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  • Using the measured approach curves we determined the force a

    2018-10-26

    Using the measured approach curves, we determined the force acting on the probe from the sample surface as the product of the cantilever spring constant k by the piezoscanner movement value dZ (this quantity is plotted on the abscissa in Fig. 2b). Next, we constructed the F(δ) dependences to find Young\'s modulus of the sample. The experimental points obtained were then approximated by the dependence described by formula (1); the method of least squares, where Young\'s modulus E acted as the fitting parameter, was used for this tlr inhibitor purpose. The results of the regression analysis performed for a separate approach curve are shown in Fig. 3b. One of the main issues in solving the contact problem while studying the temperature dependence of Young\'s modulus is in correctly determining the constant k. It is used for calculating the force F acting from the sample on the probe tip in contact mode. The difficulty lies in the fact that the cantilever spring constant depends on temperature. Therefore, the constant k must be determined for each temperature point before solving the Hertz problem. We used the Sader method [6] to find the cantilever spring constant. It allows to correlate the normal spring constant of a flexible cantilever with the range of its thermal vibrations in a medium with known viscosity and density values. To find the constant k, we measured the spectrum of thermal vibrations of the cantilever, called for short the thermal peaks (Fig. 3a). The shape of the resulting spectrum was approximated by the following function: where Q is the quality factor, is the natural resonant frequency of the probe, and А0 is the peak amplitude. These fitting parameters were then used for calculating the spring constant by the formula where ρ and η are the density and the viscosity of the medium; b and L are the width and the length of the cantilever; Q is the quality factor of its vibrations; is the frequency of the first resonance peak; Γ is the imaginary component of the hydrodynamic function. The results of the approximations by formulae (2) and regression analysis of the approach curve by formula (1) are shown (a and b, respectively).
    Results and discussion The mechanical properties of polylysine were studied using an AttoAFM I cryogenic atomic force microscope (Attocube Systems, Germany). The NSC15 probes (MMasch, Bulgaria) with the cantilever spring constant lying in the 20–75N/m range and the resonant frequency of 265–400kHz were chosen for the measurements. We used slides coated with a 1mm thick layer of poly-L-lysine (Yancheng Huida Medical Instruments CO, LTD, China). We measured the surface topography of the sample in a 15µm×15µm-sized region in the temperature range from 60 to 300K, with a step of 30K. We selected 16 points in this region so that the distance between them was not less than 1µm. The approach curves were measured in each of the points. Young\'s modulus was then determined for each approach curve as described above. The obtained values of Young\'s modulus were averaged over 16 approach curves. A typical form of the obtained surface topography of polylysine is shown in Fig. 4. The analysis of the results led us to conclude that this surface is relatively smooth, with small round inclusions. The average surface roughness defined in the 15µm×15µm area is 1.75nm. The dependence of the cantilever spring constant on temperature, calculated by the Sader method, is shown in Fig. 5. As can be seen from the data, this constant increases linearly with a decrease in temperature, while its value at 5K is about 6–7 times higher than the respective value at room temperature. The experimental curves of the force F acting on the probe from the sample versus the δ value for different temperatures are shown in Fig. 6a. Young\'s moduli for polylysine were found for the obtained experimental dependences based on the solution for the Hertz problem in a predetermined temperature range; the temperature dependence of the cantilever spring constant was taken into account in doing so (see Fig. 5). For comparison, Table 1 shows the values of Young\'s modulus calculated without this temperature dependence taken into account. It was found that in the temperature range of 90–295K, Young\'s modulus of polylysine gradually increases with a decrease in temperature (Fig. 6b). According to the results obtained, the values of Young\'s modulus of polylysine at T=90K are 2.5 times higher than the respective values at room temperature. Young\'s modulus of polylysine increases abruptly (by 7 times) below 90K compared with the values obtained for room temperatures. The observed difference, namely, a sharp rise on the temperature curve of the elastic properties of polylysine at about 80K, is likely caused by the structural modification of the polymer under these conditions.