Occurrence of Single- and Double-Peaked Emission Profiles of

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On the Occurrence of Single- and DoublePeaked Emission Profiles of Synthetic Chemicals Li Li, and Frank Wania Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b06478 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 27, 2018

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Environmental Science & Technology

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On the Occurrence of Single- and Double-Peaked Emission Profiles of Synthetic

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Chemicals

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Li Li,* Frank Wania

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Department of Physical and Environmental Sciences, University of Toronto Scarborough, 1265 Military

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Trail, Toronto, Ontario, Canada M1C 1A4

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* Corresponding Author: Li L.; E-mail: [email protected]. Phone: +1 (416) 287-5659. Fax:

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+1 (416) 287-7279.

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ORCID:

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Li Li: 0000-0002-5157-7366

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Frank Wania: 0000-0003-3836-0901

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TOC Art

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ACS Paragon Plus Environment


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Abstract

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This work aims to elucidate the circumstances that can lead to two peaks in the temporal emission

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profile of synthetic chemicals. Using a simplified substance flow model, we explore how emission

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factors, product lifespan and degradation half-life in waste stock influence the (i) relative importance of

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emissions from three lifecycle stages (industrial processes, use phase and waste disposal), and (ii) the

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resulting composite emission profile. A double-peaked emission profile occurs if the lifespan of

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products containing the chemical is longer than half of its production period, and the gross emission

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factor from waste disposal exceeds that from the use phase. Since most chemicals fail to meet these two

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conditions, it is reasonable to use single-peaked emission profile as the default in environmental studies.

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Based on their emission profiles and contributions from individual lifecycle stages, we can categorize

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chemicals into “simple single-peakers”, “composite single-peakers” and “double-peakers”. Our

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simplified model derived emission profile for five real chemicals that agree well with earlier, more

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sophisticated calculations, indicating the model’s ability to capture the essential features of actual

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emissions. It is hoped that the model and conclusions in this work will benefit both environmental

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modelers and decision makers.

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Introduction

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Synthetic chemicals may results in adverse impacts on ecosystems and human health once they migrate

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into the environment from industrial processes, use, waste disposal and other lifecycle stages.1 Notorious

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examples include persistent organic pollutants (POPs)2 with high resistance to degradation in the

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environment, and contaminants with continuous occurrence in the environment due to ongoing intensive

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emissions, e.g., pharmaceuticals and personal care products (PPCPs).3 Knowledge about the time course

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(in particular the inter-annual trend) of their emissions, i.e., the emission profile, is essential both for

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evaluating the long-term fate of chemicals in the environment and for formulating effective risk

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reduction policies. Numerous emission estimation studies have identified single peaked (bell-shaped)

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emission profiles, whereby an initial rise is followed by a decline, for a wide range of chemicals

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including polychlorinated biphenyls (PCBs),4-6 polybrominated diphenyl ethers (PBDEs),7,

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dichlorodiphenyltrichloroethane (DDT),9 hexachlorohexanes (HCHs),10, 11 and per- and polyfluoroalkyl

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substances (PFASs).12, 13 The rise reflects increasing production and use of a substance, and the decline

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occurs when, in some cases, concerns about the detrimental effects of that use become manifest and

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elicit a change in behavior, or in other cases, better and cheaper alternatives become available.

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Accordingly, modeling studies often assume that emission profiles have the shape of logistic14-19 or

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Gaussian distributions,20, 21 especially if temporally explicit emission information is not available.

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Can we be sure that there are no situations that give rise to increasing emissions after an initial peak in

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emissions has passed? One mechanism leading to such a double-peaked emission profile occurs if a

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fraction of chemical accumulates temporarily in natural and anthropogenic reservoirs, from which the

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chemical can be mobilized when external conditions change. For example, Bogdal et al.22 have

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demonstrated that rapid glacial melt driven by a warming climate can result in a second peak of high

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water contamination in alpine lakes, caused by the release of pollutants deposited to glaciers during the

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first peak of high emissions. Such temporary natural reservoirs, e.g., glacier, soil and sediment, are often

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referred to as “secondary sources”, distinguishing them from “primary” emissions arising from

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anthropogenic activities.23 In addition, temporary anthropogenic reservoirs, e.g., products in service (in-


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use stock) and waste (waste stock),24 can also buffer and re-mobilize chemicals, causing a second

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emission peak. An example is the use of hexabromocyclododecane (HBCDD) in thermal insulation for

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buildings in mainland China,19 where an emission peak associated with the manufacture of insulating

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styrene boards is temporally separated from an emission peak hypothesized to occur when those

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products reach the end of their service life and need to be disposed decades later. To date, intensive

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efforts have been devoted into addressing secondary emissions of synthetic chemicals, in particular very

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persistent and multimedia ones, from reversible natural reservoirs;20, 21, 23, 25 however, systematic and

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mechanistic investigations into the emissions from temporary anthropogenic stocks are still limited.

