J. Phys. Chem. B 1999, 103, 8267-8271
8267
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 by γ rays and heavy ion beams has been investigated. Only the slightest increase in the radiation chemical yield of 3.1 molecules/100 eV was found from γ rays to protons of 5-15 MeV. A gradual increase in yield was observed on further increasing the linear energy transfer of the incident particles. This increase amounted to almost a doubling in the hydrogen yield from 10 eV/nm protons to about 800 eV/nm carbon ions. The exact reason for the increase in molecular hydrogen yield is uncertain, but it may involve reactions of excited states or enhanced combination reactions of carbon-centered radicals, thereby allowing more hydrogen to escape the particle tracks. Diffusion from 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 in polyethylene to be 2.2 × 10-6 cm2/s.
Introduction Extensive knowledge has been obtained on the chemical processes induced in polyethylene by the passage of ionizing γ or fast electron radiation.1 Much is also known about the radiation-induced physical changes in its bulk properties.2,3 One of the important chemical products in the radiolysis of polyethylene is molecular hydrogen because its yield gives a good indication of net polymer degradation by the radiation. Any carbon-hydrogen bond breakage that is not repaired should be accompanied by the production of hydrogen. Unfortunately, no systematic radiation chemistry studies have examined the production of molecular hydrogen as a function of the type of irradiating particle. It is well-known that heavy charged particles in liquids can give very different yields of molecular hydrogen than observed with γ rays because of the variation in track structure.4,5 Fundamental information on particle tracks can be obtained by examining the radiation chemical effects in the solid phase. A very important practical problem is involved in the production of hazardous gases such as hydrogen by the radiolysis of polymeric materials associated with nuclear waste materials. Alpha particles produced by transuranic decay are constantly changing waste composition, causing difficulties in handling, shipping, and storage of these materials.6,7 Polyethylene is often a composition of the waste or can be used as a model for other materials. Several studies have been made on the formation of molecular hydrogen in the radiolysis of polyethylene with γ rays and fast electrons as a function of temperature or other characteristics of the bulk material.8-15 There is still some uncertainty in the radiation chemistry, but it appears that hydrogen atoms are first produced followed by hydrogen abstraction reactions or atomatom combination reactions to give molecular hydrogen. A few experiments have been performed with heavy charged particles.16-18 However, particle energies were only a few MeV at the most and no systematic dependence on particle type or energy can be inferred from these studies because of the scarcity of data. Basic information on the radiation chemistry occurring in particle tracks can be obtained by carefully controlled experiments using various particles over a range of energies.
In the present work, the molecular hydrogen yields in highdensity polyethylene (HDPE) irradiated with protons, helium ions, and carbon ions have been investigated as a function of incident particle energy. Companion studies with γ radiolysis were performed for comparison with the many investigations using conventional irradiation. The experiments measured radiation chemical yields in bulk and granulated material. It was found that the diffusion of hydrogen plays an important role in the dynamics of hydrogen evolution from the polymer and may have unexpected consequences on the prediction and monitoring of hazardous gas in nuclear waste management. Therefore, a real-time technique was employed to observe the dynamic profile of gas evolution and a one-dimensional diffusion model was used to evaluate the influence of diffusion on the observed yields of molecular hydrogen. Experimental Section Particle irradiations were performed using 1H, 4He, and 12C ions obtained from the 10 MeV FN Tandem Van de Graaff of the University of Notre Dame Nuclear Structure Laboratory. The window assembly and irradiation procedure were essentially the same as previously reported.19,20 Particle energy was determined by magnetic analysis, and energy loss to the windows was calculated using standard stopping power tables.21 Absolute dosimetry was obtained by collecting and integrating the charge from the sample cell in combination with the particle energy. Beam currents were 5 nA, and total energy deposited was usually (1-5) × 1018 eV given within a few seconds. The beam diameter was 6.35 mm, and completely stripped ions were used, so the particle flux was about 1011/Q particles/(cm2 s), where Q is the charge per particle. The variation in sample configurations and range of particles gave a variety of absolute doses. Two different sample configurations were used. One experimental configuration used a quartz sample cell with a mica window, ∼ 4 mg/cm2, containing pellets of polymer sample. Nitrogen, UHP grade, was used as a carrier gas and passed through the sample cell throughout the irradiation. In the second experimental configuration, a solid polymer disk of 25 mm
10.1021/jp9921250 CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999
8268 J. Phys. Chem. B, Vol. 103, No. 39, 1999
Figure 1. Dynamic profile of the evolution of hydrogen from polyethylene in γ radiolysis of 120 s duration. The points are experimental data, and the curve is the model fit to give a diffusion coefficient of hydrogen in polyethylene of 2.2 × 10-6 cm2/s.
