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Polymers
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Research on Polymer Simulation, Modeling and Computation
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Research on Polymer Simulation, Modeling and Computation

A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Polymer Physics and Theory".

Deadline for manuscript submissions: closed (30 October 2023) | Viewed by 14236

Special Issue Editors

Dr. Shengfeng Cheng

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Guest Editor
Department of Physics, Macromolecules Innovation Institute, Center for Soft Matter and Biological Physics, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA
Interests: polymer informatics; molecular dynamics simulation; polymer physics; polymer nanocomposites
Special Issues, Collections and Topics in MDPI journals
Dr. Jiajia Zhou

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Guest Editor
School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
Interests: soft matter dynamics; theory and simulation
Special Issues, Collections and Topics in MDPI journals
Dr. Ting Ge

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Guest Editor
Department of Chemistry and Biochemistry, University of South Carolina, Columbia 29208, USA
Interests: polymer conformation; dynamics; rheology and mechanics; molecular simulations; multi-scale modeling of polymers
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In silico simulation, modeling, and computation have evolved into powerful tools to reveal the molecular mechanisms underlying the macroscopic phenomena and behavior of polymers, predict their physicochemical properties, and discover and design next-generation polymeric materials. A wide range of simulation methods and packages, from those based on quantum mechanics with subatomic resolutions to continuum frameworks dealing with bulk materials, are at the disposal of researchers to study polymers over a full spectrum of length, time, and energy scales under various conditions. Multiscale models are also in rapid development and validation. This Special Issue aims to serve as a platform to allow polymer researchers to exchange exciting results, recent progress, and emerging ideas on understanding polymers from the perspectives of simulation, modeling, and computation. The issue welcomes reports and reviews covering any aspect of polymer modeling, using methods including but not limited to density functional theory, molecular dynamics simulation, Monte Carlo simulation, coarse-grained modeling, lattice Boltzmann simulation, self-consistent field theory, mesh-free methods, multiscale simulation, and machine learning algorithms.

Dr. Shengfeng Cheng
Dr. Jiajia Zhou
Dr. Ting Ge
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Polymers is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (10 papers)

