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We explore the cellular uptake process of PEGylated liposomes and bicelles by investigating their membrane wrapping process using large-scale molecular dynamics simulations. We find that due to the mobility of ligands on the liposome/bicelle, the membrane wrapping process of a PEGylated liposome/bicelle can be divided into two stages, whose transition is determined by a critical wrapping fraction fc; it is reached when all the ligands are exhausted and bound to receptors within the cell membrane. Before this critical scenario is approached, the grafted polyethylene glycol (PEG) polymers aggregate together within the membrane-wrapped region of the liposome/bicelle, driven by ligand-receptor binding. For wrapping fractions f > fc, membrane wrapping cannot proceed unless a compressive membrane tension is provided. By systematically varying the membrane tension and PEG molar ratio, we establish phase diagrams about wrapping states for both PEGylated liposomes and bicelles. According to these diagrams, we find that the absolute value of the compressive membrane tension required by a fully wrapped PEGylated bicelle is smaller than that of the PEGylated liposome, indicating that the PEGylated bicelle is easily internalized by cells. Further theoretical analysis reveals that compared to a liposome, the flatter surface at the top of a bicelle makes it energetically more favored beyond the critical wrapping fraction fc. Our simulations confirm that the interplay between ligand mobility and NP geometry can significantly change the understanding about the influence of NP geometry on the membrane wrapping process. It can help us to better understand the cellular uptake process of the PEGylated liposome/bicelle and to improve the design of lipid-like NPs for drug delivery.

Dendronized polymers (DPs) are large and compact main-chain linear polymers with a cylindrical shape and cross-sectional diameters of up to ∼15 nm. They are therefore considered molecular objects, and it was of interest whether given their experimentally accessible, well-defined dimensions, the density of individual DPs could be determined. We present measurements on individual, deposited DP chains, providing molecular dimensions from scanning and transmission electron microscopy and mass-per-length values from quantitative scanning transmission electron microscopy. These results are compared with density values obtained from small-angle X-ray scattering on annealed bulk specimen and with classical envelope density measurements, obtained using hydrostatic weighing or a density gradient column. The samples investigated comprise a series of DPs with side groups of dendritic generations g = 1-8. The key findings are a very large spread of the density values over all samples and methods, and a consistent increase of densities with g over all methods. While this work highlights the advantages and limitations of the applied methods, it does not provide a conclusive answer to the question of which method(s) to use for the determination of densities of individual molecular objects. We are nevertheless confident that these first attempts to answer this challenging question will stimulate more research into this important aspect of polymer and soft matter science.

Structural elucidation of 2D polymer monolayers proving long-range order is a challenge that limits the pace in which this recent field of polymer chemistry and of synthetic 2D materials develops. To overcome this bottleneck, we here present a method in which tip-enhanced Raman spectroscopy is combined with a random growth crystallization model to obtain global features from local spectroscopic information. Concretely, we prove the nature and determine the conversion number X of the cross-links for two new 2D homopolymers and one (of three) new 2D copolymers. Assuming random and in-plane growth, our model results in crystallinity degrees of 93.1% to 99.7% and mean radii of defect-free crystalline areas of 3-15 nm for conversion numbers of 84% < X < 98%. Thus, we provide strong evidence for the synthetic monolayer 2D materials presented that they qualify as 2D polymers and are therefore perfectly suited for in-depth studies both in a more fundamental direction as well as toward application. This example shows how our method can affect current research on covalent sheets.

The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of self-avoidance appears. This insight is essential for understanding the limitations of polymer physical models, and it motivated us to discuss the advantages and disadvantages of this approach in comparison to the commonly applied scattering techniques.

The gas-liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor-liquid interface, we apply our recently developed approach (Phys. Chem. Chem. Phys., 2018, 20, 16238) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas-liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks-Chandler-Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas-liquid dividing line and the corresponding line tensions.

We have studied the effect of cross-linking on the tribological behavior of polymer brushes using a combined experimental and theoretical approach. Tribological and indentation measurements on poly(glycidyl methacrylate) brushes and gels in the presence of dimethylformamide solvent were obtained by means of atomic force microscopy. To complement experiments, we have performed corresponding molecular dynamics (MD) simulations of a generic bead-spring model in the presence of explicit solvent and cross-linkers. Our study shows that cross-linking leads to an increase in friction between polymer brushes and a counter-surface. The coefficient of friction increases with increasing degree of cross-linking and decreases with increasing length of the cross-linker chains. We find that the brush-forming polymer chains in the outer layer play a significant role in reducing friction at the interface., Competing Interests: The authors declare no competing financial interest., (Copyright © 2018 American Chemical Society.)

