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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 12824

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Special Issue Editors

Prof. Dr. Juan J. Freire

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Guest Editor

Department of Sciences and Physical Chemistry, Universidad Nacional de Educacion a Distancia (UNED), Madrid, Spain
Interests: conformational properties; flexible chains; polymers; simulations

Prof. Dr. Costas H. Vlahos

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Guest Editor

Department of Chemistry, University of Ioannina, Ioannina, Greece
Interests: simulations; micelles; brushes; polyelectrolytes
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Special Issue Information

Dear Colleagues,

Progress in modelling and simulation is crucial for an improved understanding of polymers. Although purely theoretical work has established the foundations of polymer science, the variety and complexity of polymer structures and systems can only be fully understood with the help of numerical simulations. Historically, the design of very simple polymer models in lattices has been successfully used to predict or verify basic scaling laws, such as the one that describes the dependence between size and number of monomers, or molecular weight. Nowadays, there are a growing number of problems requiring simulation work. Although lattice, bead-spring or freely jointed bead models are still being used to investigate general features of different types of polymeric systems, more realistic representations are needed in many other instances to understand the properties of specific polymers as well as to explore their potential applications. Hyperbranched polymers and dendrimers constitute nanostructures with significant applications, including drug carrying and delivering, that can only be properly addressed through fully atomistic simulation including solvent molecules. Coarse-grained models, where several atoms or atomic groups are included in simplified units, are useful to provide specific chemical details without involving as much computation as purely atomistic models.

This Special Issue offers a broad spectrum of polymer simulations, considering different models and addressing a variety of current interests in terms of systems and applications. Namely, simulation on polymers as drug carriers, compatibilization of polymer mixtures, behaviour of polymer nanostructures under different solvent conditions, physical properties of polymers under stress or physical constrains, formation of the glass state and crystallization and the study of complex systems composed of polymers and nano-objects are included on the list of considered topics.

Prof. Dr. Juan J. Freire
Prof. Dr. Costas H. Vlahos
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.

Keywords

polymer models
novel simulation methods for polymer systems
simulation of polymeric nanostructures
simulation on complex polymeric systems
simulation of polymer properties

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Published Papers (10 papers)

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Research

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23 pages, 7330 KiB

Open AccessArticle

Entropy-Driven Crystallization of Hard Colloidal Mixtures of Polymers and Monomers

by Olia Bouzid, Daniel Martínez-Fernández, Miguel Herranz and Nikos Ch. Karayiannis

Polymers 2024, 16(16), 2311; https://doi.org/10.3390/polym16162311 - 15 Aug 2024

Viewed by 442

Abstract

The most trivial example of self-assembly is the entropy-driven crystallization of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. Inspired by the difference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. As a first result, a more precise determination of the melting point for freely jointed chains of tangent hard spheres is extracted. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres, as quantified by the Voronoi polyhedron, is systematically more spherical and more symmetric compared to that of spheres belonging to chains. In turn, the local environment of the ordered phase is more symmetric and more spherical compared to that of the initial random packing, demonstrating the entropic origins of the phase transition. In general, increasing the polymer content reduces the degree of crystallinity and increases the melting point to higher volume fractions. According to the present findings, relative concentration is another determining factor in controlling the phase behavior of hard colloidal mixtures based on polymers. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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24 pages, 11838 KiB