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Research

20 pages, 3418 KiB  
Article
Interpretable Machine Learning Framework to Predict the Glass Transition Temperature of Polymers
by Md. Jamal Uddin and Jitang Fan
Polymers 2024, 16(8), 1049; https://doi.org/10.3390/polym16081049 - 10 Apr 2024
Viewed by 354
Abstract
The glass transition temperature of polymers is a key parameter in meeting the application requirements for energy absorption. Previous studies have provided some data from slow, expensive trial-and-error procedures. By recognizing these data, machine learning algorithms are able to extract valuable knowledge and [...] Read more.
The glass transition temperature of polymers is a key parameter in meeting the application requirements for energy absorption. Previous studies have provided some data from slow, expensive trial-and-error procedures. By recognizing these data, machine learning algorithms are able to extract valuable knowledge and disclose essential insights. In this study, a dataset of 7174 samples was utilized. The polymers were numerically represented using two methods: Morgan fingerprint and molecular descriptor. During preprocessing, the dataset was scaled using a standard scaler technique. We removed the features with small variance from the dataset and used the Pearson correlation technique to exclude the features that were highly connected. Then, the most significant features were selected using the recursive feature elimination method. Nine machine learning techniques were employed to predict the glass transition temperature and tune their hyperparameters. The models were compared using the performance metrics of mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2). We observed that the extra tree regressor provided the best results. Significant features were also identified using statistical machine learning methods. The SHAP method was also employed to demonstrate the influence of each feature on the model’s output. This framework can be adaptable to other properties at a low computational expense. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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21 pages, 4466 KiB  
Article
Translocation of Hydrophobic Polyelectrolytes under Electrical Field: Molecular Dynamics Study
by Seowon Kim, Nam-Kyung Lee, Min-Kyung Chae, Albert Johner and Jeong-Man Park
Polymers 2023, 15(11), 2550; https://doi.org/10.3390/polym15112550 - 31 May 2023
Cited by 1 | Viewed by 1008
Abstract
We studied the translocation of polyelectrolyte (PE) chains driven by an electric field through a pore by means of molecular dynamics simulations of a coarse-grained HP model mimicking high salt conditions. Charged monomers were considered as polar (P) and neutral monomers as hydrophobic [...] Read more.
We studied the translocation of polyelectrolyte (PE) chains driven by an electric field through a pore by means of molecular dynamics simulations of a coarse-grained HP model mimicking high salt conditions. Charged monomers were considered as polar (P) and neutral monomers as hydrophobic (H). We considered PE sequences that had equally spaced charges along the hydrophobic backbone. Hydrophobic PEs were in the globular form in which H-type and P-type monomers were partially segregated and they unfolded in order to translocate through the narrow channel under the electric field. We provided a quantitative comprehensive study of the interplay between translocation through a realistic pore and globule unraveling. By means of molecular dynamics simulations, incorporating realistic force fields inside the channel, we investigated the translocation dynamics of PEs at various solvent conditions. Starting from the captured conformations, we obtained distributions of waiting times and drift times at various solvent conditions. The shortest translocation time was observed for the slightly poor solvent. The minimum was rather shallow, and the translocation time was almost constant for medium hydrophobicity. The dynamics were controlled not only by the friction of the channel, but also by the internal friction related to the uncoiling of the heterogeneous globule. The latter can be rationalized by slow monomer relaxation in the dense phase. The results were compared with those from a simplified Fokker–Planck equation for the position of the head monomer. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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28 pages, 14567 KiB  
Article
Rheological Properties of Small-Molecular Liquids at High Shear Strain Rates
by Wenhui Li, JCS Kadupitiya and Vikram Jadhao
Polymers 2023, 15(9), 2166; https://doi.org/10.3390/polym15092166 - 02 May 2023
Viewed by 1344
Abstract
Molecular-scale understanding of rheological properties of small-molecular liquids and polymers is critical to optimizing their performance in practical applications such as lubrication and hydraulic fracking. We combine nonequilibrium molecular dynamics simulations with two unsupervised machine learning methods: principal component analysis (PCA) and t-distributed [...] Read more.
Molecular-scale understanding of rheological properties of small-molecular liquids and polymers is critical to optimizing their performance in practical applications such as lubrication and hydraulic fracking. We combine nonequilibrium molecular dynamics simulations with two unsupervised machine learning methods: principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), to extract the correlation between the rheological properties and molecular structure of squalane sheared at high strain rates (106–1010s−1) for which substantial shear thinning is observed under pressures P∈0.1–955 MPa at 293 K. Intramolecular atom pair orientation tensors of 435×6 dimensions and the intermolecular atom pair orientation tensors of 61×6 dimensions are reduced and visualized using PCA and t-SNE to assess the changes in the orientation order during the shear thinning of squalane. Dimension reduction of intramolecular orientation tensors at low pressures P=0.1,100 MPa reveals a strong correlation between changes in strain rate and the orientation of the side-backbone atom pairs, end-backbone atom pairs, short backbone-backbone atom pairs, and long backbone-backbone atom pairs associated with a squalane molecule. At high pressures P≥400 MPa, the orientation tensors are better classified by these different pair types rather than strain rate, signaling an overall limited evolution of intramolecular orientation with changes in strain rate. Dimension reduction also finds no clear evidence of the link between shear thinning at high pressures and changes in the intermolecular orientation. The alignment of squalane molecules is found to be saturated over the entire range of rates during which squalane exhibits substantial shear thinning at high pressures. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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15 pages, 8618 KiB  
