# Interfacial thermal resistance between nano-confined water and functionalized silica: Molecular dynamics simulations

William Gonçalves, Konstantinos Termentzidis

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William Gonçalves, Konstantinos Termentzidis. Interfacial thermal resistance between nano-confined water and functionalized silica: Molecular dynamics simulations. International Journal of Heat and Mass Transfer, 2025, 242, pp.126838. 10.1016/j.ijheatmasstransfer.2025.126838. hal-04989137

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# Interfacial thermal resistance between nano-confined water and functionalized silica: Molecular dynamics simulations

## Article in International Journal of Heat and Mass Transfer · February 2025

DOI: 10.1016/j.ijheatmasstransfer.2025.126838

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William Gonçalves

Institut National des Sciences Appliquées de Lyon

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Konstantinos Termentzidis

French National Centre for Scientific Research

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Interfacial thermal resistance between nano-confined
water and functionalized silica: molecular dynamics
simulations.

William Gonçalves<sup>a,*</sup>, Konstantinos Termentzidis<sup>a</sup>

<sup>a</sup>Univ. Lyon, INSA-Lyon, CETHIL UMR5008, F-69621, Villeurbanne, France

Abstract

Nanoscale engineering enables precise tuning of materials properties through
surface functionalization, impacting energy conversion and heat dissipation
in nanodevices. We used molecular dynamics simulations to observe the
impact of grafting hydrophobic trimethylsilane molecules on the interfacial
thermal resistance between silica and water at the nanoscale. As the level
of hydrophobicity increases, both the cosine of the contact angle and the
water density peak near the interface exhibit linear trend. The hydrogen
bond network of water, initially completed by the silanol (Si-OH) groups
of the silica surface, is disrupted by the hydrophobic molecules. This re-
sults in an exponential variation of the interfacial thermal resistance. We
finally provide a law that relates the cosine of the contact angle and the
interfacial thermal resistance between functionalized silica and water. Our
results are of great interest for experimental researchers using Scanning Ther-
mal Microscopy under humid environments and the multiscale heat transfer
modeling in functionalized nanoporous materials.

*Corresponding author. Email: william.goncalves@tutamail.com

Preprint submitted to International Journal of Heat and Mass Transfer February 24, 2025
*Keywords:* Molecular Dynamics, interfacial thermal resistance, silica/water interface, surface functionalization

Understanding and tuning the interfacial physical properties of water adsorbed on/at solid surfaces is a central theme across many scientific disciplines. Adsorption of water from the surrounding environment onto solid surfaces is inevitable unless the surface is chemically inert or has extremely low surface energy. Its extent plays a crucial role in a wide range of industrial processes, such as nano-manufacturing, electronic devices, electromechanical devices/sensors etc. Water condensation, which specifically modifies heat dissipation within systems, is especially a serious problem in nano-engineering when the dimensions of the involved solid objects shrink to nanoscale. The ratio of surface area to volume increases greatly and the contribution of the liquid-solid interface on heat transport becomes significant, impacting the material and device performance [1–3].

Most inorganic material surfaces exposed to ambient air can adsorb water, and hydrogen bonding interactions between adsorbed water molecules can vary depending on intrinsic properties of material surfaces (e.g., atomic structure, dangling bond, wettability, chemical activity, and surface roughness), and the working conditions (e.g., temperature, humidity, and atmosphere) [4, 3]. Accordingly, the molecular arrangement and vibrational properties of water near solid/liquid interfaces contrast with those of bulk water [3, 5]. Surface chemical functionalization has furthermore appeared as a promising solution for tuning the heat transfer at solid-liquid interfaces. For example, intermediate molecules, whose thermal properties, hydrophilicity, and wettability characteristics match better those of the surrounding liquid, can be
used to tune the thermal mismatch at solid-fluid interfaces [6, 7]. However, because of the discrete nature of the water molecular structure, macroscopic models such as Fourier's law or the Effective Media Approach (EMA) are unable to provide reliable predictions for the effective thermal conductance at the solid-fluid interface.

