<figure><img src="image_1.png" /></figure>

HAL
open science

# Reactive molecular dynamics simulation approach to plasma polymerization

Pascal Brault, Maxime Mikikian

► To cite this version:

Pascal Brault, Maxime Mikikian. Reactive molecular dynamics simulation approach to plasma polymerization. 2025. hal-05407038

HAL Id: hal-05407038

https://hal.science/hal-05407038v1

Preprint submitted on 9 Dec 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Reactive molecular dynamics simulation approach to
plasma polymerization

Pascal Brault<sup>a,b</sup>, Maxime Mikikian<sup>a</sup>

<sup>a</sup>GREMI, CNRS, Université d'Orléans, CNRS, 14 rue d'Issoudun, 45067, Orléans, France

<sup>b</sup>MS4ALL, 1 avenue du champ de Mars, 45100, Orléans, France

**Abstract**

Reactive Molecular Dynamics (rMD) simulations have emerged as a powerful
tool for investigating atomic-scale processes in plasma-polymer interactions
(at surfaces and in volume), particularly in plasma polymerization: a radical-
driven chemical vapor deposition process. This review focuses on the applica-
tion of rMD to hydrocarbon plasma-polymer systems, highlighting the use of
reactive potentials such as REBO, AIREBO, and ReaxFF to model bond for-
mation, breaking, and surface interactions. The limitations of rMD, including
simulation size constraints (10⁸ to 10¹⁰ atoms), are discussed, alongside the
methodologies for simulating plasma processes, such as ion bombardment,
film growth, and surface functionalization. Key findings include the role of
kinetic energy transfer in etching, grafting, and cross-linking mechanisms,
as well as the influence of substrate temperature and precursor composition
on film structure and properties. The review also addresses the challenges
of replicating realistic plasma conditions and the importance of integrating
plasma kinetics models to enhance simulation accuracy. Overall, rMD pro-
vides critical insights into the mechanisms governing plasma-polymer inter-
actions, bridging the gap between experimental observations and theoretical
predictions.

*Keywords:* Molecular Dynamics, simulation, reactive potential, ReaxFF, REBO, plasma polymerization
# 1. INTRODUCTION

Reactive Molecular Dynamics (rMD) simulations are a powerful tool for investigating atomic-scale processes occurring in plasma volume and at material boundaries, such as surfaces where thin film growth or plasma treatments, including oxidation, grafting, and cross-linking, take place [1–3]. In this context, plasma polymerization refers to a radical-dominated chemical vapor deposition process occurring in a plasma reactor, where monomer gases are excited to generate reactive species that form thin polymerized coatings on substrates (see Figure 1). This process typically results in amorphous and cross-linked structures [4–10].

<figure><img src="image_3.png" /><figcaption>Figure 1: Schematic representation of plasma polymerization. Reprinted with permission from [8].</figcaption></figure>

The fundamental mechanism underlying polymerization involves the chemical reactivity between monomers and radicals, which are both produced in the plasma and interact further with surfaces, including substrates for thin film growth. Given that molecular dynamics studies on hydrocarbon plasmas are more extensive than those on organosilicon plasmas, this review will focus exclusively on hydrocarbon plasma-polymer interactions. A primary limitation of rMD in studying plasma-polymer systems is the maximum achievable simulation size, which ranges up to (100-500 nm)$^3$, corresponding to approximately $10^8$ to $10^{10}$ atoms.
## 2. MOLECULAR DYNAMICS: PRINCIPLES AND METHOD-OLOGY

Molecular Dynamics is a simulation method that describes the behavior of an N-body system by treating each of the N species as distinct entities governed by Newtonian mechanics. Each atom i is characterized by a defined position and velocity, which depend solely on the forces exerted on it. The equations of motion are given by Newton's second law [11–14]:

$$m_i \frac{d^2 \vec{r}_i(t)}{dt^2} = \vec{f}_i(t), \quad \text{with} \quad \vec{f}_i(t) = -\frac{\partial V(\vec{r}_1(t), \vec{r}_2(t), \dots, \vec{r}_n(t))}{\partial \vec{r}_i(t)}, \quad (1)$$

where $\vec{r}_i(t)$ is the position of atom i at time t, $m_i$ is its mass, and $\vec{f}_i(t)$ represents the force acting on atom i at time t. The interaction potential $V(\vec{r}_1(t), \vec{r}_2(t), \dots, \vec{r}_n(t))$ defines the forces between atoms. By iteratively solving these equations, the behavior of the atomic assembly over time can be determined.

To accurately simulate these systems, the initial configuration should ideally match experimental conditions. The forces between atoms are derived from the interaction potential $V$. Potentials can be categorized into two main types: ab initio potentials, which are based on quantum mechanical calculations and require substantial computational resources [15], and semi-empirical potentials, which approximate these forces. They enable significantly faster simulations, since they are built as "universal" mathematical functional forms, parametrized on experimental or quantum chemistry results.

For plasma polymerization or grafting, reactive potentials (including variable charge models) are essential to account for bond formation and breaking. Several suitable force fields are available, although their transferability may vary. Preliminary tests (bond lengths and angles, stability of the monomer, etc) are necessary to verify their applicability to the specific system under investigation.

The simplest and fastest reactive potential is the Reactive Bond Order (REBO) potential, which was developed for carbon, hydrocarbon, and fluorocarbon systems [16–21]. The REBO potential is an extension of the Tersoff potential [22–24], with modifications introduced by Brenner to improve the description of bond order, repulsive interactions, and attractive pair terms.
There are two generations of the REBO potential [16–18, 25]. In the first-generation potential, the total energy of hydrocarbons is expressed as:

$$E = \sum_{i} \sum_{j(>i)} [V_{R}(r_{ij}) - \bar{B}_{ij}V_{A}(r_{ij})], \quad (2)$$

where $\bar{B}_{ij}$, $V_R(r_{ij})$, and $V_A(r_{ij})$ represent the bond order, repulsive, and attractive potential terms, respectively. The bond order term $\bar{B}_{ij}$ is defined as:

$$\bar{B}_{ij} = \frac{b_{ij} + b_{ji}}{2} + F_{ij}(N_{i}^{(t)}, N_{j}^{(t)}, N_{ij}^{(\text{conj})}), \quad (3)$$

where $F_{ij}$ is an interpolation function used to ensure the continuity of the potential, employing the cutoff function $f_c(r)$:

$$f_c = \begin{cases} 1 & \text{if } r < R - D, \\ \frac{1}{2} - \frac{1}{2} \sin \left[ \frac{1}{2} \pi (r - R) / D \right] & \text{if } R - D < r < R + D, \\ 0 & \text{if } r > R + D. \end{cases} \quad (4)$$

Here, $N_i^{(t)}$ and $N_j^{(t)}$ denote the number of atoms bonded to atoms i and j, respectively, defining the total number of neighbors, while $N_{ij}^{(\text{conj})}$ is the conjugated term for atoms i and j. R and D are some specific cutoff lengths. The full details of each term are provided by Brenner [17].

