Molecular dynamics simulation of amine groups formation during plasma processing of polystyrene surfaces

Plasma treatment and plasma polymerization processes aiming to form amine groups on polystyrene surfaces were studied in-silico with molecular dynamics simulations. The simulations were compared with two experiments, (i) plasma treatment in N2/H2 bipolar pulsed discharge and (ii) plasma polymerization in cyclopropylamine/Ar radio frequency (RF) capacitively coupled discharge. To model favorable conditions for the incorporation of primary amine groups, we assumed the plasma treatment as the flux of NH2 radicals and energetic NH3 ions, and the plasma polymerization as the flux of cyclopropylamine molecules and energetic argon ions. It is shown in both the simulation and the experiment that the polystyrene treatment by the bipolar pulsed N2/H2 plasmas with an applied voltage of about ±1 kV formed a nitrogen-rich layer of a thickness of only a few nm. The simulations also showed that, as the NH3 incident energy increases, the ratio of primary amines to the total number of N atoms on the surface decreases. It is because the energetic ion bombardment brakes up N–H bonds of primary amines, which are mostly brought to the surface by NH2 radical adsorption. Our previous experimental work on the CPA plasma polymerization showed that increased RF power invested in the plasma leads to the deposition of films with lower nitrogen content. The MD simulations showed an increase of the nitrogen content with the Ar energy and a limited impact of the energetic bombardment on the retention of primary amines. Thus, the results highlighted the importance of the gas-phase processes on the nitrogen incorporation and primary amines retention in the plasma polymers. However, the higher energy flux towards the growing film clearly decreases amount of hydrogen and increases the polymer cross-linking.


Introduction
Plasma modification of materials by amine groups is promising for applications in which cells interact with the surface as well as for immobilization of proteins and covalent bonding of drugs [1]. The simplest technique relies on introducing amine groups on the polymer surface by plasma treatment in nitrogen (N 2 ), nitrogen and hydrogen (N 2 /H 2 ) or ammonia (NH 3 ) discharges [2,3]. An alternative way to create amine surfaces is plasma deposition, either the co-polymerization of hydrocarbon monomers C x H y (e.g., acetylene C 2 H 2 , ethylene C 2 H 4 ) with NH 3 [4][5][6] or the plasma polymerization of various monomers containing amine groups [7][8][9][10][11][12][13].
Different approaches have been developed to maximize the concentration of the introduced primary amine groups. Plasma treatment of polymers was intensively studied in many configurations, generally showing optimum for a certain power, mixture, pulsing settings and treatment time [14][15][16]. Plasmachemical mechanism of primary amine incorporation into hydrocarbons was studied particularly for N 2 , N 2 /H 2 and NH 3 , showing the importance of NH and NH 2 radicals [2,17]. In absence of hydrogen, the combined action of excited nitrogen N 2 (A) and ground state N radical was suggested as a plausible mechanism for the formation of labile nitrogen groups, which subsequently hydrolyze to a primary amine in the open air [17].
A very high specificity of primary amine incorporation was, however, reported only in processes without ion bombardment, such as NH 3 afterglow process ([NH 2 ]/[N] >70%, at [N] ≈ 5 at.%) [3]. Moreover, simple plasma treatment of polymers has only limited stability in time [18]. A possible way to prevent this effect of hydrophobic recovery is to deposit an amine-containing layer.
In the case of plasma polymerization, the high retention of the original precursor is usually achieved by using low specific power which, however, has to be balanced with the film stability [1,19,20]. Other approaches have been also reported, recently e.g., method based on the deposition of protonated precursor ions via α-γ transition [21]. Despite these efforts, the amine concentration is usually limited to few atomic percent, especially in conditions with treated surface or growing layer subjected to ion bombardment [8,20,[22][23][24]. It should be empathized, that reported primary amine concentrations based on TFBA derivatization should be considered as an upper estimate due to possible ambiguity of TFBA nucleophilic addition reactions [25].
In plasma processing, energetic ions incident upon the surface typically provide necessary energy to initiate surface chemical reactions, so that surface modification, film deposition, or surface etching can take place at low surface temperature in non-thermodynamical-equilibrium conditions [26]. Molecular dynamics (MD) simulation for gas-phase ions and atoms interacting with atoms of a solid material can reveal some aspects of such non-equilibrium surface chemical reactions taking place during plasma treatment of polymers at the atomic level [27,28].
