Engineered Quartz and Kaolinite Nanoparticles in Biomedical and Reservoir Fluids: Quantifying Aggregation Behavior in Saline Water with Surfactants

Abstract

In this study, two nanoparticles (NPs) (kaolinite NP of 9 crystal units (9­[Al₂Si₂O₅(OH)₄]) and quartz NP of 18 units (18­[Si₃O₆])) are engineered based on the established crystal unit cell data. The aggregation behavior of NPs in saline water with a nonionic PEG-alkane surfactant (C12E3) is simulated by molecular dynamics (MD) simulations. The simulation shows a helix aggregation of quartz NPs and layer formation (surface-to-surface, surface-to-site, surface deformation) of kaolinite NPs. The simulation also shows a relatively faster aggregation of C12E3 into a spherical micelle, whereas the anionic sodium dodecyl sulfate (SDS) and cationic cetyltrimethylammonium bromide (CTAB) form more complex rod-, funnel-, and slab-like clusters. The proposed kaolinite and quartz NPs have essential colloidal and interfacial properties for simulating reservoir or biomedical fluids with drugs, surfactants, or lipids. The NP design approach in this study can be easily adopted for any desired NPs for drug encapsulation and delivery or enhanced oil recovery (EOR).

1. Introduction

The application of nanoparticles (NPs) in reservoirs or biomedical fluids is well recognized, and the development of nanotechnology is an active area of research. Nanofluids (fluids with NPs) have been used in enhanced oil recovery (EOR) methods, such as chemical, thermal, miscible, polymer, and microbiological flooding. Crystal NPs are recommended for use in drilling fluids, wastewater treatment, and altering interfacial tension (IFT). Kaolinite NPs are recognized as potential drug delivery vehicles due to their strong biocompatibility, high surface area, and layered structure, which allow for encapsulating poorly soluble drugs (i.e., chemotherapy drugs doxorubicin and paclitaxel). NPs can be synthesized and modified to obtain the desired properties for biomedical applications (such as drug encapsulation and delivery or optical imaging). Engineered NPs with surfactants can uniquely enhance drug delivery by encapsulating both hydrophilic and hydrophobic drugs or by optimizing EOR by lowering the IFT. In this study, two NPs (quartz and kaolinite) were built by utilizing the crystal unit cell data, and the engineering aspects (colloidal and interfacial properties) of the NP in saline water with surfactants were quantified. A comprehensive review of the related literature and the potential impact of this research study on kaolinite and quartz NPs in drug delivery or EOR is provided.

The adsorption of nonionic surfactants in water was diffusion-controlled. For ionic surfactants, the surface potential can act as an adsorption barrier as they attempt to accumulate at the interface. The addition of salt to the system reversed the process back to diffusion-controlled due to the electrostatic potential in the presence of the added electrolyte. − In a hydrocarbon/brine system with a nonionic surfactant, salt can be depleted near the interface, subsequently disrupting the hydrogen bonding network in water. In contrast, ionic surfactants form a charged monolayer at the interface and subsequently restore the network. IFT at equilibrium is a function of the surface excess concentration, which is related to the bulk concentration of surfactants or polymers through the well-known Gibbs adsorption equation. Serrano-Saldaña et al. measured the IFT of nC12 (n-dodecane) vs water at different SDS and NaCl concentrations. They showed minimum IFT at the critical micelle concentration (CMC) of SDS, which remained unchanged with the addition of SDS. Deshiikan et al. investigated the changes in IFT of nC12–water with surfactants SDS, CTAB, and salt concentrations. The changes in IFT in their analysis were claimed to be primarily caused by changes in the concentration of the species making up the interface. The diffusion of surfactant from the bulk to the interface and its subsequent adsorption was assumed to be the cause of variation in IFT over time.

Clay and silica particles are widely present in reservoir pore water and interact with surfactants. Surfactant molecules have hydrophilic/hydrophobic moieties and are adsorbed onto solid surfaces to a significant extent, even at very low concentrations. − The adsorption of surfactants on reservoir rocks changes a variety of interfacial phenomena, such as wetting behavior (oil displacement, flotation) and colloid stability (dispersion, flocculation). Synthesized NPs with surfactants can be used for industrial applications (such as NPs as sensors, enhanced oil recovery agents, , stabilizing oil-in-water emulsions, , and drilling fluid additives). Regarding colloidal stability in reservoir fluids, Rezvani et al. studied nanoparticle–surfactant mixtures in calcite-rich reservoirs. The surfactant–nanoparticle blend showed pH-responsive behavior at the solid–fluid and fluid–fluid interfaces with particles serving as carriers, resulting in varying degrees of rock wettability alteration and emulsification. Cationic surfactants exhibit better flocculation over a wide pH range, and their adsorption can reduce the electrostatic repulsive force between kaolinite NPs. The forces between NPs were studied using the expanded DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory to understand the aggregation mechanism. The kaolinite electric double layer caused by the addition of salt reduces the electrostatic repulsive force and facilitates kaolinite aggregation. Kaolinite edge adsorption sites were found to be more active at the lowest matric potential than their basal surfaces due to the protonation and deprotonation processes of the dangling oxygen.

