# Fluctuation-induced dispersion forces on thin DNA films

Lixin Ge<EMAIL_ADDRESS>School of Physics and Electronic Engineering,
Xinyang Normal University, Xinyang 464000, China  Xi Shi  Department of
physics, Shanghai Normal University, Shanghai, 200234, China  Binzhong Li
School of Physics and Electronic Engineering, Xinyang Normal University,
Xinyang 464000, China  Ke Gong  School of Physics and Electronic Engineering,
Xinyang Normal University, Xinyang 464000, China

###### Abstract

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 the air or water,
the Casimir force is attractive, and its magnitude increases with decreasing
the 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 signs 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 are investigated. The Casimir force is dominant by the repulsive
interactions at a small DNA-film thickness for both the air and water
environment. In a water environment, the Casimir force turns out to be
attractive at a large DNA-film thickness, and a stable Casimir equilibrium can
be found. In addition to the adhesion stability, our finding could be
applicable to the problems of condensation and de-condensation of DNA, due to
the fluctuation-induced dispersion forces.

##  I Introduction

The dispersion force is generated by the fluctuating dipoles, resulting from
the zero-point vacuum fluctuation and thermal fluctuation Feinberg et al.
(1989). When the consuming time for propagating waves between the fluctuation
dipoles is larger or comparable with the lifetime of fluctuating dipoles, the
retardation effect (or wave effect) can modified the separation-dependence
decaying laws of dispersion force Rodriguez et al. (2011). Specifically, the
dispersion force is known as the van der Waals force for closely spaced
objects or interfaces Parsegian (2005), where the retardation is negligible.
The retardation effect manifests when the separation distance is large, and
the dispersion force is also named as retarded van der Waals forceDagastine et
al. (2002) or the Casimir force Bordag et al. (2009); Klimchitskaya et al.
(2009). In some configurations, the retardation effect can be apparent even at
the separation of several nanometersLee and Sigmund (2001). The dispersion
force and its free energy play an important role in various disciplines,
ranging from nanomechanicsGong et al. (2021); Somers et al. (2018); Ge et al.
(2020a); Munkhbat et al. (2021); Esteso et al. (2015), wetting phenomenaHough
and White (1980); Boinovich and Emelyanenko (2011); Squarcini et al. (2022),
to ice pre-melting and formation Li et al. (2022); Luengo-Márquez and
MacDowell (2021); Esteso et al. (2020); Fiedler et al. (2020) etc. In
addition, the dispersion force and its free energy across organic films were
also investigated intensely Lu and Podgornik (2015); Blackwell et al. (2021);
Baranov et al. (2019); Klimchitskaya et al. (2020, 2021, 2022). It was
reported that the attractive dispersion force would make the organic films
more stable, while the repulsive force has an opposite effectBaranov et al.
(2019); Klimchitskaya et al. (2020, 2021, 2022).

Deoxyribonucleic acid (DNA) composed of two helical polynucleotide chains is
one of the most important substances in biology. Along with its biological
functions, the material properties of DNA are of great interest for the state-
of-art of nanotechnology, motivated by the promising applications in a variety
of fields, such as self-assembly of colloidal nanoparticles Nykypanchuk et al.
(2008); Chou et al. (2014); Rogers et al. (2016); Cui et al. (2022), DNA-based
nanomedicinesCampolongo et al. (2010); Hu et al. (2018); Weiden and Bastings
(2021); Gu et al. (2021), organic nanophotonics Steckl (2007); Bui et al.
(2019) etc. As one of the crucial elements, the DNA films have been widely
applied in many bio-organic nanoscale devices Kawabe et al. (2000); Zhang et
al. (2012); Khazaeinezhad et al. (2017); Jung et al. (2017). The DNA films are
generally deposited on inorganic substrates using the spin coating process
Jung et al. (2017). The structure stability of double-stranded DNA is
determined by the hydrogen bonds between nucleotides and the base-stacking
interactionsYakovchuk et al. (2006). However, the adhesion stability of DNA
films placed on a substrate is dependent on the surface forces Boinovich and
Emelyanenko (2011), such as ionic or electrostatic forces, intra-hydrogen
bonds, dispersion forces etc. The dispersion force is an important ingredient
at the surface forces, particularly, when the thickness of a bio-organic film
is miniaturized to a sub-micro scaleBaranov et al. (2019). Moreover, the other
surface forces (e.g., intra-hydrogen bonds) could be absent at the surface of
some specific substrates. Then, it is expected that the contribution from the
dispersion force becomes more prominent, and the quantitative calculations of
this force are necessary.

