Special Issue "Theory of Polymers at Interfaces"

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

Deadline for manuscript submissions: closed (31 August 2020).

Special Issue Editors

Prof. Dr. Jens-Uwe Sommer
E-Mail Website
Guest Editor
1. Leibniz-Institut für Polymerforschung Dresden, Hohe Strasse 6, 01069 Dresden, Germany
2. Institut für Theoretische Physik, Technische Universität Dresden, Zellescher Weg 17, 01062 Dresden, Germany
Interests: theoretical polymer and biopolymer physics; computer simulations in soft matter; statistical physics; polymers at interfaces; polymer networks; polymer solutions; polymer crystallization; polymers and nanoparticles
Special Issues and Collections in MDPI journals
Prof. Dr. Martin Kröger
E-Mail Website1 Website2
Guest Editor
Polymer Physics, Department of Materials, ETH Zurich, Leopold-Ruzicka-Weg 4, CH-8093 Zurich, Switzerland
Interests: polymer physics; computational physics; applied mathematics; stochastic differential equations; coarse-graining; biophysics
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Macromolecules in the vicinity of interfaces, adsorbed, attached, or depleted from surfaces, subject to confinement, or as part of self-assembled structures, nanocomposites, or multiphase systems often exhibit properties that make them differ significantly from their bulk counterparts. Adsorbed and grafted polymers change the effective surfaces and interface properties significantly and lead to new properties, such as switchable surfaces and exceptional tribological and crystallization behavior. The conformation properties and phase transitions of polymers are strongly affected by the presence of one or more phase boundaries, and many of the resulting problems of statistical physics are not yet resolved, despite the fact that polymers at surfaces and interfaces take an integral part in polymer physics research and education today. There exist a number of fundamental results for the adsorption and interface localization of flexible and semiflexible chains, polymers under confinement, and for the properties of adsorbed and grafted polymer layers. However, many important questions remain and new problems emerge in the context of polymer/biological interfaces, the influence of monomer sequences in copolymers, depletion, tack and friction effects, or multicomponent solutions in contact with surfaces and interfaces.

This Special Issue is concerned with the statics and dynamics, theory and simulation of polymers at interfaces and surfaces, including systems and phenomena listed below, in both equilibrium and out-of-equilibrium situations. The issue may thus also address polymers at interfaces subjected to flow, external stimuli or fields. New methods to model polymers at interfaces can be reported as well. Ideally, contributions focus on fundamental results, theory developments, models, mechanisms, algorithms, statistical physics, conformational statistics, and/or applications that will help to compile the current state-of-the-art and to highlight the range of application of polymers at interfaces.

Prof. Dr. Jens-Uwe Sommer
Prof. Dr. Martin Kröger
Guest Editors

Manuscript Submission Information

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Keywords

  • Interface-induced phase transitions
  • Brushes
  • Films
  • Pores
  • Confined geometries
  • Nanocomposites
  • Coatings
  • Adsorption
  • Chemisorption
  • Translocation
  • Depletion
  • Wetting
  • Crystallization
  • Wear
  • Friction
  • Scaling behavior
  • Field theories
  • Conformational statistics
  • Statistical polymer physics
  • Kinetic theory
  • Computer simulation

Published Papers (21 papers)

