Polymer Density Profile Research Articles

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is utilized to study the effects of temperature on polymer brushes. The brushes are represented by a discrete energy spectrum, and energy degeneracies obtained through the replica-exchange Wang-Landau algorithm. The SEAQT equation of motion is applied to the density of states to establish a unique kinetic path from an initial thermodynamic state to a stable equilibrium state. The kinetic path describes the brush's evolution in state space, as it interacts with a thermal reservoir. The predicted occupation probabilities along the kinetic path are used to determine the expected thermodynamic and structural properties. The polymer density profile of a polystyrene brush in cyclohexane solvent is predicted using the equation of motion, and it agrees qualitatively with the experimental density profiles. The Flory-Huggins parameter chosen to describe brush-solvent interactions affects the solvent distribution in the brush but has a minimal impact on the polymer density profile. Three types of nonequilibrium kinetic paths with differing amounts of entropy production are considered: a heating path, a cooling path, and a heating-cooling path. Properties such as tortuosity, radius of gyration, brush density, solvent density, and brush chain conformations are calculated for each path.

Novel Insights on the Three-dimensional Shape of Microgels at Fluid Interfaces

Mechanically soft colloids (microgels) adsorbed at the interface between two fluids offer superior advantages over hard counterparts for a variety of applications ranging from foams/emulsion stabilization to the assembly of two-dimensional (2D) materials. Particle deformability and compressibility impart additional responses to microgel-laden interfaces that can be controlled on-demand by varying single-particle properties (e.g. crosslinking content and polymer density profile) and/or external parameters (e.g. interfacial compression and tension, temperature, oil polarity). In order to understand how single-particle softness influences the resulting material properties, a detailed quantification of the microgel’s 3D conformation when confined at the fluid interface is of utmost importance. This article describes how different methodologies can be used to visualize, and in some case quantify, the conformation of adsorbed microgels, putting particular emphasis on the multiple advantages offered by in situ atomic force microscopy imaging at the fluid interface. The influence of the internal particle architecture, as well as that of temperature, interfacial tension and solubility in the organic phase, will be discussed. Finally, some perspectives on how softness can be exploited to tune the structural and mechanical properties of microgel monolayers will be provided.

Simulation of Solvent Evaporation from a Diblock Copolymer Film: Orientation of the Cylindrical Mesophase

Using particle-based Monte Carlo simulations and continuum modeling, we study the self-assembly of asymmetric diblock copolymers in the course of solvent evaporation. We examine the effects of evaporation rate and solvent selectivity on the structure formation, especially the alignment of the cylindrical domains of the minority block. The comparison of the two simulation techniques facilitates identifying general trends upon parameter variation, while their inherent differences help us to understand the role of single-chain dynamics, fluctuations, and additional model details. In both cases, the simulation models feature a liquid and a gas phase with an explicit surface, across which solvent evaporates. We propose a “layer evolution model” that links processing parameters to the final morphology via the time dependence of layers, in which characteristic microphases, for example, spherical or cylindrical, can form. The evolution of these layers varies with the processing conditions and determines the morphology. This allows us to discuss the interplay of various experimentally accessible parameters, which we support by respective simulations. Our results single out two main factors to ensure the formation of minority-block cylinders, perpendicular to the film surface: (i) Fast evaporation rates induce a steep gradient in the polymer-density profile; that is, the polymer density immediately beneath the gas–liquid surface rapidly exceeds the critical value for cylinder formation. This confines cylinder formation into a layer that is thinner than the actual cylinder diameter, forcing a perpendicular alignment. (ii) A certain selectivity of the gas phase for the matrix-forming, majority block is necessary to disrupt an otherwise entropically favored surface layer of the minority block that would lead to parallel cylinder alignment.

