Modeling the Transport of the ‘New-Horizon’ Reduced Graphene Oxide—Metal Oxide Nanohybrids in Water-Saturated Porous Media

Abstract

Little is known about the fate and transport of the ‘new-horizon’ multifunctional nanohybrids in the environment. Saturated sand-packed column experiments (n=66) were therefore performed to investigate the transport and retention of reduced graphene oxide (RGO)—metal oxide (Fe₃O₄, TiO₂, and ZnO) nanohybrids under environmentally-relevant conditions (mono- and di-valent electrolytes and natural organic matter). Classical colloid science principles (Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and colloid filtration theory (CFT)) and mathematical models based on the one-dimensional convection-dispersion equation were employed to describe and predict the mobility of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids in porous media. Results indicate that the mobility of the three nanohybrids under varying experimental conditions is overall explainable by DLVO theory and CFT. Numerical simulations suggest that the one-site kinetic retention model (OSKRM) considering both time- and depth-dependent retention accurately approximated breakthrough curves (BTCs) and retention profiles (RPs) of the nanohybrids concurrently; whereas, others (e.g., two-site retention model) failed to capture the BTCs and/or RPs. This is primarily because blocking BTCs and exponential/hyperexponential/uniform RPs occurred, which is within the framework of OSKRM featuring time- (for kinetic Langmuirian blocking) and depth-dependent (for exponential/hyperexponential/uniform) retention kinetics. Employing fitted-parameters (maximum solid-phase retention capacity: S_max=0.0406–3.06 cm³/g; and first-order attachment rate coefficient: k_a=0.133–20.6 min^–1) extracted from the OSKRM and environmentally-representative physical variables (flow velocity (0.00441–4.41 cm/min), porosity (0.24–0.54), and grain size (210–810 μm)) as initial input conditions, the long-distance transport scenarios (in 500-cm long sand columns) of nanohybrids were predicted via forward simulation. Our findings address the existing knowledge gap regarding the impact of physicochemical factors on the transport of the next-generation, multifunctional RGO—metal oxide nanohybrids in the subsurface.

Graphical Abstract

INTRODUCTION

Compared with single-component nanomaterials (NMs), the ‘new-horizon’ nanohybrids that are nano-/hierarchical assemblies of multiple NMs hold great promise for addressing issues and meeting challenges within water-energy-agriculture-environment nexus,¹ due to their enhanced properties, optimized multi-functionalities, and maximized performances.^{2, 3} Among others, the reduced graphene oxide (RGO)—metal oxide nanohybrids are the most commonly pursued combinations owing to their exceptional and highly-tunable physicochemical (electronic, thermal, mechanical, optical, photocatalytic, and magnetic) and biological (bioactive, biocompatible, and antimicrobial) properties⁴ arising from the synergistic interplay of parent NM components within the nanoheterostructures.^{5, 6} For example, RGO-magnetite (RGO-Fe₃O₄), RGO-titanium dioxide (RGO-TiO₂), and RGO-zinc oxide (RGO-ZnO) nanohybrids have attracted immense interest for various applications including drug delivery,⁷ sensors,⁸ supercapacitors,⁹ solar cells,¹⁰ biomolecule immobilizer,¹¹ and environmental remediation (removing heavy metals, organic contaminants, and pathogens).¹² Of considerable interest within the framework of environmental remediation is the employment of magnetically-recyclable RGO-Fe₃O₄ and easily-regenerative RGO-TiO₂ and RGO-ZnO nanohybrids for photoredox/photocurrent/photocatalytic degradation of diverse recalcitrant compounds.^{12, 13} This is because nanoheteroconjugating Fe₃O₄, TiO₂, and ZnO NMs with two-dimensional RGO nanosheets that can strongly pre-concentrate contaminants via sorption, effectively inhibits the aggregation and surface passivation of metal oxide NMs¹⁴ and decreases the recombination rate of photo-generated electron-hole pairs,^{12, 15} thereby significantly improving degradation efficiency of contaminants. Increasing production and use of multifunctional RGO—metal oxide nanohybrids necessitate fundamental understandings of environmental remediation and potential environmental/human health impacts and risks (e.g., unknown toxicity of nanohybrids, or detached RGO, TiO₂, and ZnO NMs, or dissolved Zn(II) ions)^{2, 16} due to unintentional release during nanohybrids production, usage, and other relevant end-of-life stages¹⁷ (e.g., wastewater treatment plant^{18, 19} and land application of sewage sludge²⁰).

Aggregation and transport propensities of single-component NMs and multi-component nanohybrids dictate their performances in environmental remediation (e.g., in-situ contaminated site nanoremediation),^21–23 fate,²⁴ transformations,²⁵ and potential environmental/human health impacts and risks.²⁶ Over the past decade, substantial efforts have been devoted to unravelling the transport of singular NMs in the subsurface, documenting that NMs’ mobility is governed by the interplay of physicochemical properties of NMs (e.g., size/shape/coating/surface charge) and porous media (e.g., grain size/porosity/surface chemistry), hydrodynamics (e.g., flow velocity), and surrounding solution chemistries (e.g., pH/ionic strength (IS)/natural organic matter (NOM))^{27, 28}, which can be explained by colloid science principles of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory^{29, 30} and colloid filtration theory (CFT)³¹ qualitatively or semi-quantitatively. However, little is known about the transport of nanohybrids in the subsurface; and the critical knowledge gaps such as “Will nanohybrids behave/transport similarly (or distinctly) as NMs do?” and “Can DLVO theory and CFT qualitatively or semi-quantitatively describe the transport behaviors of nanohybrids as well?” need to be addressed before mass production and widespread application of multifunctional nanohybrids occur.

Numerical simulations have long-been used to mechanistically describe the transport and retention of colloids/NMs in porous media, and model-fitted parameters, in turn, furnish valuable insights into understanding the intrinsic mechanisms dominating colloids/NMs’ mobility. For instance, upon incorporating a depth-dependent straining term into the one-dimensional (1D) convection-dispersion equation (CDE), Bradford et al.³² accurately simulated the hyperexponential deposition of colloids, introducing a new mechanism (physical straining) for colloid retention. In addition to the data-fitting functionality (inverse-algorithm), numerical simulation (e.g., forward-algorithm) also has enormous potential to forecast possible outcomes of colloids/NMs with adjustable input parameters including initial boundary conditions.³³ This is of practical significance given that laboratory experiments are costly, time-consuming, or even impossible to implement due to certain limitations. Specifically, forward simulation can predict the long-distance transport of colloids/NMs with varying input conditions (e.g., flow velocity, porosity, and grain size)³³ commonly encountered in the subsurface, some of which cannot be achieved or maintained in laboratory experiments (e.g., one cannot experimentally investigate the mobility of colloids/NMs at low subsurface flow velocity scenarios since low-flow-rate injection of NMs results in particle clogging in packed-column tubing system due to aggregation/agglomeration).

