A model for plasma modification of polypropylene using atmospheric pressure discharges

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2 INSIUE F PYSIS PUBLISING JURNAL F PYSIS D: APPLIED PYSIS J. Phys. D: Appl. Phys. 6 ) PII: S-77)569- A model for plasma modification of polypropylene using atmospheric pressure discharges Rajesh Dorai, and Mark J Kushner, University of Illinois, Department of hemical Engineering, 6, West Green Street, Urbana, IL 68, USA University of Illinois, Department of Electrical and omputer Engineering, 6, West Green Street, Urbana, IL 68, USA mjk@uiuc.edu Received November Published 6 February nline at stacks.iop.org/jphysd/6/666 Abstract Atmospheric pressure plasmas are commonly used to improve the wetting and adhesion properties of polymers. In spite of their use, the mechanisms for achieving these properties are unclear. In this regard, we report on a computational investigation of the gas phase and surface kinetics during humid-air corona treatment of polypropylene PP) and the resulting modification of its surface properties while varying energy deposition, relative humidity R), web speed, and gas temperature. Using results from a global plasma chemistry model validated against experiments, we found that increasing energy deposition increased the densities of alcohol, carbonyl, acid, and peroxy radicals on the PP surface. In doing so, significant amounts of gas phase and N x y are produced. Increasing the R increased the production of peroxy and acid groups, while decreasing those of alcohol and carbonyl groups. Production of decreased while that of N increased. Increasing the temperature decreased the concentrations of alcohol, carbonyl, and acid groups on PP while those of the peroxy radicals increased. For a given energy deposition, higher web speeds resulted in decreased concentrations of alcohols, peroxy radicals, carbonyl, and acid groups on PP.. Introduction Plasmas sustained at atmospheric pressure are commonly used to improve the adhesion and printing properties of polymers []. In these surface treatments, only the top hundreds of angstroms of the material are modified leaving the bulk polymer largely unaffected []. Although low-pressure plasma processes can be used for this purpose, atmospheric pressure processes are attractive for industrial applications because of their lower cost, higher throughput, and ability to operate without vacuum systems. A variety of polymers have been treated by plasmas, including polypropylene PP) [ 9], polyethylene PE) [, 5], polytetrafluoroethylene) [6], polyimide [7, 8], Present address: Varian Semiconductor Equipment Associates, 5 Dory Road, Gloucester, MA 9, USA. Author to whom correspondence should be addressed. polystyrene [5], polycarbonate [9, ]. he aim of these treatments is generally to improve the wetting and adhesion properties of the polymers. For example, Shenton et al [] observed that atmospheric pressure plasma treatment of low density PE and polyethylene terephthalate) improved adhesion by factors of two to ten. In general, the surface energy of untreated polymers is too small for good adhesion. For optimum adhesion, the surface energy of the polymer should be larger than that of the material to be bonded with. Similarly, for effective wetting by a liquid, the surface energy of the polymer should exceed the surface tension of the liquid. he surface energy of untreated PP is 7 mj m [5, ], whereas the surface tensions of typical water-based adhesives are 5 mj m and those of waterbased inks are 5 56 mj m []. he surface energy depends on the liquid used for measurement, and the polar and nonpolar components of the surface energy are determined by -77//6666+$. IP Publishing Ltd Printed in the UK 666

3 A model for plasma modification of PP using polar and non-polar solvents []. In general, plasma surface treatment can increase the overall surface energy of PP above that of these classes of adhesives and inks, thereby enabling bonding and printing. For example, in studies of atmospheric pressure plasma treatment of PP in e containing ppm levels of and ) by Massines and Gouda [5], the surface energy of PP increased from 7 mj m to as high as 6 mj m. he increase was attributed primarily to the bonding of atoms to the PP surface. Plasma surface treatment of polymers primarily results in the oxidation of the surface by the generation of functional groups such as alcohol), hydroperoxide), = aldehyde), = carbonyl), = ester), peroxy), = acid), ) carbonate), and N amine). For example, following the treatment of PE by an air plasma, Foerch et al [] observed the formation of ester, alcohol, carbonyl, and acid groups by x-ray photoelectron spectroscopy. Surface physicochemistry studies of air-corona-discharge-treated PP by are et al [5] showed the presence of alcohol, peroxide, acid, ester, carbonyl, and carbonate groups on the surface. In addition to functionalization, other phenomena such as ablation of the polymer, chain scission, and cross-linking may occur with corona treatment [, 6]. louet and Shi [] used hexatriacontane 6 7 ) as a proxy for high-density PE to study the gas phase products of plasma surface oxidation and ablation. hey found that,,, and were the primary products in an oxygen rich plasma. ansen et al [7] studied the effects of atomic oxygen on polymers such as PE, PP, polyimide, and polysulfide. Emission of was observed and correlated with the ablation of the polymer at a rate directly proportional to the duration of the treatment. plasmas have been found to result in less ablation of PP compared to plasmas [8]. he ablation of the polymer occurs through chain scissions and the formation of low molecular weight oxidized materials LMWMs). he volatile components of LMWM can leave the surface [8, 9]. Under select conditions, LMWMs have been found to agglomerate into globules at the surface due to a large difference in interfacial free energy between the underlying hydrophobic substrate and the oxygenated overlayer []. In studies of point-to-grid D corona discharge treatment of PE, akahashi et al [] observed the formation of LMWM when the energy deposition exceeded a threshold value. hey also found that properties such