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Chemicals behave differently with respect to the storage in, and releases from, anthropogenic stocks,

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because they vary in their properties and the way that they are used. For instance, emission factors,

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which describe the capability of a chemical to enter the environment from various anthropogenic stocks,

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vary among PCB congeners by up to four orders of magnitude as a result of different volatilities and

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applications.4 In another example, in contrast to pesticides (e.g., DDT9 and HCHs10, 11), whose emissions

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rise and fall almost in concert with their production, emissions of a number of industrial and consumer

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chemicals (e.g., PCBs4-6, 26 and PBDE8) can often be expected to continue for decades or even centuries

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beyond the cessation of production, because of the presence of these compounds in long-lived durable

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goods and waste. In a notable example, the continued presence of joint sealant materials in old buildings

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contributes to the observed high PCB contamination of indoor and urban environments four decades

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after the ban.27,

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associated products is essential if we want to gain a mechanistic understanding of the bewildering

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variability in emission profiles of different chemicals.

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This work aims to address two research questions: (i) What are the conditions that give rise to single- or

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double-peaked emission profiles? (ii) How, and to what extent, do the properties of a chemical and its

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associated products influence these emission profiles? In the following, batch numerical calculations

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with a simplified substance flow model are first performed to explore the influence that emission factors

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and time scales of residence in anthropogenic stocks have on (i) the contribution of emissions from

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Thus, linking the emission behavior with the properties of a chemical and its


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individual lifecycle stages to the overall emission (referred to as source composition hereafter), and (ii)

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the emission profile. Next, based on the emission profile and source composition, we categorize the

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emissions of synthetic chemicals into three classes and illustrate the actual emission profile for

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representatives of each class. The modeled emission profiles of five actual chemicals are compared with

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estimates from previous studies to evaluate the performance of our modeling approach. The simplified

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modeling approach provided in this work can be a reliable and powerful tool for understanding and

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screening the emission profile for a wide range of emerging synthetic chemicals; conclusions here can

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also aid in future environmental fate modeling and decision-making.

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Methods

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Model equations

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In the real world, the life phases of a chemical and its associated products vary substantially among

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chemicals, products and regions, and with time. Therefore, a generic model suitable for screening needs

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to simplify (“streamline”) the intricate lifecycle stages and processes, i.e., keep relevant ones but treat

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them in less detail.29 To remain compatible with earlier emission estimation practice,29,

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lifecycle of an investigated chemical is assumed to comprise three stages:

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(i) Industrial processes, comprising all realistic industrial activities such as production, formulation,

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processing, industrial/professional use, and product installation. Emissions from industrial processes,

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denoted as Eind(t) in [MT-1], are estimated as the product of the amount of chemical (including

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production, import and/or reused/recycled volume) subject to industrial processes, i.e., P(t) in [MT-1],

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and a dimensionless overall industrial emission factor, i.e., EFind (0 ≤ EFind ≤ 1), which lumps together

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emission rates from multiple industrial activities;

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(ii) Use phase, which is characterized as an in-use stock representing all in-service industrial and

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consumer products in various applications (also referred to as function or use categories). A chemical

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maintains its designed functions during the entire use phase. Emission from in-use stock, denoted as

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Euse(t) in [MT-1], are estimated as the product of the size of in-use stock, i.e., U(t) in [M], and an


30

here the


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aggregate use-related emission factor, i.e., EFuse in [T-1], which characterizes the average emission

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strength associated with multiple realistic applications over a long period;

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(iii) Waste management, i.e., a waste stock generalizing all waste disposal activities such as landfills,

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dumps and recovery. Emissions from the waste phase, denoted as Ewaste(t) in [MT-1], are estimated as the

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product of the size of a waste stock, i.e., W(t) in [M], and an aggregate waste-related emission factor, i.e.,

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EFwaste in [T-1], which is related to the average emission strength from multiple waste stocks over a long

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period.