Clay particles have versatile properties, including high adsorption and ion exchange capacity, colloid and thixotropy, chemical inertness, swelling properties, and unique drug release behaviors from the drug–clay nanohybrids. Several papers have provided a comprehensive review of the recent developments in clay mineral research, focusing on their application for the delivery and sustained release of biologically active species. − Peixoto et al. showed that some multilayered minerals can be used as nanocarriers (with a typical drug load of 1–10 wt %) for a wide range of anticancer drugs to the tumor site and sustained controlled release. Kaolinite and its derivatives have been considered as promising materials in many biomedical areas, such as drug and protein delivery, based on their high interaction capacities with organic and biochemical molecules, bioadhesion, and cellular uptake. Liu et al. studied the aggregation behavior of kaolinite particles with different surfactants using fractal dimension analysis, adsorption test, infrared spectroscopy analysis, and ζ-potential measurements. Their results showed that accelerated aggregation occurred in the presence of cationic surfactants compared to that in the presence of anionic and nonionic surfactants. The micellization of cationic and anionic surfactants drives synergistic interactions, where the electrostatic attraction between the oppositely charged head groups leads to a significantly lower CMC and the formation of versatile catanionic structures (such as vesicles, worm-like micelles, coacervates). , Surfactants can make NP highly hydrophobic by forming a monolayer below the CMC or hydrophilic by a bilayer above the CMC. The adsorption of surfactant molecules can enhance the steric hindrance and electrostatic repulsion between kaolinite NPs, helping to keep them dispersed in suspension. Miyazawa et al. provided a critical review on surfactant-coated nanoparticles in nanomedicine and food nanotechnology.

Silica is an amorphous polymerized material that is produced from Si­(OH)₄. The polymerization of monomeric silicic acid to form larger silica particles follows various condensation reactions with dimers, oligomers, and aggregates. Silicas in biological systems show a narrow particle size distribution for specific structural motifs. Modeling the interactions of biomolecules with nanomaterials is crucial for ensuring the biocompatibility and potential biomedical applications of new nanomaterials. , Regarding surfactants for nanomaterial solubilization, Al-Ghamdi et al. conducted experiments on sennoside A (dianthrone glycoside) and sennoside A-capped silver NPs (Ag/sennoside A) with surfactant CTAB. UV–visible data showed that the optical properties (absorption peaks of sennoside A) of the resulting NPs were dominated by sennoside A, which formed the J-type of aggregates. Regarding surfactant–drug interactions/binding, Zaheer et al. showed through spectroscopic studies that flurbiprofen fluorescence was quenched significantly and formed a complex with gemini surfactants (according to the chain length and CMC).

Colloidal-sized nanoaggregation is a characteristic property of surfactants that occurs at a specific concentration. Dai and Luo studied molecular self-assembly at water–trichloroethylene (TCE) interfaces containing hydrocarbon nanoparticles and surfactant SDS. They showed that the interfacial properties (such as the interfacial thickness and IFT) were significantly influenced by the presence of surfactants, but not by the nanoparticles. They also showed that surfactants can aggregate along the water–TCE interfaces with and without the presence of nanoparticles. Their argument was that the self-assembly of surfactant molecules or polymers at liquid–liquid interfaces was essential in the preparation and stabilization of conventional emulsions. Surfactant interfacial self-assembly can be critical in numerous processes, such as lubrication, detergency, biological transfer, and polymer processing. Sammalkorpi et al. simulated the structural transition of SDS aggregates in water. They observed that, in aqueous solutions at higher CMC, surfactants formed insoluble crystals at low temperatures (below the critical micellization temperature) and micelles at elevated temperatures (above the critical micellization temperature). The micellization of common surfactants or lipids (such as SDS and dodecylphosphocholine (DPC)) in water was studied by molecular dynamics (MD) simulations. , Lipid-based nanocarriers (liposomes, nanoparticles) have significant potential for drug delivery. NPs interact with membrane lipids via electrostatic interactions and hydrogen bonding. Computational simulations using all-atom (AA) or coarse-grained (CG) models have shown that silica NPs stabilize lipid bilayers (as silica–lipid hybrid structures), which can enhance drug delivery by increasing cellular uptake. ,

In this study, the following two NPs are engineered by utilizing the established crystal unit cell data: kaolinite NP of 9 crystal units 9­[Al₂Si₂O₅(OH)₄] and quartz NP of 18 units 18­[Si₃O₆]. The engineering aspects of the NP (i.e., mobility, aggregation, structural conformation) are simulated in saline water with the nonionic PEG-alkane surfactant (C12E3). Section presents the atomic structures and force field topology of the kaolinite and quartz NPs. The physical structures (such as bond lengths and bond angles) of the NPs are refined through energy minimization and MD production simulation. Process simulation models are set up for quantifying engineered aspects of the NP in saline water with surfactants. Section analyzes the mobility, adsorption, and aggregation dynamics of the surfactants and NPs. The study concludes that the proposed quartz and kaolinite NPs have the essential colloidal and interfacial properties and can be used to simulate reservoir fluids or pharmaceuticals and biomedicines (such as biochemistry simulations with drugs, lipids, or proteins).

2. Nanoparticle Design Methods

This study develops two NPs (quartz and kaolinite) based on the established crystal unit cell data. NPs have representative colloidal and interfacial properties for simulating macroscopic emerging behaviors when interacting with surfactants, lipids, or drugs. The Methods section presents the atomic structures and force field topology of the NPs and the engineered aspects of the simulation strategy with surfactants. The GROMACS simulation package is employed for all molecular dynamics simulations.

2.1. Atomic Structures and Bonded Topology

For biomedical applications, the overall dimension (such as shape, surface area) of the NPs and their basic crystallographic properties are important considerations. The following two NPs were selected in this study: 9 unit cell kaolinite NPs and 18 unit cell quartz NPs. The specific volumes sufficiently represent the real-world mineral behavior in reservoirs or biomedical applications. The atomic coordinates of the NP are defined based on the established crystal unit cell data. All bonds and angles are calculated and set up in the bonded topology with the correct initial conditions. A computer program written in our earlier works , is employed to build the atomic coordinates and bonded topology files in the GROMACS format. The computational algorithm (bonds, angles, dihedrals), atomic coordinates, and force field parameters are provided in Supporting Information (S3).