The repulsive and attractive pair terms are given by [17]:

$$V_R(r_{ij}) = f_{ij}(r_{ij}) \frac{D_{ij}^{(e)}}{S_{ij} - 1} \exp \left[ -\sqrt{2S_{ij}} \beta_{ij} (r - R_{ij}^{(e)}) \right], \quad (5)$$

$$V_A(r_{ij}) = f_{ij}(r_{ij}) \frac{D_{ij}^{(e)} S_{ij}}{S_{ij} - 1} \exp \left[ -\sqrt{2/S_{ij}} \beta_{ij} (r - R_{ij}^{(e)}) \right]. \quad (6)$$

The function $f_{ij}(r)$, which restricts the pair potential to nearest neighbors, is defined as:

$$f_{ij}(r) = \begin{cases} 1 & \text{if } r < R_{ij}^{(1)}, \\ \frac{1}{2} \left[ 1 + \cos \left( \frac{\pi (r - R_{ij}^{(1)})}{R_{ij}^{(2)} - R_{ij}^{(1)}} \right) \right] & \text{if } R_{ij}^{(1)} < r < R_{ij}^{(2)}, \\ 0 & \text{if } r > R_{ij}^{(2)}. \end{cases} \quad (7)$$
This formulation highlights the correspondence to Morse potentials. If $S_{ij} = 2$, the pair terms reduce to the standard Morse potential, where the parameters $D_{ij}^{(e)}$, $R_{ij}^{(e)}$, and $\beta_{ij}$ correspond to the usual Morse parameters.

Since the first-generation REBO potential does not account for different bond types (e.g., single, double, or triple bonds), the second-generation REBO potential was developed [25]. This version introduces a generalized bond order function $B_{ij}$:

$$ \bar{B}_{ij} = \frac{1}{2} [b_{ij}^{\sigma-\pi} + b_{ji}^{\sigma-\pi}] + b_{ji}^{\pi}, \qquad (8) $$

where $b_{ij}^{\sigma-\pi}$ and $b_{ji}^{\sigma-\pi}$ depend on the local coordination and bond angles for atoms i and j. The term $b_{ji}^{\pi}$ is further expressed as:

$$ b_{ji}^{\pi} = \prod_{ij}^{RC} + \prod_{ij}^{DH}, \qquad (9) $$

where $\prod_{ij}^{RC}$ depends on whether the conjugate bond between atoms i and j exhibits radical character, and $\prod_{ij}^{DH}$ depends on the dihedral angle for carbon-carbon double bonds. The term $b_{ij}^{\sigma-\pi}$ in Equation (8) is given by:

$$ b_{ij}^{\sigma-\pi} = \left[ \sum_{k \neq i, j} f_{ik}^{c}(r_{ik}) G(\cos(\theta_{ijk})) \exp(\lambda_{ijk}) + P_{ij}(N_{i}^{(C)}, N_{i}^{(H)}) \right]^{-1/2}, \quad (10) $$

where $f_{ik}^{c}$ is a cutoff function ensuring that only nearest-neighbor interactions are considered, $G(\cos(\theta_{ijk}))$ is the angular function, and $P_{ij}$ is a bicubic spline for potential interpolation. The quantities $N_{i}^{(C)}$ and $N_{i}^{(H)}$ represent the number of carbon and hydrogen atoms, respectively, that are neighbors of atom i:

$$ N_{i}^{(C)} = \sum_{k \neq i, j}^{\text{carbon atoms}} f_{ik}^{c}(r_{ik}), \qquad (11) $$

$$ N_{i}^{(H)} = \sum_{l \neq i, j}^{\text{hydrogen atoms}} f_{il}^{c}(r_{il}). \qquad (12) $$
To enhance flexibility and account for long-range interactions between hydrocarbon species, the second-generation REBO potential was extended by incorporating torsional and Lennard-Jones terms, resulting in the AIREBO (Adaptive Intermolecular Reactive Empirical Bond Order) potential. The total energy in the AIREBO framework is given by:

$$E = E^{\text{REBO}} + E^{\text{LJ}} + E^{\text{tors}}, \qquad (13)$$

where $E^{\text{REBO}}$ is given by Equation (2), $E^{\text{LJ}}$ is the Lennard-Jones potential, which accounts for long-range interactions, and $E^{\text{tors}}$ is the torsional contribution, essential for studying the reactivity of large hydrocarbon molecules. A similar approach, based on the Stillinger-Weber potential [26, 27] but without bond order calculations, has also been developed to describe plasma-polymer interactions [28].

For systems beyond hydrocarbons (i.e. including other atoms than C and H), the ReaxFF force field is often employed [29–32]. In ReaxFF, the bond order is defined as distance-dependent, enabling precise descriptions of bond formation and breaking. This force field also allows for variable atomic charges [33, 34], based on electronegativity equalization and three key assumptions: (a) the electronegativity of an atomic site depends on the atom type and charge, and is influenced by the electrostatic potential from neighboring atoms; (b) charge transfer between atomic sites respects electronegativity equality; and (c) variable charges follow an extended Lagrangian formalism, where they are treated as dynamic variables with fictitious mass, velocity, and kinetic energy, evolving according to Newtonian mechanics.

In the ReaxFF potential, the total energy of the system is expressed as the sum of various interaction contributions [29]:

$$E_{\text{system}} = E_{\text{bond}} + E_{\text{Lp}} + E_{\text{over}} + E_{\text{under}} + E_{\text{val}} + E_{\text{pen}} + E_{\text{coa}} + E_{C_2} + E_{\text{tors}} \\ + E_{\text{conj}} + E_{\text{H-bond}} + E_{\text{vdW}} + E_{\text{Coulomb}}, \qquad (14)$$

where: $E_{\text{bond}}$ is the bond energy, $E_{\text{Lp}}$ is the lone pair energy, $E_{\text{over}}$ is the overcoordination energy, $E_{\text{under}}$ is the undercoordination energy, $E_{\text{val}}$ is the valence angle term, $E_{\text{pen}}$ is the penalty energy, $E_{\text{coa}}$ is the three-body conjugation term, $E_{C_2}$ is the correction for $C_2$, $E_{\text{tors}}$ is the torsion angle term, $E_{\text{conj}}$ is the four-body conjugation term, $E_{\text{H-bond}}$ is the hydrogen bond interaction energy, $E_{\text{vdW}}$ is the van der Waals interaction energy, and $E_{\text{Coulomb}}$
is the Coulomb interaction energy between atoms, determined by partial charges assigned via the Electronegativity Equalization Method [35, 36].

