Theoretical Calculation of Product Contents

Environ. Sci. Technol. 2003, 37, 2016-2019

Theoretical Calculation of Product Contents: Battery and Cathode Ray Tube Examples VALERIE M. THOMAS* Princeton Environmental Institute, Guyot Hall, Princeton University, Princeton, New Jersey 08544

Most product environmental assessments are based on manufacturer-supplied data on the material content of the product. This paper explores the potential for the material content of key components to be estimated with theoretical calculations. Two examples, the amount of cadmium in a nickel-cadmium battery and the amount of lead in a TV or computer CRT monitor, are developed. Both an upper and a lower limit on the amount of cadmium in a nickelcadmium battery are calculated on the basis of the battery’s chemical reaction. The amount of lead shielding needed in a TV or CRT computer monitor is estimated on the basis of the potential difference through which electrons are accelerated and the absorption length of photons in lead. Such calculations can be used as benchmarks in product environmental assessments, providing validation of manufacturer-supplied data and providing insight into the composition and design of products.

phased out. Use of lead is now largely confined to the large lead-acid batteries used for automobiles and similar applications, although small lead-acid batteries continue to be used in toys, tools, and lighting products. The use of nickelcadmium batteries remains common in consumer products and has been increasing. For this reason, the analysis here will focus on nickel-cadmium batteries. The largest use of nickel-cadmium batteries is as the power supply for cordless products, including laptop computers, camcorders, cordless telephones, and cordless power tools (Figure 1). Not all power supply batteries are nickel-cadmium batteries; newer products often use lithium ion or nickelmetal hydride batteries, and lead-acid batteries were used occasionally in older products. Nickel-cadmium batteries were phased out for laptop computer power supplies by about 1995, both because of their environmental liabilities and because other batteries have better performance characteristics. Nickel-cadmium batteries are widely used in other products, such as cordless and cellular telephones, cordless power tools, vacuum cleaners, shavers, and kitchen appliances. And until about 1994, nickel-cadmium batteries were used as the small backup batteries that maintain the clock and system settings in all computers (Figure 2). More recent computers use lithium ion batteries for backup power. To estimate the cadmium content of a nickel-cadmium battery, one can use its chemical reaction and either its mass or its capacity or both. The battery mass can readily be determined. The battery capacity is sometimes printed on the battery, and in some cases the capacity can be found from a web search or on the packaging. The chemical reaction of a sealed nickel-cadmium battery is (3)

Cd + 2NiOOH + 2H2O T Cd(OH)2 + 2Ni(OH)2 (1)

Introduction In recent years there has been increasing attention to the presence of toxic materials in products. Batteries have received a great deal of attention, as have the cathode ray tubes used in televisions and computer monitors, and electronics products in general (1, 2). Despite this interest, there is relatively little information on the amount of toxic materials in products. Much of the information that is available is based on reports from product manufacturers. Direct measurement of the material content of products is rarely undertaken. This paper explores the potential for physical theory to provide bounds on the key material content of products or components. These calculations cannot provide exact quantification of the material content because they rely on general principles rather than precise design specifications. But such calculations can be useful in analysis of the environmental impacts of products. Moreover, such estimates can provide insight into why the material content is what it is, and they can provide clues as to how the material content might change with new designs or technological improvements. This paper provides two examples of this approach: the amount of cadmium in nickel-cadmium batteries and the amount of lead in a cathode ray tube.