In this work, we study the Casimir force of DNA films within the framework of
Lifshitz theory. The influences of Casimir forces due to DNA-film thicknesses,
water volume fractions, background media and substrates are investigated by
numerical calculations. We find that the Casimir pressure is attractive for a
DNA film suspended in the air or water, and its magnitude increases by
decreasing the DNA-film thickness and water volume fraction. For a DNA film
placed on a silica substrate in the air background, the Casimir pressure shows
a similar trend as that in the suspended configuration. However, the Casimir
pressure exhibits rich features when the setup is immersed in the water. Under
specific water volume fraction, switching sign of the Casimir pressure across
a wet DNA film is revealed by increasing the DNA-film thickness. Finally, the
Casimir pressure for a DNA film placed on a metallic substrate is also
calculated. It is found that the Casimir pressure is dominant by the repulsive
interactions at a small DNA-film thickness for both the air and water
environment. Interestingly, a stable Casimir equilibrium is found when the DNA
film is immersed in the water. Our findings could be applicable to the
problems of adhesive stability, condensation and de-condensation of DNA films,
due to the fluctuation-induced dispersion forces.

##  II Theoretical models

We consider a DNA film with thickness $a$ sandwiched between a cladding medium
and a substrate. The thicknesses of the cladding layer and substrate are
assumed to be semi-infinite. In addition, the whole system is in thermal
equilibrium at room temperature $T$. The Casimir pressure of the DNA film is
calculated based on the framework of the Lifshitz theory Klimchitskaya et al.
(2009, 2020):

$P_{\mathrm{c}}(d)=-\frac{k_{b}T}{\pi}\overset{\infty}{\underset{n=0}{\sum}}^{\prime}\int_{0}^{\infty}k_{\|}k_{3}dk_{\|}\underset{\alpha=s,p}{\sum}\frac{r_{1}^{\alpha}r_{2}^{\alpha}e^{-2k_{3}a}}{1-r_{1}^{\alpha}r_{2}^{\alpha}e^{-2k_{3}a}},$
(1)

where the prime in summation denotes a prefactor 1/2 for the term $n=0$,
$k_{b}$ is the Boltzmann’s constant,
$k_{3}=\sqrt{k_{\parallel}^{2}+\varepsilon_{\mathrm{D}}(i\xi_{n})\xi_{n}^{2}/c^{2}}$
is the vertical wavevector in the DNA film, $k_{\parallel}$ is the parallel
wavevector, $c$ is the speed of light in vacuum,
$\varepsilon_{\mathrm{D}}(i\xi_{n})$ is the permittivity of the dry DNA film,
$\xi_{n}=2\pi\frac{k_{b}T}{\hbar}n(n=0,1,2,3...)$ are the discrete Matsubara
frequencies, $\hbar$ is the reduced Planck constant, $r^{\alpha}(\alpha=s,p)$
are the reflection coefficients for the DNA film, where the superscripts
$\alpha=s$ and $p$ correspond to the polarizations of transverse electric
($\mathbf{TE}$) and transverse magnetic ($\mathbf{TM}$) modes, respectively.
The subscripts $1$ and $2$ denote the reflection coefficients at the top and
bottom interfaces of DNA film, respectively.

The reflection coefficients for an electromagnetic wave incident from the DNA
film to a medium (with permittivity $\varepsilon_{1}$) is given as
Klimchitskaya et al. (2020):

$\displaystyle r^{\mathrm{TM}}$ $\displaystyle=$
$\displaystyle\frac{\varepsilon_{1}(i\xi_{n})k_{3}(i\xi_{n},k_{\parallel})-\varepsilon_{\mathrm{D}}(i\xi_{n})k_{1}(i\xi_{n},k_{\parallel})}{\varepsilon_{1}(i\xi_{n})k_{3}(i\xi_{n},k_{\parallel})+\varepsilon_{\mathrm{D}}(i\xi_{n})k_{1}(i\xi_{n},k_{\parallel})}$
(2) $\displaystyle r^{\mathrm{TE}}$ $\displaystyle=$
$\displaystyle\frac{k_{3}(i\xi_{n},k_{\parallel})-k_{1}(i\xi_{n},k_{\parallel})}{k_{3}(i\xi_{n},k_{\parallel})+k_{1}(i\xi_{n},k_{\parallel})}$
(3)

where
$k_{1}=\sqrt{k_{\parallel}^{2}+\varepsilon_{1}(i\xi_{n})\xi_{n}^{2}/c^{2}}$ is
the vertical wavevector in the medium 1. Here, the medium 1 can be the air,
water, silica or gold.

