Molecular Hydrogen Production in the Radiolysis of High-Density Polyethylene

Z. Chang and Jay A. LaVerne*Radiation Laboratory, UniVersity of Notre Dame, Notre Dame, Indiana 46556

ReceiVed: June 24, 1999; In Final Form: August 6, 1999

The production of molecular hydrogen in the radiolysis of high-density polyethylene byγ rays and heavy ionbeams has been investigated. Only the slightest increase in the radiation chemical yield of 3.1 molecules/100eV was found fromγ rays to protons of 5-15 MeV. A gradual increase in yield was observed on furtherincreasing the linear energy transfer of the incident particles. This increase amounted to almost a doubling inthe hydrogen yield from 10 eV/nm protons to about 800 eV/nm carbon ions. The exact reason for the increasein molecular hydrogen yield is uncertain, but it may involve reactions of excited states or enhanced combinationreactions of carbon-centered radicals, thereby allowing more hydrogen to escape the particle tracks. Diffusionfrom the bulk material was found to have a dominant role on the observed dynamic profiles of hydrogen gas.A simple one-dimensional diffusion model was used to estimate the diffusion constant of hydrogen inpolyethylene to be 2.2× 10-6 cm2/s.

Introduction

Extensive knowledge has been obtained on the chemicalprocesses induced in polyethylene by the passage of ionizingγor fast electron radiation.1 Much is also known about theradiation-induced physical changes in its bulk properties.2,3 Oneof the important chemical products in the radiolysis of poly-ethylene is molecular hydrogen because its yield gives a goodindication of net polymer degradation by the radiation. Anycarbon-hydrogen bond breakage that is not repaired should beaccompanied by the production of hydrogen. Unfortunately, nosystematic radiation chemistry studies have examined theproduction of molecular hydrogen as a function of the type ofirradiating particle. It is well-known that heavy charged particlesin liquids can give very different yields of molecular hydrogenthan observed withγ rays because of the variation in trackstructure.4,5 Fundamental information on particle tracks can beobtained by examining the radiation chemical effects in the solidphase. A very important practical problem is involved in theproduction of hazardous gases such as hydrogen by theradiolysis of polymeric materials associated with nuclear wastematerials. Alpha particles produced by transuranic decay areconstantly changing waste composition, causing difficulties inhandling, shipping, and storage of these materials.6,7 Polyeth-ylene is often a composition of the waste or can be used as amodel for other materials.

Several studies have been made on the formation of molecularhydrogen in the radiolysis of polyethylene withγ rays and fastelectrons as a function of temperature or other characteristicsof the bulk material.8-15 There is still some uncertainty in theradiation chemistry, but it appears that hydrogen atoms are firstproduced followed by hydrogen abstraction reactions or atom-atom combination reactions to give molecular hydrogen. A fewexperiments have been performed with heavy charged par-ticles.16-18 However, particle energies were only a few MeV atthe most and no systematic dependence on particle type orenergy can be inferred from these studies because of the scarcityof data. Basic information on the radiation chemistry occurringin particle tracks can be obtained by carefully controlledexperiments using various particles over a range of energies.

In the present work, the molecular hydrogen yields in high-density polyethylene (HDPE) irradiated with protons, heliumions, and carbon ions have been investigated as a function ofincident particle energy. Companion studies withγ radiolysiswere performed for comparison with the many investigationsusing conventional irradiation. The experiments measuredradiation chemical yields in bulk and granulated material. It wasfound that the diffusion of hydrogen plays an important role inthe dynamics of hydrogen evolution from the polymer and mayhave unexpected consequences on the prediction and monitoringof hazardous gas in nuclear waste management. Therefore, areal-time technique was employed to observe the dynamicprofile of gas evolution and a one-dimensional diffusion modelwas used to evaluate the influence of diffusion on the observedyields of molecular hydrogen.