diameter with an exposed diameter of 6.35 mm and a thickness of 1.0 or 3.0 mm was sealed 3 mm from the beam exit window. Nitrogen carrier gas was passed through the void between the exit window and the polymer disk. Hydrogen generated in either sample configuration was continuously swept away by the carrier gas at a flow rate of 30 mL/min. The effluent of the carrier gas was monitored throughout the radiolysis using an inline technique similar to that previously described.22 A quadrupole mass spectrometer (Blazers, QMA140 analyzer with axially mounted SEM) was used to sample the carrier gas downstream from the sample cell through a capillary tube (φ ) 50 µm, L ) 20 cm). Hydrogen was observed at the mass-to-charge ratio of 2. Calibration of the system was carried out by injecting hydrogen gas with a microliter syringe. Radiation doses were adjusted to remain in the linear region of the relationship between H2 volume and peak area. Three vendors of high-density polyethylene samples were used in the experiments: commercial grade, Goodfellow, and Aldrich. No variation in hydrogen yields was observed for the three sources, and only the Goodfellow sample is known to contain added stabilizers. All samples were listed as high-density polyethylene, and Aldrich specified its product with a weightaverage molecular weight of ∼125 000 and a density of 0.95 g/cm3. The samples were mechanically processed into different shapes and surface cleaned with cyclohexane followed by methanol and then dried before the irradiations. A Shepherd Co-60 source was used to conduct γ radiolysis experiments. The dosimetry was determined using the Fricke dosimeter as described previously.23 Electron density normalization was used to convert to the equivalent dose for polyethylene, which was 27.9 krad/min. The polyethylene samples were loaded in a quartz cell that was mechanically moved into the irradiation zone of the cobalt source. Nitrogen gas with a flow rate of 30 mL/min was passed through the quartz cell continuously and the effluent monitored in the same manner as in the particle radiolysis. Results and Discussion γ Radiolysis. Polyethylene samples with different physical shapes were used in the γ radiolysis. Figure 1 shows one of the experimental dynamic profiles for hydrogen evolution observed in the radiolysis of 1.0 mm thick polyethylene sheet. It can be seen that the relative intensity of hydrogen increases rapidly to
Chang and LaVerne
Figure 2. Dose response for the production of hydrogen gas in γ radiolysis.