Molecular Dynamics (MD) simulations have emerged as a powerful and versatile computational tool to study such complex molecular systems with atomic-level precision. Numerous attempts have been made to explain the heat transfer across liquid-solid interfaces [8–10]. For silicon-water interfaces, Yenigun et al. [11] observed that the thickness of the solid nanofilm has an impact on the interfacial thermal resistance (Kapitza resistance) due to variations of the silicon thermal conductivity caused by size effects. Barisik et al. [12] also investigated the wettability and temperature dependence of the Kapitza resistance. They showed that the interfacial thermal resistance decreases as the interface temperature increases. They also controlled the wettability of the silicon surface by changing the strength of the silicon-water interatomic interactions. They obtained larger Kapitza resistance values for surfaces with strong hydrophobicity. In a recent study [13], our group observed that the thermal conductivity of the water slab converges for thicknesses larger than 8 nm, consistent with the study of Liu et al. [14]. Thus, we did not observe any significant impact of the water slab thickness on the interfacial thermal resistance for slabs with a thickness in the order of 10 nm. We have shown that the difference of temperature between the thermostats, $\Delta T$, causes non-linear effects on the relationship between temperature and Kapitza resistance for $\Delta T \ge 50$ K. These studies on the interface between
pure silicon and water lack a more realistic representation of the interface
chemistry. Under ambient conditions, silicon is generally covered by an ox-
ide layer. It is therefore crucial to characterize the thermal conductance
between silicon dioxide (silica) and water.

Silica-based materials present remarkable surface modification capabili-
ties because of the numerous functional groups that can be grafted at their
surface [15–19]. They are promising candidates for tuning the heat trans-
fer at solid-liquid interfaces. However, the experimental measurement of the
thermal conductance using Scanning Thermal Microscopy (SThM) is diffi-
cult because the water meniscus at the mechanical contact between the tip
and the sample creates capillary forces that impact the thermal conductivity
measurements [20, 21]. On the other hand, MD studies require reliable in-
teratomic potentials that include all the specific interactions for bulk silica,
silica surface, hydrophobic surfactant molecules and water, which is still un-
der active development. Goicochea et al. [6] computed the heat conductance
between hydrophilic functionalized silica surfaces and water using MD sim-
ulations. They observed that the surface functionalization using hydrophilic
molecules greatly increases the heat conductance at the interface. Sun et
al. [22] investigated the interfacial heat transfer between hydroxylated silica
and various organic liquids. They observed that silanol groups act as phonon
bridges, promoting the heat conductance at the solid-organic liquid interface.
To tune the hydrophobicity of the silica surface, recent studies [23] still at-
tempt to modify the strength of the interatomic interactions between Si-O
atoms of the silica surface and water. In our present study, our approach
will be to simulate the full chemical structure of the silica surface with hy-
drophobic surfactant molecules. The purpose is to characterize the interfacial
thermal resistance at the water-silica interface with a hydrophobicity tuned
by the surface modification of silica using different surfactant coverages. We
introduce a unique combination of MD forcefields to simulate the interactions
between functionalized silica and water and provide silica water interfacial
thermal resistance values. To our best knowledge, this is the first time that
Kapitza resistance values have been computed for functionalized silica with
a mix of hydrophilic silanol and hydrophobic trimethylsilane at various levels
of surface coverage. The results are promising for experimental researchers
working with SThM where the probe-sample thermal interactions are still not
well understood and, more broadly, for communities interested in optimizing
heat transfer at the nanoscale.