The reflection coefficients are strongly dependent on the permittivity at
different Matsubara frequencies. Here, the dielectric functions of used
materials are fitted by a model of the modified harmonic oscillator, which is
adopted from a recent literatureMoazzami Gudarzi and Aboutalebi (2021):

$\varepsilon(i\xi)=1+\underset{j}{\overset{}{\sum}}\frac{C_{j}}{1+(\xi/\omega_{j})^{\beta_{j}}},$
(4)

where $C_{j}$ corresponds to the oscillator strength for the $j$-th resonance
frequency $\omega_{j}$, $\beta_{j}$ is a power exponent. In addition to the
Kramers-Kronig relations, the influences of the electronic dielectric
constant, optical bandgap, density, and chemical composition are taken into
account in the Eq.(4), where the parameters for the dry DNA, water and silica
are shown in Table 1.

Table 1: The parameters for the used materials Moazzami Gudarzi and Aboutalebi (2021). DNA: |  $C_{j}$ |  $\omega_{j}$(eV) |  $\beta_{j}$
---|---|---|---
$j$=1 |  1.766 |  0.0056 |  1.03
$j$=2 |  1.431 |  12.95 |  1.67
Water: |  |  |
$j$=1 |  73.48 |  8.1$\times 10^{-5}$ |  0.988
$j$=2 |  2.534 |  0.016 |  1.1
$j$=3 |  0.755 |  16.1 |  1.751
Silica: |  |  |
$j$=1 |  1.843 |  0.0725 |  1.678
$j$=2 |  1.105 |  15.33 |  1.71

It is worth mentioning that the dielectric function of the dry DNA given by
the parameters in Table 1 matches the measured data of DNA over a wide range
of frequencies, from zero frequency to the far ultraviolet Moazzami Gudarzi
and Aboutalebi (2021); Wittlin et al. (1986); Inagaki et al. (1974); Weidlich
et al. (1987); Paulson et al. (2018). Based on the Clausius-Mossotti equation,
the permittivity for a wet DNA (denoted by
$\varepsilon_{\mathrm{D}}^{{}^{\prime}}$) is given by the following form
Baranov et al. (2019); Hough and White (1980):

$\frac{\varepsilon_{\mathrm{D}}^{{}^{\prime}}(i\xi_{n})-1}{\varepsilon_{\mathrm{D}}^{{}^{\prime}}(i\xi_{n})+2}=\Phi\frac{\varepsilon_{\text{w}}(i\xi_{n})-1}{\varepsilon_{\text{w}}(i\xi_{n})+2}+(1-\Phi)\frac{\varepsilon_{\mathrm{D}}(i\xi_{n})-1}{\varepsilon_{\mathrm{D}}(i\xi_{n})+2},$
(5)

where $\varepsilon_{\text{w}}(i\xi_{n})$ is the permittivity of water, and
$\Phi$ is the volume fraction of water in the DNA film.

The dielectric function of gold is given by summing up the Drude model and the
modified harmonic oscillator, which is written as: Moazzami Gudarzi and
Aboutalebi (2021)

$\varepsilon(i\xi)=1+\frac{C_{1}}{1+(\xi/\omega_{1})^{\beta_{1}}}+\frac{\omega_{p}^{2}}{\xi^{2}+\gamma\xi},$
(6)

where the parameters $C_{1}$=6.5, $\omega_{1}$=5.9 (eV), $\beta_{1}$=1.42,
$\omega_{p}$=9.1 (eV), and $\gamma$=0.06 (eV). We find that the Casimir
calculations based on the gold permittivity in the Eq.(6) are the same as
those given by the generalized Drude-Lorentz modelGe et al. (2020b).

##  III Results and discussions

Figure 1(a) shows the permittivity of the applied materials evaluated in the
imaginary frequency. The results show that the permittivity of a dry DNA is
larger than those of the water and silica for the Matsubara term $n>0$. The
permittivity of water is the smallest over a wide range of frequencies. Figure
1(b) shows the permittivity of DNA under different water volume fractions. As
expected, the permittivity of a wet DNA decreases by increasing the magnitude
of $\Phi$, due to the elevated contribution from the low-refractive-index
water.

