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At least 181 records · Page 10

Fluid dynamic simulation and analysis of water-cooling systems for the Electron-Ion Collider

The Electron-Ion Collider is the newest large-scale project at Brookhaven National Laboratory. The collider’s purpose is to provide further advancements in the knowledge of the universe’s origin by accelerating particles near the speed of light. Our project for this 3.8 km ring was to create a thermal hydraulic steady-state simulation design of the water-cooling system to be cost-effective and energy efficient, as envisioned by Charlie Foltz, the EIC Infrastructure Division Director. The system would include a supply and return header, which cools several thousand components of the ring. The water would then be returned and cooled down using a system of cooling towers and plate and frame heat exchangers. Due to the size of the system and the complexity of the network analysis, a fluid dynamic simulation software, AFT Fathom, was used. Since previous methods of maintaining systems relied on building upon smaller real-life models and implementing empirical data, this flow model was unique and first of a kind in the domain of accelerator design, construction and operation. Therefore, our hydraulic team piloted a new method to perform network analysis on a large scale cooling system. We successfully created several test scenarios for system behavior in a shorter time compared to the method of performing hand calculations. Cooling specifications for heat rejection, pressure drop, flow rate, and pipe sizing were changed based on the individual systems of the vacuum, radio frequency (RF), magnet and power supply, and cryogenics sections. Finally, we used DOE guidelines to perform life-cycle cost analysis with net present value and carbon saving analysis on the systems where pipe size could be optimized.

43 PARTICLE ACCELERATORS↗

Microscale mechanical property variations of Al-substituted LLZO: insights from compression testing and molecular dynamics simulations

Ceramic solid electrolytes based on LLZO (Li 7 La 3 Zr 2 O 12 ) are promising candidates for all-solid-state batteries due to their high ionic conductivity and good apparent stability vs. lithium metal, however they are prone to mechanical failure. Lithium metal intrusions, alongside cell stack pressure, transition polycrystalline solid electrolyte grains into a compressed state that promotes crack propagation and fracture. Here this work examines the mechanical response of Al-substituted LLZO to compressive forces by measuring ultimate strength under pillar compression with a flat punch tip. Failure modes characterized by in situ scanning electron microscopy show diverse splitting patterns arising from internal porosity, grain boundaries, and slip planes. Large correlated variations in compressive strength (0.93–2.63 GPa) and Young's modulus (72.1–150.97 GPa) are observed across microscale regions of the solid electrolyte. Molecular dynamics simulations of LLZO with different porosities describe the variation of compressive strength and Young's modulus, and enable a microscale porosity model to be fit accounting for Young's modulus reduction across the solid electrolyte. Overall, the results indicate the importance of microscale mechanical testing of ceramic solid electrolytes to identify preferential sites for mechanical degradation and Li intrusion, and ensure the robust design of all-solid-state lithium metal batteries.

25 ENERGY STORAGE↗

Cluster dynamics simulations of tritium and helium diffusion in lithium ceramics

Tritium (T) and He diffusion in LiAlO 2 and LiAl 5 O 8 phases influences the performance of tritium producing burnable absorber rods (TPBARs) by affecting the gas release, swelling and thermal conductivity of Li-bearing ceramic pellets. Frenkel pair defects and clusters created by irradiation can attract T and He interstitials and form clusters of the type He i x Li, He i x Al, He i x O, T i x Li, T i x Al, and T i x O, 1 ≤ x ≤ 4 in a Li, Al or O vacancy site (notation denotes x He or T atoms in a 1 Li, 1 Al or 1 O vacant site). The concentration and mobility of each of these clusters collectively contribute to the diffusion of the He and T gases in LiAlO 2 and LiAl 5 O 8 . Here, in this work, free energy cluster dynamics simulations implemented in the Centipede code, are used to obtain the concentration and diffusivities of these clusters which are then used to calculate the total diffusivity of T and He gases in LiAlO 2 and LiAl 5 O 8 . The results show that diffusivity of T is at least one order of magnitude higher in LiAlO 2 as compared to that in LiAl 5 O 8 whereas He diffusion is 2–13 orders of magnitude higher in LiAlO 2 as compared to that in LiAl 5 O 8 . There is a higher concentration of highly diffusive species (T interstitials and T i 03 Li for the case of tritium and He i 01 Li, He i 02 Li, and He i 03 Li for the case of He) in LiAlO 2 than in LiAl 5 O 8 which increase the total diffusion of T and He in LiAlO 2 .