Prediction of the structure and mechanical properties of polycaprolactone–silica nanocomposites and the interphase region by molecular dynamics simulations: the effect of PEGylation

Polymer/silica (PS) nanocomposites are, among numerous combinations of inorganic/organic nanocomposites, one of the most important materials reported in the literature and have been employed in a wide variety of applications. Due to this great interest in the scientific and industry community, knowledge about their physiochemistry allows for a better understanding of their development and improvement. One area of interest found in biopolymers is silica, where silica nanoparticles can be used to increase their mechanical properties and give them higher opportunities to replace synthetic plastics. With this aim in mind, molecular dynamics (MD) simulations were used to predict the structure and mechanical properties of the interphase region and nanocomposite systems of polycaprolactone (PCL), a common poly(hydroxy acid) type biopolymer, reinforced with silica nanoparticles. Two types of nanoparticles were studied to assess the effect of PEGylation: hydroxyl (ungrafted) and polyethylene glycol (PEG) (grafted or PEGylated) functionalized silica. The interaction energy between the nanoparticle and the polymeric matrix was determined, showing an increase of the affinity between each component due to the PEGylation of the nanoparticle. Through the analysis of polymer density profiles, the structure and thickness of the interphase region were determined, and it was observed that PEGylation increased the interphase thickness from 10.80 Å to 13.04 Å while it decreased the peak and average polymer density of the interphase region. Using compressed and expanded molecular models of the neat PCL polymer, the mechanical properties of the interphase region were related to its density through an interpolation model, and mechanical property profiles were obtained, from which the average values of the Young's modulus, Poisson's ratio and shear modulus of the interphase region were calculated. Finally, the mechanical properties of the nanocomposites were determined by molecular mechanics simulations, showing that the silica nanoparticles increased the stiffness of the composite system to about 7-8% with respect to that of the neat polymer, having a 2.09% weight of bare silica or 2.82% weight of PEGylated silica. PEGylation did not show an additional effect on the overall mechanical properties. A mean field micromechanics model (Mori-Tanaka) corroborated the properties calculated for the interphase region using MD simulations. It was concluded that the PEGylation of the nanoparticle improved the affinity, and thus the dispersion, of the silica nanoparticles towards the PCL matrix, but with no further increase in the mechanical properties of the composite.

Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles.

Metal nanoparticles are used to modify/enhance the properties of a polymer matrix for a broad range of applications in bio-nanotechnology. Here, we study the properties of polymer/gold nanoparticle (NP) nanocomposites through atomistic molecular dynamics, MD, simulations. We probe the structural, conformational and dynamical properties of polymer chains at the vicinity of a gold (Au) NP and a functionalized (core/shell) Au NP, and compare them against the behavior of bulk polyethylene (PE). The bare Au NPs were constructed via a systematic methodology starting from ab-initio calculations and an atomistic Wulff construction algorithm resulting in the crystal shape with the minimum surface energy. For the functionalized NPs the interactions between gold atoms and chemically adsorbed functional groups change their shape. As a model polymer matrix we consider polyethylene of different molecular lengths, from the oligomer to unentangled Rouse like systems. The PE/Au interaction is parametrized via DFT calculations. By computing the different properties the concept of the interface, and the interphase as well, in polymer nanocomposites with metal NPs are critically examined. Results concerning polymer density profiles, bond order parameter, segmental and terminal dynamics show clearly that the size of the interface/interphase, depends on the actual property under study. In addition, the anchored polymeric chains change the behavior/properties, and especially the chain density profile and the dynamics, of the polymer chain at the vicinity of the Au NP.

Sorption Characteristics of Polymer Brushes in Equilibrium with Solvent Vapors.

While polymer brushes in contact with liquids have been researched intensively, the characteristics of brushes in equilibrium with vapors have been largely unexplored, despite their relevance for many applications, including sensors and smart adhesives. Here, we use molecular dynamics simulations to show that solvent and polymer density distributions for brushes exposed to vapors are qualitatively different from those of brushes exposed to liquids. Polymer density profiles for vapor-solvated brushes decay more sharply than for liquid-solvated brushes. Moreover, adsorption layers of enhanced solvent density are formed at the brush–vapor interface. Interestingly and despite all of these effects, we find that solvent sorption in the brush is described rather well with a simple mean-field Flory–Huggins model that incorporates an entropic penalty for stretching of the brush polymers, provided that parameters such as the polymer–solvent interaction parameter, grafting density, and relative vapor pressure are varied individually.