This research is set forth to bridge the knowledge gap regarding the influence of physicochemical factors on the transport of RGO—metal oxide nanohybrids in the subsurface. The most influential environmental factors (mono- and di-valent electrolytes and NOM)³⁴ controlling NMs’ mobility were chosen. Saturated sand-packed column experiments were conducted to investigate the transport and retention of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids under environmentally-relevant concentrations of NaCl, CaCl₂, and NOM. DLVO theory, CFT, and numerical simulation were employed to delineate the transport behaviors of nanohybrids. Fitted-parameters from the best modelling approach were used in combination with the physical variables commonly encountered in the subsurface to predict long-distance transport (in 500-cm long sand columns) of nanohybrids via forward-simulation. Coupling laboratory experiments with numerical simulations provides a robust venue for accurately describing and assessing the mobility of the ‘new-horizon’ nanohybrids in the subsurface.

MATERIALS AND METHODS

Preparation of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO Nanohybrid Influent Suspensions and Solution Chemistries

The RGO-Fe₃O₄ nanohybrid stock suspension (10,000 mg/L) well-dispersed in acetone (~80%, v/v) was purchased from Sigma-Aldrich (product #803804). The RGO-TiO₂ and RGO-ZnO nanohybrid powders were synthesized in-house. Physicochemical properties of the RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids were characterized using multiple techniques including high-resolution transmission electron microscopy (HR-TEM), field-emission scanning electron microscopy (FE-SEM), Fourier-transform infrared (FT-IR) spectroscopy, X-ray photoelectron spectroscopy (XPS), and ultraviolet-visible (UV-Vis) spectroscopy. Detailed procedures of synthesizing the RGO-TiO₂ and RGO-ZnO, and physicochemical characterizations of the three nanohybrids are provided in the Supporting Information (SI) S1. Environmentally-relevant solution chemistries (Table 1) were chosen to examine the mobility of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids in water-saturated porous media including mono- (1, 10, 50, and 100 mM NaCl) and di-valent (0.5, 1, 5, and 10 mM CaCl₂) electrolytes, and the presence of NOM (0, 1, 5, and 10 mg C/L Suwannee River humic acid (SRHA); procedures for preparing SRHA stock suspension are given in SI S2). The nanohybrid influent suspensions at the desired solution chemistries (Table 1) were freshly prepared via ultrasonication (100 W and 42 kHz; Branson 3510R-DTH sonicator, Danbury, CT) for 30–60 min at 25 °C. The concentration of all nanohybrid influents for column experiments was 10 mg/L, and influent pH was unadjusted (pH=7.0–7.5). Compared to the RGO-TiO₂ and RGO-ZnO nanohybrids suspended in water (100%), the RGO-Fe₃O₄ influent suspension includes ~0.08% (v/v) acetone (10,000 mg/L stock suspension was diluted 1,000 times to obtain 10 mg/L influent).

Table 1.

Electrokinetic properties and hydrodynamic sizes of RGO—metal oxide (RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO) nanohybrids in the influent suspensions; and mass recoveries of the nanohybrids in column experiments for different solution chemistries.

Type	NaCl (mM)	CaCl2 (mM)	SRHA (mg C/L)	ζ-potential (mV) (n=3)	DH (nm) (n=3)	Mass recovery (%) (n = 2)
						Meff	Mret	Mtot
RGO-Fe3O4	1	0	0	−36.0±4.7	1075±46	89.9±2.0	10.1±2.0	100±0.02
	10	0	0	−28.3±3.7	1146±34	74.0±2.7	25.4±1.7	99.4±0.94
	50	0	0	−26.3±4.4	1178±24	67.9±1.7	32.4±2.1	100±0.45
	100	0	0	−23.9±3.6	1363±37	64.8±1.5	35.5±1.9	100±0.39
	0	0.5	0	−18.5±3.0	1386±58	64.9±3.3	36.7±2.9	102±0.37
	0	1	0	−14.6±3.0	1443±25	60.9±2.4	38.9±2.0	99.8±0.38
	0	5	0	−12.8±3.0	1488±6	50.5±0.12	49.5±0.14	100±0.02
	0	10	0	−7.5±1.2	1552±42	45.6±0.80	54.4±0.81	100±0.01
	10	0	1	−45.9±2.4	888±163	76.9±0.88	23.1±0.95	100±0.06
	10	0	5	−48.6±4.5	866±86	90.8±2.6	11.3±2.9	102±0.25
	10	0	10	−52.7±2.6	851±74	94.8±1.2	5.4±1.2	100±0.04
RGO-TiO2	1	0	1	−47.4±3.0	247±67	85.5±2.8	14.7±1.9	100±0.87
	10	0	1	−45.8±2.7	293±107	38.2±0.41	67.3±0.89	106±0.47
	50	0	1	−39.8±2.3	398±117	14.5±1.0	85.4±1.1	99.9±0.10
	100	0	1	−37.2±2.3	446±139	10.0±0.13	90.7±0.90	101±1.0
	0	0.5	1	−20.7±1.2	331±137	53.9±2.4	48.5±1.7	102±0.67
	0	1	1	−19.6±1.2	391±183	10.0±0.35	90.3±0.91	100±0.56
	0	5	1	−0.22±0.23	531±120	6.3±0.21	94.1±0.13	100±0.19
	0	10	1	−0.14±0.11	562±126	5.2±0.26	95.1±0.47	100±0.21
	10	0	0	−18.8±0.86	481±143	2.0±0.49	98.0±0.41	100±0.08
	10	0	5	−48.4±3.1	271±67	84.6±0.47	15.4±0.30	100±0.17
	10	0	10	−51.3±2.2	250±48	90.3±0.90	9.8±0.89	100±0.01
RGO-ZnO	1	0	5	−35.4±3.1	2663±260	92.8±1.4	7.0±1.7	99.8±0.31
	10	0	5	−32.8±2.4	3171±280	85.5±1.4	14.7±1.3	100±0.10
	50	0	5	−30.9±0.42	3287±185	76.6±3.5	23.3±3.3	99.9±0.18
	100	0	5	−27.8±2.3	3485±132	73.5±4.3	26.5±3.9	100±0.42
	0	0.5	5	−17.8±2.0	3311±173	78.6±1.8	21.4±0.59	100±1.2
	0	1	5	−16.0±1.4	3591±142	67.4±1.3	32.7±1.4	100±0.08
	0	5	5	−15.2±0.94	3712±188	41.1±0.37	58.6±0.05	99.7±0.32
	0	10	5	−9.2±1.4	3970±135	30.0±2.0	69.4±1.8	99.3±0.28
	10	0	0	−19.7±1.7	5328±348	2.4±0.02	102±0.10	104±0.11
	10	0	1	−27.8±4.1	2500±263	68.4±1.4	31.2±1.3	99.6±0.15
	10	0	10	−35.0±2.2	2259±139	92.2±0.06	7.8±0.03	100±0.03

SRHA: Suwannee River humic acid; ζ-potential: zeta potential; D_H: average hydrodynamic diameter; and M_eff, M_ret, and M_tot are mass percentages of nanohybrids recovered from effluent, retentate, and total column, respectively. Mean values ± standard deviations are reported. For different NaCl/CaCl₂ concentration tests, 1 and 5 mg C/L SRHA were added into RGO-TiO₂ and RGO-ZnO nanohybrid influent suspensions, respectively, to stabilize the nanohybrids.