Batteries The content of lead, mercury, cadmium, and other elements in batteries has been a significant environmental concern. Use of mercury in batteries has now been essentially entirely * Telephone: (609)258-4665; [email protected]. 2016

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For the purposes of the calculation, the compounds involved in this reaction will be termed the “active materials” of the battery. One approach to estimating the total cadmium content is to assume that the entire mass of the battery is the active material indicated in eq 1 and to calculate the amount of cadmium from the battery’s chemical reaction. This provides an upper bound because the battery also contains electrolyte and inert materials such as the battery casing. Another approach is to estimate the amount implied by the capacity of the battery. This provides a lower bound, both because this does not include the battery casing and other structural materials and because the battery does not achieve its theoretical maximum energy production. Both approaches will be discussed below. Upper Limit from Battery Mass. An upper bound on the active material in a battery can be calculated from the chemical reaction by assuming that the mass of the inactive materials is zero. The chemical reaction of the nickelcadmium battery shown in eq 1 and the atomic weights of cadmium (112), nickel (59), oxygen (16), and hydrogen (1) imply that the active part of a sealed nickel-cadmium battery is 34% cadmium and 36% nickel by weight. This provides a theoretical upper bound on the cadmium content of a battery. For example, Table 1 shows that a nickel-cadmium computer memory backup battery weighs 11 g. If all of this were active material, the cadmium content would be 34% of 11 g or 3.7 g. Lower Limit from Battery Capacity. The capacity of a battery is the total quantity of electricity involved in the electrochemical reaction in ampere-hours (Ah). Theoretically, 1 g-equiv weight of material will deliver 26.8 Ah, where 1 10.1021/es0210300 CCC: $25.00

 2003 American Chemical Society Published on Web 04/04/2003

this could be provided by 0.33 g of active battery material (60 mAh divided by 180 mAh/g). As discussed above, 34% of the active material is cadmium; thus, a lower bound on the cadmium content is 34% of 0.33 g or 0.11 g of cadmium. This theoretical minimum cadmium content is shown in the last column of Table 1. The two approaches to estimate the material content of a nickel-cadmium memory backup battery show that the actual cadmium mass must be between 0.11 and 3.7 g. Laboratory measurements have shown that the cadmium content of nickel-cadmium batteries averages 16%, ranging from 10 to 20 wt % (5). This implies that the actual cadmium content of an 11-g nickel-cadmium battery is in the range of 1.1-2.2 g. This also implies that the active materials in a nickel-cadmium battery are about half the total mass and that the actual capacity of a nickel-cadmium battery is a factor of 4 or 5 less than the theoretical capacity. This pattern is typical of other battery types as well (6). Table 1 shows upper and lower bound estimates of the cadmium content of a selection of nickel-cadmium batteries. For each battery, the mass was measured directly, and the capacity was either printed directly on the battery or was reported elsewhere on packaging or product specifications. The table shows that the upper bound is typically more than 1 order of magnitude greater than the lower bound, which is consistent with the nonactive battery materials comprising at least half of the battery mass as discussed above. For the cordless phone and the camcorder batteries, the nonactive material may be especially large because these batteries form part of the external structure of the product. In contrast, for the AA high-capacity battery, the upper and lower bounds differ by only a factor of 2, indicating a comparatively efficient battery design.

FIGURE 1. Nickel-cadmium laptop power supply battery.

Cathode Ray Tubes FIGURE 2. Nickel-cadmium computer backup battery.

TABLE 1. Estimated Cadmium Content of a Selection of Nickel-Cadmium Batteries upper bound Cd content

lower bound Cd content

cell type

mass (g)

max Cd (g)

capacity (mAh)

min. Cd (g)

computer memory backup AA high capacity D cordless phone camcorder laptop power supply