To predict the sign of Casimir pressure, the permittivity at $n=0$ is
significant since it plays a dominant role at a large thickness (or
separation) as reported in Baranov et al. (2019); Esteso et al. (2016). The
static permittivity for the silica, DNA and water are about 3.9, 4.2 and 81,
respectively. However, the dielectric function of a wet DNA film at $n=0$
shows a different trend, compared with the high-frequency one. The static
permittivity $\varepsilon_{\mathrm{D}}^{{}^{\prime}}$ increases from 4.2 to
11.9, with increasing $\Phi$ from 0 to 0.6.

Figure 1: (a)The permittivity of used materials evaluated in imaginary
frequency. (b)The permittivity of wet DNA containing different volume
fractions of water.

###  III.1 The Casimir pressures for suspended DNA films

We first consider the Casimir force of a DNA film suspended in a homogeneous
background medium. The Casimir force would be attractive as reported for
suspended peptide films Klimchitskaya et al. (2020). The absolute Casimir
pressure versus the thickness of suspended DNA film is shown in Fig. 2(a),
where the solid and dash lines represent the background media to be the air
and water, respectively. It is found that the magnitude of Casimir pressure
decreases monotonously by increasing the DNA thickness. The Casimir pressure
for the air is larger than the case of the water at a small thickness, while
it is smaller at a larger thickness.

The sign and magnitude of the Casimir pressure are dependent on the dielectric
responses of materials. Considering the DNA film is surrounded by medium 1 and
medium 2, the Casimir pressure would be proportional to the permittivity
contrasts of the media Dzyaloshinskii et al. (1961)

$P_{c}\propto\left(\frac{\varepsilon_{\mathrm{1}}(i\xi)-\varepsilon_{\mathrm{D}}(i\xi)}{\varepsilon_{\mathrm{1}}(i\xi)+\varepsilon_{\mathrm{D}}(i\xi)}\right)\left(\frac{\varepsilon_{\mathrm{2}}(i\xi)-\varepsilon_{\mathrm{D}}(i\xi)}{\varepsilon_{\mathrm{2}}(i\xi)+\varepsilon_{\mathrm{D}}(i\xi)}\right),$
(7)

where $\varepsilon_{\mathrm{1}}$ and $\varepsilon_{\mathrm{2}}$ is the
permittivity of the medium 1 and medium 2, respectively. We have
$\varepsilon_{\mathrm{1}}(i\xi)=\varepsilon_{\mathrm{2}}(i\xi)=1,\varepsilon_{\mathrm{1}}(i\xi)=\varepsilon_{\mathrm{2}}(i\xi)=\varepsilon_{\mathrm{w}}(i\xi)$
when the DNA film is suspended in the air and water, respectively. The
permittivity contrasts between DNA film and the air are larger than those of
water for $n>$0\. It is known that the high frequency components are dominant
for the calculation of Casimir force at a small separationYang et al. (2010).
As a result, the Casimir pressure for the air is larger than the that of the
water at a small DNA thickness. By contrast, the dielectric contrast between
DNA film and the water is much larger than that of the air at $n$=0, which is
the leading term for a large DNA-film thickness. Thus, there is no surprise
that the Casimir pressure in water environment is larger than the
configuration of the air for a large thickness (e.g., $a>$500 nm).

Figure 2: (a)The magnitude of Casimir pressure versus the thickness of a dry
DNA film suspended in the background of air and water. (b) The Casimir
pressure for thinner DNA films in the 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.

On the other hand, it would be interesting to consider the Casimir pressure
across a wet DNA film. As an example, we set the thickness $a$=100 nm, and the
Casimir force versus the volume fraction of water in DNA film is shown in the
inset of Fig. 2(b). The results show that the magnitude increases with
decreasing the value of $\Phi$. At the limit $\Phi$=0, the attractive Casimir
pressures at the air and water environment are about 0.2 and 0.6 Pa,
respectively. The magnitude of Casimir pressure is hundreds of times larger
than the gravity of the DNA film (about 1.7 mPa for $a$=100 nm), manifesting
the important role of the fluctuation-induced force. It can be seen that the
magnitude of Casimir pressure can be enlarged over 10 times, when the
thickness $a$ decreases further from 100 nm to 50 nm. Note that the
condensation of DNA will decline its thickness and the volume fraction of
water (i.e., squeezing the water out of the DNA film). Hence, it can be
concluded that DNA films trends to condensation for suspended configurations,
due to the attractive Casimir force.