as surface energy saturated for energies above the threshold. Strobel and Lyons [] investigated the consequences of LMWM produced by corona treatment of PP on its sticking properties by adhering different materials to the modified surface: a polyamide printing ink, vapour coated aluminium, a synthetic rubber pressure-sensitive adhesive, and an acrylate based pressuresensitive adhesive. hey found that the adhesion was enhanced for the ink and the acrylate based material where the LMWM was incorporated into the adherate. When the LMWM was not incorporated into the adherate, as in the case for the metal and the rubber-based adhesive, they found that LMWM acts as a weak boundary layer inhibiting adhesion. he relative concentrations of functional groups on a treated surface generally depend on the operating conditions of the plasma generator such as energy deposition and gas composition for a given polymer being processed. hese interrelations can be quite complex. In studies of N microwave plasma modification of PP, Poncin-Epaillard et al [6] detected.5 cm of amino groups for a power deposition of W. igher concentrations of these groups were observed on PE for treatments with shorter durations higher frequency) and powers greater than 5 W. ansen et al [7] found that the rates of oxidation of branched polymers such as PP were higher compared to the relatively unbranched hydrocarbon polymers such as PE for otherwise the same operating conditions. Some systematic trends are however, clear. xygen plasma treatment generally increases the surface energy of polymers, whereas flourocarbon plasma treatment generally decreases the surface energy by creating F or F functional groups thereby making the polymer more hydrophobic and chemically inert [, ]. Low surface energies can also be obtained by the insertion of oriented methyl groups into the polymer chain []. In this regard, several gases have been investigated for modifying the surface properties of PP, including e [5], [8], N [6, ], N [], and air [9,, 5]. Studies by Massines et al [5] on the role of gas composition in the dielectric barrier discharge DBD) treatment of PP showed that, even when present in small quantities, can significantly affect the surface chemistry and hence the level of surface transformation. When.% of was added to N, the percentage of on the surface doubled while that of N decreased by a factor of five [5]. Meiners et al [6] showed that exposure of PP to an Ar plasma followed by exposure to pure acetylene gas ) increased the surface energy from to 7 mj m. A thin polymeric film was formed on the PP surface which both increased and stabilized the surface energy. When only an air or Ar plasma was used, the surface energy reached mj m. he nature of the discharge also affects the surface properties of the polymer. Under controlled operating conditions, stable, uniform, non-filamentary or glow discharges, can be produced which are often more effective for surface modification compared to filamentary discharges [5]. Massines et al [5] showed that the surface energy of PP increased from 7 to 6 mj m when using a glow nonfilamentary) atmospheric discharge, whereas with filamentary discharges, the surface energy increased to only 5 mj m. he contact angle for the glow discharge treated PP was and that for the filamentary discharge treated PP was 57 the smaller the contact angle, the larger is the wettability). Plasma modified polymer surfaces may age, a process commonly attributed to the migration of groups on the surface after treatment, surface reorientation, and exposure to oxidizing environments []. Ageing depends on the type of polymer and the process conditions. For example, studies of air-corona-discharge-treatment of PP by Strobel et al [] showed the effects of ageing to be minimal. he / ratio on the surface did not significantly change while the wettability decreased by <5% after days. his change was attributed to the reorientation of surface groups. Guimond et al [] showed that the increase in surface energy of PP produced by an glow discharge decreased by ageing. After treatment, the surface energy was 5 mj m. After days, the surface energy stabilized to mj m. 667

4 R Dorai andmjkushner In this paper, we present results from our computational investigations on the gas phase and surface kinetics during the modification of PP in humid-air plasmas. A pseudohomogeneous global kinetics model interfaced to a surface site balance model was developed and validated against experiments. he consequences of process variables which have experimentally been found to control the resulting surface properties [] energy deposition, relative humidity R), gas temperature, and web speed) were investigated. We found that increasing energy deposition not only increases densities of peroxy and acid groups on the PP surface, but also increases the production of gas phase byproducts such as N x y and. Increasing the R decreased the production of and increased the concentrations of peroxy and acid groups on the surface. he surface concentrations of peroxy radicals increased with R while those of alcohol, carbonyl, and acid groups decreased. Increasing the gas temperature increased the surface concentration of peroxy radicals and decreased the concentrations of alcohol, carbonyl, and acid groups. For a given energy deposition, increasing the web speed decreased the densities of peroxy, alcohol, carbonyl, and acid groups on the PP surface. he model used for the study, GLBAL KIN is described in section. he gas phase reaction mechanism for humidair and the surface reaction mechanism for PP are described in sections and. Results for plasma surface modification of PP are presented in section 5. oncluding remarks are in section 6. a) LLER RLL s Switch DIELERI GRUNDED ELERDE L PLASMA PWERED SE ELERDE p IG VLAGE PWERSUPPLY d ~ FEED RLL Rs R p. Description of the model A schematic of a typical corona device used for plasma surface modification is shown in figure a). he device consists of a grounded electrode covered with a dielectric and a metal shoe electrode, across which tens of kilovolts sinusoidal pulses at tens of kilohertz are typically applied to produce discharges in