Fluctuation-induced dispersion forces on thin DNA films

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Figure 1

(a) The permittivity of used materials evaluated in imaginary frequency. (b) The permittivity of wet DNA containing different volume fractions of water.

Figure 2

(a) The magnitude of Casimir pressure versus the thickness of a dry DNA film suspended in backgrounds of air and water. (b) The Casimir pressure for thinner DNA films on a linear scale. The inset shows the Casimir pressure as a function of water volume fraction, where the DNA-film thickness $a=100$ nm is fixed. The temperature is 300 K.

Figure 3

The Casimir pressure versus the thickness of DNA films under different volume fractions $\mathrm{\Phi }$. The substrate consists of semi-infinite silica. (a) The DNA film is exposed to air. (b) The DNA film is immersed in water. The inset in (b) shows the Casimir pressure for $\mathrm{\Phi }=0.2$ with a clearer plot scale. The positive (negative) sign of the pressure corresponds to the repulsive (attractive) force.

Figure 4

The Casimir pressure versus the thickness of DNA films with a gold substrate. (a) The DNA film is exposed in air for $\mathrm{\Phi }=0$ (solid) and 0.4 (dashed). (b) The DNA film is immersed in water. The inset shows the corresponding Casimir pressure as a function of $\mathrm{\Phi }$. The labels 1, 2, and 3 represent the thicknesses of DNA film of 150, 200, and 250 nm, respectively.

Figure 5

The Casimir pressure versus the thickness of DNA films under different Debye lengths of water. (a) The DNA film is suspended in water. (b) The DNA film deposited on the silica substrate is immersed in water. (c) The DNA film deposited on the Au substrate is immersed in water. The water volume fraction in DNA films is set to be 0.4.