Column Experiments

Ottawa sands (U.S. Silica, Berkeley Springs, WV) having an average diameter of 360-μm were selected as representative aquifer materials. Prior to use, the sands were cleaned using a sequential acid-deionized (DI) water wash procedure.³⁵ Transport experiments were conducted in duplicates using glass chromatography columns (1.7-cm i.d. × 10-cm long). The column was dry-packed with cleaned sands, purged with CO₂ gas for 30 min, and then slowly-saturated with DI water. Column porosity was gravimetrically determined to be ~0.334. Following the saturation step, a nonreactive tracer (50 mM NaNO₃) experiment was performed to determine the hydrodynamic properties of the packed-columns, including pore-water velocity and dispersivity, which were then used in numerical modeling of the transport of nanohybrids in the column experiments.

Following the completion of tracer experiment, the column was pre-equilibrated with desired background electrolyte solution (Table 1) to standardize pore-water solution chemistries. A two-step transport experiment was then initiated by injecting 3 pore volumes (PVs) of 10 mg/L of nanohybrid influents (Table 1) followed by elution with 7 PVs of nanohybrid-free background electrolyte solution. Darcy velocity was maintained at 0.44 cm/min³⁵ for all experiments. Column effluents were collected continuously via a fraction collector. After completion of each breakthrough experiment, the spatial distribution of nanohybrids retained in the column was determined (dissection experiment; SI S3). The concentrations of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids in the effluents and retentates (collected from dissection experiments) were determined spectrophotometrically at their peak wavelengths (264, 252, and 264 nm, respectively, for RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids; SI Figure S4). Calibration curves were constructed by diluting 10 mg/L nanohybrid influent suspension, which was linear within the concentration range of 0–10 mg/L (R²=1.0; SI Figure S5). Mass balances were calculated by comparing the quantities of nanohybrids recovered in the effluents and retentates to those injected in the column.

Electrokinetic Properties and Hydrodynamic Sizes of Nanohybrids and Sand Grains

Electrokinetic properties and hydrodynamic sizes of nanohybrids indicating their aggregation and transport propensities³⁶ were determined. Specifically, electrophoretic mobility of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids in the influents (10 mg/L) and sand grains (pulverized colloidal particles of sands as surrogates)³⁵ at desired solution chemistries (Table 1) was determined using the Zetasizer Nano-ZS ZEN3600 analyzer (Malvern Instruments Ltd., Malvern, Worcestershire, U.K.) in triplicates at 25 °C, and then converted to zeta (ζ)-potential using the Smoluchowski equation.³⁷ The hydrodynamic diameter (D_H) of nanohybrids in the influents was determined using dynamic light scattering (DLS) on the same Zetasizer analyzer in triplicates at 25 °C.³⁵ Prior to measurements, ultrasonication was performed in a water bath (25 °C) at 100 W and 42 kHz for 30 min to obtain a homogeneous suspension. The ζ-potential and D_H values of nanohybrids and sand grains were used to calculate the average interaction energy between nanohybrids and sand grains under different experimental conditions using DLVO theory. Within the framework of the DLVO theory, the van der Waals and electrostatic double layer interaction energies were calculated for the nanohybrid-sand system, assuming a sphere-plate configuration (SI S4).

Numerical Simulations

The breakthrough curves (BTCs) and retention profiles (RPs) of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids under different experimental conditions were simulated using the 1D CDE with one- (site 1) or two-site (sites 1 and 2, respectively) kinetic retention. The one-site kinetic retention model (OSKRM) is described as follows:⁴⁰

$$\frac{\partial \theta C}{\partial t}+{\rho }_{\text{b}}\frac{\partial S}{\partial t}=\frac{\partial }{\partial x}\left(\theta D\frac{\partial C}{\partial x}\right)- \frac{\partial qC}{\partial x}$$ [1]

$${\rho }_{\text{b}}\frac{\partial S}{\partial t}=\theta k_{\text{a}}\psi C-{\rho }_{\text{b}}{k}_{\text{d}}S$$ [2]

$$\psi =\left(1-\frac{S}{S_{\text{max}}}\right){\left(\frac{d_{\text{c}}+x}{d_{\text{c}}}\right)}^{-\beta }$$ [3]

where θ is volumetric water content [–]; C is nanohybrid concentration in aqueous-phase [NL^–3, where N and L denote number and length, respectively]; t is time [T, where T denotes time]; ρ_b is bulk density of porous media [ML^–3, where M denotes mass]; S is nanohybrid concentration on solid-phase [NM^–1]; x is the spatial coordinate [L]; D is the hydrodynamic dispersion coefficient [–]; q is flow rate [LT^–1]; k_a and k_d are first-order attachment and detachment rate coefficients [T^–1], respectively; ψ is a dimensionless function considering both time- and depth-dependent retention; S_max is the maximum solid-phase retention capacity [NM^–1]; d_c is average diameter of sand grains; and β is an empirical parameter controlling the shape of RPs [–]. The OSKRM can describe time-dependent BTCs (e.g., kinetic Langmuirian blocking)⁴¹ and RPs that are uniform, exponential, or hyperexponential with depth.^{40, 42} The first and second terms on the right-hand side of equation [3] account for time-dependent Langmuirian attachment,⁴¹ and depth-dependent retention, respectively. Exponential RPs occur when β=0, consistent with CFT prediction.³¹ Conversely, when β>0, hyperexponential RPs occur with greater retention near the column inlet.⁴³ Four model formulations (M1–M4) were considered within the framework of OSKRM (SI Table S1): M1—CFT when ψ=1; M2—time-dependent Langmuirian attachment when β=0; M3—depth-dependent retention when β=0.432;³² and M4—both time- and depth-dependent retention when β=0.432 and (1-S/S_max)<0.⁴⁰

In comparison, the two-site kinetic retention model (TSKRM) that assumes site 1 as first-order reversible attachment-detachment kinetics and site 2 as Langmuirian blocking (M5) or depth-dependent retention (M6) was also applied to simulate nanohybrids’ BTCs and RPs:⁴³

$$\frac{\partial \theta C}{\partial t}+{\rho }_{\text{b}}\frac{\partial \left(S_1\right)}{\partial t}+{\rho }_{\text{b}}\frac{\partial (S_2)}{\partial t}=\frac{\partial }{\partial x}\left(\theta D\frac{\partial C}{\partial x}\right)- \frac{\partial qC}{\partial x}$$ [4]

$${\rho }_{\text{b}}\frac{\partial (S_1)}{\partial t}=\theta k_{1\text{a}}C-{\rho }_{\text{b}}{k}_{1\text{d}}{S}_1$$ [5]

$${\rho }_{\text{b}}\frac{\partial (S_2)}{\partial t}=\theta k_{2\text{a}}\psi C$$ [6]

where S₁ and S₂ are nanohybrid concentrations on the solid-phases associated with sites 1 and 2, respectively; k_1a and k_1d are first-order attachment and detachment rate coefficients, respectively, on site 1; and k_2a is first-order attachment rate coefficient on site 2. For M5–M6, ψ is defined in equations [7] and [8], respectively:

$$\psi =\left(1-\frac{S_2}{S_{\text{max}2}}\right)$$ [7]

$$\psi ={\left(\frac{d_{\text{c}}+x}{d_{\text{c}}}\right)}^{-\beta }$$ [8]

where S_max2 is maximum solid-phase retention capacity on site 2 (Table S1).