Experimental Section

Particle irradiations were performed using1H, 4He, and12Cions obtained from the 10 MeV FN Tandem Van de Graaff ofthe University of Notre Dame Nuclear Structure Laboratory.The window assembly and irradiation procedure were essentiallythe same as previously reported.19,20 Particle energy wasdetermined by magnetic analysis, and energy loss to thewindows was calculated using standard stopping power tables.21

Absolute dosimetry was obtained by collecting and integratingthe charge from the sample cell in combination with the particleenergy. Beam currents were 5 nA, and total energy depositedwas usually (1-5) × 1018 eV given within a few seconds. Thebeam diameter was 6.35 mm, and completely stripped ions wereused, so the particle flux was about 1011/Q particles/(cm2 s),where Q is the charge per particle. The variation in sampleconfigurations and range of particles gave a variety of absolutedoses.

Two different sample configurations were used. One experi-mental configuration used a quartz sample cell with a micawindow, ∼ 4 mg/cm2, containing pellets of polymer sample.Nitrogen, UHP grade, was used as a carrier gas and passedthrough the sample cell throughout the irradiation. In the secondexperimental configuration, a solid polymer disk of 25 mm

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10.1021/jp9921250 CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 09/11/1999

diameter with an exposed diameter of 6.35 mm and a thicknessof 1.0 or 3.0 mm was sealed 3 mm from the beam exit window.Nitrogen carrier gas was passed through the void between theexit window and the polymer disk. Hydrogen generated in eithersample configuration was continuously swept away by thecarrier gas at a flow rate of 30 mL/min.

The effluent of the carrier gas was monitored throughout theradiolysis using an inline technique similar to that previouslydescribed.22 A quadrupole mass spectrometer (Blazers, QMA140analyzer with axially mounted SEM) was used to sample thecarrier gas downstream from the sample cell through a capillarytube (φ ) 50 µm, L ) 20 cm). Hydrogen was observed at themass-to-charge ratio of 2. Calibration of the system was carriedout by injecting hydrogen gas with a microliter syringe.Radiation doses were adjusted to remain in the linear region ofthe relationship between H2 volume and peak area.

Three vendors of high-density polyethylene samples wereused in the experiments: commercial grade, Goodfellow, andAldrich. No variation in hydrogen yields was observed for thethree sources, and only the Goodfellow sample is known tocontain added stabilizers. All samples were listed as high-densitypolyethylene, and Aldrich specified its product with a weight-average molecular weight of∼125 000 and a density of 0.95g/cm3. The samples were mechanically processed into differentshapes and surface cleaned with cyclohexane followed bymethanol and then dried before the irradiations.

A Shepherd Co-60 source was used to conductγ radiolysisexperiments. The dosimetry was determined using the Frickedosimeter as described previously.23 Electron density normaliza-tion was used to convert to the equivalent dose for polyethylene,which was 27.9 krad/min. The polyethylene samples wereloaded in a quartz cell that was mechanically moved into theirradiation zone of the cobalt source. Nitrogen gas with a flowrate of 30 mL/min was passed through the quartz cell continu-ously and the effluent monitored in the same manner as in theparticle radiolysis.

Results and Discussion

γ Radiolysis. Polyethylene samples with different physicalshapes were used in theγ radiolysis. Figure 1 shows one of theexperimental dynamic profiles for hydrogen evolution observedin the radiolysis of 1.0 mm thick polyethylene sheet. It can beseen that the relative intensity of hydrogen increases rapidly to

the end of the radiation exposure at 120 s. The intensity thendecays as the hydrogen is carried from the sample. The yieldof hydrogen was estimated by integrating the peak area of theexperimental curve and comparing with standard injectedsamples. The radiation chemical yield,G value, was calculatedfrom the molecular yield, and the energy absorbed by the sampleand is given in units of molecules/100 eV. A plot of hydrogenyield as a function of the absorbed irradiation energy usuallygave a straight line through the origin as shown in Figure 2.There is a range of literature values from 3.0-4.4 for the yieldof molecular hydrogen at room temperature.8-15 However, themore reliable experiments suggestG values between 3.0 and3.3, in good agreement with the value of 3.1 molecules/100 eVobserved here.