For clarity, the detailed expressions for each energy term are omitted here but are fully described elsewhere [29, 30]. The bond order concept in ReaxFF is particularly well-developed and is expressed as the sum of three contributions: single, double, and triple bonds, where relevant. The bond order $BO_{ij}$ between atoms i and j is defined as:

$$BO_{ij} = BO_{ij}^{\sigma} + BO_{ij}^{\pi} + BO_{ij}^{\pi\pi}, \qquad (15)$$

where:

$$BO_{ij}^{\sigma} = \exp \left[ p_{bo,1} \left( \frac{r_{ij}}{r_{0}^{\sigma}} \right)^{p_{bo,2}} \right],$$

$$BO_{ij}^{\pi} = \exp \left[ p_{bo,3} \left( \frac{r_{ij}}{r_{0}^{\pi}} \right)^{p_{bo,4}} \right],$$

$$BO_{ij}^{\pi\pi} = \exp \left[ p_{bo,5} \left( \frac{r_{ij}}{r_{0}^{\pi\pi}} \right)^{p_{bo,6}} \right].$$

Here, $BO_{ij}$ depends on the local environment. For carbon-carbon interactions, all three contributions in Equation (15) are utilized, yielding a maximum bond order of 3, while for C-H interactions, only the $\sigma$ contribution is considered, resulting in a maximum bond order of 1 [30].

This concise overview of interaction potentials summarizes the primary families of potentials used to model plasma-polymer interactions. It is important to note that electrons are not explicitly described in rMD simulations due to their exceedingly low mass, which would significantly increase computational demands. However, electrons are incorporated in two force fields: eFF [37, 38] and eReaxFF [31, 39, 40]. The eFF force field is non-reactive and primarily dedicated to studies of warm dense matter. While eReaxFF can describe electron motion in plasmas, it does not capture electron-induced dissociation or excitation mechanisms, which are critical in plasma environments. Additionally, in these force fields, the electron mass is modeled as a non-reactive H⁻ ion (1.0 g.mol⁻¹), which limits the accurate description of electron collision processes, particularly energy transfer mechanisms.

The next step involves defining a simulation box that represents the targeted experiment. As shown in Equation (1), two initial conditions are re-
quired to solve the equations of motion: initial positions (determined by the
system under study) and initial velocities (which capture the essential dy-
namics of the problem). In gas-phase polymerization simulations, the initial
positions of radicals and monomers are typically randomly distributed within
the simulation box, while initial velocities are sampled from a thermal distri-
bution at the operating temperature. If the vapor interacts with a substrate,
the substrate's atomic positions are derived from exact crystal coordinates
for crystalline materials or prepared separately for amorphous substrates. In
cases where the substrate is a polymer subjected to ion bombardment, ion
velocities are calculated from their kinetic energies, and their initial positions
are randomly assigned above the substrate surface.

3. PLASMA PROCESSES, RESULTS, AND DISCUSSION

3.1. PLASMA-POLYMER MECHANISMS UNDER STUDY

The application rMD simulations to plasma-polymer interactions began
in the late 1990s, following the development of the REBO potential. Early
studies focused on the interactions of ions, such as Ar+, N+, O+, C_xH_y+, and
C_xF_y+, with polymer films, as well as deposition and etching processes [19, 41–
54]. These species were selected for study because they are expected to form
in plasma environments. Notably, ions are not treated as charged particles
in these simulations; instead, they are assumed to be neutralized close to the
substrate surface and modeled as "fast" neutral radicals. This assumption is
justified by the neutralization of ions in the plasma sheath as they approach
the surface. The primary objective of these studies is to elucidate the mech-
anisms underlying plasma-surface interactions. Most "interaction" studies
were conducted between 1995 and 2010, but recent work has expanded to
include polyatomic ions (e.g., CH_x, C_2H_x) and their interactions with sub-
strate surfaces to simulate polymer film growth from hydrocarbon plasmas
[55–58]. Additionally, studies have explored the interactions of hydrocarbon
clusters with surfaces [59, 60]. Research on volume polymerization remains
limited [61], likely due to the extensive body of work already dedicated to
soot formation in flames, a problem closely related to plasma volume poly-
merization of hydrocarbon species, particularly when considering neutrals
and heavy ions [62–66]. Nevertheless, studying plasma volume polymeriza-
tion at usual plasma processing temperature remains useful for characterizing
hydrocarbon plasma chemistry [61].
Beyond describing plasma polymerization at surfaces or within plasma volumes, rMD is also used to evaluate the properties of polymer films, including tribology [67–70], aging [71, 72], and behavior under extreme conditions [73, 74]. This implementation of (r)MD for these purposes is out of scope of this chapter. Thus interested reader are invited to examine these references [67–74].

## 3.2. RESULTS AND DISCUSSION

The interactions of plasma ions with surfaces have been extensively studied to elucidate the role of kinetic energy transfer. Key processes include the effects of atomic ions on polymers, such as etching, grafting, cross-linking, and thin film growth, both on polymer surfaces and on silicon substrates.

### 3.2.1. Plasma Ion Interactions with Polymers

Pioneering work by the Graves group [48–50] established the methodology for studying ion-surface interactions. They investigated the interactions of $Ar^+$ and F/H radicals with model polymers to calculate carbon removal sputtering yields from $Ar^+$ alone and in combination with F and/or H radicals (see Figure 2). Adding F or H is a first step to include plasma reactive species. A dehydrogenated layer forms as a result of competing processes: sputtering, ion-induced dehydrogenation, and cross-linking. Hydrogen is preferentially removed from these layers, and once significant cross-linking occurs, the layer rapidly transitions to a final amorphized state as steady-state etching is approached. These mechanisms are considered generic, regardless of the initial polymer. The addition of F or H to $Ar^+$ bombardment shifts the balance between sputtering, ion-induced dehydrogenation, and cross-linking away from cross-linking, thereby enhancing the etch yield by inhibiting the cross-linking step. These results align with experimental findings on low-energy ion irradiation of polymers [75].

