Block Copolymers Under Shear Flow

Summary: Microphase separation transition in block copolymer melts and solutions in equilibrium and under shear flow is reviewed. The non‐equilibrium molecular dynamics (NEMD) computer simulation methodology is presented in detail including the derivation of the SLLOD equations of motion, Gaussian thermostat, and operator‐splitting symplectic integrators. Results of our recent NEMD computer simulation studies of diblock copolymers in a selective solvent under shear flow are presented. Shear‐dependent structural, rheological, and microscopical properties are described. New phase transitions are discovered. The parallel‐perpendicular orientational transition in a weak‐strong flow is revealed. Theoretical approaches are reviewed including the Edwards Hamiltonian, Landau‐Ginzburg model, self‐consistent mean field theory, field‐theoretic simulation, as well as the time‐dependent Landau‐Ginzburg framework and its application to the studies of complex fluids.

     

Determining the Local Shear Viscosity of a Lipid Bilayer System by Reverse Non‐Equilibrium Molecular Dynamics Simulations

The parallel shear viscosity of a dipalmitoylphosphatidylcholine (DPPC) bilayer system is studied by reverse non‐equilibrium molecular dynamics simulations (RNEMD) with two different united‐atom force fields. The results are related to diffusion coefficients and structural distributions obtained by equilibrium molecular simulations. We investigate technical issues of the algorithm in the bilayer setup, namely, the dependence of the velocity profiles on the imposed flux and the influence of the thermostat on the calculated shear viscosity. We introduce the concept of local shear viscosity and investigate its dependence on the slip velocity of the monolayers and the particle density at the headgroup–water interface and the tail–tail interface. With this we demonstrate that the lipid bilayer is more viscous than the surrounding water phase, and that slip takes place near the headgroup region and in the centre of the bilayer where the alkyl tails meet. We also quantify the apparent increase in viscosity of the water molecules entangled at the water–headgroup interface.     

Order and Phase Behavior of a Cylinder Forming Diblock Copolymers and Nano‐Particles Mixture in Confinement: A Molecular Dynamics Study

We study a coarse grained model of cylinder forming diblock copolymers and nano‐particles (NPs) mixture confined between Lennard–Jones hard walls. Two models for non‐selective interactions between monomers and NPs are applied. In the case of purely repulsive interactions between NPs and monomers (athermal case) strong segregation of NPs at the film surfaces and the formation of droplets of particles inside the copolymer film can be observed. For weakly attractive interactions between NPs and monomers (thermal case) formation of droplets of particles disappears and segregation on the film surfaces depend on temperature. The uptake of NPs by the copolymer film in the thermal case displays a non‐monotonic dependence on temperature which can be qualitatively explained by a mean‐field model. In both cases of non‐selective interactions NPs are preferentially localized at the interface between the microphase domains.

     

Dissipative Particle Dynamics Simulation of Microphase Separation and Properties of Linear–Dendritic Diblock Copolymer Melts under Steady Shear Flow

Summary: Dissipative particle dynamic simulations were performed on the microphase separation, end‐to‐end distance, and shear viscosity of linear–dendritic diblock copolymers under steady shear flow. The results show that their microstructure and properties depend on both the shear rate and the degree of branching, and they can incorporate the characteristics of both linear and dendritic polymers to lead to new materials with unique properties.

Schematic structure for the linear‐dendritic copolymer G4 described in this work.     

Linear Viscoelastic Behavior of Unentangled Polymer Melts via Non‐Equilibrium Molecular Dynamics

Summary: We present and assess the use of non‐equilibrium molecular dynamics (NEMD) simulation method for the direct study of the linear viscoelastic behavior of polymer melts. The polymer melt is modeled by a collection of repulsive, anharmonic multibead chains subjected to small amplitude oscillatory shear flow. We present results for chain lengths below the critical entanglement length and obtain good agreement with theoretical results for the viscoelastic behavior of melts of low molecular weight. The range of oscillation frequencies attainable in the simulation is of a few decades. Thus we use, as in experiments, a time‐temperature superposition rule to extend the frequency domain. As a side result, we confirm the so‐called Cox‐Merz rule.