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Research

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Article
Gradient of Segmental Dynamics in Stereoregular Poly(Methyl Methacrylate) Melts Confined between Pristine or Oxidized Graphene Sheets
Polymers 2021, 13(5), 830; https://doi.org/10.3390/polym13050830 - 08 Mar 2021
Cited by 3 | Viewed by 809
Abstract
Segmental dynamics in unentangled isotactic, syndiotactic, and atactic poly(methyl methacrylate) (i-, a-, and s-PMMA) melts confined between pristine graphene, reduced graphene oxide, RGO, or graphene oxide, GO, sheets is studied at various temperatures, well above glass transition temperature, via atomistic molecular dynamics simulations. [...] Read more.
Segmental dynamics in unentangled isotactic, syndiotactic, and atactic poly(methyl methacrylate) (i-, a-, and s-PMMA) melts confined between pristine graphene, reduced graphene oxide, RGO, or graphene oxide, GO, sheets is studied at various temperatures, well above glass transition temperature, via atomistic molecular dynamics simulations. The model RGO and GO sheets have different degrees of oxidization. The segmental dynamics is studied through the analysis of backbone torsional motions. In the vicinity of the model nanosheets (distances less than ≈2 nm), the dynamics slows down; the effect becomes significantly stronger with increasing the concentration of the surface functional groups, and hence increasing polymer/surface specific interactions. Upon decreasing temperature, the ratios of the interfacial segmental relaxation times to the respective bulk relaxation times increase, revealing the stronger temperature dependence of the interfacial segmental dynamics relative to the bulk dynamics. This heterogeneity in temperature dependence leads to the shortcoming of the time-temperature superposition principle for describing the segmental dynamics of the model confined melts. The alteration of the segmental dynamics at different distances, d, from the surfaces is described by a temperature shift, ΔTseg(d) (roughly speaking, shift of a characteristic temperature). Next, to a given nanosheet, i-PMMA has a larger value of ΔTseg than a-PMMA and s-PMMA. This trend correlates with the better interfacial packing and longer trains of i-PMMA chains. The backbone torsional autocorrelation functions are shown in the frequency domain and are qualitatively compared to the experimental dielectric loss spectra for the segmental α-relaxation in polymer nanocomposites. The εT(f) (analogous of dielectric loss, ε(f), for torsional motion) curves of the model confined melts are broader (toward lower frequencies) and have lower amplitudes relative to the corresponding bulk curves; however, the peak frequencies of the εT(f) curves are only slightly affected. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Structural and Dynamical Characteristics of Short-Chain Branched Ring Polymer Melts at Interface under Shear Flow
Polymers 2020, 12(12), 3068; https://doi.org/10.3390/polym12123068 - 21 Dec 2020
Cited by 1 | Viewed by 665
Abstract
We present a detailed analysis of the interfacial chain structure and dynamics of confined polymer melt systems under shear over a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations, paying particular attention to the rheological influence of the closed-loop ring [...] Read more.
We present a detailed analysis of the interfacial chain structure and dynamics of confined polymer melt systems under shear over a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations, paying particular attention to the rheological influence of the closed-loop ring geometry and short-chain branching. We analyzed the interfacial slip, characteristic molecular mechanisms, and deformed chain conformations in response to the applied flow for linear, ring, short-chain branched (SCB) linear, and SCB ring polyethylene melts. The ring topology generally enlarges the interfacial chain dimension along the neutral direction, enhancing the dynamic friction of interfacial chains moving against the wall in the flow direction. This leads to a relatively smaller degree of slip (ds) for the ring-shaped polymers compared with their linear analogues. Furthermore, short-chain branching generally resulted in more compact and less deformed chain structures via the intrinsically fast random motions of the short branches. The short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone, which is mostly aligned in the flow direction, thereby enhancing the dynamic wall friction of the moving interfacial chains toward the flow direction. These features afford a relatively lower ds and less variation in ds in the weak-to-intermediate flow regimes. Accordingly, the interfacial SCB ring system displayed the lowest ds among the studied polymer systems throughout these regimes owing to the synergetic effects of ring geometry and short-chain branching. On the contrary, the structural disturbance exerted by the highly mobile short branches promotes the detachment of interfacial chains from the wall at strong flow fields, which results in steeper increasing behavior of the interfacial slip for the SCB polymers in the strong flow regime compared to the pure linear and ring polymers. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study
