O^·, H^·, and ^·OH radical etching probability of polystyrene obtained for a radio frequency driven atmospheric pressure plasma jet

The modification of the surface properties of polymers is essential for improving adhesion, printing, or biocompatibility.^1,2 The application of low-pressure plasmas to modify the surface of polymers has been widely studied.^1,3–5 Wertheimer et al. elucidated the role of vacuum ultraviolet (VUV) photons, reactive species, and ions in the surface modification of polymers by a low-pressure plasma.⁴ Chan et al. reported the differences between the modification of polymers using plasma and UV produced by a high power mercury lamp.⁶ Sapieha et al. and Shenton and Stevens reported on the differences in the characteristics of polymers treated by an atmospheric pressure and a low-pressure air plasma.^7,8 A key difference between atmospheric pressure and low-pressure plasmas is that the ion energy is near thermal for steady-state atmospheric pressure plasma near the interface while the ion energy can be highly energetic in low-pressure plasmas due to collisionless ion acceleration in sheaths near the interfaces.⁹ This enables effective sputtering in low-pressure plasmas while interactions at atmospheric pressure will have more pronounced contributions of neutral reactive species.

A key advantage of atmospheric pressure plasmas over low-pressure plasmas is that they obviate the need for the vacuum systems and also offer roll-to-roll processing capability compared to the inherent batch processing of low-pressure plasmas. Corona treatment of polymers operating in ambient air is extensively used in industry. They enhance the surface wettability, surface roughness, surface energy, and adhesion properties of polymers.^10–13 Atmospheric pressure plasma jets (APPJs) have emerged as an additional promising tool for processing of various materials. APPJs are often operated in a noble gas such as helium or argon. The plasma is typically generated with a radio frequency (RF), kHz, or high repetition rate nanosecond pulses.¹⁴ RF modulation and low repetition rate pulses help in having high chemical reactivity while maintaining the gas temperature close to room temperature. The amount of the chemical species generated by the plasma can be enhanced by adding different molecular admixtures to the noble feed gas such as $O2$⁠, $H2$⁠, $H2O$⁠, or air.^15–17 The reactive species from an APPJ are mainly generated between the electrodes and transported out of the APPJ by convection of the gas flow.¹⁸ This enhanced chemical reactivity and the remote operation of APPJs make them attractive for heat sensitive applications such as surface modification of polymers. Plasma jet treatment of polymers is performed for the surface activation for higher adhesion,¹⁹ surface cleaning,²⁰ improvement of hydrophobic or hydrophilic properties,²¹ and etching of polymers.^22,23

While plasmas are extensively used for surface modification, the process of how these modifications occur is challenging to control and is not well understood. Several researchers have conducted experimental measurements and numerical simulations to understand the plasma polymer interaction mechanisms. Dorai and Kushner²⁴ reported a computational investigation of the gas phase and surface reactions during the modification of polypropylene (PP) in a humid-air corona discharge. They reported the change of functional groups present at the polymer surface after treatment by the plasma with variations in deposition of energy, relative humidity, gas temperature, and web speed. $⋅OH$ and $O⋅$ radicals were suggested to play a dominant role in the initiation, propagation, and termination of PP chains resulting in the formation of alcohols and acids on the surface of PP.

Shaw et al. reported an experimental study of the mechanisms underpinning the surface energy increase of PP using the afterglow of a helium APPJ with oxygen admixture.¹⁹ A strong correlation between the production of atomic oxygen in the APPJ and the change in the water contact angle of the plasma treated PP surface was observed. Knoll et al. studied the effect of VUV photons from APPJs driven by RF and kHz excitation on the etching of polystyrene (PS).²⁵ The presence of O$2$ results in the suppression of VUV photon-induced effects on the polymer. A higher etching rate was observed for an $Ar−O2$ RF driven APPJ than for the same jet in pure argon. Luan et al. reported the PS etching probability of atomic oxygen radicals to be of the order of $10−4$ by directly correlating the experimentally measured bulk atomic oxygen density in a free APPJ to the etching depth of PS in an oxygen containing APPJ.²² Similarly, the PS etching probability of the order of $10−2$ was estimated for $⋅OH$ radicals.²³ However, recombination, diffusion, and convection are important in the interfacial boundary layer above the polymer surface at atmospheric pressure and can cause significant species gradients. Hence, the density of reactive species at the surface can be significantly different from the bulk density. In addition, the radical species density profile at the substrate is expected to be much broader than the initial plasma jet diameter. Further, the density of the reactive species at the PS surface will depend on the surface reaction probability (⁠$β$⁠). Our previously reported estimates of the etching probability of $O⋅$ and $⋅OH$ did not consider these important interfacial effects and the possible impact of interfacial boundary layer processes on the estimated etching probability remains a key question.