the end of the radiation exposure at 120 s. The intensity then decays as the hydrogen is carried from the sample. The yield of hydrogen was estimated by integrating the peak area of the experimental curve and comparing with standard injected samples. The radiation chemical yield, G value, was calculated from the molecular yield, and the energy absorbed by the sample and is given in units of molecules/100 eV. A plot of hydrogen yield as a function of the absorbed irradiation energy usually gave 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 yield of molecular hydrogen at room temperature.8-15 However, the more reliable experiments suggest G values between 3.0 and 3.3, in good agreement with the value of 3.1 molecules/100 eV observed here. A number of n-paraffins, both liquid and solid, exhibit G values for hydrogen production similar to that observed here for polyethylene.24 Low molecular weight liquid unbranched alkanes typically have hydrogen yields of 5-6 molecules/100 eV,13 and water has a yield of 0.45 molecules/100 eV.4 Clearly, there can be a wide range of molecular hydrogen yields depending on the medium and the exact mechanism leading to its formation. The radiation chemistry of hydrocarbons involves significant carbon-hydrogen bond breakage followed by hydrogen atom abstraction reactions and hydrogen atom-atom combination reactions.13,24 Radiolysis of cyclic alkanes with relatively small ring strain energy almost exclusively gives a hydrogen atom and the parent radical followed by hydrogen atom abstraction reactions. Cyclohexane and most of the cyclic alkanes have a molecular hydrogen yield of about 5.6 molecules/ 100 eV.13 For straight-chain alkanes of C6 to C10, increasing the number of secondary hydrogen atoms to the primary ones appears to lead to a decrease in molecular hydrogen.13 Normal paraffins of C20-C30 have hydrogen yields of 2-3 molecules/ 100 eV.24 The appearance of significant carbon-carbon bond breakage in the paraffins and polyethylene is an effective sink for energy loss with no corresponding formation of molecular hydrogen. A number of external factors can influence the molecular hydrogen yield in polyethylene.1 Oxygen is a good radical scavenger, and it could interfere with the radical precursor to molecular hydrogen. The use of oxygen as a carrier gas instead of nitrogen was found to have little influence on the hydrogen yield. Similar results have been observed elsewhere.15 Any radical scavenging by oxygen is probably occurring on the surface, and apparently most of the hydrogen is being formed
Radiolysis of Polyethylene
Figure 3. Radiation chemical yield of molecular hydrogen in γ radiolysis as a function of polyethylene specific surface area.
in the bulk material. It is generally accepted that the yield of hydrogen increases with increasing temperature.11,13,14 In fact, no hydrogen is observed at temperatures below about 200 K.9,12 Diffusion of hydrogen from the bulk material is thought to be the main reason for this observation. Clearly, the hydrogen must diffuse through the material to be observed at the surface, and this process may play an important role in hydrogen observation and measurement. It was found that the hydrogen yields are related to the shape of polyethylene samples. Samples in rods, pellets, and sheets gave relatively low yields, whereas samples in coils, films, and small particles had higher hydrogen yields. This observation is related to the diffusion of hydrogen in the bulk material. It is known that the ionization of polyethylene by the radiation and the following reactions producing hydrogen molecules are much faster than the time scale of the observed evolution of hydrogen by the detector.1 Of course, the diffusion of hydrogen is dependent on the temperature and may be the reason that no gas was observed below 200 K.9,12 At a given temperature, the apparent evolution of hydrogen from the bulk polymer can be increased by decreasing the effective diffusion distance in the bulk or increasing the specific surface area (surface area per unit weight) of the polymer. If the specific surface area is increased large enough so that the diffusion can be completed in the analysis time, the diffusion process will no longer affect the observed yields. Figure 3 shows the observed G values as a function of the specific surface area. It is apparent that the G value is related to the specific surface area. The G value for hydrogen increases with increasing specific area until about 50 cm2/g. Above this specific surface area the yield of hydrogen is constant at 3.1 molecules/100 eV. Diffusion Model. A model was constructed according to the one-dimensional Fick’s equation to simulate the experimentally observed evolution of hydrogen.25,26 The hydrogen molecules were assumed to be uniformly generated in the irradiation zone and the diffusion coefficient of hydrogen molecules to be invariant to the concentration and position. The evolution of hydrogen was calculated by the flux at the surface, J ) -D(dC/ dX), where D is the diffusion coefficient and dC/dX is the local concentration gradient. The partial differential diffusion equation was numerically solved by means of the finite difference Crank-Nicholson difference scheme.25 This method is secondorder-accurate in time and space and unconditionally stable. Brent and Powell optimization methods were combined with the diffusion model to extract the optimum values of the diffusion coefficient and the yield to match the experimental