MD simulations are performed using the Large-scale Atomic/Molecular
Massively Parallel Simulator (LAMMPS) [24]. The equations of motion are
integrated using a velocity-Verlet algorithm with a 1.0 fs timestep. Our sys-
tem is composed of silica (Si-O atoms), hydrophilic silanol groups (Si-OH) at
the surface, hydrophobic Trimethylsilane surfactant molecules (C₃H₉Si) and
water molecules (H₂O) as depicted in Fig. 1a. Interatomic interactions are
defined using a combination of Emami et al. [25] forcefield for silica bulk and
silanol (COMPASS form), the SPC/E model [26, 27] for water molecules and
a Lennard-Jones (LJ) potential with GROMOS 54A7 parameters [28] taken
from the Automated force field Topology Builder (ATB) [29]. A 10 Å cut-off
is applied to all non-bonded interactions, and the Particle-Particle Particle-
Mesh (PPPM) method with an error tolerance of 10⁻⁴ is used for long-range
electrostatic interactions, using the same cut-off for real space calculation.
Non-bonded interactions are disabled for all 1-2 (directly bonded) and 1-3 (angle) neighbors in both silica (including silanols) and trimethylsilane molecules. For silica and silanol groups, the COMPASS style for non-bonded interactions writes:

$$E_{\text{silica}} = \sum_{ij} \varepsilon_{ij} \left[ 2 \left( \frac{\sigma_{ij}}{r_{ij}} \right)^9 - 3 \left( \frac{\sigma_{ij}}{r_{ij}} \right)^6 \right] + \frac{1}{4\pi\varepsilon_0} \sum_{ij} \frac{q_i q_j}{r_{ij}} \quad (1)$$

with all the self-term parameters listed in Tab. 1.

The non-bonded interactions for water and hydrophobic trimethylsilane molecules are simulated using LJ potentials with Coulombic terms:

$$E_{\text{water/trim}} = \sum_{ij} 4\varepsilon_{ij} \left[ \left( \frac{\sigma_{ij}}{r_{ij}} \right)^{12} - \left( \frac{\sigma_{ij}}{r_{ij}} \right)^{6} \right] + \frac{1}{4\pi\varepsilon_0} \sum_{ij} \frac{q_i q_j}{r_{ij}} \quad (2)$$

with self terms listed in Tab. 2.

The mixed terms are calculated using arithmetic mixing rules with the LJ form (eq. 2):

$$\varepsilon_{ij}^{\text{mix}} = \sqrt{\varepsilon_i \varepsilon_j}, \quad \sigma_{ij}^{\text{mix}} = \frac{\sigma_i + \sigma_j}{2} \quad (3)$$

Due to the LJ exponents, which have stronger repulsive interactions than the COMPASS style used for silica, the initially calculated values for the mixed terms in the silica-water interactions were excessively strong. This was evident from the calculated contact angle between hydrophilic silica (silica with surface silanol groups) and water. To address this, we reduced $\varepsilon_{ij}^{\text{mix}}$ for the interactions between silica (Si, $O_{\text{bulk}}$, $O_{\text{silanol}}$, $H_{\text{silanol}}$) and water molecules, making the contact angle values more consistent with experimental observations. The final values were adjusted to 10% of the initial $\varepsilon_{ij}^{\text{mix}}$ calculated using eq. 3. A detailed discussion of this modification is available
in the Supporting Information. After the interaction model has been calibrated, no further modifications are made to it. The hydrophobicity of the silica surface is adjusted solely by grafting trimethylsilane molecules.

Bonded interactions are simulated using harmonic bond and angle potentials.

$$E_{bond} = \sum_{ij,bonded} K_{r,ij} (r_{ij} - r_{0,ij})^2 \quad (4)$$

$$E_{angle} = \sum_{ijk,bonded} K_{\theta,ijk} (\theta_{ijk} - \theta_{0,ijk})^2 \quad (5)$$

The bonds and angles of the water molecules are constrained using the SHAKE algorithm [30]. For silica atoms (Tab. 1), 2 harmonic bonds (Si–O<sub>bulk</sub> or silanol, O<sub>silanol</sub>–H<sub>silanol</sub>) and 3 harmonic angles (O<sub>bulk</sub>–Si–O<sub>bulk</sub>, Si–O<sub>bulk</sub>–Si, Si–O<sub>silanol</sub>–H<sub>silanol</sub>) are used to model the silica bulk structure as described in Emami et al. study [25]. Hydrophobic trimethylsilane are grafted to the silica surface at the silanol sites. The hydrogen atom (H<sub>silanol</sub>) is removed and replaced by the C<sub>3</sub>H<sub>9</sub>Si molecule that compensates the same electric charge of +0.4e, keeping the charge neutrality of the system. One Si<sub>trim</sub>–O<sub>silanol</sub> bond and 3 O<sub>silanol</sub>–Si<sub>trim</sub>–C<sub>trim</sub> (one for each Carbon atom) + 1 Si–O<sub>silanol</sub>–Si<sub>trim</sub> harmonic angles are used to fix the molecule on the surface. All the bonding and angle parameters are given in Tab. 3