In this manuscript, we investigate the near interfacial gradients and radical species distributions near the substrate and use the gas phase study to assess their effects on the previously reported etching probability. The gas phase $H⋅$⁠, $O⋅$⁠, and $⋅OH$ radical fluxes reaching the PS surface were obtained by a combination of a 2D axisymmetric reacting fluid dynamics model and experimentally measured $H⋅$⁠, $O⋅$⁠, and $⋅OH$ densities for $Ar+1%H2$⁠, $Ar+1%O2$⁠, and $Ar+1%H2O$ plasmas. The modeling in addition to the experiments is required because it is challenging to spatially resolve the species density gradients in the boundary layer near the substrate at atmospheric pressure by laser induced fluorescence (LIF). The work presented in this manuscript is predominantly focused on experiments and the model is not intended to be self-consistent and does not describe the entire studied process. The model is only used to deduce fluxes of radicals to the polymer substrate. Using this detailed investigation, we assess the impact of these previously neglected effects on the polystyrene etching probability of $O⋅$⁠, $H⋅$⁠, and $⋅OH$ radicals. We obtained the etching probability by correlating the area integrated flux of the gas phase reactive species at the surface to the area integrated flux of C atoms removed from the material surface by an APPJ. The etching profiles of the material surface were taken from previously published results.^22,23 As $H⋅$ radicals are not expected to lead to significant etching, we investigate the origin of the observed etching using $Ar+1%H2$ plasma. The effect of the reaction probability (a parameter not accurately known for the experimental conditions being investigated but that can impact significantly the absolute radical flux) on the etching probability of PS by $O⋅$⁠, $H⋅$⁠, and $⋅OH$ radicals is also reported.

A RF driven modulated APPJ, as shown in Fig. 1, was used in this work. A detailed description of the APPJ can be found in Refs. 26–29. In short, a $1.6mm(ID)×3mm(OD)$ cylindrical quartz tube surrounds a 1 mm (⁠$ϕ$⁠) tungsten needle electrode. A 20 kHz modulated RF signal (13.6 MHz) with a duty cycle of 20% was generated by a function generator (Tektronix AFG 2021) amplified by an RF amplifier (Amplifier Research AF75A250A) and applied through a matching box to the tungsten needle electrode. Argon with 1% admixtures of $O2$⁠, $H2$⁠, or $H2O$ at a total flow rate of 1.5 standard liters per minute (slm) flows through the quartz tube and acts as a feed gas for generating the plasma.

The polymer treatment by the APPJ was performed by placing a PS substrate below the APPJ nozzle in a sealed chamber with controlled gas atmosphere.²³ The substrate was placed at distances 4, 8, 12, 16, and 20 mm from the APPJ nozzle. The plasma power was adjusted such that the tip of the visible plasma plume was 0.5 mm above the substrate when the substrate was 4 mm below the APPJ nozzle. The corresponding plasma dissipated power in the $Ar+1%O2$⁠, $Ar+1%H2$⁠, and $Ar+1%H2O$ plasmas for such APPJ-substrate distances was 2 W, 1.26 W, and 2 W, respectively.

The treatment of the polymer surface was performed on a time scale of minutes. However, the time scale of the measurement of gas phase densities by the LIF took hours to finish because of the required measurement of the quenching time constants (⁠$τQ$⁠) of the laser excited state and gas temperatures. In a sealed chamber, the composition of the gas surrounding the APPJ is expected to change during the long duration of the measurement. In order to keep the gas composition in the measurement region constant for the duration of all the LIF measurements and enable $O2$ free measurements, a shielding flow of $N2$ (10 slm) was applied through an acrylic tube [$12.7mm(ID)×19mm(OD)$] surrounding the plasma jet (Fig. 1). Etching of PS by the APPJ changes the surface morphology and the distance between the APPJ nozzle and the substrate on long time scales. To avoid such excessive etching of the polymer during the long duration of the gas phase density measurements, an inert alumina plate (⁠$2.5×2.5cm2$⁠) with a thickness of 1 mm was used as a substrate. A grounded aluminum block of the same size as the alumina plate was positioned below the alumina plate. The gas phase density measurements are performed by placing the substrate 4, 8, and 12 mm from the APPJ nozzle. The chemical composition of alumina (⁠$Al2O3$⁠) and PS [$(C8H8)n$] are widely different. The density of the reactive species at the alumina and polymer surfaces could be different due to the chemical reactions of the reactive species with the substrates. However, the measurement has insufficient spatial resolution to resolve the steep near boundary species gradients to directly measure the density of radical species at the substrate.

