Negative Mass in the Systems Driven by Entropic Forces

The paper addresses the phenomena of negative effective mass and negative effective density emerging in systems driven by entropic elastic forces. The elasticity of polymers is, at least partially, of entropic origin, and it represents the tendency of a polymer to evolve into a more probable state, rather than into one of lower potential energy. Entropy forces are temperature-dependent; thus, the temperature dependence of the effective mass and effective density arises. The effect of the negative effective mass is a resonance effect, emerging in core-shell mechanical systems, which takes place when the frequency of the harmonic external force acting on a core-shell system connected by an ideal spring approaches from above to the eigen-frequency of the system. We address the situation when the ideal spring connecting the core to the shell is made from a polymer material, and its elasticity is of an entropic origin. The effective mass is calculated, and it is temperature-dependent. The chain of core-shell units connected with a polymer spring is studied. The effective density of the spring is temperature-dependent. Optical and acoustical branches of vibrations are elucidated. The negative mass and density become attainable under the variation of the temperature of the system. In the situation when only one of the springs demonstrates temperature dependence, entropic behavior is investigated. Exemplifications of the effect are addressed.