air. hese discharges are usually in the form of microstreamers which are typically tens to hundreds of micrometre in diameter, with an area density of tens to hundreds per square centimetre and durations of a few to hundreds of nanoseconds [5]. ypical web speeds are tens to hundreds of metre per minute and the polymer usually spends a maximum of a few seconds in the discharge. Energy depositions are usually. to a few joules per square centimetre. Although the plasma equipment used industrially for polymer processing are typically called corona discharges, due to the dielectrics on the electrodes and the capacitance of the polymer, the devices function as DBDs. he model used in this study is a modified version of a homogeneous plasma chemistry simulator called GLBAL KIN [7]. o address the reactions on and near the polymer surface, a heterogeneous model was developed and incorporated into GLBAL KIN. In GLBAL KIN, the temporal evolution of volume-averaged species densities is modelled. Based on the user defined reaction mechanism, the rate equations for the production and consumption of species both in the gas phase and on the polymer surface are constructed. Rate constants for heavy particle reactions were calculated using Arrhenius expressions based on the gas temperature. he rate constants for electron-impact reactions c) GAP BULK PLASMA DIFFUSIN REGIME ELERDE DIELERI BUNDARY LAYER Figure. Model for plasma polymer surface treatment. a) Schematic of the plasma polymer surface treatment process. A plasma is created in air by applying tens of kilovolts sinusoidal pulses at tens of kilohertz across a few millimetre gap. he polymer web traverses the plasma region at speeds of tens to a few hundreds of metres per minute. ypically, the residence time of the polymer in the plasma is at most a few seconds. Discharge circuit used in the model. c) Quasi homogeneous model for species transport to the polymer surface. wo zones above the PP surface are considered a diffusion boundary layer and homogeneous bulk plasma. Species produced in the bulk plasma diffuse through the boundary layer, react with the polymer surface, and the products diffuse back to the bulk through the boundary layer. were obtained as a function of electron temperature by solving the two-term spherical harmonic expansion of Boltzmann s equation for the electron energy distribution and parametrizing for several values of the reduced electric field [9]. PP 668

5 A model for plasma modification of PP he reaction set typically includes: electron-impact processes in the gas phase which result in ionization, dissociation, excitation, electron ion recombination, and attachment; heavy species reactions in the gas phase that result in neutral chemistry, charge exchange, ion ion neutralization; reactions of gas phase species with species on the surface; and reactions between surface species. he reaction mechanism involves 9 species 65 in the gas phase and 5 on the polymer surface) and nearly reactions. he complete set of reactions can be found in [8]. he electron temperature is determined by the energy gained by Joule heating, and the energy dissipated in elastic and inelastic collisions, ) d dt n ek B e = j E ) n me eν mi k B e i ) M i i + n e k l N l ε l. ) l n e is the electron density, e is the electron temperature, j and E are the current density and the electric field in the discharge, ν mi is the electron momentum transfer collision frequency with species i, m e is the electron mass, k B is the Boltzmann s constant, and M i and i are the mass and temperature of species i. For the lth electron impact process, k l is the reaction rate coefficient, N l is the density of the gas phase collision partner, and ε l is the change in the electron energy. he average gas temperature g is obtained by accounting for heating from elastic and inelastic collisions with electrons, enthalpy of heavy particle reactions, and heat transfer to surfaces, d dt Nc p g ) = i n eν mi me M i ) k B e i ) + n e k j N j ε j g w j R j h eff, ) d j j gap where N is the total gas density, c p is the specific heat, and j and R j are the change in enthalpy and rate of the jth reaction. h eff is the effective heat transfer coefficient with the discharge walls having temperature w, and d gap is the electrode separation. he first and second terms in equation ) account for heating due to momentum transfer collisions with electrons and dissociative electron impact processes which produce Frank ondon heating. We estimated that h eff Wm K based on flow over a flat plate []. he external circuit used to drive the DBD is shown in figure. he storage capacitance is s and the peaking capacitor is p. he plasma in the DBD is modelled as a resistor R p and the capacitances of the polymer and the dielectrics on the electrodes are collectively represented by the capacitor d. he inductor L is added to obtain the desired L time constant for the circuit. A ballast resistance R s may be used to control the energy deposition in the plasma. he reaction mechanism for plasma polymer interactions is implemented using a quasi-homogeneous model which distinguishes two regions above the polymer surface; a homogeneous bulk gas phase and a gas-surface boundary layer, as shown in figure c). he radical concentration profile in the boundary layer is mainly driven by diffusion and surface reactions. A gas phase species i is characterized by its density in the bulk of the gas phase, n ig, and near the surface of the polymer, n is. he state of the polymer is characterized by the fractional occupancy of its surface sites by different species. he time-evolution of the bulk density of species i is given by dn ig = W ig + W id, ) dt where W ig and W id are the net rate of production of species i by the gas phase reactions and diffusion through the boundary layer. Assuming Fick s law for diffusion, ) ) n ig n is S W id = D i, ) δ V where D i is the diffusion coefficient, δ is the boundary layer thickness, S is the polymer geometric surface area and V is the volume of the bulk plasma. he diffusion boundary layer thickness may be taken to be a few mean free paths microns for air at atm). For the conditions of this study, diffusion is