The atom coordinates for the amorphous silica structure (SiO<sub>2</sub>+ Si–OH silanol groups at the surface) are taken from the Supporting Information of Emami et al. [25]. From the surface fully covered by hydrophilic silanol groups, we randomly replace the silanols by the hydrophobic trimethylsilane molecules. Fig. 1b shows that the surface density of silanols (ρ<sub>S-SiOH</sub>) decreases as the surface density of trimethylsilane (ρ<sub>S-C<sub>3</sub>H<sub>9</sub>Si</sub>) increases. In
other words, we increase the hydrophobicity of the silica surface by increasing
the trimethylsilane surface density. Our trimethylsilane-coated surface (100%
coverage in Fig. 1b) still contains a few silanol groups (≈ 1.2 SiOH/nm²).
Because of the amorphous structure, some silanol groups are confined inside
the silica near the surface. As the volume of the trimethylsilane molecule is
much larger than a silanol group, we simply left the silanols unchanged to
avoid overlapping atoms and complications during the surface relaxation.

For the relaxation of the solid substrate of silica, periodic boundaries are
used and we ensure that the length of the system in the direction normal to
the surface is much larger than the cut-off distance (minimum 2 times larger)
so that unwanted long-range interactions do not affect the system across the
boundaries. Temperature is gradually introduced to the system from 0 to
300 K while a zero pressure is maintained during 100 ps using an anisotropic
Nose-Hoover barostat with a damping parameter of 5000 fs. The first stud-
ied configuration is a nanodroplet of water on a functionalized silica film of
dimensions 16 × 8 × 3 nm³ (x,y,z) shown in Fig. 1c. The contact angle,
θc, between the water droplet and the solid surface indicates the level of the
surface hydrophobicity. The contact angle value is calculated from the water
isodensity line that corresponds to 50% of the bulk density. For more infor-
mation about the contact angle calculation, we used the same methodology
as Isaiev et al.[31]. For the second configuration, a water nanoslab is sand-
wiched between two silica films, identical in dimensions to those in the first
system, featuring functionalized surfaces (Fig. 1d). For this second system,
a second equilibration phase of 100 ns is applied. The barostat equilibrates
the system in the periodic directions, while the positions of the solid plates
exhibit slight oscillations in the non-periodic direction due to the equilibra-
tion of the water molecules. After equilibration, the barostat is removed, and
only the thermostat is retained to regulate the temperature. Following the
Non-Equilibrium Molecular Dynamics (NEMD) methodology, a fixed layer
of atoms is imposed (as illustrated in Fig. 1d) and a heat flux is applied to
the system by using a hot source at 330 K and a cold sink at 270 K. At
the solid-liquid interface, a temperature jump can be observed in the tem-
perature profile. This temperature jump is used to compute the interfacial
thermal resistance (Kapitza resistance). More details about the methodology
can be found in the Supporting Information and in our previous study [13]
as we used the same methodology. The average temperature in all of our
simulations is 300 K. To evaluate the error bars of our results, we performed
three simulations for each configuration, each with a different distribution of
initial velocities.

