Mesoscale Particle-Based Model of Electrophoretic Deposition

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Mesoscale Particle-based Model of Electrophoretic Deposition Brian Giera, Luis A. Zepeda-Ruiz, Andrew J. Pascall, and Todd H. Weisgraber Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04010 • Publication Date (Web): 20 Dec 2016 Downloaded from http://pubs.acs.org on December 24, 2016

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Mesoscale Particle-based Model of Electrophoretic Deposition

Brian Giera∗ , Luis A. Zepeda-Ruiz∗ , Andrew J. Pascall, and Todd H. Weisgraber Lawrence Livermore National Laboratory, Livermore, California 94550, USA Abstract We present and evaluate a semi-empirical particle-based model of electrophoretic deposition using extensive mesoscale simulations. We analyze particle configurations in order to observe how colloids accumulate at the electrode and arrange into deposits. In agreement with existing continuum models, the thickness of the deposit increases linearly in time during deposition. Resulting colloidal deposits exhibit a transition from highly ordered and bulk disordered region that can give rise to an appreciable density gradient under certain simulated conditions. The overall volume fraction increases and falls within a narrow range as the driving force due to the electric field increases and repulsive inter-colloidal interactions decrease. We postulate ordering and stacking within the initial layer(s) dramatically impacts the microstructure of the deposits. We find a combination of parameters, i.e. electric field and suspension properties, whose interplay enhances colloidal ordering beyond the commonly known approach of only reducing the driving force. ∗

To whom correspondence should be addressed. E-mail: [email protected]

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1

Introduction

Electrophoretic deposition (EPD) occurs when electric field-driven colloidal particles suspended in a fluid migrate towards an electrode or liquid-liquid interface 1 where they assemble into a deposit. The deposition rate depends on many parameters, such as the applied field strength, volume fraction of colloids, and electrophoretic mobility. 2 The electrophoretic mobility is a function of the colloidal suspension properties, e.g. ionic strength, 3 permittivity, and viscosity of the suspension as well as the electric potential difference between the surface of the colloid and suspension (termed the zeta-potential). Due to the vast material set inherent to colloidal suspensions, 4 EPD has been demonstrated in systems of aqueous electrolytes, 5 non-polar solvents, 6,7 and ionic liquids 8 that stabilize colloids comprised of ceramics, 9 graphene-related materials, 10 nanometals, 11 polymers, 12 phosphors, 13 or biological materials. 14 EPD is central to numerous applications 15 that include industrial coating, 16 fabrication of supercapacitor electrodes 17 and quantum-dot light-emitting devices, 18 near-shape manufacturing of tubes or structured parts, 19 and controlled growth of artificial opals. 20 Recently, two additive manufacturing techniques were developed that relay on EPD with photoconductive 21 and coaxial cable 22 electrodes. Since its discovery more than two centuries ago, 5 EPD has maintained practical relevance in academia and industry because of its versatility and scalability. 23 Despite widespread usage, an understanding of the underlying mechanisms of deposit formation and microstructure evolution during EPD is presently lacking. 24 EPD kinetics are determined typically by weighing the deposited film at different time points, 25 which is a purely ex situ technique. While there are some emergent in situ probes that utilize a quartz crystal microbalance, 26 the only data collected is total mass of the deposit – no particle level details of deposition kinetics are obtained. Usually, the morphology of the deposit is determined by SEM or scattering measurements; however, this requires drying of the deposit that can introduce artifacts due to, e.g., capillary forces are well known to rearrange particles into crystals, cracking resulting from mismatched shrinkage of the film and substrate, 23 etc. 2