The Sinnott group also made significant contributions to this field [45, 46] by examining the impact of $C_xF_y^+$ ions on carbon nanotube (CNT)/polymer nanocomposites and polystyrene (PS). A key achievement was the development of a REBO C-H-F parameterization, which extended the potential to describe interactions involving fluorinated hydrocarbon radicals and ions [46]. This REBO potential enabled the study of $C_xF_y^+$ radical ion interactions with complex CNT/polymer nanocomposites, revealing phenomena such as the effects of ion energy, cross-linking, and nanocomposite structure. In summary,
<figure><img src="image_4.png" /><figcaption>Figure 2: Schematic of ion and radical interactions with a polymer: (a) initial 300 K relaxed polystyrene polymer, (b) snapshot after Ar⁺ and F⁺H radical exposure, (c) quantitative sputtering yields under different exposure conditions. Reprinted with permission from [49].</figcaption></figure>
it was demonstrated that when CNTs are located near the exposed composite surface, polyatomic ion interactions at incident energies of 50-80 eV per ion can induce cross-linking between CNTs and the polymer matrix without significantly damaging the CNT structure. These rMD simulations provide valuable insights into the optimal conditions for the chemical functionalization of CNTs via polyatomic ion exposure, offering guidance for the in situ engineering of CNT/polymer composite interfaces.

More recently, amine group grafting [58] and nitridation [54] have garnered attention in molecular dynamics studies driven by the potential to enhance polymer properties such as hydrophobicity, hydrophilicity, and electrical conductivity characteristics. Amine group formation was investigated using a dedicated REBO potential [58], simulating N₂/H₂ plasma exposure on polystyrene. The study included a flux of NH₂ radicals combined with energetic NH₃ bombardment. Results showed that increasing the energy of NH₃ molecules reduced the amine content from 52% at 0 eV to 30% at 200 eV. Regardless of the NH₃ energy, a nitrogen-rich layer approximately 20 Å thick formed due to the competition between surface modification and etching. Additionally, simulations [54] of interactions between N, NH, NH₂, and NH₃ at energies ranging from 5 to 20 eV with single-walled graphene sheets revealed defect formation consistent with nitrogen-based plasma experiments (see Figure 3). The simulated defect types agreed with XPS and NEXAFS experimental observations [54].

Interactions between hydrogen neutrals and ions with graphene and multilayer graphene have also been studied using rMD [76–78]. The goal was to understand the behavior of hydrogen plasma species (H, H⁺, H₂⁺, H₃⁺) interacting with various graphene surfaces (monolayers, nanoribbons, multilayers) to develop plasma processes for cleaning, functionalizing, and patterning graphene layers. Experimental and simulation results indicate that only fast H/H⁺ (less than tens of eV) can adsorb onto clean graphene surfaces, while lower-energy H atoms adsorb primarily at graphene edge sites. Modifications to graphene surfaces by energetic Hₓ⁺ ions depend on their kinetic energy, similar to nitrogen interactions [54]. At low energies (0.03-0.3 eV), lateral etching occurs without affecting the inner part of the graphene plane, while higher energies (0.3-10 eV) create defects and surface hydrogenation. At even higher energies (10-100 eV), bulk defects form in multilayer graphene (graphite), depending on the H⁺ dose. H₂⁺ and H₃⁺ ions primarily cause surface damage, resulting in less subsurface damage.

While these studies provide valuable insights, they often overlook the
<figure><img src="image_5.png" /><figcaption>Figure 3: Types of defects observed in simulations: (a) vacancies, (b) bridge nitrogen, (c) on-top N, (d) pyridinic N, (e) graphitic N, (f) on-top NH, (g) amine. Free N₂ in (f) and (g) is not bound to the graphene sheet. Reprinted with permission from [54].</figcaption></figure>

fact that in real plasma experiments, substrates are simultaneously exposed
to numerous reactive radicals and various energetic (polyatomic) ions. Thus,
rMD simulations incorporating a "realistic" composition of incoming species
are highly desirable.

3.2.2. Plasma Polymer Film Growth

In this context, the primary objectives are to calculate sticking coefficients and analyze the resulting thin film structure, including atomic composition, H/C ratio, and sp-sp²-sp³ hybridization [53, 55, 57]. These hydrocarbon polymer films are typically amorphous, consistent with experimental observations.

This section focuses on recent studies that incorporate a "typical" volume
composition of an hydrocarbon plasma above a substrate, building on earlier
work related to chemical vapor deposition [79]. Zarshenas [55] investigated
interactions involving C₂H₂ and radicals expected in a plasma environment:
C₂, C₂H, CH, H. No ions were included in this study. The authors com-
pared several force fields, reaxFF, REBO, and AIREBO, and found that
reaxFF introduced energy barriers not present in density functional theory
(DFT) calculations. These barriers were absent in REBO and AIREBO,
and since REBO is computationally faster than AIREBO, it was selected for further studies. A vapor composition above the substrate was created based on experimental data. The simulations revealed that film growth is dominated by the deposition of C₂H₂ and C₂H radicals, with hydrogen radicals contributing to C-C bond opening. No bond scissions in the growing film were observed at a gas-phase precursor temperature of 300 K. Increasing the substrate temperature enhanced cross-linking due to thermally promoted reactions between the growing film and incoming species. Regarding film structure, cross-linking was present at 300 K, meaning all carbon chains were connected into a single network. At higher temperatures, the 3D films transitioned from a branched to a cross-linked structure, while the degree of polymerization remained largely unchanged.

<figure><img src="image_6.png" /><figcaption>Figure 4: Top view of two-dimensional film growth after 2.4 ns of acetylene precursor deposition (a) and side view of three-dimensional film growth after 18 ns of deposition (b) at a substrate temperature of 300 K. Red represents C atoms, and white represents H atoms. Reprinted with permission from [55].</figcaption></figure>

To further improve realism, it is essential to include a more accurate composition of the vapor phase above the substrate. However, precisely determining the plasma volume phase composition remains experimentally challenging, despite the availability of high-performance mass and optical spectrometry tools [80, 81]. A relevant approach is to calculate the initial precursors responsible for film growth using plasma kinetics models [82–85].
This was implemented for Ar-4%CH₄ plasmas, where both film growth and plasma volume behavior were evaluated using rMD [61, 56, 57].