Snapshot from a non‐equilibrium molecular dynamics (3D) simulation of a polymer melt with 100 chains and 40 beads.     

Multicompartment Micellar Solutions in Shear: A Dissipative Particle Dynamics Study

Summary: Dissipative particle dynamics simulations were performed to study the effect of shear on the rheological behavior of multicompartment micellar solutions, demonstrating that both shear thickening and thinning can occur, and the macroscopic behavior was elucidated at a molecular level. In addition, a novel shear‐induced morphology of “sphere‐on‐rod” was observed. This work provides useful information towards a complete understanding of the properties and morphologies of multicompartment micelles that is useful for future rational synthesis of novel micelles.

Shear‐induced morphological transitions and rheological behavior in multicompartment micellar solutions formed from star triblock copolymers.     

Molecular Dynamics Investigation of the Thermo‐Responsive Polymer Poly(N‐isopropylacrylamide)

Using molecular dynamics simulations with an OPLS force field, the lower critical solution temperature (LCST) of single‐ and multiple‐chain PNIPAM solutions in water is investigated. The sample containing ten polymer chains shows a sudden drop in size and volume at 305 K. Such an effect is absent in the single‐chain system. Large fluctuations of the physical properties of a short single‐chain prevent any clear detection of the LCST for the chosen model system, at least on the time scale of 200 ns. The results provide evidence that a critical number of PNIPAM monomer units must be present in the simulated system before MD simulations are capable to detect conformational changes unambiguously.

     

Changes in the Hydration State of a Block Copolymer of Poly(N‐isopropylacrylamide) and Poly(ethylene oxide) on Thermosensitive Micellization in Water

A diblock copolymer of poly(N‐isopropylacrylamide) and poly(ethylene oxide) (PiPA‐b‐PEO) has been prepared by radical polymerization with a ceric ion initiation system. Its thermosensitive micellization has been investigated by means of IR and fluorescence spectroscopy. The PiPA segments are critically dehydrated above 33.5°C (5 wt.‐%) and associate through hydrophobic interaction to form the hydrophobic core of the micelle. In contrast, the change in the hydration state of the PEO segments upon micellization is small.     

Glass Transition Temperature and Chain Flexibility of Ethylene‐Norbornene Copolymers from Molecular Dynamics Simulations

Summary: Model chains of ethylene‐norbornene copolymers were built up using the results of ¹³C NMR spectral analysis of copolymer samples synthesized with metallocene‐based catalysts. Our models statistically reproduce the microstructure, composition, and tacticity of the copolymer chains of experimental samples. They were used to test if MD simulations are suitable to investigate the relationships between microstructure and macroscopic properties. In particular, MD simulations were applied to calculate the glass transition temperature and to study the chain flexibility by the analysis of ACF of specific virtual bonds. Plots of specific volume versus temperature computed for models of four copolymer samples having different microstructures and norbornene contents yield T_g values in good agreement with experiments. Moreover, comparison of the ACFs provides some qualitative indications about the relationship between chain stereochemistry and T_g.

ACF functions of the virtual bonds with microstructures NENE (bottom) and ENNE (top).     

Preparation of Size Controllable Polypyrrole Sub‐Microcapsules Using SEBS Copolymer as the Building Block

Summary: SEBS is used as building blocks to fabricate size controllable polypyrrole (PPy) capsules. Polypyrrole shells grow on the surfaces of the size controllable oxidant sub‐microparticles dispersed in the solution cast film of a SEBS copolymer by vapor phase polymerization. After washing in ethanol, PPy sub‐microcapsules dispersed in a SEBS matrix are obtained. This technique shows advantages of lower cost and less pollution, as compared with the gold‐template method reported in the literature.

A TEM image of polypyrrole sub‐microcapsules dispersed in a SEBS matrix.     