J. Phys. Chem. B, Vol. 103, No. 39, 1999 8269 points. The solid line in Figure 1 shows an example of a simulated curve fitted to the experimental data. It can be seen that the simulated curve matches the experimental points very well. The diffusion coefficient and the yield of hydrogen were simultaneously optimized in this example. The configuration for hydrogen analysis used in this work allows for mixing and diffusion during the transport from the sample to the analyzer. However, variation of carrier flow rates experimentally showed that this effect was negligible for samples not thinner than 0.15 mm. Simulations on thick polyethylene samples gave diffusion coefficients independent of carrier flow rate. A thinner sample of polyethylene, 0.01 mm, did show variation in the diffusion coefficient with carrier gas flow rate. With thin samples, the derived diffusion coefficient was found to increase with increasing carrier flow rate, and only at very high flow rates did the simulated diffusion coefficient become constant. Diffusion from the bulk material can compete with other mixing processes inherent in the technique when very thin samples are used. The average diffusion coefficient of hydrogen in polyethylene was determined to be 2.2 × 10-6 cm2/s. This value is to be compared to previous estimates of >10-7 cm2/s, ref 27, and 4 × 10-6 cm2/s, ref 28, and an early direct measurement of 3.9 × 10-6 cm2/s, ref 29. A later indirect measurement of the diffusion coefficient for hydrogen in polyethylene obtained a range of values from 1.2 × 10-6 to 3.1 × 10-6 cm2/s. 30 The value of the diffusion coefficient determined here is estimated to be within (10% and considerably more accurate than previous determinations. By comparison, the diffusion coefficient for hydrogen in water is 3.4 × 10-5 cm2/s and an estimate for hydrogen in liquid heptane is 2.5 × 10-5 cm2/s.31 There appears to be at least an order of magnitude drop in the diffusion coefficient from the liquid to solid phases. It is not known if this change is due only to the differences in viscosity of the media or to other intermolecular forces. Heavy Ion Radiolysis. The tracks of heavy charge particles are different than those produced by γ rays.4,5 With increasing linear energy transfer (LET ) stopping power of the medium), the concentration of the reactive species formed by the ionizing radiation increases. Energy deposition by γ rays is only about 0.2 eV/nm in passing through polyethylene, while 5 MeV helium ions have a rate of about 97 eV/nm.21 The effects of this large increase in LET on the radical chemistry in liquids are qualitatively well understood.4,5 With increasing radical concentration radical-radical reactions become more dominant than radical diffusion out of the track into the bulk liquid. Diffusion processes in polyethylene are obviously much slower than in liquids. The carbon-centered radicals formed in carbonhydrogen bond breakage will probably not diffuse far because of the relatively long length of the polymer chain. Molecular hydrogen production dependence on LET is considerably more complicated to predict, even in liquids. Some of the hydrogen is produced in “unimolecular” processes. The states responsible for these processes are probably LET-dependent but in complicated ways depending on the exact nature and lifetime of the species. Molecular hydrogen production due to radicalradical reactions, such as hydrogen atom-atom reactions, is expected to increase with increasing LET. However, in hydrocarbons, including polyethylene, hydrogen atoms are expected to mainly react by hydrogen abstraction reactions. This process gives one molecule of molecular hydrogen for every hydrogen atom, while hydrogen atom-atom reactions give half as much molecular hydrogen. It is very difficult to predict the outcome without detailed experimental results.
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Figure 4. Dependence of molecular hydrogen yields on track average LET for the various particles: (9, 0) 1H, (b, O) 4He, (2) 12C, closed symbols for polymer pellets and open symbols for polymer sheets, this work; (~) 1H, (.) 4He, ref 16; (boxed cross) 1H, (X) 4He, ref 18; (+) 4He, ref 34.
