Impacts of a Silver-Coated Future

Particle Flow Analysis of Silver Nanoparticles

Authors


Rickard Arvidsson
Environmental Systems Analysis, Energy and Environment
Chalmers University of Technology
Rännvägen 6
412 96 Gothenburg
Sweden
rickard.arvidsson@chalmers.se
http://www.chalmers.se/ee/SV/personal/arvidsson-rickard

Summary

Silver is a compound that is well known for its adverse environmental effects. More recently, silver in the form of silver nanoparticles (Ag NPs) has begun to be produced in increasingly larger amounts for antibacterial purposes in, for instance, textiles, wound dressings, and cosmetics. Several authors have highlighted the potential environmental impact of these NPs. To contribute to a risk assessment of Ag NPs, we apply a suggested method named “particle flow analysis” to estimating current emissions from society to the environment. In addition, we set up explorative scenarios to account for potential technology diffusion of selected Ag NP applications. The results are uncertain and need to be refined, but they indicate that emissions from all applications included may increase significantly in the future. Ag NPs in textiles and electronic circuitry may increase more than in wound dressings due to the limited consumption of wound dressings. Due to the dissipative nature of Ag NPs in textiles, the results indicate that they may cause the highest emissions in the future, thus partly confirming the woes of both scientists and environmental organizations. Gaps in current knowledge are identified. In particular, the fate of Ag NPs during different waste-handling processes is outlined as an area that requires more research.

Introduction

Silver is one of the most toxic metals to aquatic organisms (Eisler 1996; Ratte 1999; Luoma 2008), and, recently, silver nanoparticles (Ag NPs) have begun to be produced in increasingly large amounts. Studies have outlined NPs (Colvin 2003; Baun et al. 2008; Ju-Nam and Lead 2008; Klaine et al. 2008)—and Ag NPs in particular (Luoma 2008; Blaser et al. 2008)—as a potential environmental risk. Nanosilver is by far the most frequently found nanomaterial (NM) in consumer products (Project on Emerging Nanotechnologies 2009) and is used mainly for its antibacterial properties (Luoma 2008). In addition, Ag NPs are used in electronic circuitry: They have the benefit of being easier to apply onto circuitry at low curing temperatures and with a lower resource demand, although NPs have the drawback of a lower conductivity, compared to bulk silver (Caglar et al. 2008; Kunnari et al. 2009). This application is often called “nanosilver ink.” Many of the products containing Ag NPs are currently limited in use, but the few estimates of Ag NM production and consumption show a similar pattern of market growth (figure 1). For instance, Ag NPs in wound dressings have gained significant market shares. The global consumption was estimated at $25 million in 2007, or 4% of the wound dressings market, with an annual growth rate of 31% since 2003 (McWilliams 2008). Together, this information implies that a “silver-coated future,” the suggestive term Henig (2007) introduced to denote a world in which many Ag NPs and other silver substances cover larger areas than today, may be a possible scenario. Note, however, that the term “NMs” includes NPs but also nanosized surfaces, films, and bulk materials (Hansen et al. 2007).

Figure 1.

Production of silver nanoparticles (Ag NPs) or silver nanomaterials (Ag NMs) according to some estimates (Pérez et al. 2005; McWilliams 2008; Silver Institute 2008). The annual silver production is about 20,000 metric tons (Brooks 2009).

As part of the effort to evaluate the risks of Ag NPs, the aim of this study is to estimate emissions of Ag NPs from society to the environment for some product groups. Emissions of Ag NPs has been estimated in previous studies (Boxall et al. 2007; Mueller and Nowack 2008; Gottschalk et al. 2009). In addition, Blaser and colleagues (2008) studied silver exposure due to emerging antimicrobial silver applications, but that study was not limited to NPs. All these studies have two major limitations in common, however. First, mass was used as indicator of magnitude rather than particle number, and particle properties were not included. The second limitation is that potential technology diffusion was not taken into account. Boxall and colleagues (2007) did include market diffusion by assuming a future market share of 100% of the included NPs, but they focused on Ag NPs as one substance rather than on specific technologies and hence gave limited guidance regarding on which products to focus further societal and scientific attention. To address these limitations, this study applies the suggested method of particle flow analysis (PFA) to estimate emissions of Ag NPs. In PFA, flows and stocks are described by particle number as metric instead of mass, which facilitates the inclusion of specific NP properties in the analysis. In addition, explorative scenarios are used to account for potential technology diffusion. In a way, this explorative scenario accounts for the possible occurrence of a “silver-coated future.” Besides estimating current and future potential emissions of Ag NPs, this methodology highlights gaps in the current knowledge of Ag NPs to guide future monitoring and measurement activities. The selected technologies, or product groups, included in this study are wound dressings, textiles, and nanosilver ink in electronic circuitry. The textile materials included are cotton and polyester, which are common textiles to be coated with Ag NPs (Geranio et al. 2009).