A number ofn-paraffins, both liquid and solid, exhibitGvalues for hydrogen production similar to that observed herefor polyethylene.24 Low molecular weight liquid unbranchedalkanes typically have hydrogen yields of 5-6 molecules/100eV,13 and water has a yield of 0.45 molecules/100 eV.4 Clearly,there can be a wide range of molecular hydrogen yieldsdepending on the medium and the exact mechanism leading toits formation. The radiation chemistry of hydrocarbons involvessignificant carbon-hydrogen bond breakage followed by hy-drogen atom abstraction reactions and hydrogen atom-atomcombination reactions.13,24 Radiolysis of cyclic alkanes withrelatively small ring strain energy almost exclusively gives ahydrogen atom and the parent radical followed by hydrogenatom abstraction reactions. Cyclohexane and most of the cyclicalkanes have a molecular hydrogen yield of about 5.6 molecules/100 eV.13 For straight-chain alkanes of C6 to C10, increasingthe number of secondary hydrogen atoms to the primary onesappears to lead to a decrease in molecular hydrogen.13 Normalparaffins of C20-C30 have hydrogen yields of 2-3 molecules/100 eV.24 The appearance of significant carbon-carbon bondbreakage in the paraffins and polyethylene is an effective sinkfor energy loss with no corresponding formation of molecularhydrogen.

A number of external factors can influence the molecularhydrogen yield in polyethylene.1 Oxygen is a good radicalscavenger, and it could interfere with the radical precursor tomolecular hydrogen. The use of oxygen as a carrier gas insteadof nitrogen was found to have little influence on the hydrogenyield. Similar results have been observed elsewhere.15 Anyradical scavenging by oxygen is probably occurring on thesurface, and apparently most of the hydrogen is being formed

Figure 1. Dynamic profile of the evolution of hydrogen frompolyethylene in γ radiolysis of 120 s duration. The points areexperimental data, and the curve is the model fit to give a diffusioncoefficient of hydrogen in polyethylene of 2.2× 10-6 cm2/s.

Figure 2. Dose response for the production of hydrogen gas inγradiolysis.

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in the bulk material. It is generally accepted that the yield ofhydrogen increases with increasing temperature.11,13,14In fact,no hydrogen is observed at temperatures below about 200 K.9,12

Diffusion of hydrogen from the bulk material is thought to bethe main reason for this observation. Clearly, the hydrogen mustdiffuse through the material to be observed at the surface, andthis process may play an important role in hydrogen observationand measurement.

It was found that the hydrogen yields are related to the shapeof polyethylene samples. Samples in rods, pellets, and sheetsgave relatively low yields, whereas samples in coils, films, andsmall particles had higher hydrogen yields. This observation isrelated to the diffusion of hydrogen in the bulk material. It isknown that the ionization of polyethylene by the radiation andthe following reactions producing hydrogen molecules are muchfaster than the time scale of the observed evolution of hydrogenby the detector.1 Of course, the diffusion of hydrogen isdependent on the temperature and may be the reason that nogas was observed below 200 K.9,12 At a given temperature, theapparent evolution of hydrogen from the bulk polymer can beincreased by decreasing the effective diffusion distance in thebulk or increasing the specific surface area (surface area perunit weight) of the polymer. If the specific surface area isincreased large enough so that the diffusion can be completedin the analysis time, the diffusion process will no longer affectthe observed yields. Figure 3 shows the observedG values asa function of the specific surface area. It is apparent that theGvalue is related to the specific surface area. TheG value forhydrogen increases with increasing specific area until about 50cm2/g. Above this specific surface area the yield of hydrogenis constant at 3.1 molecules/100 eV.

Diffusion Model. A model was constructed according to theone-dimensional Fick’s equation to simulate the experimentallyobserved evolution of hydrogen.25,26 The hydrogen moleculeswere assumed to be uniformly generated in the irradiation zoneand the diffusion coefficient of hydrogen molecules to beinvariant to the concentration and position. The evolution ofhydrogen was calculated by the flux at the surface,J ) -D(dC/dX), whereD is the diffusion coefficient and dC/dX is the localconcentration gradient. The partial differential diffusion equationwas numerically solved by means of the finite differenceCrank-Nicholson difference scheme.25 This method is second-order-accurate in time and space and unconditionally stable.Brent and Powell optimization methods were combined withthe diffusion model to extract the optimum values of thediffusion coefficient and the yield to match the experimental

points. The solid line in Figure 1 shows an example of asimulated curve fitted to the experimental data. It can be seenthat the simulated curve matches the experimental points verywell. The diffusion coefficient and the yield of hydrogen weresimultaneously optimized in this example.