As a practical motivation for the paper, we performed induced pluripotent stem (iPS) cells cultivation on non-treated cultivation polystyrene Petri dish and dishes treated by N 2 /H 2 inverter and plasma polymerized cyclopropylamine (CPA).
In preliminary experiments, we observed that compared with the control case the inverter plasma-treated dishes and the CPA plasma polymerized dishes help iPS cells retain their multipotency. Although the details of underlying cell-surface interaction remain unclear, the critical part is the selective binding of mediating proteins (albumins) and proteins of extracellular matrix to amine groups. The adsorbed proteins effectively create coating with specific ligands required for iPS cells attachment and proliferation [29,30]. Despite this is merely a qualitative observation, this result suggests that both surfaces modified by plasma processes result in surfaces with sufficient concentration of primary amine groups for cell attachment.
MD simulations were carried out to assess a possible difference between the plasma treatment of polymers aiming to introduce amine groups at the surface and plasma polymerization in the mixture with high potential to produce amine-rich thin films. The simulation initial conditions were chosen to resemble some relevant experiments into which the simulation results could bring more understanding and to which they could be compared. The first case assumed that NH 2 radicals arriving at the surface of polystyrene with near thermal energy together with fast NH 3 molecule having the energy of 100 eV. These conditions can represent some of the best yet realistic situation for the introduction of NH 2 groups onto polystyrene and can be linked to the N 2 /H 2 inverter plasma experiment. A highly simplified view on the plasma polymerization with a precursor containing NH 2 groups was obtained by the MD simulations in which cyclopropylamine molecules arrived at the polystyrene surface with near thermal energy together with Ar atoms with low energy of 10 eV. Furthermore, the energy of fast particles in respective simulations was varied to study the effect of bombardment energy. Particularly for CPA/Ar mixtures, this can represent the plasma polymerization in radiofrequency (RF) capacitively coupled plasma (CCP) of various configurations and DC self-bias imposed at the substrate electrode.

Outline of molecular dynamics simulations
A classical MD simulation approach based on the integration of Newton's equations of motion was used to obtain some insight into the process of plasma-based amine ion implantation and amine plasma polymerization on a polystyrene substrate. Interactions among atoms were described by multibody potential functions are essentially the same as those described in reference [27], which extended Stillinger-Weber type interatomic potential functions [31][32][33][34] to double and triple bonds and was used for MD studies on various plasmapolymer interactions [27,[35][36][37][38][39]. The details of the potential functions are provided in Supplementary Information (https://stacks.iop.org/PSST/29/105020/mmedia), section 1.
A model of polystyrene, a rectangular box with the base dimensions 2.32 nm by 2.08 nm, was constructed as a substrate for plasma treatment and deposition. The exact lateral dimensions conveniently fit a prebuilt model of polystyrene, which consisted of horizontally aligned spiral polystyrene chains (see figure S2 in supplementary information). The base dimensions of about 2 × 2 nm and the height of ≈ 11 nm were chosen as a compromise between computational time (number of particles and therefore computational time increases as the product of length and width), the fidelity of simulated polymer properties (which requires long chains) and the depth of energetic particle penetration that should not reach the bottom of the box. The periodic boundaries were imposed to simulate larger surfaces.
Impinging particles were inserted into the simulation with the velocity vector in the direction normal to the surface. All particles were modeled as charge-neutral, assuming the Auger neutralization process for bombarding ions. Each cycle the MD simulation was performed for 2000 fs. For each impact, the simulation was performed in the microcanonical conditions for 1000 fs. Then the system was brought to thermal equilibrium at 300 K by the Langevin and subsequently Berendsen thermostat for 900 and 100 fs, respectively, applied to all particles. Desorbed particles were removed from the system at the end of the microcanonical sub-cycle and at the end of the cycle, so their rescaled velocities do not affect the subsequent simulation. With this artificial cooling and relaxation process, excess heat is removed from the system and makes the system ready for the subsequent energetic particle injection. The thermostat algorithm, however, cannot well reproduce long-term thermal relaxation processes of the surface that ensue for microseconds or even milliseconds after each impact of an energetic particle.
