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NSF: EF-0830117 Constant-Number Monte Carlo Simulations of Nanoparticles Agglomeration Yoram Cohen, Haoyang Haven Liu, Sirikarn Surawanvijit, Robert Rallo and Gerassimos Orkoulas Center for Environmental Implications of nanotechnology and Department of Chemical and Biomolecular Engineering University of California, Los Angeles http://www.cein.ucla.edu/ This materials is based on work supported by the National Science Foundation and Environmental Protection Agency under Cooperative Agreement # NSF-EF0830117. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the Environmental Protection Agency.

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NSF: EF-0830117 OUTLINE Motivation Toward predictive models of NP agglomeration o Basic approach o Monte Carlo numerical simulations o Comparison of predictions with experimental data o Dependence of NP agglomeration on basic system parameters o Future work

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NSF: EF-0830117 eNMs may be released to the environment throughout their life-cycle Preliminary in vitro (with various cell lines) and in-vivo studies with simple organisms (e.g., zebrafish) suggest that certain eNMs may be toxic at certain exposure concentration levels The transport and fate of eNMs in the environment is governed by their agglomeration state The toxicity of eNMs may be impacted by their primary size and their agglomeration state The removal of eNMs from aqueous streams can be facilitated by controlling their aggregation state Motivation Nanoparticle Toxicity Exposure Fate & Transport Particle Size Distribution Particle-Cell Interactions Nanoparticle Aggregation

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NSF: EF-0830117 Environmental Multimedia Fate & Transport of eNMs The transport and fate of nanoparticles is governed by their agglomeration state

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NSF: EF-0830117 Environmental Intermedia Transport of Particles Dry Deposition Wind Soil Resuspension Wet Scavenging Aerosolization

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NSF: EF-0830117 Atmospheric Deposition of Particles onto Water Surfaces The dry deposition velocity of particles varies with particle size Deposition Velocity (cm/s) Particle Diameter, (µm) 1 nm Diffusion Impaction 1 10 10 -2 10 -3 10 -1 1 10 10 2 0.1 0.01 Williams, R.M., A model for the dry deposition of particles to natural water surfaces. Atmospheric Environment (1967), 1982. 16(8): p. 1933-1938 The dry deposition velocity of particles varies with particle size

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NSF: EF-0830117 Rain Scavenging of Nanoparticles Efficiency of NP removal from the atmosphere via wet deposition depends on particle size Cohen, Y. and P. A. Ryan, "Multimedia Transport of Particle Bound Organics: Benzo(a)Pyrene Test Case,” Chemosphere, 15, 31-47 (1986). Cohen, Y. and P. A. Ryan, "Multimedia Transport of Particle Bound Organics: Benzo(a)Pyrene Test Case,” Chemosphere, 15, 31-47 (1986). Efficiency of NP removal from the atmosphere via wet deposition depends on particle size

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NSF: EF-0830117 Gravitational Sedimentation of Nanoparticles in Aqueous Media

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NSF: EF-0830117 eNM Size Distribution in Aqueous Systems DLS is the standard approach to quantifying the size distribution of nanoparticles The reliability of DLS measurements is dependent on the NP concentration and suspension stability Suspension stability is impacted by NP agglomeration (aggregation)/disaggregation which directly affect particle gravitational sedimentation Detector 90° ~40μm

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NSF: EF-0830117 Experimental Procedure 1000 ppm suspension Nanoparticle powder Detector DLS 20ppm suspension Sonicate for 30 minutes in T- controlled bath Sonicate for 5 minutes Time delays between consecutive steps ~5 s Dilute IS adjusted pH adjusted aqueous solution NPs: TiO 2 (21 nm, IEP=6.5, 21% A/79%R) CeO 2 (15 nm, IEP=7.8)

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NSF: EF-0830117 eNP Particle-Particle Interactions (Classical DLVO)

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NSF: EF-0830117 DLVO Theory (slide shows forumlas for types of interaction Type of Interactions Expression EDL <5 EDL >5 vdW

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NSF: EF-0830117 Particle-Particle Interactions Classical DLVO only accounts for vdW and EDL Classical DLVO assumes hard sphere –O.K. for environmental application as most frequently used eNMs are spherical –Non-spherical particles exist Nano-rod, nano-wire, etc. DLVO does not account for: –Steric, hydration, magnetic, etc. Modified DLVO can be utilized to account for additional interaction energies and particle shape (e.g., sphericity)

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NSF: EF-0830117 Size distribution of NPs in Aqueous Systems

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NSF: EF-0830117 Nanoparticle Brownian Motion & Settling Stokes’ Settling velocity Diffusion length r

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NSF: EF-0830117 Monte Carlo Simulation of eNM Agglomeration.