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Therefore, the overall emission of a chemical is calculated according to Eq.1:

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E (t ) = Eind (t ) + Euse (t ) + Ewaste (t ) = EFind ⋅ P(t ) + EFuse ⋅U (t ) + EFwaste ⋅W (t )

(1)

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Emissions of a chemical can occur at any of the three stages, or all. For instance, chemicals used as

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processing aids and intermediates are emitted primarily in industrial processes. The bulk of “down-the-

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drain” chemicals (e.g., detergent ingredients) is discharged during consumer use.31 Excess pesticide

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residuals remaining in soil or vegetation after application can be “emitted” into the wider environment,10,

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11

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as a special variant of waste stocks, because the “lifespan” of a pesticide is assumed to end once pests

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are controlled.

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Our objective is to deduce the temporal trend of E(t) (i.e., emission profile), and the relative contribution

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of Eind(t), Euse(t) and Ewaste(t) (i.e., source composition). Mathematically, an emission profile is deemed

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“single-shaped” if E(t) has a single stationary point and is concave down. The calculation is performed

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on an annual basis, as our interest is in the long-term inter-annual trend in overall emissions; we do not

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discuss the seasonal or episodic fluctuations in overall emissions.

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Following ref.32, we calculate the change in the in-use stock dU(t)/dt by subtracting the discard and

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emissions flows from in-use stock from the annual production P(t):

e.g. by vaporization into air or run-off to aquatic systems. We therefore view such pesticide residuals


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d U (t ) = P (t ) ⋅ (1 − EFind ) − D (t ) − U (t ) ⋅ EFuse dt

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whereby the discard flow, D(t) in [MT-1], is calculated as a convolution of the annual production, P(t),

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and a lifespan distribution function, f(t), which determines the fraction of a chemical (equivalent to that

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of associated products) entering waste stock at the use age of t years:33

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D (t ) = ∫ P (τ ) ⋅ (1 − EFind ) ⋅ f (t − τ )dτ , in which

t

0

(2)

∫

∞

0

f (t )dt = 1 .

(3)

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The chemical is assumed not to degrade in in-use stock, because chemicals are intentionally designed to

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remain stable over the product lifespan, i.e., before the associated products expire or are discarded.

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Similarly, we calculate the change in waste stocks dW(t)/dt by subtracting the degradation and emissions

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flows from waste stocks from the discard flow into waste stock:

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dW (t ) = Fwaste ⋅ D (t ) − W (t ) ⋅ EFwaste − k ⋅ W (t ) dt

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where Fwaste denotes the fraction of waste entering waste stock, instead of being subjected to

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environmentally sound management (e.g., complete destruction or irreversible transformation) that

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results in no or negligible release into the environment. k is a pseudo-first-order rate constant describing

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degradation loss from the waste stock in [T-1], which corresponds to a degradation half-life HL in [T]:

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k = ln2 / HL

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Equations 1 – 5 describe our conceptual model. In the real world, a chemical is often used in multiple

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applications, formulated with different co-formulants, and embedded in different product materials,

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which means input parameters to the model, e.g., product lifespan, degradation half-life and emission

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factors, may vary widely. Fortunately, the model is linear and additive. As a result, it is always

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mathematically feasible to use one set of input parameters to a single simulation of emissions to

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represent the sum of emissions from a variety of industrial processes, in-use stocks, and waste stocks.

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Generic calculations for hypothetical chemicals

(4)

(5)



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The equations above involve two groups of input parameters: (i) the time scales of a chemical’s

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residence in stocks, including the product lifespan (LS) in in-use stock and the degradation half-life

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(HL) in waste stock; and (ii) the gross emission factors from industrial processes, use and waste disposal.

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In order to explore the extent to which the emission profile of a chemical is determined by these two

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groups of parameters, we simulate the emission profile for a series of hypothetical chemicals with

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different combinations of:

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1.

HLs of 0.1, 1, 10 and 100 years, respectively,

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2.

LSs of 10, 25, 50 and 100 years, respectively, and

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3.

Logarithmic ratios of EFwaste/EFind (in year-1) and EFuse/EFind (in year-1) ranging from -6 to 1.

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For simplification, we assume that the “generic” temporal trend of production follows a Gaussian

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distribution, which starts in the first year of simulation and peaks in the 40th year, with 95% of

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cumulative production occurring within a window of 25 years (designated as the “half-duration” of the

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production history thereafter) before and after the peak year. Such a half-duration is believed to be

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typical for many synthetic chemicals and has thus been adopted in earlier modeling studies.20, 21 Since

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we focus on the emission profile instead of absolute emissions, the cumulative chemical production over

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the simulation period is arbitrary, e.g., a unit. In addition, we assume that the product lifespan follows a

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Gaussian distribution, with a standard deviation 0.3 times its mean. At the end of a product’s life, a

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chemical is assumed to be completely subject to waste disposal (Fwaste = 100%).