Figure 3: The Casimir pressure versus the thickness of DNA films under
different volume fractions $\Phi$. The substrate consists of semi-infinite
silica. (a)The DNA film is exposed to the air. (b) The DNA film is immersed in
the water. The inset in (b) shows the Casimir pressure for $\Phi$=0.2 with a
clearer plot scale. The positive (negative) sign of the pressure corresponds
to the repulsive (attractive) force.

###  III.2 The Casimir pressures for a silica substrate

In many organic devices, the DNA film is generally deposited on a dielectric
substrate. The Casimir pressure for a DNA thin film placed on a silica
substrate is shown in Fig. 3(a), where the cladding background medium is the
air. The result shows that the Casimir pressure is negative, and its magnitude
increases by decreasing the DNA-film thickness. We note that the magnitude of
the Casimir pressure is about 0.07 Pa for the dry DNA film at 100 nm, which
declines considerably compared with the suspended configuration (about 0.6
Pa). In addition, the magnitude of the Casimir pressure for wet DNA film
declines further with increasing volume fraction $\Phi$. The pressure is only
about 0.04 Pa with volume fraction $\Phi$=0.4. Nonetheless, the Casimir
pressure for a wet DNA deposited on a silica substrate is still much larger
than the gravity of the DNA film. Overall, a thin DNA film and a low water
volume fraction are preferred for stability of the DNA film.

As the DNA film is immersed in the water, some complicated or even reverse
conclusions are obtained, in comparison with the air configurations. The
Casimir pressure as a function of the thickness $a$ is shown in Fig. 3(b). The
results show that the Casimir pressure is long-range negative at low volume
fractions 0 and 0.1, and its magnitude decreases rapidly with increasing the
DNA-film thickness. These properties suggest that a thin DNA film is favored
for stability due to the attractive Casimir force, similar to the case of air
in Fig. 3(a). However, the Casimir pressure for a large $\Phi$ shows different
features. For $\Phi$=0.4, the Casimir pressure is long-range positive, which
means that a thin thickness is harmful to the stability of DNA films. For an
intermediate value $\Phi$=0.2, the Casimir pressure turns from negative to
positive with increasing the thickness $a$, as shown in the inset of Fig.
3(b). Then, a maximum peak for the Casimir repulsion can be found near 60 nm,
which contributes negatively to the stability. The Casimir pressure would
decrease with increasing the thickness $a$ further.

The unusual behavior of Casimir pressure at the water background can be
interpreted by the competition between the attractive and repulsive Casimir
components. For a small $\Phi$, the permittivity of the wet DNA is larger than
those of silica and water over a wide range of frequencies ($n>0$). The
dielectric permittivity of the DNA and silica are very close at zero
frequency, resulting in a negligible contribution from the term $n=0$.
Therefore, the Casimir pressure is attractive according to the Eq. (7), and
its magnitude increases rapidly with decreasing the DNA-film thickness, as
demonstrated with $\Phi$=0 and 0.1 in Fig 3(b). For a large $\Phi$=0.4, the
permittivity of the wet DNA is smaller(larger) than that of silica(water) for
$n>0$, resulting in repulsive Casimir force. At static frequency with $n$=0,
the permittivity of the wet DNA is larger (smaller) than that of silica
(water), which also leads to repulsive Casimir force. Hence, the Casimir
pressure would be long-range repulsive for a large $\Phi$. For an intermediate
$\Phi$=0.2, the permittivity of the wet DNA is still larger than that of
silica(water) for $n>0$, resulting in attractive Casimir force at a small
thickness $a$. However, the contribution for $n$=0 is still positive,
resulting in repulsive Casimir force at a large value of $a$. Due to the
competition between the attractive and repulsive Casimir components, the peak
for Casimir repulsion is expected at an intermediate thickness, as shown in
the inset of Fig. 3(b).

Figure 4: The magnitude of the Casimir pressure versus the thickness of DNA
films with a gold substrate. (a)The DNA film is exposed in the air for
$\Phi$=0 (solid) and 0.4 (dash). (b) The DNA film is immersed in the water.
The inset shows the corresponding Casimir pressure as a function of $\Phi$.
The labels 1, 2 and 3 represent the thickness of DNA film are 150 nm, 200 nm
and 250 nm, respectively.