Polymer brush relaxation during and after polymerization – Monte Carlo simulation study

The polymer chain growth in brushes takes place in a non-uniform environment which is one of the reasons of higher dispersity. Some active chain ends grow in monomer-reach regions while others in polymer-rich regions where the monomer concentration is lower. This effect depends on grafting density but also on the polymerization and diffusion rates. If chains grow fast, they adopt non-equilibrium conformations which change the polymer density profile and the growth conditions. In this paper we study this effect and chain relaxation using Monte Carlo simulation method. The growth of polymer brushes by living polymerization at various conditions was simulated until some average molecular weight was attained. Then, the polymerization was stopped and the changes of polymer parameters in time were monitored. The chain end-to-end distance increases and consequently the brush thickness increases in time. Polymer concentration decreases, especially near the grafted surface. The effect is stronger for higher polymerization rate and for higher grafting density. For low polymerization rates and lower grafting density, chain relaxation takes place during polymerization and the brush structure essentially does not change in time whenthe polymerization is finished. Such conditions assure also lower dispersity.

Structure of asymmetrical peptide dendrimers: Insights given by self-consistent field theory

Structural properties of asymmetric peptide dendrimers up to the 11th generation are studied on the basis of the self-consistent field Scheutjens-Fleer numerical approach. It is demonstrated that large scale properties such as, e.g., the gyration radius, are relatively weakly affected by the asymmetry that is, by difference in the length of short and long spacers. However, the asymmetry has strong influence on the internal structure of the dendrimers and on the radial distribution of polymer density and terminal segments. In particular, symmetrical and weakly asymmetrical dendimers are characterized by quasi-uniform intramolecular concentration profiles of monomer units whereas strongly asymmetric dendrimers are characterized by sharply decreasing in a radial direction polymer density profile reminiscent to that in star-shaped polymers. This finding may have important implication for the use of peptide dendrimers as carriers for biologically active molecules.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge.

In this work the equilibrium distribution of ions around a thermo-responsive charged nanogel particle in an electrolyte aqueous suspension is explored using coarse-grained Monte Carlo computer simulations and the Ornstein-Zernike integral equation theory. We explicitly consider the ionic size in both methods and study the interplay between electrostatic and excluded-volume effects for swollen and shrunken nanogels, monovalent and trivalent counterions, and for two different nanogel charges. We find good quantitative agreement between the ionic density profiles obtained using both methods when the excluded repulsive force exerted by the cross-linked polymer network is taken into account. For the shrunken conformation, the electrostatic repulsion between the charged groups provokes a heterogeneous polymer density profile, leading to a nanogel structure with an internal low density hole surrounded by a dense corona. The results show that the excluded-volume repulsion strongly hinders the ion permeation for shrunken nanogels, where volume exclusion is able to significantly reduce the concentration of counterions in the more dense regions of the nanogel. In general, we demonstrate that the thermosensitive behaviour of nanogels, as well as their internal structure, is strongly influenced by the valence of the counterions and also by the charge of the particles. On the one hand, an increase of the counterion valence moves the swelling transition to lower temperatures, and induces a major structuring of the charged monomers into internal and external layers around the crown for shrunken nanogels. On the other hand, increasing the particle charge shifts the swelling curve to larger values of the effective radius of the nanogel.

Specific Anion Effects on the Internal Structure of a Poly(N-isopropylacrylamide) Brush

The effect of anion identity and temperature on the internal nanostructure of poly(N-isopropylacrylamide) brushes were investigated using neutron reflectometry (NR), atomic force microscopy (AFM), and quartz crystal microbalance with dissipation monitoring (QCM-D). NR and QCM-D measurements showed that addition of strongly kosmotropic acetate anions shifted the lower critical solution temperature (LCST) to lower temperatures relative to pure D2O/H2O, while strongly chaotropic thiocyanate anions shifted the LCST to higher temperatures. Polymer density profiles derived from NR showed direct evidence of vertical phase separation at temperatures around the LCST in all conditions. Results indicate that the density profiles were not simple modulations of structures observed in D2O to higher or lower temperatures, with both anion identity and ionic strength found to influence the qualitative features of the profiles. In particular, the presence of thiocyanate broadened the LCST transition which is attributed to ...

