Environmental Science Nano PERSPECTIVE The road to nowhere: equilibrium partition coefficients for nanoparticles Cite this: Environ. Sci.: Nano,2014, 1,317 Antonia Praetorius,*a Nathalie Tufenkji,b Kai-Uwe Goss,c Martin Scheringer,a Frank von der Kammerd and Menachem Elimeleche Adequate fate descriptors are crucial input parameters in models used to predict the behaviour and transport of a contaminant in the environment and determine predicted environmental concentrations for risk assessment. When new fate models are being developed for emerging contaminants, such as engineered nanoparticles (ENPs), special care has to be applied in adjusting conventional approaches and fate descriptors to a new set of substances. The aim of this paper is to clarify misconceptions about the applicability of equilibrium partition coefficients, such as the octanol–water partition coefficient (Kow) or the soil–water distribution coefficient (Kd), whose application in the context of ENP fate assessment is frequently suggested despite lacking scientific justification. ENPs are present in the environment as Received 17th March 2014, thermodynamically unstable suspensions and their behaviour must be represented by kinetically Accepted 9th June 2014 controlled attachment and deposition processes as has been established by colloid science. Here, we illustrate the underlying theories of equilibrium partitioning and kinetically controlled attachment and DOI: 10.1039/c4en00043a discuss why the use of any coefficient based on equilibrium partitioning is inadequate for ENPs and can rsc.li/es-nano lead to significant errors in ENP fate predictions and risk assessment. 1. Introduction and are derived from experiments which determine the ratio of e.g. dissolved and particle-bound fraction in the state of a Our ability to predict the behaviour of nanoparticles in natu- thermodynamic equilibrium. Distribution coefficients have ral aquatic systems is directly linked with our understanding proven extremely powerful for the assessment and prediction of the processes governing the fate of nanoparticles in the of transport, retardation and accumulation of a wide range of environment and the adequate translation of these processes substances, including metals and organic chemicals such as into conceptual models. Those models, while inherently pesticides and polycyclic aromatic hydrocarbons (PAHs).1,2 being a simplified representation of the conceptualized The reason for the successful application of these distribu- system, require a solid mechanistic foundation based on the tion coefficients is that the underlying concept (distribution physico-chemical processes that govern the real system. For between two phases at equilibrium) describes well the long, the environmental behaviour of organic chemicals and processes taking place in the real system for a well-defined metals has been assessed using distribution coefficients such group of substances (typically non-ionizable organic as the Henry's law constant or distribution functions of the chemicals). Freundlich or Langmuir type.1,2 These coefficients are quanti- In recent years, growing concern about the fate of tative descriptors of how a substance distributes between engineered nanoparticles (ENPs) in natural and engineered certain phases (air/water, water/organic carbon, water/soil) systems has led to a need to identify adequate fate descrip- – tors to be used in ENP transport and fate models.3 5 Naturally, the straightforward determination and application a – Institute for Chemical and Bioengineering, Swiss Federal Institute of Technology of distribution coefficients in the field of environmental ETH Zurich, Vladimir-Prelog-Weg 1, 8093 Zurich, Switzerland. science resulted in the temptation to apply these established E-mail: [email protected]; Fax: +41 44 632 1189; 3 Tel: +41 44 633 92 36 and relatively simple concepts to ENPs. However, when b Department of Chemical Engineering, McGill University, applying a concept well established for a specific group of Montreal, Quebec H3A 0C5, Canada substances to a fundamentally different type of material c Department of Analytical Environmental Chemistry, Helmholtz-Centre for with distinctly different properties, caution needs to be used Environmental Research – UFZ, Leipzig, D-04318, Germany d Department of Environmental Geosciences, University of Vienna, 1090 Vienna, Austria to ensure that the underlying concepts are still valid for the 4,6 e Department of Chemical and Environmental Engineering, Yale University, new material. Limitations of distribution coefficients to New Haven, CT 06520, USA specific cases, such as polar and ionizable organic chemicals, This journal is © The Royal Society of Chemistry 2014 Environ. Sci.: Nano,2014,1,317–323 | 317 