###  III.3 The Casimir pressures for a metallic substrate

Now we consider the case of DNA films deposited on the metallic substrate. The
magnitudes of the Casimir pressure as a function of thickness $a$ are shown in
Fig. 4(a), where the cladding medium is the air. According to Eq.(7), we can
predict that the Casimir pressure is long-range repulsive because
$\varepsilon_{\mathrm{air}}<\varepsilon_{\mathrm{D}}^{\prime}<\varepsilon_{\mathrm{Au}}$
is satisfied for $n\geq 0$ (see, e.g., Ref.Munday et al. (2009)). The
magnitude of Casimir pressure decreases monotonously with increasing the DNA-
film thickness. As a result, the dispersion forces make the DNA film less
stable for thin thickness. Note that the discrepancy of Casimir pressures
acting on the DNA film is small between volume fractions $\Phi$=0 and 0.4.

The Casimir pressure acting on the DNA film immersed in the water exhibit
different characteristic shown in Fig. 4(b). The Casimir pressure is repulsive
at a thin thickness, while it becomes attractive for a large thickness. At a
specific thickness, a stable Casimir equilibrium, i.e., the pressure equals to
zero, is found. The critical thickness for the Casimir equilibrium can be
modulated by the magnitude of $\Phi$. As the $\Phi$ increases from 0 to 0.4,
the critical thickness decreases correspondingly from about 237 to 174 nm. The
interesting Casimir equilibrium at the water background can be understood by
the contrast of permittivity at the Eq. (7). The repulsive relation
$\varepsilon_{\mathrm{w}}<\varepsilon_{\mathrm{D}}^{\prime}<\varepsilon_{\mathrm{Au}}$
is satisfied for $n>0$, and the permittivity contrast between the water and
wet DNA decreases with increasing the $\Phi$, resulting in a smaller Casimir
repulsion. On the other side, the attractive Casimir interaction at a large
thickness $a$ is attributed to the relation
$\varepsilon_{\mathrm{w}}>\varepsilon_{\mathrm{D}}^{\prime}$ at the leading
term $n=0$.

The inset in Fig. 4(b) shows the Casimir pressure changed by the volume
fraction of water with a fixed DNA-film thickness. We find that switching the
sign of the Casimir pressure from positive to negative is achieved by
increasing the volume fraction $\Phi$ for thickness 150 nm and 200 nm. For
thickness 250 nm, the Casimir pressure is negative and its magnitude increases
by increasing the volume fraction $\Phi$. Hence, the DNA film deposited on the
metallic substrate tends to be de-condensation in the water environment,
according to the properties of its dispersion force.

##  IV Conclusions

In summary, the Casimir pressure of a DNA film is calculated in several
configurations based on the Lifshitz theory. The Casimir pressure is
attractive when a DNA film is suspended in the air or water, and its magnitude
increases with decreasing the thickness of DNA film or/and the water volume
fraction. Hence, the suspended DNA film trends to condensation due to the
Casimir force. The Casimir pressure is hundreds of times larger than the
gravity of the DNA film for a moderate thickness (e.g., 100 nm), manifesting
the important role of the fluctuation-induced interactions. For DNA films
deposited on the silica substrate, the Casimir pressure is attractive for the
air background. Also, a thin DNA film and a low water fraction are favored for
the stability. Instead, the Casimir pressure shows rich features in a water
background. The Casimir pressure can be changed from attractive to repulsive
by increasing the DNA-film thickness and the water fraction. At the end, the
Casimir force of a DNA film deposited on a metallic substrate is explored. The
Casimir pressure is dominant by the repulsive interactions at a small DNA-film
thickness for both the air and water environment. For the setup immersed in a
water environment, the Casimir pressure turns out to be attractive at a large
DNA-film thickness, and a stable Casimir equilibrium can be found at a
specific thickness. Our finding provides a theoretical guide for the adhesion
stability, condensation, and de-condensation of DNA films, resulting from the
fluctuation-induced dispersion forces.

###### Acknowledgements.

This work is supported by the National Natural Science Foundation of China
(Grant No. 11804288 and No. 61974127), and Shanghai Pujiang Program
(21PJ1411400). The research of L.X. Ge is further supported by Nanhu Scholars
Program for Young Scholars of XYNU.