The influence of bulk diffusion on the observed G values for hydrogen production was minimized in the heavy ion experiments by using polyethylene pellets with diameters smaller than 1.0 mm. Studies with γ rays suggest that hydrogen can be readily observed quantitatively using the present technique on this size of sample. The observed dynamic profiles of hydrogen from 1H, 4He, and 12C radiolysis were sharp and with tailless peaks. It was apparent that the bulk diffusion out of the solid polyethylene does not affect the G values observed with these particles. The yields of molecular hydrogen are shown in Figure 4 as a function of particle track average LET.32 It can be seen that the G values with protons range from 3.2 to 3.3 at a track average LET of 10-20 eV/nm and are slightly greater than that observed in γ radiolysis. A gradual increase in molecular hydrogen is observed with further increase in particle LET. For helium ions of LET from 80 to 160 eV/nm, the G values vary from 3.3 to 4.5. Carbon ions give hydrogen yields in the range 4.8-5.7 at LET from 660 to 840 eV/nm. It is not understood precisely how the increase in LET leads to an increase in molecular hydrogen. As discussed above, hydrogen abstraction reactions and hydrogen atom-atom reactions alone should give a net decrease in molecular hydrogen yield with increasing LET. Ionic or excited-state chemistry may be involved at the highest LET. It is also possible that the increase in concentration of carbon-centered radicals leads to a significant increase in their reaction with each other, thereby decreasing recombination reactions with hydrogen atoms. The later reactions essentially “repair” the polymer and deplete the net production of hydrogen atoms that would ultimately give molecular hydrogen. Heavy ion radiolysis was also performed using polyethylene disks with thicknesses of 1.0 and 3.0 mm, and the results given in Figure 4. Hydrogen evolving from these samples showed considerable tailing due to diffusion from the bulk polymer. The observed G values using both protons and helium ions decrease with increasing particle energy (decreasing LET). At the lowest available LET, the yield of molecular hydrogen from thick samples of polyethylene is considerably lower than observed with γ radiolysis. This observation is not believed to be the result of changes in the chemistry, but from the diffusion of hydrogen in bulk polyethylene. As the energy of ion beam increases, the range of the ion into the polymer increases. Therefore, the hydrogen molecules generated along the track
Chang and LaVerne of the ion will take a longer time to diffuse out with a resulting smaller observed G value. The ranges of 5, 10, and 15 MeV protons in polyethylene are 0.3, 1.2, and 2.4 mm, respectively. The highest energy particles pass through the sample, and the LET represents the energy lost in the sample divided by its thickness. The samples were backed with aluminum, and little hydrogen is thought to be lost by diffusion into the aluminum and away from the front surface where hydrogen is collected. The maximum range of the helium ions used in these experiments is 0.3 mm for 20 MeV ions. This range is virtually the same as that for the lowest energy protons. It is seen that the low penetration depths of the helium ions result in less dependence of hydrogen yields on particle energy or sample thickness than observed with protons. Samples in which hydrogen must diffuse less than about 0.5 mm are sufficient to collect all of the gas on the time scales of the technique used in this work. It should be noted that in these experiments hydrogen was continuously removed from the sample during the irradiation. The radiolysis of static samples will allow hydrogen to build up and possibly alter the outcome of the radiolysis. Dole and co-workers found that molecular hydrogen yield decreases with increasing hydrogen pressure.10 They concluded that the decrease is due to molecular hydrogen reaction with an ionized or excited state of polyethylene to break a carbon-carbon bond and add two hydrogen atoms. The net result is equivalent to a chain scission reaction. At high LET excited states may be formed in proximity and react with each other. If one or both states are quenched, the result will be fewer excited states to react with molecular hydrogen, resulting in an increase in its yield as is observed. A decrease in the yield of excited states with increasing LET has been determined in the radiolysis of benzene.33 The present results with protons and helium ions using pellets