Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Coarse-grained models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Convective and Orographic Origins of the Mesoscale Kinetic Energy Spectrum

The mesoscale spectrum describes the distribution of kinetic energy in the Earth's atmosphere between length scales of 10 and 400 km. Since the first observations, the origins of this spectrum have been controversial. At synoptic scales, the spectrum follows a –3 spectral slope, consistent with two-dimensional turbulence theory, but a shallower –5/3 slope was observed at the shorter mesoscales. The cause of the shallower slope remains obscure, illustrating our lack of understanding. Through a novel coarse-graining methodology, we are able to present a spatio-temporal climatology of the spectral slope. We find convection and orography have a shallowing effect and can quantify this using “conditioned spectra.” These are typical spectra for a meteorological condition, obtained by aggregating spectra where the condition holds. This allows the investigation of new relationships, such as that between energy flux and spectral slope. Potential future applications of our methodology include predictability research and model validation.

54 ENVIRONMENTAL SCIENCES↗

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reactive transport modeling of organic carbon degradation in marine methane hydrate systems

Abstract Natural methane hydrate has often been observed in sand layers that contain no particulate organic carbon (POC), but are surrounded by organic-rich, fine-grained marine muds. In this paper, we develop a reactive transport model (RTM) of a microbially-mediated set of POC degradation reactions, including hydrolysis of POC driven by extracellular enzymes, fermentation of the resulting high-molecular weight dissolved organic carbon (HMW-DOC), and methanogenesis that consumes low-molecular weight dissolved organic carbon (LMW-DOC). These processes are mediated by two groups of microbes, fermenters and methanogens that are heterogeneously distributed in different lithologies, with the largest numbers of microbes in the large pores of coarse-grained layers. We find that the RTM can reproduce methane hydrate occurrences observed in two different geological environments, at Walker Ridge Site 313-H (Gulf of Mexico) and IODP Site U1325 (Cascadia Margin). We also find that microbes can degrade POC even if they are physically separated, as extracellular enzymes and DOC can diffuse away from where they are produced by microbes. Microbial activity is highest at relatively early times after burial at shallow depths and near lithological boundaries, where concentration gradients transport solutes to intervals that contain the most microbes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. In this paper, we use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk [Phys. Rev. Res. 6, L022052 (2024)]. We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

Nikulsin, N. (ORCID:0000000318611777)↗

Influence of Rigidity–Hydration Coupling on Size-Dependent Diffusion in Hydrated Polymer Membranes

Selective ion transport in polymer membranes depends critically on how penetrant motion couples to polymer dynamics and hydration. Yet, the mechanistic interplay between polymer rigidity, water content, and penetrant size remains poorly understood, especially in the regime where the penetrant diameter, polymer Kuhn length, and correlation length are comparable. Here, we employ coarse-grained molecular dynamics simulations to systematically investigate penetrant diffusion in hydrated polymer networks across a broad range of water volume fractions, chain rigidities, and penetrant sizes. The results reveal a transition from a decoupled regime, where small penetrants diffuse nearly independently of polymer relaxation, to a coupled regime in which large penetrants require cooperative polymer motion for transport. Increasing polymer rigidity amplifies the sensitivity of diffusivity to hydration, particularly at low water content, leading to pronounced deviations from Stokes−Einstein scaling. Comparison with scaling theories and free-volume models shows that classical nanoparticle-based frameworks fail to capture this intermediate regime. To address this gap, we extend the Yasuda model to incorporate polymer rigidity through a single parameter that quantifies the dynamic contribution of chain stiffness to free-volume fluctuations. The resulting model collapses diffusivity data across all sizes, water contents, and rigidities, providing a unified description of penetrant transport in hydrated polymer matrices. Furthermore, these findings establish polymer rigidity as a key, tunable determinant of diffusion and offer a framework for interpreting size-dependent transport in ion-selective membranes.

diffusion↗

Measuring scale-dependent shape anisotropy by coarse-graining: Application to inhomogeneous Rayleigh-Taylor turbulence

