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# br Conclusion To summarize we have developed a method

Conclusion
To summarize, we have developed a method for determining Young\'s modulus of the sample surface using an AFM with an optical system for detecting the position of the probe organized by the interferometric principle. We have obtained the temperature dependence for the spring constant of the AFM probe cantilever in the range from 30 to 295K. The proposed technique was used to determine the temperature dependence of Young\'s modulus of polylysine in view of the elastic properties of the AFM changing in the temperature range from 60 to 295K.

Acknowledgment
The study was conducted with the financial support of the President of the Russian Federation grant for state support of young Russian scientists MK 7005.2016.8.

Introduction
Dusty plasma is an ionized gas containing charged particles of condensed matter. This type of plasma can be used to fabricate fundamentally new nanostructured and composite materials. The electric charge that dust particles can acquire in the discharge plasma is one of the major problems in dusty plasma physics [1]. Despite the fact that a number of works take into account the effects of collisions and of ionization of the gas atoms in calculating the ion current onto the surface of particles [2,3], no theory has been developed for describing the charging of dust particles under transient conditions that cannot be fully explained by either the drift-diffusion approximation [4] or the orbital-motion-limited approximation [5]. The rapidly evolving methods of molecular dynamics [6–8] or the particle-in-cell Monte Carlo collision method [9] prove to be too difficult for modeling real problems. Solving such problems is complicated by the presence of various types of tlr signaling emission processes (secondary and electron-ion types, photo and thermal-field types) from the surface of dust particles.

The system of moment equations and Poisson\'s equation
To describe the charging process of a spherical dust particle of radius a under transient conditions, we shall use the particle balance equations, the equations of motion and Poisson\'s equation [10] in spherical coordinates:
where r is the coordinate, is the ion (electron) concentration, is the radial directed velocity of ions (electrons), is the ionization frequency, is the electric field intensity, is the temperature of ions (electrons) in energy units, is the mass of ions (electrons), ν is the frequency of ion (electron) collisions with atoms, e is the elementary charge, ε0 is the dielectric constant.
As the radial directed velocity of electrons is slow compared to the random one, neglecting the inertial term and bulk friction forces ((ν=0) allows to obtain a simple equation for the motion of electrons (2) with the temperature . In this case, the electrons obey the Boltzmann distribution regardless of the regime of ion motion onto the surface of the dust particle. Thus, the density of the electron current onto the particle follows the expression
where 0 is the electron concentration at the boundary of the perturbed region, is the potential of the dust particle surface.
Let us introduce the dimensionless quantities:
where .
Then Eqs. (1)–(4) take the following form:

The dimensionless similarity parameters , , are determined by the charging regimes of the dust particles; is the electron Debye length [11]; τ= / is the normalized electron temperature used in the calculations of atom (ion) temperature, with

The quasi-neutrality of the plasma is violated near the dust particle. The characteristic scale of the perturbed region of the plasma is the electron Debye length λ. The ratios between the characteristic lengths of the problem, namely a, λ and λ, describe a particular charging regime of the dust particles in the discharge plasma. Here is the free path of the ion, is the atom concentration, σ is the averaged transport cross-section of the ion-electron collisions [12], .
The potential, the electric field and the radial directed velocity are equal to zero at the boundary of the perturbed region (let us denote it as r0), while the ion and electron concentrations may differ [1], i.e.,