Dissipative Particle Dynamics Model Research Articles

Construction of Multiscale Dissipative Particle Dynamics (DPD) Models from Other Coarse-Grained Models.

We present a general scheme for converting coarse-grained models into Dissipative Particle Dynamics (DPD) models. We build the corresponding DPD models by analogy with the de novo DPD coarse-graining scheme suggested by Groot and Warren (J. Chem. Phys., 1997). Electrostatic interactions between charged DPD particles are represented though the addition of a long-range Slater Coulomb potential as suggested by González-Melchor et al. (J. Chem. Phys., 2006). The construction is illustrated by converting MARTINI models for various proteins into a DPD representation, but it not restricted to the usual potential form in the MARTINI model-viz., Lennard-Jones potentials. We further extended the DPD scheme away from the typical use of homogeneous particle sizes, therefore faithfully representing the variations in the particle sizes seen in the underlying MARTINI model. The accuracy of the resulting construction of our generalized DPD models with respect to several structural observables has been benchmarked favorably against all-atom and MARTINI models for a selected set of peptides and proteins, and variations in the scales of the coarse-graining of the water solvent.

Influence of the internal structure of straight microchannels on inertial transport behavior of particles

The rapid advancement of Micro-Electro-Mechanical Systems (MEMS) technology has established microfluidics as a pivotal field. This technology marks the onset of a new era in various applications, including drug testing, cell culture, and disease monitoring, underscoring its extensive practicality and potential for future exploration. This research delves into the intricate behavior of particle inertial migration within microchannels, particularly focusing on the impact of different channel structures and Reynolds numbers (Re). Our studies reveal that particles in microchannels with one-sided sharp-cornered microstructures migrate towards the sharp corner at a relative position of 0.4 under low flow rates, and towards the straight wall side at a relative position of 0.8 under high flow rates. The migration pattern of equilibrium positions varies with different arrangements of sharp-corner structures, achieving stability at the channel's center only when the sharp corners are symmetrically arranged on both sides. Our investigation into the shape of microstructures indicates that sharp-cornered structures generate a more stable secondary flow compared to rectangular and semi-circular structures, preventing particle aggregation at the outlet. To address the challenges associated with handling variable cross-section geometries and solid-wall boundaries in dissipative particle dynamics methods effectively, we have developed a dissipative particle dynamics model specifically for analyzing such microchannels. Building upon our previous research, this model introduces a conservative force coefficient for particles within the microstructured region and an interaction zone that only involves repulsive forces, aligning well with experimental outcomes. Through the study of microstructures' geometric shapes, this paper offers guidance for designing microchannels for particle enrichment. Furthermore, the dissipative particle dynamics model established for the particle flow and solid structure interaction within microstructured channels provides insights into the mesoscale dynamics of liquid-solid two-phase flow and particle motion. In conclusion, this paper aims to enhance particle motion sample preparation techniques, thereby broadening the scope of microfluidic applications in the biomedical field.

Mesoscopic Model for Reversible Adsorption Stage of Albumin and Fibrinogen on TiO2 Surface.

The competitive behavior of proteins in the reversible adsorption stage plays a crucial role in determining the composition of the protein layer and the subsequent biological responses to the biomaterial. However, such competitive adsorption is a mesoscopic process at physiological protein concentration, and neither a macroscopic experiment nor microscopic MD (molecular dynamics) simulation is suitable to clarify it. Here, we proposed a mesoscopic DPD (dissipative particle dynamics) model to illustrate the competitive process of albumin and fibrinogen on TiO2 surface with its parameters deduced from our previous MD simulation, and proved the model well retained the diffusion and adsorption properties of proteins in the competitive adsorption on the plane surface. We then applied the model to the competitive adsorption on the surfaces with different nanostructures and observed that when the nanostructure size is much larger than that of protein, the increase in surface area is the main influencing factor; when the nanostructure size is close to that of protein, the coordination between the nanostructure and the size and shape of protein significantly affects the competitive adsorption process. The model has revealed many mechanical phenomena observed in previous experimental studies and has the potential to contribute to the development of high-performance biomaterials.