The simulations of plasma treatment and deposition were performed by alternating the insertion of the energetic particle (i.e. NH 3 molecule and Ar atom, respectively) and slow neutral particles (i.e. NH 2 radicals and CPA molecules, respectively). Each simulation was performed with one selected energy of the energetic particle in order to represent the effect of ion bombardment. In the case of the plasma treatment, the cycle with NH 3 molecule injection with the selected energy from interval 50-200 eV was followed by 4 cycles each with the injection of 25 NH 2 radicals having near thermal energy of 0.5 eV. Similarly, for the CPA plasma deposition, the cycle with the injection of Ar with the selected energy from interval 10-110 eV was followed by 4 cycles each with the injection of 16 CPA molecules with the near thermal energy of 0.1 eV. The figure 1 visually summarizes typical simulation procedures. All the simulations were run for a total of 2000 cycles. Additionally, simulations without energetic particles were run for both presented models. To achieve the same dose of neutrals, the number of cycles was reduced to 1600 with otherwise the same conditions.

N 2 /H 2 plasma treatment in bipolar pulsed DC glow discharge
The polystyrene dishes (35 mm in diameter) were treated in bipolar pulsed dc glow discharge ignited in N 2 /H 2 . The bottom molybdenum electrode, 190 mm in diameter, was connected to the inverter power supply whereas the top aluminum electrode (80 mm) was grounded (figure 2) [40,41]. The distance between the electrodes was 38 mm. The plasma chamber was pumped by a turbomolecular pump backed by a rotary pump. The pressure during the discharge operation was 250 Pa. The flow rates of N 2 and H 2 were 13.3 and 5 sccm, respectively. The applied positive and negative voltage pulses had the width of 1 μs and the applied voltages were 1.3 and −1.1 kV, respectively. The repetition frequency was 5 kHz. The samples were treated for 30 min.

CPA plasma polymerization in capacitively coupled plasma
The CPA plasma polymers (CPA PPs) into the polystyrene dishes and on Si substrates (double-side polished) were prepared in a custom build stainless steel parallel plate reactor similarly as in the previous work of Manakhov et al. [42]. The bottom electrode, 420 mm in diameter, was connected via a matching box to an RF generator working at the frequency of 13.56 MHz. The gases were supplied into the chamber through a grounded upper showerhead electrode, 380 mm in diameter. The distance between the electrodes was 55 mm. The bottom electrode with substrates was negatively DC self-biased due to the reactor geometric asymmetry. The reactor was pumped down to ≈ 10 −4 Pa by a turbomolecular pump backed by a rotary pump. The deposition was carried out with the rotary pump only. The leak rate including wall desorption was below 0.1 sccm.
The CPA was polymerized in square pulsed CPA/Ar plasma at the nominal power of 100 W and the pressure of 50 Pa. The pulse duty cycle and repetition frequency were 33% and 500 Hz, respectively. The flow rate of Ar was set to 28 sccm and regulated by an electronic flow controller Hastings, whereas the flow rate of CPA vapors was set to 2 sccm by a needle valve. The substrates were sputter-cleaned by pulsed Ar plasma for 10 min prior to the deposition. The deposition time was 60 min. The film thickness measured by ellipsometry in the UV-visible range was 249 nm.

Sample analysis
The quantitative atomic composition (without hydrogen) of the CPA PPs on Si substrate was obtained by monochromatized X-ray photoelectron spectroscopy (XPS) using the Axis Supra spectrometer (Kratos Analytical) at the pass energy of 20 eV. The maximum lateral dimension of the analyzed area was 0.7 mm. A sample differential charging was avoided by a charge neutralization in the overcompensated mode. The depth profiling was performed with Ar cluster gun rastering over a square area with the side dimension of 1.9 mm. Argon clusters with an average size of 500 atoms were accelerated to the energy of 20 keV.
The quantitative atomic compositions of the samples prepared by the N 2 /H 2 plasma treatment of the polystyrene were obtained by non-monochromatized XPS ESCA850M (Shimadzu Corporation) using pass energy of 75 eV. The spot diameter was 8 mm. The depth profiling was performed by Ar ion gun with the accelerating voltage of 1 kV.