The bonded structures (kaolinite NP of 9 crystal units (9­[Al₂Si₂O₅(OH)₄]) and quartz NP of 18 units (18­[Si₃O₆])) are optimized using an energy minimization simulation. Harmonic and G96 cosine potentials are applied for bond stretching and bond angle rotation, respectively. The Ryckaert–Bellemans option is chosen for the dihedrals (torsion angles). The force constants are refined against other available force field data. The ClayFF force field, parametrized to model clays and clay-like minerals, was recommended to simulate hydrated materials, including hydroxides and oxyhydroxides, in which interatomic interactions should be treated as nonbonded. Underwood et al. used ClayFF to simulate the montmorillonite clay and organic interactions in saltwater. The objective of this study is to set up NP force fields that are consistent with ClayFF and reliable when simulating a complex biological system.

2.1.1. Kaolinite NP

The kaolinite clay minerals considered in this study are widely encountered in industrial processes, ranging from ceramics manufacturing, oil exploration and production, and tailing ponds to nuclear waste management. The kaolinite crystals have been studied extensively using infrared (IR) and Fourier transform Raman spectroscopy (FFRS). − The kaolinite unit cell lattice parameters, atomic positions, surface properties, and interlayer hydrogen bonds have been analyzed by many researchers. This study utilizes the published experimental observations and idealizations as a starting point to design kaolinite NPs (Figure ).

1.

Kaolinite physical model showing atomic bonding: (a) 9 unit cells of kaolinite NP (k-NP) (bonds with Al are not shown), (b) unit cell Al₂Si₂O₅(OH)₄ (O1, O2apical oxygen, O3, O4, O5bridging oxygen, OH1, OH2, OH3interlayer hydroxide, OH4inner-layer hydroxide).

The kaolinite NP in Figure is composed of 9 unit cells of Al₂Si₂O₅(OH)₄ (unit cell molecular mass of 258.149 g/mol). The overall sizes of this NP are 1.890, 2.501, and 0.693 nm in the x, y, and z directions, respectively (model coordinates). This is a 1:1 layer clay mineral composed of an aluminum octahedral sheet, Al₂(OH)₄, and a silicon tetrahedral sheet, Si₂O₅, with pseudohexagonal symmetry. Interlayer hydroxide groups extend from the octahedral sheet into the interlayer region, where they form hydrogen bonds with the basal oxygen of the opposing tetrahedral silicate sheet.

For validation of the NP, atomic conformational changes (such as bond stretching and angle rotation) in the water bath are studied using energy minimization and MD production runs. In order to avoid undercoordinated atoms at the edges, only the center unit cell is probed to study the bond stretching and angle rotation statistics. Table summarizes the initial atomic bonds and angles (experimental observations and idealizations) and the values refined by the energy minimization and MD production runs (averaged over all trajectories). The results show two sets of coordination: six Si–O bonds, three Al–O, and five Al–OH within the cell, and another four Si–O, two Al–O, and three Al–OH (identified as i, j, k, l) cell-to-cell coordination. There are 16 bond angles within the cell and 7 angles for cell-to-cell coordination. The results show some variations in the bonds and angles between the energy minimization and production runs. The variations in the bond contraction/expansion and angle rotations during the production runs agree with some experimental idealizations and are well within the expected theoretical predictions.

1. Bonds and Angles Statistics of the Kaolinite NP.

atomic bond (nm)	initial crystal	min. energy	MD production	atomic angle (deg)	initial crystal	min. energy	MD production
Si1–O1	0.1559	0.1614	0.1621(±0.0011)	O1–Si1–O3	113.044	108.805	110.455(±1.217)
Si1–O3	0.1800	0.1655	0.1639(±0.0010)	O1–Si1–O4	110.956	109.435	109.331(±1.493)
Si1–O4	0.1727	0.1660	0.1648(±0.0005)	O1–Al1–O2	107.401	104.869	104.193(±1.085)
Si2–O2	0.1562	0.1619	0.1620(±0.0017)	O1–Al1–OH1	83.131	74.724	74.328(±0.439)
Si2–O4	0.1764	0.1656	0.1639(±0.0023)	O1–Al1-OH2	171.349	176.556	173.787(±1.409)
Si2–O5	0.1794	0.1641	0.1637(±0.0005)	O2-Al2–OH2	63.935	72.254	72.174(±0.529)
O3–Si2(i)	0.1774	0.1654	0.1639(±0.0015)	O2–Al2-OH3	168.124	175.376	173.418(±0.702)
O5–Si1(j)	0.1784	0.1641	0.1620(±0.0012)	O2–Al2–OH4	107.553	107.817	109.114(±0.698)
Si1–O5(k)	0.1771	0.1641	0.1621(±0.0020)	Al1–O2–Al2	112.367	104.580	105.073(±0.505)
Si2–O3(l)	0.1784	0.1648	0.1641(±0.0016)	Al1–O2–Si2	105.104	107.911	108.032(±1.067)
Al1–O1	0.1991	0.1944	0.1956(±0.0007)	Al1–O1–Si1	102.042	109.677	109.404(±1.441)
Al1–O2	0.1930	0.1944	0.1947(±0.0009)	Al2–O2–Si2	106.594	110.913	109.067(±1.714)
Al1–OH1	0.1928	0.1888	0.1882(±0.0010)	Si1–O4–Si2	133.786	124.431	121.544(±1.163)
Al1–OH2	0.1853	0.1872	0.1891(±0.0016)	OH1–Al1–OH2	104.336	107.734	108.711(±1.768)
Al2–O2	0.1936	0.1952	0.1956(±0.0012)	O3–Si1–O4	101.774	111.106	108.748(±0.295)
Al2–OH2	0.1897	0.1877	0.1891(±0.0019)	OH3–Al2–OH4	82.829	72.179	70.377(±1.259)
Al2–OH3	0.1962	0.1880	0.1875(±0.0018)	Si1–O3–Si2(i)	136.093	124.068	120.659(±0.555)
Al2–OH4	0.1984	0.1906	0.1899(±0.0017)	Si1–O1–Al2(i)	104.027	107.155	106.352(±0.315)
O1–Al2(i)	0.1980	0.1946	0.1935(±0.0021)	Si2–O5–Si1(j)	138.647	122.391	119.533(±1.488)
Al2–O1(l)	0.2070	0.1934	0.1937(±0.0008)	Al1–O1–Al2(i)	123.141	108.452	108.031(±0.983)
Al2–OH1(j)	0.1920	0.1889	0.1895(±0.0014)	Al1–OH1–Al2(k)	130.705	113.599	112.652(±0.732)
Al1–OH3(i)	0.1957	0.1887	0.1890(±0.0008)	Al2–OH4–Al1(j)	118.533	110.995	111.145(±0.669)
Al1–OH4(k)	0.2041	0.1912	0.1907(±0.0018)	Al2–OH3–Al1(l)	131.556	113.826	114.905(±0.614)
OH1–H1	0.1004	0.0976	0.0986(±0.0027)
OH2–H2	0.1012	0.0976	0.0982(±0.0015)
OH3–H3	0.1002	0.0978	0.0987(±0.0022)
OH4–H4	0.1018	0.0991	0.1010(±0.0034)

