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arXiv:2609.03841

The Casimir free energy of peptide films on a silicon substrate: Impact of dielectric-to-metal transition in silicon and nanoparticles in peptide

G. L. Klimchitskaya, V. M. Mostepanenko

cond-mat.mes-hallquant-phSubmitted Sep 3, 2026• Announced Sep 4, 2026
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Abstract

Using the Lifshitz theory of the van der Waals and Casimir forces, we calculate the Casimir free energy of thin peptide films deposited on silicon substrates. The Casimir free energy is found as a function of film thickness for different fractions of water in the film, in the presence of either nonmagnetic or magnetic nanoparticles, and under the impact of irradiation of a silicon substrate with laser pulses or dopants resulting in the dielectric-to-metal phase transition. It is shown that for a dielectric silicon there is the borderline value of the film thickness, such that the Casimir free energy is negative and contributes to the film stability for thicker films, but is positive and makes the film less stable for thinner ones. According to our results, the borderline value of peptide film thickness decreases with increasing volume fractions of water and in the film. This decrease is more pronounced for the magnetic nanoparticles and becomes stronger with increasing their radius. The borderline value of peptide film thickness is found as a function of the fraction of water in the film. If the silicon substrate is in metallic state, the Casimir free energy of peptide coating is always positive, which makes it less stable. Possible applications of the obtained results in organic electronics and biomedicine are discussed.

Journal reference
J. Chem. Phys. v.165, 094704 (2026)
DOI
10.1063/5.0349756
Comments
10 pages, 6 figures