From the calculated initial composition, the volume phase chemistry obtained by rMD showed the formation of a majority of relatively stable C₂H₆ and C₃H₄ molecules through the recombination of CH₃ and its inter-action with C₂H across the temperature range of 300-1000 K. Larger CₙHm (n ≥ 3) molecules were also formed through reactions involving intermediate molecules such as C₄H₂ and C₄H₃. These large molecules were predominantly unsaturated hydrocarbons, with minor amounts of alicyclic and aromatic compounds, and their number increased with temperature, with a preference for the formation of six-carbon rings. Consistent with experiments, the C₂H radical was identified as the main precursor for these molecules at all temperatures, with C₂H₂ and CH₃ radicals also contributing to the formation of larger molecules.

Regarding film growth, the vapor was directed onto a 306L stainless steel model substrate. A key finding was the contribution of various mechanisms to film growth and reactivity: CH₃ was primarily lost through surface re-combination, forming volatile products with minimal contribution to film growth. The surface loss probability of C₂H was consistent with literature values, although rMD simulations indicated that its primary loss mechanism was surface recombination rather than sticking [57]. Since Ar⁺ and C₂H₃⁺ ions were the most abundant under the experimental conditions explored, they were included in the deposition process. For C₂H₃⁺ ions, the balance be-tween deposition and etching was energy-dependent in the 50-100 eV range: below 50 eV, the film continued to grow, while above 50 eV, etching domi-nated. Ar⁺ ions with kinetic energies above 50 eV etched the film, whereas lower energies had no visible effect. The film's H/C ratio was also calculated as a measure of bonding type, revealing that the resulting C:H films were un-saturated at all temperatures, with C=C double bonds as the predominant bond type.

# 4. CONCLUSION

Reactive Molecular Dynamics simulations offer a robust framework for exploring the complex interactions between plasma species and polymer sur-faces, enabling a deeper understanding of processes such as plasma poly-merization, etching, and functionalization. Through the use of reactive po-tentials like REBO, AIREBO, and ReaxFF, rMD has successfully modeled
the formation and breaking of chemical bonds, the growth of thin films,
and the modification of surface properties under various plasma conditions.
While challenges remain, such as the limited simulation size and the need
for more accurate representations of plasma compositions, advances in inte-
grating plasma kinetics models and experimental data are paving the way for
more realistic and predictive simulations. The insights gained from rMD not
only enhance our fundamental understanding of plasma-polymer interactions
but also provide practical guidance for optimizing industrial processes, such
as the development of functional coatings, nanocomposites, and advanced
materials. Future work should focus on refining simulation methodologies,
expanding the scope of reactive potentials, including development of reactive
machine learning interaction potentials (MLIP), and further bridging the gap
between computational predictions and experimental validation.

References

[1] D. B. Graves, P. Brault, Molecular dynamics for low temperature plasma-surface interaction studies, Journal of Physics D: Applied Physics 42 (2009). doi:10.1088/0022-3727/42/19/194011.

[2] E. Neyts, P. Brault, Molecular dynamics simulations for plasma-surface interactions, Plasma Processes and Polymers 14 (2017) 1600145. doi: 10.1002/ppap.201600145.

[3] P. Brault, Practical classical molecular dynamics simulations for low-temperature plasma processing: a review, Reviews of Modern Plasma Physics 8 (2024) 1–26. doi:10.1007/S41614-023-00140-5/METRICS.

[4] M. Joshi, The impact of nanotechnology on polyesters, polyamides and other textiles, in: B. Deopura, R. Alagirusamy, M. Joshi, B. Gupta (Eds.), Polyesters and Polyamides, Woodhead Publishing Series in Textiles, Woodhead Publishing, 2008, pp. 354–415. doi:https://doi.org/10.1533/9781845694609.2.354.

[5] H. K. Yasuda, Some important aspects of plasma polymerization, Plasma Processes and Polymers 2 (2005) 293–304. doi:10.1002/PPAP.200400071.
[6] J. Friedrich, Mechanisms of plasma polymerization – reviewed from a chemical point of view, *Plasma Processes and Polymers* 8 (2011) 783–802. doi:10.1002/PPAP.201100038.

[7] J. W. Abraham, A. Hinz, T. Strunskus, F. Faupel, M. Bonitz, Formation of polymer-based nanoparticles and nanocomposites by plasma-assisted deposition methods, *The European Physical Journal D* 72 (2018) 1–10. doi:10.1140/EPJD/E2017-80426-9.

[8] G. Nageswaran, L. Jothi, S. Jagannathan, Plasma assisted polymer modifications, in: S. Thomas, M. Mozetič, U. Cvelbar, P. Špatenka, P. K.M. (Eds.), *Non-Thermal Plasma Technology for Polymeric Materials*, Elsevier, 2019, pp. 95–127. doi:https://doi.org/10.1016/B978-0-12-813152-7.00004-4.

[9] I. Levchenko, S. Xu, O. Baranov, O. Bazaka, E. P. Ivanova, K. Bazaka, *Plasma and polymers: Recent progress and trends*, Molecules 2021 26 (2021) 4091. doi:10.3390/MOLECULES26134091.

[10] T. Dufour, *From basics to frontiers: A comprehensive review of plasma-modified and plasma-synthesized polymer films*, Polymers 15 (2023) 3607. doi:10.3390/POLYM15173607.

[11] J. M. Haile, *Molecular dynamics simulation: elementary methods*, John Wiley & Sons, Inc., 1992. doi:10.1002/adma.19930050319.

[12] D. C. Rapaport, *The art of molecular dynamics simulation*, Cambridge university press, 2004. doi:10.1017/CBO9780511816581.

[13] M. P. Allen, D. J. Tildesley, *Computer Simulation of Liquids*, Oxford University Press, 2017. doi:10.1093/oso/9780198803195.001.0001.

[14] D. Frenkel, B. Smit, *Understanding molecular simulation* 2nd edition, Academic Press, London, UK, 2002. doi:10.1016/B978-0-32-390292-2.00002-7.

[15] D. Marx, J. Hutter, *Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods*, Cambridge University Press, 2009. doi:10.1017/CBO9780511609633.
[16] D. W. Brenner, Relationship between the embedded-atom method and Tersoff potentials, Physical Review Letters 63 (9) (1989) 1022–1025. doi:10.1103/PhysRevLett.63.1022.