not the rate limiting step and hence the thickness of the diffusion boundary layer is not critical. Since gas phase chemistry is neglected in the boundary layer, the time variation of the density near the polymer surface is governed by the balance between the fluxes of species entering the boundary layer by diffusion and the consumption or production of species by heterogeneous reactions at the polymer surface. he mass balance in the boundary layer is [ ] d dt n n ig n is ig + n is )V B = D i S + R di R ai )S, 5) δ where V B is the volume of the boundary layer. R di and R ai are the rates of desorption, and adsorption and abstraction per unit surface of polymer for species i. he net rate of consumption by adsorption and abstraction is a ) ij γ j v i n is j a ) ij γ j v j n js, γ j = γ j ρ j ρ, R ai = j 6) where γ j is the adsorption probability for the jth process, and v i the thermal speed of species i at the surface of the polymer, v i = 8k g /πm i. γ j is the adsorption probability per unit area, ρ j is the density of surface sites available to reaction j and ρ is the density of surface sites on a virgin polymer surface. a ) ij and a ) ij denote the left-hand side LS) and right-hand side RS) stoichiometric coefficients of species i in reaction j. v j and n js are the thermal speed and density of the gas phase species in the LS of reaction j. In equation 6), the first sum is for consumption by adsorption and abstraction reactions and the second sum is for production by abstraction reactions. he production rate of species i due to desorption reactions is R di = j a ) ij k j N is ), 7) where k j is the rate of the jth desorption reaction, and N is is the surface density of the surface species. Although the model can also address adsorption and desorption without reaction, that is physisorption, our reaction mechanism does not include such reactions. In this discussion, desorption refers to species leaving the surface following reactions. he consequences of physisorption are largely site blocking, where the presence of the physically adsorbed species prevents reactions with surface sites by other species. 669

6 R Dorai andmjkushner dn is dt he densities of the surface species are obtained from a ) ij γ n is j v i a ) ij k ) j N is = j + j a ) ij a ) ij ) j ) kj l N a) lj ls ), 8) where the first sum is over adsorption or abstraction reactions, the second over desorption reactions, and the third over reactions between surface species. n is is the density of the gas phase species involved in the adsorption or abstraction reaction. he ordinary differential equations for electron temperature equation )), gas temperature equation )), species density equations ), 5), and 8)) along with those for circuit parameters are integrated in time using VDE, a stiff equation solver [].. Gas phase reaction mechanism for humid-air onsider humid-air plasma treatment of PP having N / / = 79// % corresponds to a R of approximately % at K, atm). he fractional energy deposition by electron impact processes as a function of electric field/total gas number density E/N) is shown in figure at K, atm, N. 9 cm ). he current pulse typically lasts a few nanoseconds during which E/N 6 d d = ownsend =. 7 Vcm ).For these E/N, energy is dissipated mainly by electronic excitation and ionization of N and, dissociation of N, and vibrational excitation of N, e+n N +e, 9) e+ +e, ) e+n N + +e+e, ) e+ + +e+e, ) e+n N+N+e, ) e+n N v) +e. ) In equations 9) and ), N and represent the sum of excited states of N and. We used N A) and ) for their characteristics. Most of the N relaxes to N by collisions with N while some collide with to produce atoms, N +N N +N, k =.9 cm s [], 5) N + ++N, k =.5 cm s [], 6) where k is the rate coefficient for the reaction. Most of the is consumed by the reaction with ozone), while a smaller fraction is quenched by collisions with N, + + +, k = 5. exp 8 ) cm s, k 98 =.8 5 cm s [], 7) a) Fractional Energy Deposition Fractional Energy Deposition N -Vibrational Excitation N -Electronic Excitation -Electronic Excitation. 6 8 E/N d)... N - Dissociation N -Ionization -Ionization. 6 8 E/N d) Figure. Fractional disposition of energy deposition by electron impact processes as a function of electric field/gas number density E/N)d=. 7 Vcm ). onditions are: N / / = 78.9/./., atm, K. he E/Ns of interest are 6 d. a) Electronic and vibration excitation. Dissociation and ionization. +N +N, k =. 8 exp ) cm s, k 98 =.5 8 cm s [], 8) where k 98 is the reaction rate coefficient at 98 K. he reaction mechanism for the charged species is shown in figure a). he initiation reactions are the ionization of N,, and producing secondary electrons, N + equation )), + equation )) and +, e+ + +e+e. 9) Most of the N + reacts with N to form N + while some N+ undergo charge exchange with and to produce + and +, N + +N + M N + + M, k =. 9 cm 6 s [5], ) N N, k = 5. cm s [5], ) N N, k =. 9 cm s [6], ) where M represents any other species. 67

7 a) + N N e + + N N e e N + e + + e + e, N N N N, N N N A) A model for plasma modification of PP Most of the electrons are lost by three-body attachment to, while some are consumed by recombination with + and +, e+ + M + M, 8) e , 9) e ) + and + are also neutralized by reactions with forming,, and, , k =. 6 cm s [5], ) , k =. 6 cm s [5]. ) he reaction mechanism developed here for the free radical chemistry in the gas phase is shown in figure. he initiating reactions are the electron impact dissociations of N equation )),, and producing N,, and, e+ ++e, ) e+ ++e. ) e N e e ) Figure. Reaction mechanism for gas phase chemistry in humid-air plasma. a) harged species chemistry. Free radical chemistry. + is also formed by the dissociative charge exchange reaction of N + with, N N +N, k =.5 cm s [5]. ) Most of the + react with to form the cluster ion + which further reacts with to form +, + + +M + +M, k =.5 8 cm 6 s [5], ) , k =. 9 cm s [5]. 5) + also reacts with to form + and, , k =.7 9 cm s [5]. 6) Most of the + then form the cluster ion + by reaction with, + + +M + +M, k = 5. 7 cm 6 s [5]. 7) N atoms are consumed by the reactions with, N, and forming N and N, N+ N+, ) 85 k =.8 exp cm s, k 98 = cm s [7], 5) N+N N +, k =. exp ) cm s, k 98 =. cm s [8], 6) N+ N+, k =. exp ) cm s, k 98 = cm s [7]. 7) Apart from the electron impact dissociation of, other pathways for production include dissociation of by N equation 6)), and dissociation of by equation 7)). atoms are consumed to a large extent by the reactions with to form, and to a smaller extent by the reactions with,, and, + + M + M, ). k =. cm 6 s [8], 8) , k =.9 exp ) cm s, k 98 =.5 cm s [7], 9) + +, ) k =. exp cm s, k 98 =. cm s [9], ) 67