^aBased on the physical model built in this study using published crystal experimental data.

2.1.2. Quartz NP

The quartz NP (Figure ) used in this study is composed of 18 α-quartz unit cells, Si₃O₆ (unit cell molecular mass of 180.236 g/mol). The overall dimensions of this rhombus-shaped NP are 1.385, 1.530, and 1.114 nm in the x, y, and z directions, respectively. The surface characteristics can be described as follows: opposite faces normal to the x and y directions are oxygen and silicon exposed, faces normal to the z direction are identical, and oxygen-dominated. This quartz NP consists of corner-sharing tetrahedra, SiO₄, where Si is bonded to four oxygens, and each oxygen atom is coordinated in two separate tetrahedra. It should be noted that, in the quartz crystal lattice, the pyramidal building blocks are arranged in the form of conjoined helices, all pointing in a single direction, known as the optical direction. The structure is acentric, so it exists in right- and left-handed enantiomorphs. The crystal has a hexagonal structure with a space group of P3121 (right-handed) or P3221 (left-handed). This inherent property has some interesting consequences for the aggregation dynamics of quartz NP in saline water.

2.

Quartz physical model atomic bonding: (a) 18 unit cell quartz NP (q-NP) (showing undercoordinated atoms for layers 1 and 2; Si<,O‑ indicates layer 2 with 2 bonds available for Si and 1 for O), and (b) unit cell Si₃O₆ (functional charge group SiO₂).

The bond contraction/expansion and angle rotation of the quartz NP are analyzed for energy minimization and production run trajectories. Energy minimization is a common practice to correct atomic positions, X-ray diffraction patterns, and vibrational density of states. Table presents the calculated lattice parameters, bond lengths, and Si–O–Si bond angles for the unit cell. The seven Si–O bonds listed have slightly different bond lengths. All Si–O–Si angles are symmetry equivalents, but there are five different O–Si–O angles, which are all very close to the ideal tetrahedral value of 109.451°, and two O–Si–O angles are slightly higher than the tetrahedral value. The two Si–O–Si angles show the most noticeable deviations from their initial values. The atomic coordinates and bonded topology are defined by utilizing the established α-quartz unit cell data.

2. Bond and Angle Statistics of the Quartz NP.

atomic bond (nm)	initial crystal	min. energy	MD production	atomic angle (deg)	initial crystal	min. energy	MD production
Si1–O1	0.1586	0.1620	0.1627(±0.0015)	O1–Si1–O2	110.748	110.897	108.622(±1.211)
Si1–O2	0.1716	0.1616	0.1624(±0.0015)	O3–Si2–O4	103.666	110.602	110.184(±1.500)
Si2–O3	0.1722	0.1617	0.1617(±0.0015)	O5–Si3–O6	104.641	111.174	111.451(±1.715)
Si2–O4	0.1628	0.1626	0.1620(±0.0013)	O1–Si3–O3	103.351	108.878	109.780(±1.300)
Si3–O5	0.1595	0.1624	0.1615(±0.0001)	O1–Si3–O5	109.551	108.730	110.295(±1.000)
Si3–O6	0.1771	0.1621	0.1625(±0.0005)	O1–Si3–O6	113.069	108.745	108.773(±1.540)
Si3–O1	0.1614	0.1633	0.1629(±0.0005)	O3–Si3–O5	110.609	109.639	108.875(±1.050)
Si3–O3	0.1716	0.1621	0.1622(±0.0005)	O3–Si3–O6	111.012	109.631	107.175(±2.000)
				Si1–O1–Si3	140.684	153.324	154.617(±0.684)
				Si2–O3–Si3	146.348	153.941	151.921(±1.500)

^aBased on the α-quartz unit cell coordinate data from the literature.

2.2. Nonbonded Interaction Parameters

The atomistic nonbonded parameters (e.g., atomic mass, sigma, and epsilon) in Table are consistent with those of ClayFF and OPLS/AA. The Lennard-Jones (LJ) and Coulomb potential parameters for the kaolinite NP, quartz NP, and surfactants are defined based on published data. , The LJ potential energies for these atoms as a function of separation distance, r, are shown in Figure . In the MD simulation, a geometric average option is used to construct the nonbonded LJ parameter matrix. The nonbonded potential is modified by a shift function in order to improve the cutoff effects.