The column experimental data (BTCs and RPs) were simulated using the HYDRUS-1D software package (version 4.16).³⁸ The HYDRUS-1D code numerically solves the Richards equation for saturated-unsaturated water flow and convection-dispersion type equations for solutes and colloids/NMs transport. The code incorporates a nonlinear-least-squares optimization routine (Levenberg-Marquardt algorithm)³⁹ that allows model parameters to be inversely-fitted to BTCs and RPs of colloids/NMs in column experiments. Weighted fitting of experimental data is optimized, so the contribution to minimized objective function by summing the squared deviations of measured vs. fitted data is approximately the same for BTCs and RPs.^{38, 40} In addition to the inverse-fitting commonly used in HYDRUS-1D, the code can also implement direct (forward) simulation to predict long-distance transport of colloids/NMs^{36, 40} over a wide-range of environmentally-relevant physicochemical conditions that cannot be easily obtained in laboratory experiments. In this study, the forward algorithm coded in HYDRUS-1D was employed to approximate the long-distance transport (e.g., 500-cm long sand column) of nanohybrids at various velocities (0.00441, 0.0441, 0.441, and 4.41 cm/min), porosities (0.24, 0.34, 0.44, and 0.54), and grain sizes (210-, 360-, 510-, 660-, and 810-μm).

Specifically, for numerical simulations, we first employed each model (M1–M6) to simulate both BTCs and RPs of nanohybrids via inverse-fitting. We then employed each model (M1–M6) to forward predicting the long-distance (500-cm) transport of nanohybrids using the fitted-parameters obtained from the paired model (e.g., use M1 to forward simulating the long-distance transport of nanohybrids using M1-fitted parameters as initial input conditions). The long-distance transport simulation was set at 500-cm since this distance is long enough as field lysimeter transport studies^{44, 45} showed that NMs (CNT and Ag) were primarily (>99%) retained in the upper 0–40 cm of the soil columns. To predict the mobility of nanohybrids under environmentally-relevant velocities, porosities, and grain sizes, forward simulations were also performed via the best model (M4; as described below) using M4-fitted parameters (SI S5–S7) and known velocity/porosity/grain size as initial input conditions in HYDRUS-1D (there are specified locations for inputting the fitted-parameters and velocity/porosity/grain size in HYDRUS-1D).

RESULTS AND DISCUSSION

Physicochemical Properties of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO Nanohybrids

Physicochemical properties of three nanohybrids were characterized using multiple techniques. The HR-TEM (Figure 1) and FE-SEM imaging (SI Figure S1) coupled with elemental (C, O, and Fe/Ti/Zn) mapping analyses confirmed the successful hybridization of RGO with metal oxides (Fe₃O₄, TiO₂, and ZnO). The nanostructures exhibited several wrinkle structures due to the extremely thin layer (~1 nm) of RGO.⁴⁶ The morphology, size, loading capacity, and distribution of metal oxide onto RGO nanosheets varied with metal oxide type and synthetic strategy. Specifically, spherically smaller Fe₃O₄ (5–25 nm) and TiO₂ (20–30 nm) nanoparticles were more uniformly distributed on the RGO surfaces via in-situ nucleation and/or crystallization;⁴⁷ whereas, globular-shaped larger 350–650 nm ZnO particles were heterogeneously deposited on RGO surfaces via solvothermal route.⁴⁸ The loading capacity of metal (Fe/Ti/Zn) onto RGO for the nanohybrids (which is expressed as mass percentage) was 32.6% (Fe), 50.3% (Ti), and 13.1% (Zn), respectively, for RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids (Figure S1). The nanohybrids’ Hamaker constant was calculated using a simple linear relationship between the Hamaker constants of parent NM components and their elemental compositions (SI S4),³⁵ which was then applied to compute the DLVO interaction energy between nanohybrids and sand grains under different experimental conditions.

Figure 1.

Representative HR-TEM images of RGO-Fe₃O₄ (a), RGO-TiO₂ (b), and RGO-ZnO nanohybrids (c); and corresponding mapping of individual elements (C, O, Fe, Ti, and Zn) and conjugated nanohybrids using high-angle annular dark-field (HAADF) imaging technique.

Surface functional group identifications (FT-IR spectra; SI Figure S2) showed that the peaks at 3442 and 2920 cm^–1 corresponded to O–H and C–H stretching vibrations of RGO.⁴⁹ Metal oxide exhibited low-frequency bands below 1000 cm^–1, which were ascribed to the vibrations of metal-oxygen (e.g., Fe–O (669 cm^–1), Zn–O (405 cm^–1), and Ti–O–Ti/C) bonds.^{50, 51} Some characteristic functional groups of RGO (e.g., C=O at 1726 cm^–1)^{49, 50} disappeared completely (e.g., RGO-TiO₂ due to high loading of TiO₂) due to the coverage (“surface masking”) of metal oxides on RGO surfaces. Surface chemistry analysis using XPS (SI Figure S3) showed that the strong C1s peaks of RGO located at 284.8–285.0 and 292.8–293.0 eV corresponded to non-oxygenated carbon (C–C/C=C) and oxygen-containing carbon (O–C=O) moieties, respectively.⁴⁹ The deconvolution of O1s spectra shows that the peaks at 531.2–531.4 eV corresponded to carbonyl and carboxyl oxygen (C=O) moieties, and the C–O bonds occurred at relatively high binding energy (532.6 and 536.2 eV for RGO-Fe₃O₄).⁵² The characteristic bonds at 709.4 and 724.8 eV, 458.2 and 463.8 eV, and 1022.4 and 1045.5 eV corresponded to Fe2p_3/2 and Fe2p_1/2,⁵¹ Ti2p_3/2 and Ti2p_1/2,⁵³ and Zn2p_3/2 and Zn2p_1/2⁵⁴ spin-orbital splitting photoelectrons, respectively. The UV-Vis scanning spectrum survey (SI Figure S4) displayed that the peak wavelengths of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids were 264, 252, and 264 nm, respectively, which are close to the characteristic wavelength of RGO (268 nm).⁵⁵ These findings indicate the predominance of RGO in the constitution of the nanohybrids.