Brownian motion of soft particles near a fluctuating lipid bilayer.

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft-soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈10-20nm in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈0.05τd (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface.

Stochastic optimal control of mesostructure of supramolecular assemblies using dissipative particle dynamics and dynamic programming with experimental validation

The self-assembly process, where molecules form complex structures through interaction forces, has broad applications in various fields. However, controlling the dynamics of self-assembling molecules presents challenges, such as kinetic trapping, and the stochastic and nonlinear nature of governing equations. Recent studies have used Markov decision processes to control self-assemblies, but this approach may not be suitable for more complex systems and may result in disassembly or irreversible changes. To address these limitations, a novel integrated framework for the systematic development of control schemes for self-assembling systems is proposed. The framework uses a dissipative particle dynamics model to accurately capture self-assembly and generate a high-fidelity representation of relevant nanostructures. The probabilities of transitioning between states are calculated, which enables the formulation of a stochastic optimal control problem. To solve this problem, dynamic programming is employed. The framework is applied to a case study involving dynamic binary complexes with multiple unwanted metastable states, which serves to experimentally demonstrate the efficacy of the controller in driving the system towards desired morphologies. Finally, the closed-loop simulation results highlight that the proposed framework can drive the system of thermosensitive DBCs towards target morphologies while avoiding kinetic traps.

Hydrodynamic and transport behavior of solid nanoparticles simulated with dissipative particle dynamics

Inertial migration of micro- and nanoparticles flowing through microchannels is commonly used for particle separation, sorting, and focusing on many lab-on-a-chip devices. Computer simulations of inertial migration of nanoparticles by mesoscale simulation methods, such as Dissipative Particle Dynamics (DPD) would be helpful to future experimental development of these lab-on-a-chip devices. However, the conventional DPD approach has a low Schmidt number and its ability to model inertial migration is questioned. In this work, we examine the ability of DPD simulations to investigate the inertial migration of rigid nanoparticles flowing through a slit channel. By varying the exponent and cutoff distance in the weight function of the random and dissipative forces, DPD models with Schmidt number varying between 1 and 370 were examined. We show that solvent penetration into nanoparticles and solvent-induced attraction between nanoparticles can be controlled by choosing appropriate interaction coefficients of the DPD conservative force and that these properties are not influenced by the Schmidt number of the DPD model. On the other hand, hydrodynamic properties and transport behaviour of rigid nanoparticles are influenced by the Schmidt number. With the conventional DPD model, nanoparticles tend to be evenly distributed across the channel and do not remain in steady-state positions during flow. At high Schmidt numbers, the particles migrate to long-lasting steady-state positions located between the channel center and walls, in agreement with known experimental observations. We conclude that to properly simulate inertial migration, modifications to the conventional DPD model that yield a high Schmidt number are required.

Insights into Waterflooding in Hydrocarbon-Bearing Nanochannels of Varying Cross Sections from Mesoscopic Multiphase Flow Simulations

Waterflooding is one of the geotechniques used to recover fuel sources from nanoporous geological formations. The scientific understanding of the process that involves the multiphase flow of nanoconfined fluids, however, has lagged, mainly due to the complex nanopore geometries and chemical compositions. To enable the benchmarked flow of nanoconfined fluids, architected geomaterials, such as synthesized mesoporous silica with tunable pore shapes and surface chemical properties, are used for designing and conducting experiments and simulations. This work uses a modified many-body dissipative particle dynamics (mDPD) model with accurately calibrated parameters to perform parametric flow simulations for studying the influences of waterflooding-driven power, pore shape, surface roughness, and surface wettability on the multiphase flow in heptane-saturated silica nanochannels. Remarkably, up to an 80% reduction in the effective permeability is found for water-driven heptane flow in a baseline 4.5-nm-wide slit channel when compared with the Hagen-Poiseuille equation. In the 4.5-nm-wide channels with architected surface roughness, the flow rate is found to be either higher or lower than the baseline case, depending on the shape and size of cross sections. High wettability of the solid surface by water is essential for achieving a high recovery of heptane, regardless of surface roughness. When the solid surface is less wetting or nonwetting to water, the existence of an optimal waterflooding-driven power is found to allow for the highest possible recovery. A detailed analysis of the evolution of the transient water-heptane interface in those nanochannels is presented to elucidate the underlying mechanisms that impact or dictate the multiphase flow behaviors.