Effect of Microstructures on the Phase Transition Behavior of P(CL‐GL)‐PEG‐P(CL‐GL) Triblock Copolymer Aqueous Solutions

Amphiphilic poly[(ε‐caprolactone)‐co‐glycolide]‐block‐poly(ethylene glycol)‐block‐poly[(ε‐caprolactone)‐co‐glycolide) [P(CL‐GL)‐PEG‐P(CL‐GL)] triblock copolymers with different average lengths of caproyl sequences (L_CL) were synthesized by ring‐opening polymerization at different temperatures. A 25% aqueous solution of the copolymer with L_CL = 11.0 formed a gel, owing to strong crystallinity‐induced hydrophobicity at low temperature, and underwent a gel‐sol transition (UCST behavior) when the temperature was increased to 40 °C. In contrast, the solution of copolymer with L_CL = 6.7 underwent a sol‐gel transition (LCST behavior) due to micelle aggregation. However, a clear sol‐turbid sol phase transition was observed for the copolymer with more random microstructures (L_CL = 5.2).

     

Equilibrium Swelling of an Epoxy‐Resin in Contact with Water – A Molecular Dynamics Simulation Study

Full Paper: We have studied the equilibrium swelling of an idealized model network based on a realistic epoxy‐resin in contact with water using the molecular dynamics simulation method. We use a novel method to measure the water chemical potential inside the network as function of water concentration. The equality of the water chemical potential computed in this fashion with the bulk water chemical potential under the same thermodynamic conditions determines the equilibrium water content and the swelling ratio. We study the dependence of the water content as function of temperature and as function of the size of the atomic partial charges.

Schematic representation of the simulation volume. Spheres represent epoxy units with n = 0. The dashed lines represent curing agent units with m = 5.     

Continuous Thermodynamic Integration in Field‐Theoretic Simulations of Structured Polymers

This work explores the use of continuous thermodynamic integration in field‐theoretic simulations of a symmetric diblock copolymer melt. Free energies of the lamellar and disorder phases are evaluated by thermodynamic integration from a reference state (an Einstein crystal, λ = 0) to a diblock copolymer (λ = 1). This is followed by integration over the interaction parameter, χ_b , to locate the order–disorder transition (ODT). Then the equilibrium lamellar spacing and free energy cost of stretching and compressing lamellae are examined. The ODT, lamellar spacing, and compression modulus are consistent with previous calculations, though found faster and more precisely. The above quantities do not depend on simulation box size, suggesting that finite‐size effects are small and simulating two lamellar periods is sufficient to accurately evaluate bulk behavior. Furthermore, the statistical uncertainty in the ODT increases quickly with system size, suggesting that small systems may lead to more precise results.     

Polyelectrolyte micelles in salt‐free solutions: Micelle size and electrostatic potential

The structural and electrical characteristics of polyelectrolyte micelles formed by diblock copolymers with one charged block and one solvophobic block are studied by the means of molecular dynamics simulations using the Primitive model at different Bjerrum lengths. The properties of interest are the mean aggregation number, the shape, the electrical potential as a function of the distance of the micelle's center of mass and the zeta potential. We found that for partially charged short A blocks the micelles’ mass distribution function is at least bimodal, indicating the coexistence of small and large micelles in agreement with theoretical and experimental findings. The zeta potential is not a monotonic function of the length of the charged block. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 924–934     

Azobenzene‐Containing Block Copolymers as Light‐Induced Reworkable Adhesives: Effects of Molecular Weight,Composition, and Block Copolymer Architectures on the Adhesive Properties

We previously reported that ABA‐type triblock copolymers with azobenzene‐containing terminal blocks can be utilized as a light‐induced reworkable adhesive that enables repeatable bonding and debonding on demand. The reworkability was based on the photoisomerization of the azobenzene moiety and concomitant softening and hardening of the azo blocks. Our aim in this study is to investigate the effect of the composition, molecular weight, and block copolymer architectures on the reworkable adhesive properties. For this purpose, we prepared AB diblock, ABA triblock, and 4‐arm (AB)₄ star‐block copolymers consisting of polymethacrylates bearing an azobenzene moiety (A block) and 2‐ethylhexyl (B block) side chains and performed adhesion tests by using these block copolymers. As a result, among the ABA block copolymers with varied compositions and molecular weights, the ABA triblock copolymers with an azo block content of about 50 wt % and relatively low molecular weight could achieve an appropriate balance between high adhesion strength and low residual adhesion strength upon UV irradiation. Furthermore, the 4‐arm star‐block structure not only enhances the adhesion strength, but also maintains low residual adhesion strength when exposed to UV irradiation. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 806–813     

