Emergence of Strong Nonlinear Viscoelastic Response of Semifluorinated Alkane Monolayers Salomé Mielke 1, Taichi Habe 1,#, Mariam Veschgini 1, Xianhe Liu 2, Kenichi Yoshikawa 3, Marie Pierre Krafft 2, and Motomu Tanaka 1,4,* 1 Institute of Physical Chemistry, University of Heidelberg, 69120 Heidelberg, Germany 2 Institut Charles Sadron (CNRS), University of Strasbourg, 67034 Strasbourg, France 3 Faculty of Life and Medical Sciences, Doshisha University, 610-0321 Kyotanabe, Japan 4 Institute foradvanced Study, Kyoto University, 606-8501 Kyoto, Japan Supporting Information Fig S1: Measurement of shear elastic modulus G' and shear viscous modulus G'' of di(f10h18) with an interfacial shear rheometer (Camtel) at 1 mn/m (A) and 5 mn/m (B). The measurements were performed at a frequency of 3 Hz and an amplitude of 1.5 mrad. (A) It was not possible to reach equilibrium even after 180 s (also at other frequency / amplitude conditions). (B) At surfaces pressures above 1 mn/m, the film was too stiff and the values of G' exceeded the sensitivity of the rheometer (~ 26 mn/m).
Fig S2: Influence of strain amplitude on dilational interfacial rheology of di(f10h16) at π = 5 mn/m, f = 10 mhz. (A) 0.5 % strain amplitude, (B) 1 % strain amplitude, (C) 2 % strain amplitude. The upper panel shows the oscillation of the surface pressure π(t) over time, the lower panel shows the corresponding Lissajou plot (surface pressure versus molecular area). (D) Fractions of the higher mode amplitudes plotted as a function of strain amplitude showing the emergence of the second mode at 2 % strain amplitude.
Fig S3: Dilational interfacial rheology of di(f10h16) at 10 mn/m surface pressure. (A-C) Raw data of oscillation of the surface pressure and molecular area at 1 mhz (A), 10 mhz (B) and 100 mhz (C).(D) Elastic modulus E' (triangles) and viscous modulus E'' (circles) fitted with Kelvin-Voigt model. The results of the model are given in the graph. (E) Phase shift between surface pressure and area change for f = 1-150 mhz. Fig S4: Analysis of nonlinear interfacial dilational rheology of di(f10h16) at 10 mn/m surface pressure threshold. (A) Fourier Spectrum at 100 mhz in real space and imaginary space (inset).(b) Amplitude Fractions of the higher mode amplitudes plotted as a function of frequency.
Fig S5: Influence of spreading amount on the phase separation. Different amounts of volume of di(f10h16) molecules were spread on the surface, i.e. the distance between the barriers and the pressure sensor was different. This influences the phase separation between stress and strain. The measurements were performed at 1 % strain amplitude. Fig S6: Fourier series fit quality of the raw data. Signals of the surface pressure oscillation of di(f10h16) at 1 mhz (A), 10 mhz (B) and 100 mhz (C). The signal was fitted with a Fourier series expansion (red line), where the left plots show only the first mode (linear model), and
the right plot shows the fitting with up to 5 modes. (D) The corresponding values of the fit quality χ 2 in dependence of the number of modes included. Fig S7: Although a target pressure of 5 mn/m was set, the offset of the sine oscillation π 0 depends on the position of the barriers before starting the measurement. Reducing the molecular area in order to get to 5 mn/m leads to an increase of π 0, increasing the area leads to a reduction π 0 accompanied with a slower response of the surface pressure after starting the oscillations. This however has no effect on the calculation of the viscoelastic properties. Anyway, the barrier was always stopped at the same position to avoid any influence on the data
Fig S8 Overview of di(f10h18) data. (A) Raw data of the oscillation of surface pressure versus time and versus the molecular area (Lissajou plot) for the frequencies 1, 10 and 100 mhz. The fitting curves (red solid lines) correspond to the Fourier expansion up to the fifth mode. (B) Fractions of the higher mode amplitudes plotted as a function of frequency. Fig S9 Overview of di(f10h20) data. (A) Raw data of oscillation of surface pressure versus time and versus the molecular area (Lissajou plot) for the frequencies 1, 10 and 100 mhz The
fitting curves (red solid lines) correspond to the Fourier expansion up to the fifth mode. (B) Fractions of the higher mode amplitudes plotted as a function of frequency. Fig. S10 Phase shift between stress and strain in dependency of the frequency for mode 1, 3 and 5 for all three tetrablock molecules. In contrast to the phase shift of the linear term, the phase shifts of the third and fifth mode show no linear increase with frequency, which suggest the absence of nonlinear viscosity terms. As expected from the shape of the Fourier fitting,.