Open AccessArticle

Lagrangian Split-Step Method for Viscoelastic Flows

by Martina Bašić, Branko Blagojević, Branko Klarin, Chong Peng and Josip Bašić

Polymers 2024, 16(14), 2068; https://doi.org/10.3390/polym16142068 - 19 Jul 2024

Viewed by 463

Abstract

This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier–Stokes equations, is introduced for incompressible viscoelastic flows in a Lagrangian context. The Lagrangian differencing dynamics (LDD) method, which is a thoroughly validated Lagrangian method for Newtonian and non-Newtonian incompressible flows, is extended to solve the introduced split-step scheme to simulate viscoelastic flows based on the Oldroyd-B constitutive model. To validate and evaluate the new method’s capabilities, the following benchmarks were used: lid-driven cavity flow, droplet impact response, 4:1 planar sudden contraction, and die swelling. These findings highlight the LDD method’s effectiveness in accurately simulating viscoelastic flows and capturing large deformations and memory effects. Even though the extra stress was directly modeled without any regularization approach, the method produced stable simulations for high Weissenberg numbers. The stability and performance of the the Lagrangian numerics for complex temporal evolution of material properties and stress responses encourage its use for industrial problems dealing with polymers. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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17 pages, 7439 KiB

Open AccessArticle

Enhancing Polymer Blend Compatibility with Linear and Complex Star Copolymer Architectures: A Monte Carlo Simulation Study with the Bond Fluctuation Model

by Juan J. Freire and Costas Vlahos

Polymers 2024, 16(12), 1626; https://doi.org/10.3390/polym16121626 - 8 Jun 2024

Viewed by 1265

Abstract

A Monte Carlo study of the compatibilization of A/B polymer blends has been performed using the bond fluctuation model. The considered compatibilizers are copolymer molecules composed of A and B blocks. Different types of copolymer structures have been included, namely, linear diblock and 4-block alternating copolymers, star block copolymers, miktoarm stars, and zipper stars. Zipper stars are composed of two arms of diblock copolymers arranged in alternate order (AB and BA) from the central unit, along with two homogeneous arms of A and B units. The compatibilization performance has been characterized by analyzing the equilibration of repulsion energy, the simulated scattering intensity obtained with opposite refractive indices for A and B, the profiles along a coordinate axis, the radial distribution functions, and the compatibilizer aggregation numbers. According to the results, linear alternate block copolymers, star block copolymers, and zipper stars exhibit significantly better compatibilization, with zipper stars showing slightly but consistently better performance. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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16 pages, 2973 KiB

Open AccessArticle

Geant4 Simulation of Photon- and Neutron-Shielding Capabilities of Biopolymer Blends of Poly(lactic acid) and Poly(hydroxybutyrate)

by Hanan Akhdar and Maryam Alshehri

Polymers 2023, 15(21), 4257; https://doi.org/10.3390/polym15214257 - 29 Oct 2023

Cited by 1 | Viewed by 1446

Abstract

Simulation is used by scientists to imitate a real-life experimental setup in order to save time, costs and effort. Geant4, a toolkit based on the Monte Carlo method, has been widely used in investigating the radiation-shielding properties of different materials. In many recent studies, researchers have focused on polymers and their shielding capabilities. Poly(lactic acid) (PLA) is a widely used biopolymer in many applications due to its excellent mechanical properties. However, it has limitations related to its degree of crystallinity and molecular characteristics, which could be improved through blending with other biodegradable polymers such as poly(hydroxybutyrate) (PHB). Previous published studies have shown that the mechanical properties of such blends can be improved further. In this work, the effect of blending PHB with PLA on the photon- and neutron-shielding capabilities will be investigated using Geant4 over a wide energy range, as well as the effect of doping those blends with metal oxides. The results show that the shielding properties of the polymers are affected by blending with other polymers and by doping the polymer blends with different metal oxides, and they confirm that Geant4 is a very reliable tool that can simulate any material’s shielding properties against photons and neutrons. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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11 pages, 6839 KiB