Methods

Particle Flow Analysis

In PFA, particle number is applied as flow and stock metric rather than mass. Mass has been used to indicate magnitude of flows and stocks of chemical substances in substance flow analysis (Van der Voet 2002) as well as exposure and effect of chemicals in environmental and chemical risk assessments (Suter et al. 1993; Van Leeuwen and Vermeire 2007). There are strong indications, however, that mass may not be a relevant indicator of flow and stock magnitude, exposure, or toxic effects for the case of NPs (Oberdörster et al. 2005; Handy et al. 2008; Ju-Nam and Lead 2008; Van Hoecke et al. 2008; Arvidsson et al. 2011). When particle number is applied instead of mass as the flow and stock metric, relevant particle properties, such as size, can be accounted for. In addition, frameworks describing different types and properties of NPs, such as those by Hansen and colleagues (2007) and Jiang and colleagues (2009), can be utilized in the analysis. The framework for characterization of NPs by Hansen and colleagues (2007) includes particles that are surface bound, suspended in liquid, suspended in solids, or airborne. The categorization framework of NPs by Jiang and colleagues (2009) divides particles into primary particles, agglomerates (primary particles held together by weak, Van der Waals forces), and aggregates (primary particles held together by strong, covalent bonds). Processes that change particle number, such as agglomeration, melting of particles, dissociation of particles into ions, and grinding (which produces more particles), can be included by the addition of a source (or sink) factor to a substance flow model (see figure 2). Thus, the convenient law of mass conservation on which substance flow analysis is based is not sufficient to describe flows and stocks of particle numbers. Instead of the law of mass conservation, a similar equation can describe the particle flows and stocks of a compartment, with the source or sink term included:

image(1)

where N denotes the particle number (particles) stock and n the particle number flow (particles per year). Note that the source or sink term (nS) can be either positive or negative. Due to lack of data, only the NP use phase (the same as the substance use phase in a substance life cycle) and related flows and stocks have been investigated in this study. The production phase relates to working environment, and NP emissions in that phase may be more dependent on companies’ management practices than on NP properties. The waste-handling process is not included due to poor knowledge of the fate of Ag NPs during that phase. The parameters estimated in this study are thus the use phase in-flow (nu), the use phase stock (Nu), and the use phase emissions (neu), as shown in figure 2. These parameters are estimated for all three Ag NP applications included. Data on Ag NP production is often reported on a mass basis, however. For the technologies selected in this article, no well-defined particle size distributions of Ag NPs have been found. Hence, the average particle diameter is used as proxy for particle size, and the following equation is used to convert mass to particle number:

image(2)

where m is the mass flow; ρ is the density in kilograms per cubic meter (kg/m3), which is 10,500 kg/m3 for Ag NPs; and d is the average particle diameter in meters (m). Note, however, that although spherical silver NPs are used in the applications included in this article (see below), other shapes are possible (Pal et al. 2007). If nonspherical NPs were present, equation (2) would need to be modified.

Figure 2.

Particle flow analysis model applied in this study to quantify the flows and stocks of silver nanoparticles (Ag NPs) and the emissions of Ag NPs to the environment. N= particle number stock; n= particle number flow; p= production; u= use phase; w= waste handling; e= emission; r= recycling; s= source. Note that ns may be negative, indicating a sink for particles (e.g., agglomeration) rather than a source (e.g., grinding).