are significantly higher than found in most previous reports as shown in Figure 4.16-18 In these studies polyethylene samples were 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 reasons observed here with thick samples.17,18 Foti and co-workers employed thin samples where relatively little energy is loss by the incident ion. It is not clear why their results are lower than in the present case. Very high beam fluxes and total doses were used in these examinations. Foti used up to 1016 particle/cm2, while Lee employed on the order of 1014 particles/cm2. By comparison, the present work used doses on the order of 1011 particles/cm2. Experiments and calculations show rapid degradation of the sample with reduced hydrogen yields at doses above about 1014 particles/cm2.18 Absolute determination of the response of the detection system to hydrogen is directly performed in the present technique, whereas a more indirect method must be used in high vacuum radiolysis. The use of a high vacuum technique for radiolysis apparently requires considerably more dose than in the present technique. One reported result of 4.8 molecules of hydrogen/100 eV for 100 keV helium ions agrees very well with the present results.34 However, the exact experimental conditions for this measurement are not known. The one-dimensional diffusion model was used to estimate the diffusion coefficients and G values that best match the experimental hydrogen evolution curves for the heavy ions. It was found that the simulated diffusion coefficients were about 1.5 × 10-6 cm2/s, which is smaller than found in the γ radiolysis. A one-dimensional diffusion model may not be suitable to apply to ion beam irradiation. In γ radiolysis the
Radiolysis of Polyethylene sample is uniformly irradiated, whereas in the heavy ion experiments definite geometries exist for both the irradiated area and the sample. For instance, the diameter of the cross section of the beam was about 6 mm, while the diameter of the sample disk was 2.5 cm. Diffusion of hydrogen in the polymer along the plane perpendicular to the axis of the ion beam would spread a part of the hydrogen molecules out of the irradiation zone. More robust multidimensional models have been used to analyze gas evolution in ion beam irradiated polymers.35 It is beyond the scope of the present work to examine the diffusion processes in great detail, but such an effort will be performed at a future time. Conclusions The production of molecular hydrogen in high-density polyethylene samples irradiated by γ rays and heavy ion beams has been investigated. The γ radiolysis using various sample configurations found that the observed hydrogen yield is about 3.1 molecules/100 eV and is dependent on the specific surface area when the latter is relatively small. Diffusion of hydrogen in bulk polyethylene is responsible for the observed dynamic profiles of hydrogen evolution. A simple one-dimensional diffusion model was able to estimate the diffusion constant of hydrogen in polyethylene to be 2.2 × 10-6 cm2/s. Heavy ion radiolysis was carried out with 1H, 4He, and 12C ions. Small pellets of polyethylene gave increasing hydrogen yields with increasing LET of the particle. G values varied from 3.2 with 15 MeV protons (LET ) 10 eV/nm) to 5.7 molecules/ 100 eV with 10 MeV carbon ions (LET ) 840 eV/nm). The exact mechanism for this increase is unknown, but it may involve quenching of excited states or rapid combination reactions of carbon-centered radicals, thereby allowing more molecular hydrogen to escape the particle tracks. Heavy particle radiolysis of 1 and 3 mm thick disks gave much lower hydrogen yields and in the case of protons a strong dependence on particle energy. This observation is due to the relatively deep penetration of the light, energetic particles and subsequent long times for diffusion of hydrogen from the bulk to the surface. Acknowledgment. We thank Professor J. J. Kolata for making the facilities of the Notre Dame Nuclear Structure Laboratory available. The latter is funded by the National Science Foundation. The Environmental Management Science Program of the U. S. Department of Energy supported the work described herein. This contribution is NDRL-4158 from the Notre Dame Radiation Laboratory. References and Notes (1) Dole, M. Radiation Chemistry of Polyethylene. In AdVances in Radiation Chemistry; Burton, M., Magee, J. L., Eds.; John Wiley & Sons: New York, 1974; p 307. (2) Radiation Induced Processes in Polyethylene; Brede, Ed.; Akademie der Wissenschaften der DDR: Leipzig, 1987.