8 R Dorai andmjkushner + +, k = 8. exp 6 ) cm s, k 98 = 8. 5 cm s [7]. ) radicals are produced by the electron impact dissociation of equation )) and by the reactions of with, + with, and with, + +, k =. exp 7 ) cm s, k 98 =.9 cm s [8], ) , k =. 9 cm s [5], ) + +, ) k =.9 exp cm s, k 98 = 5.7 cm s [8]. ) is primarily consumed by the reactions with N equation 5)) and forming N and, and secondarily by the reactions with atoms equation )),, and N, + +, k = 8. cm s [8], 5) + +, k =.9 exp ) cm s, k 98 = 6.6 cm s [5], 6) + N + M N + M, ).9 k =. cm 6 s [8]. 7) 98 atoms are produced by the electron impact dissociation of equation )) and by the reactions of N with equation 5)), with equation )), and + with equation )). atoms are mainly consumed by reactions with to form equation )), and by reactions with to form, + + M + M, ).8 k =.8 cm 6 s [5]. 8) 98 radicals mutually react to produce hydrogen peroxide ), which is also produced by mutual reactions of, + + M + + M, ) 98 k =.9 exp cm 6 s, k 98 = 5. cm 6 s [], 9) + + M + M, ).8 k = 6.9 cm 6 s []. 5) 98 is consumed by reactions with to form and, + +, k =.9 exp 6 ) cm 6 s, k 98 =.7 cm s []. 5) Major N-containing products in the gas phase include N, N,N, N 5, N, and N. N is produced dominantly by the reactions of N with equation 5)), N with equation 7)), and with N, +N N+, ) k = 6.5 exp cm s, k 98 = 9.7 cm s [7]. 5) N is consumed primarily by reactions with N equation 6)),,, and, forming N, N, N, and N, respectively, N+ N +, k =. exp 598 ) cm s, k 98 =. cm s [5], 5) N++M N + M, ).5 ) k = 8.6 exp cm 6 s, 98 k 98 = 9.7 cm 6 s [5], 5) N+ N +, ) k =.5 exp cm s, k 98 = 7.8 cm s [5]. 55) N is produced mainly by the reactions of N with and equations 5) and 55)), and by the reaction of with N, + N N +, k =.8 exp 9 ) cm s, k 98 =.9 cm s [8]. 56) Important consumption channels for N include reactions with,, and N forming N equation 7)), N equation 5)), N nitrous oxide), and N, N +N N +, k =. cm s [5], 57) N ++M N + M, ). k = 9. cm 6 s [8]. 58) 98 N is also produced by the reaction of with N, + N N +, ) 65 k =.5 exp cm s, k 98 =. cm s [5]. 59) 67

9 A model for plasma modification of PP N is consumed by the reactions with N forming N 5 dinitrogen pentoxide), N +N + M N 5 + M, ). k =.7 cm 6 s [7]. 6) 98 N 5 decomposes to regenerate N and N, N 5 N +N, k = ). exp ) 8 s, k 98 =.7 s []. 6) N is primarily produced by the reaction of with N equation 5)) and dominantly consumed by the reaction with to form N equation 56)). N is produced by the reaction of with N equation 7)) and is consumed by the reaction with to form N equation 59)).. Surface reaction mechanism for PP PP is a saturated hydrocarbon polymer with a carbon backbone containing hydrogen and methyl ) groups arranged in an alternating fashion. We used 5 cm for the total density of surface sites, as reported for virgin PP [6]. he reactivities of the hydrogen groups in PP depend on the nature of the atom to which they are attached. here are three types of atoms in any given monomer unit of PP, primary, to which only one atom is bonded; secondary, to which two atoms are bonded; and tertiary, to which three atoms are bonded see figure a)). In general, the reactivities of hydrogen bound to these atoms scale as: tert > sec > pri. A monomer unit of PP consists of two secondary atoms, a tertiary atom, and a methyl ) group. We acknowledge that these groups are typically configured in such a manner as to minimize the overall surface energy. his a) Primary ertiary,, Secondary, n Figure. Surface reaction mechanism. a) A monomer unit in PP. Surface site balance model. PP is a saturated hydrocarbon polymer consisting of two secondary atoms, a tertiary, and a methyl group attached to a carbon backbone. he total number of surface sites is allowed to vary. could result in their preferentially being larger proportions of one group on the surface than given by its stoichiometry. owever, due to lack of data to differentiate their relative surface concentrations, we assumed a equal likelihood for any of these four groups to be pointing out towards the plasma, and so their initial surface densities are, N,sec =.5 5 cm, N,tert =.5 5 cm, and N methyl =.5 5 cm. he total number of surface sites is, however, allowed to vary with treatment time. When a hole is made in the PP chain, the diffusing species are allowed to react with the newly formed dangling bonds in the broken chains as well as with the exposed PP chain below, as shown in figure. he plasma surface modification of PP is primarily oxidative by reactions with free radicals in the gas phase. he reactions with gas phase ions can be neglected in comparison. he loss frequencies for ions in the gas phase are orders of magnitude larger than their loss frequencies with PP and as a result, ions are preferentially consumed in the gas phase. For example, the loss frequency for + in the gas phase is 7 s. For a unit probability for reaction with the PP surface, the loss frequency for + is s. he fluxes of free radicals to the surface are at least three orders of magnitude larger than those of ions. For reactions of ions to be comparable to those of free radicals, their reaction probabilities would need to greatly exceed those of free radicals. As reaction probabilities of free radicals are typically >, those for ions would need to be near unity. aving said that, there may be unique reactions which only ions can initiate by virtue of the large activation energy and, in some cases, kinetic energy they bring to the surface; and there is evidence that plasma modification of polymers is sensitive to the ratio of neutral to ionized species []. For our conditions, the ions arriving at the PP surface are thermal due to the collisional sheath and so