The gas phase density of hydroxyl radicals (⁠$⋅OH$⁠) was performed by LIF identical to the method described in Ref. 30. A nanosecond pulsed Nd:YAG laser [Spectra-Physics LAB-170-10H, full width at half maximum $(FWHM)≈5.8ns$] with a second harmonic output at 532 nm was used to pump a dye laser (Sirah Precision Scan) to generate a laser beam after second harmonic generation at the appropriate wavelength to excite the ground state $⋅OH$ radicals. An intensified charge-coupled device (ICCD) camera (Andor IStar 340) with a UV Nikor lens placed perpendicular to the laser beam was used to capture the fluorescence. The ICCD gate was set at 50 ns, which is larger than the fluorescence lifetime of the OH(A) state measured. Rhodamine 6G dye was used to generate a laser beam with a wavelength of $≈565nm$⁠, which was subsequently converted by a second harmonics generation (SHG) crystal into a laser beam with a wavelength of 282.59 nm. A combination of a spherical lens (⁠$f=25cm$ or $f=12.5cm$⁠) and a cylindrical lens (⁠$f=50cm$⁠) shape the laser beam into a sheet with a FWHM of $206μm$ and height of either 3.8 or 7.8 mm, respectively. The excitation scheme and the four levels used for obtaining the absolute $⋅OH$ density is shown in Fig. 2(a). Fluorescence at 309 nm was recorded through a bandpass filter (307 nm,$FWHM=10nm$⁠) placed in front of the ICCD camera. The absolute calibration of the $⋅OH$ density was performed by Rayleigh scattering of air and a four-level model that considers collisional transfer and quenching from ambient gas molecules. The reader is referred to Ref. 30 for details of the used method. The lifetime of the OH(A) state was calculated by using the gas concentration profiles obtained by a computational fluid dynamics model described in Sec. II C. The decay time constants of the fluorescence intensity were measured by measuring the fluorescence at different times after the end of the laser pulse. These time constants were verified to be consistent with the fluorescence decay time calculated using the gas concentration profiles from the computational fluid dynamics model. As the lifetime of the excited state was similar or smaller than the laser beam pulse width, the accuracy of the gas composition obtained by the model was higher.

The gas phase density of atomic hydrogen radicals (⁠$H⋅$⁠) was performed using two-photon absorption laser induced fluorescence (TaLIF).^31,32 The laser system used for TaLIF is the same as described in Sec. II B 1. A 4-(Dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) special dye was used to generate fluorescence at 615 nm. The resulting laser beam was frequency doubled by using an SHG $β$-barium borate (BBO) crystal to generate a laser beam at a wavelength of 307.5 nm. The required radiation of approximately $205$ nm for TaLIF was generated by mixing the original 615 nm with the 307.5 nm beam through a second BBO crystal. The resulting laser beam was focused inside the effluent of the APPJ by a plano–convex lens with a focal length of 25 cm. The cylindrical laser beam spot had an FWHM of $157μm$ at the location of the plasma. The schematic of the two-photon excitation of $H⋅$ is shown in Fig. 2(b). The fluorescence was recorded through a bandpass filter (656 nm, $FWHM=10nm$⁠) placed in front of the ICCD camera. The two-photon excitation scheme of krypton used for calibration is shown in Fig. 2(b). The fluorescence at 587.1 nm was recorded through a bandpass filter (590 nm, $FWHM=10nm$⁠) placed in front of the ICCD camera. The absolute density of $H⋅$ was obtained by the following equation:³¹ 

where the subscripts $H⋅$ and Kr represent the quantities for atomic $H⋅$ and krypton, respectively, $n$ is the density, $T$ is the gas temperature, $η$ is the photon transmission efficiency of the setup, $σ(2)$ is the two-photon absorption cross section, $hν$ is the photon energy, $a$ is the branching ratio, $g$ is the two-photon overlap integral, and $S$ is the fluorescence intensity. The ratio of $σ(2)$ for Kr and $H⋅$ is $σKr(2)σH(2)=0.62$ as reported in Ref. 32. The two-photon overlap integral was calculated from the laser beam wavelength profile (⁠$FWHM=0.60pm$⁠) and the measured absorption profile.^31,33

The branching ratio $a$ is defined as

where $kq$ is the quenching rate coefficient for quencher labeled “$q$” of the excited state, $n$ is the density of the quencher (Ar, Kr, $O2$⁠, $N2$⁠, $H2O$⁠, and $H2$⁠), $Aij$ is the spontaneous emission coefficient of the measured transition, and $Ai=1/τ$ is the total spontaneous emission rate from the excited state. The branching ratio for $H⋅$ is determined using the constants in Table I and the gas concentration density obtained from the computational fluid dynamics (CFD) model described in Sec. II C. The branching ratio for Kr for the calibration condition used in this work was previously measured.³¹ However, the recommended $Aij$ and $Ai$ in the NIST database was changed since the publication of Ref. 31. Using the recommended and updated coefficients from the NIST database,³⁶ the branching ratio of Kr for $Ar+0.58%$ Kr at room temperature (295 K) and atmospheric pressure becomes $aKr=2.05×10−4$⁠.