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Realistic calculations for actual chemicals

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We further simulate realistic emission profiles of five specific chemicals: perfluorooctanoic acid and its

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salts (PFOA) in developed regions (defined as Japan, Western Europe and the United Sates), β-HCH on

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the global scale, two PCB congeners (volatile PCB-28 and less volatile PCB-180) on the global scale,

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and technical HBCDD in mainland China. For each actual chemical, we gathered realistic HL, LS,

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emission factors and Fwaste data from the literature (Table S1). The temporal trend of production, i.e.,


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P(t), was “smoothed out” as a Gaussian distributed function with parameters estimated by fitting

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literature-reported annual production data.5, 12, 34, 35 Note that such a normalization does not mean that

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our model is only applicable to Gaussian distributed production data. The confidence of the fit between

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actual and smoothed production data is expressed using the coefficient of determination (R2). To

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evaluate the modeling performance, the modeled emission profiles are compared with literature

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estimates.6, 11, 12, 35

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Results and discussion

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Theoretical analysis of the emission profile

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We first illustrate how emissions from individual stages of a chemical’s lifecycle, namely Eind, Euse and

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Ewaste, constitute the overall emission and how their relative importance affects the shape of an emission

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profile. Because expressing our model in analytical form makes the relationship between variables

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explicit and intuitive (i.e., “tractable” in mathematics), we discuss here a simplified case for which

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analytical solutions can be obtained (Text 1 in the Supporting Information). This case assumes (i) the

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annual production trend is single peaked, which is the case for most problematic chemicals (see a review

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in ref.21); (ii) the change in in-use and waste stocks due to emission is negligible; and (iii) 100% of the

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generated waste enters waste stocks (i.e., no chemical-specific environmentally sound management).

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Note that this case is merely illustrative and the model itself is not limited in its applicability to

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chemicals for which these assumptions are valid.

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We first discuss the simplest case that the overall emission is entirely composed of, or overwhelmingly

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dominated by, one of the three life stages. Theorem 1 in the SI proves that, if the temporal trend of

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production, P(t), possesses a single peak, the temporal trend of in-use stock, U(t), is single peaked as

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well. Thus, when assuming a constant EFuse, we can anticipate that use phase emissions, Euse(t), exhibit a

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single peak. Similarly, as proved by Theorem 2 in the SI, the temporal trend of waste stock, W(t), is also

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single peaked if the degradation half-life is not infinite (otherwise the waste stock will eventually level

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off after the in-use stock is depleted). Again, when assuming a constant Ewaste, we can expect waste stock



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emissions, Ewaste(t), to be single peaked. Therefore, in a word, the emission profile will have a single

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peak, if either Eind, Euse or Ewaste dominates the overall emission.

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Furthermore, if two or more chemical life stages contribute notably to overall emissions, it depends on

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which stages combine that decides whether the emission profile is single or double peaked (Figure 1).

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Theorem 3 in SI demonstrates that the sub-total of Eind and Euse (i.e., Eind/use) is always single peaked

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irrespective of their relative size, as illustrated in Figure 1a. In other words, the emission profile has only

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a single peak if waste-stage emissions are negligible. Dominance of Eind over Euse leads Eind/use to peak

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soon after the peak time of Eind; otherwise, Eind/use peaks closer to the peak time of Euse. This means that

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the emission profile is not necessarily symmetric even if the production is assumed to follow the

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symmetric Gaussian distribution. Likewise, Theorem 4 in the SI demonstrates that the sub-total of Euse

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and Ewaste (Euse/waste) peaks only once when the degradation half-life is finite. Again, this means that the

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emission profile displays a single peak if industrial emissions are negligible.

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The emission profile is diverse when Eind and Ewaste become more prominent. Since the curve

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representing Eind shares the same peak with that of Euse (i.e., the single peak of Eind/use) and so does that

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of Ewaste (i.e., the single peak of Euse/waste), use-phase emissions serve as a bridge between emissions from

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the other two life stages. Therefore, unless Euse is small, it can swamp Eind and Ewaste, hence causing the

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peaks representing Eind/use and Euse/waste to merge to form a single peak, as indicated in Figure 1b. Double

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peaks therefore occur if (i) the product lifespan is sufficiently long to separate the peaks of Eind and

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Ewaste, and (ii) Euse is sufficiently small so as not to swamp the peaks of Eind and Ewaste (Figure 1c). Given

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that a long production lifespan leads to an increased size of in-use stock, a low EFuse is required to meet

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the second condition of maintaining a low Euse. The analogy of chromatographic peak separation helps

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to illustrate the two conditions. The time profiles of Eind and Ewaste can be viewed as two

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chromatographic peaks, and Euse represents the level of background noise. A longer product lifespan

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corresponds to a larger difference in chromatographic retention time: the greater the difference, the

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better the separation. Meanwhile, a lower use-related emission factor equates to an increased signal-to-

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noise ratio.