Simulation of NH 2 /NH 3 surface treatment
The MD simulation performed with slow NH 2 radicals and NH 3 energetic molecules represents one of the best scenarios for the formation of primary amine groups at the polystyrene surface treated in plasma with support of energetic ions. The resulting structures are evaluated after 2000 simulation cycles, which is sufficient to reach a steady-state of presented observable quantities. As an example, we discuss the simulation with the NH 3 energy of 100 eV. Few snapshots of the atomic configurations during simulation can be found in the supplementary information, figure S3. Figure 3 depicts the depth profiles of elements (a) and interatomic bonds in carbon and nitrogen environments (b and c, respectively). The simulation predicts overall slow etching of the original polystyrene surface. Approximately 0.2 carbon atom is removed per impact of energetic particle.
A locally higher concentration of nitrogen than carbon can be noted near the surface in figure 3(a). We will first introduce a naive approach to the calculation of nitrogen content as it would appear by XPS analysis of simulated surfaces and refine it later. Since the nitrogen concentration is not constant, the lower edge of the modified layer was considered as the depth in which the nitrogen intensity reaches half of the maximum. The nitrogen content of the modified layer is calculated only from the volume above the edge of the modified layer. can be explained by the simultaneous introduction of many NH 2 radicals. During the impact, NH 2 radicals readily form hydrazine (N 2 H 4 ) which is incorporated into the surface. This is further supported by CPA/Ar simulations where N-N bonds are practically not present.
The highly cross-linked nature of mixing surface layer is highlighted by low hydrogen content of 44%, significantly lower than the estimate for the CPA simulations even at the highest argon atom energy. Based on the nitrogen environment shown in figure 3(c), two sublayers can be roughly distinguished in the nitrogen-rich layer: a highly cross-linked C-N rich sublayer close to the surface, and an N-H rich sublayer closer to the bulk polystyrene. Since the stopping distance of particles with the energy of 100 eV is just a few atomic layers [43], the majority of its energy is released in the topmost layer, causing surface mixing and cross-linking, while deeper layers are relatively unaffected. The evaluation of amine groups in the whole volume gives the content of primary amines of 30%, secondary 39% and tertiary 31%. If we focus only on the top C-N rich sublayer, the relative concentrations shift towards more cross-linked (primary amines is 23%, secondary 42% and tertiary 35%) showing that primary amine groups are preferentially buried deeper as suggested in the previous paragraph. Further analysis also shows the formation of some nitriles (triple bonded C ≡ N), which are not present in CPA/Ar simulations.
The reflected and etched species are dominated by nonsticking NH 2 radicals and volatile products such as N 2 H 4 and NH 3 . Further, less abundant species produced by surface reactions are H 2 , N 2 , CN and CNH. There is no prevalent channel of carbon removal from the original polystyrene surface. Various small molecules (e.g., C 2 H 2 , CN or CNH), and even some large ones (typically C 5+ N 10+ H 15+ ) contribute to etching.

Simulation of CPA/Ar plasma deposition
Unlike in high voltage N 2 /H 2 and NH 3 plasma treatment [2], the plasma polymerization is performed under much milder energetic conditions because the functional groups of the monomer should be retained as much as possible [20]. Therefore, the MD simulation of CPA/Ar with the Ar atom energy of 10 eV was chosen as a typical example for the discussion of the process in this section. Few snapshots of the atomic configurations during the simulation can be found in the supplementary information, figure S4.
The film composition profiles (elements and chemical bonds) obtained from the MD simulation are shown in figure 4. Even at such low energy, the nitrogen concentration extends below the original substrate-level due to partial etching of polystyrene and the creation of the mixing layer. This effect is even more pronounced for higher energies as discussed below.
It should be noted that, besides Ar kinetic energy, effectively also internal potential energy is introduced with each CPA molecule. Due to high internal bond stress, the CPA carbon ring is prone to relax by ring-opening and formation of a radical. Thus, each CPA molecule brings ≈ 6.5 eV of internal energy. It can be considered as plasma activation, which is in fact required as non-radical CPA neutrals would have very low sticking probability.