36 MATERIALS SCIENCE↗

Molecular Dynamics Simulation of Atomic Interactions in the Vancomycin Binding Site

Vancomycin is a glycopeptide antibiotic produced by Amycolaptopsis orientalis used to treat serious infections by Grampositive pathogens including methicillin-resistant Staphylococcus aureus. Vancomycin inhibits cell wall biosynthesis by targeting lipid II, which is the membrane-bound peptidoglycan precursor. The heptapeptide aglycon structure of vancomycin binds to the D-Ala-D-Ala of the pentapeptide stem structure in lipid II. The third residue of vancomycin aglycon is asparagine, which is not directly involved in the dipeptide binding. Nonetheless, asparagine plays a crucial role in substrate recognition, as the vancomycin analogue with asparagine substituted by aspartic acid (V D ) shows a reduction in antibacterial activities. To characterize the function of asparagine, binding of vancomycin and its aspartic-acid-substituted analogue V D to L-Lys-D-Ala-D-Ala and L-Lys-D-Ala-D-Lac was investigated using molecular dynamic simulations. Binding interactions were analyzed using root-mean-square deviation (RMSD), two-dimensional (2D) contour plots, hydrogen bond analysis, and free energy calculations of the complexes. The analysis shows that the aspartate substitution introduced a negative charge to the binding cleft of V D , which altered the aglycon conformation that minimized the repulsive lone pair interaction in the binding of a depsipeptide. Our findings provide new insight for the development of novel glycopeptide antibiotics against the emerging vancomycin-resistant pathogens by chemical modification at the third residue in vancomycin to improve its binding affinity to the D-Ala-D-Lac-terminated peptidoglycan in lipid II found in vancomycin-resistant enterococci and vancomycinresistant S. aureus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient perturbation-tracking method for directly probing the spectral phonon properties from molecular dynamics simulations

Existing methods for directly extracting the spectral phonon properties from molecular dynamics (MD) simulations, like the normal mode analysis (NMA) and spectral energy density analysis, all require a very long simulation time to produce reliable results with good convergence. So far, these methods are mainly applied in studies using small systems and with empirical potentials, as the heavy computational load has greatly hindered their further applications. Here we propose a perturbation-tracking (PT) method for directly probing the mode-wise phonon anharmonic frequencies and lifetimes. We show that results obtained from our method are in excellent agreement with those from the conventional NMA approach, using Si as the model material system. Comparing with the NMA approach, the PT method offers a greater accuracy and significant improvement of efficiency. It takes an average of two orders of magnitude and up to three orders of magnitude less simulation time to obtain the same lifetime result of a phonon mode with intermediate to high accuracy. Meanwhile, our method preserves all the dynamics of probed phonon mode from a particular state, which means it is capable of studying the transient thermal transport processes in a nonequilibrium system. Besides the exceptional efficiency, our method also comes with freedom to choose to probe only those modes of interest. This makes it ideal for use with large systems and in computationally demanding applications, such as ab initio MD simulations. Moreover, the PT method we propose here is very straightforward and easy to implement.

74 ATOMIC AND MOLECULAR PHYSICS↗

Development of a machine-learning-based ionic-force correction model for quantum molecular dynamic simulations of warm dense matter

In this work Δ learning is used to map orbital-free density functional theory (OF-DFT) ionic forces to the corresponding Kohn-Sham (KS) DFT ionic forces. The development of the approximate force difference in terms of the ion positions is constructed and serves as a stand in for the ground truth force difference. Descriptor vectors for ion configurations are constructed using all distance between ions in conjunction with an indexing based on a nearest neighbor ranking. It is demonstrated that such a scheme of descriptors can uniquely describe an ionic configuration up to a rotation and reflection when no ambiguity in the nearest neighbor ranking exists. How to handle the case when an ambiguity exists in the nearest neighbor ranking is discussed. As a proof of principle, the model is trained and tested on warm dense hydrogen at temperatures between 1 and 15 eV. Once tested, the model was used to perform molecular dynamic simulations of warm dense hydrogen. Furthermore, the resulting energies and pressures are within 1% and 2% of their respective target KS values.