3. LJ Potential Parameters for Atoms in the Kaolinite and Quartz Nanoparticles.

model atom	molecular mass	σ (nm)	ε (kJ/mol)
Si1, Si2	28.080	0.3385	2.4470
Al1, Al2	26.981	0.3275	2.1470
O1, O2	15.9994	0.3118	0.8368
O3, O4, O5	15.9994	0.3000	0.7112
OH1, OH2, OH3	15.9994	0.3200	1.0460
OH4	15.9994	0.3070	0.7112

3.

LJ potential, V _LJ, as a function of the separation distance between atoms of the kaolinite and quartz NPs.

2.2.1. Simulation Parameters

Each simulation system is initialized with an energy minimization run to reduce the excessive forces on any atom. This is accomplished using a steepest descent algorithm, with convergence achieved once the maximum force on any atom is less than 100 kJ mol^–1 nm^–1. After initialization, NPT simulations are performed using the Berendsen barostat and Berendsen thermostat with coupling time constants of 1.0 and 0.1 ps, respectively. A grid-based twin-range cutoff for nonbonded interactions of 1.0/1.0 nm is used with a time step of 2 fs and a neighbor list update every 10th step. The full particle-mesh Ewald method is employed for long-range electrostatic interactions with a cubic interpolation order of 4 and a grid spacing of 0.16 for the FFT. The Verlet cutoff scheme is employed using the default Verlet buffer size set to 0.005 kJ/mol/ps energy drift per atom.

2.3. Engineered Aspects Simulation

This section presents the molecular structures of three well-known surfactants and several MD process models for quantifying the engineered aspects of NPs in saline water. The colloidal and interfacial properties of quartz and kaolinite NPs are evaluated by analyzing the aggregation process, radius of gyration, and hydrogen bonding. The process simulation justifies the proposed NP for simulating reservoirs or biomedical fluids with drugs, surfactants, or lipids.

2.3.1. Surfactant Selection

For the MD process simulations, nonionic (C12E3) and ionic (SDS, CTAB) surfactants are selected. The surfactant C12E3 here is a nonionic triethylene glycol dodecyl ether. It has a block copolymer topology given by CH₃(CH₂) _y−1(CH₂CH₂O) _x OH, where x (=3) represents the number of ethylene glycol units and y (=12) represents the number of carbons in the alkane block. The bulky head linear PEG-alkane surfactant is a particularly good candidate for a generic study because of its efficiency and effectiveness at lowering the oil–water interfacial tension. The other two ionic surfactants are widely used in laboratory and field studies. The anionic sodium dodecyl sulfate (SDS, [CH₃(CH₂)₁₁(SO₄)]⁻[Na]⁺) and cationic cetyltrimethylammonium bromide (CTAB, [CH₃(CH₂)₁₅N­(CH₃)₃]⁺[Br]⁻) are both readily soluble in water, and the partition coefficient in toluene was measured to be zero at a pH of 7. The head groups [OSO₃Na] of 12-carbon-tail SDS and [N­(CH₃)₃Br] of 16-carbon-tail CTAB are nearly spherical.

2.3.2. Process Simulation Setup

MD process simulation is presented step by step and justifies the aggregation dynamics of the nanoparticles (kaolinite NP of 9 crystal units (9­[Al₂Si₂O₅(OH)₄]) and quartz NP of 18 units (18­[Si₃O₆])). The first important task is to set up a representative process simulation model (such as model composition for reservoir fluids charged with electrolytes, surfactants, clay minerals, and silica particles). Two separate process models are set up for the kaolinite and quartz NPs. Each model contains 8 NPs and 60 C12E3 surfactants in SPC water at several salt concentrations (salinity varies from fresh to seawater). Table summarizes the selected cases and model compositions (salinity status, number of molecules). These are aqueous solutions with salinities varying from 0.0 to 32 ppt containing 8 NPs (quartz or kaolinite) and 60 surfactant molecules. The cases are classified as 1a and 1b in the absence of NP, 2a to 2d with quartz NP, and 3a to 3d with kaolinite NP. Each case is first initialized with an energy minimization run. NPT (constant number of particles, pressure, and temperature ensemble) production simulation is then performed until equilibrium is reached. C12E3 has a hydrophobic affinity comparable to that of lipid dodecylphosphocholine (DPC). C12E3 and DPC are both nonionic surfactants with bulky heads. The 60 C12E3 in this study and 54 DPC in SPC water , are analogous, representing a single spherical micelle. The CMC value of C12E3 is about 7.50 × 10^–3 M.

4. Process Model Composition and Component Physical Properties.

MD system	salinity (ppt)	quartz NP 18[Si3O6]	kaolinite NP 9[Al2Si2O5(OH)4]	C12E3 surfactant CH3(CH2)11(OC2H4)3OH	H2O SPC	ions Na+/Cl–
1a	0			60	24,603	0/0
1b	32			60	24,363	120/120
2a	0	8		60	24,603	0
2b	11	8		60	24,523	40/40
2c	21	8		60	24,443	80/80
2d	32	8		60	24,363	120/120
3a	0		8	60	24,603	0
3b	11		8	60	24,523	40/40
3c	21		8	60	24,443	80/80
3d	32		8	60	24,363	120/120

3. Results and Discussion

The following variables are analyzed over the MD trajectories: density, potential energy, mean-square displacement, radial distribution functions, gyration radius, and hydrogen bonding statistics. MD trajectories over the first 1.0 ns period are discarded from the analysis, as it is assumed to be the user induction phase. The basic properties (aggregation, diffusivity, IFT) of the surfactants are simulated in bulk SPC water and hydrocarbon systems (provided in Supporting Information S1).