Here, we generalize the “filtering spectrum” to probe scales along different directions by spatial coarse-graining. This multidimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multidimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of two-dimensional (2D) and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results that large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small-scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

42 ENGINEERING↗

Attention-based functional-group coarse-graining: a deep learning framework for molecular prediction and design

Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML training. In this study, we report a data-efficient, deep-learning framework for molecular discovery that integrates a coarse-grained functional-group representation with a self-attention mechanism to capture intricate chemical interactions. Our approach exploits group-contribution concepts to create a graph-based intermediate representation of molecules, serving as a low-dimensional embedding that substantially reduces the data demands typically required for training. Using a self-attention mechanism to learn the subtle but highly relevant chemical context of functional groups, the method proposed here consistently outperforms existing approaches for predictions of multiple thermophysical properties. In a case study focused on adhesive polymer monomers, we train on a limited dataset comprising only 6,000 unlabeled and 600 labeled monomers. The resulting chemistry prediction model achieves over 92% accuracy in forecasting properties directly from SMILES strings, exceeding the performance of current state-of-the-art techniques. Furthermore, the latent molecular embedding is invertible, enabling the design pipeline to automatically generate new monomers from the learned chemical subspace. We illustrate this functionality by targeting several properties, including high and low glass transition temperatures (Tg), and demonstrate that our model can identify new candidates with values that surpass those in the training set. The ease with which the proposed framework navigates both chemical diversity and data scarcity offers a promising route to accelerate and broaden the search for functional materials.

Han, Ming [Univ. of Chicago, IL (United States)]↗

Stockmayer fluid simulations for viscosity and glass transition temperature of ionic liquids

We develop a Stockmayer fluid model for molecular dynamics simulations of ionic liquids that captures molecular polarization, ionic conductivity, viscosity, and glass transition temperature, using ethylammonium nitrate (EAN) as an example. The ions in EAN are treated as spheres interacting via the Lennard-Jones potential with an embedded point charge and a permanent dipole moment. We show that our simulation results for EAN are consistent with experimental data and then explore the effects of the molecular parameters on the viscosity of ionic liquids. Our results indicate that viscosity monotonically increases with ionic charge and dipole moment but non-monotonically changes with ionic diameter (or molar volume). This non-monotonic trend arises from the competition among the electrostatic interactions, molecular packing, and size asymmetry between the cation and anion. In conclusion, our model also shows that long-lived ion pairs result in higher viscosities.

Coarse-grained simulations↗

Investigating PVC polymer–plasticizer interactions with atomistic MD simulations and potential of mean force calculations

For this work, atomistic molecular dynamics (MD) simulations coupled with potential of mean force (PMF) calculations were employed to investigate the interactions between PVC polymer chains containing 6–20 repeating units and various plasticizers, with the goal of identifying potential replacements for the toxic plasticizer di(2-ethylhexyl)phthalate (DEHP) used in blood bags. The selected plasticizers belong to various chemical families, such as orthophthalates, citrates, adipates, and the terephthalate DEHT. Both the polymer and the plasticizers lack ionizable groups, and their interactions are primarily governed by van der Waals and electrostatic forces. A model correlating PMF profiles with interaction forces was developed and validated across polyvinyl chloride (PVC) polymers of different lengths and all investigated plasticizers. This model provides insight into how structural variations in plasticizers influence their respective PMF values. The study ranks the investigated plasticizers based on binding affinity, identifying TOTM (tris(2-ethylhexyl) trimellitate, TEHTM), BTHC (butyryl trihexyl citrate, Citroflex B-6), ATHC (acetyl trihexyl citrate, Citroflex A-6, CA-6), and DEHT (bis(2-ethylhexyl)terephthalate, DOTP/DEHTP) as promising alternatives for further investigation. This comprehensive study encompasses PVC polymers of four different lengths and 14 plasticizers, with all data averaged over 30 independent simulations. The approach provides a deeper understanding of molecular interactions, enabling the tailoring of polymer–plasticizer systems for diverse applications, including extractables and leachables, with relevance spanning materials science to biomedical engineering, and also serves as a basis for developing coarse-grained simulation protocols. Overall, this study provides valuable insights for designing safer and more efficient plasticizer substitutes and is well supported by other studies.