Polymers 2020, 12(11), 2591; https://doi.org/10.3390/polym12112591 - 04 Nov 2020
Cited by 1 | Viewed by 945
Abstract
We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular [...] Read more.
We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular dynamics simulations. NP dispersion can be achieved in either oligomeric or entangled polymeric matrices due to the presence of electrostatic interactions. We show that the overall conformations of ionic oligomer chains, as characterized by their radii of gyration, are affected by the presence and the amount of charged NPs, while the dimensions of charged entangled polymers remain unperturbed. Both the dynamical behavior of polymers and NPs, and the lifetime and amount of temporary crosslinks, are found to depend on the ratio between the Bjerrum length and characteristic distance between charged monomers. Polymer–polymer entanglements start to decrease beyond a certain NP loading. The dynamics of ionic NPs and polymers is very different compared with their non-ionic counterparts. Specifically, ionic NP dynamics is getting enhanced in entangled matrices and also accelerates with the increase of NP loading. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Forward Flux Sampling of Polymer Desorption Paths from a Solid Surface into Dilute Solution
Polymers 2020, 12(10), 2275; https://doi.org/10.3390/polym12102275 - 03 Oct 2020
Viewed by 542
Abstract
We compute desorption rates for isolated polymers adsorbed to a solid wall with a rare event sampling technique called multilevel splitting, also known as forward flux sampling. We interpret computed rates with theories based on the conjecture that the product [...] Read more.
We compute desorption rates for isolated polymers adsorbed to a solid wall with a rare event sampling technique called multilevel splitting, also known as forward flux sampling. We interpret computed rates with theories based on the conjecture that the product tdesDRg2 of the desorption time tdes and diffusivity D divided by squared radius of gyration Rg scales with exp(h/Rg) where h is the equilibrium ratio of adsorbed surface concentration of polymer Γ to bulk concentration of polymer c. As the polymer–wall interaction energy is increased, the slope of lntdesDRg2 vs. NVMFkBT nearly approaches unity, as expected for strongly-adsorbing chains, where N is the degree of polymerization and VMF is the height-averaged monomer–wall interaction energy for a strongly adsorbed chain. However, we also find that this scaling law is only accurate when adsorption strength per monomer exceeds a threshold value on the order of 0.3–0.5 kBT for a freely jointed chain without or with excluded volume effects. Below the critical value, we observe that tdesDRg2 becomes nearly constant with N, so that tdesNα, with α2. This suggests a crossover from “strong” detachment-controlled to a “weak” diffusion-controlled desorption rate as VMF/kBT drops below some threshold. These results may partially explain experimental data, that in some cases show “strong” exponential dependence of desorption time on chain length, while in others a “weak” power-law dependence is found. However, in the “strong” adsorption case, our results suggest much longer desorption times than those measured, while the reverse is true in the weak adsorption limit. We discuss possible reasons for these discrepancies. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts
Polymers 2020, 12(10), 2205; https://doi.org/10.3390/polym12102205 - 25 Sep 2020
Cited by 2 | Viewed by 737
Abstract
The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in [...] Read more.
The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
A Microscopically Motivated Model for Particle Penetration into Swollen Biological Networks
Polymers 2020, 12(9), 1912; https://doi.org/10.3390/polym12091912 - 25 Aug 2020
Viewed by 808
Abstract
Biological gels (bio-gels) are hydrated polymer networks that serve diverse biological functions, which often lead to intentional or unintentional exposure to particulate matter. In this work, we derive a microscopically motivated framework that enables the investigation of penetration mechanisms into bio-gels. We distinguish [...] Read more.
Biological gels (bio-gels) are hydrated polymer networks that serve diverse biological functions, which often lead to intentional or unintentional exposure to particulate matter. In this work, we derive a microscopically motivated framework that enables the investigation of penetration mechanisms into bio-gels. We distinguish between two types of mechanisms: spontaneous (unforced) penetration and forced penetration. Using experimental data available in the literature, we exploit the proposed model to characterize and compare between the microstructures of respiratory, intestinal, and cervicovaginal mucus and two types of biofilms. Next, we investigate the forced penetration process of spherical and ellipsoidal particles into a locally quadrilateral network. The proposed framework can be used to improve and complement the analysis of experimental findings in vitro, ex vivo, and in vivo. Additionally, the insights from this work pave the way towards enhanced designs of nano-medicines and allow the assessment of risk factors related to the nano-pollutants exposure. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Atomistic Investigation on the Wetting Behavior and Interfacial Joining of Polymer-Metal Interface
