Microstructural evolution and reverse flow in shear-banding of entangled polymer melts.

The temporal and spatial evolution of shear banding under startup of shear flow was simulated for highly entangled, linear, monodisperse polyethylene melts of differing molecular weight, C750H1502, C1200H2402, and C3000H6002, using a high-fidelity coarse-grained dissipative particle dynamics method. It was determined that shear stress was dominated by segmental orientation of entangled strands at low shear rates, but at a critical shear rate below the reciprocal of the Rouse time, flow-induced disentanglement resulted in the onset of chain tumbling that reduced the average degree of orientation, leading to a regime of decreasing shear stress, with a commensurate onset of increasing average chain extension imposed by the strong flow kinematics that ultimately drove the steady-state shear stress higher. During startup of shear flow, shear band development began immediately after the maximum in the first normal stress difference, where distinct fast and slow bands formed. The slow bands consisted of relatively entangled and coiled molecules, whereas the fast bands consisted of more disentangled and extended chains that experienced quasiperiodic rotation/retraction cycles. The simulation results often exhibited a generation of temporary reverse flow, in which the local fluid velocity was temporarily opposite to that of the bulk flow direction, at the onset of the shear-banding phenomena; this effect was consistent with earlier experiments and theoretical results. The physical mechanism for the generation of reverse flow during shear-band formation was investigated and found to be related to the recoil of the molecules comprising the slow band. Overall, the phenomenon of shear banding appeared to arise due to flow-induced disentanglement from orientational ordering and segmental stretching that affected individual chains to different degrees, ultimately resulting in regions of relatively coiled and entangled chains that evolved into a slow band, whereas the locally disentangled chains, experiencing quasiperiodic stretch-rotation cycles, formed a fast band. The transitional period resulted in a kinematic instability that generated the temporary reverse-flow phenomenon.

Turbulent Taylor-Couette flow of dilute polymeric solutions: a 10-year retrospective.

This retrospective aims to present a coherent history of important findings in direct numerical simulations and experiments in turbulent Taylor-Couette (TC) flow of dilute polymeric solutions in the last decade. Specifically, the sequence of flow transitions due to a continuous increase of fluid elasticity from classical Newtonian, to inertially and in turn to elastically dominated, and finally to the inertialess purely elastic turbulence, is presented. In each elastically modified flow state, the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kinetic energy production, spectral features as well as the self-sustaining cycles of turbulence, are discussed. Finally, to provide a broader perspective, an overview of important similarities and differences between elastically induced turbulence in prototypical curvilinear and rectilinear shear flows including the curvature-free limit of TC flow, namely, the spanwise-rotating plane Couette flow, is presented. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation.

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C1000H2002 polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory.

A method for calculating the nonequilibrium entropy of a flowing polymer melt via atomistic simulation.

Nonequilibrium thermodynamics as applied to polymeric liquids is limited by the inability to quantify the configurational entropy. There is no known experimental method to determine it rigorously. Theoretically, entropy is based entirely on the configurational microstate of the material, but for polymer liquids, the number of available configurations is immense and covers long length scales associated with the chain-like nature of the constituent molecules. In principle, however, it should be possible to calculate the entropy from a realistic molecular dynamics simulation that contains positional data for each atomic unit making up the polymer macromolecules. However, there are two challenges in calculating the entropy from an atomistic simulation: it is necessary to relate atomic positions to configurational mesostates, depending on the degree of coarse-graining assumed (if any), and then to entropy, and considerable computational resources are required to determine the three-dimensional probability distribution functions of the configurational mesostates. In this study, a method was developed to calculate nonequilibrium entropy using 3d probability distributions for a linear, entangled polyethylene melt undergoing steady-state shear and elongational flow. An approximate equation expressed in terms of second moments of the 3d distributions was also examined, which turned out to provide almost identical values of entropy as the fully 3d distributions at the mesoscopic level associated with the end-to-end vector of the polymer chains.

A theory for the coexistence of coiled and stretched configurational phases in the extensional flow of entangled polymer melts.