We investigate the conformation, position, and dynamics of core-shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly( N-isopropylacrylamide) shell at a water-oil interface for a systematic range of core sizes and shell thicknesses. We first present a free-energy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which is in good agreement with our experimental data. Remarkably, based on the knowledge of the polymer shell deformability, the equilibrium particle position relative to the interface plane, an often elusive experimental quantity, can be extracted by measuring its radial dimensions after adsorption. For all the systems studied here, the interfacial dimensions are always larger than in bulk and the particle core resides in a configuration, wherein it just touches the interface or is fully immersed in water. Moreover, the stretched shell induces a larger viscous drag at the interface, which appears to depend solely on the interfacial dimensions, irrespective of the portion of the CSNP surface exposed to the two fluids. Our findings indicate that tailoring the architecture of CSNPs can be used to control their properties at the interface, as of interest for applications including emulsion stabilization and nanopatterning.

Pluronic (PL) block copolymers have been widely used as delivery carriers, molecular templates for porous media, and process additives for affecting rheological behavior. Unlike most surfactant systems, where unimer transforms into micelle with increased surfactant concentration, anomalous large PL aggregates below the critical micelle concentration (CMC) were found throughout four types of PL (F108, F127, F88 and P84). We characterized their structures using dynamic light scattering and small-angle X-ray/neutron scattering. Molecular dynamics simulations suggest that the PPO segments, though weakly hydrophobic interaction (insufficient to form micelles), promote the formation of large aggregates. Addition of acid or base (e.g. citric acid, acetic acid, HCl and NaOH) in F108 solution significantly suppresses the aggregate formation for up to 20 days due to the repulsion force from the attached H3O+ molecules on the EO segment in both PEO and PL and the reduction of CMC through the salting out effect, respectively.

The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases-whereas for concentrated polymer solutions it increases-with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate., Competing Interests: The authors declare no conflict of interest.

Graphene is recognized as an emerging 2D nanomaterial for many applications. Assembly of graphene sheets into 3D structures is an attractive way to enable their macroscopic applications and to preserve the exceptional mechanical and physical properties of their constituents. In this study, we develop a coarse-grained (CG) model for 3D graphene foams (GFs) based on the CG model for a 2D graphene sheet by Ruiz et al (2015 Carbon 82 103-15). We find that the size of graphene sheets plays an important role in both the structural and mechanical properties of 3D GFs. When their size is smaller than 10 nm, the graphene sheets can easily stack together under the influence of van der Waals interactions (vdW). These stacks behave like building blocks and are tightly packed together within 3D GFs, leading to high density, small pore radii, and a large Young's modulus. However, if the sheet sizes exceed 10 nm, they are staggered together with a significant amount of deformation (bending). Therefore, the density of 3D GFs has been dramatically reduced due to the loosely packed graphene sheets, accompanied by large pore radii and a small Young's modulus. Under uniaxial compression, rubber-like stress-strain curves are observed for all 3D GFs. This material characteristic is dominated by the vdW interactions between different graphene layers and slightly affected by the out-of-plane deformation of the graphene sheets. We find a simple scaling law [Formula: see text] between the density ρ and Young's modulus E for a model of 3D GFs. The simulation results reveal structure-property relations of 3D GFs, which can be applied to guide the design of 3D graphene assemblies with exceptional properties.