do not contribute to energy activated reactions such as sputtering. n this basis, we have not differentiated ions from the free radicals with respect to their reactivities. he surface reaction mechanism for PP is given in table. In general, the reactions can be classified as: initiation, propagation, and termination... Initiation he initiating reactions are abstractions of hydrogen from the PP chain. Although the cleavage of PP at the bond is possible, the resulting radicals, due to their mutual proximity have been found to quickly recombine to yield back the polymer. Potentially, the species in the gas phase that can react with PP are,,,n,,, and. Investigations have shown that reactions on saturated hydrocarbons are slow at best [5]. he rate constant for reactivity on PP is. cm s [55], which is at least a few orders of magnitude smaller than both the rate constant for the gas phase consumption of and the rate constant for the reaction of or with PP which is cm s [8]). he reactivities for abstraction by atoms are two to four orders of magnitude smaller than those for or and hence, atoms are less likely to be a significant source of abstraction [56]. Similarly, the reactivities of N and towards PP are significantly smaller compared to those of and and so can be safely neglected. Direct oxidation by molecular oxygen 67

10 R Dorai andmjkushner Reaction a able. Surface reaction mechanism for PP. Probabilities or reaction rate coefficient b Initiation g +PP PP + g,, 5 c g +PP PP + g.5,.5,.5 c Propagation PP + g PP,, c PP +,g PP.,.,5. c PP +,g PP +,g.,.5,.5 c PP +PP PP + PP cm s PP aldehydes + PP s PP ketones + PP 5 s g +PP= g + PP=. g +PP= g + PP=. g + PP=,g + PP. g + PP= )PP=. PP +PP PP + PP 8. cm s g + PP PP + g 7.5 g + PP PP + g 8. ermination g +PP PP.,.,. c g +PP PP.,.,. c a Subscript g denotes gas phase species. PP denotes PP. b hose coefficients without units are reaction probabilities. c Reaction probabilities for tertiary, secondary, and primary radicals, respectively. omments has high activation energies requiring gas temperatures above 7 K to be important. As a result, these processes are not considered here. has been observed spectroscopically during the oxidation of hydrocarbon polymers by atomic oxygen as evidence of -abstraction [7]. can be abstracted from any of the primary, secondary, and tertiary sites in PP. he probability of abstraction scales as tert > sec > pri and this ranking is generally independent of the nature of the attacking radical [57]. his trend is supported by the observation that oxidative attack in atactic PP a configuration of PP in which the methyl groups are placed randomly on both sides of the chain) at tertiary sites is times faster than at secondary sites [58]. Another example is the abstraction of from isobutane iso- ) by atoms, + iso- + iso- 9, k iso, 98 =. 5 cm s [8], 6) + iso- + tert- 9, k tert, 98 = 5. k iso, 98 [8]. 6) he rate of tertiary abstraction is 5 times larger than that of secondary. Similar trends have been observed in reactions of with n-heptane where rate constants for abstraction of secondary hydrogen are approximately two orders of magnitude larger than those for primary hydrogen [8]. atoms abstract from PP to produce a PP alkyl radical and, g) + ~ ~ ~ ~ + g). 6) he tilde denotes a species in the PP backbone, and g) denotes gas phase species). Based on the work by Gomez et al [59], at atmospheric pressure, the surface reaction probability for this process is <.. For this work, we used γ tert =, γ sec =, and γ pri = 5. radicals also abstract from PP to produce an alkyl radical and, g) + ~ ~ ~ ~ +. g) 65) As reaction probabilities for abstraction by are not well known, estimates were obtained based on analogies with rate constants for gas phase reactions of with long chain saturated hydrocarbons. he rate constant for the reaction of with large hydrocarbon molecules e.g. 6 ) is.5 cm s [8]. A gas-kinetic rate constant is cm s. Assuming that a unit surface reaction probability corresponds to a gas phase kinetic rate constant, the surface reaction probability for abstraction from PP by can be estimated as γ tert =.5. Also, the branching ratios for abstractions from the tertiary, secondary, and primary sites of long chain saturated hydrocarbons in the gas phase are such that k tert /k sec 5 and k sec /k pri [8]. herefore, we estimated that γ sec =.5 and γ pri =.5. his method of deriving surface reaction probabilities typically provides only an estimate. here are other factors such as the orientation of the reactant with respect to the surface, its angle of incidence, and the catalytic activity of the surface which influence the surface reaction probabilities. For a strong interaction with the surface, this approach likely provides a reasonable lower limit to the reactivity because of the neglect of the catalytic effect of the surface. For a weak interaction, this method provides a better estimate. If the reactions are sterically hindered, this method provides an upper limit. 67

11 A model for plasma modification of PP.. Propagation he PP alkyl radicals produced by abstraction by and equations 66) and 67)) react with to form PP peroxy radicals, g) + ~ ~ peroxy radical) 66) he reactivity of, however, depends on the nature of the alkyl radicals. Studies by Kuzuya et al [6] showed that midchain alkyl radicals are much less reactive with compared to end-chain alkyl radicals. he reactions with end-chain radicals are usually diffusion controlled [57] and can be taken to occur at close to the encounter frequency [6]. he PP alkyl radicals can also react with to form alkoxy radicals [7], g) + ~ ~ ~ ~. alkoxy radical) 67) his direct pathway to the formation of alkoxy radicals is not significant in corona discharges. ydrocarbon alkyl radicals are known to react with in the gas phase at a rate up to five times faster than [6]. he analogous process for the reactions of with alkyl surface groups could be a possible route to alkoxy radical formation, g) + ~ ~ ~ ~. ~ ~ + g). 