It has recently been demonstrated via nonequilibrium molecular dynamics (NEMD) simulation [M. H. Nafar Sefiddashti, B. J. Edwards, and B. Khomami, J. Chem. Phys. 148, 141103 (2018); Phys. Rev. Lett. 121, 247802 (2018)] that the extensional flow of entangled polymer melts can engender, within a definite strain-rate regime [expressed in terms of the Deborah number (De) based on the Rouse time], the coexistence of separate domains consisting primarily of either coiled or stretched chain-like macromolecules. This flow-induced phase separation results in bimodal configurational distributions, where transitions of individual molecules between the coiled and stretched states occur very slowly by hopping over an apparent energy activation barrier. We demonstrate that the qualitative aspects of this phenomenon can be described via the single-mode Rolie-Poly model including Convective Constraint Release (CCR) and finite extensibility of the chain-like macromolecules. This analysis reveals the physical mechanism for the configurational coexistence, namely, the nonlinear rate of change of the average entropic restoring force of a given entangled chain with extension. Under conditions of significant flow-induced disentanglement, the rate of change of the effective restoring force initially decreases with extension (effective spring softening) and then increases (hardens) as the maximum chain length is approached. When balanced by flow-induced chain stretching, we find that there can be two configuration states within the same De regime, as covered by the NEMD simulations; therefore, a region of conformational coexistence can indeed exist. However, we demonstrate that this coexistence of configurational microstates is only possible when the magnitude of the CCR parameters is consistent with the rate of flow-induced disentanglement, as observed in the NEMD simulations.

An Atomistic Molecular Dynamics Study of Titanium Dioxide Adhesion to Lipid Bilayers.

Titanium dioxide (TiO2) nanoparticles are found in an array of consumer and industrial products, and human exposure to these nanoparticles involves interaction with biological membranes. To understand the effect of the membrane lipid composition on bilayer perturbation by TiO2, we performed all-atom molecular dynamics simulations of nanosized TiO2 interacting with three single component bilayers differing only in their headgroup composition: the zwitterionic DOPC, which is overall neutral containing negatively charged phosphate and positively charged choline in its head, DOPG, which is overall anionic containing negatively charged phosphate and neutral glycerol, and the anionic DOPS, containing negatively charged phosphate attached to the hydroxyl side-chain of the amino acid, serine containing negatively charged carboxyl and positively charged ammonium. The nanoparticle adheres to all three bilayers causing a negative curvature on their top leaflet. However, the local deformation of DOPG was more pronounced than DOPC and DOPS. The anionic DOPG, which is the thinnest of the three bilayers, interacted most strongly with the TiO2. DOPS has the next strongest interaction; however, its high bending modulus enables it to resist deformation by the nanoparticle. DOPC has the weakest interaction with the nanoparticle of the three as it has the highest bending modulus and its zwitterionic head groups have strong cohesive interactions. We also observed a nonuniform response of the bilayers: the orientational order of the lipids near the nanoparticle decreases, while that of the lipids away from the nanoparticle increases. The overall thickness and bending modulus of DOPG increased upon contact with the nanoparticle owing to overall stiffening of the bilayer despite local softening, while the average structural and mechanical properties of DOPC and DOPS remain unchanged, which can be explained in part by the greater bilayer bending elasticicty of DOPC and DOPS. The above findings suggest that regions of biological membranes populated by anionic lipids with weaker bending elasticity will be more susceptible to perturbation by TiO2 nanoparticles than zwitterionic-rich regions.

Self-assembly of linear diblock copolymers in selective solvents: from single micelles to particles with tri-continuous inner structures.

Large-scale dissipative particle dynamics (DPD) simulations have been performed to investigate the self-assembly of over 20 000 linear diblock copolymer chains in a selective solvent. Specifically, we found that the transition from spherical to cylindrical vesicles and in turn to disk-like and onion-like vesicles, and finally to tri-continuous spherical particles is mainly due to the increase in the aggregation number. In addition, the structures with large aggregation numbers are formed through the fusion of smaller aggregates and the length of the corona block of the block copolymer plays a critical role in the resulting morphology. Furthermore, our simulations indicate that the very larger amount of polymer in our simulation is the key to the observation of a state of dynamic equilibrium between free chains and aggregates in solution, as well as the formation of more complex structures from linear diblock copolymers in selective solvents. Overall, this study paves the way for future coordinated experimental/computational studies on the formation of nanoparticles with complex morphologies from diblock copolymers, an area of great scientific and industrial interest.

Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts.