Article
Analysis and Validation of Varied Simulation Parameters in the Context of Thermoplastic Foams and Special Injection Molding Processes
by Dimitri Oikonomou and Hans-Peter Heim
Polymers 2023, 15(9), 2119; https://doi.org/10.3390/polym15092119 - 28 Apr 2023
Cited by 3 | Viewed by 1318
Abstract
The simulation solutions of different plastic injection molding processes are as multifaceted as the field of injection molding itself. In this study, the simulation of a special injection molding process, which generates partially foamed integral components, was parameterized and performed. This partial and [...] Read more.
The simulation solutions of different plastic injection molding processes are as multifaceted as the field of injection molding itself. In this study, the simulation of a special injection molding process, which generates partially foamed integral components, was parameterized and performed. This partial and physical foaming is realized by a defined volume expansion of the mold cavity. Using the injection molding simulation software Moldex 3D, this so-called Pull and Foam process was digitally reconstructed and simulated. Since the Pull and Foam process is a special injection molding technique for producing foamed components, the validity of the simulation results was analyzed and evaluated. With the use of Moldex 3D, varied settings such as different bubble growth models and mesh topologies were set, parameterized, and then analyzed, to provide differentiated numerical calculation solutions. Actual manufactured components represent the experimental part of this study and are produced for reference. Different evaluation methods were used to quantify morphological quantities such as porosities, local densities, and cell distributions. These methods are based on two-dimensional and three-dimensional imaging techniques such as optical microscopy and X-ray microtomography (µ-CT). Thus, this structural characterization of the manufactured samples serves as the validation basis for the calculated results of the simulations. According to the illustrated results, the adequate selection of bubble growth models and especially mesh topologies must be considered for valid simulation of specific core-back techniques, such as the Pull and Foam injection molding process. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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20 pages, 1319 KiB  
Article
Molecular Weight Distribution of Branched Polymers: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory
by Chengyuan Wen, Roy Odle and Shengfeng Cheng
Polymers 2023, 15(7), 1791; https://doi.org/10.3390/polym15071791 - 04 Apr 2023
Cited by 4 | Viewed by 1578
Abstract
It is challenging to predict the molecular weight distribution (MWD) for a polymer with a branched architecture, though such information will significantly benefit the design and development of branched polymers with desired properties and functions. A Monte Carlo (MC) simulation method based on [...] Read more.
It is challenging to predict the molecular weight distribution (MWD) for a polymer with a branched architecture, though such information will significantly benefit the design and development of branched polymers with desired properties and functions. A Monte Carlo (MC) simulation method based on the Gillespie algorithm is developed to quickly compute the MWD of branched polymers formed through step-growth polymerization, with a branched polyetherimide from two backbone monomers (4,4′-bisphenol A dianhydride and m-phenylenediamine), a chain terminator (phthalic anhydride), and a branching agent (tris[4-(4-aminophenoxy)phenyl] ethane) as an example. This polymerization involves four reactions that can be all reduced to a condensation reaction between an amine group and a carboxylic anhydride group. A comparison between the MC simulation results and the predictions of the Flory-Stockmayer theory on MWD shows that the rates of the reactions are determined by the concentrations of the functional groups on the monomers involved in each reaction. It further shows that the Flory-Stockmayer theory predicts MWD well for systems below the gel point but starts to fail for systems around or above the gel point. However, for all the systems, the MC method can be used to reliably predict MWD no matter if they are below or above the gel point. Even for a macroscopic system, a converging distribution can be quickly obtained through MC simulations on a system of only a few hundred to a few thousand monomers that have the same molar ratios as in the macroscopic system. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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9 pages, 1160 KiB  
Communication
Correlations in Hard- and Soft-Core Generic Polymer Models
by Qiang Wang
Polymers 2023, 15(5), 1180; https://doi.org/10.3390/polym15051180 - 26 Feb 2023
Cited by 1 | Viewed by 1158
Abstract
Generic polymer models capturing the chain connectivity and the non-bonded excluded-volume interactions between polymer segments can be classified into hard- and soft-core models depending on their non-bonded pair potential. Here we compared the correlation effects on the structural and thermodynamic properties of the [...] Read more.