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Furthermore, experimental measurements of deposits provide volumetric information and are always destructive. The limits of these experimental probes underscore the need for predictive models of EPD dynamics and the final structure of deposits. The majority of available models provide continuum level descriptions of EPD 27 that relate mass deposition rates to the electrophoretic velocity, deposition area, and a “sticking parameter” that accounts for the fraction of colloids that irreversibly incorporate into the deposit. 9,28–30 Film thickness models suggest nonuniform deposits occur when the colloidal particle permittivity exceeds that of the suspension 31 or near electrode edges where electric field singularities locally enhance deposition rates. 32 Continuum models inherently neglect inter-colloidal interactions within the bulk suspension, growth front, and deposit. Alternative particle-based modeling of EPD is still nascent, 33 but promises to offer more detailed predictive information about deposit formation and packing morphology than traditional continuum-level approaches. For instance, two-dimensional Discrete Element Method EPD simulations were used to construct “tentative phase diagrams” that imply particle area fraction of 2D deposits depends on electrolyte pH and concentration and electrode current density. 34 Brownian Dynamic simulations of “low dimensional” systems of colloids reveal grain boundary relaxation mechanisms in 2D colloidal crystal formation in an effort to tune voltages to avoid kinetic bottlenecks associated with slow grain boundary dynamics. 35 We recently presented a 3D mesoscale particle-based model of electrophoresis 36 that accurately captures the diffusive and electrophoretic motion of colloids over a comprehensive range of experimentally relevant conditions. Although our model successfully characterizes mass transport of bulk colloidal suspensions, it did not yet account for colloid-wall interactions, which are necessary to investigate particle rearrangement, defect formation, and the ultimate microstructure of the deposit. Here, we develop and evaluate a particle-based model of colloidal suspensions that undergo electrophoretic motion and deposition using an extensive set of mesoscale simulations representative of experimentally relevant colloidal suspensions. Since the model explicitly

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computes inter-colloidal interactions, it is uniquely poised to elucidate how deposition conditions influence defect structures and particle rearrangement within electrophoretic deposits. We use the model to investigate how empirical parameters, such as electric field strength and the range of inter-colloidal repulsion between electric double layers, can be tuned in order to control the degree of colloidal ordering versus non-ordering that occurs during EPD. We observe spatial-temporal particle density profiles and examine colloidal ordering throughout the deposit. We find the deposit density increases for suspensions characterized by high ionic strength under strong driving forces. The degree of colloidal ordering increases for suspensions characterized by moderate ionic strength under weak driving forces.

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Model Details

We perform mesoscale particle dynamics simulations of monodisperse colloidal suspensions in a uniform field, bounded by a flat electrode in order to model the electrophoretic motion and deposition of colloids. We use LAMMPS 37 to evaluate the internal (solvent-colloid and colloid-colloid) and external (electric field and wall) interactions that govern colloidal transport and deposit morphology within our simulations. Below, we describe these interaction potentials, the empirical properties they depend on, and how they are implemented.

2.1

Internal and External Interactions

In a system of Ncol colloids, the total energy acting on any particle is expressed as a sum of the internal Uinternal and external Uexternal energy components that depend on the pairwise separation distance between colloids r = |ri − rj | and each colloid’s distance from electrode surface z U (r

Ncol

)=

Ncol X

Uinternal (r) +

i 214, the resulting deposit is

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indicating it is possible to optimize ordering within a range of Debye lengths. While for Pe=214 the fraction of ordered particles at 12.5 nm is nearly double that of all other λD , at Pe=26.5 the ordered fraction within 6.25 nm≤ λD ≤ 25 nm is three times as large as Nordered /N outside of that range. A surprising finding is the existence of such a window of Debye lengths that allows for a dramatic improvement in ordering as the driving force decreases. We believe that the range of optimal values in λD can be attributed to DLVO interactions. Since the DLVO potential contains appreciable attractive energy wells for λD ≤ 6.25 nm (see Fig. 1), there are many possible locations (at a lattice site or otherwise) for a colloid to incorporate into the deposit that results in sufficiently low energy configurations. Thus, colloids with attractive interactions are trapped where they land on the deposit and do not rearrange into more favorable sites. At the values of λD that favor ordering, repulsive forces are sufficient to drive depositing colloids towards locations within newly formed layers with lower energy. In the case of systems with λD = 50 nm, colloids in suspension experience mostly repulsive forces allowing them to incorporate into the deposit nearly everywhere with little difference in energy change. For λD = 12.5 nm, the extreme cases in ordering are shown for the lowest and highest Pe in Figures 7(b1-b3) and 7(c1-c3), respectively. The snapshot in Fig. 7b1 shows a higher number of ordered particles (blue) that extend further from the electrode than Fig. 7c1. The densification at the larger field correlates with a reduction in colloidal ordering. For clarity, we remove disordered particles (grey) to better view this difference in Figs. 7b2 and c2. In these panels, particles that appear isolated/floating are surrounded by a local environment characterized by short-ranged order. Finally, top views in Figs. 7b3 and c3 showing only ordered colloids away from electrode confirm domain sizes decrease with increasing Pe, which is consistent with observations of ordering at the electrode in Fig. 5.