The configuration for hydrogen analysis used in this workallows for mixing and diffusion during the transport from thesample to the analyzer. However, variation of carrier flow ratesexperimentally showed that this effect was negligible forsamples not thinner than 0.15 mm. Simulations on thickpolyethylene samples gave diffusion coefficients independentof carrier flow rate. A thinner sample of polyethylene, 0.01 mm,did show variation in the diffusion coefficient with carrier gasflow rate. With thin samples, the derived diffusion coefficientwas found to increase with increasing carrier flow rate, and onlyat very high flow rates did the simulated diffusion coefficientbecome constant. Diffusion from the bulk material can competewith other mixing processes inherent in the technique when verythin samples are used.

The average diffusion coefficient of hydrogen in polyethylenewas determined to be 2.2× 10-6 cm2/s. This value is to becompared to previous estimates of>10-7 cm2/s, ref 27, and4 × 10-6 cm2/s, ref 28, and an early direct measurement of3.9 × 10-6 cm2/s, ref 29. A later indirect measurement of thediffusion coefficient for hydrogen in polyethylene obtained arange of values from 1.2× 10-6 to 3.1× 10-6 cm2/s. 30 Thevalue of the diffusion coefficient determined here is estimatedto be within (10% and considerably more accurate thanprevious determinations. By comparison, the diffusion coef-ficient for hydrogen in water is 3.4× 10-5 cm2/s and an estimatefor hydrogen in liquid heptane is 2.5× 10-5 cm2/s.31 Thereappears to be at least an order of magnitude drop in the diffusioncoefficient from the liquid to solid phases. It is not known ifthis change is due only to the differences in viscosity of themedia or to other intermolecular forces.

Heavy Ion Radiolysis. The tracks of heavy charge particlesare different than those produced byγ rays.4,5 With increasinglinear energy transfer (LET) stopping power of the medium),the concentration of the reactive species formed by the ionizingradiation increases. Energy deposition byγ rays is only about0.2 eV/nm in passing through polyethylene, while 5 MeV heliumions have a rate of about 97 eV/nm.21 The effects of this largeincrease in LET on the radical chemistry in liquids arequalitatively well understood.4,5 With increasing radical con-centration radical-radical reactions become more dominant thanradical diffusion out of the track into the bulk liquid. Diffusionprocesses in polyethylene are obviously much slower than inliquids. The carbon-centered radicals formed in carbon-hydrogen bond breakage will probably not diffuse far becauseof the relatively long length of the polymer chain. Molecularhydrogen production dependence on LET is considerably morecomplicated to predict, even in liquids. Some of the hydrogenis produced in “unimolecular” processes. The states responsiblefor these processes are probably LET-dependent but in com-plicated ways depending on the exact nature and lifetime ofthe species. Molecular hydrogen production due to radical-radical reactions, such as hydrogen atom-atom reactions, isexpected to increase with increasing LET. However, in hydro-carbons, including polyethylene, hydrogen atoms are expectedto mainly react by hydrogen abstraction reactions. This processgives one molecule of molecular hydrogen for every hydrogenatom, while hydrogen atom-atom reactions give half as muchmolecular hydrogen. It is very difficult to predict the outcomewithout detailed experimental results.

Figure 3. Radiation chemical yield of molecular hydrogen inγradiolysis as a function of polyethylene specific surface area.