The APPJ was modulated at 20 kHz with a duty cycle of 20%. The plasma was on for $10μs$ and off for $40μs$⁠. The $⋅OH$ density close to the jet changes during the duty cycle while the $H⋅$ density remains constant (Fig. 3). However, the $⋅OH$ density near the substrate was in good approximation constant during the RF modulation cycle. While the $H⋅$ and $⋅OH$ densities at the substrate do not vary more than 10% during the RF cycle(Fig. 3), the density of $H⋅$ and $⋅OH$ reported in this work is the mean of the density $2μs$ after the plasma is switched off and $2μs$ before the start of the RF pulse.

The gas temperature of the plasma effluent in the region between the APPJ nozzle and the substrate was measured by Rayleigh scattering.³⁷ The Nd:YAG laser beam at 532 nm was focused inside the plasma plume and the scattered photons perpendicular to the laser beam were captured by an ICCD camera with a UV Nikkor lens.³⁸ The intensity of the scattered photons is proportional to the density of the gas.³⁷ The recorded Rayleigh scattering signal when the plasma was off was used as a reference signal. The gas temperature was deduced by using the ideal gas law as follows:

where $T$ is the gas temperature and $I$ is the Rayleigh scattering intensity. $TPlasmaOff$ was the ambient room temperature of 295 K. The possible enhanced mixing of the surrounding $N2$ in the argon effluent due to the plasma does not significantly impact the Rayleigh scattering signal as the differential cross section for argon and $N2$ are very similar.^39,40

The goal of the model described in this section is to obtain the flux of $H⋅$⁠, $O⋅$⁠, and $⋅OH$ species to the polymer substrate and only accounts for the reactions in the plasma effluent as for a radio frequency driven plasma jet, and the radical species are mostly produced inside the quartz tube and blown out of the nozzle by the gas flow.⁴¹ The etching measurements were performed for conditions where the visible plasma plume was not in contact with the substrate even for the closest treatment distance of 4 mm. The numerical simulation of the plasma–polymer interaction was performed in a two-dimensional axisymmetric cylindrical geometry in comsol multiphysics. The geometry used in the model reflecting the experimental configuration is shown in Fig. 4. The feed gas with the reactive species produced by the plasma exit the nozzle and interact with the shielding gas and ambient air from the surroundings. A total of 12 species [Ar, $O2$⁠, $H2$⁠, $N2$⁠, $H2O$⁠, $O⋅$⁠, $O2(a1Δg)$⁠,$O3$⁠, $H⋅$⁠, $⋅OH$⁠, $HO2⋅$⁠, and $H2O2$] were considered in the model. The reactions considered in the model are listed in Table II. Reactions involving $N2$ were not considered as they do not significantly impact the $O⋅$⁠, $H⋅$⁠, and $⋅OH$ densities for the investigated experimental conditions. This was also the reason for using $N2$ as the shielding gas. However, reactions of $H⋅$ and $O⋅$ with O$2$ were included (Table II: R20 and R21) as they dominantly contribute to the depletion of $H⋅$ and $O⋅$⁠. Charged species are expected to be predominantly present inside the APPJ tube and the visible plasma plume region. We ignore the effect of the additional production of the radical species due to charged species in the visible plume region. The good correspondence of the radical densities from the experiment and the model suggests that this assumption is valid. This approach has been successfully implemented by several groups.^53,54 Hence, electron and ion-induced reactions were neglected in the model. For $Ar+O2$ plasma, Van Gaens et al. showed that the production/destruction reactions of $O⋅$ were dominantly neutral reactions in the afterglow.⁵⁵ Verlackt et al. used the same approach to model the afterglow of a plasma.⁵³ Excited short-lived species such as atomic oxygen O(⁠$1$S) and O(⁠$1$D) have not been considered in the current model.

Experimentally measured reactive species densities at the nozzle such as $H⋅$⁠, $O⋅$⁠, and $⋅OH$ were used as the boundary conditions for the flow model. The other species densities such as $HO2⋅$ and $H2O2$ at the nozzle were taken from the plug flow model results in Ref. 56. While these species are introduced through boundary 1, no reactions are considered within the quartz tube. The inlet concentrations at boundary 1 are shown in Table III. For $Ar+1%H2O$ plasma, the density of $O⋅$ atoms about 0.4 times the density of $H⋅$ atoms at the jet nozzle exit to allow for species conservation as all other O-containing species have a much smaller concentration.⁵⁶ 