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Figure 1. Conceptual illustration of the overall emission (E) being a composite of emissions

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from industrial processes (Eind), use phase (Euse) and waste disposal (Ewaste): (a) a single-

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peaked emission profile with contributions from Eind and Euse, (b) a single-peaked emission

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profile with contributions from Eind, Euse and Ewaste, and (c) a double-peaked emission profile

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with contributions from Eind, Euse and Ewaste. As we limit our discussion to the shape of the

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overall emission and the relative magnitude of individual emissions, the vertical axis has no

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absolute scale.

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Influence of time scales of residence and emission factors on the emission profile



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To investigate the extent that properties of a chemical and associated products influence the emission

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profiles, we perform numerical batch (as opposed to the analytical) calculations for a set of hypothetical

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chemicals with different combinations of emission factors and time scales of residence in stocks. The

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use of hypothetical chemicals enables us to (i) comprehensively cover the “universe” of all plausible

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actual chemicals, and (ii) avoid the uncertainty associated with selecting and assigning appropriate

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values to specific properties of real chemicals.36-38 Calculation results are summarized and visualized in

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two-dimensional graphs (Figure 2), which plot the number of peaks and the relative size of double peaks

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as a function of log(EFwaste/EFind) and log(EFuse/EFind). The graphs are further arranged in columns

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according to degradation half-life in waste (HL), and in rows according to product lifespan (LS).

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In Figure 2, colored areas designate combinations of properties leading to a double-peaked emission

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profile. Different colors denote differences in the relative size between the first and second peaks

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(Emax1/Emax2): Red indicates a larger first peak whereas green denotes a larger second peak. In particular,

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recalling that Eind dominates the first peak while Ewaste dominates the second one, we can deduce from

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Figure 2 how combinations of properties control the relative importance of Eind and Ewaste. The

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remaining areas in Figure 2 represent combinations of properties leading to single-peaked emission

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profiles: Black, grey and light grey designate the dominance of Eind, Euse and Ewaste, respectively, in the

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single peak. Note that a “dominant” source here contributes most to the overall emissions at the peak

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time and not necessarily over the entire calculation period. In Figure 2, colored areas are located in

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regions where black and light grey areas converge, which indicates that double-peaked emission profiles

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will not occur if the magnitudes of peaks representing Eind and Ewaste are too different, i.e., Emax1/Emax2

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larger than 105 or smaller than 10-2.

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The colored area is absent in the top row of panels in Figure 2 and becomes more prevalent in the lower

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rows, which demonstrates that the longer the LS, the more likely the emission profile is double peaked.

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As explained above, a longer LS delays the chemical flow from in-use stock to waste stock, hence

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results in a clearer separation of the peaks in Eind and Ewaste. Notably, when LS (10 years) is shorter than

260

the production history (an assumed “half-duration” of 25 years in this case), the emission profile is


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single-peaked regardless of degradation half-life and emission factors (the top row in Figure 2).

262

Interestingly, many contaminants of current concern, e.g., PBDEs and PFASs, have relatively long

263

production half-durations of >20 years, exceeding the lifespan (50 years) (Figures 2i, 2o, 2p), the

309

separation coincides with the 1:1 line; while in the remaining panels, the separation line bends to the

310

upper left. This indicates that a double peak will not emerge if EFwaste is smaller than EFuse, irrespective

311

of their absolute magnitudes. In other words, that EFwaste is greater than EFuse is a necessary condition

312

for a double-peaked emission profile. As discussed above, a double-peaked emission profile occurs on

313

the condition that the peak of Euse is small compared with that of Ewaste (Figure 1c). However, Figure S1

314

demonstrates that, in most cases, the peak size of waste stock is much smaller than that of in-use stock.

315

Therefore, only in cases where EFwaste is much higher than EFuse can the peak size of Ewaste be of the

316

same order of magnitude as that of Euse, i.e., can we observe a double-peaked emission profile.