3.1. Surfactants Dynamics Analysis

MD process models quantify the aggregation dynamics and structural transitions of surfactants. The self-assembling aggregation kinetics of C12E3 are observed to be the dominant mechanism due to its strong hydrophobic affinity. A rapid aggregation of the C12E3 molecules into a single spherical micelle was observed. The aggregation structural transitions for SDS and CTAB are more complex with rod-, funnel-, and slab-like clusters of different sizes during the evolution process.

The evolution of the potential energy, surfactant diffusion, and interfacial tension (IFT) is analyzed using an exponential decay relaxation function. The effect of temperature on the surfactant diffusivity and oil–water IFT is in excellent agreement with some published data. The equilibrium diffusion constants for the three cases at temperatures of 278.15, 293.15, 313.15, and 333.15 K are shown on the Arrhenius plot in Figure . As discussed earlier, a relaxation test is performed to obtain the equilibrium diffusion constants. The statistical variation in the predicted diffusion constants is less than 1%. Deshiikan et al. reported two sets of diffusivity data for SDS and CTAB based on their dodecane–water interface experiments at varying surfactant concentrations. For SDS, the diffusivity varies from 2.242 × 10^–6 to 5.849 × 10^–8 cm²/s. For CTAB, the diffusivity varies from 1.082 × 10^–5 to 1.492 × 10^–8 cm²/s. Our predicted diffusivity values for SDS and CTAB in nbC10-water are well within the reported range.

4.

C12E3, SDS, and CTAB diffusion constants vs temperatures on an Arrhenius plot.

Supplementary simulations are conducted to quantify the surfactant aggregation and adsorption kinetics in a biphasic (oil–water) system (Supporting Information S1.3). The effect of surfactants on oil/water IFT shows good agreement with some experimental data. The supplementary results provide a general reliability of the proposed MD approach for simulating quartz and kaolinite NPs in aqueous solutions with surfactants or lipids.

Table summarizes the predicted basic properties (density and diffusion) of the three classes of MD systems at temperatures of 293.15 and 333.15 K. The predictions are based on the MD trajectories over the final 50 to 60 ns simulation periods. These simulations may be continued for longer periods in order to further refine these properties (diffusion, adsorption, and aggregation). Theoretical and experimental observations support the existence of some highly localized slow-evolving processes (such as unsettled molecular orientation) in complex multicomponent systems.

5. Summary of the Basic Bulk Equilibrium Properties: (1) Base Case (in the Absence of NP), (2) Quartz NP, and (3) Kaolinite NP.

MD systems	salinity (ppt)	density (kg/m3)	C12E3 diffusion coefficient × 10–6 (cm2/s)
T = 333.15 K
1a	0	949.887(±0.082)	3.585(±0.259)
1b	32	960.352(±0.075)	3.319(±0.126)
2a	0	979.059(±0.058)	5.576(±0.302)
2d	32	989.186(±0.120)	4.406(±0.187)
3a	0	986.032(±0.158)	5.045(±0.595)
3d	32	996.352(±0.095)	3.363(±0.217)
T = 293.15 K
2a	0	1013.008(±0.058)	1.632(±0.657)
2b	11	1016.564(±0.100)	1.654(±0.827)
2c	21	1020.084(±0.074)	1.851(±0.667)
2d	32	1023.578(±0.128)	1.836(±0.151)
3a	0	1016.766(±0.200)	1.569(±0.990)
3b	11	1019.694(±0.066)	1.521(±0.348)
3c	21	1023.082(±0.100)	1.117(±0.818)
3d	32	1026.188(±0.092)	1.377(±0.510)

The effects of salinity and temperature on the density and diffusion in Table are known general trends. The simulation results can be summarized as follows: (1) the linear decline in the potential energy with increasing salinity is directly correlated with the linear increase in density. The density and energy levels of the kaolinite systems are slightly higher than those of the quartz systems. (2) There are some noticeable variations in the C12E3 diffusivity. This is mainly attributed to the adsorption and aggregation of C12E3 and NP mobility. The mean-square displacement analysis shows that the mobility of C12E3 and NP is strongly correlated. At a higher temperature of 333.15 K, the C12E3 diffusion coefficients decreased slightly at higher salinities. Such a reduction is not noticeable in the simulations at a lower temperature of 293.15 K. Earlier studies , have shown a similar correlation between the diffusion coefficients and the temperature in reservoir fluids. Next, a comprehensive analysis of the predicted bulk properties (density, potential energy) in Section and surfactant and NP aggregations (C12E3, quartz NP, kaolinite NP) in Section is discussed.

3.2. Time Evolution: Bulk Properties

For any effective application of NPs (such as drug administration), it is vitally important to know the initial higher energy state and the rate at which the system decays to a lower energy state. In order to quantify such an earlier transient phase, this study presents an analysis option in this section (Figures , , and ).

5.

Effect of salinity on the equilibrium evolution of quartz NP/C12E3 systems. Markers with fitted lines: potential energy. Dotted lines: density.

6.

Effect of salinity on the equilibrium evolution of kaolinite NP/C12E3 systems. Markers with fitted lines: potential energy. Dotted lines: density.

7.

Equilibrium evolution of the base case (1b) in the absence of NP, quartz NP (2d), and kaolinite NP (3d). Markers with fitted lines: potential energy. Dotted lines: density.

As mentioned earlier, the NPT production run is conducted for 61 ns, of which 1.0 ns is regarded as an initial user-induced (external disturbances) phase. The simulation trajectories at 1.0 ns are assumed to be the initial state, where the system pressure, temperature, and density are stabilized. The density and potential energy (sum of all LJ, Coulomb, and bonded energies) over every 2.0 ns simulation trajectory are predicted using the GROMACS analysis program “g_energy”.