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The influence of bulk diffusion on the observedG valuesfor hydrogen production was minimized in the heavy ionexperiments by using polyethylene pellets with diameters smallerthan 1.0 mm. Studies withγ rays suggest that hydrogen can bereadily observed quantitatively using the present technique onthis size of sample. The observed dynamic profiles of hydrogenfrom 1H, 4He, and12C radiolysis were sharp and with taillesspeaks. It was apparent that the bulk diffusion out of the solidpolyethylene does not affect theG values observed with theseparticles. The yields of molecular hydrogen are shown in Figure4 as a function of particle track average LET.32 It can be seenthat theG values with protons range from 3.2 to 3.3 at a trackaverage LET of 10-20 eV/nm and are slightly greater than thatobserved inγ radiolysis. A gradual increase in molecularhydrogen is observed with further increase in particle LET. Forhelium ions of LET from 80 to 160 eV/nm, theG values varyfrom 3.3 to 4.5. Carbon ions give hydrogen yields in the range4.8-5.7 at LET from 660 to 840 eV/nm. It is not understoodprecisely how the increase in LET leads to an increase inmolecular hydrogen. As discussed above, hydrogen abstractionreactions and hydrogen atom-atom reactions alone should givea net decrease in molecular hydrogen yield with increasing LET.Ionic or excited-state chemistry may be involved at the highestLET. It is also possible that the increase in concentration ofcarbon-centered radicals leads to a significant increase in theirreaction with each other, thereby decreasing recombinationreactions with hydrogen atoms. The later reactions essentially“repair” the polymer and deplete the net production of hydrogenatoms that would ultimately give molecular hydrogen.

Heavy ion radiolysis was also performed using polyethylenedisks with thicknesses of 1.0 and 3.0 mm, and the results givenin Figure 4. Hydrogen evolving from these samples showedconsiderable tailing due to diffusion from the bulk polymer.The observedG values using both protons and helium ionsdecrease with increasing particle energy (decreasing LET). Atthe lowest available LET, the yield of molecular hydrogen fromthick samples of polyethylene is considerably lower thanobserved withγ radiolysis. This observation is not believed tobe the result of changes in the chemistry, but from the diffusionof hydrogen in bulk polyethylene. As the energy of ion beamincreases, the range of the ion into the polymer increases.Therefore, the hydrogen molecules generated along the track

of the ion will take a longer time to diffuse out with a resultingsmaller observedG value. The ranges of 5, 10, and 15 MeVprotons in polyethylene are 0.3, 1.2, and 2.4 mm, respectively.The highest energy particles pass through the sample, and theLET represents the energy lost in the sample divided by itsthickness. The samples were backed with aluminum, and littlehydrogen is thought to be lost by diffusion into the aluminumand away from the front surface where hydrogen is collected.

The maximum range of the helium ions used in theseexperiments is 0.3 mm for 20 MeV ions. This range is virtuallythe same as that for the lowest energy protons. It is seen thatthe low penetration depths of the helium ions result in lessdependence of hydrogen yields on particle energy or samplethickness than observed with protons. Samples in whichhydrogen must diffuse less than about 0.5 mm are sufficient tocollect all of the gas on the time scales of the technique used inthis work. It should be noted that in these experiments hydrogenwas continuously removed from the sample during the irradia-tion. The radiolysis of static samples will allow hydrogen tobuild up and possibly alter the outcome of the radiolysis. Doleand co-workers found that molecular hydrogen yield decreaseswith increasing hydrogen pressure.10 They concluded that thedecrease is due to molecular hydrogen reaction with an ionizedor excited state of polyethylene to break a carbon-carbon bondand add two hydrogen atoms. The net result is equivalent to achain scission reaction. At high LET excited states may beformed in proximity and react with each other. If one or bothstates are quenched, the result will be fewer excited states toreact with molecular hydrogen, resulting in an increase in itsyield as is observed. A decrease in the yield of excited stateswith increasing LET has been determined in the radiolysis ofbenzene.33