68) he PP peroxy radicals abstract hydrogen from other polymer chains or from neighbouring sites on the same chain to yield PP hydroperoxides [57]. he ratio of intermolecular to intramolecular attack on the sites by peroxy radicals is : [5]. he intramolecular attack, being more favoured, leads to sequences of neighbouring hydroperoxide groups along a backbone. his series of reactions has been observed during the early stages of oxidation of PP [5], ~ ~ + ~ ~ ~ ~ + ~ ~. 69) ~ ~ ~ ~ ~ + g) ~. 7) he resulting alkyl radicals then react with abundant to form peroxy radicals. he mean time for the reaction of polymer peroxy radicals between propagation steps, based on their reaction with neighbouring tertiary radicals, is 5 s [5]. Decomposition of the resulting hydroperoxides leads to a variety of oxidized functional groups [57]. his decomposition, is however slow compared to the formation of alkoxy or peroxy radicals. For example, Poncin-Epaillard et al [9] exposed PP previously treated by a N plasma to. ydroperoxides were formed, with densities up to 6 cm, which then decomposed with a half life of h. his long term decomposition of the hydroperoxides is excluded from the reaction mechanism as the residence times for the conditions of interest are at best a few seconds. owever, it should be noted made that the hydroperoxides are not necessarily the end products. Polymer alkoxy radicals P ) are the main source of the chain backbone scission that typically occurs during the oxidation of PP [57, 6]. he rate coefficient for the β-scission of PP alkoxy radicals is s [5]. Such β-scissions on tertiary carbon atoms lead to the formation of ketones while those on secondary carbon atoms result in aldehydes, ~ ~ ~ ~ ~ a b + ketones) ~ ~ + ~ + ketones) ~. aldehyde) ~. 7) 7) 675

12 R Dorai andmjkushner In the β-scission of tertiary alkoxy radicals equation 7)), channel is more favourable because the resulting secondary polymer hydrocarbon radical is more stable than the primary radical formed by channel a). β-scission is known to account for only 65% of the alkoxy degradation. he remaining alkoxies react with the PP matrix to produce alcohol groups [6]. ~ ~ + ~ ~ ~ ~ + ~ ~. 7) Further reactions of the alcohol groups with and radicals regenerate alkoxy radicals, g) + ~ ~ g) + ~ ~ ~ ~ + g), 7) ~ ~ + g). 75) Ablation of PP to produce gas phase products is initiated by the abstraction of in the aldehyde groups by or to produce carbonyl radicals. hese carbonyl radicals further react with atoms to produce and PP alkyl radicals, ~ = + g), g) ~ = + g), g) ~ + g) 76) he etched product exposes the site beneath for further oxidation... ermination + g). While hydrogen atoms are less likely than or to abstract from PP, they compete with and for the PP alkyl radicals [], g) + ~ ~ ~ ~. 77) Reactions of with alkyl and carbonyl radicals result in the formation of alcohols and acids, g) + ~ ~ g) + ~ = ~ ~, ~ =. 78) 79) hese reactions are considered terminal because of the higher stability of the end products compared to the free radicals. We acknowledge that there are additional surface reaction processes such as cross-linking, reactions initiated by UV radiation from the plasma [57], and reactions resulting in unsaturation in the carbon backbone. Although these reactions can mechanically be incorporated into the model, we chose not to include them in part due to lack of fundamental data and in part by our conclusions that for our operating conditions the dominant reaction pathways are those discussed here. For example, in other work, the contributions of UV radiation to surface modification for these conditions were estimated to be small [65]. In this regard, operating with significantly different conditions open up new reaction pathways. For example, lowpressure capacitively coupled radio frequency discharges have significantly higher ratios of ion-to-radical fluxes, the ions have super-thermal energies and UV radiation is plentiful, and so a different hierarchy of reactions may be important [66]. 5. Plasma surface modification of PP o validate the surface reaction mechanism, comparisons were made to experiments conducted by are et al [5] for humid-air plasma treatment of PP. he gas composition was N / / = 78.9/./., at atm and initially K.% corresponds to a R of %). he downstream electrode length is cm and the PP web speed is 5 cm s producing a gas residence time of.5 s. he applied voltage is sinusoidal at 9.6 kz across a mm gap providing 6 voltage pulses per site. he energy deposition was varied.5 J cm ) by changing the applied voltage kv). he base case uses.8 J cm. he electron density n e ) and electron temperature e ) for the first, last, and select intermediate pulses as a function of time for the base case are shown in figure 5. he timescale is relative to the beginning of each voltage pulse. During the first voltage pulse, the potential across the gap is mainly a result of the applied voltage. he seed electrons accelerated by the electric field gain energy and ionize the background gases, N,, and, producing secondary electrons, N +, +, and + equations ), ), and 9)). For the first pulse, the peak electron temperature is. ev and the peak electron density is 7 cm. With the flow of current through the discharge, the dielectric on the surface of the electrodes is charged, thereby removing voltage from the gap and terminating the discharge. 676

13 A model for plasma modification of PP a) Electron Density cm - ) c) N * cm - ) d) *cm - ) Electron emperature ev) ime s) imes) imes) imes) -6-7 Figure 5. Plasma parameters and densities of excited species for the base case conditions. a) Electron density n e ). Electron temperature e ).c) N.d). onditions are N / / = 78.9/./., atm, K.