Polymers 2020, 12(8), 1696; https://doi.org/10.3390/polym12081696 - 29 Jul 2020
Cited by 2 | Viewed by 911
Abstract
Polymer-metal hybrid structures can reduce the weight of components while ensuring the structural strength, which in turn save cost and subsequently fuel consumption. The interface strength of polymer-metal hybrid structure is mainly determined by the synergistic effects of interfacial interaction and mechanical interlocking. [...] Read more.
Polymer-metal hybrid structures can reduce the weight of components while ensuring the structural strength, which in turn save cost and subsequently fuel consumption. The interface strength of polymer-metal hybrid structure is mainly determined by the synergistic effects of interfacial interaction and mechanical interlocking. In this study, the wetting behavior of polypropylene (PP) melt on metal surface was studied by molecular dynamics simulation. Atomistic models with smooth surface and nano-column arrays on Al substrate were constructed. Influences of melt temperature, surface roughness and metal material on the wetting behavior and interfacial joining were analyzed. Afterwards the separation process of injection-molded PP-metal hybrid structure was simulated to analyze joining strength. Results show that the initially sphere-like PP model gradually collapses in the wetting simulation. With a higher temperature, it is easier for molecule chains to spread along the surface. For substrate with rough surface, high density is observed at the bottom or on the upper surface of the column. The contact state is transitioning from Wenzel state to Cassie–Baxter state with the decrease of void fraction. The inner force of injection-molded PP-Fe hybrid structure during the separation process is obviously higher, demonstrating a greater joining strength. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Self-Consistent Field Modeling of Pulling a Test-Chain away from or Pushing It into a Polymer Adsorption Layer
Polymers 2020, 12(8), 1684; https://doi.org/10.3390/polym12081684 - 28 Jul 2020
Cited by 1 | Viewed by 601
Abstract
We consider single chain force measurements to unravel characteristics of polymers at interfaces and to determine parameters that control adsorption or probe layer characteristics that are difficult to access otherwise. The idea is to have at the tip of an atomic force microscope [...] Read more.
We consider single chain force measurements to unravel characteristics of polymers at interfaces and to determine parameters that control adsorption or probe layer characteristics that are difficult to access otherwise. The idea is to have at the tip of an atomic force microscope (AFM), a probe chain and measure its behaviour near interfaces by pushing it to, or pulling it away from it. The self-consistent field modeling of this reveals that in the pulling mode—i.e., when the chain has an affinity for the surface—a typically inhomogeneous flower-like conformation forms with an adsorbed ’pancake’ and a stretched stem (tether) from the surface to the tip of the AFM. When about half the segments is in the tether it snaps loose in a first-order like fashion. The critical distance of the end-point from the surface and the critical force are experimentally accessible. Details of this transition depend on the surrounding of the test chain. Inversely, and this opens up many possibilities, the test chain reports about its surroundings. Our focus is on the classical case of homopolymers at interfaces. Pulling experiments may reveal the adsorption strength, the (average) chain length and/or the polymer concentration of the freely dispersed/adsorbed polymers. When the test-chain is non-adsorbing we envision that pushing this test-chain into the adsorption layer reports about various layer characteristics such as the layer thickness and (local) density. Moreover, when the test-chain has a length longer than the entanglement length, we can imagine that non-trivial dynamical properties of loops and tails may be scrutinised. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures
Polymers 2020, 12(7), 1576; https://doi.org/10.3390/polym12071576 - 16 Jul 2020
Viewed by 998
Abstract
Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer–polymer (OP) and oligomer–gel ( [...] Read more.
Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer–polymer ( O P ) and oligomer–gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel–oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz–Slyozov–Wagner (LSW) law ( τ ) τ 1 / 3 . Our work allows for rational design of polymer/gel–oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
A Coarse-Grained Force Field for Silica–Polybutadiene Interfaces and Nanocomposites
Polymers 2020, 12(7), 1484; https://doi.org/10.3390/polym12071484 - 02 Jul 2020
Cited by 6 | Viewed by 1040
Abstract