Estimating Nanoparticle Emissions

Some applications included in this article are dissipative or nonrecyclable, which means that the emissions of NPs are much larger than the number of particles proceeding to waste handling, and no stock is formed—that is, neunw and Nu≈ 0. For those cases, neunu. Typically, dissipative use applies for particles suspended in a liquid or airborne particles (see Hansen and colleagues 2007). For nondissipative use of applications consisting of NPs suspended in a solid or on a surface (see Hansen et al. 2007), emissions can be estimated for the general case according to the following:

image(3)

where Au is the surface area of the use phase product stock (in square meters [m2]), cQ is the Ag NP concentration in the product stock, and k is an emission factor. “Product” refers to a wound dressing, textile, or electronic device in this article. The categorization framework of Hansen and colleagues (2007) becomes useful here, because, depending on whether the product contains NPs suspended in a solid or bound to a surface, the units of c and k vary. For NPs suspended in a solid, cQ represents the particle concentration in the solid (in particles per cubic meter), and k is measured in meters per second (m/s). For particles bound to a surface, cQ is a surface concentration (in particles per square meter), and k is measured in (1/s). Often, as in the case of silver nanoparticle (Ag NP) production, concentrations of Ag NPs are given on a mass basis and must be recalculated. By assuming spherical particles, one can then estimate the particle concentration using

image(4)

where x is the mass concentration. No data on stocks of electronic circuitry have been found, and thus it has been estimated with an approximate equation that assumes that the emissions neunu:

image(5)

where τ is the lifetime of electronic circuitry. The typology of Jiang and colleagues (2009) also becomes useful here, because sintered NPs that are held together by hard bonds should have a lower affinity to being emitted. This gives a lower emission factor (k), which strengthens the assumption that the emissions are significantly lower than the in-flow to use phase for Ag NPs in electronic circuitry.

Explorative Scenario

Modeling technological diffusion is difficult. Indeed, nobody knows to what extent products containing Ag NP will be used in the future. To avoid making dubious forecasts, we apply an explorative scenario here to assess the potential of the included applications. The term “explorative scenario” denotes a possible scenario that answers the question of what could happen given a certain development (Börjeson et al. 2006). We make no claims regarding how likely the scenario is, however. An example of explorative scenarios is the emissions scenarios applied by the Intergovernmental Panel on Climate Change (Börjeson et al. 2006). The explorative scenario applied here aims at estimating the potential emissions from the included Ag NP applications and thus involves the following assumptions: (1) The Ag NP application will reach 100% market share within the product group in question; (2) the per capita in-flow to use phase and stock of the product group will be equal to those found in today's high-income regions, such as the United States or Europe; and (3) the world population will increase to 10 billion people, as forecasted by the United Nations (2008) for 2050 (medium to high growth rate variants). Hence, this scenario constitutes a worst-case scenario or an extreme value scenario with regard to potential Ag NP emission. Although the scenario is exaggerated, it provides information about whether Ag NP emissions could become a concern in the future, and such simplified extreme value scenarios are often valuable when one is dealing with complex environmental questions (Harte 1988). This scenario has been given the index 1, whereas the scenario that represents the current situation has been given the index 0. Note that the current situation approximately refers to 2008. The use phase in-flow and stock of Ag NPs for the explorative scenario have been estimated as

image(6)
image(7)

where P stands for population in the explorative scenario (i.e., 10 billion); qi/Pi and Qi/Pi stand for the current per capita product flow and stock of product in developed countries, respectively; and cq is the concentration of Ag NPs in the product flow. The reader may note the similarity between these equations and the well-known IPAT equation, which is described, for instance, by Chertow (2000). Again, the units of cq, cQ, qi/Pi, and Qi/Pi change depending on application.

Model Input Data

The input data for the analysis can be found in table 1. The current mass-based in-flow of Ag NPs (mu,0) in wound dressings was found in the work from McWilliams (2008), and information about their particle size (d) was drawn from the work of Gibbins (2005; see table 1). According to interviews with practitioners at Swedish hospitals, both wound dressings that contain silver and those that do not are changed regularly, from several times per day up to one time per week. There is thus no significant stock of wound dressings formed in the use phase. Some Ag NPs, however, are emitted during the use phase—that is, when the dressing is taped onto the wound—and some are still in the dressing when it is thrown away. No data on emission factor (k) for Ag NPs in wound dressing have been found, but Gibbins (2005) showed that the release of Ag NPs in SilvaGard is at a rate of about 10% of the initial loading in 10 days, given an original concentration of 0.8 micrograms per square centimeter (μg/cm2). Because most dressings are changed within 10 days, the release of 10% of the particles is considered a worst case and applied in this study—that is, neu≈ 0.1 ×nu. Although 10% is probably weight percent, the Ag NPs in wound dressings are quite monodisperse, with a size range of only 2–7 nanometers (nm; Gibbins 2005), which makes 10% fair to use also for particle concentrations. The Ag NP concentration (cq) can range from 1 to 32 μg/cm2 for the product SilvaGard (Gibbins 2005) and from 0.84 to 1.34 mg/cm2 for the product Acticoat (McWilliams 2008). This variation in mass concentration could be due to the use of smaller particles in SilvaGard, but this has not been possible to confirm. Considering this variation, a range of 1 milligram per square centimeter (mg/cm2) to 1 μg/cm2 has been applied for the parameter cq. The per capita in-flow to use phase of wound dressings (qi/Pi) in the United States was calculated from data provided by McWilliams (2008).