Shet, Sai Athmeeya G. [Sri Sathya Sai Institute of↗

Distinct universality classes of diffusive transport from full counting statistics

The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and nonintegrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. Here, we discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Minimal implicit-solvent coarse-grained simulation of Pluronic block copolymers with ionic liquids

Pluronic block copolymers, composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) in a triblock structure (PEO–PPO–PEO), are well known for their amphiphilic character and ability to self‐assemble into micelles in aqueous solution. The addition of ionic liquids (ILs) can further modulate the core–shell structures of these copolymers, influencing their stability, critical micellization temperature, and size. However, fully atomistic simulations often become prohibitively expensive due to the size and complexity of these systems. In this work, coarse‐grained simulations using a minimal implicit‐solvent model were performed to examine how two classes of ILs, namely, 1‐alkyl‐3‐methylimidazolium ([C n C 1 im]) and 1‐alkyl‐3‐methylpyrrolidinium ([C n C 1 pyrr]), change the micellization of Pluronic block copolymers in aqueous solution. The effects of IL concentration and alkyl group length were investigated, and the model greatly improved the efficiency of simulating large‐scale micelle systems. Furthermore, the numerical simulations are qualitatively compared with experimental investigations. Our results show that adding ILs expands the micelle core by embedding IL tails among the PPO blocks, thereby increasing overall micelle size. Less polar ILs generally induce more pronounced micellar growth. However, the effect of IL tail length on conformation and micellar packing is non‐monotonic. Up to moderate chain lengths (around C8–C10), the IL tails can extend sufficiently to increase local separation within the micelle; at longer tail lengths, enhanced hydrophobic clustering and steric hindrance cause the tails to bend or fold, capping further expansion. In addition, although block copolymer chains tend to pack more closely in the presence of longer‐tailed ILs, the random coil size of an individual polymer chain does not necessarily shrink. Meanwhile, these insights provide a deeper understanding of how Pluronic/IL systems interact, informing applications in drug delivery, cosmetics, food, and environmental engineering. Finally, our minimal implicit‐solvent model can be applied to larger systems and longer timescales, substantially reducing computational cost while reproducing key structural trends observed experimentally.

Atomistic simulations↗

Emergence of Orchestrated and Dynamic Metabolism of Saccharomyces cerevisiae

Microbial metabolism is a fundamental cellular process that involves many biochemical events and is distinguished by its emergent properties. While the molecular details of individual reactions have been increasingly elucidated, it is not well understood how these reactions are quantitatively orchestrated to produce collective cellular behaviors. Here we developed a coarse-grained, systems, and dynamic mathematical framework, which integrates metabolic reactions with signal transduction and gene regulation to dissect the emergent metabolic traits of Saccharomyces cerevisiae. Our framework mechanistically captures a set of characteristic cellular behaviors, including the Crabtree effect, diauxic shift, diauxic lag time, and differential growth under nutrient-altered environments. It also allows modular expansion for zooming in on specific pathways for detailed metabolic profiles. Furthermore, this study provides a systems mathematical framework for yeast metabolic behaviors, providing insights into yeast physiology and metabolic engineering.

59 BASIC BIOLOGICAL SCIENCES↗

Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility

Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

From Spin to Pseudospin Symmetry: The Origin of Magic Numbers in Nuclear Structure

Magic numbers lie at the heart of nuclear structure, reflecting enhanced stability in nuclei with closed shells. While the emergence of magic numbers beyond 20 is commonly attributed to strong spin-orbit coupling, the microscopic origin of the spin-orbit potential remains elusive, owing to its dependence on the resolution scale and renormalization scheme of nuclear forces. Here, we investigate the evolution of nuclear shell structure with varying momentum resolution in nuclear interactions derived from chiral effective field theory, using the similarity renormalization group to link different scales. We uncover a novel transition from spin symmetry to pseudospin symmetry as the resolution scale decreases, during which magic numbers emerge naturally. A similar pattern is found in calculations using relativistic one-boson-exchange potentials, underscoring the robustness of the phenomenon. This establishes a direct connection between realistic nuclear forces with a high resolution scale and effective nuclear forces at coarse-grained scales, offering a first-principles explanation for the origin of magic numbers and pseudospin symmetry in nuclear shell structure and new insights into the structure of exotic nuclei far from stability