We present a coarse-grained force field for modelling silica–polybutadiene interfaces and nanocomposites. The polymer, poly(cis-1,4-butadiene), is treated with a previously published united-atom model. Silica is treated as a rigid body, using one Si-centered superatom for each SiO2 unit. The parameters for the [...] Read more.
We present a coarse-grained force field for modelling silica–polybutadiene interfaces and nanocomposites. The polymer, poly(cis-1,4-butadiene), is treated with a previously published united-atom model. Silica is treated as a rigid body, using one Si-centered superatom for each SiO 2 unit. The parameters for the cross-interaction between silica and the polymer are derived by Boltzmann inversion of the density oscillations at model interfaces, obtained from atomistic simulations of silica surfaces containing both Q 4 (hydrophobic) and Q 3 (silanol-containing, hydrophilic) silicon atoms. The performance of the model is tested in both equilibrium and non-equilibrium molecular dynamics simulations. We expect the present model to be useful for future large-scale simulations of rubber–silica nanocomposites. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Directed Polymers and Interfaces in Disordered Media
Polymers 2020, 12(5), 1066; https://doi.org/10.3390/polym12051066 - 06 May 2020
Cited by 2 | Viewed by 628
Abstract
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field [...] Read more.
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field space is analysed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent ξ = ( 4 d ) / 2 , also obtained by the conventional replica method for the replica symmetric scenario. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
Article
Interface Characteristics of Neat Melts and Binary Mixtures of Polyethylenes from Atomistic Molecular Dynamics Simulations
Polymers 2020, 12(5), 1059; https://doi.org/10.3390/polym12051059 - 06 May 2020
Viewed by 815
Abstract
Molecular dynamics simulations of free-standing thin films of neat melts of polyethylene (PE) chains up to C150H302 and their binary mixtures with n-C13H28 are performed employing a united atom model. We estimate the surface tension values of [...] Read more.
Molecular dynamics simulations of free-standing thin films of neat melts of polyethylene (PE) chains up to C150H302 and their binary mixtures with n-C13H28 are performed employing a united atom model. We estimate the surface tension values of PE melts from the atomic virial tensor over a range of temperatures, which are in good agreement with experimental results. Compared with short n-alkane systems, there is an enhanced surface segregation of methyl chain ends in longer PE chains. Moreover, the methyl groups become more segregated in the surface region with decreasing temperature, leading to the conclusion that the surface-segregation of methyl chain ends mainly arises from the enthalpic origin attributed to the lower cohesive energy density of terminal methyl groups. In the mixtures of two different chain lengths, the shorter chains are more likely to be found in the surface region, and this molecular segregation in moderately asymmetric mixtures in the chain length (C13H28 + C44H90) is dominated by the enthalpic effect of methyl chain ends. Such molecular segregation is further enhanced and dominated by the entropic effect of conformational constraints in the surface for the highly asymmetric mixtures containing long polymer chains (C13H28 + C150H3020). The estimated surface tension values of the mixtures are consistent with the observed molecular segregation characteristics. Despite this molecular segregation, the normalized density of methyl chain ends of the longer chain is more strongly enhanced, as compared with the all-segment density of the longer chain itself, in the surface region of melt mixtures. In addition, the molecular segregation results in higher order parameter of the shorter-chain segments at the surface and deeper persistence of surface-induced segmental order into the film for the longer chains, as compared with those in neat melt films. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Dissipative Particle Dynamics Modeling of Polyelectrolyte Membrane–Water Interfaces
Polymers 2020, 12(4), 907; https://doi.org/10.3390/polym12040907 - 14 Apr 2020
Cited by 2 | Viewed by 857
Abstract
Previous experiments of water vapor penetration into polyelectrolyte membrane (PEM) thin films have indicated the influence of the water concentration gradient and polymer chemistry on the interface evolution, which will eventually affect the efficiency of the fuel cell operation. Moreover, PEMs of different [...] Read more.