Phase Behavior of Alkyl Ethoxylate Surfactants in a Dissipative Particle Dynamics Model.

We present a dissipative particle dynamics (DPD) model capable of capturing the liquid state phase behavior of nonionic surfactants from the alkyl ethoxylate (CnEm) family. The model is based upon our recent work [Anderson et al. J. Chem. Phys. 2017, 147, 094503] but adopts tighter control of the molecular structure by setting the bond angles with guidance from molecular dynamics simulations. Changes to the geometry of the surfactants were shown to have little effect on the predicted micelle properties of sampled surfactants, or the water-octanol partition coefficients of small molecules, when compared to the original work. With these modifications the model is capable of reproducing the binary water-surfactant phase behavior of nine surfactants (C8E4, C8E5, C8E6, C10E4, C10E6, C10E8, C12E6, C12E8, and C12E12) with a good degree of accuracy.

Dissipative particle dynamics for anti-icing on solid surfaces

The problem of surface icing brings great inconvenience to people's daily life and production. It is important to develop effective surface anti-icing technology. The study of droplet freezing mechanism is beneficial to the development of surface anti-icing technology. At the mesoscopic scale, the freezing of droplets on the superhydrophobic surfaces with hierarchical structure involves complex thermodynamic processes such as interfacial heat transfer and phase transition. In these processes, the comprehensive influence of the factors such as droplet wetting state, surface topological structure and environment on the heat transfer and phase change near the solid–liquid-gas three-phase contact line is the key to the ice nucleation inside the droplets and the whole freezing process. In the present paper, the lastest study on anti-icing surfaces and droplet freezing mechanism are introduced in the first. And then the relevant numerical methods in multiphase flow are discussed. Finally, we prospect the particle-based dissipative particle dynamics model’s potential in mimicking the droplet freezing in the future.

A Mori–Zwanzig Dissipative Particle Dynamics Approach for Anisotropic Coarse Grained Molecular Dynamics

Coarse grained (CG) molecular dynamics simulations are widely used to accelerate atomistic simulations but generally lack a formalism to preserve the dynamics of the system. For spherical particles, the Mori-Zwanzig approach, while computationally complex, has ameliorated this problem. Here we present an anisotropic dissipative particle dynamics (ADPD) model as an extension of this approach, which accounts for the anisotropy for both conservative and nonconservative interactions. For a simple anisotropic system we parametrize the coarse grained force field representing ellipsoidal CG particles from the full-atomistic simulation. To represent the anisotropy of the system, both the conservative and dissipative terms are approximated using the Gay-Berne (GB) functional forms via a force-matching approach. We compare our model with other CG models and demonstrate that it yields better results in both static and dynamical properties. The inclusion of the anisotropic nonconservative force preserves the microscopic dynamical details, and hence the dynamical properties, such as diffusivity, can be better reproduced by the aspherical model. By generalizing the isotropic DPD model, this framework is effective and promising for the development of the CG model for polymers, macromolecules, and biological systems.

A DPD model of soft spheres with waterlike anomalies and poly(a)morphism.

Core-softened approaches have been employed to understand the behavior of a large variety of systems in soft condensed matter, from biological molecules to colloidal crystals, glassy phases, and water-like anomalies. At the same time, dissipative particle dynamics (DPD) is a powerful tool suitable for studying larger length and time scales. In this sense, we propose a simple model of soft molecules that exhibits a wide range of interesting phenomena: polyamorphism, with three amorphous phases, polymorphysm, including a recently found gyroid phase and a cubic diamond structure, reentrant liquid phase, and density, diffusion, and structural water-like anomalies. Each molecule is constituted by two collapsing beads, representing a harder central core and a softer corona. This induces a competition between distinct conformations that leads to their unique behavior. This provides a basis for the development of more accurate water-like DPD models that can then be parameterized for specific systems and even used to model and understand the self-assembly of colloidal crystals.