Open AccessArticle

Thermal Reflow Simulation for PMMA Structures with Nonuniform Viscosity Profile

by Fedor Sidorov and Alexander Rogozhin

Polymers 2023, 15(18), 3731; https://doi.org/10.3390/polym15183731 - 11 Sep 2023

Viewed by 1180

Abstract

This paper presents a new approach to the simulation of the thermal reflow of e-beam-exposed polymethyl methacrylate (PMMA) taking into account its nonuniform viscosity profile. This approach is based on numerical “soapfilm” modeling of the surface evolution, processed by the free software “Surface Evolver” in area normalization mode. The PMMA viscosity profile is calculated via the simulation of the exposed PMMA number average molecular weight distribution using the Monte-Carlo method and empirical formulas. The relation between the PMMA viscosity and the mobility of PMMA surface vertices was determined via the thermal reflow simulation for uniform PMMA gratings using analytical and numerical approaches in a wide viscosity range. The agreement between reflowed profiles simulated with these two approaches emphasizes the applicability of “soapfilm” modeling in the simulation of polymer thermal reflow. The inverse mobility of PMMA surface vertices appeared to be proportional to the PMMA viscosity with a high precision. The developed approach enables thermal reflow simulations for complex nonuniform structures, which allows the use of predictable reflow as a stage of 3D microfabrication. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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22 pages, 31131 KiB

Open AccessArticle

Investigation of Auxetic Structural Deformation Behavior of PBAT Polymers Using Process and Finite Element Simulation

by Yanling Schneider, Vinzenz Guski, Ahmet O. Sahin, Siegfried Schmauder, Javad Kadkhodapour, Jonas Hufert, Axel Grebhardt and Christian Bonten

Polymers 2023, 15(14), 3142; https://doi.org/10.3390/polym15143142 - 24 Jul 2023

Cited by 1 | Viewed by 1056

Abstract

The current work investigates the auxetic tensile deformation behavior of the inversehoneycomb structure with 5 × 5 cells made of biodegradable poly(butylene adipate-coterephthalate) (PBAT). Fused deposition modeling, an additive manufacturing method, was used to produce such specimens. Residual stress (RS) and warpage, more or less, always exist in such specimens due to their layer-by-layer fabrication, i.e., repeated heating and cooling. The RS influences the auxetic deformation behavior, but its measurement is challenging due to its very fine structure. Instead, the finite-element (FE)-based process simulation realized using an ABAQUS plug-in numerically predicts the RS and warpage. The predicted warpage shows a negligibly slight deviation compared to the design topology. This process simulation also provides the temperature evolution of a small-volume material, revealing the effects of local cyclic heating and cooling. The achieved RS serves as the initial condition for the FE model used to investigate the auxetic tensile behavior. With the outcomes from FE calculation without consideration of the RS, the effect of the RS on the deformation behavior is discussed for the global force–displacement curve, the structural Poisson’s ratio evolution, the deformed structural status, the stress distribution, and the evolution, where the first three and the warpage are also compared with the experimental results. Furthermore, the FE simulation can easily provide the global stress–strain flow curve with the total stress calculated from the elemental stresses. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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17 pages, 5684 KiB

Open AccessArticle

Chemical Feedback in Templated Reaction-Assembly of Polyelectrolyte Complex Micelles: A Molecular Simulation Study of the Kinetics and Clustering

by Christos Gioldasis, Apostolos Gkamas, Othonas A. Moultos and Costas Hristos Vlahos

Polymers 2023, 15(14), 3024; https://doi.org/10.3390/polym15143024 - 12 Jul 2023

Cited by 1 | Viewed by 945

Abstract

The chemical feedback between building blocks in templated polymerization of diblock copolymers and their consecutive micellization was studied for the first time by means of coarse-grained molecular dynamics simulations. Using a stochastic polymerization model, we were able to reproduce the experimental findings on the effect of chemical feedback on the polymerization rates at low and high solution concentrations. The size and shape of micelles were computed using a newly developed software in Python conjugated with graph theory. In full agreement with the experiments, our simulations revealed that micelles formed by the templated micellization are more spherical and have a lower radius of gyration than those formed by the traditional two-step micellization method. The advantage of molecular simulation over the traditional kinetic models is that with the simulation, one studies in detail the heterogeneous polymerization in the presence of the oppositely charged template while also accounting for the incompatibility between reacted species, which significantly influences the reaction process. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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14 pages, 3228 KiB