Electrokinetic Properties and Hydrodynamic Diameters of Nanohybrids

The ζ-potential and D_H of nanohybrids in the influents at varying solution chemistries are shown in Table 1. Both nanohybrids and sand grains (shown in ref. 35) were negatively charged, suggesting unfavorable attachment conditions. The O-containing (carboxyl, carbonyl, and hydroxyl) functional groups identified by FT-IR (Figure S2) and XPS (Figure S3) contributed to the negative ζ-potential of nanohybrids. Consistent with literature-documented results for colloids/NMs³⁷ and nanohybrids (RGO-TiO₂⁵⁶ and CNT-Fe₃O₄³⁵), increasing NaCl/CaCl₂ or decreasing SRHA concentration caused a decrease in nanohybrids’ ζ-potential (less negative) due to enhanced charge screening (for both Na⁺ and Ca²⁺) and neutralization (for divalent Ca²⁺ only as Ca²⁺ neutralizes the negative surface charge of nanohybrids) effects³⁷ or reduced sorption of SRHA onto the nanohybrids. Greater aggregation (larger D_H) of nanohybrids occurred at higher ISs or lower SRHA concentrations due to the less repulsive interactions (e.g., lower ζ-potential), which is within the framework of DLVO theory. Compared with the D_H of RGO-Fe₃O₄ (851–1552 nm) and RGO-TiO₂ (247–562 nm), the D_H of RGO-ZnO nanohybrids (2259–5328 nm) was much larger (Table 1). This is primarily due to the larger size of ZnO (350–650 nm) than that of Fe₃O₄ (5–25 nm) and TiO₂ (20–30 nm) in the nanoheterostructures (Figure 1). Another possible explanation is that, ZnO has a much higher pH_PZC (point of zero charge; pH_PZC=8–9.8) than that of Fe₃O₄ (pH_PZC=6.4–8) and TiO₂ (pH_PZC=5.2–6.8),⁵⁸ yielding a less negative ζ-potential of RGO-ZnO nanohybrids, despite the loading of ZnO was relatively low. For example, the ζ-potential of RGO-ZnO (–27.8 mV) was significantly less negative than that of RGO-Fe₃O₄ (–45.9 mV) and RGO-TiO₂ nanohybrids (–45.8 mV) under 10 mM NaCl and 1 mg C/L SRHA. It should be mentioned that the RGO-Fe₃O₄ (compared with RGO-TiO₂ and RGO-ZnO) nanohybrids exhibited much less variability in ζ-potential and D_H versus varying solution chemistries. For instance, the ζ-potential of RGO-Fe₃O₄ and RGO-TiO₂ decreased from –18.5 to –7.5 mV (SRHA=0) and from –20.7 to –0.14 mV (SRHA=1 mg C/L), respectively, when CaCl₂ concentration was increased from 0.5 to 10 mM (Table 1). This is attributed to the presence of acetone (~0.08%) in the RGO-Fe₃O₄ nanohybrid influent, acting as “cushion” of protecting nanohybrids from quick-aggregation. Haghighi and Poursalehi⁵⁹ examined the colloidal stability of nickel nanoparticles in water, ethanol, methanol, and acetone; and similarly observed the highest colloidal stability of nickel nanoparticles in acetone due to the strong dipole-dipole interaction of acetone molecules with nanoparticles. Because acetone is a compound with both polar and nonpolar characteristics, its strong polar and nonpolar interactions with RGO-Fe₃O₄ (RGO and Fe₃O₄ NMs) nanohybrids and water molecules substantially alleviate the direct impact of aforementioned charge screening and neutralization effects from Na⁺/Ca²⁺ cation, thereby stabilizing the nanohybrids effectively. Nonetheless, the D_H was larger for RGO-Fe₃O₄ than RGO-ZnO nanohybrids at equivalent solution chemistries due partly to the different source of RGO for synthesizing the nanohybrids (S1). Alternatively, the magnetic attraction of RGO-Fe₃O₄³⁵ contributed to their larger D_H than that of non-magnetic RGO-TiO₂ nanohybrids.

Transport of Nanohybrids under Environmentally-Relevant Solution Chemistries

• Transport Model Selection

Total mass recoveries (M_tot) of nanohybrids in the effluents (M_eff) and retentates (M_ret) from column experiments are shown in Table 1, confirming a high degree of confidence in our experimental measurements because virtually all (M_tot=99.3–106%) nanohybrids were recovered. The aggregation-dispersion status of the nanohybrids in column influents and effluents may be different, so as to their UV-Vis spectroscopic response during concentration measurements. This likely explains the observed results of M_tot>100% for some column experiments as the calibration curves for quantifying the nanohybrids were constructed using the column influents (described above). A high mass recovery (M_tot=100±10%) is a prerequisite for reliable numerical simulation using CDE. Six model formulations (M1–M6; Table S1) were used to simulate nanohybrids’ BTCs and RPs simultaneously. Figure 2 presents inverse-fitting results for the three nanohybrids in 1 mM NaCl without/with SRHA; and all model-fitted parameters are given in SI S5–S7. Herein, the criteria of model selection/screening include: i) goodness-of-fit describing the discrepancy between experimental data and model-fitted data; ii) physical meanings of model-fitted parameters for interpreting the transport mechanisms of nanohybrids at varying experimental conditions; and iii) number (N) of fitted parameters (as shown in Table S1). The Pearson’s correlation coefficient (R²), and Akaike and Bayesian Information Criterion (AIC and BIC) quantitatively characterize the goodness-of-fit for M1–M6.

Figure 2.

Observed (dots) and fitted (lines) breakthrough curves (a, c, and e) and retention profiles (b, d, and f) of RGO-Fe₃O₄ (a−b; no SRHA), RGO-TiO₂ (c−d; in 1 mg C/L SRHA), and RGO-ZnO nanohybrids (e−f; in 5 mg C/L SRHA) in water-saturated sand columns under 1 mM NaCl (pH=7.0−7.5) via inverse-fitting. Breakthrough curve describes the normalized effluent concentration of nanohybrids, C/C_o (where C_o is the initial influent concentration of nanohybrids) as a function of pore volume; and retention profile shows the normalized solid-phase retention concentration of nanohybrids, S/C_o (where S is retention amount of nanohybrids per gram dry sand) as a function of distance from the column inlet. Six particle transport models (M1−M6) based on the one-dimensional convection-dispersion equation (CDE) were used to simulate the breakthrough curves and retention profiles simultaneously (see SI Table S1) including: classical colloid filtration theory model (M1), Langmuirian attachment model (M2), depth-dependent retention model (M3), time- and depth-dependent retention model (M4), two-site kinetic retention model with Langmuirian attachment on one site (M5), and two-site kinetic retention model with depth-dependent retention on one site (M6). Models 1 to 4 (M1−M4) are one site kinetic retention models (particle retention occurs on one type of site; Site 1); whereas, models 5 and 6 (M5−M6) are two site kinetic retention models with two different types of retention sites (Site 1 and Site 2, respectively). Column experiments were performed in water-saturated sands having an average grain size of 360-μm at a Darcy velocity of 0.441 cm min⁻¹. The error bars represent the standard deviations between duplicate experiments (n = 2). Model (M1−M6) fitted transport parameters via inverse-fitting are shown in SI S5–S7. Clearly, the M4 (red solid line) provided the best descriptions for both breakthrough curves and retention profiles of the three nanohybrids.