Fig. 2 shows the density maps for the water nanodroplets on the silica
substrate with ρ<sub>S-C<sub>3</sub>H<sub>9</sub>Si</sub> = 0, 1.48 and 2.81 C<sub>3</sub>H<sub>9</sub>Si per nm<sup>2</sup>, along with the
cosine of the contact angles, as described by Young's equation for surface
free energy. Without any hydrophobic molecule on the substrate (ρ<sub>S-C<sub>3</sub>H<sub>9</sub>Si</sub> =
0 N<sub>C<sub>3</sub>H<sub>9</sub>Si</sub>·nm<sup>-2</sup>), the silica surface is completely hydrophilic and exhibits
a cosine of contact angle of approximately 0.65 (θ<sub>c</sub> = 49°, see the results in
Fig. 2b). As the surface density of trimethylsilane increases, the cosine of the
contact angle decreases linearly, reaching -0.5 (θ<sub>c</sub> = 120°) for ρ<sub>S-C<sub>3</sub>H<sub>9</sub>Si</sub> = 2.81.
This result confirms the increase of the silica surface hydrophobicity by the
graft of trimethylsilane molecules. However, as discussed in the Supporting
information, the absolute value of the contact angle may slightly change
for different atomistic models. Thus, the main information revealed by our
results in Fig. 2b is the linear trend relating the cosine of the contact angle
and the hydrophobic molecule surface density. Similar trends have been
observed by simply changing the $\epsilon_{water-silica}^{mix}$ in the Lennard-Jones potential
[32, 23, 12].

The shape of the water nanodroplet remains symmetric as $\rho_{S-C_3H_9Si}$ increases, due to the random distribution of the hydrophobic molecules on the surface. On the water density maps (Fig. 2a), large values of density (up to $1.4-1.6 \text{ g.cm}^{-3}$) are locally observed close to the interface for the hydrophobic surface ($\rho_{S-C_3H_9Si}=2.81 \text{ N}^{C_3H_9Si}.\text{nm}^{-2}$). Likewise, for the water slab system sandwiched between two hydrophobic silica films, the water density profile in Fig. 3a shows a water density peak value around $1.1-1.2 \text{ g.cm}^{-3}$. In our previous study for silicon surfaces [13], these values were slightly larger (approximately $1.4 \text{ g.cm}^{-3}$ for the water density near crystalline silicon and $1.2 \text{ g.cm}^{-3}$ near amorphous silicon). Compared to the literature on the silicon-water interface [31, 33], our water density map for the hydrophobic surface reveals a less ordered and discontinuous stratification of water density, which tends to decrease the mean value of the peak near the interface (Fig. 3a). Indeed, the hydrophobicity of our surface is tuned by the randomly grafted trimethylsilane molecules. As a result, discontinuities in the surface hydrophobicity appear and are reflected in the water stratification. In Fig. 3b, the maximum of the water density (which corresponds to the peak value near the interface in Fig. 3a) is plotted against the trimethylsilane surface density. A linear increasing trend is observed from $1 \text{ g.cm}^{-3}$ (≈ the bulk value) for the hydrophilic silica surface to $1.12 \text{ g.cm}^{-3}$ for the hydrophobic surface. From
the literature, we find that hydrophilic substrates show stratified adsorption
structures because of strong solid-liquid interactions [34, 22], which is not
consistent with our results of Fig. 3b. This is likely due to the dominant
influence of the hydrogen bond network structure on the water structural
properties near the interface. The water stratification is induced by a modi-
fication of the hydrogen bond network (and therefore the orientation of the
water molecules) at the hydrophobic solid/liquid interface [4, 35, 3]. Malani
et al. [36] explained that the oxygen and hydrogen atoms of the OH groups at
the surface of hydrophilic silica complete the hydrogen bond network of the
water. These authors observed that the water close to the hydrophilic surface
exhibits bulk-like properties, which is consistent with our results where den-
sity stratification disappears for the hydrophilic surface (see the black boxes
in Fig. 3). To confirm this statement, we compared the orientations of the
water molecules in the bulk and at the hydrophilic, hydrophobic interfaces.
The results provided in our supporting information (section S3) confirm the
bulk-like structure at the hydrophilic interface and the stratified structure
at the hydrophobic interface. We therefore conclude that the lack of water
stratification for the hydrophilic substrate is due to the interfacial OH groups
that lead to a bulk-like structure by completing the hydrogen bond network
of the water at the interface. We will now evaluate the impact of the surface
tuning on the interfacial thermal resistance.