317

Furthermore, when both HL and LS are sufficiently long, in-use and waste stocks have similar peak size

318

(Figures S1i and S1p); under such a circumstance, almost equal EFwaste and EFuse can make the peak size

319

of Ewaste exceed that of Euse, which explains why the 1:1 line separates areas with and without double

320

peaks.

321

Whereas the above findings are based on the assumption of a “generic” Gaussian distributed temporal

322

trend of production, additional calculations demonstrate that they are valid if other temporal trends of

323

production are applied, e.g., a Gaussian distribution (a half-duration of 40 years), a left-skewed

324

distribution or a triangular distribution (Figure S2). Plots in Figure S2 indicates that, while the numerical

325

values can differ between different assumed temporal trends of production, they become alike when the

326

time scales of residence in in-use and waste stocks are sufficiently long.

327

Understanding the emission profile of real chemicals

328

We have demonstrated that the emission profile and source composition vary among chemicals in

329

associated products. Here, we categorize various chemicals in associated products into three classes

330

based on (i) whether the emission profile is single- or double-peaked, and (ii) how the overall emission

331

is composed of emissions from individual lifecycle stages. For each class, we select representative actual

332

cases to illustrate the emission profile and source composition (Figure 3). The placement of those five


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cases in the panels of Figure 2 is also given to illustrate the difference in their properties and those of the

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associated products.

335 336

Figure 3. Modelled emission profiles (red solid curves) and source compositions (red, blue and

337

yellow shadings) against literature reported profiles (black dashed curves) of the overall

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emission of (a) PFOA to all environmental media of developed regions,12 (b) β-HCH to the

339

global atmosphere,11 (c) PCB-28 and (d) PCB-180 to the global atmosphere,6 and (e) technical

340

HBCDDs to all environmental media of mainland China.35

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We first compared the modeled emission profiles with those derived using sophisticated methods in the

342

literature (Figure 3). While the red curves representing modeled emission profiles are smoother than the

343

dashed curves taken from the literature, in all five cases the two profiles agree well with each other with

344

respect to both shape and peak timing. This comparison indicates that our simplified approach succeeds



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in capturing the essential features of the emission profiles of a diverse range of chemicals. By extension,

346

it also justifies the assumption underlying this approach that the two sets of properties, i.e., the time

347

scales of residence in stocks and emission factors, are sufficient to characterize an emission profile. In a

348

word, our generic conclusions on the emission profile of chemicals are reliable and meaningful.

349

The first class includes chemicals with a single-peaked emission profile dominated by either industrial,

350

in-use or waste disposal emissions (“simple single-peakers”). These chemicals are often located in the

351

periphery of the panels in Figure 2 because of extreme values of EFuse/EFind and EFwaste/EFind. For such

352

chemicals, environmentally sound management of the dominant emission stage can instantly lead to

353

overall emissions abatement. Typical examples of “simple single-peakers” include: (i) industrial

354

chemicals, e.g., PFOA as a processing aid in manufacturing fluoropolymers (Figure 3a); (ii) “down-the-

355

drain” chemicals, e.g., detergent ingredients; and (iii) pesticides, e.g., β-HCH (Figure 3b). Overall, the

356

dominance of a single emission stage is due to an emission factor that is remarkably higher in that stage

357

than in the others, which results from either a substantial loss of a chemical in that stage or strict

358

regulation of emissions in other stages. For instance, the bulk of PFOA is already lost in industrial

359

processes (EFind = 75%) before it enters and accumulates in in-use and waste stocks (Table S1).

360

Therefore, the overall emission of PFOA (Figure 3a) changes in concert with the change in production

361

with a negligible or marginal lag time.

362

The second class includes chemicals with a single-peaked emission profile comprised of notable

363

contributions from more than one chemical lifecycle stage (“composite single-peakers”). Such chemicals

364

can either (i) be used in products with LS shorter than the half-duration of their chemical production, or

365

(ii) have higher emission factors during use than during waste disposal (EFwaste < EFuse), as summarized

366

above. The chemicals are located in areas shaded black, grey and light grey in Figure 2. PCBs are an

367

example of “composite single-peakers” (Figures 3c and 3d). Fitting realistic PCB production data with a

368

Gaussian distribution function (Table S1) indicates that 95% of the world’s production of PCB-28 and

369

PCB-180 occurred in windows of 25.5 and 31.0 years, respectively, which are longer than the weighted

370

average of the expected lifespan of products containing PCBs (~16 years5). Meanwhile, for both