The PEGylated liposome, composed of an aqueous core and a fluid state lipid bilayer shell, is one of the few Food and Drug Administration (FDA) approved drug delivery platforms. To prevent the absorption of serum proteins, the surface of a liposome is decorated by hydrophilic and bio-compatible polyethylene glycol (PEG) polymers, which can significantly extend the blood circulation time of liposomes. In this work, with the help of dissipative particle dynamics (DPD) simulations, we explore how the tethered PEG polymers will affect the membrane wrapping process of PEGylated liposomes during endocytosis. Specifically, we compare the membrane wrapping process of a PEGylated rigid nanoparticle (NP) with a PEGylated liposome under identical conditions. Due to the mobility of grafted PEG polymers on the liposome's surface, the complete wrapping of a PEGylated liposome can be dramatically delayed and blocked, in comparison with a PEGylated rigid NP. For the first time, we observe the aggregation of PEG polymers in the contact region between a PEGylated liposome and the membrane, which in turn leads to a ligand-free region on the surface of the liposome during endocytosis. Subsequently, the partially wrapped PEGylated liposome can be bounced back to a less wrapped state. Through free energy analysis, we find that the aggregation of PEG polymers during the membrane wrapping process of a PEGylated liposome introduces a dramatic free energy penalty of about ∼800k B T, which is almost twice that of a PEGylated rigid NP. Here k B and T are the Boltzmann constant and temperature, respectively. Such a large energy barrier and the existence of a ligand-free region on the surface of PEGlylated liposomes prevent their membrane wrapping, thereby reducing the chance of internalization by tumor cells. Therefore, our DPD simulation results provide a possible explanation for the inefficient cellular uptake of PEGylated liposomes. In addition, we suggest that by increasing the repulsive interactions between grafted PEG polymers it might be possible to limit their aggregation, and in turn, facilitate the internalization of PEGylated liposomes. The current study provides fundamental insights into the endocytosis of PEGylated liposomes, which could help to design this platform with high efficacy for drug delivery.

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

The authors of the present study have recently presented evidence that the tumbling-snake model for polymeric systems has the necessary capacity to predict the appearance of pronounced undershoots in the time-dependent shear viscosity as well as an absence of equally pronounced undershoots in the transient two normal stress coefficients. The undershoots were found to appear due to the tumbling behavior of the director u when a rotational Brownian diffusion term is considered within the equation of motion of polymer segments, and a theoretical basis concerning the use of a link tension coefficient given through the nematic order parameter had been provided. The current work elaborates on the quantitative predictions of the tumbling-snake model to demonstrate its capacity to predict undershoots in the time-dependent shear viscosity. These predictions are shown to compare favorably with experimental rheological data for both polymer melts and solutions, help us to clarify the microscopic origin of the observed phenomena, and demonstrate in detail why a constant link tension coefficient has to be abandoned.

A core-polyethylene glycol-lipid shell (CPLS) nanoparticle consists of an inorganic core coated with polyethylene glycol (PEG) polymers, surrounded by a lipid bilayer shell. It can be self-assembled from a PEGylated core with surface-tethered PEG chains, where all the distal ends are covalently bonded to lipid molecules. Upon adding free lipids, a complete lipid bilayer shell can be formed on the surface driven by the hydrophobic nature of lipid tails, leading to the formation of a CPLS nanoparticle. The stability of CPLS nanoparticles in shear flow has been systematically studied through large scale dissipative particle dynamics simulations. CPLS nanoparticles demonstrate higher stability and less deformation in shear flow, compared with lipid vesicles. Burst leakage of drug molecules inside lipid vesicles and CPLS NPs can be induced by the large pores at their tips. These pores are initiated by the maximum stress in the waist region. It further grows along with the tank-treading motion of vesicles or CPLS NPs in shear flow. However, due to the constraints applied by PEG polymers, CPLS NPs are less deformed than vesicles with comparable size under the same flow conditions. Thus, the less deformed CPLS NPs express a smaller maximum stress at waists, demonstrating higher stability. Pore formation at waists, evolving into large pores on vesicles, leads to the burst leakage of drug molecules and complete rupture of vesicles. In contrast, although similar drug leakage in CPLS nanoparticles can occur at high shear rates, pores initiated at moderate shear rates tend to be short-lived and close due to the constraints mediated by PEG polymers. This kind of 'self-healing' capability can be observed over a wide range of shear rates for CPLS nanoparticles. Our results suggest self-assembled CPLS nanoparticles to exhibit high stability during blood circulation without rapid drug leakage. These features make CPLS nanoparticles candidates for a promising drug delivery platform.