11 11 71 74 140 450

3.7 3.7 24 25 48 150

60 1000 2000 600 800 3200

0.11 1.9 3.8 1.1 1.5 6.0

g-equiv is the molecular weight of the material divided by the number of electrons involved in the reaction. (The charge on an electron is 1.6 × 10-19 C, there are 6.02 × 1023 molecules per mole, and 1 amp is equal to 1 C/s.) For a nickel-cadmium reaction of eq 1, both the cadmium reaction and the nickel oxide reaction must be considered. The molecular weight of cadmium is 112, and two electrons are involved in the reaction, so 1 g-equiv of cadmium in this reaction is 56.2 g. This g-equiv mass will deliver 26.8 Ah; therefore, the cadmium reaction provides 2.1 g/Ah. Similarly, the nickel oxide cathode material has a molecular weight of 92, and one electron is involved in the reaction; thus, the nickel oxide reaction provides 3.4 g/Ah. The overall reaction thus provides 3.4 + 2.1 ) 5.5 g/Ah or 180 mAh/g, all to two significant figures (4). This theoretical capacity density can be used to calculate a lower bound on the mass of cadmium or nickel in the battery. For the memory backup battery cell, for example, Table 1 shows that the reported capacity is 60 mAh. In theory,

A second example of the use of theoretical calculations to gain insight into product content is provided by the cathode ray tube (CRT). This is the display technology used in most televisions and desktop computers. The tube produces a beam of electronics (“cathode rays”) that produces light when it hits the luminescent materials in the front screen. When electrons hit the materials inside the tube, X-ray radiation is produced. To prevent human exposure to these X-rays, lead is added to the glass of the CRT tube. A simple theoretical calculation can be used to estimate the amount of lead in a CRT. The amount of lead required will depend on the maximum energy of the X-rays. By conservation of energy, the energy of the X-rays cannot be greater than the energy of the electrons in the electron beam. The electrons produced by the electron gun are accelerated toward the front screen by a voltage, which is typically about 30 kV for a color television and somewhat less for a desktop computer monitor (7). An electron accelerated in a 30-kV potential receives a kinetic energy of 30 keV. Thus, the upper limit of the X-ray energy is 30 keV. The intensity (I) of the X-rays that pass through matter of thickness (x) is given by

Iout ) Iine-x/L

(2)

where L is the photon absorption length of the material. As shown in Figure 4, the photon absorption length of a 30-keV photon in lead is about 0.035 g/cm2. The density of lead is about 11 g/cm3; thus, the absorption length is equivalent, to one significant figure, to 3 × 10-3 cm. From eq 2, to reduce the intensity by a factor of 2 requires a lead thickness of

x ) 3 × 10-3 ln 2

(3)

or about 2 × 10-3 cm of lead. This is called the half-value thickness. VOL. 37, NO. 9, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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dimension (D). The 3 × 4 aspect ratio implies that the height and width of the screen can be expressed as H ) 3/5D and W ) 4/5D. The surface area of the neck, funnel, and screen can be expressed as

FIGURE 3. Cathode ray tube from a computer monitor.

Sneck ) 2πrneck × Lneck

(4)

Sfunnel ) πH2 ) 9/25πD2

(5)

Sscreen ) H × W ) 12/25πD2

(6)

where rneck and Lneck are the radius and length of the neck, and H and W are the height and width of the screen. On the basis of CRT shown in Figure 3, Lneck is about 15 cm, and rneck is about 1.5 cm, which implies a neck surface area of about 140 cm2. The size of the neck will be assumed to be independent of the screen size. For a typical 14-in. (35-cm) diameter screen, for example, the funnel would have a surface area of about 1400 cm2, the screen would have a surface area of about 1800 cm2, and the neck would have a surface area of about 140 cm2 for a total CRT surface area of 3340 cm2. Assuming, as discussed above, a lead shielding of 0.02 cm (10 times the half-value) and given that the density of lead is 11 g/cm3, this implies a total lead mass of about 730 g. Similarly, for a 27-in. CRT (69 cm), the surface area would be about 12 800 cm2 (140 cm2 for the neck, 5390 cm2 for the funnel, and 7230 cm2 for the screen), and the amount of lead would be about 2800 g. This theoretical estimate can be compared with reports from manufacturers, which indicate that in total a 14-in. (35-cm) color TV CRT contains roughly 400 g of Pb, and a 27-in. CRT contains about 1400 g of Pb (10). This shows that the order of magnitude calculations above are of the correct order of magnitude, although on the high side. One issue that has been neglected in this simple calculation is the angular distribution of the X-radiation. For a nonrelativistic electron, the angular dependence of the power of the X-radiation is