The governing equations for the neutral gas model consist of the momentum conservation equation, i.e., Reynolds-averaged Navier–Stokes equation, the mass continuity equation, species balance equations, and the heat transfer equation:

where $u$ is the fluid velocity, $Ci$ is the concentration of reactive species $i$⁠, and $τ$ is the stress tensor, calculated from components with, respectively, molecular and viscosity. The $k−ε$ turbulence model was used to enable simulation of the mixing near the substrate. $Di$ is the effective diffusion coefficient of the $i$th species with the mixture. The turbulent mixing is accounted for through additional diffusivity given by $νt/Sct$⁠, where $νt$ is the turbulent kinematic viscosity and $Sct$ is the turbulent Schmidt number, set to 0.7. The mixture viscosity is $μ$ = $μT$ + $μ′$⁠, where $μ′$ is based on Wilke’s mixture rule⁵⁷ and $μT$ is the turbulent viscosity. The gas density of the mixture is calculated as $ρ=∑ρixi$⁠, where the $ith$ gas density $ρi$ is the function of gas temperature $T$⁠, and $xi$ is the mole fraction of the $ith$ species. $Cp$ is the specific heat capacity and $λ$ is the thermal conductivity of the gas mixture. The pressure is assumed to obey the ideal gas law. $Ri$ describes the production and loss of reactive species $i$ due to reactions in the plasma afterglow.

The boundary conditions are summarized in Table IV. For fluid flow, the velocity at the inlets are given by

where $Q$ is the flow rate, $n$ is the normal vector to the inlet surface, and $S$ is the inlet surface. At the remote boundary 4, the Dirichlet-type boundary condition for pressure is imposed: $p=1atm$⁠. The temperature at the needle electrode surface and the feed gas at the inlet were assumed to be equal to the measured temperature at the nozzle exit. This approach ensures that the simulated gas temperature at the nozzle is equal to the measured gas temperature and provides the appropriate initial condition to model the reactions in the plasma effluent. The boundary conditions at the substrate surface depend on the reactivity of the species. When an atom/molecule impinges on to a surface, it can reflect from the surface or stick to the surface and potentially undergo further reactions. The relative probability of such occurrences is often not known and hence a model that considers all the surface losses with a single loss term was used to describe the behavior of the reactive species in the vicinity of the surface. The loss in the flux of a reactive species at the surface can be described by^58,59

where $n$ and $vth$ are the specific species density and thermal velocity, respectively. $β$ is the surface loss probability. The reported surface loss probability of the different reactive species for PS and other materials are tabulated in Table V. Due to the long lifetime and low internal energy of $O2(a1Δg)$ and $O3$⁠, they were assumed to reflect from the substrate (⁠$β=0$⁠). The effect of the large variation in the reported values of $β$ on the species density gradients near the substrate is discussed in Sec. III C.

Schneider et al. correlated the $Γloss$ term to the flux of C atoms removed from the surface to obtain the etching probability.⁵⁹ The surface loss probability (⁠$β$⁠) of materials for different reactive species has not been extensively studied and their values are often not reported. For example, $β$ of $⋅OH$ radicals has not been reported for polystyrene. $Γloss$ depends on $β$ and correlating $Γloss$ to the flux of C atoms removed from the surface impacts the species flux to the substrate and hence adds uncertainty to the calculation of the etching probability. In this work, we define etching probability of a reactive species as the ratio of the area integrated flux of etched C atoms (⁠$NC$⁠) from the polymer surface to the area integrated flux of reactive species reaching the polymer surface. This definition is closely analogous to the definition of etching probability used in the low-pressure plasmas. The amount of etched C atoms was measured by scanning the APPJ over an area of $9.6×9.6mm2$ and the amount of etched C atoms was obtained from previously reported measurements.^22,23 The absolute fluxes of reactive gas phase species to the polymer surface were estimated by the reacting flow model described in Sec. II C. Specific details for each radical are discussed in Sec. III. $Ar+1%O2$ and $Ar+1%H2$ plasmas dominantly generate $O⋅$ and $H⋅$ atoms, respectively, although we will show that for $Ar+1%H2$ plasma impurities dominate the etching process. The PS etching probability of $O⋅$ and $H⋅$ was obtained by the slope of the linear relation between the amount of etched C atoms per unit time with the area integrated flux of $O⋅$ and $H⋅$ atoms from $Ar+1%O2$ and $Ar+1%$ $H2$ plasmas, respectively (Secs. III D 1 and III D 2). $Ar+1%H2O$ plasma dominantly generates a combination of $O⋅$⁠, $H⋅$⁠, and $⋅OH$ radicals. The rate of C atoms removed due to $⋅OH$ radicals in this case was obtained by subtracting the effect of the rate of C atoms etched by $O⋅$ and $H⋅$ atoms from the rate of C atoms removed by $Ar+1%$ $H2O$ plasma, neglecting the possible synergy between different species. The PS etching probability of $⋅OH$ radicals was obtained by the slope of the linear relation between the rate of C atoms removal and the area integrated flux of $⋅OH$ radicals from and to the polymer surface, respectively (Sec. III D 3).