% corresponds toarof %). he energy deposition is.8 J cm and the applied voltage is 5 kv. Due to the charging of the dielectric, the e and n e are larger for later pulses. being a relatively stable species, has a longer lifetime and its density accumulates with time. During subsequent pulses, the voltage across the dielectric adds to the gap voltage, enabling a more rapid avalanche and shorter current pulses producing larger n e 5 cm ) and e 6. ev) compared to the first pulse. he differences in n e after 7 s for pulses later than the first are due to changes in the composition of the background gases. he peak E/N during later discharge pulses is d for which nearly 7% of the energy deposition is expended in the electronic excitation of N equation 9)) and about % is expended in the electron excitation of equation )). he densities of N and during the first, last, and select intermediate pulses as a function of time are shown in figure 5. Most of the N >9%) and smaller amounts of <%) are quenched by collisions with the background gases equations 5) and 8)). ther channels for N consumption <%) include reactions with to produce equation 6)). he dominant channel for consumption is the reaction with to produce equation 7)). is less reactive compared to N and hence, its density accumulates over the pulses. ther channels for electron energy loss include ionization of N and to produce N + and + equations ) and )), whose densities are shown in figure 6. Due to the nearly constant density of N and and similarity in loss channels, the differences in the densities of N + and + with pulses after the first are small. N + is lost by association with N to form N + equation )). N+ charge exchanges with to form + equation )), which further reacts with to form the cluster ion + equation )). + reacts with to form +, which further reacts with to produce + equations 5) and 7)). he time dependence of the densities of + and the dominant negative ion,, for the first, last, and select intermediate pulses are also shown in figure 6. is produced by the attachment of electrons to equation 8)). + and neutralize to yield,, and equations ) and )). Electron impact dissociation of the background gases produces N,, and equations ), ), and )), whose densities are shown in figure 7. N atoms are consumed by reactions with and equations 5) and 7)) to produce N; and with N to produce N equation 6)). he contributions of the reactions with, N, and towards N consumption are %, 5%, and %, respectively. N being less reactive than other radicals, accumulates in the discharge between to pulses. he electron impact dissociation of equation )) accounts for 5% of the atom production; while dissociation of by N equation 6)) and by equation 7)) each contribute %. atoms are primarily consumed by reactions with 85%) to form equation 8)); and with 6%), %), and %) to produce equations 9) )). After a few hundreds of pulses, the density of reaches a periodic steady state. Although the initial inventory of in a given pulse is created by electron impact dissociation of equation )), the contribution of this process to the overall production of is only %. Dominant channels for production include reactions of with equation )), + with equation )), and with equation )) with their contributions being 5%, 5%, and %, respectively. is 677

14 R Dorai andmjkushner a) N + cm - ) 5-6 a) N cm - ) 5 5 ~ ime s) ime s) + cm - ) ime s) -6-5 cm - ) c) ime s) +. cm - ) ime s) -6-5 c) cm - ) 6 ~ d) ime s) cm - ) ime s) -6-5 Figure 6. ime dependence of densities of charged species. a) N +. +.c) +. d).n+ and + are formed mainly by the electron impact ionization of N and.n + is mainly consumed by reactions with N to form N + equation )). + is primarily consumed by the reactions with to form the cluster ion +. he end result of the ion chemistry is the production of the + and. Figure 7. Densities of primary radicals as a function of time. a)n..c). N being less reactive than and accumulates between pulses. and are largely consumed in the interpulse period. primarily consumed by the reactions with N equation 5)) and equation 5)) forming N %) and %), respectively; and by the reactions with equation )), equation 6)), and N equation 7)) with their contributions being %, 8%, and 7%. he density of increases with pulses due to the increase in the density of see below), which reacts with to produce equation )). Similar to, the density of reaches a periodic steady state after a few hundreds of pulses. he densities of,, and as a function of time are shown in figure 8. atoms are mainly produced by 678

15 A model for plasma modification of PP a) a) 8 cm - ) 5 6 N cm - ) 6 ~ cm - ) cm - ) 6 ~.5.5. c) 8 ~ ime s) imes) imes) Figure 8. Densities of radicals as a function of time. a)..c). and being less reactive compared to accumulate over pulses. the reactions of N with equation 5)), with equation )), and + with equation )), with their contributions being 8%, 5%, and %. atoms primarily react with to form equation )), and with to form equation 8)). he density of reaches a periodic steady state within s of pulses. hydroperoxy) radicals are formed by the reactions of with equation 8)). he production of dominantly occurs during the first microsecond. Later, consumption of by reactions with equation 9)) and N equation 55)) to produce and N dominate. As is less reactive, its density also accumulates from pulse to pulse. is produced by the reaction of with equation 8)) and is primarily consumed by reactions with 66%, N cm - ) ime s) 75 5 ~ ime s) Figure 9. Densities of N y as a function of time. a) N. N. Most of the N and N are converted to N equation 7)) and N equation 57)). equation 7)), %, equation )), and %, equation 6)) to form,, and. he rapid production of from and dominates over losses and so accumulates from pulse to pulse. N-containing products in the gas phase include N and N, whose densities are shown in figure 9. N is produced by the reactions of N with equation 5)), N with equation 7)), and with N equation )), with their contributions being 7%, 5%, and %. N is consumed primarily by the reactions with N,,, and to produce N equation 6)), N equation 5)), N equation 5)), and N equation 55)), respectively, with contributions of 6%, %, %, and %. Due to the increase in the density of N and with time see figure 7), more N is progressively generated by the reaction of N with equation 5)). N is produced mainly by the reactions of N with and equations 5) and 55)), and with N equation 56)), with their contributions being 5%, %, and %, respectively. N is primarily consumed by the reactions with,, N forming N equation 7)), N equation 5)), and N equation 57)) with their contributions being 5%, %, and %. Approximately, 5% of N is consumed by the reactions with forming N equation 58)). Since the densities of and N increase with time, the density of N accumulates over the pulses. 679