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NSF: EF-0830117 Constant-Number MC Simulations of Particles in a Box Box is expanded to maintain the particle concentration upon aggregation events and replenishment of particles to maintain a constant number

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NSF: EF-0830117 Simulations of Nanoparticles Agglomeration Dynamic Monte Carlo Simulation Solver Primary NP Information (e.g., primary size, surface chemistry) Solution Chemistry/Media Parameters (e.g., ionic strength, pH, temperature, dielectric constant) Output: -Particle size distribution (PSD) -NP concentration Output: -Particle size distribution (PSD) -NP concentration Measured or Calculated Model Parameters (e.g., d p, zeta potential, IS Hamaker constant) Aggregation Model: - DLVO -Sedimentation -Particles in a “box” Aggregation Model: - DLVO -Sedimentation -Particles in a “box” Computational (Constant-Number Monte Carlo) model of NP agglomeration making use of the DLVO theory accounting for NP sedimentation Computational Cluster: 10 Nodes with a total of 20 Intel Quad-Core Xeon processors (2.2 – 3.0 GHz) with 176 GB RAM

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NSF: EF-0830117 Importance of Including Sedimentation in Model Simulations Average of 10 simulations of 5000 particles CeO 2 TiO 2 ζ CeO2 = -24.5 mVζ TiO2 = -29 mV A H, = 42 zJ A H, = 21 zJ pH = 8, IS= 0.065 mM

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NSF: EF-0830117 Convergence of Simulations 10 (nm) Number of Simulation Particles n (nm) Number of Simulations, n Number of Simulation Particles Average of 10 simulations S mean particle size (%) S mean particle size, nm

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NSF: EF-0830117 Comparison of Experimental and Simulation Results

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NSF: EF-0830117 eNP (a) Type z [mV] (pH)IS [mM]d p [nm]d exp [nm]d sim [nm]% abs. error (b) Jiang, et al.TiO 2 38 (3.3)115809620.5 TiO 2 36 (3.8)1158510219.8 TiO 2 34 (4.45)1158710823.7 TiO 2 28.5 (5.3)1152332528.1 TiO 2 -30 (7.8)11521825115.5 TiO 2 -38 (8.2)11516212125.2 TiO 2 -43 (8.7)11592901.9 TiO 2 -47.5 (9.65)11593858.7 TiO 2 -45 (10.4)115987820.2 TiO 2 36 (4.6)0.0115907714.6 TiO 2 42 (4.6)1159010718.8 TiO 2 40 (4.6)51516017811.3 TiO 2 36 (4.6)101550039221.6 French, et al.TiO 2 35 (4.5)4.559010920.8 TiO 2 35 (4.5)8.5550063213.5 TiO 2 35 (4.5)12.5570062810.3 Ji, et al.TiO 2 30.2 (6.1)1212002021.0 Present StudyTiO 2 41 (3)0.37211631620.6 TiO 2 -30 (8)0.027211731751.2 TiO 2 -35 (10)0.12211721710.6 CeO 2 32 (3)0.37152712690.7 CeO 2 -23.5 (8)0.027152662640.8 CeO 2 -30 (-30)0.12152402431.3 (b) % abs. error (a) eNP – Engineered Nanoparticle Summary of Experimental & Simulation Conditions

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NSF: EF-0830117 Particles Size Distributions (t=24 h)

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NSF: EF-0830117 Dependence of TiO 2 Agglomeration on pH Simulations:

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NSF: EF-0830117 Dependence of Agglomerate Size on Ionic Strength

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NSF: EF-0830117 Dependence of NP Agglomeration on the Hamaker Constant

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NSF: EF-0830117 Dependence of Agglomerate Size on Primary NP Size NP primary size ↑ PSD tail of small aggregates ↑ Average NP aggregate size (in suspension) ↓ For present primary size range:

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NSF: EF-0830117 Summary and Future work Monte Carlo (MC) simulations of NP agglomeration based on the Smoluchowski equation and classical DLVO theory demonstrated reasonable quantitative predictions of NP agglomeration (average size and size distribution) over a range of solution conditions (pH= 3-10, IS= 0.03-12.5 mM for TiO2 and CeO2 NPs) The present approach can be extended to include various modifications/extensions of the DLVO theory With extension and additional validation of the current modeling approach it will be feasible to develop a practical parameterized model of NP agglomeration New experimental DLS data are being generated over a wide range of conditions specifically for extended model extension and validation A machine learning approach is being developed to guide the task of data generation and parameterized model development

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