36 MATERIALS SCIENCE↗

Self-Assembly of Silica Nanoparticles at Water–Hydrocarbon Interfaces: Insights from In Operando Small-Angle X-ray Scattering Measurements and Molecular Dynamics Simulations

To achieve tunable controls on the interactions of siliceous materials in subsurface environments bearing water and hydrocarbons, it is essential to determine the influence of hydrocarbon–water interfaces on the self-assembly of the silica particles. The hydrophilic silica particle have a tendency to aggregate on the water front of the interface. Self-assembly of silica nanoparticles proceeds via the migration of these nanoparticles to the water–hydrocarbon interface followed by aggregation at the interface. Fractal-like morphologies of assembled silica nanoparticles at water–hydrocarbon interfaces are observed. Rapid assembly of the hydrophilic silica nanoparticles at water–hydrocarbon interfaces corresponds to an overall reduction in the surface tension of water–toluene and water–heptane systems. These studies demonstrate the silica aggregation that is the precursor of silica polymerization, or nucleation and growth is influenced by the presence of hydrocarbons in subsurface geologic environments. These insights were derived from in operando ultrasmall and small-angle X-ray scattering (USAXS/SAXS) measurements, cryo-scanning electron microscopy (Cryo-SEM) imaging, and classical molecular dynamics simulations. As a result, these studies are intended to inform current and future efforts aimed at tuning silica reactivity in subsurface geologic environments to enhance permeability, the design and use of silica-based proppants to enhance fractures, and the development of effective strategies to control silica-based scaling behavior in subsurface reservoirs.

42 ENGINEERING↗

Consistent and reproducible computation of the glass transition temperature from molecular dynamics simulations

In many fields, from semiconductors for opto-electronic applications to ionic liquids (ILs) for separations, the glass transition temperature (Tg) of a material is a useful gauge for its potential use in practical settings. As a result, there is a great deal of interest in predicting Tg using molecular simulations. However, the uncertainty and variation in the trend shift method, a common approach in simulations to predict Tg, can be high. This is due to the need for human intervention in defining a fitting range for linear fits of density with temperature assumed for the liquid and glass phases across the simulated cooling. The definition of such fitting ranges then defines the estimate for the Tg as the intersection of linear fits. We eliminate this need for human intervention by leveraging the Shapiro–Wilk normality test and proposing an algorithm to define the fitting ranges and, consequently, Tg. Through this integration, we incorporate into our automated methodology that residuals must be normally distributed around zero for any fit, a requirement that must be met for any regression problem. Consequently, fitting ranges for realizing linear fits for each phase are statistically defined rather than visually inferred, obtaining an estimate for Tg without any human intervention. The method is also capable of finding multiple linear regimes across density vs temperature curves. We compare the predictions of our proposed method across multiple IL and semiconductor molecular dynamics simulation results from the literature and compare other proposed methods for automatically detecting Tg from density–temperature data. We believe that our proposed method would allow for more consistent predictions of Tg. We make this methodology available and open source through GitHub.

Chemistry↗

Characterization of Heparin’s Conformational Ensemble by Molecular Dynamics Simulations and Nuclear Magnetic Resonance Spectroscopy