The MD simulation predicts slow deposition of nitrogencontaining thin film, with relatively constant concentration profiles. Only about one carbon or nitrogen atom is on average deposited per CPA cycle, i.e., per 64 CPA molecules. The resulting thin film is significantly different from layer predicted in NH 2 /NH 3 simulation in both the elemental composition and chemistry. The simulated nitrogen concentration captured by the ratio [N]/([N] + [C]) of 0.18 is only about one third of the value for NH 2 /NH 3 . Compared to the NH 2 /NH 3 simulation, the CPA film is also more hydrogenated ([H] > 0.53).
As expected from elemental composition, the bond profiles show that dominant bonds are terminating C-H, followed by cross-linking C-C and C-N bond. In the nitrogen environment, the concentration of N-H bonds is significantly lower than cross-linking C-N bonds. It suggests that the majority of nitrogen forms secondary or tertiary amines.
The species reflected and sputtered from the surface during the deposition are volatile and non-sticking products of surface reactions. Interestingly, the most prominent fragment is not CPA (C 3 NH 7 ) reflected from the surface but C 2 NH 5 fragment, followed in abundance by NH 2 , C 3 H 5 and then C 3 NH 7 . All these fragments smaller then CPA are products of single dissociation of linear C 3 NH 7 . Fragments larger than the original molecule are also present, however, with a lower relative  abundance which is significantly decreasing with the fragment mass.

Effect of particle energy in MD simulations
To study further the effect of ion bombardment on the plasma treatment and deposition we run series of simulations with varying energy of fast NH 3 molecule and Ar atom, respectively. The density of the nitrogen-rich layer formed in the polystyrene (figure 6(a)) exhibits a maximum at 100 eV of NH 3 and then decreases for the highest energy of 200 eV. We assume that sputtering effects at 200 eV result in fast removal of material from the surface. Even though the energy and momentum are higher in the 200 eV case, the residence time in the surface volume is significantly shortened and overall physical densification by energetic bombardment is, therefore, lower than for the lower bombardment energy. At the same time, the chemical effects of energetic bombardment show simple trends even for the highest energy ( figure 6). The content of hydrogen, the relative amount of terminating N-H bonds and weak N-N bonds are decreasing with the NH 3 energy, while the relative amount of strong cross-linking C-N bonds in the nitrogen environment increases. Figure 7 shows the effect of ion bombardment on the relative concentrations of different amine groups. The content of primary amines of 52% is obtained in the simulation without  energetic bombardment. Although such simulation represents an almost ideal case for the functionalization of polystyrene by primary amine groups, the surface reactions initiated by the NH 2 radicals are sufficient to reduce the primary amine specificity to approximately a half. The content of primary amines is decreasing with the NH 3 energy down to ≈ 30%. Secondary amines exhibit quite stable concentration at ≈ 35%, slightly increasing to ≈ 40% for the higher energies. The concentration of highly cross-linked tertiary amines is increasing from 13% to 25% with the NH 3 bombardment energy.
We show products of energetic bombardment by NH 3 in figure 8 depicting number of selected species desorbed or sputtered from the surface during the total of 400 energetic NH 3 cycles. Populations of all the species are increasing with the energy of incident NH 3 molecule. The high number of NH 2 and N 2 H 4 even for the lowest energy of 50 eV suggest that these species remain weakly attached to the surface from the previous cycles and are readily removed even by relatively low energy bombardment. The figure also highlights C 2 H 2 molecule as the main channel for carbon etching by high energy bombardment. Figure 9 shows that the deposition rate decreases with the energy of Ar atom in CPA/Ar simulation. It suggests that the internal energy of CPA is sufficient for radical formation and promotion of sticking probability even without a surface activation by energetic particles. Increasing energy of Ar atom causes a gradual decrease of the deposition rate which is becoming significantly steeper for the energy of 50 eV and higher. Unlike metals, polymers do not show a threshold energy for sputtering. A variety of physical and chemical effects is induced by particle bombardment, including both atomic and molecular motion regimes of collision cascade inside a polymer chain and collisional mixing [44]. In principle, any particle with kinetic energy higher than the dissociation energy is able to release fragments from the surface, although with a very low probability for small energies. The physical sputtering of polymers by very low energy argon ions (<100 eV) was not studied in detail to our knowledge. However, extrapolating from limited published data, sputtering of the polymer can become significant at this energy [45].

CPA/Ar plasma deposition.