The characteristics of shear banding were investigated in entangled, polydisperse, linear polymer melts under steady-state and startup conditions of simple shear flow. This virtual experimentation was conducted using course-grained nonequilibrium dissipative particle dynamics simulations expressed in terms of a force-field representation that faithfully models the atomistic system dynamics. We examined melts with two mean molecular bead numbers of Nn = 2 50 and 400 and polydispersity indexes of 1.0, 1.025, and 1.05. The wide range of relaxation timescales in the polydisperse melts decreased the nonmonotonic character of the steady-state shear stress vs. shear rate profile compared to a monodisperse linear melt. The polydispersity level required to observe a stress plateau in the shear stress profile at intermediate shear rates was correlated with the nominal entanglement density. Startup of shear flow simulations revealed the development of spatial inhomogeneities and dynamic instabilities in polydisperse fluids containing both monotonic and nonmonotonic shear stress flow curves. Although the shape and duration of instabilities were found to be correlated with the monotonicity of the shear stress profile, the onset and underlying mechanism leading to the formation of shear bands were generally universal. The simulations revealed that perturbations arose soon after the occurrence of a large stress overshoot under startup conditions, and that banded structures stemmed from local reorientation and subsequent deconstruction of the entanglement network. Furthermore, data indicated that the inception of strain localization occurred at shear rates near the reciprocal of the Rouse characteristic timescale, [small gamma, Greek, dot above] > τR-1. Transient shear banding was observed in shorter chain melts undergoing startup of shear flow in which instabilities arose after the appearance of a stress overshoot. These instabilities eventually decayed, but only long after the stresses had attained their steady-state values. The longer chain melt exhibited a shear band structure that remained indefinitely after the stresses had attained steady state.

Configurational Microphase Separation in Elongational Flow of an Entangled Polymer Liquid.

Manufacturing of plastics is typically performed via flow processing of a molten polymeric fluid. Until recently, conventional knowledge has maintained that the deformation of the constituent molecules under flow is homogeneous and obeys Gaussian statistics. In this study via virtual experimentation, an entangled polyethylene melt subjected to planar elongational flow displays an unanticipated microphase separation into a heterogeneous liquid composed of regions of either highly stretched or tightly coiled macromolecules, thus providing a natural realization of a biphasic coil-stretch transition.

Communication: A coil-stretch transition in planar elongational flow of an entangled polymeric melt.

Virtual experimentation of atomistic entangled polyethylene melts undergoing planar elongational flow revealed an amazingly detailed depiction of individual macromolecular dynamics and the resulting effect on bistable configurational states. A clear coil-stretch transition was evident, in much the same form as first envisioned by de Gennes for dilute solutions of high polymers, resulting in an associated hysteresis in the configurational flow profile over the range of strain rates predicted by theory. Simulations conducted at steady state revealed bimodal distribution functions, in which equilibrium configurational states were simultaneously populated by relatively coiled and stretched molecules which could transition from one conformational mode to the other over a relatively long time scale at critical values of strain rates. The implication of such behavior points to a double-well conformational free energy potential with an activation barrier between the two configurational minima.

Lipid-Detergent Phase Transitions During Detergent-Mediated Liposome Solubilization.

We investigate the phase transition stages for detergent-mediated liposome solubilization of bio-mimetic membranes with the motivation of integrating membrane-bound Photosystem I into bio-hybrid opto-electronic devices. To this end, the interaction of two non-ionic detergents n-dodecyl-ß-D-maltoside (DDM) and Triton X-100 (TX-100) with two types of phospholipids, namely DPhPC (1,2-diphytanoyl-sn-glycero-3-phosphocholine) and DPPG (1,2-dipalmitoyl-sn-glycero-3-phospho-(1'-rac-glycerol)), are examined. Specifically, solubilization processes for large unilamellar liposomes are studied with the aid of turbidity measurements, dynamic light scattering, and cryo-transmission electron microscopy imaging. Our results indicate that the solubilization process is well depicted by a three-stage model, wherein the lamellar-to-micellar transitions for DPhPC liposomes are dictated by the critical detergent/phospholipid ratios. The solubilization of DPhPC by DDM is devoid of formation of a "gel-like" phase. Furthermore, our results indicate that DDM is a stable candidate for DPhPC solubilization and proteoliposome formation. Finally, although the solubilization of DPPG with DDM indicated the familiar three-stage process, the same process with TX-100 indicate structural deformation of vesicles into complex network of kinetically trapped micro- and nanostructured arrangements of lipid bilayers.

Elucidating the Molecular Processes for Creating Large or Bimodal Soft Nanoparticles from Block Copolymers via Blending.