Heparin is a highly charged, polysulfated polysaccharide and serves as an anticoagulant. Heparin binds to multiple proteins throughout the body, suggesting a large range of potential therapeutic applications. Although its function has been characterized in multiple physiological contexts, heparin’s solution conformational dynamics and structure–function relationships are not fully understood. Molecular dynamics (MD) simulations facilitate the analysis of a molecule’s underlying conformational ensemble, which then provides important information necessary for understanding structure–function relationships. However, for MD simulations to afford meaningful results, they must both provide adequate sampling and accurately represent the energy properties of a molecule. The aim of this study is to compare heparin’s conformational ensemble using two well-developed force fields for carbohydrates, known as GLYCAM06 and CHARMM36, using replica exchange molecular dynamics (REMD) simulations, and to validate these results with NMR experiments. In this work, the anticoagulant sequence, an ultra-low-molecular-weight heparin, known as Arixtra (fondaparinux, sodium), was simulated with both parameter sets. The results suggest that GLYCAM06 matches experimental nuclear magnetic resonance three-bond J-coupling values measured for Arixtra better than CHARMM36. In addition, NOESY and ROESY experiments suggest that Arixtra is very flexible in the sub-millisecond time scale and does not adopt a unique structure at 25 C. Moreover, GLYCAM06 affords a much more dynamic conformational ensemble for Arixtra than CHARMM36.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Intermediate scattering functions of a rigid body monoclonal antibody protein in solution studied by dissipative particle dynamic simulation

In the past decade, there was increased research interest in studying internal motions of flexible proteins in solution using Neutron Spin Echo (NSE) as NSE can simultaneously probe the dynamics at the length and time scales comparable to protein domain motions. However, the collective intermediate scattering function (ISF) measured by NSE has the contributions from translational, rotational, and internal motions, which are rather complicated to be separated. Widely used NSE theories to interpret experimental data usually assume that the translational and rotational motions of a rigid particle are decoupled and independent to each other. To evaluate the accuracy of this approximation for monoclonal antibody (mAb) proteins in solution, dissipative particle dynamic computer simulation is used here to simulate a rigid-body mAb for up to about 200 ns. The total ISF together with the ISFs due to only the translational and rotational motions as well as their corresponding effective diffusion coefficients is calculated. The aforementioned approximation introduces appreciable errors to the calculated effective diffusion coefficients and the ISFs. For the effective diffusion coefficient, the error introduced by this approximation can be as large as about 10% even though the overall agreement is considered reasonable. Thus, we need to be cautious when interpreting the data with a small signal change. In addition, the accuracy of the calculated ISFs due to the finite computer simulation time is also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Elucidation of Agonist and Antagonist Dynamic Binding Patterns in ER-α by Integration of Molecular Docking, Molecular Dynamics Simulations and Quantum Mechanical Calculations

Estrogen receptor alpha (ERα) is a ligand-dependent transcriptional factor in the nuclear receptor superfamily. Many structures of ERα bound with agonists and antagonists have been determined. However, the dynamic binding patterns of agonists and antagonists in the binding site of ERα remains unclear. Therefore, we performed molecular docking, molecular dynamics (MD) simulations, and quantum mechanical calculations to elucidate agonist and antagonist dynamic binding patterns in ERα. 17β-estradiol (E2) and 4-hydroxytamoxifen (OHT) were docked in the ligand binding pockets of the agonist and antagonist bound ERα. The best complex conformations from molecular docking were subjected to 100 nanosecond MD simulations. Hierarchical clustering was conducted to group the structures in the trajectory from MD simulations. The representative structure from each cluster was selected to calculate the binding interaction energy value for elucidation of the dynamic binding patterns of agonists and antagonists in the binding site of ERα. The binding interaction energy analysis revealed that OHT binds ERα more tightly in the antagonist conformer, while E2 prefers the agonist conformer. The results may help identify ERα antagonists as drug candidates and facilitate risk assessment of chemicals through ER-mediated responses.

59 BASIC BIOLOGICAL SCIENCES↗

Rupture Dynamics Simulations of Shallow Crustal Earthquakes on Reverse Slip Faults