[17] D. W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B 42 (15) (1990) 9458–9471. doi:10.1103/PhysRevB.42.9458.

[18] S. J. Stuart, A. B. Tutein, J. A. Harrison, A reactive potential for hydrocarbons with intermolecular interactions, Journal of Chemical Physics 112 (2000) 6472–6486. doi:10.1063/1.481208.

[19] J. Tanaka, C. F. Abrams, D. B. Graves, New C–F interatomic potential for molecular dynamics simulation of fluorocarbon film formation, Journal of Vacuum Science & Technology A 18 (2000) 938–945. doi:10.1116/1.582279.

[20] B. Ni, K.-H. Lee, S. B. Sinnott, A reactive empirical bond order (REBO) potential for hydrocarbon–oxygen interactions, Journal of Physics: Condensed Matter 16 (2004) 7261–7275. doi:10.1088/0953-8984/16/41/008.

[21] A. F. Fonseca, G. Lee, T. L. Borders, H. Zhang, T. W. Kemper, T.-R. Shan, S. B. Sinnott, K. Cho, Reparameterization of the REBO-CHO potential for graphene oxide molecular dynamics simulations, Physical Review B 84 (2011) 075460. doi:10.1103/PhysRevB.84.075460.

[22] J. Tersoff, Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon, Physical Review Letters 61 (1988) 2879–2882. doi:10.1103/PhysRevLett.61.2879.

[23] J. Tersoff, New empirical approach for the structure and energy of covalent systems, Physical Review B 37 (1988) 6991–7000. doi:10.1103/PhysRevB.37.6991.

[24] J. Tersoff, Empirical interatomic potential for silicon with improved elastic properties, Physical Review B 38 (1988) 9902–9905. doi:10.1103/PhysRevB.38.9902.
[25] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, S. B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, Journal of Physics: Condensed Matter 14 (4) (2002) 783–802. doi:10.1088/0953-8984/14/4/312.

[26] F. H. Stillinger, T. A. Weber, Computer simulation of local order in condensed phases of silicon, Physical Review B 31 (1985) 5262–5271. doi:10.1103/PhysRevB.31.5262.

[27] T. A. Weber, F. H. Stillinger, Dynamical branching during fluorination of the dimerized si(100) surface: A molecular dynamics study, The Journal of Chemical Physics 92 (1990) 6239–6245. doi:10.1063/1.458348.

[28] H. Yamada, S. Hamaguchi, Numerical analyses of surface interactions between radical beams and organic polymer surfaces, Plasma Physics and Controlled Fusion 47 (2005) A11. doi:10.1088/0741-3335/47/5A/002.

[29] A. C. T. van Duin, S. Dasgupta, F. Lorant, W. A. Goddard, Reaxff: A reactive force field for hydrocarbons, The Journal of Physical Chemistry A 105 (2001) 9396–9409. doi:10.1021/jp004368u.

[30] K. Chenoweth, A. C. T. van Duin, W. A. Goddard, ReaxFF Reactive Force Field for Molecular Dynamics Simulations of Hydrocarbon Oxidation, The Journal of Physical Chemistry A 112 (2008) 1040–1053. doi:10.1021/jp709896w.

[31] T. P. Senftle, S. Hong, M. M. Islam, S. B. Kylasa, Y. Zheng, Y. K. Shin, C. Junkermeier, R. Engel-Herbert, M. J. Janik, H. M. Aktulga, T. Verstraelen, A. Grama, A. C. T. van Duin, The reaxff reactive force-field: development, applications and future directions, npj computational 2 (2016) 15011. doi:10.1038/npjcompumats.2015.11.

[32] I. Leven, H. Hao, S. Tan, X. Guan, K. A. Penrod, D. Akbarian, B. Evangelisti, M. Jamil Hossain, M. Mahbubul Islam, J. P. Koski, S. Moore, H. Metin Aktulga, A. C. T. van Duin, T. Head-Gordon, Recent Advances for Improving the Accuracy, Transferability, and Efficiency of Reactive Force Fields, Journal of Chemical Theory and Computation 17 (2021) 3237–3251. doi:10.1021/acs.jctc.1c00118.
[33] A. K. Rappe, W. A. Goddard III, Charge equilibration for molecular dynamics simulations, The Journal of Physical Chemistry 95 (1991) 3358–3363. doi:10.1021/j100161a070.

[34] S. W. Rick, S. J. Stuart, B. J. Berne, Dynamical fluctuating charge force fields: Application to liquid water, The Journal of Chemical Physics 101 (1994) 6141–6156. doi:10.1063/1.468398.

[35] W. J. Mortier, S. K. Ghosh, S. Shankar, Electronegativity-equalization method for the calculation of atomic charges in molecules, Journal of the American Chemical Society 108 (2002) 4315–4320. doi:10.1021/JA00275A013.

[36] G. O. Janssens, H. Toufar, B. G. Baekelandt, W. J. Mortier, R. A. Schoonheydt, The electronegativity equalization method (eem) as a promising tool for the analysis of zeolite catalyzed reactions, Studies in Surface Science and Catalysis 105 (1997) 725–732. doi:10.1016/S0167-2991(97)80622-2.

[37] J. T. Su, W. A. Goddard, Excited electron dynamics modeling of warm dense matter, Physical Review Letters 99 (2007) 185003. doi:10.1103/PhysRevLett.99.185003.

[38] A. Jaramillo-Botero, J. Su, A. Qi, W. A. Goddard, Large-scale, long-term nonadiabatic electron molecular dynamics for describing material properties and phenomena in extreme environments, Journal of Computational Chemistry 32 (2011) 497–512. doi:10.1002/JCC.21637.

[39] M. M. Islam, G. Kolesov, T. Verstraelen, E. Kaxiras, A. C. T. van Duin, ereaxff: A pseudoclassical treatment of explicit electrons within reactive force field simulations, Journal of Chemical Theory and Computation 12 (2016) 3463–3472. doi:10.1021/acs.jctc.6b00432.

[40] D. Akbarian, K. Ganeshan, W. H. Woodward, J. Moore, A. C. V. Duin, Atomistic-scale insight into the polyethylene electrical breakdown: An ereaxff molecular dynamics study, The Journal of Chemical Physics 154 (2021) 024904. doi:10.1063/5.0033645.