Phase behaviour of coarse-grained fluids.

Soft condensed matter structures often challenge us with complex many-body phenomena governed by collective modes spanning wide spatial and temporal domains. In order to successfully tackle such problems, mesoscopic coarse-grained (CG) statistical models are being developed, providing a dramatic reduction in computational complexity. CG models provide an intermediate step in the complex statistical framework of linking the thermodynamics of condensed phases with the properties of their constituent atoms and molecules. These allow us to offload part of the problem to the CG model itself and reformulate the remainder in terms of reduced CG phase space. However, such exchange of pawns to chess pieces, or 'Hamiltonian renormalization', is a radical step and the thermodynamics of the primary atomic and CG models could be quite distinct. Here, we present a comprehensive study of the phase diagram including binodal and interfacial properties of a dissipative particle dynamics (DPD) model, extended to include finite-range attraction to support the liquid-gas equilibrium. Despite the similarities with the atomic model potentials, its phase envelope is markedly different featuring several anomalies such as an unusually broad liquid range, change in concavity of the liquid coexistence branch with variation of the model parameters, volume contraction on fusion, temperature of maximum density in the liquid phase and negative thermal expansion in the solid phase. These results provide new insight into the connection between simple potential models and complex emergent condensed matter phenomena.

Experimental and Computational Evaluation of Self-Assembled Morphologies in Diblock Janus Bottlebrush Copolymers.

Diblock Janus-type "A-branch-B" bottlebrush copolymers (di-JBBCPs) consist of a backbone with alternating A and B side chains, in contrast to the side chain arrangement of conventional bottlebrush copolymers. As a result, A and B blocks of di-JBBCPs can microphase-separate perpendicular to the backbone, which is located at the interface between the two blocks. A reparametrized dissipative particle dynamics (DPD) model is used to theoretically investigate the self-assembly of di-JBBCPs and to compare with the experimental results of a range of polystyrene-branch-polydimethylsiloxane di-JBBCPs. The experimentally formed cylinder, gyroid, and lamellar morphologies showed good correspondence with the model phase diagram, and the effect of changing volume fraction and backbone length is revealed. The DPD model predicts a bulk-stable perforated lamella morphology together with two unconventional spherical phases, the Frank-Kasper A15 spheres and the hexagonally close-packed spheres, indicating the diversity of morphologies available from complex BCP molecular architectures.

Dissipative particle dynamics simulations for biological systems: From protein structures to cell mechanics

<p indent="0mm">Dissipative particle dynamics (DPD) is a mesoscopic coarse-grained simulation method developed in recent years, which is an important method for studying the dynamic behaviors of soft matter and complex fluids. In this method, each DPD particle represents a coarse-grained virtual cluster of a set of atoms or groups of matter. The position and momentum of the DPD particle are updated in a continuous phase but spaced at discrete time steps. The coarse-grained DPD particles are subject to simplified pairwise interacting conservative, dissipative, and random forces. Especially, the dissipative force and random force in the DPD method act as a heat sink and a source, respectively, and the combined effect of these two forces act as a thermostat, which conserves momentum and thus provides the correct description of hydrodynamic interactions for the model system. In addition, a common choice of the soft repulsion for the conservative force allows using larger integration time steps in DPD simulations than that usually allowed in classical molecular dynamics (MD) simulations. Hence, compared with the MD method, the computational cost of the DPD simulation is significantly reduced due to the smaller number of modeled particles and the larger computational time step, enabling the simulations of the static and dynamic behaviors of complex fluids and soft matter systems at physically attractive length scale and time scale. Moreover, the particle-based framework of the DPD method enables people to easily incorporate additional physical features into the model systems and extend its application to complex systems. For these reasons, the DPD method and its extension have been successfully applied to numerous soft matter and complex fluid systems such as oil/water/surfactant systems, chemical morphology, microscopic morphology, phase separation, as well as dynamics and rheological properties of polymer solutions and colloidal suspensions. In this paper, we first introduce the theoretical formulation and parameterization of the DPD method. Then, we review recent advances in DPD modeling of biological systems, focusing on its applications at the molecular and cellular scales. At the molecular scale, we highlight examples of successful simulations of the protein structures and their interactions, the structure and dynamics of amphiphilic lipid molecule membranes (e.g., the self-assembly of lipid molecules, the structure and properties of lipid membranes, the fusion of lipid membranes, and the budding and fission of lipid membranes), the interaction of lipid membranes with protein molecules, and the interaction of nanoparticles with lipid membranes; at the cellular scale, we focus on the DPD modeling of blood cell flow and blood rheological behaviors in the blood microcirculatory systems, including the shape deformation and flow dynamics of red blood cells, the margination and adhesion dynamics of white blood cells, the margination and aggregation behaviors of platelets, the hemorheological behavior of blood flow, as well as the separation of circulating tumor cells from blood flow using microfluidic devices. Additionally, we compare the advantages and disadvantages of the microscale blood flow simulations between the continuum-based methods and particle-based methods, including the DPD method. Finally, we briefly present the development trends and application prospects of DPD modeling in biological systems.