Perspective Environmental Science: Nano – have been widely discussed,1,7 9 but it seems that confusion significantly for different substance types (as for example exists regarding the question of how the distribution behav- organic chemicals and ENPs). In some cases, adsorption or iour of ENPs should be described. Several recent publications absorption are driven by thermodynamics and distribution – report measured distribution coefficients for ENPs10 16 or isotherms (e.g. based on the Langmuir or Freundlich equa- propose their application in the context of ENP fate and risk tions) can be used to describe adsorption, or distribution assessment3,13,17 without acknowledging or sufficiently coefficients to describe absorption, based on the assumption discussing the associated limitations. that the system reaches a thermodynamic equilibrium. On Although ENPs are often treated as a fundamentally new the other hand, when adsorption or absorption are purely class of materials, processes of colloidal particle aggregation kinetically controlled, different mechanistic explanations are and attachment to surfaces have been investigated for required to adequately describe the underlying processes as decades and the findings have been integrated into theories well as the quantitative macroscopic effect. and models which have been demonstrated to accurately describe these processes in well controlled and relatively – simple systems.18 20 Those models and theories are based on 2.1. Equilibrium partitioning and partition coefficients entirely kinetically controlled processes and have been used The equilibrium partitioning of organic chemicals (MW < − to describe aggregation, surface attachment (deposition) and 500 g mol 1) is mainly the result of two processes: molecular transport processes of natural colloids and nanoparticles in diffusion due to thermal motion and intermolecular interac- the environment.21 To our knowledge, neither in traditional tions.2 Molecular diffusion alone would result in a uniform nor in environmental colloid science, the concept of an distribution of all molecules throughout space. However, in equilibrium distribution coefficient (Kd) has ever been condensed phases (and non-ideal gas phases), neighbouring successfully employed to describe colloidal particle behaviour. moleculesinteractwitheachotherinvariouswaysandthis The purpose of this paper is to clarify the fundamental influences their partitioning. There are various types of inter- differences between the two concepts of equilibrium par- actions (e.g. non-specific van-der-Waals interactions, specific titioning and kinetically controlled attachment. We describe H-bond interactions, and ionic interactions). Depending on the underlying theories and discuss why the use of Kd or an these interactions, moleculesprefertoresideinonephase analogous coefficient based on the same equilibrium dis- versus another. If the intermolecular interactions for mole- tribution concept easily leads to erroneous interpretations cule i are more attractive in phase B than in phase A, then and predictions of nanoparticle transport, distribution among the velocity or likelihood for a molecule i to diffuse out of environmental compartments and accumulation in the phase A into phase B is increased. This leads to an enrich- food chain. ment of molecules i in phase B (Fig. 1a). Once the system reaches thermodynamic equilibrium, the number of mole- 2. Theoretical bases of equilibrium cules i in phase A times their likelihood to move from phase partitioning and particle attachment A to phase B is the same as the number of molecules i in phase B times their likelihood to move from phase B to In this section, we summarize the theoretical concepts phase A. That is, at equilibrium, the number of molecules governing the behaviour of organic chemicals and ENPs in a moving back and forth between the two phases is the same. two-phase system and highlight the most important differ- At equilibrium, the ratio of the equilibrium concentrations ences between equilibrium partitioning of dissolved mole- Ci,A/Ci,B equals the ratio of the rate constants ki,BA/ki,AB with cules and kinetically controlled attachment or deposition of which the molecules i move from phase B to phase A or vice particles. Fig. 1 illustrates the processes acting on organic versa (Fig. 1a). The ratio of Ci,A/Ci,B at equilibrium is referred – – chemicals (Fig. 1a) and ENPs (Fig. 1b d) at a liquid liquid to as the partition (or distribution) coefficient, Ki,AB. and solid–liquid interface. Note that the focus of this paper Typical equilibrium partition coefficients used in the con- is on the applicability of equilibrium partitioning to ENPs text of chemical fate predictions and risk assessment are the – and not on general