Blocking BTCs (increasing effluent concentration with time) and exponential/hyperexponential/uniform RPs occurred for the nanohybrids in 1 mM NaCl without/with SRHA (Figure 2). Similar BTCs and RPs occurred under other solution chemistries (described below); and have also been reported for single-component NMs (e.g., GO,⁶⁰ Fe₃O₄,⁶¹ TiO₂,⁶² and ZnO⁶¹). Numerical simulations show that M1 (CFT)³¹ failed to reproduce blocking BTCs and particularly the hyperexponential RPs (Figure 2b), as reflected by the low R² values (R²(RP)=0.824–0.894; SI S5–S7). This is because CFT assumes an invariant attachment rate coefficient (k_a) for particle retention in “clean-bed” system (i.e., subsequent retention of particle is irrelevant to particle retention history). Upon introducing a Langmuirian attachment term⁴¹ that explicitly records particle retention history, M2 well approximated the blocking BTCs with R²(BTC)=0.962–0.977 (SI S5–S7). Both AIC and BIC are measures of goodness-of-fit,⁶³ and the model with the lowest AIC/BIC value is generally preferred. However, while low AIC/BIC occurred occasionally for M2 (SI S5), the model intrinsically could not capture exponential/hyperexponential RPs (e.g., R²(RP)=8×10^–16–0.567; SI S5–S7) since M2 considers linear retention of particle with transport distance (Figure 2). Similarly, M3 failed to simulate either blocking BTCs or exponential/uniform RPs (Figure 2) because no particle retention history is considered and hyperexponential retention (β=0.432)³² is pre-defined within M3. In contrast, M4 that features both kinetic Langmuirian attachment and depth-dependent retention accurately described blocking BTCs and hyperexponential/exponential/uniform RPs (Figure 2), which is supported by the high R² (particularly R²(RP)=0.984–1.0) and low AIC/BIC values. Intriguingly, in contrast with previous observations, incorporating more fitted parameters (compared with OSKRM; Table S1) into CDE did not necessarily improve the simulation capability of TSKRM (Figure 2) due, in part, to over-parameterization.⁶⁴ Instead, much higher AIC/BIC values occurred for TSKRM than OSKRM because AIC/BIC penalizes for adding new fitted parameters.⁶³ Particularly, over-parameterization often yields unaccommodating fitted-parameters, likely masking and confounding the true transport mechanisms of nanohybrids (discussed below). Altogether, M4 provided the best descriptions for both BTCs and RPs (high R² and low AIC/BIC values; SI S5–S7) with minimized number (N=2) of fitted parameters.

• Mobility Comparison Among Three Nanohybrids

Measured and M4-fitted BTCs and RPs of RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO nanohybrids at environmentally-relevant concentrations of NaCl (1–100 mM), CaCl₂ (0.5–10 mM), and SRHA (0–10 mg C/L) are shown in Figures 3, S6, and S7, respectively. All model (M1–M6)-fitted parameters for the three nanohybrids are provided in SI S5, S6, and S7, respectively. Again, blocking BTCs and exponential/hyperexponential/uniform RPs occurred under different combinations of NaCl/CaCl₂/SRHA, with the exception of the one (ripening BTC; decreasing effluent concentration with time)^{65, 66} for RGO-ZnO nanohybrids when NaCl=10 mM and SRHA=1 mg C/L (Figure S7e). The ripening phenomenon suggests that low SRHA concentration (1 mg C/L) cannot effectively stabilize RGO-ZnO nanohybrids (large D_H; Table 1) and that deposited particles in porous media act as more favorable carriers than sand grains for trapping subsequent particles due to the larger specific surface area and less repulsive interaction between particle-particle (carrier) than between particle-collector.⁶⁷ Numerical simulations exhibit relatively low R² values (R²(BTC)/R²(RP)/R²(BTC+RP)) of M1–M3, indicative of their incapability for describing either BTCs or RPs of nanohybrids. While high R² was frequently obtained for M5–M6, high AIC/BIC was accompanied accordingly due to the increased number (N) of fitted parameters (described above). Again, M4 provided the best approximations for both BTCs and RPs with physically meaningful fitted-parameters (SI S5–S7), which were employed to interpret and predict the mobility of nanohybrids under environmentally-relevant physicochemical conditions (described below).

Figure 3.

Observed (dots) and fitted (lines) breakthrough curves (a, c, and e) and retention profiles (b, d, and f) of RGO-Fe₃O₄ (a−b; no SRHA), RGO-TiO₂ (c−d; in 1 mg C/L SRHA), and RGO-ZnO (e−f; in 5 mg C/L SRHA) nanohybrids in water-saturated sand columns at different concentrations of NaCl (1, 10, 50, and 100 mM) using the time- and depth-dependent retention model (M4) via inverse-fitting. Other model-fitted parameters via inverse-fitting are shown in SI S5–S7. Column experiments were performed in water-saturated sands having an average grain size of 360-μm at a Darcy velocity of 0.441 cm min⁻¹. The error bars represent the standard deviations between duplicate experiments (n = 2).

Consistent with previous findings for colloids/NMs,⁴³ increasing IS (NaCl/CaCl₂; Figures 3 and S6) or decreasing SRHA concentration (Figure S7) yielded lower breakthrough and greater retention of nanohybrids (see M_eff and M_ret; Table 1). Greater degrees of blocking and hyperexponential retention occurred at higher ISs or lower SRHA concentrations due to larger maximum retention capacity (S_max) and k_a predicted by M4 (SI S5–S7). Larger S_max is expected to induce more retarded breakthrough and less steep blocking BTCs (i.e., RGO-TiO₂ and RGO-ZnO nanohybrids).⁴⁰ However, this is not the case for RGO-Fe₃O₄ nanohybrids that were “protected” by organic solvent (acetone); the magnitude of blocking and retarded breakthrough varied indiscernibly with varying solution chemistries (even in 100 mM NaCl or 10 mM CaCl₂), highlighting the robustness of organic solvent in maintaining the mobility of nanohybrids in aqueous solution. Overall, the transport behaviors of three nanohybrids for varying solution chemistries are consistent with DLVO theory predictions (Table S2 and Figure S8). Lower maximum repulsive energy barriers (Φ_max) and deeper secondary minima (Φ_min2) in DLVO interaction energy profiles resulted in greater retention of nanohybrids at higher ISs or lower SRHA concentrations (Table S2) due to larger S_max (primary and secondary minima are parts of S_max; Figure S8). As mentioned above, inconsistent/abnormal trends of S_max, k_a, and k_d vs. NaCl/CaCl₂/SRHA concentrations occurred for M5–M6 due to: 1) over-parameterization; 2) incorporation of detachment kinetics (k_d); or more likely a combination of both. The absence of tailing in nanohybrids’ BTCs suggests that spontaneous detachment kinetics was unlikely to occur, which validates the reliability of M4 that precludes detachment kinetics within its model formulation.