The gas flow from the APPJ for the same APPJ operating in ambient air without the presence of a substrate was found to not have vortices up to five nozzle diameters (10 mm) at a flow rate of 1.5 slm.⁷³ However, the presence of a substrate induces vortices in the flow. Figure 5 shows a comparison of the gas temperature along the axis of symmetry obtained from the experiment, from a laminar flow model and a low turbulence flow model (⁠$Schmidtnumber=0.7$⁠). The laminar model did not capture the enhanced mixing in the plasma effluent and the Ar,$H2O$⁠, $O2$⁠, and $N2$ concentrations from the laminar model did not lead to an OH(A) quenching time that corresponds well with the experimentally measured quenching time of OH(A) (Fig. 5). The Ar, $H2O$⁠, $O2$⁠, and $N2$ concentrations from the low intensity turbulent model lead to a calculated quenching time of the OH(A) state to show a better correspondence with the experimentally measured OH(A) fluorescence lifetimes. Hence, the low intensity turbulent model was used to obtain the flux of reactive species reaching the substrate. This choice was made to accurately describe the conditions of the near substrate region in spite that the flow inside the tube will be laminar (⁠$Reynoldsnumber≈710$⁠).

The steady-state 2D velocity field obtained from the model is shown in Fig. 6. The presence of a substrate below the APPJ obstructs the free flow of the gas into the ambient atmosphere. As the gas flow approaches the surface of the substrate, the axial gas velocity reduces resulting in a stagnation point of zero axial velocity close to the substrate. The reduction in the axial velocity results in the increase of the radial component of the velocity and the flow becomes parallel to the surface in close proximity to the substrate. Figure 7 shows the axial velocity between the nozzle exit and the surface of the substrate on the axis of symmetry (⁠$r=0$ mm) and on a line parallel to this axis midway between the needle surface and the inner surface of the quartz tube (⁠$r=0.65$ mm). The conical tip of the needle electrode results in a stagnation point in the vicinity of the needle tip. This stagnation point causes an initial increase in the axial velocity along the axis of symmetry as the flow exits the tube of the nozzle, while such an increase does not occur at the radial position corresponding to $r=0.65$ mm. The axial velocity at both the radial locations reduces with the increase in the distance from the APPJ nozzle reaching a zero axial velocity in close proximity of the substrate. The rapid decrease in the axial velocity magnitude near the surface of the substrate results in a change in the dominant transport mechanism of chemical species from convection in the bulk region to diffusion in this interfacial region in the vicinity of the substrate. This increases the time required by the reactive species to reach the substrate and is the key reason why the boundary layer at the substrate can have a huge impact on the flux of the reactive species to the substrate.

The inlet boundary conditions for $H⋅$ and $⋅OH$ densities used in the model are determined based on the experimental results near the nozzle. The densities of $H⋅$⁠, $⋅OH$⁠, $O⋅$⁠, $H2O2$⁠, and $HO2⋅$ at the nozzle used in the model for $Ar+1%H2O$ plasma are shown in Table III. A comparison of the measured and modeled $H⋅$ and $⋅OH$ densities for $Ar+1%H2O$ plasma with a substrate 8 mm below the APPJ nozzle is shown in Fig. 8. The measured and simulation results agree within the uncertainty of the measured results for distances in excess of 2.5 mm from the nozzle. The difference between the model and the experiment does not exceed a factor of 2.25. The $H⋅$ density decreases monotonically with the distance from the jet nozzle. However, the measured $⋅OH$ density peaks at 1 mm from the APPJ nozzle and decreases for larger distances. This maximum in the density of $⋅OH$ was, however, not captured in the simulation, where the $⋅OH$ density was observed to peak at the nozzle and monotonously decreased with increasing distance from the APPJ nozzle. This discrepancy could be a consequence of not considering the time dependent variation in the $⋅OH$ density near the nozzle in the model. The $H⋅$ and$⋅OH$ densities show a steep gradient at the substrate surface. Laser scattering, vignetting of the observed fluorescence near the substrate, and the uncertainty in the concentrations of the quenchers of the excited state of $H⋅$ and $⋅OH$ (⁠$O2$⁠, $N2$⁠, and $H2O$⁠) that diffuse into the reactive species zone hamper the accurate experimental determination of the density of species in the close vicinity of the substrate. Vignetting was corrected by using the reference Rayleigh scattering signal. With this correction, we were able to measure up to $50μm$ above the substrate; however, the correction for vignetting is a source of significant uncertainties in the obtained radical densities close to the substrate. Hence, the simulation results are used to obtain the radical densities reaching the surface of the polymer.

