in data accuracy can be obtained by better controlling the layer homogeneity. The uncertainties introduced by inaccuracies in the refractive index are inherent to the applied measurement method; they can be minimized [62], but not avoided completely. Furthermore, for the glassy materials, it would be interesting to store the samples for much longer timescales of multiple years in order to assess the final (equilibrium) solvent concentration that is reached inside these layers.…”

“…Readers unfamiliar with spectroscopic ellipsometry are referred to Ogieglo et al [30] for a clear description of the advantages, disadvantages and limitations of using spectroscopic ellipsometry for measuring swelling polymer films. For a thorough discussion on possible errors and inherent measurement uncertainties, the reader is referred to Tempelman et al [62]. Throughout this manuscript, uncertainties are quantified and given as error bars, which denote the standard error.…”

“…For most of the solvents, an offset in the refractive index at the start of the measurement is recorded. This offset can be the consequence of an inaccuracy that is either caused by the introduction of the solvent into the measurement cell as shown by Tempelman et al in [62], or is the consequence of an initial process that is too fast (in the timescale of seconds) to capture using spectroscopic ellipsometry. Upon comparing the data at the end of the short-term measurement to the more accurate data obtained on multiple sample spots after 1 day (Fig.…”

“…For toluene, the swelling dynamics appear to be similar to that of the ketones, also following a Case II-diffusion mechanism (CIIo). The unexpected behavior of the normalized refractive index can be attributed to the high refractive index of toluene in combination with the used measurement cell, which is known to result in a high susceptibility of the experiment to external perturbations, such as small temperature variations [62]. It could be argued that for the polar aprotic solvents, the absence of an increase in the normalized refractive index during the apparent overshoot dynamics would hint at a slow dissolution of these polymers.…”