J. Phys. Chem. B, Vol. 103, No. 39, 1999 8271 (3) Irradiation of Polymers, Fundamentals and Technological Applications; Clough, R. L., Shalaby, S. W., Eds.; ACS Symposium Series 620; American Chemical Society: Washington, DC, 1966. (4) Allen, A. O. The Radiation Chemistry of Water and Aqueous Solutions; Van Nostrand: New York, 1961. (5) Farhataziz; Rodgers, M. A. J. Radiation Chemistry: Principles and Applications; VCH Publishers: New York, 1987. (6) Henrie, J. O.; Flesher, D. J. Effects of Radiation on Organic Matrix Waste Forms. Influence of Radiation on Material Properties: 13th International Symposium (Part II), ASTM STP 956; Garner, F. A., Henager, C. H., Jr., Igata, N., Eds; American Society for Testing and Materials: Philadelphia, 1987; pp 615-636. (7) Henrie, J. O.; Flesher, D. J. Hydrogen Control in the Handling, Shipping, and Storage of Wet Radioactive Waste. Influence of Radiation on Material Properties: 13th International Symposium (Part II), ASTM STP 956; Garner, F. A., Henager, C. H., Jr., Igata, N., Eds.; American Society for Testing and Materials: Philadelphia, 1987; pp 636-646. (8) Charlesby, A.; Davison, W. H. T. Chem. Ind. 1957, 232. (9) Lawton, E. J.; Balwit, J. S.; Powell, R. S. J. Polym. Sci. 1958, 32, 257. (10) Dole, M.; Williams, T. F.; Arvia, A. J. The Radiation Chemistry of a Typical Macromolecule, Polyethylene. In Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy; United Nations: Geneva, 1958; Vol. 29, p 171. (11) Williams, T. F.; Dole, M. J. Am. Chem. Soc. 1959, 81, 2919. (12) Cracco, F.; Arvia, A. J.; Dole, M. J. Chem. Phys. 1962, 37, 2449. (13) Kimura, T.; Fueki, K.; Kuri, Z. Bull. Chem. Soc. Jpn. 1970, 43, 1657. (14) Mitsui, H.; Shimizu, Y. J. Polym. Sci., Polym. Chem. Ed. 1979, 17, 2805. (15) Arakawa, K.; Seguchi, T.; Watanabe, Y.; Hayakawa, N. J. Polym. Sci, Polym. Chem. Ed. 1982, 20, 2681. (16) Calcagno, L.; Foti, G. Appl. Phys. Lett. 1986, 47, 15. (17) Lewis, M. B.; Lee, E. H. Nucl. Instrum. Methods Phys. Res. 1992, B69, 341. (18) Lewis, M. B.; Lee, E. H.; Mansur, L. K.; Coghlan, W. A. J. Nucl. Mater. 1994, 208, 61. (19) LaVerne, J. A.; Schuler, R. H. J. Phys. Chem. 1987, 91, 5770. (20) LaVerne, J. A.; Schuler, R. H. J. Phys. Chem. 1987, 91, 6560. (21) Ziegler, Z. F.; Biersack, J. P.; Littmark, U. The Stopping Power and Range of Ions in Solids; Pergamon: New York, 1985. (22) LaVerne, J. A. J. Phys. Chem. 1988, 92, 2808. (23) Pastina, B.; LaVerne, J. A. J. Phys. Chem. 1999, 103, 1592. (24) Seguchi, T.; Hayakawa, N.; Tamura, N.; Tabata, Y.; Katsumura, Y.; Hayashi, N. Radiat. Phys. Chem. 1985, 25, 399. (25) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes: The Art of Scientific Computing; Cambridge University Press: Cambridge, 1986. (26) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, 1970. (27) Venkatesan, T.; Brown, W. L.; Murray, C. A.; Marcantonio, K. J.; Wilkens, B. J. Polym. Eng. Sci. 1983, 23, 931. (28) Alekseenko, N. N.; Volobuev, P. V.; Trubin, S. B. SoV. At. Energy 1982, 53, 734. (29) Ash, R.; Barrer, R. M.; Palmer, D. G. Polymer 1970, 11, 421. (30) Deas, T. M., Jr.; Hofer, H. H.; Dole, M. Macromolecules 1972, 5, 225. (31) Reid, R. C.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1958. (32) Track average LET is defined by LET ) (1/E0)∫E0 0 (dE/dx) dE. (33) LaVerne, J. J. Phys. Chem. 1996, 100, 18757. (34) Venkatesan, T.; Calcagno, L.; Elman, B. S.; Foti, G. In Ion Beam Modification of Insulators; Mazzoldi, P., Arnold, G. W., Eds.; Elsevier: New York, 1987; p 301. (35) Pathak, R.; Menon, V. J.; Chaturvedi, U. K.; Nigam, A. K. Nucl. Instrum. Methods Phys. Res. 1989, B36, 38.