Molecular modeling and simulation of atactic polystyrene/amorphous silica nanocomposites

The local structure, segmental dynamics, topological analysis of entanglement networks and mechanical properties of atactic polystyrene - amorphous silica nanocomposites are studied via molecular simulations using two interconnected levels of representation: (a) A coarse - grained level. Equilibration at all length scales at this level is achieved via connectivity - altering Monte Carlo simulations. (b) An atomistic level. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well- equilibrated coarse-grained configurations. By analyzing atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. Atomistic simulation results for the mechanical properties are compared to the experimental measurements and other computational works.

Density functional theory for polymeric systems in 2D

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Multiscale simulations of PS-SiO2 nanocomposites: from melt to glassy state.

The interaction energetics, molecular packing, entanglement network properties, segmental dynamics, and elastic constants of atactic polystyrene-amorphous silica nanocomposites in the molten and the glassy state are studied via molecular simulations using two interconnected levels of representation: (a) a coarse-grained one, wherein each polystyrene repeat unit is mapped onto a single "superatom" and the silica nanoparticle is viewed as a solid sphere. Equilibration at all length scales at this level is achieved via connectivity-altering Monte Carlo simulations. (b) A united-atom (UA) level, wherein the polymer chains are represented in terms of a united-atom forcefield and the silica nanoparticle is represented in terms of a simplified, fully atomistic model. Initial configurations for UA molecular dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. By analysing microcanonical UA MD trajectories, the polymer density profile is studied and the polymer is found to exhibit layering in the vicinity of the nanoparticle surface. An estimate of the enthalpy of mixing between polymer and nanoparticles, derived from the UA simulations, compares favourably against available experimental values. The dynamical behaviour of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation and dihedral angle time autocorrelation functions. At low concentration in the molten polymer matrix, silica nanoparticles are found to cause a slight deceleration of the segmental dynamics close to their surface compared to the bulk polymer. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm, yielding a slightly lower density of entanglements in the filled than in the neat systems. UA melt configurations are glassified by MD cooling. The elastic moduli of the resulting glassy nanocomposites are computed through an analysis of strain fluctuations in the undeformed state and through explicit mechanical deformation by MD, showing a stiffening of the polymer in the presence of nanoparticles. UA simulation results for the elastic constants are compared to continuum micromechanical calculations invoked in homogenization models of the overall mechanical behaviour of heterogeneous materials. They can be interpreted in terms of the presence of an "interphase" of approximate thickness 2 nm around the nanoparticles, with elastic constants intermediate between those of the filler and the matrix.

Ideal Mixing in Multicomponent Brushes of Branched Polymers

We predict theoretically that in contrast to composite brushes of end-tethered linear polymers that exhibit vertical stratification, chemically identical branched macromolecules with different molecular weights and selected architectures can distribute their free ends all over the volume of composite brush and produce a unified polymer density profile. As a result of this, we expect the presence of terminal end-groups of all constituent macromolecular species in the vicinity of the external boundary of such composite brush. The predictions of the analytical theory are supported by numerical self-consistent field calculations. Unified brushes offer new possibilities in the design of polymer-decorated surfaces and might improve our understanding of natural biointerfaces.

Unusual structural properties of polymers confined in a nanocylinder**Project supported by the National Natural Science Foundation of China (Grant Nos. 21474051, 21074053, and 51133002), the National Basic Research Program of China (Grant No. 2012CB821503), and the Program for Changjiang Scholars and Innovative Research Team in University, China.

Structural properties of polymers confined in nanocylinders are investigated by Monte Carlo simulation, which is successfully used to consider the conformational property of constrained polymers. The conformational properties of the polymers close to the walls exhibit different features. The density profiles of polymers are enhanced near the wall of the nanocylinder, which shows that the packing densities differ near the wall and far from the wall. The highest densities near the wall of the nanocylinder decrease with increasing radius of the nanocylinder. Furthermore, the density excess is not only near the wall of the nanocylinder, but also shifts to the center of the nanocylinder at lower temperatures. The radius of gyration and the bond length of polymers in the nanocylinder show that the polymer chains tend to extend along the axis of the nanocylinder in highly confined nanocylinder and contract at lower temperature. Our results are very helpful in understanding the packing induced physical behaviors of polymers in nanocylinders, such as glass transition, crystallization, etc.