## References

  * Feinberg et al. (1989) G. Feinberg, J. Sucher, and C.-K. Au, Phys. Rep. 180, 83 (1989).
  * Rodriguez et al. (2011) A. W. Rodriguez, F. Capasso, and S. G. Johnson, Nature photonics 5, 211 (2011).
  * Parsegian (2005) V. A. Parsegian, _Van der Waals forces: a handbook for biologists, chemists, engineers, and physicists_ (Cambridge university press, 2005).
  * Dagastine et al. (2002) R. R. Dagastine, D. C. Prieve, and L. R. White, J. Colloid Interface Sci. 249, 78 (2002).
  * Bordag et al. (2009) M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, _Advances in the Casimir effect_ , vol. 145 (OUP Oxford, 2009).
  * Klimchitskaya et al. (2009) G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009).
  * Lee and Sigmund (2001) S.-w. Lee and W. M. Sigmund, J. Colloid Interface Sci. 243, 365 (2001).
  * Gong et al. (2021) T. Gong, M. R. Corrado, A. R. Mahbub, C. Shelden, and J. N. Munday, Nanophotonics 10, 523 (2021).
  * Somers et al. (2018) D. A. Somers, J. L. Garrett, K. J. Palm, and J. N. Munday, Nature 564, 386 (2018).
  * Ge et al. (2020a) L. Ge, X. Shi, L. Liu, and K. Gong, Phys. Rev. B 102, 075428 (2020a).
  * Munkhbat et al. (2021) B. Munkhbat, A. Canales, B. Küçüköz, D. G. Baranov, and T. O. Shegai, Nature 597, 214 (2021).
  * Esteso et al. (2015) V. Esteso, S. Carretero-Palacios, and H. Míguez, J. Phys. Chem. C 119, 5663 (2015).
  * Hough and White (1980) D. B. Hough and L. R. White, Adv. Colloid Interface Sci. 14, 3 (1980).
  * Boinovich and Emelyanenko (2011) L. Boinovich and A. Emelyanenko, Adv. Colloid Interface Sci. 165, 60 (2011).
  * Squarcini et al. (2022) A. Squarcini, J. M. Romero-Enrique, and A. O. Parry, Phys. Rev. Lett. 128, 195701 (2022).
  * Li et al. (2022) Y. Li, K. A. Milton, I. Brevik, O. I. Malyi, P. Thiyam, C. Persson, D. F. Parsons, and M. Boström, Phys. Rev. B 105, 014203 (2022).
  * Luengo-Márquez and MacDowell (2021) J. Luengo-Márquez and L. G. MacDowell, J. Colloid Interface Sci. 590, 527 (2021).
  * Esteso et al. (2020) V. Esteso, S. Carretero-Palacios, L. G. MacDowell, J. Fiedler, D. F. Parsons, F. Spallek, H. Míguez, C. Persson, S. Y. Buhmann, I. Brevik, et al., Phys. Chem. Chem. Phys. 22, 11362 (2020).
  * Fiedler et al. (2020) J. Fiedler, M. Bostro?m, C. Persson, I. Brevik, R. Corkery, S. Y. Buhmann, and D. F. Parsons, J. Phys. Chem. B 124, 3103 (2020).
  * Lu and Podgornik (2015) B.-S. Lu and R. Podgornik, Phys. Rev. E 92, 022112 (2015).
  * Blackwell et al. (2021) R. Blackwell, A. Hemmerle, A. Baer, M. Späth, W. Peukert, D. Parsons, K. Sengupta, and A.-S. Smith, J. Colloid Interface Sci. 598, 464 (2021).
  * Baranov et al. (2019) M. A. Baranov, G. L. Klimchitskaya, V. M. Mostepanenko, and E. N. Velichko, Phys. Rev. E 99, 022410 (2019).
  * Klimchitskaya et al. (2020) G. L. Klimchitskaya, V. M. Mostepanenko, and E. N. Velichko, Phys. Rev. B 102, 161405(R) (2020).
  * Klimchitskaya et al. (2021) G. L. Klimchitskaya, V. M. Mostepanenko, and E. N. Velichko, Phys. Rev. B 103, 245421 (2021).