The main goal of this study was to perform dynamic rupture simulations in order constrain the characterization of kinematic rupture models implemented in techniques for simulating strong ground motion for crustal earthquakes. First, we investigated the rupture process of the 2008 Iwate-Miyagi Nairiku earthquake by developing a dynamic rupture model on a reverse fault using a trial-and-error technique that produced a slip distribution and near-fault ground motion that matched the recorded ones. The simulations were performed in the frequency range 0-2 Hz, using a 3D staggered grid finite-difference method and a linear slip weakening friction law. Constrained by the observed slip distribution and consistent with dynamic rupture models, the derived kinematic rupture model of the Iwate-Miyagi Nairiku earthquake contains areas with relatively large slip rate, representing strong motion generation areas, set against lower amplitude heterogeneous background slip, and a relatively low slip rate in the weak zone of the top-most crust (upper 3km). Second, we performed rupture dynamics modeling to constrain shallow slip characterization in rupture models for strike-slip crustal earthquakes. The objective was to establish general rules about the characterization of slip rate function and slip at shallow depths and in the strong motion generation areas (SMGAs). The simulations of spontaneous rupture were performed in the frequency range 0-2.0Hz, using a 3D staggered-grid finite-difference method and a layer over half-space 1D crustal velocity model with a minimum shear-wave velocity of 2.8 km/s. In order to account for changes in material ductility and reduction of stress drop, observed in the shallow crust (upper 3-5 km), and the transition from ductile state to brittle state in the upper seismogenic zone, in our stress models we included a shallow weak zone (<4km). In this zone the stress drop was set to zero at the free surface and gradually increased with depth, while the slip weakening distance was set to 75 cm at the free surface and decreased to 50 cm at the base of the weak zone. As in the case of reverse faulting during the Iwate-Miyagi Nairiku earthquake, from these computations we found a systematic change in the shape of the slip-rate function, from Kostrov-type in the deeper part of the fault to a more symmetric cosine-type in the upper few kilometers, near the free-surface. Moreover, the average slip duration in the weak zone, with respect to slip duration in the deeper parts of the fault, increases by at most a factor of 1.5. We found a systematic and gradual change in the shape of the slip-rate function from Kostrov-type in the asperity areas (SMGAs), to more symmetric cosine-type in the upper few km near the free-surface, on the long period motion generation area (LMGA). The effective rise time in the LMGA, with respect to that in the SMGAs, increases by at most a factor of 2. Effective rise time is the time difference between the time at which the slip rate drops to a level that is equal to 25% of its peak and the onset time of the signal. In addition, the slip in the LMGA located above the SMGAs is almost the same as the one in the SMGAs, and about 1.5 times larger than the average slip.

58 GEOSCIENCES↗

Periodic boundary conditions for arbitrary deformations in molecular dynamics simulations

A generalization of the Lees-Edwards periodic boundary conditions (gLE-PBC) for molecular dynamics (MD) simulations is developed to allow for arbitrary deformations to be applied to the domain. The gLE-PBC domain remains a rectangular cuboid regardless of the applied deformation in contrast with the Lagrangian-rhomboid periodic boundary conditions (LR-PBC) where the domain deforms according to the applied deformation. Furthermore, the kinematics of gLE-PBC are validated against pure shear. The gLE-PBC method for interacting systems is then validated against the LR-PBC method and analytical solutions for a solid under isotropic compression, one-dimensional shearing, three-dimensional extension and shearing and for a liquid under Couette flow. Bulk physical properties extracted from the gLE-PBC simulations agree well with values calculated from equilibrium MD simulations. Three dimensional shearing and a deformation with a full velocity gradient matrix are also simulated, showing the range of problems gLE-PBC can explore.

74 ATOMIC AND MOLECULAR PHYSICS↗

Accelerating discrete dislocation dynamics simulations with graph neural networks

Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.

36 MATERIALS SCIENCE↗

A Poisson equation method for prescribing fully developed non-Newtonian inlet conditions for computational fluid dynamics simulations in models of arbitrary cross-section