Generic polymer models capturing the chain connectivity and the non-bonded excluded-volume interactions between polymer segments can be classified into hard- and soft-core models depending on their non-bonded pair potential. Here we compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory, and found different behaviors of the soft-core models at large invariant degree of polymerization (IDP) depending on how IDP is varied. We also proposed an efficient numerical approach, which enables us to accurately solve the PRISM theory for chain lengths as large as 106. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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14 pages, 5245 KiB  
Article
The Relationship between Structure and Performance of Different Polyimides Based on Molecular Simulations
by Peng Zhang, Yadong Dai, Hansong Liu, Botao Dong, Yilun Yao, Jinsong Sun, Tao Yang, Xiangyu Zhong and Jianwen Bao
Polymers 2023, 15(3), 646; https://doi.org/10.3390/polym15030646 - 27 Jan 2023
Viewed by 1483
Abstract
A polyimide (PI) molecular model was successfully constructed to compare the performance of PIs with different structures. In detail, the structure of the cross-linked PI resin, the prepolymer melt viscosity, and the glass-transition temperature (Tg) were investigated using molecular simulations. The [...] Read more.
A polyimide (PI) molecular model was successfully constructed to compare the performance of PIs with different structures. In detail, the structure of the cross-linked PI resin, the prepolymer melt viscosity, and the glass-transition temperature (Tg) were investigated using molecular simulations. The results indicate that benzene ring and polyene-type cross-linked structures dominate the properties of the PIs. Moreover, the prepolymer melt viscosity simulations show that the 6FDA-APB and the ODPA-APB systems have a low viscosity. The results for the Tg and the distribution dihedral angle reveal that the key factor affecting bond flexibility may be the formation of a new dihedral angle after cross-linking, which affects the Tg. The above results provide an important reference for the design of PIs and have important value from the perspective of improving the efficiency of new product development. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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18 pages, 2058 KiB  
Article
A Feynman Path Integral-like Method for Deriving Reaction–Diffusion Equations
by Changhao Li, Jianfeng Li and Yuliang Yang
Polymers 2022, 14(23), 5156; https://doi.org/10.3390/polym14235156 - 27 Nov 2022
Viewed by 1119
Abstract
This work is devoted to deriving a more accurate reaction–diffusion equation for an A/B binary system by summing over microscopic trajectories. By noting that an originally simple physical trajectory might be much more complicated when the reactions are incorporated, we introduce diffusion–reaction–diffusion (DRD) [...] Read more.
This work is devoted to deriving a more accurate reaction–diffusion equation for an A/B binary system by summing over microscopic trajectories. By noting that an originally simple physical trajectory might be much more complicated when the reactions are incorporated, we introduce diffusion–reaction–diffusion (DRD) diagrams, similar to the Feynman diagram, to derive the equation. It is found that when there is no intermolecular interaction between A and B, the newly derived equation is reduced to the classical reaction–diffusion equation. However, when there is intermolecular interaction, the newly derived equation shows that there are coupling terms between the diffusion and the reaction, which will be manifested on the mesoscopic scale. The DRD diagram method can be also applied to derive a more accurate dynamical equation for the description of chemical reactions occurred in polymeric systems, such as polymerizations, since the diffusion and the reaction may couple more deeply than that of small molecules. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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45 pages, 1972 KiB  
Article
Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids
by Hugo A. Castillo-Sánchez, Leandro F. de Souza and Antonio Castelo
Polymers 2022, 14(22), 4958; https://doi.org/10.3390/polym14224958 - 16 Nov 2022
Cited by 3 | Viewed by 1737
Abstract
In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite [...] Read more.
In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the HiGTree/HiGFlow system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software RheoTool that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation (VVF). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the HiGFlow software. More importantly, we show that our methodology implemented in the HiGTreee/HiGFlow system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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27 pages, 13232 KiB  
Article
Polymorphism and Perfection in Crystallization of Hard Sphere Polymers
by Miguel Herranz, Katerina Foteinopoulou, Nikos Ch. Karayiannis and Manuel Laso
Polymers 2022, 14(20), 4435; https://doi.org/10.3390/polym14204435 - 20 Oct 2022
Cited by 7 | Viewed by 1573
Abstract
We present results on polymorphism and perfection, as observed in the spontaneous crystallization of freely jointed polymers of hard spheres, obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous [...] Read more.
We present results on polymorphism and perfection, as observed in the spontaneous crystallization of freely jointed polymers of hard spheres, obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration, after an initial dominance of the hexagonal closed packed (HCP) polymorph and a transitory random hexagonal close packed (rHCP) morphology, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal, compared to the amorphous state. In spite of the significant local re-arrangements, as reflected in the bending and torsion angle distributions, the average chain size remains unaltered during crystallization. Polymers in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant. Full article
(This article belongs to the Special Issue Research on Polymer Simulation, Modeling and Computation)
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