The simulated nitrogen content [N]/([N] + [C]) for higher energies of Ar atom is shown in figure 10. Surprisingly, we observe an increasing trend with argon energy. The data points at higher energies have worse statistics as there is a slower deposition rate and, therefore, a lower number of film particles in the simulation. However, this effect cannot account for the increasing trend. In a highly cross-linked material subjected to energetic bombardment, nitrogen could be considered more volatile than carbon, as it has one bond less. Since the simulated films are still far from fully cross-linked (with about 50% of hydrogen), we conjecture that some geometrical effect of CPA dissociation might be responsible for preferential carbon removal. We further discussed the increasing trend of nitrogen concentration with energy in section 4.4.
The increasing cross-linking of simulated CPA thin films with Ar energy is reflected in the concentration of hydrogen and thin film density shown in figure 11(a). Since hydrogen cannot participate in the chain propagation its concentration can be used as a rule of the thumb for polymer cross-linking [46]. The decrease in hydrogen content and densification by bombardment is reflected also by the calculated density shown in the figure right axis. The simulated densities increase from 1.17 to 1.57 g cm −3 with increasing bombardment energy, consistently with both, the experiment and theory [47]. The trend in cross-linking is further supported by figure 11(b) showing an increasing ratio of C-N bonds in the nitrogen environment.
Further analysis of different amine groups in figure 12 reveals that their relative concentrations are relatively stable, particularly for the lower energy of Ar atom. The relative content of primary amines is lower than in the case of NH 2 /NH 3 simulations. Even without energetic bombardment (0 eV), it is limited to 21% and remains similar for low bombardment energy (<50 eV). Finally, for the energy of 50 eV and higher, the relative content of primary amines decreases to ≈16%. The relative content of secondary amines is ≈ 35%. The concentration of highly cross-linked tertiary amines is increasing with bombardment energy, from ≈ 40% to ≈ 50%. Since primary and secondary amines contain both C-N and N-H bonds, the effect of bombardment ( figure 11(b)) almost cancels out, yielding a relatively stable concentration, while tertiary amines formed by C-N bonds increase with the Ar energy. Thus the analysis reveals that even though ion bombardment has a significant effect on thin film deposition rate, cross-linking and densification, the impact onto the chemistry is rather limited. We hypothesize that once the surface is given sufficient energy the system tends to stabilize at a state with minimum energy, that is likely the chemistry with a lower content of primary amines. Moreover, in the experiment, the lower accessibility of primary amines due to increased cross-linking and densification can further contribute to a lower detected concentration of primary amines for higher power and bombardment energy conditions [48].
Comparing populations of species desorbed or sputtered during the energetic Ar cycles (total of 400) in figure 13 gives further hints on bombardment effects on the surface. The majority of species with a high abundance are products of CPA dissociation (C 2 NH 5 , C 3 H 5 , NH 2 , CH 3 ) and CPA itself (C 3 NH 7 ). Populations of all these are largely unaffected by bombardment and are removed even by Ar bombardment with the lowest energy of 10 eV, suggesting that they are only loosely bonded to the surface and might be eventually released even without bombardment. Contrary, some small molecules (H, H 2 , C 2 H 2 and C 2 H 2 ) exhibit clear increasing trend with Ar bombardment energy, implying that they are sputtered by the bombardment. Note that this sputtering is preferential to carbon, as the nitrogen-containing species do not display on average such strong dependence to Ar energy. We assume, the preferential sputtering is a geometrical effect is caused by dissociation and bonding pattern of CPA molecule.