Page 19 of 27


371

congeners, EFuse is greater than EFwaste, and PCB-28 has a higher EFuse/EFwaste ratio than PCB-180 as

372

the former is more volatile and more easily escapes from consumer products. It is noteworthy that,

373

although both PCB congeners have similar single-peaked emission profiles, the source composition of

374

the peak emission is different. At its peak year of 1972, 58% of the overall emission of the PCB-28 is

375

associated with product use (Figure 3c), whereas at its peak year of 1968, 75% of that of PCB-180

376

comes from industrial processes (Figure 3d). Therefore, although the time profile of annual production is

377

assumed to be symmetric (a Gaussian distribution) for the two congeners, the curve representing overall

378

emissions is skewed late (right) for PCB-28 and skewed early (left) for PCB-180. This infers that, when

379

the emissions decrease, PCB-28 has a slower rate of decrease than PCB-180, which agrees with earlier

380

monitoring results, such as those in Hung et al.39 In addition, the decline in the overall emissions of

381

composite single-peakers usually lags behind the ban of their production and new uses. Therefore,

382

observing whether immediate declines exist in overall emissions (and by extension the monitored

383

concentrations in environmental and biota samples) or not may not be an ideal option to evaluate the

384

effectiveness of regulations on composite single-peakers.

385

The third class includes chemicals with a double-peaked emission profile, which requires notable

386

contributions from both the industrial and waste disposal stages (“double-peakers”). These chemicals,

387

represented by areas in color in Figure 2, have the potential for causing “double exposure”, i.e., humans

388

can experience twice the peak exposure to these chemicals. The most prominent feature of “double-

389

peakers” is that they are used in products whose lifespans are long relative to the half-duration of their

390

production. This condition is met either when a product is highly durable (decades to centuries), or when

391

the production history is short (years). On a global scale, the production of a chemical typically

392

continues for a few decades, even half of a century, before its health and environmental hazards are fully

393

recognized and thus the production decreases or discontinues. It is thus not common to find a product

394

with a lifespan sufficiently long to exceed the half-duration of its production. Therefore, double-peaked

395

emission profiles are rare on a worldwide scale. However, a short production history can often arise on a

396

regional scale, e.g., if a developing nation is phasing out a substance that it had commercialized for only

397

a few years, because of environmental concerns discovered in developed countries with a much longer



Page 20 of 27

398

history of commercialization of that substance. For example, by the time mainland China is required to

399

cease production of HBCDD pursuant to the Stockholm Convention, the period of national production

400

will not have exceeded 20 years, which is shorter than the lifespan of most Chinese buildings (~30

401

years), i.e., the lifetime that the chemical is in service as a flame retardant in insulation materials (Table

402

S1). Meanwhile, EFwaste of HBCDD is larger than its EFuse (Table S1) because HBCDD-containing

403

insulating boards are often sealed under render coatings during use. As such, the nation-wide emission

404

profile of HBCDD is double-peaked (Figure 3e). In addition, since the first emission peak is governed

405

mainly by industrial emissions, we can anticipate an immediate decline in overall emissions and/or

406

monitored contamination of double-peakers after industrial emissions are regulated. For instance, recent

407

monitoring and biomonitoring evidence40-42 has recognized appreciable decreases in HBCDD

408

contamination soon after the cessation of production and new use, although emissions from in-use and

409

waste stocks are still ongoing.

410

The emission profile reflects combined properties of both chemicals and products. A chemical can

411

switch between simple single-peaker, composite single-peaker and double-peaker when emission factors

412

and time scales of residence in stocks vary as a result of its use in different products or in regions with

413

different regulations. For example, whereas HBCDD is identified as a double-peaker in mainland China,

414

it might become a single-peaker in North America because of a longer production history and/or a lower

415

EFwaste due to sound waste management.43 In a practical sense, regional differences in emission profiles

416

warrant region-specific modeling and regulation strategies.