Entanglement Characteristic Time from Complex Moduli via i-Rheo GT.

Tassieri et al. have introduced a novel rheological tool called "i-Rheo GT" that allows the evaluation of the frequency-dependent materials' linear viscoelastic properties from a direct Fourier transform of the time-dependent relaxation modulus G(t), without artifacts. They adopted i-Rheo GT to exploit the information embedded in G(t) derived from molecular dynamics simulations of atomistic and quasi-atomistic models, and they estimated the polymers' entanglement characteristic time (τe) from the crossover point of the moduli at intermediate times, which had never been possible before because of the poor fitting performance, at short time scales, of the commonly used generalized Maxwell models. Here, we highlight that the values of τe reported by Tassieri et al. are significantly different (i.e., an order of magnitude smaller) from those reported in the literature, obtained from either experiments or molecular dynamics simulations of different observables. In this work, we demonstrate that consistent values of τe can be achieved if the initial values of G(t), i.e., those governed by the bond-oscillation dynamics, are discarded. These findings have been corroborated by adopting i-Rheo GT to Fourier transform the outcomes of three different molecular dynamics simulations based on the following three models: a dissipative particle dynamics model, a Kremer-Grest model, and an atomistic polyethylene model. Moreover, we have investigated the variations of τe as function of (i) the 'cadence' at which G(t) is evaluated, (ii) the spring constant of the atomic bone, and (iii) the initial value of the shear relaxation modulus G(O). The ensemble of these results confirms the effectiveness of i-Rheo GT and provide new insights into the interpretation of molecular dynamics simulations for a better understanding of polymer dynamics.

Particle flow characteristics in the pipeline of a nonmetallic ore powder air classifier using a DPD-DEM coupled method

Understanding particle flow characteristics can help improve the efficiency of nonmetallic ore powder air classifiers. In this paper, dissipative particle dynamics (DPD) and the discrete element method (DEM) were adopted to study the interactions between the gas phase and solid particles. Gas and solid phases were coupled using the single-particle DPD model. Taking sepiolite particles as an example, at the optimal input air velocity in the pipeline, the gas particle velocity distribution, solid particle velocity distribution, solid particle concentration distribution, and solid particle position distribution were analyzed by numerical simulations. A comparison of numerical simulation and experimental results showed that when the input air velocity in the pipeline was 17 m/s, the velocity of particles and gas in the pipeline gradually increased from the wall to the center of the pipeline. The velocity near the pipeline wall changed rapidly, and the velocity in the main flow area remained basically unchanged. Particles left the pipeline in a uniform and dispersed state and were carried into the classification area. As the input air velocity increased, the pressure drop across the pipeline also increased. Therefore, the optimal input air velocity value could be reasonably selected to minimize energy consumption.