The present results with protons and helium ions using pelletsare significantly higher than found in most previous reports asshown in Figure 4.16-18 In these studies polyethylene sampleswere irradiated in high vacuum by low-energy (0.1-1.5 MeV)particles. Lee and co-workers used thick polyethylene samples,and their results may be low because of the same reasonsobserved here with thick samples.17,18 Foti and co-workersemployed thin samples where relatively little energy is loss bythe incident ion. It is not clear why their results are lower thanin the present case. Very high beam fluxes and total doses wereused in these examinations. Foti used up to 1016 particle/cm2,while Lee employed on the order of 1014 particles/cm2. Bycomparison, the present work used doses on the order of 1011

particles/cm2. Experiments and calculations show rapid degrada-tion of the sample with reduced hydrogen yields at doses aboveabout 1014 particles/cm2.18 Absolute determination of theresponse of the detection system to hydrogen is directlyperformed in the present technique, whereas a more indirectmethod must be used in high vacuum radiolysis. The use of ahigh vacuum technique for radiolysis apparently requiresconsiderably more dose than in the present technique. Onereported result of 4.8 molecules of hydrogen/100 eV for 100keV helium ions agrees very well with the present results.34

However, the exact experimental conditions for this measure-ment are not known.

The one-dimensional diffusion model was used to estimatethe diffusion coefficients andG values that best match theexperimental hydrogen evolution curves for the heavy ions. Itwas found that the simulated diffusion coefficients were about1.5 × 10-6 cm2/s, which is smaller than found in theγradiolysis. A one-dimensional diffusion model may not besuitable to apply to ion beam irradiation. Inγ radiolysis the

Figure 4. Dependence of molecular hydrogen yields on track averageLET for the various particles: (9, 0) 1H, (b, O) 4He, (2) 12C, closedsymbols for polymer pellets and open symbols for polymer sheets, thiswork; (~) 1H, (.) 4He, ref 16; (boxed cross)1H, (X) 4He, ref 18; (+)4He, ref 34.

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sample is uniformly irradiated, whereas in the heavy ionexperiments definite geometries exist for both the irradiated areaand the sample. For instance, the diameter of the cross sectionof the beam was about 6 mm, while the diameter of the sampledisk was 2.5 cm. Diffusion of hydrogen in the polymer alongthe plane perpendicular to the axis of the ion beam would spreada part of the hydrogen molecules out of the irradiation zone.More robust multidimensional models have been used to analyzegas evolution in ion beam irradiated polymers.35 It is beyondthe scope of the present work to examine the diffusion processesin great detail, but such an effort will be performed at a futuretime.

Conclusions

The production of molecular hydrogen in high-densitypolyethylene samples irradiated byγ rays and heavy ion beamshas been investigated. Theγ radiolysis using various sampleconfigurations found that the observed hydrogen yield is about3.1 molecules/100 eV and is dependent on the specific surfacearea when the latter is relatively small. Diffusion of hydrogenin bulk polyethylene is responsible for the observed dynamicprofiles of hydrogen evolution. A simple one-dimensionaldiffusion model was able to estimate the diffusion constant ofhydrogen in polyethylene to be 2.2× 10-6 cm2/s.

Heavy ion radiolysis was carried out with1H, 4He, and12Cions. Small pellets of polyethylene gave increasing hydrogenyields with increasing LET of the particle.G values varied from3.2 with 15 MeV protons (LET) 10 eV/nm) to 5.7 molecules/100 eV with 10 MeV carbon ions (LET) 840 eV/nm). Theexact mechanism for this increase is unknown, but it mayinvolve quenching of excited states or rapid combinationreactions of carbon-centered radicals, thereby allowing moremolecular hydrogen to escape the particle tracks. Heavy particleradiolysis of 1 and 3 mm thick disks gave much lower hydrogenyields and in the case of protons a strong dependence on particleenergy. This observation is due to the relatively deep penetrationof the light, energetic particles and subsequent long times fordiffusion of hydrogen from the bulk to the surface.

Acknowledgment. We thank Professor J. J. Kolata formaking the facilities of the Notre Dame Nuclear StructureLaboratory available. The latter is funded by the NationalScience Foundation. The Environmental Management ScienceProgram of the U. S. Department of Energy supported the workdescribed herein. This contribution is NDRL-4158 from theNotre Dame Radiation Laboratory.

References and Notes

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