Previous experiments of water vapor penetration into polyelectrolyte membrane (PEM) thin films have indicated the influence of the water concentration gradient and polymer chemistry on the interface evolution, which will eventually affect the efficiency of the fuel cell operation. Moreover, PEMs of different side chains have shown differences in water cluster structure and diffusion. The evolution of the interface between water and polyelectrolyte membranes (PEMs), which are used in fuel cells and flow batteries, of three different side-chain lengths has been studied using dissipative particle dynamics (DPD) simulations. Higher and faster water uptake is usually beneficial in the operation of fuel cells and flow batteries. The simulated water uptake increased with the increasing side chain length. In addition, the water uptake was rapid initially and slowed down afterwards, which is in agreement with the experimental observations. The water cluster formation rate was also found to increase with the increasing side-chain length, whereas the water cluster shapes were unaffected. Water diffusion in the membranes, which affects proton mobility in the PEMs, increased with the side-chain length at all distances from the interface. In conclusion, side-chain length was found to have a strong influence on the interface water structure and water penetration rates, which can be harnessed for the better design of PEMs. Since the PEM can undergo cycles of dehydration and rehydration, faster water uptake increases the efficiency of these devices. We show that the longer side chains with backbone structure similar to Nafion should be more suitable for fuel cell/flow battery usage. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Electroresponsive Polyelectrolyte Brushes Studied by Self-Consistent Field Theory
Polymers 2020, 12(4), 898; https://doi.org/10.3390/polym12040898 - 13 Apr 2020
Cited by 2 | Viewed by 1047
Abstract
End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong [...] Read more.
End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong and weak (pH-sensitive) polyelectrolytes to applied electrical field in both salt-free and salt-containing solutions. We demonstrate that both strong and weak polyelectrolyte brushes exhibit segregation of polyions in two populations if the surface is oppositely charged with respect to the brush. This segregation gives rise to complex patterns in the dependence of the brush thickness on salt concentration. We demonstrate that adjustable ionization of weak polyelectrolytes weakens their conformational response in terms of the dependence of brush thickness on the amplitude of the applied voltage. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement
Polymers 2020, 12(4), 799; https://doi.org/10.3390/polym12040799 - 03 Apr 2020
Cited by 1 | Viewed by 867
Abstract
Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme [...] Read more.
Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme conditions correspond to the case where the distance between the plates approaches the monomer size. An analysis of the local structure, based on the characteristic crystallographic element (CCE) norm, detects crystal nucleation and growth at packing densities well below the ones observed in bulk analogs. In a second step, we map the confined polymer chains into self-avoiding random walks (SAWs) on restricted lattices. We study all realizations of the cubic crystal system: simple, body centered, and face centered cubic crystals. For a given chain size (SAW length), lattice type, origin of SAW, and level of confinement, we enumerate all possible SAWs (equivalently all chain conformations) and calculate the size distribution. Results for intermediate SAW lengths are used to predict the behavior of long, fully entangled chains through growth formulas. The SAW analysis will allow us to determine the corresponding configurational entropy, as it is the driving force for the observed phase transition and the determining factor for the thermodynamic stability of the corresponding crystal morphologies. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Modeling of Stripe Patterns in Photosensitive Azopolymers
Polymers 2020, 12(4), 735; https://doi.org/10.3390/polym12040735 - 26 Mar 2020
Cited by 3 | Viewed by 962
Abstract
Placed at interfaces, azobenzene-containing materials show extraordinary phenomena when subjected to external light sources. Here we model the surface changes induced by one-dimensional Gaussian light fields in thin azopolymer films. Such fields can be produced in a quickly moving film irradiated with a [...] Read more.
Placed at interfaces, azobenzene-containing materials show extraordinary phenomena when subjected to external light sources. Here we model the surface changes induced by one-dimensional Gaussian light fields in thin azopolymer films. Such fields can be produced in a quickly moving film irradiated with a strongly focused laser beam or illuminating the sample through a cylindrical lens. To explain the appearance of stripe patterns, we first calculate the unbalanced mechanical stresses induced by one-dimensional Gaussian fields in the interior of the film. In accordance with our orientation approach, the light-induced stress originates from the reorientation of azobenzenes that causes orientation of rigid backbone segments along the light polarization. The resulting volume forces have different signs and amplitude for light polarization directed perpendicular and parallel to the moving direction. Accordingly, the grooves are produced by the stretching forces and elongated protrusions by the compressive forces. Implementation into a viscoplastic model in a finite element software predicts a considerably weaker effect for the light polarized along the moving direction, in accordance with the experimental observations. The maximum value in the distribution of light-induced stresses becomes in this case very close to the yield stress which results in smaller surface deformations of the glassy azopolymer. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Semiflexible Polymers Interacting with Planar Surfaces: Weak versus Strong Adsorption