dP/dΩ ∼ sin2θ

FIGURE 4. Absorption length of photons in lead as a function of photon energy (data from ref 9). Dashed lines show 30 and 35 keV. The thickness of lead needed to reduce the radiation to an acceptable level depends on the details of the spectrum of the radiation and the angular distribution of the radiation. But as a basis for an order of magnitude estimate, a thickness of 10 times this half-value thickness will be assumed or 0.02 cm. This thickness has been cited as “sufficient to provide virtually complete radiation absorption” in technical manuals on CRTs. For comparison, the thickness of CRT glass is about 0.25 cm in the neck, 0.5 cm in the funnel, and 1 cm in the screen (8). This thickness can simply be multiplied by the surface area of the CRT. As can be seen in Figure 3, the basic geometry of a CRT includes the front screen, a funnel-shaped part, and a cylindrical part at the back, called the neck, which contains the electron gun. The funnel is roughly conical, with a length about equal to the height of the screen. The screen is roughly rectangular, with a typical aspect ratio of 3 × 4 (7). CRT screen sizes are usually reported as the diagonal 2018

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(7)

where θ is the angle measured from the electron beam and Ω is the solid angle (11). (The electrons can be considered nonrelativistic because their energy is 30 keV, considerably smaller than the mass of the electron, which when expressed as mec2 is 511 keV.) Equation 7 indicates that the X-radiation would ideally be zero at the center of the front of the screen and would increase as sin2θ at wider angles from the front center. For the front screen, the maximum X-radiation would be at the edges. For the geometry of the CRT described above, sin2θ at the edge of the front screen is 0.2. Thus, the front screen could be shielded only 20% as much as the rest of the CRT and still provide comparable protection. It was estimated above that 0.02 cm of lead would be needed to screen the highest energy X-rays, so 20% screening would require 0.004 cm of lead. Applying this approximation to the 14- and 27in. CRT examples, the total lead requirements would be 420 and 1500 g, respectively. These estimates are very close to the reported values of 400 and 1400 g. Manufacturers report that the lead content of the front screen of CRTs is typically only about 2%. Some have no lead at all, although other elements in the screen provide some shielding. Given that the density of unleaded regular glass is about 2.5 g/cm3 (12) and that the thickness of glass in the screen is about 1 cm (8), the 2% lead in the screen is equivalent to about 0.004 cm of lead or less. This is consistent with the approximation above. This calculation was for a normally operating CRT. In fact, since 1970 the lead shielding in CRTs has been designed not merely to attenuate the X-rays produced by normal

operation of the CRT but also to attenuate any higher energy X-rays that might be produced under abnormal or failure mode operating conditions (13). CRTs are designed to protect against anode voltages of about 35 kV, not merely the 30 kV of normal operation. As shown in Figure 4, the photon absorption length of a 35-keV photon in lead is about 0.052 g/cm2, about 50% higher than for a 30-keV photon (9). These shielding designs date from the 1970s. Now, however, many CRTs have overvoltage protection to turn off the power to a failing power supply before the voltage reaches a potentially dangerous level (14, 15). If this overvoltage protection is reliable, there could be potential to somewhat reduce the use of lead in CRTs.

Discussion These calculations are based almost entirely on first principles and do not take into account detailed design, material, or engineering constraints. This type of calculation would not be useful for specialized product designers, who would already be familiar with vastly more detailed design options and constraints. Rather, these calculations are intended to assist the generalist, who may need to assess the environmental impact of a range of products. In current practice, environmental assessors begin with data on the material content of products. These product data are rarely validated, and the data are typically accepted at face value, without inquiry into why the data are what they are. The environmental impact of a product is affected not only by its material content but also by how the product is manufactured, used, and disposed or recycled (16). But the material content of products is nevertheless a key parameter in many product environmental assessments. The calculations shown here indicate that first principle calculations can provide estimates of the material content of product components. Beyond providing an independent check on data provided by manufacturers, this type of calculation could open new approaches to environmental assessment. By understanding the factors that constrain the material content of products, environmental assessors could explore the potential for change.