417

Implications and perspectives

418

Both environmental modelers and decision makers might benefit from the model and conclusions

419

presented here, especially given the following two aspects. First, this work offers a simplified, yet

420

reliable and powerful, approach to mechanistically describing the regional or global emission profile of

421

a synthetic chemical. We recognize that by omitting detailed mechanisms, such a simplified model

422

cannot always replace sophisticated approaches. However, apart from being more interpretable, intuitive

423

and less error prone,44 the most prominent advantage of our model over earlier complicated models is


Page 21 of 27


424

that it requires minimal input data. Using the cases of five actual chemicals, we demonstrated that two

425

sets of properties, i.e., emission factors and time scales of residence in stocks, are sufficient to capture

426

the essential aspects of the behavior of a chemical and its associated products before emission (i.e., the

427

fate in the anthroposphere). These basic properties are retrievable for most chemicals and associate

428

products. For example, emission factors have been characterized, categorized and compiled for use in

429

official documents such as the OECD Emission Scenario Documents45 or EU Technical Guidance

430

Documents.30 Information on product use and lifespan is searchable in databases such as the “Lifespan

431

database for Vehicles, Equipment, and Structures (LiVES)”46 and “Chemical and Product Categories

432

(CPCat)”.47 In addition, computational techniques for calculating degradation half-life, e.g., the

433

BIOWINTM model in EPIsuiteTM,48 are well established. Therefore, our model allows for high-

434

throughput quantitative screening of emissions of a vast variety of synthetic chemicals, as advocated by

435

Breivik et al.49, even if detailed lifecycle information may be inadequate or missing. Furthermore, earlier

436

modeling studies have indicated that the fate of a chemical after emission (i.e., in the physical

437

environment) can be characterized by its partitioning properties (equilibrium partitioning coefficients

438

between air, water and octanol) and degradability (degradation half-lives in atmosphere and surface

439

media).36,

440

minimum set of data required for establishing a modeling continuum from production to environmental

441

occurrence.

442

Second, the graphic visualization and categorization in this work can aid in the identification and

443

prioritization of chemicals of potential concern. Chemicals with double-peaked emission profiles are

444

troublesome because they can lead to “double exposure”, i.e. two subsequent periods of human and

445

wildlife exposure. Most current regional and international regulations, e.g., the Stockholm Convention,

446

aim to curb chemical contamination by banning production and new uses. For some compounds,

447

however, a second contamination crest due to emissions from in-use stocks and waste disposal can be

448

expected to occur if existing products and waste remain unregulated. By superimposing existing or

449

emerging chemicals in our plots (Figure 2) based on their emission factors and time scales of residence,

450

we can identify and screen chemicals with double-peaked emission profiles, thus offering early warnings

37

Therefore, combined with those earlier conclusions, the current contribution defines a



Page 22 of 27

451

against a second contamination crest in the future. In particular, we can investigate region-to-region

452

difference in the emission profile of the same chemical. Locating a substance based on different region-

453

specific parameters in the plots allows us to find out whether single- or double-peaked emission profiles

454

are likely in a region. We can also deduce the contribution of different chemical lifecycle stages to the

455

total emissions, thus concentrating our focus on the dominant source. Such a practice is of special

456

importance when screening emerging chemicals, because their production may just have started and a

457

complete emission profile cannot yet be observed. It enables us to predict the entire shape of an emission

458

profile and to forecast where the regulatory emphasis should be placed.

459

Future efforts may be directed at expanding the applicability domain of our generic approach and

460

conclusions to a wider range of cases. For instance, the assumption of mass balance may be challenged

461

in a few regional cases because inter-regional trade of products and waste, e.g., import of e-waste to

462

developing regions,6 can result in additional emission peaks. Also, in some cases it may be necessary to

463

allow for time-variant emission factors, such as declining EFind of substances of very high concern in

464

response to increasingly stringent regional regulations,12, 13 or exponentially declining EFuse of volatile

465

organic chemicals whose emission is controlled by internal diffusion within product materials.50

466

Meanwhile, our models could be multiplied and coupled for the investigation of the interconversion

467

between multiple species, e.g., transformation between isomers, congeners or homologues,51, 52 or the

468

generation of a chemical from its precursors.53 In all cases, there is a need to strike the right balance

469

between the performance and parsimony of the model.

470

Acknowledgement

471

The authors thank Jingyuan Shen for her assistance in the mathematical analysis. L. L. acknowledges a

472

scholarship from the Shanghai Tongji Gao Tingyao Environmental Science and Technology

473

Development Foundation.

474

Supporting Information

475

The Supporting Information is available free of charge on the ACS Publications website at DOI:

476

10.1021/acs.est.XXXXXXXXX.


Page 23 of 27


477

Mathematic proofs of single-peaked time course of stocks and composite emissions therefrom; a

478

table describing parameters used in the realistic calculations for actual chemicals; and figures

479

illustrating the evolution of stocks with time, and calculation results with different assumed

480

temporal trends of production.

481

Notes

482

The authors declare no competing financial interest.

483

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Occurrence of Single- and Double-Peaked Emission Profiles of

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