In Fig. 4, the Kapitza resistance is shown as a function of the cosine of the
contact angle. Our results exhibit a clear exponential decay of the interfacial
thermal resistance as the hydrophobicity level of the silica substrate decreases
(increase of cos(θc)). As the tuned hydrophobicity decreases, the structure of
the water near the interfaces shifts from a stratified to a bulk-like structure. The hydrophilic OH groups of the silanols complete the hydrogen bond network of the interfacial water which enhance the phonon transmission. The consequence on the Kapitza resistance is exponential, quantified by the fit function shown in Fig. 4. It is important to note that the absolute values of the contact angle may vary slightly depending on the atomistic model and the strength of the interactions between silica and water. However, we expect that the exponential relationship between the interfacial thermal resistance and the cosine of the contact angle will remain consistent, regardless of the simulation model used.

In conclusion, we introduced a combination of two atomistic models for the simulation of functionalized silica surfaces. The first model for hydrophilic silica is taken from Emami et al.[25] study. We replaced the hydrophilic silanol groups by hydrophobic trimethylsilane molecules using GROMOS 54A7 forcefield parameters [28, 29] and prepared samples with increasing hydrophobicity levels. Our results reveal that the cosine of the contact angle and the water density stratification both exhibit linear trends as a function of the trimethylsilane surface density. On the other hand, the interfacial thermal resistance decreases exponentially with decreasing hydrophobicity. According to our results, the interfacial thermal resistance is five times larger between water and hydrophobic silica than with hydrophilic silica, offering great potential to tune the heat conductance at nanoscale using surface modification. Further studies should be carried out to determine the impact of the different vibrational modes on the exponential growth of the interfacial thermal resistance. For the moment, our resulting equation can be used for
various applications such as SThM models at the tip-sample contact in hu-
mid conditions [20, 21], multiscale modeling of heat transfer in nanoporous
materials with functionalized silica surfaces [37, 38], tuning heat dissipation
in Micro/Nano Electro-Mechanical Systems (MEMS/NEMS) under ambient
conditions.

Acknowledgements

This work was funded by the ANR project "Hotline" ANR-19-CE09-0003. We are also thankful to GENCI-IDRIS for providing computational ressources with the grant 2021-A0110911092. We would like to thank Vladimir Lysenko, Oksana Makukha, Mykola Isaiev and Séverine Gomès for the fruitful discussions.

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<table><caption>Table 1: Interaction table for the non-bonded interactions in silica taken from Emami et al. [25].</caption><thead><tr><th rowspan="2"></th><th rowspan="2">charge (e)</th><th colspan="2">COMPASS</th></tr><tr><th>σ<sub>ii</sub> [Å]</th><th>ε<sub>ii</sub> [eV]</th></tr></thead><tbody><tr><td><strong>silica</strong></td><td></td><td></td><td></td></tr><tr><td>Si</td><td>+1.1</td><td>4.2</td><td>0.0034696</td></tr><tr><td>O<sub>bulk</sub></td><td>-0.55</td><td>3.6</td><td>0.0017348</td></tr><tr><td>O<sub>silanol</sub></td><td>-0.675</td><td>3.6</td><td>0.0052044</td></tr><tr><td>H<sub>silanol</sub></td><td>+0.4</td><td>1.098</td><td>0.00056381</td></tr></tbody></table>

<table><caption>Table 2: Interaction table for the non-bonded interactions of the water [27] and trimethylsilane [28, 29] molecules.</caption><thead><tr><th></th><th>charge (e)</th><th>σ<sub>ii</sub> [Å]</th><th>ε<sub>ii</sub> [eV]</th></tr></thead><tbody><tr><td><strong>water</strong></td><td></td><td></td><td></td></tr><tr><td>O<sub>H<sub>2</sub>O</sub></td><td>-0.8476</td><td>3.166</td><td>0.0067366</td></tr><tr><td>H<sub>H<sub>2</sub>O</sub></td><td>+0.4238</td><td>0</td><td>0</td></tr><tr><td><strong>trimethylsilane</strong></td><td></td><td></td><td></td></tr><tr><td>C<sub>trim</sub></td><td>-0.548</td><td>3.581</td><td>0.0028774</td></tr><tr><td>H<sub>trim</sub></td><td>+0.122</td><td>2.373</td><td>0.0012279</td></tr><tr><td>Si<sub>trim</sub></td><td>+0.946</td><td>3.385</td><td>0.025379</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>d</figcaption></figure>