[41] D. R. Alfonso, S. E. Ulloa, Molecular-dynamics simulations of methyl-radical deposition on diamond (100) surfaces, Physical Review B 48 (1993) 12235–12239. doi:10.1103/PhysRevB.48.12235.
[42] A. Licciardello, M. E. Fragalà, G. Foti, G. Compagnini, O. Puglisi, Ion beam effects on the surface and on the bulk of thin films of poly-memylmethacrylate, Nucl. Instrum. Methods Phys. Res. 116 (1996) 168. doi:10.1016/0168-583x(96)00029-8.

[43] C. F. Abrams, D. B. Graves, Atomistic simulation of fluorocarbon deposition on si by continuous bombardment with energetic cf+ and cf2+, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 19 (2001) 175-181. doi:10.1116/1.1322652.

[44] I. Jang, R. Phillips, S. B. Sinnott, Study of c3h5+ ion deposition on polystyrene and polyethylene surfaces using molecular dynamics simulations, Journal of Applied Physics 92 (2002) 3363-3367. doi: 10.1063/1.1500788.

[45] Y. Hu, S. B. Sinnott, Molecular dynamics simulations of polyatomic-ion beam deposition-induced chemical modification of carbon nanotube/polymer composites, Journal of Materials Chemistry 14 (2004) 719-729. doi:10.1039/B311215B.

[46] I. Jang, S. B. Sinnott, Molecular dynamics simulations of the chemical modification of polystyrene through c xf y+ beam deposition, Journal of Physical Chemistry B 108 (2004) 18993-19001. doi:10.1021/JP049283Y.

[47] M. Yamashiro, H. Yamada, S. Hamaguchi, Molecular dynamics simulations of organic polymer dry etching at high substrate temperatures, Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers 46 (2007) 1692-1699. doi:10.1143/JJAP.46.1692.

[48] J. J. Vegh, D. Nest, D. B. Graves, R. Bruce, S. Engelmann, T. Kwon, R. J. Phaneuf, G. S. Oehrlein, B. K. Long, C. G. Willson, Near-surface modification of polystyrene by ar+: Molecular dynamics simulations and experimental validation, Applied Physics Letters 91 (2007) 233113. doi:10.1063/1.2821226.

[49] J. J. Vegh, D. Nest, D. B. Graves, R. Bruce, S. Engelmann, T. Kwon, R. J. Phaneuf, G. S. Oehrlein, B. K. Long, C. G. Willson, Molecular
dynamics simulations of near-surface modification of polystyrene: Bombardment with ar+ and ar+/radical chemistries, Journal of Applied Physics 104 (2008) 34308. doi:10.1063/1.2963708/956597.

[50] J. J. Vegh, D. B. Graves, Molecular dynamics simulations of ar++-organic polymer interactions, Plasma Processes and Polymers 6 (2009) 320-334. doi:10.1002/PPAP.200800223.

[51] G. K. Choudhary, J. J. Végh, D. B. Graves, Molecular dynamics simulations of oxygen-containing polymer sputtering and the ohnishi parameter, Journal of Physics D: Applied Physics 42 (2009) 242001. doi:10.1088/0022-3727/42/24/242001.

[52] F. Soberon, Surface activation of cyclo olefin polymer by oxygen plasma discharge: a molecular dynamics study, Modelling and Simulation in Materials Science and Engineering 22 (2014) 055020. doi:10.1088/0965-0393/22/5/055020.

[53] L. Schwaederlé, P. Brault, C. Rond, A. Gicquel, Molecular dynamics calculations of ch<inf>3<</inf> sticking coefficient onto diamond surfaces, Plasma Processes and Polymers 12 (2015) 764-770. doi: 10.1002/ppap.201400223.

[54] A. Jagodar, J. Berndt, E. von Wahl, T. Strunskus, T. Lecas, E. Kovacevic, P. Brault, Nitrogen incorporation in graphene nanowalls via plasma processes: Experiments and simulations, Applied Surface Science 591 (2022) 153165. doi:10.1016/j.apsusc.2022.153165.

[55] M. Zarshenas, K. Moshkunov, B. Czerwinski, T. Leyssens, A. Delcorte, Molecular dynamics simulations of hydrocarbon film growth from acetylene monomers and radicals: Effect of substrate temperature, Journal of Physical Chemistry C 122 (2018) 15252-15263. doi:10.1021/ACS.JPCC.8B01334.

[56] G. O. Kandjani, P. Brault, M. Mikikian, A. Michau, K. Hassouni, Molecular dynamics simulation of the interaction of an ar/ch4 plasma with a surface: Growth, structure, and sputtering of the deposited c:h films, Plasma Processes and Polymers 21 (2024) 2400084. doi: 10.1002/PPAP.202400084.
[57] G. C. Otakandza-Kandjani, P. Brault, M. Mikikian, A. Michau, K. Has-souni, Molecular dynamics approach for the calculation of the sur-face loss probabilities of neutral species in argon-methane plasma, Plasma Processes and Polymers 21 (2024) 2300120. doi:10.1002/PPAP.202300120.

[58] M. Michlíček, S. Hamaguchi, L. Zajíčková, Molecular dynamics simula-tion of amine groups formation during plasma processing of polystyrene surfaces, Plasma Sources Science and Technology 29 (2020) 105020. doi:10.1088/1361-6595/ABB2E8.

[59] L. Qi, S. B. Sinnott, Atomistic simulations of organic thin film deposition through hyperthermal cluster impacts, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 16 (1998) 1293-1296. doi: 10.1116/1.581276.

[60] H. Yamada, S. Hamaguchi, Molecular-dynamics simulations of organic polymer etching by hydrocarbon beams, Journal of Applied Physics 96 (2004) 6147-6152. doi:10.1063/1.1808907.

[61] G. O. Kandjani, P. Brault, M. Mikikian, G. Tetard, A. Michau, K. Has-souni, Molecular dynamics simulations of reactive neutral chemistry in an argon-methane plasma, Plasma Processes and Polymers 20 (2023) 2200192. doi:10.1002/PPAP.202200192.

[62] C. A. Schuetz, M. Frenklach, Nucleation of soot: Molecular dynamics simulations of pyrene dimerization, Proceedings of the Combustion In-stitute 29 (2002) 2307-2314. doi:10.1016/S1540-7489(02)80281-4.

[63] A. Violi, Modeling of soot particle inception in aromatic and aliphatic premixed flames, Combustion and Flame 139 (2004) 279-287. doi: 10.1016/J.COMBUSTFLAME.2004.08.013.