Table 1.  Input data to equations (2) through (6)
Input parameterSymbol and unitWound dressingsTextilesElectronic circuitry
  1. Note: nm = nanometer; kg/yr = kilograms per year; μg/cm2= micrograms per square centimeter; mg/kg = milligrams per kilogram; m = meter; Insign. = insignificant; n.a. = not available. For references, see the Model Input Data section.

Particle diameterd (nm)10105
Current mass productionmu (kg/yr)254<4,700<4,700
Mass concentration in flowxq0.001 to 1 (μg/cm2)1 to 10,000 (mg/kg)1 (mg/kg)
Mass concentration in stockxQ----1 (mg/kg)
Emission factork (particles/m2/year)----n.a.
Stock surface areaAu (m)----n.a.
Explorative scenario usageqi/Pi7 cm2/capita/year32 kg/capita/year12 (kg/capita)
Lifetimeτ (years)Insign.Insign.10

No data on current in-flow to use phase of Ag NPs in textiles (mu,0) have been found, but the Silver Institute (2008) states that the total amount of Ag NPs consumed is 4,700 kilograms (kg), which indicates that the number should be smaller than that. According to the company Uvex, their cloths contain particles with a diameter of less than 20 nm (d), and, thus, 10 nm has been assumed a fair approximation for Ag NPs in textiles. This is supported by the fact that the smallest size of Ag NPs emitted from textiles measured by Benn and Westerhoff (2008) was 10 nm. Measurements on Ag NP release from textiles indicate that it is reasonable to assume that most particles will be emitted within a few washes (Benn and Westerhoff 2008; Geranio et al. 2009), and thus the use of Ag NPs in textiles is regarded as dissipative. The per capita in-flow to the use phase of cotton and polyester fiber in the United States was obtained from the work of Meyer and colleagues (2008) and Aizenshtein (2006), respectively, and added to obtain Qi/Pi for textiles. There is a great variation in the Ag NP concentration in textiles (cq), which is not surprising from a technological change point of view: The early phase of the technological life cycle is characterized by varying, competing designs (Grübler 1998). In a similar manner, there was a great diversity in filament material (bamboo, osmium, tantalum, and, eventually, tungsten) in the formative phase of the incandescent light bulb (Smil 2005). Results from the concentration measurements of the seven products containing Ag NPs included in the work of Benn and Westerhoff (2008) and the six products containing Ag NPs in the work of Geranio and colleagues (2009) are reproduced in figure 3. To include this large variation in Ag NP concentration, we have applied a range of 1 to 10,000 micrograms per gram (μg/g).

Figure 3.

Results from measurements of silver nanoparticle (Ag NP) concentrations in antimicrobial textiles in two studies. Also shown is the range applied in this study.

Similar to Ag NPs in textiles, no data on the current in-flow to use phase of Ag NPs in electronic circuitry (mu,0) have been found, but it should be smaller than 4,700 kg, which was the total consumption of Ag NPs estimated by the Silver Institute (2008). The size of the Ag NPs (d) in silver ink is obtained from the paper by Caglar and colleagues (2008). The average content of silver in circuit boards (cq and cQ) is obtained from the article by Lanzano and colleagues (2006). Experts report, however, that for applications that do not require high current-carrying capability, nanosilver ink uses 50% to 75% less silver than conventional bulk silver applications (Jablonski 2010). Thus, the silver concentration has been reduced by half for the case of Ag NPs. The European per capita in-flow to the use phase of electronic circuitry was obtained from Lanzano and colleagues’ (2006) article. In both scenarios, we assume a lifetime of 10 years to estimate the stock of Ag NPs in electrical circuits. We could not confirm this lifetime with references, but it is probably within the right order of magnitude. No information regarding surface areas of electronic circuits (Au) or emissions of Ag NPs from such areas (k) has been found. The only thing known for sure is that the emissions of Ag NPs from electronic circuits must be lower than the in-flow to the use phase, probably substantially lower because the Ag NPs are sintered.