By simply blending two diblock copolymers with the same chemistry but with different compositions one is able to create well-defined larger soft -nanoparticles as well as bimodal soft nanoparticles. Specifically, blending two diblock copolymers in a solvent good for both blocks followed by a gradual introduction of a non-solvent results in a mixed micelle, larger than their pure block-copolymer-forming micelles. The formation of well-defined larger micelle is due to the balance between the ability of the mixed micelles to assemble or merge in comparison to their pure diblock copolymer micelles. Evidently, the blending ratio, the mixing protocol, and non-solvent addition rate are crucial to achieving well-defined larger or bimodal micelles.

Elucidating the role of methyl viologen as a scavenger of photoactivated electrons from photosystem I under aerobic and anaerobic conditions.

We present detailed electrochemical investigations into the role of dissolved O2 in electrolyte solutions in scavenging photoactivated electrons from a uniform photosystem I (PS I) monolayer assembled on alkanethiolate SAM (self-assembled monolayer)/Au surfaces while using methyl viologen (MV(2+)) as the redox mediator. To this end, we report results for direct measurements of light induced photocurrent from uniform monolayer assemblies of PS I on C9 alkanethiolate SAM/Au surfaces. These measurements, apart from demonstrating the ability of dissolved O2 in the electrolyte medium to act as an electron scavenger, also reveal its essential role in driving the solution-phase methyl viologen to initiate light-induced directional electron transfer from an electron donor surface (Au) via surface assembled PS I trimers. Specifically, our systematic electrochemical measurements have revealed that the dissolved O2 in aqueous electrolyte solutions form a complex intermediate species with MV that plays the essential role in mediating redox pathways for unidirectional electron transfer processes. This critical insight into the redox-mediated electron transfer pathways allows for rational design of electron scavengers through systematic tuning of mediator combinations that promote such intermediate formation. Our current findings facilitate the incorporation of PS I-based bio-hybrid constructs as photo-anodes in future photoelectrochemical cells and bio-electronic devices.

A new bead-spring model for simulation of semi-flexible macromolecules.

A bead-spring model for semi-flexible macromolecules is developed to overcome the deficiencies of the current coarse-grained bead-spring models. Specifically, model improvements are achieved through incorporation of a bending potential. The new model is designed to accurately describe the correlation along the backbone of the chain, segmental length, and force-extension behavior of the macromolecule even at the limit of 1 Kuhn step per spring. The relaxation time of different Rouse modes is used to demonstrate the capabilities of the new model in predicting chain dynamics.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation.

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ∼ cs (-0.5) as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Block copolymer morphology formation on topographically complex surfaces: a self-consistent field theoretical study.

A self-consistent field theoretic study is performed to study morphological development of lamellae-forming diblock copolymers on substrates with a well-defined roughness, modeled as trenches of varying depth and width engraved into the substrates. There are three possible lamellar orientations observed: horizontal lamellae, vertical lamellae that are parallel to the trench direction, and vertical lamellae that are perpendicular to the trench direction. Which of these three morphologies formed depends upon the trench width and surface affinity; however, trench depth has a relatively insignificant effect on the morphological development. Therefore, tuning trench width, but not trench depth, should allow for a reduction of the morphological defect density in directed self-assembly of lamellar morphology of diblock copolymers.

Computationally efficient algorithms for incorporation of hydrodynamic and excluded volume interactions in Brownian dynamics simulations: a comparative study of the Krylov subspace and Chebyshev based techniques.

Excluded volume and hydrodynamic interactions play a central role in macromolecular dynamics under equilibrium and non-equilibrium settings. The high computational cost of incorporating the influence of hydrodynamic interaction in meso-scale simulation of polymer dynamics has motivated much research on development of high fidelity and cost efficient techniques. Among them, the Chebyshev polynomial based techniques and the Krylov subspace methods are most promising. To this end, in this study we have developed a series of semi-implicit predictor-corrector Brownian dynamics algorithms for bead-spring chain micromechanical model of polymers that utilizes either the Chebyshev or the Krylov framework. The efficiency and fidelity of these new algorithms in equilibrium (radius of gyration and diffusivity) and non-equilibrium conditions (transient planar extensional flow) are demonstrated with particular emphasis on the new enhancements of the Chebyshev polynomial and the Krylov subspace methods. In turn, the algorithm with the highest efficiency and fidelity, namely, the Krylov subspace method, is used to simulate dilute solutions of high molecular weight polystyrene in uniaxial extensional flow. Finally, it is demonstrated that the bead-spring Brownian dynamics simulation with appropriate inclusion of excluded volume and hydrodynamic interactions can quantitatively predict the observed extensional hardening of polystyrene dilute solutions over a broad molecular weight range.