The changes in the densities and potential energies at a temperature of 293.15 K for quartz NP and kaolinite NP are shown in Figures and , respectively. The time evolution of the quartz and kaolinite cases at a temperature of 333.15 K is compared with that of the base case (in the absence of NP) in Figure . The potential energy for each model system is normalized with the corresponding initial values and plotted in the same graph in order to quantify the relative variations. In order to characterize system relaxation, the following simple exponential decay function is fitted with the predicted data points as follows: U ­(t) = U̅ _e + (U̅ ₀ – U̅ _e) exp­(−t/τ), where τ is the relaxation time and U̅ ₀ and U̅ _e are the normalized initial and equilibrium potential energies, respectively.

The evolution of the kaolinite systems is more complex and very transient compared to that of the quartz systems. The plots illustrate the significant expansion/contraction behaviors of the kaolinite systems. The fluctuations in the potential energy appear to be strongly correlated with the density fluctuations. Interestingly, a drastic change in the potential energy near 12 ns is observed for all kaolinite cases. The first declining phase is likely due to the rearrangement of the initial water molecules (as a box initially filled with SPC water using the GROMACS program “genbox”) on the octahedral and tetrahedral surfaces of the kaolinite NP. The octahedral and tetrahedral surfaces of the kaolinite layer have different chemical natures and can be considered as hydrophilic and hydrophobic, respectively. On the octahedral side, the water layer forms relatively strong hydrogen bonds with the surface hydroxyl groups. On the other hand, the water molecules on the tetrahedral surface have the tendency to aggregate and form hydrogen bonds among themselves. Only weak hydrogen bonds with the basal oxygen atoms of the tetrahedral surface are formed.

The second drastic increase and subsequent decay phase can be described by the aggregation of dispersed kaolinite NP and the dynamics of the hydrogen bonds. The drastic increase of the energy curves is likely due to an increase in the system volume by displacing water molecules with the rapid stacking of kaolinite NP. In order to capture this drastic increase and decrease in the energy near 12 ns, quantitative structural changes (e.g., spatial distribution of kaolinite NPs and surfactants) are analyzed for simulation trajectories at every nanosecond over a 20 ns run. The spatial distribution analysis showed rapid aggregation of kaolinite NPs within the first 10 ns. This structural change (e.g., NP–NP distance evolution to a lower energy state) leads to a rapid decline in the system’s potential energy. This state of the system is highly unstable, and it collapses near 12 ns due to numerical artifacts, such as periodic boundary conditions or force field instability, followed by a drastic increase in potential energy. This internal structural shift redefined the new initial condition near 12 ns, followed by a stable decay evolution path. The follow-up phase can be treated as a conventional system decay phase. Some small fluctuations in the entire production phase can be explained by the hydrogen bond dynamics with the mobility of the aggregated NPs. In the literature, this type of system expansion behavior is known to exist in macroscale thermodynamic systems, where new phases appear or disappear. The gas bubble evolution in oil is one of the classic examples of such expansion.

3.3. Spatial Distribution: Surfactant and NP Aggregation

3.3.1. Surfactant C12E3

Figure shows a comparison of the C12E3 aggregation in pure water and saltwater. The C12E3 molecules in both cases aggregated into a single spherical particle, as expected. The simulations show several microaggregation scenarios along their evolution pathways. A significant delay is observed in the aggregation process in the saltwater case. This is confirmed by a thorough examination of the MD trajectories along their evolution pathways. C12E3 evolution shows good agreement with the reported dodecylphosphocholine (DPC) aggregation in SPC water. ,

8.

Effect of salinity on the aggregation of C12E3 at a temperature of 333.15 K. H₂O: red dot. Na⁺: large blue points. Cl^–: large cyan points. C12E3 head: O­(red)/C­(cyan). C12E3 tail: C­(cyan). C12E3 aggregated spherical micelle: tails (hydrophobic) inwardly packed; heads (hydrophilic) toward the water).

The gyration radius is calculated and analyzed over the entire simulation trajectory using the GROMACS analysis program “g_gyrate”. The MD in all cases reached an equilibrium gyration radius of 2.5 (±0.10) nm, which is consistent with the theoretical or experimental values. Assuming a bond length of 0.152 ns and a bond angle of 109°, the estimated gyration radius of the nonionic surfactant, H­(CH₂)₁₂ (tail)–(OCH₂CH₂)₃ (head), is about 2.6 ns. The reported experimental values are in the range of 2.0–3.0 nm at the room temperature. The aggregation radius of the surfactants is calculated as $R_{\mathrm{g}}=\sqrt{\frac{\sum {||r_i^{\mathrm{g}}||}^2{m}_i}{\sum m_i}}$ , where m_i is the mass of atom i, and r _i ^g is the position of atom i with respect to the group center of all molecules.

3.3.2. Quartz NP

Figure shows quartz NP aggregated into a helix shape, and C12E3 adsorption along this helix in saltwater. This helix aggregation in pure water is not very definitive. In other cases (not shown here), quartz NP has a higher tendency to aggregate into a helical shape. This aggregation tendency is likely due to the shape and surface properties of the quartz NP model. It is known in crystallographic study that the growth of α-quartz building block, SiO₄, takes a helix shape.

9.

Effect of salinity on the adsorption and aggregation of quartz NP and C12E3 at a temperature of 293.15 K. In the plots on the right, C12E3 is not shown for clarity of NP aggregation. H₂O: red dot. Na ⁺ : large blue points. Cl^–: large cyan points. O: red. Si: yellow. Initial state: 8 NPs are randomly distributed. Final state at 60 ns: 8 NPs are aggregated into a helix.