Prescribing inlet boundary conditions for computational fluid dynamics (CFD) simulations of internal flow in complex geometries such as anatomical vascular models is challenging. In the absence of patient-specific inlet velocity data, a common approach for long blood vessels is to assume that the inlet flow is fully developed. In vessels of irregular cross section, however, prescribing fully developed conditions is complicated due to the lack of a general closed-form analytical solution. In this study, we develop a simple Poisson equation method for prescribing fully developed inlet conditions for the flow of either Newtonian or non-Newtonian fluids in CFD models of arbitrary cross-section. We first derive the generalized Poisson equation for fully developed flow of a non-Newtonian fluid and we then develop and verify a methodology for numerically computing the solution on any planar boundary domain. In addition, we develop a simple extension of the method for prescribing a non-orthogonal inlet velocity that represents fully developed flow from an upstream tube that is connected to the CFD inlet at a non-orthogonal angle. This may be used to investigate a common source of uncertainty in CFD simulations of internal flow that is due to a lack of information concerning the exact streamwise flow direction at the inlets. Comparison to several Newtonian and non-Newtonian benchmark verification solutions shows the method to be extremely accurate. As a practical demonstration case, we use the method to prescribe fully developed conditions on multiple non-circular inlets for the non-Newtonian flow of blood in a patient-specific model of the inferior vena cava (IVC). Finally, we further demonstrate the utility of the method by performing a sensitivity study using the patient-specific IVC model, wherein we investigate the influence of inlet velocity flow direction on the non-Newtonian IVC hemodynamics. Given its simplicity and computational efficiency, the method is shown to be far superior to alternative approaches for prescribing fully developed inlet conditions in such complicated geometries. In conclusion, to facilitate the adoption of our Poisson equation method, we have distributed our OpenFOAM source code and the associated test cases from this study as open-source software.

97 MATHEMATICS AND COMPUTING↗

Deep potential molecular dynamics simulations of low-temperature plasma-surface interactions

Machine learning approaches to potential generation for molecular dynamics (MD) simulations of low-temperature plasma-surface interactions could greatly extend the range of chemical systems that can be modeled. Empirical potentials are difficult to generalize to complex combinations of multiple elements with interactions that might include covalent, ionic, and metallic bonds. This work demonstrates that a specific machine learning approach, Deep Potential Molecular Dynamics (DeepMD), can generate potentials that provide a good model of plasma etching in the Si-Cl-Ar system. Comparisons are made between MD results using DeepMD models and empirical potentials, as well as experimental measurements. Pure Si properties predicted by the DeepMD model are in reasonable agreement with experimental results. Simulations of Si bombardment by Ar + ions demonstrate the ability of the DeepMD method to predict sputtering yields as well as the depth of the amorphous-crystalline interface. Etch yields as a function of flux ratio and ion energy for simultaneous Cl 2 and Ar + impacts are in good agreement with previous simulation results and experiment. Predictions of etch yields and etch products during plasma-assisted atomic layer etching of Si-Cl 2 -Ar are shown to be in good agreement with MD predictions using empirical potentials and with experiment. Finally, good agreement was also seen with measurements for the spontaneous etching of Si by Cl atoms at 300 K. Further, the demonstration that DeepMD can reproduce results from MD simulations using empirical potentials is a necessary condition to future efforts to extend the method to a much wider range of systems for which empirical potentials may be difficult or impossible to obtain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Understanding the structural mechanics of ligated DNA crystals via molecular dynamics simulation

DNA self-assembly is a highly programmable method to construct arbitrary architectures based on sequence complementarity. Among various constructs, DNA crystals are macroscopic crystalline materials formed by assembling motifs via sticky end association. Due to their high structural integrity and size ranging from tens to hundreds of micrometers, DNA crystals offer unique opportunities to study the structural properties and deformation behaviors of DNA assemblies. For example, enzymatic ligation of sticky ends can selectively seal nicks resulting in more robust structures with enhanced mechanical properties. However, the research efforts have been mostly on experiments involving different motif designs, structural optimization, or new synthesis methods, while their mechanics are not yet fully understood. The complex properties of DNA crystals are difficult to study via experiments alone, and numerical simulation can complement and aid the experiments. The coarse-grained molecular dynamics (MD) simulation is a powerful tool that can probe the mechanics of DNA assemblies. Here, we investigate DNA crystals made of four different motif lengths with various ligation patterns (full ligation, major directions, connectors, and in-plane) using oxDNA, an open-source, coarse-grained MD platform. We found that several distinct deformation stages emerge in response to mechanical loading and that the number and the location of ligated nucleotides can significantly modulate structural behaviors. These findings should be useful for predicting crystal properties and thus improving the design.

DNA crystal↗