Modeling surface segregation of smart PU coatings at hydrophilic and hydrophobic interfaces via coarse-grained molecular dynamics and mesoscopic simulations

Developing adaptive coatings having desired functionalities at targeted interfaces is one of the major efforts in the coatings science area. The adaptation of the surface functionality to the changing surface conditions can be maintained by introducing dangling chains with different properties to the cross-linked polymer coatings. In this work, we strive to investigate the change in interfacial morphology of PU coatings as exposed to hydrophilic (HPI) and hydrophobic (HPB) interfaces by employing molecular simulations at the coarse-grained and mesoscopic levels. The molecular structure and surface segregation dynamics are studied for PU coatings having pure HPI, mixture of HPI and HPB, and amphiphilic dangling chains. The dual-scale simulations, Dissipative Particle Dynamics (DPD) and MARTINI model, yield results about the dangling chain structures at the interface in terms of their end-to-end distances, where HPI chains adopt a more extended conformation in water in comparison to oil interfaces. The reverse is observed to be valid for the HPB chains. Regarding the dangling chain dynamics, a swift migration towards the interfaces is noticed at about 10 ns for both of the simulation methods. The structures of the dangling chains and their interaction with the interfaces are also characterized by computing the radial distribution function (RDF) profiles. Preferential interactions between the HPI/water and HPB/oil are clearly noted. The switchability of the surfaces is also studied by simulating the system in cycles, such that the interface is changed from water to oil and back to water. The migration of HPI groups in the dangling chains towards water and vice versa in each cycle is clearly shown by the simulations. In all, the inherent structure and dynamics of the dangling chains is obtained at the molecular level by the dual-scale molecular simulations. Our findings reveal a significant level of understanding about interfacial morphology of thermoset coatings modified by dangling chains, where the results can be extended to find applications in guiding the experimental studies.

Frank–Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model: SCF Results

For conformationally asymmetric diblock copolymer (DBC) melts, we proposed a model system that can be readily used in dissipative particle dynamics (DPD) simulations and performed the corresponding self-consistent field (SCF) calculations to study the stability of Frank–Kasper (FK) phases. This provides the mean-field results needed for direct comparison with the DPD simulations, without any parameter fitting, to unambiguously quantify the fluctuation/correlation effects inherently neglected by the SCF theory but important in the low-molecular-weight DBC melts forming FK phases in experiments. Our SCF calculations of the DPD model are faster and use less memory, both by at least one order of magnitude, than those of the “standard” model and give accurate results. Among the five FK (i.e., A15, C14, C15, Z, and σ) phases considered here, C14 is found to be the only stable one; its stability is due to the conformational asymmetry and, in particular, it is stabilized over other FK phases by entropy. This is the first time C14 is predicted to be stable in SCF calculations of neat DBC melts. Our SCF phase diagrams for the DPD model of conformationally asymmetric DBCs are qualitatively different from those for the “standard” model reported in the literature, which may be due to the model differences and numerical accuracy.

Dissipative particle dynamics modeling of MR fluid flow in a novel magnetically optimized mini-MR damper

Dissipative particle dynamics modeling of MR fluid flow in a novel magnetically optimized mini-MR damper

Modeling Alkyl Aromatic Hydrocarbons with Dissipative Particle Dynamics.

Building on previous work studying alkanes, we develop a dissipative particle dynamics (DPD) model to capture the behavior of the alkyl aromatic hydrocarbon family under ambient conditions of 298 K and 1 atmosphere. Such materials are of significant worldwide industrial importance in applications such as solvents, chemical intermediates, surfactants, lubricating oils, hydraulic fluids, and greases. We model both liquids and waxy solids for molecules up to 36 carbons in size and demonstrate that we can correctly capture both the freezing transition and liquid-phase densities in pure substances and mixtures. We also demonstrate the importance of including specialized bead types into the DPD model (rather than solely relying on generic bead types) to capture specific local geometrical constructs such as the benzene ring found in the benzyl chemical group; this can be thought of as representing subtle real-world many-body effects via customized pairwise non-bonded potentials.