The mobility of RGO-Fe₃O₄ was much higher than that of RGO-TiO₂ and RGO-ZnO nanohybrids for equivalent solution chemistries. For example, M_eff=74.0%, 2.0%, and 2.4%, respectively, for RGO-Fe₃O₄, RGO-TiO₂, and RGO-ZnO when NaCl=10 mM and SRHA=0 (Table 1), where hyperexponential retention was pronounced for RGO-TiO₂ and RGO-ZnO nanohybrids (Figure S7). This indicates a low mobility of RGO-TiO₂ and RGO-ZnO nanohybrids without SRHA. Adding 1 mg C/L SRHA into the influent still cannot stabilize the RGO-ZnO nanohybrids, as evidenced by the large D_H and ripening BTC. Both CFT³¹ and Tufenkji-Elimelech equation (a correlation equation of CFT)⁶⁸ predict a monotonic increase in colloid retention with size when particle diameter is ≥1 μm due to interception and gravitational sedimentation, so the large D_H (≥2500 nm; Table 1) of RGO-ZnO nanohybrids coupled with straining^{32, 69} contributed to the observed low mobility and hyperexponential retention when SRHA≤1 mg C/L. Similar findings were recently highlighted in the transport of CNT-Fe₃O₄ nanohybrids in packed-column studies in the presence of the stabilizer—carboxymethylcellulose.³⁵ Conversely, blocking BTC and uniform RP occurred for RGO-TiO₂ nanohybrids when NaCl=10 mM and SRHA=1 mg C/L (Figure S7), suggesting that low SRHA concentration can effectively stabilize RGO-TiO₂ nanohybrids (D_H=293 nm; Table 1). When SRHA≥5 mg C/L, high breakthrough and limited retention (uniform RPs) occurred for either nanohybrids due to the large Φ_max between particle-collector (≥911 kT, where k is Boltzmann constant and T is absolute temperature; Table S2 and Figure S8) and steric repulsion arising from SRHA molecules.⁵⁷ The low S_max predicted by M4 (S_max≤0.139 cm³/g; SI S5–S7) also indicates limited sites for particle retention partly because SRHA masks/pre-occupies these favorable retention sites.^{43, 70} Further, lower S_max and larger k_a (faster deposition) yielded steeper blocking BTCs at higher SRHA concentrations. The lowest S_max and highest M_eff values of RGO-Fe₃O₄ predicted by M4 at different SRHA concentrations confirmed the greatest mobility of RGO-Fe₃O₄ among the three nanohybrids.

With the aid of SRHA, both RGO-TiO₂ (SRHA=1 mg C/L) and RGO-ZnO nanohybrids (SRHA=5 mg C/L) exhibited appreciable mobility at low ISs (≤10 mM NaCl or ≤0.5 mM CaCl₂; Figures 3 and S6). At high ISs, however, low SRHA concentration (1 mg C/L) cannot sustain the high mobility of RGO-TiO₂ as the nanohybrids were almost immobilized in the packed-columns; M_eff≤14.5% when NaCl≥50 mM or CaCl₂≥1 mM (Table 1). This is due partly to the deep secondary minima (Φ_min2=–8.28 to –21.5 kT; Table S2) and high S_max (SI S6) for RGO-TiO₂ nanohybrids when NaCl≥50 mM. In contrast with previous findings, strong bridging (e.g., for fullerene)⁷¹ between RGO-ZnO nanohybrids in the co-presence of high concentration of SRHA (negatively charged carboxyl groups) and Ca²⁺ cation did not occur (D_H was comparable under NaCl vs. CaCl₂; Table 1). Instead, high mobility of RGO-ZnO nanohybrids was obtained when SRHA=5 mg C/L. For RGO-Fe₃O₄ nanohybrids, much less variability in mobility (compared with RGO-TiO₂ and RGO-ZnO) occurred at varying NaCl/CaCl₂ concentrations even without SRHA due, again, to the “protection effect” of acetone. Nonetheless, the shape of RPs for RGO-Fe₃O₄ nanohybrids evolved from exponential to hyperexponential with increasing IS likely due to enhanced contribution of straining.^{32, 35, 69} The larger S_max predicted by M4 (SI S5–S7) under NaCl vs. CaCl₂ for either nanohybrids signifies the greater impact of CaCl₂ in inhibiting nanohybrids’ mobility, consistent with recent results for CNT-Fe₃O₄ nanohybrids.³⁵ Among three nanohybrids, the RGO-Fe₃O₄ exhibited the highest mobility due to the “protection effect” of acetone, although the acetone content was extremely low (~0.08% v/v).

Predicting the Long-Distance Transport of Nanohybrids

The beauty of numerical simulation relates to its capability for inverse- but also forward-prediction of possible outcomes over a wide variety of scenarios, e.g., long-distance transport of nanohybrids in the subsurface. Using model (M1–M6)-fitted parameters as initial input conditions, the retention of RGO-Fe₃O₄ (SRHA=0), RGO-TiO₂ (SRHA=1 mg C/L), and RGO-ZnO nanohybrids (SRHA=5 mg C/L) in 500-cm long sand columns was simulated via forward-fitting (Figure 4). The transport distance requires to attenuate the solid-phase concentration (S/C_o; log-scale y-axis) of nanohybrids to the perceived background NM concentration in soil (1×10^–5 cm³/g)⁷² was estimated. M1 (CFT) predicts an exponential decay versus depth. M2/M5 delineates an initial insignificant attenuation followed by an abrupt decrease in nanohybrids mobility (designated as “L-type” RP) with limited maximum transport distance (L_max≈120 and 180 cm for M2 and M5, respectively; Figure 4a). The simulated “L-type” RP is due to the large S_max and k_a (see discussion below) and the pre-defined linear RP of M2/M5. Similar hyperexponential retention occurred for M3/M4/M6 since depth-dependent retention (β=0.432) is considered on one site; but a dramatic decrease in nanohybrids mobility occurred for M6 during the later phase of transport (≥450 cm depth) due to the impact of retention kinetics on the other site. Deviations of model outputs became more pronounced with increasing depth; and M4 provided the most reliable approximation of nanohybrids’ mobility since M4 exhibited the best descriptions for both BTCs and RPs (described above). Model outcomes of M4 again substantiated the highest mobility of RGO-Fe₃O₄ (no SRHA) among three nanohybrids with S/C_o≈8×10^–3 cm³/g at 500 cm depth (Figure 4a). Taken together, our findings substantiate the importance of employing the best model for describing (inverse-fitting; e.g., Figures 2–3) and predicting (forward simulation; e.g., Figure 4) the transport and retention of colloids including NMs/nanoparticles/nanohybrids in porous media.

Figure 4.

Simulated retention profiles of RGO-Fe₃O₄ (a; no SRHA), RGO-TiO₂ (b; in 1 mg C/L SRHA), and RGO-ZnO nanohybrids (c; in 5 mg C/L SRHA) under 1 mM NaCl in 500-cm long columns packed with sands having an average grain size of 360-μm at a Darcy velocity of 0.441 cm min⁻¹ using six different models (M1−M6) via forward simulation. Specifically, forward simulation was performed for each model (from M1 to M6) using the inversely-fitted parameters obtained from the paired model as initial input conditions. The normalized solid-phase concentration (S/C_o) is plotted as a function of distance from the column inlet on a log-scale. Parameters for the forward simulations are shown in SI S5–S7. Simulations of M6 for RGO-Fe₃O₄ (a) and M5 for RGO-TiO₂ (b) nanohybrids were not shown because model-predicted retention profiles exhibited multiple retention peaks, which is inconsistent with the results of observed retention profiles shown in Figures 2−3.