Herein a new multifunctional formulation, referred to as a core-polyethylene glycol-lipid shell (CPLS) nanoparticle, has been proposed and studied in silico via large scale coarse-grained molecular dynamics simulations. A PEGylated core with surface tethered polyethylene glycol (PEG) chains is used as the starting configuration, where the free ends of the PEG chains are covalently bonded with lipid molecules (lipid heads). A complete lipid bilayer is formed at the surface of the PEGylated particle core upon addition of free lipids, driven by the hydrophobic properties of the lipid tails, leading to the formation of a CPLS nanoparticle. The self-assembly process is found to be sensitive to the grafting density and molecular weight of the tethered PEG chains, as well as the amount of free lipids added. At low grafting densities the assembly of CPLS nanoparticles cannot be accomplished. As demonstrated by simulations, a lipid bud/vesicle can be formed on the surface when an excess amount of free lipids is added at high grafting density. Therefore, the CPLS nanoparticles can only be formed under appropriate conditions of both PEG and free lipids. The CPLS nanoparticle has been recognized to be able to store a large quantity of water molecules, particularly with high molecular weight of PEG chains, indicating its capacity for carrying hydrophilic molecules such as therapeutic biomolecules or imaging agents. Under identical size and surface chemistry conditions of a liposome, it has been observed that the CPLS particle can be more efficiently wrapped by the lipid membrane, indicating its potential for a greater efficiency in delivering its hydrophilic cargo. As a proof-of-concept, the experimental realization of CPLS nanoparticles is explicitly demonstrated in this study. To test the capacity of the CPLS to store small molecule cargo a hydrophilic dye was successfully encapsulated in the particles' water soluble layer. The results of this study show the power and potential of simulation-driven approaches for guiding the design of more efficient nanomaterial delivery platforms.

Equilibrated systems of entangled polymer melts cannot be produced using direct brute force equilibration due to the slow reptationdynamics exhibited by high molecular weight chains. Instead, these dense systems are produced using computational techniques such as Monte Carlo-Molecular Dynamics hybrid algorithms, though the use of soft potentials has also shown promise mainly for coarse-grained polymeric systems. Through the use of soft-potentials, the melt can be equilibrated via molecular dynamics at intermediate and long length scales prior to switching to a Lennard-Jones potential. We will outline two different equilibration protocols, which use various degrees of information to produce the starting configurations. In one protocol, we use only the equilibrium bond angle, bond length, and target density during the construction of the simulation cell, where the information is obtained from available experimental data and extracted from the force field without performing any prior simulation. In the second protocol, we moreover utilize the equilibrium radial distribution function and dihedral angle distribution. This information can be obtained from experimental data or from a simulation of short unentangled chains. Both methods can be used to prepare equilibrated and highly entangled systems, but the second protocol is much more computationally efficient. These systems can be strictly monodisperse or optionally polydisperse depending on the starting chain distribution. Our protocols, which utilize a soft-core harmonic potential, will be applied for the first time to equilibrate a million particle system of polyethylene chains consisting of 1000 united atoms at various temperatures. Calculations of structural and entanglement properties demonstrate that this method can be used as an alternative towards the generation of entangled equilibrium structures.

We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7-8% larger values of 〈Lpp〉, (b) 6-11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2-5% smaller values of 〈des〉, and (d) 7-11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.

The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ε' = 0, and to the rigid rod when ε' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ε'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models.

In 1968, Heskins and Guillet published the first systematic study of the phase diagram of poly(N-isopropylacrylamide) (PNIPAM), at the time a "young polymer" first synthesized in 1956. Since then, PNIPAM became the leading member of the growing families of thermoresponsive polymers and of stimuli-responsive, "smart" polymers in general. Its thermal response is unanimously attributed to its phase behavior. Yet, in spite of 50 years of research, a coherent quantitative picture remains elusive. In this Review we survey the reported phase diagrams, discuss the differences and comment on theoretical ideas regarding their possible origins. We aim to alert the PNIPAM community to open questions in this reputably mature domain., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The size, shape, surface property and material composition of polymer-coated nanoparticles (NPs) are four important parameters in designing efficient NP-based carriers for targeted drug delivery. However, due to the complex interplay between size, shape and surface property, most studies lead to ambiguous descriptions of the relevance of shape. To clarify its influence on the cellular uptake of PEGylated NPs, large scale molecular simulations have been performed to study differently shaped convex NPs, such as sphere, rod, cube and disk. Comparing systems with identical NP surface area, ligand-receptor interaction strength, and grafting density of the polyethylene glycol, we find that the spherical NPs exhibit the fastest internalization rate, followed by the cubic NPs, then rod- and disk-like NPs. The spherical NPs thus demonstrate the highest uptake among these differently shaped NPs. Based on a detailed free energy analysis, the NP shape effect is found to be mainly induced by the different membrane bending energies during endocytosis. The spherical NPs need to overcome a minimal membrane bending energy barrier, compared with the non-spherical counterparts, while the internalization of disk-like NPs involves a strong membrane deformation, responsible for a large free energy barrier. Besides, the free energy change per tethered chain is about a single kBT regardless of NP shape, as revealed by our self-consistent field theory calculations, where kB and T denote Boltzmann constant and temperature, respectively. Thus, the NP shape only plays the secondary role in the free energy change of grafted PEG polymers during internalization. We also find that star-shaped NPs can be quickly wrapped by the cell membrane, similar to their spherical counterparts, indicating star-shaped NPs can be used for drug delivery with high efficacy. Our findings seem to provide useful guidance in the molecular design of PEGylated NPs for controllable cellular uptake and help establish quantitatively rules in designing NP-based vectors for targeted drug delivery.