Polymers 2020, 12(2), 255; https://doi.org/10.3390/polym12020255 - 22 Jan 2020
Cited by 4 | Viewed by 803
Abstract
Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness [...] Read more.
Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness κ as well as the strength of the adsorption potential ϵ w a l l are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter η ) and the mean square gyration radius parallel, R g 2 | | , and perpendicular, R g 2 , to the wall. While for strongly adsorbed chains EV has negligible effect on f and η , we find that R g 2 | | is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that f , η , and R g 2 converge to their asymptotic values with 1 / N corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Adsorption of a Helical Filament Subject to Thermal Fluctuations
Polymers 2020, 12(1), 192; https://doi.org/10.3390/polym12010192 - 10 Jan 2020
Cited by 1 | Viewed by 913
Abstract
We consider semiflexible chains governed by preferred curvature and twist and their flexural and twist moduli. These filaments possess a helical rather than straight three-dimensional (3D) ground state and we call them helical filaments (H-filament). Depending on the moduli, the helical shape may [...] Read more.
We consider semiflexible chains governed by preferred curvature and twist and their flexural and twist moduli. These filaments possess a helical rather than straight three-dimensional (3D) ground state and we call them helical filaments (H-filament). Depending on the moduli, the helical shape may be smeared by thermal fluctuations. Secondary superhelical structures are expected to form on top of the specific local structure of biofilaments, as is documented for vimentin. We study confinement and adsorption of helical filaments utilizing both a combination of numerical simulations and analytical theory. We investigate overall chain shapes, transverse chain fluctuations, loop and tail distributions, and energy distributions along the chain together with the mean square average height of the monomers z 2 . The number fraction of adsorbed monomers serves as an order parameter for adsorption. Signatures of adsorbed helical polymers are the occurrence of 3D helical loops/tails and spiral or wavy quasi-flat shapes. None of these arise for the Worm-Like-Chain, whose straight ground state can be embedded in a plane. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Grafting-Induced Structural Ordering of Lactide Chains
Polymers 2019, 11(12), 2056; https://doi.org/10.3390/polym11122056 - 11 Dec 2019
Cited by 2 | Viewed by 1153
Abstract
The structure of a grafted layer of lactide chains in the “dry brush” regime immersed in a melt of chemically similar polymer was examined while varying graft lengths. To this end, microsecond atomistic molecular dynamics simulations were performed. Almost no influence of graft [...] Read more.
The structure of a grafted layer of lactide chains in the “dry brush” regime immersed in a melt of chemically similar polymer was examined while varying graft lengths. To this end, microsecond atomistic molecular dynamics simulations were performed. Almost no influence of graft length on the fraction of the grafted chains backfolded to the grafting surface was found. However, a structural ordering was unexpectedly observed in the system when the length of the grafted lactide chains was close to approximately 10 Kuhn segments. This ordering of the grafts is characterized by the formation of helical fragments whose structure is in good agreement with the experimental data for the α crystal of the lactide chains. Both the backfolding and the structural ordering may be viewed as the initial stage of the crystallization of the layer of grafted lactide chains. In contrast to the known behavior for conventional polymer brushes in the “dry brush” regime, the structure of the grafted lactide chains can be either amorphous or ordered, depending on the graft length N and the grafting density σ when their product is fixed. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Article
Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections
Polymers 2019, 11(12), 2050; https://doi.org/10.3390/polym11122050 - 10 Dec 2019
Viewed by 802
Abstract
We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. [...] Read more.
We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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Review

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Review
Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems
Polymers 2020, 12(10), 2282; https://doi.org/10.3390/polym12102282 - 05 Oct 2020
Cited by 3 | Viewed by 910
Abstract
Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range [...] Read more.
Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems. Full article
(This article belongs to the Special Issue Theory of Polymers at Interfaces)
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