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Using the Lifshitz theory of the van der Waals and Casimir forces, we calculate the Casimir free energy of thin peptide films deposited on silicon substrates. The Casimir free energy is found as a function of film thickness for different fractions of water in the film, in the presence of either nonmagnetic or magnetic nanoparticles, and under the impact of irradiation of a silicon substrate with laser pulses or dopants resulting in the dielectric-to-metal phase transition. It is shown that for a dielectric silicon there is the borderline value of the film thickness, such that the Casimir free energy is negative and contributes to the film stability for thicker films, but is positive and makes the film less stable for thinner ones. According to our results, the borderline value of peptide film thickness decreases with increasing volume fractions of water and in the film. This decrease is more pronounced for the magnetic nanoparticles and becomes stronger with increasing their radius. The borderline value of peptide film thickness is found as a function of the fraction of water in the film. If the silicon substrate is in metallic state, the Casimir free energy of peptide coating is always positive, which makes it less stable. Possible applications of the obtained results in organic electronics and biomedicine are discussed.
We consider the Casimir force in configurations with magnetic metal plates and analyze the reasons why the predictions of the Lifshitz theory using the dielectric permittivity of the Drude model are inconsistent with the measurement data. For this purpose, the contributions of the electromagnetic waves with the transverse magnetic and transverse electric polarizations to the Casimir force are computed using the Lifshitz theory expressed in terms of the pure imaginary Matsubara frequencies. Furthermore, the fractions of the evanescent and propagating waves in these contributions are found using an equivalent formulation of the Lifshitz theory along the real frequency axis. All computations are performed for Au-Ni and Ni-Ni plates using the Drude model and the experimentally consistent plasma model over the separation region from 0.5 to 6~mum, where the total force value is determined by conduction electrons. It is shown that the transverse magnetic contribution to the Casimir force does not depend on the used model of the dielectric permittivity, so that the total difference between the predictions of the Lifshitz theory using the Drude model and the measurement data is determined by the transverse electric contribution. In doing so, as opposed to the case of nonmagnetic metals, both fractions of the evanescent and propagating waves in this contribution depend on the model of the dielectric permittivity used in computations, whereas the magnetic properties of the plate metal influence the Casimir force solely through the fraction of propagating waves in the transverse electric contribution. The issue of a more adequate theoretical description of the electromagnetic response of magnetic metals is discussed.
Finite-size effects are investigated in the Gaussian model with isotropic and anisotropic short-range interactions in film geometry with nonperiodic boundary conditions (bc) above, at, and below the bulk critical temperature Tc. We have obtained exact results for the free energy and the Casimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixed bc in 1<d<4 dimensions. For the Casimir force, finite-size scaling is found to be valid for all bc. For the free energy, finite-size scaling is valid in 1<d<3 and 3<d<4 dimensions for antiperiodic, Neumann, and Dirichlet bc, but logarithmic deviations from finite-size scaling exist in d=3 dimensions for Neumann and Dirichlet bc. This is explained in terms of the borderline dimension d*=3 , where the critical exponent 1-α-ν=(d-3)∕2 of the Gaussian surface energy density vanishes. For Neumann-Dirichlet bc, finite-size scaling is strongly violated above Tc for 1<d<4 because of a cancelation of the leading scaling terms. For antiperiodic, Dirichlet, and Neumann-Dirichlet bc, a finite film critical temperature Tc,film(L)<Tc exists at finite film thickness L . Our results include an exact description of the dimensional crossover between the d -dimensional finite-size critical behavior near bulk Tc and the (d-1) -dimensional critical behavior near Tc,film(L). This dimensional crossover is illustrated for the critical behavior of the specific heat. Particular attention is paid to an appropriate representation of the free energy in the region Tc,film(L)≤T≤Tc. For 2<d<4 , the Gaussian results are renormalized and reformulated as one-loop contributions of the φ4 field theory at fixed dimension d and are then compared with the ε=4-d expansion results at ε=1 as well as with d=3 Monte Carlo data. For d=2 , the Gaussian results for the Casimir force scaling function are compared with those for the Ising model with periodic, antiperiodic, and free bc; unexpected exact relations are found between the Gaussian and Ising scaling functions. For both the d -dimensional Gaussian model and the two-dimensional Ising model it is shown that anisotropic couplings imply nonuniversal scaling functions of the Casimir force that depend explicitly on microscopic couplings. Our Gaussian results provide the basis for the investigation of finite-size effects of the mean spherical model in film geometry with nonperiodic bc above, at, and below the bulk critical temperature.
The Casimir-Polder interaction of an atom with a metallic wall is investigated in the framework of the Lifshitz theory. It is demonstrated that in some temperature (separation) region the Casimir-Polder entropy takes negative values and goes to zero when the temperature vanishes. This result is obtained both for an ideal metal wall and for real metal walls. Simple analytical representations for the Casimir-Polder free energy and force are also obtained. These results are used to make a comparison between the phenomenological potential used in the theoretical description of quantum reflection and exact atom-wall interaction energy, as given by the Lifshitz theory. Computations are performed for the atom of metastable He∗{\mathrm{He}}^{*}He∗ interacting with metal (Au) and dielectric (Si) walls. It is shown that the relative differences between the exact and phenomenological interaction energies are smaller in the case of a metallic wall. This is explained by the effect of negative entropy which occurs only for a metal wall. More accurate atom-wall interaction energies computed here can be used for the interpretation of measurement data in the experiments on quantum reflection.
Cold atoms can be trapped and guided using nanofabricated wires on microengineered surfaces, achieving the scales required by quantum information proposals on the consequences of Casimir-Polder (CP) force to its stability and lifetime. The atoms are found to be less attractive to the thin films compared to dielectric half plate, where the attractive potential drops even further when the thickness of the surface is lower than both thermal wavelength and the spacing length. Amiably, for the spherical surface, the CP potential decays even further as radial thickness decreases. We approximate the CP potential using the analytical expression obtained from the pairwise summation (PWS) calculated by taking a sum of single atom with the jumbled atoms inside the surface, treating them as two-bodies system as a whole. The means of PWS are to calculate the possibilities of geometrical effect: planar and curved surface on the CP potential.
We determine the role of the fluctuation-induced Casimir force acting between a membrane of cylindrical shape and a bottom electrode in microelectromechanical capacitive switches. For this purpose, the Casimir force is computed taking into account the real properties of both a membrane and a bottom electrode materials with account of surface roughness. The obtained results are compared with those found for the smooth surfaces using the idealization of ideal metal. It is shown that an account of both the real material properties and surface roughness is crucial for obtaining the correct values of the Casimir force. According to our results, at the shortest separations, when the switch membrane is in contact with the transmission line, the magnitudes of the Casimir force may exceed the magnitudes of the electric one depending on the value of the operating voltage. The obtained values of the Casimir force can be used for determining the thickness of the switch membrane, which ensures the necessary magnitude of the restoring elastic force required for a stable cyclic functioning of the micromechanical switch with no pull-in.
We investigate the stability of magnetically trapped atomic Bose-Einstein condensates and thermal clouds near the transition temperature at small distances $0.5\text{ }\ensuremath{\mu}\mathrm{m}\ensuremath{\le}d\ensuremath{\le}10\text{ }\ensuremath{\mu}\mathrm{m}$ from a microfabricated silicon chip. For a $2\text{ }\ensuremath{\mu}\mathrm{m}$ thick copper film, the trap lifetime is limited by Johnson noise induced currents and falls below 1 s at a distance of $4\text{ }\ensuremath{\mu}\mathrm{m}$. A dielectric surface does not adversely affect the sample until the attractive Casimir-Polder potential significantly reduces the trap depth.