The internal organization of macromonomers (MGs) consisting of all-thiophene dendrons of generation g = 2 and 3 attached to a phenyl core, as well as of the dendronized polymers resulting from polymerization of these macromonomers (PG2 and PG3, respectively), has been investigated using theoretical methods. The conformational preferences of the MGs, determined using density functional theory calculations, are characterized by the relative orientation between dendrons and core. We find that the strain of the MGs increases with the generation number and is alleviated by small conformational re-arrangements of the peripheral thiophene rings. The conformations obtained for the MGs have subsequently been used to construct models for the dendronized polymers. Classical molecular dynamics simulations have evidenced that the interpenetration of dendrons belonging to different repeat units is very small for PG2. In contrast, the degree of interpenetration is found to be very high for PG3, which also shows a significant degree of backfolding (i.e. occurrence of peripheral methyl groups approaching the backbone). Consequently, PG2 behaves as a conventional linear flexible polymer bearing bulk pendant groups, whereas PG3 is better characterized as a semirigid homogeneous cylinder. The two polymers are stabilized by π-π stacking interactions, even though these are significantly more abundant for PG3 than for PG2; the average numbers of interactions per repeat unit are 3.0 and 8.8 for PG2 and PG3, respectively. While in these interactions the thiophene rings can adopt either parallel (sandwich) or perpendicular (T-shaped) dispositions, the former scenario turns out to be the most abundant.

The term molecular object (MO) is introduced to describe single, shape persistent macromolecules that retain their form and mesoscopic dimensions irrespective of solvent quality and adsorption onto a surface. The concept is illustrated with results concerning homologous series of dendronized polymers (DP). In particular, we discuss imaging experiments quantifying deformation upon adsorption, defect characterization, and atomistic molecular dynamics simulations of DP structure. We argue that MOs such as high generation DP, with their large dimensions and high internal density, provide an opportunity to address fundamental questions regarding the onset of bulk-like behavior in single molecules. Illustrative examples of such questions concern the smallest MO exhibiting a glass transition, glassy behavior or a constant bulk density. The characteristics of DP MO are highlighted by comparison to polymer beads, polymeric micelles, globular proteins, and carbon nanotubes. We discuss future research directions and speculate on possibilities involving multiarmed and toroid DP and the effect of DP on friction and rheology, as well as their utilization for nanoconstruction.

Using coarse-grained molecular dynamics simulation, we study the motion of unentangled polymer chains dynamically confined by non-attractive nanoparticles (NPs). Both normal mode and dynamic structure factor S(q, t) analysis are adopted to analyze chain's dynamics. Relaxation behaviors of chains are found to be significantly slowed down by NPs. The relaxation times of chain's normal modes are monotonically increasing with the NP volume fraction ϕ. At the same time, chains' dynamics are becoming non-Gaussian. Inspection of S(q, t) reveals that chain's dynamics can be attributed to two 'phases', a bulk polymer phase and a confined polymer phase between NPs. The dynamics of a confined polymer is slower than that of a bulk polymer, while still exhibiting high mobility. The amount of the bulk polymer phase is found to exponentially decay with increasing ϕ. With this figure at hand, we establish a simple relationship between NP and confined/interphase polymer volume fractions. This work seems to provide the first quantitative prediction on the relationship between NP and confined/interphase polymer volume fractions.