Results and Discussion

According to table 2, currently the highest in-flow to use phase of Ag NPs may occur from their use in electronic circuitry. This result is primarily due to the smaller particle size of the Ag NPs in electronic circuitry compared to those in wound dressings and textiles. The data regarding current in-flow to use phase of Ag NPs in textiles and electronic circuitry constitute upper limits rather than exact numbers, however. It is clear that more detailed monitoring of these in-flows to use phase rates is needed to accurately assess the emissions of Ag NPs from these applications. Regarding the current use phase emissions, the results indicate that the largest use phase emissions of Ag NPs originate from textiles. In fact, this pattern remains in the explorative scenario, where the lower boundary of the Ag NP emission from textiles was four orders of magnitude higher than the highest upper boundary of Ag NPs in wound dressings. This is due to the much higher in-flow to use phase of textiles compared to wound dressings. It is, of course, much more common to wear clothes than wound dressings, and clothes normally cover a significantly larger part of the body than wound dressings for most people, even in the summertime. The results presented in table 2 thus indicate that the articulated concern regarding Ag NPs in textiles should be taken seriously, as suggested by other authors, including Henig (2007) and Blaser and colleagues (2008). It is, of course, possible that Ag NPs in textiles remain a niche product only applied in underwear and sports clothing, but the numbers in table 2 show that it has the potential to become a large emitter of nanosilver. It should be noted that the estimations of Ag NP emissions from textiles are very uncertain due to high variation in nanosilver content in experimental studies (Benn and Westerhoff 2008; Geranio et al. 2009). Also, different nanosilver textile designs may emit more or less nanosilver (Geranio et al. 2009). Geranio and colleagues (2009) note that there is a variation in the incorporation of Ag NPs that correlates with the way the silver was attached to the textile and the amount of silver emitted. For instance, when the silver was incorporated into the textile fiber matrix, the emissions were slower than when the silver was merely bound to the fiber surface. Because the sample was so small and the correlation not described numerically, however, no such considerations have been made in this study. Efforts should be put into clarifying that relationship and into further trying to establish an average concentration of Ag NPs in textiles. If one of the designs with lower emissions becomes dominant, the emissions may be significantly lower. According to table 2, Ag NPs in wound dressings will probably never be of major environmental importance due to the limited use of wound dressings. As always, however, effects could arise from locally high emissions.

Table 2.  Current in-flow to use phase, use phase stocks, and use phase emissions for the silver nanoparticle (Ag NP) applications of wound dressings, textiles, and nanosilver ink in electronic circuitry, along with the same parameters estimated for an explorative scenario
Output parameterSymbol and unitWound dressingsTextilesElectronic circuitry
  1. Note: Insign. = insignificant.

Current productionnu,0 (particles/year)4.6 × 1022<8.5 × 1023<6.8 × 1024
Current stockNu,0 (particles)Insign.Insign.<6.8 × 1025
Current emissionsneu,0 (particles/year)4.6 × 1021<8.5 × 1023<6.8 × 1024
Explorative scenario productionnu,1 (particles/year)(1 × 1022, 1 × 1025)(6 × 1028, 6 × 1032)9 × 1027
Explorative scenario stockNu,1 (particles)Insign.Insign.9 × 1028
Explorative scenario emissionsneu,1 (particles/year)(1 × 1021, 1 × 1024)(6 × 1028, 6 × 1032)<9 × 1027

Regarding electronics, an increase in Ag NPs in electronic circuitry would result in a decreased use of bulk silver for that purpose. As stated above, if bulk silver is used instead of nanosilver ink in electronic circuitry, the amount of silver per product may be twice as high or more. This implies that switching to Ag NPs in electronic circuitry may reduce the total use of silver. Nevertheless, the results in table 2 show that the use of Ag NPs in electronics may still be as large as in textiles and larger than in wound dressings. The emissions of Ag NPs from electronic circuitry were found to be a formidable challenge to estimate, because the effective surface area (Au) may vary depending on the specific application. In addition, the Ag NPs in electronic circuitry are sintered, and, to our knowledge, no measurements of NP emissions from sintered particles have ever been made. The fact that sintered particles are tightly attached by covalent bonds indicates that emissions may be low, but this needs to be confirmed by experimental studies. The Ag NPs in electronic circuitry may also be encapsulated in other materials, which initially may decrease emissions.