Open AccessArticle

Computer Simulation Insight into the Adsorption and Diffusion of Polyelectrolytes on Oppositely Charged Surface

by Anna A. Glagoleva, Alexander A. Yaroslavov and Valentina V. Vasilevskaya

Polymers 2023, 15(13), 2845; https://doi.org/10.3390/polym15132845 - 28 Jun 2023

Cited by 1 | Viewed by 1114

Abstract

In the present work, by means of computer simulation, we studied the adsorption and diffusion of polyelectrolyte macromolecules on oppositely charged surfaces. We considered the surface coverage and the charge of the adsorbed layer depending on the ionization degree of the macromolecules and the charge of the surface and carried out a computer experiment on the polymer diffusion within the adsorbed layers, taking into account its strong dependency on the surface coverage and the macromolecular ionization degree. The different regimes were distinguished that provided maximal mobility of the polymer chains along with a high number of charged groups in the layer, which could be beneficial for the development of the functional coatings. The results were compared with those of previous experiments on the adsorption of polyelectrolyte layers that may be applied as biocidal renewable coatings that can reversibly desorb from the surface. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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Review

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26 pages, 9349 KiB

Open AccessReview

Micromechanical Models for FDM 3D-Printed Polymers: A Review

by Rowin J. M. Bol and Branko Šavija

Polymers 2023, 15(23), 4497; https://doi.org/10.3390/polym15234497 - 23 Nov 2023

Cited by 6 | Viewed by 1541

Abstract

Due to its large number of advantages compared to traditional subtractive manufacturing techniques, additive manufacturing (AM) has gained increasing attention and popularity. Among the most common AM techniques is fused filament fabrication (FFF), usually referred to by its trademarked name: fused deposition modeling (FDM). This is the most efficient technique for manufacturing physical three-dimensional thermoplastics, such that FDM machines are nowadays the most common. Regardless of the 3D-printing methodology, AM techniques involve layer-by-layer deposition. Generally, this layer-wise process introduces anisotropy into the produced parts. The manufacturing procedure creates parts possessing heterogeneities at the micro (usually up to 1 mm) and meso (mm to cm) length scales, such as voids and pores, whose size, shape, and spatial distribution are mainly influenced by the so-called printing process parameters. Therefore, it is crucial to investigate their influence on the mechanical properties of FDM 3D-printed parts. This review starts with the identification of the printing process parameters that are considered to affect the micromechanical composition of FDM 3D-printed polymers. In what follows, their (negative) influence is attributed to characteristic mechanical properties. The remainder of this work reviews the state of the art in geometrical, numerical, and experimental analyses of FDM-printed parts. Finally, conclusions are drawn for each of the aforementioned analyses in view of microstructural modeling. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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41 pages, 1747 KiB

Open AccessReview

Simulational Tests of the Rouse Model

by George David Joseph Phillies

Polymers 2023, 15(12), 2615; https://doi.org/10.3390/polym15122615 - 8 Jun 2023

Cited by 1 | Viewed by 2242

Abstract

An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes [...] Read more.

⟨ {(X_{p} (0))}^{2} ⟩

and time correlation functions

⟨ X_{p} (0) X_{p} (t) ⟩

of the Rouse mode

X_{p} (t)

. The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes

⟨ {(X_{p} (0))}^{2} ⟩

do not scale as

{sin}^{- 2} (p π / 2 N)

, N being the number of beads in the polymer. For small p (say,

p \leq 3

)

⟨ {(X_{p} (0))}^{2} ⟩

scales with p as

p^{- 2}

; for larger p, it scales as

p^{- 3}

. (ii) Rouse mode time correlation functions

⟨ X_{p} (t) X_{p} (0) ⟩

do not decay with time as exponentials; they instead decay as stretched exponentials

exp (- α t^{β})

β

depends on p, typically with a minimum near

N / 2

N / 4

. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For

p \neq q

⟨ X_{p} (t) X_{q} (0) ⟩

is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood–Riseman polymer model. Full article

(This article belongs to the Special Issue Computational Modeling and Simulations of Polymers)

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