In an attempt to relate atomistic information to the rheological response of a large dendritic object, interand intramolecular hydrogen bonds and p,p-interactions have been characterized in a dendronized polymer (DP) that consists of a polymethylmethacrylate backbone with tree-like branches of generation four (PG4) and contains both amide and aromatic groups. Extensive atomistic molecular dynamics simulations have been carried out on (i) an isolated PG4 chain and (ii) ten dimers formed by two PG4 chains associated with different degrees of interpenetration. Results indicate that the amount of nitrogen atoms involved in hydrogen bonding is ~11% while ~15% of aromatic groups participate in p,pinteractions. Furthermore, in both cases intramolecular interactions clearly dominate over intermolecular ones, while exhibiting markedly different behaviors. Specifically, the amount of intramolecular hydrogen bonds increases when the interpenetration of the two chains decreases, whereas intramolecular p,pinteractions remain practically insensitive to the amount of interpenetration. In contrast, the strength of the corresponding two types of intermolecular interactions decreases with interpenetration. Although the influence of complexation on the density and cross-sectional radius is relatively small, interpenetration affects significantly the molecular length of the DP. These results support the idea of treating DPs as long colloidal molecules.

One of the great goals in polymer physics is to relate the various macroscopic features of polymeric fluids with the microscopic behavior of single chains. Here, we directly visualize the conformational dynamics of individual semiflexible polymers in a semidilute solution above the overlap concentration under shear. We observe that the tumbling dynamics are significantly slowed down, in marked contrast to the case of a dilute solution, due to steric interactions with neighboring filaments. The observed macroscopic shear thinning effect can be rationalized by a simple model based on the single filament dynamics.

The internal organization of a fifth-generation dendronized polymer (PG5) has been investigated by atomistic molecular dynamics simulations in a vacuum. This study reveals an exceptional behavior of PG5 within the homologous series of g-generation PGg polymers. Three molecular configurations, which present a heterogeneous distribution of dendrons and an amount of backfolding lower than PG4 and PG6, have been obtained for PG5. The highest stability and closest agreement with available experimental data corresponds to a helical conformation characterized by a pitch of about 30 Å, thickness of 105 Å, and average density of 0.861 g/cm(3). While small angle neutron scattering studies of PG5 in solution show a constant radial density distribution around the backbone, we here in our vacuum studies find a cylindrical volume element of sharply reduced density reminiscent of a pore. This neutral PG5 was compared with its charged deprotected analogue, dePG5 in water, to see in as much the positive charges in the periphery of this macromolecule would affect its conformational behavior. During deprotection of PG5, the tert-butyloxycarbonyl protected amine groups are converted into ammonium, mimicking the experimental situation during a divergent synthesis procedure. The repulsive interactions among the positively charged ammonium groups are responsible for a huge (~30%) reduction of the average density and a small (~1%) increase of elongation of the helical backbone, which results in a structure with a spongy appearance. Also here, we find a reduced dendron density near the backbone which is compensated for by the pore being filled with water.

We explore the dynamics of entangled polymer chains embedded into nanocomposites. From primitive path analysis, highly entangled polymer chains are found to be significantly disentangled during increment of the volume fraction of spherical nonattractive nanoparticles (NPs) from 0 to 42%. A critical volume fraction, ϕ(c)=31%, is found to control the crossover from polymer chain entanglements to "NP entanglements." While below ϕ(c), the polymer chain relaxation accelerates upon filling, above ϕ(c), the situation reverses: polymer dynamics becomes geometrically constrained upon adding NPs. Our findings provide a microscopic understanding of the dynamics of entangled polymer chains inside their composites, and offer an explanation for the unusual rheological properties of polymer composites.

Poly (N-isopropylacrylamide) (PNIPAM) brushes and hydrogels serve as temperature-responsive cell culture substrates. The cells adhere at 37 °C and are detached by cooling to below the lower critical solution temperature T(LCST) ≈ 32 °C, an effect hitherto attributed to change in PNIPAM hydration. The article proposes a mechanism coupling the change of hydration to integrin mediated environmental sensing for cell culture on brushes and hydrogels in serum containing medium. Hydration is associated with swelling and higher osmotic pressure leading to two effects: (i) The lower osmotic pressure in the collapsed brush/hydrogel favors the adsorption of serum borne extracellular matrix (ECM) proteins enabling cell adhesion; (ii) Brush/hydrogel swelling at T < T(LCST) gives rise to a disjoining force f(cell) due to confinement by the ventral membrane of a cell adhering via integrin-ECM bonds. f(cell) places the integrin-ECM bonds under tension thus accelerating their dissociation and promoting desorption of ECM proteins. Self consistent field theory of PNIPAM brushes quantifies the effect of the polymerization degree N, the area per chain Σ, and the temperature, T on ECM adsorption, f(cell) and the dissociation rate of integrin-ECM bonds. It suggests guidelines for tuning Σ and N to optimize adhesion at 37 °C and detachment at T < T(LCST). The mechanism rationalizes existing experimental results on the influence of the dry thickness and the RGD fraction on adhesion and detachment., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or "globules", which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N(in) and N(out), the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N(out), with the higher value of N(out) providing a stronger material. We also find that, if N(in) is smaller than N(out), the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials.