<figure><img src="image_7.png" /></figure>

Figure 1: a) Snapshot of the amorphous silica surface with hydrophilic silanol groups and a hydrophobic trimethylsilane molecule. b) Surface densities of trimethylsilane molecules and silanols as a function of trimethylsilane coverage percentage. c) A water nanodroplet on a functionalized silica surface for the calculation of contact angle. d) A water slab sandwiched between two functionalized silica nanofilms for the calculation of the Kapitza resistance. The frozen atoms, as well as the hot and cold thermostated regions of the silica substrate as part of the NEMD simulation methodology, are also shown in the figure.
<table><caption>Table 3: Interaction table for bonded interactions.</caption><thead><tr><th>Bonds</th><th>r<sub>0,ij</sub> [Å]</th><th>K<sub>r,ij</sub> [eV/Å<sup>2</sup>]</th></tr></thead><tbody><tr><td>Si–O<sub>bulk or silanol</sub></td><td>1.68</td><td>12.3604</td></tr><tr><td>O<sub>silanol</sub>–H<sub>silanol</sub></td><td>0.945</td><td>21.4681</td></tr><tr><td>Si<sub>trim</sub>–O<sub>silanol</sub></td><td>1.5</td><td>8.2982</td></tr><tr><td>H<sub>trim</sub>–C<sub>trim</sub></td><td>1.09</td><td>15.1585</td></tr><tr><td>Si<sub>trim</sub>–C<sub>trim</sub></td><td>1.89</td><td>15.5593</td></tr></tbody></table><table><thead><tr><th>Angles</th><th>θ<sub>0,ijk</sub> [°]</th><th>K<sub>θ,ijk</sub> [eV/rad<sup>2</sup>]</th></tr></thead><tbody><tr><td>O<sub>bulk</sub>–Si–O<sub>bulk</sub></td><td>109.5</td><td>4.337</td></tr><tr><td>Si–O<sub>bulk</sub>–Si</td><td>149.0</td><td>4.337</td></tr><tr><td>Si–O<sub>silanol</sub>–H<sub>silanol</sub></td><td>115.0</td><td>2.169</td></tr><tr><td>H<sub>trim</sub>–C<sub>trim</sub>–H<sub>trim</sub></td><td>108.0</td><td>2.177</td></tr><tr><td>H<sub>trim</sub>–C<sub>trim</sub>–Si<sub>trim</sub></td><td>111.0</td><td>2.392</td></tr><tr><td>C<sub>trim</sub>–Si<sub>trim</sub>–C<sub>trim</sub></td><td>109.5</td><td>2.070</td></tr><tr><td>O<sub>silanol</sub>–Si<sub>trim</sub>–C<sub>trim</sub></td><td>109.5</td><td>2.070</td></tr><tr><td>Si–O<sub>silanol</sub>–Si<sub>trim</sub></td><td>149.0</td><td>4.337</td></tr></tbody></table>
<figure><img src="image_8.png" /><figcaption>Figure 2: a) Density maps of water nanodroplets with increasing surface density of Trimethylsilane (C₃H₉Si). Three density maps representing different levels of hydrophobicity are depicted. b) The cosine of the contact angle as a function of the Trimethylsilane surface density.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>Figure 3: a) Density profiles of the nanoconfined water sandwiched between functionalized silica films with increasing surface density of Trimethylsilane (C₃H₉Si) b) Maximum value of the water density (height of the first density peak near the silica-water interface) as a function of the Trimethylsilane surface density.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 4: Kapitza resistance between functionalized amorphous silica and water as a function of the cosine of the contact angle.</figcaption></figure>