Star Brushes Under Deformation: Structure and Thermodynamics

SummaryA planar polymer brush of arm‐grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean‐field model of the star brush that takes into account segregation of the brush‐forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a “two‐step” shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens‐Fleer numerical self‐consistent field (SF‐SCF) approach for free (non‐deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF‐ SCF approach and the developed mean‐field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two‐population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation.

Equilibrium swelling of core–shell composite microgels

A model is developed in finite elasticity of microgels subjected to swelling. Constitutive equations are derived by means of the free energy imbalance relation for an arbitrary three-dimensional deformation with finite strains. The governing equations are applied to the analysis of equilibrium swelling of a core–shell microgel particle with a rigid core and a soft shell. The stress–strain relations involve six material constants whose effect on polymer density profile and distribution of stresses is analyzed numerically. In accord with observations, the model predicts that volume fraction of the polymer network decreases sharply near the core–shell interface, becomes practically constant in the central part of the shell, and decays to zero near the outer surface of a spherical particle.

Analytical self-consistent field model of arm-grafted starlike polymers in nonlinear elasticity regime

We develop approximate analytical (AA) model to describe the structure of a brush made of starlike polymers (regularly branched dendrons of the first generation) grafted by one arm onto a planar surface. It is demonstrated that introduction of two sub-layers with distinct populations of strongly and weakly stretched dendrons allows for adequate semi-analytical description of these end-grafted macromolecules in nonlinear elasticity regime. We calculate brush thickness, fraction of strongly stretched dendrons and monotonously decreasing polymer density profiles as a function of polymer grafting density and number of branches in starlike macromolecule. The predictions of AA model are compared with the results of numerical self-consistent field model of Sheutjens and Fleer (SF-SCF). Good agreement between the two models is found at high grafting densities and/or at large number of branches of starlike polymers.

Substrate Effect on the Phase Behavior of Polymer Brushes with Lattice Density Functional Theory

The lattice density functional theory (LDFT) is used to describe the substrate effect on the phase behavior of polymer brush grafted on different substrates. The LDFT predicts that: both attractive and repulsive interactions between the substrate and the polymer chains have effects on the thickness of brushes; when the short-range monomer–substrate interaction is larger than a certain value, the thickness and density profiles of polymer brushes almost do not change. And also an attractive substrate can increase the critical grafting density of pancake to brush transition. For temperature responsive polymer brushes, the temperature transition points are almost the same with different substrates, however, an attractive substrate can increase the swelling ratio and a repulsive substrate can decrease the swelling ratio. We also find that an increasing grafting density can decrease the substrate effect on the swelling behavior of temperature responsive polymer brushes.

Modeling Swelling Behavior of Thermoresponsive Polymer Brush with Lattice Density Functional Theory

A key problem in designing thermoresponsive polymer brushes on a solid surface is to find a relation between the targeted thermoresponsive properties and controllable conditions. Usually, a temperature-thickness curve showing the heating-induced swelling behavior of polymer brushes is chosen as the relation by either experimental or theoretical investigation. In this work, a lattice density functional theory (LDFT) developed previously is employed to investigate the temperature-thickness curves for five different types of polymer brushes, where the density profiles of polymer brushes calculated by LDFT are compared directly with simulation. It is found that the thermoresponsive behavior of a polymer brush can be characterized by the bulk phase behaviors of its corresponding polymer solution, including UCST, LCST, both UCST and LCST, closed LOOP and hourglass-shaped, which implies that the bulk phase diagram of polymer solutions can help us to find an appropriate polymer brush for a targeted thermoresponsive behavior. As an example, we show that the swelling behavior of a thermoresponsive polymer brush found in the experiment could be predicted by our LDFT results with the bulk phase diagram of real polymer solution only.