Modeling of Structural,Energetic, and Dynamic Properties of Few‐Atom Silver Clusters Embedded in Polynucleotide Strands by Using Molecular Dynamics

This work concerns the study of the structural, energetic, and dynamic properties of fluorescent systems composed of silver clusters stabilized by polynucleotide strands. To do so, classical interaction potentials relative to silver, neutral and cationic, were introduced in the AMBER force field. Molecular dynamics simulations allowed analysis of the nature and force of the interactions between the various parts of the nucleic oligomers and the silver clusters. Conformational analyses were necessary to explore the flexibility of the supramolecular assemblies, specifically by radial distribution functions and Ramachandran‐type maps.     

Speciation and Structural Properties of Hydrothermal Solutions of Sodium and Potassium Sulfate Studied by Molecular Dynamics Simulations

Aqueous solutions of salts at elevated pressures and temperatures play a key role in geochemical processes and in applications of supercritical water in waste and biomass treatment, for which salt management is crucial for performance. A major question in predicting salt behavior in such processes is how different salts affect the phase equilibria. Herein, molecular dynamics (MD) simulations are used to investigate molecular‐scale structures of solutions of sodium and/or potassium sulfate, which show contrasting macroscopic behavior. Solutions of Na?SO₄ exhibit a tendency towards forming large ionic clusters with increasing temperature, whereas solutions of K?SO₄ show significantly less clustering under equivalent conditions. In mixed systems (Na_xK_2?xSO₄), cluster formation is dramatically reduced with decreasing Na/(K+Na) ratio; this indicates a structure‐breaking role of K. MD results allow these phenomena to be related to the characteristics of electrostatic interactions between K⁺ and SO₄^2?, compared with the analogous Na⁺?SO₄^2? interactions. The results suggest a mechanism underlying the experimentally observed increasing solubility in ternary mixtures of solutions of Na?K?SO₄. Specifically, the propensity of sodium to associate with sulfate, versus that of potassium to break up the sodium–sulfate clusters, may affect the contrasting behavior of these salts. Thus, mutual salting‐in in ternary hydrothermal solutions of Na?K?SO₄ reflects the opposing, but complementary, natures of Na?SO₄ versus K?SO₄ interactions. The results also provide clues towards the reported liquid immiscibility in this ternary system.     

Cooperative Self‐Assembly of Nanoparticle Mixtures in Lamellar Diblock Copolymers: A Dissipative Particle Dynamics Study

Summary: Dissipative particle dynamics simulations are performed on the distribution of binary nanoparticle mixtures in lamellar diblock copolymers. The results show that the self‐assembly of nanoparticle mixtures in polymer matrix is a cooperative assembly that is affected by various factors, providing molecular‐level information for the rational design of new polymer nanocomposites with tailored properties.

The simulated polymer nanocomposite structure (the polymer matrix was omitted for clarity; P, gray; Q, black).     

Pulling Polymers on Energetically Disordered Surfaces: Molecular Dynamics Tests of Linear and Non‐linear Response

Equilibrium and non‐equilibrium molecular dynamics simulations of flexible polymer chains absorbed on heterogeneous surfaces are presented. The surfaces are flat but energetically disordered, consisting of a random mixture of weakly and more strongly absorbing sites (94 and 6%, respectively). For comparison, the two corresponding homogeneous surfaces are also simulated. This apparently weak energetic disorder can produce significant changes of the chain statistics, equilibrium dynamics, and non‐equilibrium response to a horizontal pulling force. On the disordered surfaces, the polymer–surface effective friction coefficient becomes strongly force‐dependent, as the dominant mode of motion changes from localized stick–slip events to smooth and continuous sliding. This is strongly reminiscent of the Schallamach model of rubber friction and the Maier–Göritz picture of the Payne effect in filled elastomers.