Energy levels↗

Efficient Parallelization of Irregular Applications on GPU Architectures

With the enlarging computation capacity of general Graphics Processing Units (GPUs), leveraging GPUs to accelerate parallel applications has become a critical topic in academia and industry. However, a wide range of irregular applications with the computation-/memory-intensive nature cannot easily achieve high GPU utilization. The challenges mainly involve the following aspects: first, data dependence leads to coarse-grained kernel and inefficient parallelism; second, heavy GPU memory usage may cause frequent memory evictions and extra overhead of I/O; third, specific computation patterns produce memory redundancies; last, workload balance and data reusability conjunctly benefit the overall performance, but there may exist a dynamic trade-off between them. Targeting these challenges, this dissertation proposes multiple optimizations to accelerate two real-world applications: many-body correlation functions to simulate nuclear physics in a large-scale scientific system; the other is the eALS-based matrix factorization recommendation system. To accelerate the calculations of many-body correlation functions, this dissertation presents three frameworks in GPU memory management and multi-GPU scheduling. Firstly, an optimized systematic GPU memory management framework, MemHC, utilizes a series of new memory reduction designs in GPU memory allocation, CPU/GPU communications, and GPU memory oversubscription. Secondly, an enhanced multi-GPU scheduling framework, MICCO, particularly by taking both data dimension (e.g., data reuse and data eviction) and computation dimension into account. MICCO designs a heuristic scheduling algorithm and a machine learning-based regression model to generate the optimal settings of a proposed new concept to manage the trade-off. Thirdly, a locality-aware multi-GPU scheduling framework. This scheduler leverages pipeline batch generation with a looking-ahead strategy by building local dependency graphs for memory transfer reduction and better data reuse, achieving up to 79.92% memory cost reduction and 1.67x speedup. To parallelize the eALS-based recommendation system, this dissertation proposes an efficient CPU/GPU heterogeneous recommendation system, HEALS. HEALS employs newly designed architecture-adaptive data formats to achieve load balance and good data locality on CPU and GPU. To mitigate the data dependence, HEALS presents a CPU/GPU collaboration model for both task parallelism and data parallelism with multiple kernel computation optimizations. In summary, this dissertation efficiently accelerates two typical irregular applications on GPUs by building four frameworks, including CPU/GPU collaboration, GPU memory management, and multi-GPU scheduling.

Wang, Qihan↗

UT-GOM2-2 Preliminary Report: Terrebonne Basin Northern Gulf of Mexico, 30 July-28 September 2023