The etching probability depends on the flux of reactive species reaching the surface of the polymer, the surface reaction probability, and the flux of C atoms removed from the polymer surface. The flux of reactive species reaching the surface will depend on the composition of the feed gas and the surroundings. In Sec. III C, we will discuss the density distribution of the gas phase reactive species generated by $Ar+1%O2$⁠, $Ar+1%H2$⁠, and $Ar+1%$ $H2O$ plasmas with a focus on the boundary layer effects. The effect of the surface reaction probability and the flux of reactive species at the surface on the etching probability will be discussed in Sec. III D.

Atomic $O⋅$⁠, $O2(a1Δg)$⁠, and $O3$ are the dominant reactive species in the afterglow region for RF driven $O2$ containing plasma jets.^56,74–77 It was previously shown that (V)UV photons do not play a role in polymer etching upon the addition of O$2$ to argon.²⁵ With the increase in the distance from the APPJ nozzle, the etching depth of the PS drops exponentially similar to the decrease in $O⋅$ density.²² The density of O$3$ increases with the increasing distance from the nozzle while the density of $O2(a1Δg$⁠) decreases at a much smaller rate than $O⋅$⁠.^22,56,76 This suggests an unlikely dominant contribution of $O3$ and $O2(a1Δg)$ to the etching of PS.

Figure 9 shows the modeled atomic $O⋅$ density along the central axis of the plasma jet for $Ar+1%O2$ plasma for substrate locations of 4, 8, and 12 mm. The figure also shows the measured$O⋅$ density measured at the nozzle by TaLIF for one condition close to the nozzle when the APPJ was operated in open air atmosphere and all other parameters are identical.⁷⁸ Atomic oxygen is produced inside the quartz tube and transported toward the target by convection. The atomic $O⋅$ density decreases along this path mainly due to the reaction of $O⋅$ with O$2$ forming ozone.^76,79 This decrease is enhanced when the APPJ is operated in ambient air surroundings due to the enhanced influx of O$2$ into the plasma effluent (Fig. 9).

Figure 10 shows the radial dependence of the $O⋅$ flux at the substrate for 4, 8, and 12 mm substrate locations. The area of the radial distribution of the atomic $O⋅$ flux at the surface for which the $O⋅$ flux is equal or more than half the maximum $O⋅$ flux is at least 11 times larger than the area encompassing the initial APPJ nozzle diameter. The radial $O⋅$ density distribution at the surface of the substrate is much narrow for an air surrounding compared to the radial $O⋅$ density distribution in $N2$ surroundings due to the fast recombination of O in the presence of in the higher density of $O2$ (Fig. 10).

The density of $O⋅$ atoms at the substrate depends on the value of $β$⁠. Figure 11 shows the variation of $O⋅$ density close to the substrate for three different values of $βO⋅$⁠. With the increase in the value of $β$⁠, the fraction of $O⋅$ atoms reacting with the substrate increase and the density of $O⋅$ atoms at the surface reduces. The $O⋅$ density and the flux at the substrate were approximately $3.4$ and 12.4 times lower for$βO⋅=10−2$ compared to $βO⋅=10−4$⁠, respectively. These results underline that the modeling of the diffusion layer above the substrate is essential for an accurate determination of species fluxes at the surface.

The dominant species generated by $Ar+1%H2$ plasma are $H⋅$ radicals. Figure 12 shows the modeled and experimentally measured $H⋅$ density as a function of the distance from the APPJ nozzle for substrate locations of 4, 8, and 12 mm. The atomic $H⋅$ density is Approximately $2.5×1022/m3$ at the nozzle of the plasma jet and reduces by 2 orders of magnitude from the nozzle to the substrate at 12 mm.

Without impurities (⁠$O2$ and $H2$O), the modeled $H⋅$ density does not match the experimentally measured $H⋅$ density beyond 5 mm from the APPJ nozzle (Fig. 12). When 30 ppm $O2$ is added to the $N2$ shielding gas, the simulated $H⋅$ density agrees well with the experiment (Fig. 12). Figure 13 shows a comparison of the measured$H⋅$ and $⋅OH$ densities with the simulated $H⋅$ and $⋅OH$ densities along the axis of symmetry in the effluent. This comparison includes the effect of $O2$ impurity gas in the $Ar+1%H2$ feed gas and in $N2$ shielding gas. In contrast to the experimentally measured $⋅OH$ density, the addition of 30 ppm $O2$ impurity in the feed gas results in a maximum of the $⋅OH$ density at the nozzle. Nonetheless, the model is also consistent with an enhanced production of $⋅OH$ radicals near the surface of the substrate. The comparison between measured and simulated $⋅OH$ densities suggests that it is difficult to model the unknown amount of impurities in the gas flow. In addition, the effect of the trace amounts of the impurities could be different between the etching measurements and the radical density measurements as they were performed in two different laboratories. Hence, no fluxes of radicals species have been used for this case to derive etching rates. Nonetheless, it can be concluded that impurities have a key impact on the radial species concentration particularly in the far effluent even if the impurities are 3 orders of magnitude smaller than the $H2$ density.