Apart from the importance of Ag NP emissions from textiles, this study points at the importance of the waste-handling phase. According to one study, only 10% of the Ag NPs attached to an antibacterial wound dressing are emitted during use (Gibbins 2005). Practitioners at Swedish hospitals report that silver-containing wound dressings are discarded in the everyday garbage, and the nanosilver still attached to the wound dressing is thus likely to end up in an incineration plant. This is probably the fate of most consumer-purchased textiles with Ag NPs as well. No studies of the fate of Ag NPs during such processes have, to our knowledge, been performed. An incineration plant normally reaches temperatures of above 800°C, which is much higher than the temperature used for sintering of Ag NPs (Caglar et al. 2008; Kunnari et al. 2009). The Ag NPs may thus undergo a transformation from one configuration state to another according to the typology suggested by Jiang and colleagues (2009). The fate of Ag NPs from electronic circuitry in the waste-handling phase is also unknown, although the waste handling of electronic circuitry has already been acknowledged as a significant environmental problem due to the electronic devices’ content of various toxic metals (see, e.g., Robinson 2009). Ag NPs in electronic circuitry may add to this problem in the future, although at the same time reduce it due to the lower silver content compared to conventional circuitry.

According to Morley and Eatherley (2008), silver is an element that deserves attention due to potential resource scarcity. The total mining of silver metal in 2009 was approximately 21,000 metric tons1 (Brooks 2009), and the known silver reserve base was estimated at about 570,000 metric tons in 2009 (Brooks 2009). If the particle number in-flow to use phase in the explorative scenario in table 2 were recalculated into mass flows, it would exceed the current total mining of silver by several orders of magnitude. Although this shows that the explorative scenario is unrealistic, it also illustrates that the Ag NP applications studied here have the potential to further contribute to the scarcity of silver, in particular when one considers the dissipative way silver is used in textiles. Finally, the significant difference between particle flows and stocks in the current state and in the envisioned future state highlights the importance of applying explorative scenarios or other methods to account for technology diffusion.

Conclusions

The results indicate that current knowledge of Ag NP emissions is very uncertain. Wound dressings will probably remain a small source. The future stock of electronic circuits may contain many Ag NPs, but the emissions of these in the use phase are unknown. The waste-handling phase was not included in the study, but the estimated low emissions of Ag NPs from wound dressings and the presumed low emissions of Ag NPs from electronic circuits suggest that the fate of Ag NPs in the waste-handling phase is an interesting object of study. The main conclusion from this study, however, is that textiles may become a large source of Ag NP emissions in the future. The use of antimicrobial nanosilver for wound dressings may be appropriate, given the efficiency of silver against a wide range of bacteria and because it is not particularly toxic to humans (Gibbins and Warner 2005; Brett 2006), although it is debated whether silver actually improves wound healing (Vermeulen et al. 2009). But the use of Ag NPs in consumer products, such as socks and other textiles, to reduce odor and/or kill bacteria has been suggested to be less beneficial, especially considering the environmental risks (Henig 2007). This article adds to the hypothesis that Ag NPs may pose an environmental risk, which has been suggested by several authors (Luoma 2008; Blaser et al. 2008). The potentially large use of Ag NPs in textiles also threatens the perhaps more beneficial use of nanosilver in wound dressings, because there is then a risk of inducing silver resistance to bacteria (Silver et al. 2006).

Acknowledgements

The financial support from the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas) and from the Swedish Foundation for Strategic Environmental Research (MISTRA) is gratefully acknowledged.

Note

  • 1

    One metric ton = 103 kilograms (kg, SI) ≈ 1.1 short tons.

About the Authors

Rickard Arvidsson is Ph.D. candidate in the Division of Environmental Systems Analysis of Chalmers University of Technology in Gothenburg, Sweden. Sverker Molander and Björn A. Sandén are professors in the Division of Environmental Systems Analysis at Chalmers University of Technology.

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