In the summer and fall of 2023, the Gulf of Mexico Deepwater Hydrate Coring Expedition (UT-GOM2-2) drilled, cored, made downhole measurements, and analyzed samples from the seafloor to the base of the gas hydrate stability zone in one location (Site H, WR313) in the Terrebonne basin, deepwater Gulf of Mexico. Analyses of data and samples from the expedition will inform biological, geochemical, and geomechanical models to constrain the role of gas hydrates in the carbon cycle and the potential for gas hydrates as an energy resource. Pressure and conventional cores were collected continuously to a depth of 155.1 meters below the seafloor (mbsf). At deeper depths, cores were taken periodically from hydrate-bearing sands and their bounding muds to a total depth of 861.3 mbsf. 162.6 m of conventional core and 54.8 m of pressure core were obtained. Twelve temperature measurements were made between 27.1 and 144.5 mbsf to determine the geothermal gradient. At the seafloor, more than 4 m of sandy silt of unknown origin was encountered. Beneath this sand, to a depth of ~200 mbsf, the section was composed of interbedded mud and biogenic carbonate ooze. The biogenic ooze correlated to low density and high porosity intervals observed in the previously acquired logging while drilling (LWD) data and as measured. Calcareous nannofossil biostratigraphy constrains the entire record to the Pleistocene (< 0.91 million years) with a pronounced increase in sedimentation rate with depth. Beneath 200 mbsf, the section was predominantly composed of mud with two thicker, hydrate-bearing coarse-grained intervals, which are commonly known as the Blue and Orange sands. The dissolved gas concentration was quantified from pressure cores. In the shallow section, dissolved methane concentration increased below the sulfate-methane transition zone (SMTZ) and reaches saturation (the limit of solubility for methane) at 147 mbsf. Gas expansion was very common in conventional and depressurized pressure (conventionalized) cores below the SMTZ. At deeper depths, the methane concentration within muds bounding the Blue and Orange reservoirs was generally found to be less than saturation. The dissolved and hydrate gas composition is consistent with a microbial source, containing greater than 99.99% methane and only trace concentrations of ethane, propane, and butane. The methane to ethane ratio (C 1 /C 2 ) and the methane to ethane plus propane (C 1 /(C 2 +C 3 )) decrease with depth down to at least 678 mbsf, mainly driven by the increase in ethane with depth. It is unclear if this trend continues through the Orange sand interval. The δ 13 C isotopic signature of methane ranges between -69.9 and -78.5 ‰ Vienna Pee Dee Belemnite (VPDB). Pressure core recovery of all sandy intervals was poor. However, pressure core logs of the Orange sand show intervals of low density and high velocity, which are indicative of high hydrate saturation. One core from within the Orange sand was composed of interbedded graded sandy silt and mud. The sandy silts from this core are composed of mainly quartz and feldspar with some lithics. Most of the recovered pressure core samples are maintained at near in-situ pressure and temperature (within the hydrate stability field) at the University of Texas Pressure Core Center awaiting analysis. In the shallow section, samples will be used to determine the flux of organic carbon through the basin system, find the rate at which that carbon was consumed, and understand the microbial population responsible for these processes. In the deeper section, samples from in and around the hydrate reservoirs will be used to determine the petrophysical properties of the reservoir and bounding seals in these systems.

03 NATURAL GAS↗

Molecular Dynamics Simulation and Theoretical Analysis of Structural Relaxation, Bond Exchange Dynamics, and Glass Transition in Vitrimers

Vitrimers are a class of polymer networks featuring dynamic covalent cross-links that can undergo associative bond exchange. There has been recent interest in these materials due to their promise as recyclable thermosets or self-healing polymers because of the ability of vitrimer networks to rearrange at the molecular level and undergo macroscopic flow. However, the practical use of these materials often occurs in the supercooled regime or glassy state, where the implications of dynamic bonds are complicated by the interplay between slow activated segmental dynamics, cross-link (i.e., bond-exchange) kinetics, and ultimately material properties. Here, in this paper, we combine coarse-grained molecular dynamics simulation and microscopic statistical mechanical theory to understand how cross-linking kinetics affect material dynamics and how this couples to segmental relaxation of the polymeric network strands across a spectrum of length and time scales, especially in the supercooled regime. We characterize the Kuhn segmental alpha relaxation time and bond exchange time for vitrimer systems across various cross-link densities, temperatures, and bond exchange rates. Simulation and theory both exhibit a bending-up behavior for bond exchange time upon cooling, suggesting a coupling between bond exchange dynamics and segmental relaxation that intensifies with faster bond exchange kinetics. We also found bond exchange dynamics have an impact on Kuhn segment alpha relaxation time, which is most significant at higher cross-link densities. Both these effects are most prominent when the bond exchange time is similar to the Kuhn segment alpha relaxation time, and the resulting coupling of these two relaxation processes is tied to both the probability of a free end to find a bonded pair and the time scale of the constraints imposed by the dynamic cross-links. This relationship is reflected by a cross-link dependence of a theoretical parameter which represents the quantitative degree of coupling between bond exchange and segmental dynamics. Overall, the combination of simulation and theory clarifies the intricate interaction between bond kinetics and segmental relaxation and demonstrates the ability to provide molecular-level insights into vitrimer dynamics over a wide temperature range.

dynamic relaxation↗