Figure 14 shows the measured and simulated densities of $H⋅$ and$⋅OH$ along the axis of symmetry for $Ar+1%H2O$ plasma. Both the $H⋅$ and the $⋅OH$ densities decrease with the increasing distance from the APPJ nozzle. The simulated densities of the major reactive species are shown in Fig. 15. The $H⋅$ and $O⋅$ densities are about 2 orders of magnitude higher than the $⋅OH$ density at the nozzle. This orders of magnitude difference between $.$OH and $H⋅$ densities is consistent with $.$OH and $H⋅$ densities reported for a high power density nanosecond pulsed spark discharge as reported by Luo et al.⁸⁰ The observed higher $O⋅$ and $H⋅$ densities in a high power density RF plasma jet might be similarly due to the electron impact dissociation of $⋅OH$ radicals in the core of the jet for conditions, where significant amount of $H2O$ is dissociated. The dominant consumption reactions of $H⋅$ are three body recombination reactions with $H⋅$ and $O⋅$ (R9 and R15 in Table II). The dominant $⋅OH$ recombination reaction is reaction R3 in Table II. $⋅OH$ is continuously produced by reaction R15 along the axial direction while $H⋅$ is being consumed. This results in the faster decrease of $H⋅$ density with increasing distance from the nozzle compared to the decrease in $⋅OH$ density.

Figure 16 shows the radial dependence of the $⋅OH$ flux at the substrate for a treatment distance of 4, 8, and 12 mm. The increase in the radial $⋅OH$ flux between 7 and 10 mm radial positions is due to the production of $⋅OH$ radicals as a result of the influx of a small amount of oxygen from the surrounding air (in spite of the $N2$ shielding gas) via reactions R11 and R17 (Table II). This increase has the same origin as the observed increase of $⋅OH$ in the afterglow in $H2O–O2$ mixtures.⁸¹ The area of the radial distribution of the $⋅OH$ flux at the surface for which the $⋅OH$ flux is equal or more than half the maximum $⋅OH$ flux is at least 10 times larger than the area encompassing the initial APPJ nozzle diameter.

Similar to the case of $O⋅$ density discussed in Sec. III C 1, the $⋅OH$ density at the substrate for 12 mm distance was a factor of approximately 13 and 2 larger for $β⋅OH=10−3$ and $β⋅OH=10−2$⁠, respectively, compared to $β⋅OH=10−1$ (data not shown). The resulting flux of $⋅OH$ at the substrate was approximately 3.4 and 27.1 times lower for $β⋅OH=10−1$ and $β⋅OH=10−2$ compared to $β⋅OH=10−3$⁠.

A linear correlation was obtained when the area integrated flux of atomic $O⋅$ to the substrate for distances of 4, 8, and 12 mm was plotted against the observed rate of removal of C atoms from the PS surface (Fig. 17). The etching probability of $O⋅$ atoms was estimated from the slope of the plots in Fig. 17. As the measured surface loss probability of $O⋅$ atoms is approximately $10−3$ for PS,⁶⁴ the etching probability of $O⋅$ atoms is $(3.2±6.8)×10−5$⁠. The uncertainty in the etching probability of $O⋅$ was calculated by assuming an uncertainty in the $O⋅$ flux to the substrate of a factor of 2. Nonetheless, the $β$ coefficient was measured for different conditions than the current work and might lead to significant uncertainties in the $O.$ flux. To this end, we assess the effect of $β$ on the determination of the etching probability by varying the surface loss probability of $O⋅$ atoms from $10−4$ to $10−2$ (Fig. 17). The corresponding etching probability of atomic $O⋅$ changes by an order of magnitude from $0.2×10−4$ to$1.4×10−4$⁠. This suggests that one C atom is removed for $104$ $O⋅$ radicals reaching the surface of polystyrene. Table VI summarizes the variation in the etching probability of $O⋅$ radicals for a range of surface reaction probability values. Assuming that the largest uncertainty is for the surface loss probability, the obtained etching probability of $(0.2–1.4)×10−4$ is nearly 1 order of magnitude smaller than the value reported by Luan et al.²² The main reason is that the $O⋅$ flux in the previous work was assumed to have a constant radial profile along the polymer surface confined to the cross sectional area of the jet nozzle. As shown in Fig. 10, the radial profile of O is much broader than the initial nozzle diameter. In addition, the atomic $O⋅$ flux at the substrate is significantly different for air and $N2$ surroundings and the average atomic $O⋅$ flux at the central point of the surface in the previous study was underestimated by using the $O⋅$ atoms density measured/calculated for an $Ar/O2$ APPJ operating in ambient air instead of $N2$ (Fig. 9).