Acknowledgments The author thanks Neil Yocom for discussions of CRTs, Rob Nelson for discussions of X-ray physics, Joseph Spatola for discussions of electronics recycling, and two anonymous reviewers for detailed review of the manuscript. This work was supported by the Union County Utilities Authority, by

an AT&T Industrial Ecology Faculty Fellowship, and by the Multi-Lifecycle Engineering Research Center at the New Jersey Institute of Technology through the New Jersey Commission on Science and Technology.

Literature Cited (1) Socolof, M. L.; Overly J. G.; Kincaid, L. E.; Geibig J. R. Desktop Computer Displays: A Life-Cycle Assessment; University of Tennessee: Knoxville, TN, 2001; EPA-744-R-01-004a,b. (2) Electronic Product Recovery and Recycling Baseline Report: Recycling of Selected Electronic Products in the United States; National Safety Council, Environmental Health Center: Washington, DC, 1999. (3) Carcone, J. A. In Handbook of Batteries, 3rd ed.; Linden, D., Reddy, T. B., Eds.; McGraw-Hill: New York, 2002; Chapter 28. (4) Linden, D. In Handbook of Batteries, 3rd ed.; Linden, D., Reddy, T. B., Eds.; McGraw-Hill: New York, 2002; Chapter 1. (5) Hurd, D. J.; Muchnick, D. M.; Schedler, M. F.; Mele, T. Recycling of Consumer Dry Cell Batteries; Pollution Technology Review 213; Noyes Data Corp.: Park Ridge, NJ, 1993. (6) Linden, D. In Handbook of Batteries, 3rd ed.; Linden, D., Reddy, T. B., Eds.; McGraw-Hill: New York, 2002; Chapter 3. (7) Miller, G. H. Cathode-ray Tube. In McGraw-Hill Encyclopedia of Science and Technology, 8th ed.; Parker, S. P., Ed.; McGrawHill: New York, 1997. (8) Cakir, A.; Hart, D. J.; Stewart, T. F. M. Visual Display Terminals; Wiley: New York, 1980. (9) Hagiwara K.; Hikasa, K.; Nakamura, K.; Tanabashi, M.; AguilarBenitez, M.; Amsler, C.; Barnett, R. M.; Burchat, P. R.; Carone, C. D.; C. Caso, C.; et al. Phys. Rev. D. 2002, 66, 10001. (10) Behrendt, S. R.; Kreibich, S.; Lundie, R.; Pfitzner, M. Sharp. Ecobalance for Complex Electronic Products; Springer: Berlin, 1998 (in German). (11) Jackson, J. D. Classical Electrodynamics; John Wiley and Sons: New York, 1975. (12) CRC. Handbook of Chemistry and Physics, 52nd ed.; Chemical Rubber Co.: Cleveland, OH, 1971. (13) EIA (Electronic Industries Association). Considerations Used in Establishing the X-radiation Ratings of Monochrome and Color Direct-View Television Picture and Data Display Tubes; TEPAC Publication 194; Electronic Industries Association: Washington, DC, 1986. (14) IBM. Radiation Safety; 2001. http://www.pc.ibm.com/ww/ healthycomputing/vdt14.html (accessed February 2003). (15) Philips. Philips Semiconductors’ GreenChip Saves Power for Consumer Manufacturers; Press Release, November 13. http://www.semiconductors.philips.com/news/content/ file_639.html (accessed February 2003). (16) Socolow, R. H.; Thomas, V. M. J. Ind. Ecol. 1997, 1 (1), 13.

Received for review November 18, 2002. Revised manuscript received February 18, 2003. Accepted February 20, 2003. ES0210300

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