Subsequent forward-fitting of nanohybrids’ long-distance transport under environmentally-relevant physicochemical conditions was implemented by M4 only since M4 provided the most reliable prediction (described above). Figure S9 presents simulated RPs of three nanohybrids at different NaCl/CaCl₂ concentrations in 500-cm long sand (360-μm) columns when velocity=0.441 cm/min. Both S/C_o and L_max were predicted to decrease with increasing IS; and the impact of Ca²⁺ (vs. Na⁺) in the decay of S/C_o and L_max was much greater. Transition between hyperexponential and “L-type” RPs was driven by the change in initial input values of S_max and k_a; i.e., larger S_max and k_a yielded “L-type” RPs at higher ISs. Depending on nanohybrids type and IS, the predicted L_max varied significantly (~25 cm to >500 cm) due to the variations of S_max and k_d. Given that S_max and k_a determine the mobility of the nanohybrids in porous media, upon employing the lowest and highest data sets of (S_max, k_a) extracted from M4 (SI S5–S7) as initial input conditions, the long-distance transport scenarios including the maximum and minimum transport potentials of the three nanohybrids were restricted in Figure S10. The simulations again show the highest mobility of RGO-Fe₃O₄ followed by a slightly lower mobility of RGO-ZnO nanohybrids, primarily, due to the aid of 5 mg C/L SRHA for the RGO-ZnO (described above). Note that the L_max of three nanohybrids was determined to be ≤60 cm using the highest data set of (S_max, k_a), implying a low mobility of nanohybrids in the subsurface. This would occur as large S_max and k_a are encountered for nanohybrids without the aid of organic solvent or NOM.

Transport of nanohybrids under environmentally-relevant physicochemical conditions including various flow velocities (0.00441–4.41 cm/min), porosities (0.24–0.54), and grain sizes (210–810 μm) in 500-cm long sand columns was simulated using the lowest (S_max, k_a) (Figure 5) and 10-times of the lowest (S_max, k_a) data sets (Figure S11). This includes one of the worst scenarios (highest mobility) of NM release during accidental spill as (0.00406 cm³/g, 0.0133 min^–1) is one of the lowest (S_max, k_a) encountered in colloids/NMs transport studies. Sensitivity analyses show that variability in S/C_o and L_max was much greater versus velocity than that with varying porosity and grain size. This is because velocity determines the magnitude of S_max and k_a.^73–75 Consistent with the results of Kasel et al.⁴⁰ and Ma et al.,⁷⁵ higher mobility of nanohybrids occurred at greater velocity, porosity, and grain size. Nonetheless, high deviations of model outcomes occurred in response to variability in porosity and grain size when using 10-times of the lowest (S_max, k_a) data set as initial input conditions (Figure S11). This is because S_max and k_a were small enough, and their influence on the variability of RP was minimal (all RPs were predicted to be hyperexponential).

Figure 5.

Simulated retention profiles using the lowest maximum solid-phase retention capacity on solid-phase (S_max) and first-order attachment rate coefficient (k_a) data set (0.406E-01 cm³ g⁻¹, 0.133E+00 min⁻¹) at varying velocities (0.00441, 0.0441, 0.441, and 4.41 cm min⁻¹, with porosity of 0.34 and grain size of 360-μm; a), porosities (0.24, 0.34, 0.44, and 0.54, with Darcy velocity of 0.441 cm min⁻¹ and grain size of 360-μm; b), and grain sizes (210-, 360-, 510-, 660-, and 810-μm, with porosity of 0.34 and Darcy velocity of 0.441 cm min⁻¹; c) in 500-cm long sand columns using the best model (M4) via forward simulation. Parameters for the forward simulations were obtained from the M4 via inverse-fitting, as shown in SI S5–S7. Note different y-axis scales in the figures.

ENVIRONMENTAL IMPLICATIONS

Our findings address the knowledge gap regarding the importance of environmentally-relevant physicochemical factors (mono- and di-valent electrolytes, NOM, flow velocity, porosity, and grain size) on the transport of the ‘new-horizon’ multifunctional RGO—metal oxide nanohybrids in the subsurface. One of our crucial findings is that, the mobility of RGO—metal oxide nanohybrids can be explained by DLVO theory and OSKRM featuring time- and depth-dependent retention (M4). There is, consequently, no urgent need to develop fundamentally new theories for describing the mobility of nanohybrids (e.g., for CNT-³⁵ and RGO-based metal oxide nanohybrids transport in sand-packed columns) at the current stage. In line with the important findings of Goldberg et al.,⁶⁴ more complicated models do not necessarily perform better than simpler ones due to over-parameterization; and physical meanings of fitted-parameters are pivotal for model selection. Numerical simulations highlight the importance of S_max and k_a for delineating and predicting the mobility of nanohybrids (e.g., evolution between hyperexponential and “L-type” RPs). Model sensitivity analyses indicate that compared with porosity and grain size, flow velocity has a greater influence on nanohybrids’ mobility due to its larger impact on S_max and k_a. Therefore, S_max and k_a are highly recommended to be quantified in future studies for accurately assessing the mobility of colloids/NMs/nanohybrids or more sophisticated nanoheteroassemblies in the subsurface.

The mobility of RGO—metal oxide nanohybrids is lower than that of parent RGO NMs since high pH_PZC metal oxides neutralize the negative ζ-potential and increase the aggregation of nanohybrids. For example, while the source of RGO was different, the mobility of our RGO-TiO₂ and RGO-ZnO nanohybrids (M_eff≤2.4%; Table 1) was significantly lower than that of RGO NMs (M_eff≥80%)^{76, 77} under similar transport conditions (in 10 mM NaCl without SRHA). Subsurface environment (soil and aquifer sediment) intrinsically exhibits more favorable retention site (larger S_max and k_a) than that of cleaned sand used here. Therefore, the potential environmental risks associated with the mobility of RGO—metal oxide nanohybrids in the subsurface would be low, which is partially reflected by the fact of ≥97.6% retention (M_ret; Table 1) of RGO-TiO₂ and RGO-ZnO nanohybrids in sand-column experiments (no SRHA). Nevertheless, environmentally-representative concentrations of NOM (1–5 mg C/L SRHA) substantially enhance the nanohybrids’ mobility. This is particularly true in the presence of a minute amount of organic solvent (~0.08% v/v acetone). Consequently, the potential adverse impacts and risks of RGO—metal oxide nanohybrids would be appreciable in contaminated sites rich in organic chemicals; and the role of organic chemicals on nanohybrids’ mobility should be included explicitly into the framework of environmental risk assessment and management for NMs.⁷⁸ While organic solvent dominates nanohybrids’ mobility, other factors such as loading capacity of metal oxides also play an appreciable role. Future efforts are needed to unravel the effect of loading capacity of metal oxides on the fate and transport of nanohybrids. Further, the Hamaker constant should be experimentally determined to accurately quantify how DLVO theory describes the colloidal stability and transport of nanohybrids in the aquatic environments.