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4

Conclusions

We present a mesoscale model of EPD that explicitly accounts for inter-colloidal interactions to provide detailed predictions about the evolution and resulting microstructure of colloidal deposits. The model is formulated within a particle dynamics framework and assumes pairwise and external potentials that require only empirically measurable parameters as inputs. In its present form, the model is poised to explore systematically the vast interplay between the wide range of empirical parameters, e.g., electrophoretic mobility, particle radius, bulk volume fraction, suspension properties, among others, that govern EPD. We simulate a variety of monodisperse colloidal suspensions (listed in Table 1) that characterize suspensions with exclusively repulsive to partially attractive inter-colloidal interactions, under moderate to extreme uniform electric fields. We analyze in detail particle configurations in order to explore how colloids accumulate at the electrode. Simulated deposits increase in thickness linearly with time in accordance with traditional continuum-based theories. Fully deposited systems exhibit highest volume fractions for suspensions with thin double layers, e.g. concentrated electrolyte, under strong electric fields at large Pe. In the opposite limit, our simulations suggest a route to building deposits with graded density. Our model results indicate the volume fraction of the deposit can be tuned with the Péclet number and that the degree of tunability increases with Debye length. Unlike what is possible for standard (non-particle-based) modeling approaches, we use the model to investigate the degree of colloidal ordering versus non-ordering that occurs within the deposit during EPD. At lower fields and intermediate λD , domain sizes of ordered colloids at the electrodes is larger, which results in an increased overall fraction of ordered colloids within the deposit. We postulate that the degree of ordering at the electrode dictates the propensity of colloidal ordering in regions farther from the deposit. Enhanced control of the shape, composition, and performance of functional materials fabricated via EPD can benefit from computationally feasible models like the one presented here that can predict formation and morphology of colloidal depositions. The computational 23


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expense of this model allows for EPD simulations across time and length scales that are amenable to direct experimental comparison. Here, we evaluate the model using a large set of simulations within a regime characterized by short times and thin deposits. For experimental validation schemes requiring thicker deposits, this model simply could be run for longer times or parameterized with larger particles, which permit longer time steps. Since the model predictions apply to wet deposits, comparisons against morphological features of dried deposits may not be reliable due to cracking that occurs from drying. Nevertheless, realtime particle tracking techniques 59 enable direct comparisons against simulated trajectories. Also, time series of weight measurements taken from wet or dry deposits offer a useful metric for assessing deposition rates. Colloidal ordering can be validated using scattering and/or tomography; however, sample preparation techniques such as gelling or freeze drying wet deposits could be used to preserve the microstructure. An immediate improvement to the model requires modification to account for changes in the resistance of and resulting potential drop across the deposit that strongly influences deposition kinetics, especially for thick deposits. Also, various treatments of the electrode/particle interface, e.g., a lattice of particles, an amorphous monolayer, surface charge heterogeneities, etc., along with spatial and temporal electric field variations can be investigated for their influence on defect structures, particle rearrangement, and deposit growth kinetics. Considering the variety and intricacies of actual colloidal suspensions, e.g. polydispersity and/or non-spherical colloids, it is fortunate that this model is extensible to simulate systems with size and/or surface potential distributions, ellipsoidal particles, or mixtures of different particle compositions. Furthermore, other non-DLVO systems, such as those with polarizable double layers, Janus or “patchy” particles, 60 or polymer coated colloids can be accounted for by including the appropriate particle interactions into the model.

Acknowledgement This work was performed under the auspices of the U.S. Department of Energy by Lawrence 24


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Livermore National Laboratory under Contract DE-AC52-07NA27344.

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