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N&#95;{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N&#95;{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

We present results about the shape, size, structure, conformational stability, and hydrodynamics of alpha-conotoxin AuIB (a disulfide-rich peptide from the venom of Conus aulicus, recognized as a nicotinic acetylcholine antagonist with great pharmaceutical potential) from very long (0.5 mus) massively parallel molecular dynamics (MD) simulations in full atomistic detail. We extract coarse-grained descriptors of protein shape (ellipsoid), and of translational and rotational mobilities, i.e., the basic components at the lowest hierarchical level in a multiscale modeling strategy. Structural analysis reveals the folded conformation and asymmetric shape to be strongly favored for conotoxin. In accordance with experimental findings, conformational stability is observed and found to be linked to the presence of the alpha-helix along the 15 residues and to the existence of the two disulfide bonds. We find rotational (D(r)) and translational (D(t)) diffusivities to be suitable descriptors of coarse-grained dynamics, i.e., of the hydrodynamic behavior, and obtain D(r) = 3.62 (+/-0.17) x 10(8) s(- 1) and D(t) = 1.08 (+/-0.4) x 10(- 10) m(2) s(- 1). We further compare the MD-computed coarse-grained descriptors with first principles theoretical predictions based on the extended Hess-Doi Fokker-Planck approach which relates particle shape and dimensions to diffusion coefficients. An excellent agreement between simulation data and analytical predictions is observed for both dynamical descriptors. This comparison strongly suggests that diffusivities of rigid biomolecules much larger than the alpha-conotoxin AuIB studied here can be obtained from the coarse-grained shape descriptor (ellipsoid) derived from relatively short MD simulations.

We generate two-dimensional Lennard-Jones networks with random topology by preparing a perfect four-functional network of identical harmonic springs and randomly cutting some of the springs. Using molecular-dynamics simulations we find that the fraction p of active springs affects both the temperature of phase separation and the type of structures observed below this temperature, from networklike high-density patterns at p>0.5 ("gel") to dropletlike structures at p<0.5 ("sol"). In the gel domain, these patterns are determined by the interplay between free energy and network topology, with the former dominant as p-->1 and the latter as p-->0.5 .

We present a thermodynamically guided, low-noise, time-scale-bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte Carlo-molecular-dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. As a by-product, we present steady-state simulation results for polymers in general flow situations, including simple, planar, and yet unexplored equibiaxial elongation. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from nonequilibrium steady states.

By identifying the maximally random jammed state of freely jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of (i) the contour length of the primitive paths and (ii) the number of entanglements per chain agree remarkably well with recent theoretical predictions in all scaling regimes. Furthermore, our simulations reveal a hitherto unsuspected connection between purely intramolecular (knots) and intermolecular (entanglements) topological constraints.

We unveil the existence of nonaffinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of nonaffinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.

This discusses two recent models, one that captures physical network formation starting from the molecular architecture of its constituents and another that contains the basic features of phase separation in cross-linked polymer gels: A) the Janus chain (multibead bead-spring type) model exhibiting semiflexibility and induced curvature and B) a stretched elastic network of Lennard-Jones particles. The length scales and related structures predicted by the two generic models are different. Model B, a generic soft solid model, exhibits hysteresis and the formation of filamentous structures in two dimensions. The Janus chain model A is able to describe the process of the formation of double helical superstructures, will be operated in three dimensions, and its internal parameters are directly deduced from atomistic simulation. Both models rely on classical ingredients which have been separately studied extensively: i) the Lennard-Jones particle system, ii) the elastic solid, and iii) the FENE-B model for semiflexible, finitely extendable nonlinear elastic (FENE) polymer chains. While model A combines i) and iii), model B combines i) and ii). This aspect of technical simplicity, however, is contrasted by the rich phenomenology observed for these models. The Janus model even resolves structure formation on the molecular scale. Intriguingly, the coarse dynamical models capture a wide range of superstructures known for polymeric networks and therefore clearly serve to understand their underlying physical mechanisms.