  * Klimchitskaya et al. (2022) G. L. Klimchitskaya, V. M. Mostepanenko, and O. Y. Tsybin, Symmetry 14, 2196 (2022).
  * Nykypanchuk et al. (2008) D. Nykypanchuk, M. M. Maye, D. Van Der Lelie, and O. Gang, Nature 451, 549 (2008).
  * Chou et al. (2014) L. Y. Chou, K. Zagorovsky, and W. C. Chan, Nat. Nanotechnol. 9, 148 (2014).
  * Rogers et al. (2016) W. B. Rogers, W. M. Shih, and V. N. Manoharan, Nat. Rev. Mater. 1, 1 (2016).
  * Cui et al. (2022) F. Cui, S. Marbach, J. A. Zheng, M. Holmes-Cerfon, and D. J. Pine, Nat. Commun. 13, 2304 (2022).
  * Campolongo et al. (2010) M. J. Campolongo, S. J. Tan, J. Xu, and D. Luo, Adv. Drug Deliv. Rev. 62, 606 (2010).
  * Hu et al. (2018) Q. Hu, H. Li, L. Wang, H. Gu, and C. Fan, Che. Rev. 119, 6459 (2018).
  * Weiden and Bastings (2021) J. Weiden and M. M. Bastings, Curr. Opin. Colloid Interface Sci. 52, 101411 (2021).
  * Gu et al. (2021) W. Gu, F. Meng, R. Haag, and Z. Zhong, J. Control. Release 329, 676 (2021).
  * Steckl (2007) A. J. Steckl, Nat. Photonics 1, 3 (2007).
  * Bui et al. (2019) H. Bui, S. A. Díaz, J. Fontana, M. Chiriboga, R. Veneziano, and I. L. Medintz, Adv. Opt. Mater. 7, 1900562 (2019).
  * Kawabe et al. (2000) Y. Kawabe, L. Wang, S. Horinouchi, and N. Ogata, Adv. Mater. 12, 1281 (2000).
  * Zhang et al. (2012) Y. Zhang, P. Zalar, C. Kim, S. Collins, G. C. Bazan, and T.-Q. Nguyen, Adv. Mater. 24, 4255 (2012).
  * Khazaeinezhad et al. (2017) R. Khazaeinezhad, S. Hosseinzadeh Kassani, B. Paulson, H. Jeong, J. Gwak, F. Rotermund, D.-I. Yeom, and K. Oh, Sci. Rep. 7, 1 (2017).
  * Jung et al. (2017) W. Jung, H. Jun, S. Hong, B. Paulson, Y. S. Nam, and K. Oh, Opt. Mater. Express 7, 3796 (2017).
  * Yakovchuk et al. (2006) P. Yakovchuk, E. Protozanova, and M. D. Frank-Kamenetskii, Nucleic Acids Res. 34, 564 (2006).
  * Moazzami Gudarzi and Aboutalebi (2021) M. Moazzami Gudarzi and S. H. Aboutalebi, Sci. Adv. 7, eabg2272 (2021).
  * Wittlin et al. (1986) A. Wittlin, L. Genzel, F. Kremer, S. Häseler, A. Poglitsch, and A. Rupprecht, Phys. Rev. A 34, 493 (1986).
  * Inagaki et al. (1974) T. Inagaki, R. Hamm, E. Arakawa, and L. Painter, J. Chem. Phys. 61, 4246 (1974).
  * Weidlich et al. (1987) T. Weidlich, S. Lindsay, and A. Rupprecht, Biopolymers: Original Research on Biomolecules 26, 439 (1987).
  * Paulson et al. (2018) B. Paulson, I. Shin, H. Jeong, B. Kong, R. Khazaeinezhad, S. R. Dugasani, W. Jung, B. Joo, H.-Y. Lee, S. Park, et al., Sci. Rep. 8, 1 (2018).
  * Ge et al. (2020b) L. Ge, X. Shi, Z. Xu, and K. Gong, Phys. Rev. B 101, 104107 (2020b).
  * Esteso et al. (2016) V. Esteso, S. Carretero-Palacios, and H. Míguez, J. Appl. Phys. 119, 144301 (2016).
  * Dzyaloshinskii et al. (1961) I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, Adv. Phys. 10, 165 (1961).
  * Yang et al. (2010) Y. Yang, R. Zeng, H. Chen, S. Zhu, and M. S. Zubairy, Phys. Rev. A 81, 022114 (2010).
  * Munday et al. (2009) J. N. Munday, F. Capasso, and V. A. Parsegian, Nature 457, 170 (2009).