Agreement between the simulations and XPS exper-
imental results. The MD simulation conditions described above are extremely simplified models of real plasma processes that involve many more species and ion energy distributions. We designed the simulations to highlight the effect of ion bombardment in conditions otherwise favorable for the formation of primary amine groups. Other problems that can hinder the agreement between the simulation and experimental results are related to limitations inherent to molecular dynamics, (i) the discrepancy between the spatial and temporal scales accessible by the MD simulation and the experiment and (ii) the precision of potential functions, particularly for slow processes and reactions. Although the simulations are not necessarily predictive for the respective experiments [28], we show in the following paragraphs that the agreement with our experiments can be reasonably good if we take into account the experimental and simulation limitations. Some observables readily accessible in the simulations, e.g., the concentration of hydrogen, are difficult to measure experimentally. We focused mainly on the XPS measurements of nitrogen, primary amines, and the XPS depth profiling of nitrogen. To compare the measured XPS and the simulated depth profiles, we calculated 'synthetic' XPS depth profiles from the simulated data by taking into account an inhomogeneity of the elemental concentration. We used the simplest approach assuming that photoelectrons are only lost due to inelastic collisions. Then, the concentration of element A, [A], is proportional to the integral of its number density N A (z) multiplied by the exponential depth decay: where λ i is the inelastic mean free path estimated for typical nitrogen-containing polymers as 30 Å [49]. Applying equation (1) )| sim xps are therefore clearly exaggerated. We assume that it is caused by shortcomings typical for molecular dynamics. The time scales during which high fluxes of particles are impacting the surfaces are only few nanoseconds in our simulations. Therefore, the simulation do not account well for slow processes such as thermal desorption of weakly bonded fragments, surface reorganization, or slow chemical reactions in general. Secondly, the potential function was optimized on a set of stable chemical compounds and its application to the functionalization of a surface by radicals might stretch it beyond its applicability.
Species in the NH 2 /NH 3 simulation were selected to facilitate favorable conditions for the formation of primary amine groups. However, the real plasma-chemical processes in the N 2 /H 2 plasma treatment experiment are expected to provide only moderate amount of NH 2 radicals [54,55]. In this regard, simulation might correspond better to NH 3 discharges. Moreover, the formation of primary amine groups in the surface was shown to be a more complicated process, likely involving also other NH x radicals, atomic nitrogen and hydrogen [3,17]. Energy and relative dose of energetic particle bombardment were chosen close to estimates for the given discharge and pressure [56,57].
The experimental conditions of CPA plasma polymerization suggest that the ion energy involved in the process is quite low, definitively much lower than in the case of N 2 /H 2 inverter plasma experiment and related MD simulations. We estimated that typical ion energy representing the CPA PP experiment is 10 eV [42,47]. The predicted elemental composition results for 10 eV Ar, captured by the ratio The predicted trend of increasing nitrogen incorporation with energetic particle energy, shown in figure 10, is opposite to our previous experimental findings. In the case of CPA/Ar deposition, we have observed a decrease of N/C within range 0.23-0.12 with the radio-frequency power [42] that is linked, in the capacitively coupled discharges, to higher mean ion energy. The disagreement between the simulated trend in N/C and the experimental results can be, to a certain degree, attributed to a decreased statistical significance in the simulation results because of decreased number of deposited particles for higher energy of particles. However, we assume that the main factor is a change of the gas phase composition when higher RF power is applied. For low ion energy (and therefore power), the plasma polymerization process is still in the energy deficient regime, with relatively similar dissociation pattern. For a higher power and the monomer deficient regime, the gas phase composition in the experiment can change quite significantly. Secondly, as we already noted for NH 2 /NH 3 simulations, our simulations poorly predict the balance between sticking and desorption of nitrogen-containing radicals, which are more likely to form in simulations with a higher energy of argon atoms.
The  [48]. This value is about half of the concentration in the CPA/Ar simulation [NH 2 ]/[N] of 16%-22%. Yet, the simulation should be considered as the upper limit estimate, as it cannot account for thermal desorption, slow chemical reactions and aging in the ambient atmosphere, which can decrease the primary amine concentration in the experiment.

Composition profiles.
We present a comparison of the experimental two plasma modified surfaces by XPS depth profiling in figure 14(a). The concentrations of nitrogen [N]/([N] + [C]) at the top surfaces are comparable. A higher nitrogen concentration of 0.25 is detected for N 2 /H 2 plasma-treated surface. The concentration, however, sharply decreases and already at depth of 20 Å is ≈0.04. Note that this depth profiling was done by energetic Ar ion beam which is known to cause surface mixing and preferential sputtering [60]. Therefore, the non-zero concentration in larger depths can be attributed to the mixing effect. The surface of plasma polymerized CPA shows It is well recognized that plasma treatment leads to the functionalization of a very thin near-surface layer usually with a short life-time [18]. On the other hand, the deposition of amine containing coating creates a relatively thick layer that does not have a strong chemical gradient at the surface and therefore does not suffer from surface reorganization. By this approach the stability of amine groups can be enhanced and, thus, the aging effect reduced [1].