PEGylated nanoparticles interact with macrophages independently of immune response factors and trigger a non-phagocytic, low-inflammatory response.

Poly-ethylene-glycol (PEG)-based nanoparticles (NPs) - including cylindrical micelles (CNPs), spherical micelles (SNPs), and PEGylated liposomes (PLs) - are hypothesized to be cleared in vivo by opsonization followed by liver macrophage phagocytosis. This hypothesis has been used to explain the rapid and significant localization of NPs to the liver after administration into the mammalian vasculature. Here, we show that the opsonization-phagocytosis nexus is not the major factor driving PEG-NP - macrophage interactions. First, mouse and human blood proteins had insignificant affinity for PEG-NPs. Second, PEG-NPs bound macrophages in the absence of serum proteins. Third, lipoproteins blocked PEG-NP binding to macrophages. Because of these findings, we tested the postulate that PEG-NPs bind (apo)lipoprotein receptors. Indeed, PEG-NPs triggered an in vitro macrophage transcription program that was similar to that triggered by lipoproteins and different from that triggered by lipopolysaccharide (LPS) and group A Streptococcus. Unlike LPS and pathogens, PLs did not increase transcripts involved in phagocytosis or inflammation. High-density lipoprotein (HDL) and SNPs triggered remarkably similar mouse bone-marrow-derived macrophage transcription programs. Unlike opsonized pathogens, CNPs, SNPs, and PLs lowered macrophage autophagosome levels and either reduced or did not increase the secretion of key macrophage pro-inflammatory cytokines and chemokines. Thus, the sequential opsonization and phagocytosis process is likely a minor aspect of PEG-NP - macrophage interactions. Instead, PEG-NP interactions with (apo)lipoprotein and scavenger receptors appear to be a strong driving force for PEG-NP - macrophage binding, entry, and downstream effects. We hypothesize that the high presence of these receptors on liver macrophages and on liver sinusoidal endothelial cells is the reason PEG-NPs localize rapidly and strongly to the liver.

Polymer-induced drag enhancement in turbulent Taylor-Couette flows: direct numerical simulations and mechanistic insight.

We report for the first time the polymer-induced breakdown of large-scale Taylor vortex structures leading to drag enhancement in viscoelastic turbulent Taylor-Couette flows. Specifically, we demonstrate that upon the addition of trace amounts of soluble high molecular weight macromolecules the Newtonian large-scale Taylor vortices are replaced by small-scale vortices in the inner and outer cylinder wall regions. This flow transition and a commensurate drag increase of up to 62% are facilitated by the presence of large polymeric normal stresses in a narrow region immediately close to the outer wall. A simple mechanism for this striking flow transition is proposed with the aim of paving the way for a mechanistic understanding of polymer-induced structure and drag modifications in high-Re turbulent curvilinear flows.

Molecular Processes Leading to Shear Banding in Entangled Polymeric Solutions.

The temporal and spatial evolution of shear banding during startup and steady-state shear flow was studied for solutions of entangled, linear, monodisperse polyethylene C3000H6002 dissolved in hexadecane and benzene solvents. A high-fidelity coarse-grained dissipative particle dynamics method was developed and evaluated based on previous NEMD simulations of similar solutions. The polymeric contribution to shear stress exhibited a monotonically increasing flow curve with a broad stress plateau at intermediate shear rates. For startup shear flow, transient shear banding was observed at applied shear rates within the steady-state shear stress plateau. Shear bands were generated at strain values where the first normal stress difference exhibited a maximum, with lifetimes persisting for up to several hundred strain units. During the lifetime of the shear bands, an inhomogeneous concentration distribution was evident within the system, with higher polymer concentration in the slow bands at low effective shear rate; i.e., γ˙<τR-1, and vice versa at high shear rate. At low values of applied shear rate, a reverse flow phenomenon was observed in the hexadecane solution, which resulted from elastic recoil of the molecules within the slow band. In all cases, the shear bands dissipated at high strains and the system attained steady-state behavior, with a uniform, linear velocity profile across the simulation cell and a homogeneous concentration.