We extend to the three-dimensional situation a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamics obtained from Grad's moment system [M. Colangeli, I. Karlin, M. Kröger, Phys. Rev. E 75, 051204 (2007)]. Proof of an H theorem is also presented.

The complete free energy density, including all eight Frank-Ericksen elastic coefficients and all anisotropic Ericksen-Leslie viscosities of nematic and discotic polydomain nematic liquid crystals are derived from the kinetic model of a spatially inhomogeneous system of uniaxial liquid crystal molecules with given shape. The authors take into account the known anisotropy of the translational diffusion tensor and its dependence on shape, rotational diffusion, and a macroscopic flow field for elongated particles (including disks). In this manuscript they release all of the previously made assumptions about closure relationships or the interrelationship between Frank elastic coefficients (such as a simple quadratic closure, or the one-constant approximation) in order to derive results which not only generalize or improve earlier results, but also apply to more general cases, and for arbitrary forms of the mean-field potential in terms of the scalar order parameter (or temperature). The kinetic model is shown to confirm all proposed inequalities between Frank-Ericksen-Leslie coefficients, i.e., satisfies the main result of the macroscopic approaches. They resolve quantitatively the effect of molecular shape, order parameters, and mean-field strength and form of the mean-field potential on all results, compare with experimental findings, theoretical predictions, and discuss some implications for various special cases of the general result derived in this work.

Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model -- a 13 moment Grad system.

We derive general expressions and present several examples for the phoretic forces and torques acting on a translationally moving and rotating convex tracer particle, usually a submicrosized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas. Point of departure is an expression of the stress tensor in terms of half-sphere integrals to be evaluated with the inhomogeneous velocity distribution function of the surrounding gas, more specifically, its approximation in terms of a finite number of moments. A worked out example covers Grad's 13 moment approximation in and out of the so-called hydrodynamic approximation. We implement an accommodation coefficient characterizing the collision process in order to derive the tracer particle's complete equations of motion in a form which offers the possibility for immediate numerical implementation, and the analytical exploration of the effect of particle shape and size on phoretic drift velocity. Explicit expressions for axisymmetric, spherical, cylindrical, and also cuboidal particles are presented, discussed, and successfully compared with the rarely available, previously treated special cases, thus supporting the unifying approach presented in this manuscript.

In this article we derive the phoretic forces acting on a tracer particle, which is assumed to be small compared to the mean free path of the surrounding nonequilibrium gas, but large compared to the size of the surrounding gas molecules. First, we review and extend the calculations of Waldmann [Z. Naturforsch. A 14A, 589 (1959)] using half-sphere integrations and an accommodation coefficient characterizing the collision process. The presented methodology is applied to a gas subject to temperature, pressure, and velocity gradients. Corresponding thermophoretic, barophoretic, and rheophoretic forces are derived, and explicit expressions for spherical particles are compared to known results. Second, nonequilibrium thermodynamics is used to join the diffusion equation for the tracer particle with the continuum equations of nonisothermal hydrodynamics of the solvent. So doing, the distinct origin of the thermophoretic and barophoretic forces is demonstrated. While the latter enters similarly to an interaction potential, the former is given by flux-flux correlations in terms of a Green-Kubo relation, as shown in detail.

The rheological properties of a dilute suspension of ellipsoidal ferromagnetic particles in the presence of a magnetic field are studied on the basis of a kinetic model, where the flow and magnetic external fields couple in qualitatively different ways to the orientational behavior of the suspension. In the uniaxial phase the stress tensor is found to be of the same form as in the Ericksen-Leslie theory for nematic liquid crystals in the steady state. Expressions for a complete set of viscosity coefficients in terms of orientational order parameters are worked out. In the low Péclet number regime, the viscosity coefficients are given as explicit functions of the magnetic field and a particle shape factor, where the shape factor may equally represent a nonspherical unit (agglomerate, chain) composed of spherical particles. Effects due to possible flow-induced breakup of units are not covered in this work. Further, by considering the magnetization as the only relevant variable, a magnetization equation within an effective field approach is derived from the kinetic equation and compared to existing magnetization equations. The alignment angle of the magnetization and the first and second normal stress coefficient are studied for the special case of plane Couette flow. The assumptions employed are tested against a Brownian dynamics simulation of the full kinetic model, and a few comparisons with experimental data are made.