[64] A. Violi, S. Izvekov, Soot primary particle formation from multiscale coarse-grained molecular dynamics simulation, Proceedings of the Com-bustion Institute 31 I (2007) 529-537. doi:10.1016/j.proci.2006.07.240.

[65] U. Khalilov, A. Bogaerts, E. C. Neyts, Atomic scale simulation of carbon nanotube nucleation from hydrocarbon precursors, Nature Communica-tions 6 (2015) 10306. doi:10.1038/NCOMMS10306.
[66] Q. Mao, A. C. van Duin, K. H. Luo, Formation of incipient soot particles from polycyclic aromatic hydrocarbons: A reaxff molecular dynamics study, Carbon 121 (2017) 380-388. doi:10.1016/J.CARBON.2017.06.009.

[67] J. C. de Oliveira, A. Airoudj, P. Kunemann, F. B.-L. Gall, V. Roucoules, Mechanical properties of plasma polymer films: a review, SN Applied Sciences 3 (2021) 1-15. doi:10.1007/S42452-021-04655-9/FIGURES/6.

[68] S. K. Sethi, S. Kadian, G. Manik, A review of recent progress in molecular dynamics and coarse-grain simulations assisted understanding of wettability, Archives of Computational Methods in Engineering 29 (2022) 3059-3085. doi:10.1007/S11831-021-09689-1/METRICS.

[69] A. Talapatra, D. Datta, A review of the mechanical, thermal and tribological properties of graphene reinforced polymer nanocomposites: a molecular dynamics simulations methods, Polymer Bulletin 80 (2023) 2299-2328. doi:10.1007/S00289-022-04216-Z/METRICS.

[70] T. Yin, G. Wang, Z. Guo, Y. Pan, J. Song, Q. Ding, G. Zhao, Molecular dynamics simulation on polymer tribology: A review, Lubricants 2024 12 (2024) 205. doi:10.3390/LUBRICANTS12060205.

[71] F. Zhang, R. Yang, D. Lu, Investigation of polymer aging mechanisms using molecular simulations: A review, Polymers 15 (2023) 1928. doi: 10.3390/POLYM15081928.

[72] X. Li, C. Dong, J. Li, G. Bin, C. Zhou, Molecular dynamics simulation of aging properties in polymer materials: a review, Polymer Bulletin 82 (2025) 1723-1753. doi:10.1007/S00289-024-05601-6/METRICS.

[73] T. Ge, F. Pierce, D. Perahia, G. S. Grest, M. O. Robbins, Molecular dynamics simulations of polymer welding: Strength from interfacial entanglements, Physical Review Letters 110 (2013) 098301. doi: 10.1103/PhysRevLett.110.098301.

[74] T. Ge, F. Pierce, D. Perahia, G. S. Grest, M. O. Robbins, Erratum: Molecular dynamics simulations of polymer welding: Strength from interfacial entanglements (physical review letters (2013) 110 (098301)
doi:10.1103/physrevlett.110.098301), Physical Review Letters 110 (3 2013). doi:10.1103/PHYSREVLETT.110.129902.

[75] V. Zaporojtchenko, J. Zekonyte, J. Erichsen, F. Faupel, Etching rate and structural modification of polymer films during low energy ion irradiation, Nucl. Instrum. Methods. Phys. Res. 208 (2003) 155-160. doi:10.1016/S0168-583X(03)00625-6.

[76] E. Despiau-Pujo, A. Davydova, G. Cunge, L. Delfour, L. Magaud, D. B. Graves, Elementary processes of h2 plasma-graphene interaction: A combined molecular dynamics and density functional theory study, J Appl Phys 113 (2013) 114302. doi:10.1063/1.4794375.

[77] E. Despiau-Pujo, A. Davydova, G. Cunge, D. B. Graves, Hydrogen plasmas processing of graphene surfaces, Plasma Chemistry and Plasma Processing 36 (2015) 213-229. doi:10.1007/S11090-015-9683-0.

[78] A. Davydova, E. Despiau-Pujo, G. Cunge, D. B. Graves, Etching mechanisms of graphene nanoribbons in downstream h2 plasmas: Insights from molecular dynamics simulations, J Phys D 48 (2015) 195202. doi:10.1088/0022-3727/48/19/195202.

[79] A. M. Ito, A. Takayama, S. Saito, N. Ohno, S. Kajita, H. Nakamura, Molecular dynamics simulation of chemical vapor deposition of amorphous carbon: Dependence on h/c ratio of source gas, Japanese Journal of Applied Physics 50 (2011) 01AB01. doi:10.1143/JJAP.50.01AB01.

[80] J. P. Booth, M. Mozetič, A. Nikiforov, C. Oehr, Foundations of plasma surface functionalization of polymers for industrial and biological applications, Plasma Sources Sci. Technol. 31 (2022) 103001. doi:10.1088/1361-6595/ac70f9.

[81] R. Snyders, D. Hegemann, D. Thiry, O. Zabeida, J. Klemberg-Sapieha, L. Martinu, Foundations of plasma enhanced chemical vapor deposition of functional coatings, Plasma Sources Science and Technology 32 (2023) 074001. doi:10.1088/1361-6595/ACDABC.

[82] I. B. Denysenko, S. Xu, J. D. Long, P. P. Rutkevych, N. A. Azarenkov, K. Ostrikov, Inductively coupled ar/ch4/h2 plasmas for low-temperature deposition of ordered carbon nanostructures, Journal of Applied Physics 95 (2004) 2713-2724. doi:10.1063/1.1642762.
[83] G. Colonna, C. D. Pintassilgo, F. Pegoraro, A. Cristofolini, A. Popoli, G. Neretti, A. Gicquel, O. Duigou, T. Bieber, K. Hassouni, L. Laguardia, Theoretical and experimental aspects of non-equilibrium plasmas in different regimes: fundamentals and selected applications, The European Physical Journal D 75 (2021) 183. doi:10.1140/EPJD/S10053-021-00186-5.

[84] G. Tetard, A. Michau, S. Prasanna, J. Mougenot, P. Brault, K. Hassouni, Discharge dynamics, plasma kinetics and gas flow effect in argon-acetylene discharges, Plasma Sources Science and Technology 30 (2021) 105015. doi:10.1088/1361-6595/AC2A17.

[85] I. B. Denysenko, M. Mikikian, N. A. Azarenkov, Plasma properties and discharging of dust particles in an ar/c2h2 plasma afterglow, Journal of Physics D: Applied Physics 57 (2024) 145202. doi:10.1088/1361-6463/AD1BOC.