The surfaces of silica particles in water can exhibit many different reactive sites depending on the undercoordinated silicon and oxygen atoms. The undercoordinated site, such as a trivalent silicon atom bonded to a protruding singly coordinated oxygen atom, readily reacts with an adjacent reactive site or water. Further, when the surface atoms were relaxed, the (001) plane of α-quartz was the most stable surface. When the surfaces were not relaxed, − the (101) surface was found to be the most stable with a surface energy of 2.59 Jm ^–2 . The helix aggregation morphology of quartz NP in Figure can be explained by the uncoordinated silicon and oxygen at the surfaces and edges of the model quartz NP.

3.3.3. Kaolinite NP

Figure shows a slab-like aggregation of 3 kaolinite NPs at the primary bonding site due to the formation of interlayer hydrogen bonding. Another kaolinite NP is attached to this group at the edge. The stacking layers exhibit some noticeable deformation. The deformation of the aggregated NP, as shown in VMD, can be described by the formation of H-bonds between water molecules and kaolinite surfaces. H-bonds form between kaolinite NP (OH groups in the octahedral Al–OH and O in the tetrahedral Si–O–Si), holding layers together and preventing swelling, while its surface H-bonding allows the adsorption of surfactants. H-bonds are determined based on a cutoff distance of 0.35 nm using the GROMACS analysis program “g_hbond”. The results show that the average number of H-bonds for the model system containing 8 kaolinite NPs is 106 and 100 at 0.0 and 32 ppt salinity, respectively. A slight decrease in salinity may likely be due to the reduction in H-bonds between water molecules and NP. Further, there are no noticeable changes in the distributions of bond angles (hydrogen–donor–acceptor) and distances (donor–acceptor), and bond autocorrelation. Any large-scale model (e.g., more NP forms more H-bonds) may likely provide better insight.

10.

Effect of salinity on the adsorption and aggregation of kaolinite NP and C12E3 at a temperature of 293.15 K. In the plots on the right, C12E3 is not shown for clarity of NP aggregation. H₂O: red dot. Na ⁺ : large blue points. Cl^–: large cyan points. O: red. Si: yellow. Al: purple. Initial state: 8 NPs are randomly distributed. Final state at 60 ns: 8 NPs show slab-like aggregation.

Ma and Eggleton provided a very fruitful characterization of layer stacking, cross fringes, and layer deformation of some kaolinite specimens based on their high-resolution transmission electron microscopy (HRTEM) images and cation exchange capacity (CEC) values. They observed that the nonbasal fringes occasionally crossed the basal (001) fringes, forming two-dimensional lattice-fringe images in which the layers were coherently stacked. At the nanoscale, the bending of several layers is commonly observed in transported kaolinites.

In summary, this research study presents two NPs (kaolinite NP of 9 units (9­[Al₂Si₂O₅(OH)₄]) and quartz NP of 18 units (18­[Si₃O₆])) by utilizing the established crystal unit cell data. The colloidal and interfacial properties of the NPs (i.e., dispersion, adsorption, and aggregation) are simulated in saline water with surfactants (analogous to biomedical or reservoir fluids). The simulated helix aggregation of quartz and layer aggregation of kaolinite are consistent with known crystallography and prior ClayFF-based MD studies. The surface curvature and nonuniform charge distribution bias the particles into helical or twisted structural assemblies as they minimize the surface energy. The proposed kaolinite and quartz NPs have essential colloidal and interfacial properties for simulating reservoir or biomedical fluids with surfactants, lipids, or drugs.

4. Conclusion

In this study, two NPs (kaolinite NP of 9 crystal units 9­[Al₂Si₂O₅(OH)₄] and quartz NP of 18 units 18­[Si₃O₆]) were engineered by utilizing established crystal unit cell data. The aggregation behavior of NPs in saline water with surfactants (C12E3) is studied by MD simulations. The simulation results are summarized as follows: (1) helix aggregation of quartz NP describing inherent crystal structural properties; (2) layer aggregation of kaolinite NP showing surface-to-surface and surface-to-site interactions and surface deformation; (3) rapid aggregation of C12E3 into a spherical shape with a small delay in saltwater, and (4) rapid increase and decrease of the potential energy and density curves for kaolinite cases demonstrating system expansion/contraction properties. The equilibrium evolution of the quartz system followed a decay property, whereas kaolinite showed significant expansion/contraction behaviors.

Supplementary simulations showed that the aggregation dynamics of the surfactants (C12E3, SDS, and CTAB) in the water and hydrocarbon phases were in excellent agreement with the experimental data. The C12E3 self-assembling aggregation kinetics were observed to be the dominant mechanism because of its strong hydrophobic affinity. A rapid aggregation of C12E3 into single spherical micelles was observed. The structural transitions for SDS and CTAB aggregation were more complex, with rod-, funnel-, and slab-like clusters of different sizes. In follow-up studies, the performance of NP can be explored with lipids, drugs, or proteins. A specific case can be selected for experimental studies by systematically simulating the MD process for alternative cases (such as NP interacting with the drug paclitaxel or phospholipids). A coarse-grained computational model can be adopted for simulating larger biomedical fluid volumes (such as a complex biochemistry of NPs, drugs, and proteins). ,

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c04629.

• Aggregation dynamics of the ionic (SDS, CTAB) and nonionic (C12E3) surfactants in oil–water (Figure S1); radial distribution functions (RDF) for the surfactants and NPs (quartz, kaolinite)­(Figure S2); atomic coordinates and force fields (bonded/nonbonded) for kaolinite NP (9­[Al₂Si₂O₅(OH)₄]) and quartz NP (18­[Si₃O₆]) (Figure S3) (PDF)

The author declares no competing financial interest.