From the simulated elemental profiles, we can also calculate the simulated XPS profile by evaluating intensity as function integral upper limit in equation (1). For simplicity we do not consider any mixing by sputtering, the simulated XPS profiles are shown in figure 14(b). For NH 2 /NH 3 simulation, apart from the non-physically high nitrogen concentration, we can still compare the decrease of nitrogen concentration with depth with the experiment. The depth for which [N]/([N] + [C])| sim xps drops to half of the maximum value is about 25 Å, which agrees well with experimental XPS depth profiling and estimates acquired for similar experiments by angle-resolved XPS in literature [61,62]. In CPA/Ar simulation, the thickness of the deposited layer is comparable with the XPS information depth and therefore we do not observe plateau as in the experiment.

Conclusion
We have presented results of molecular dynamics simulations of the plasma treatment of polystyrene by the flux of NH 2 radicals combined with NH 3 energetic bombardment and the plasma polymerization of CPA under Ar energetic bombardment. The conditions used for the simulations represent the best possible scenario for the polystyrene surface functionalization by plasma treatment. It is shown that increased energy of NH 3 molecules decreases the retention of primary amines from 52% for 0 eV to 30% for 200 eV. The plasma treatment naturally tends to a more stable state, a low content of primary amines, provided there is a sufficient energy delivered through energy flux. The treatment at any NH 3 energy formed nitrogen-rich layer with the thickness of about 20 Å due to an equilibrium between the modification of top surface and its removal by etching. In the case of CPA plasma polymerization the thickness of the deposited film decreases with the Ar energy above 50 eV. The nitrogen content in the film increases with the Ar energy but it is not related to the increase of primary amine groups. The higher energy flux leads to higher cross-linking of the films as demonstrated by a decrease of hydrogen content and an increase of the film density. However, the impact onto the chemistry is rather limited. The content of primary amines is lower than in the case of plasma treatment by NH 2 /NH 3 , 21% for 0 eV energy of Ar and about 16% for the energy of 50 eV or higher.
The results of simulations were compared with the XPS analysis of polystyrene samples prepared in N 2 /H 2 bipolar pulsed discharge and coated by plasma polymer thin film deposited in CPA/Ar capacitively coupled RF discharge. The simulation results, especially for the plasma treatment producing only 20 Å nitrogen-rich layer and for very thin CPA plasma polymer films deposited at high Ar energy, had to be recalculated taking into account the information depth of the XPS method. After the correction, the simulated XPS atomic concentration of nitrogen was lower but yet the values for NH 2 /NH 3 conditions (0.48 at 100 eV NH 3 assumed as a typical ion energy in the bipolar pulsed discharge) were too high to correspond to our or any other experimental values (below 0.22). It is explained by shortcomings typical for molecular dynamics-only a very short time scale processes accessible in the simulations and a particular selection of the interaction potential function optimized on a set of stable chemical compounds. The agreement for the CPA/Ar plasma polymerization was much better concerning the value of the nitrogen concentration (0.16 for 10 eV Ar assumed as a typical ion energy in the CPA/Ar RF discharge at 50 Pa). However, the predicted trend of increasing nitrogen concentration with Ar energy was opposite to the decreasing trend obtained in the experiments carried out with increased RF power, i.e., increased DC selfbias. It reveals that enhanced gas-phase dissociation of CPA molecules at higher RF power is much more important than the effect of ion bombardment. discharge experiments. This research was carried out under the project 18-12774S supported by the Czech Science Foundation, the project CEITEC 2020 (LQ1601) with the financial support from the Ministry of Education, Youth and Sports of the Czech Republic (MEYS CR) under the National Sustainability Programme II, Osaka University International Joint Research Promotion Program (Type B), the Japan Society of the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (S)(No. 15H05736), and JSPS Core-to-Core Program JPJSCCA2019002. CzechNanoLab project LM2018110 funded by MEYS CR is gratefully acknowledged for the financial support of the experiments at CEITEC Nano Research Infrastructure. MM was a Brno PhD Talent scholarship holder-funded by Brno city municipality.