Interfacial Phenomena in Polymer Blends: A Self-Consistent Brownian Dynamics Study

Nonequilibrium Behaviors of Entangled Diblock Copolymers at the Entangled Polymer-Polymer Interface under Steady Shear Flow

The slip phenomena and the individual configuration dynamics of interfacial copolymer chains in the entangled polymer-polymer interface under fast shear flow are analyzed using mDPD simulations on ternary blends of A125/B125/C125D125 with different incompatibilities or interface strengths. We observe two distinct power-law regions of slip velocity against interfacial shear stress: from Vs ∼ σ5 to Vs ∼ σ1 at an increasing shear rate with the interface strength. At the micro level, the two regions correspond to the integrated and incomplete interfacial entanglement network with the shear-induced disentanglement of interfacial chains, respectively. For the individual chain dynamics of interfacial copolymers, we clarify that for the weak incompatibility, the tumbling event of interfacial copolymer chains is irregular and occasional and includes six processes: align and flip, collapse, tumble, stretch, reflip, and recoil and tumble. For the system with strong incompatibility, the interfacial copolymer chain undergoes the stretched-coil conformational transition via elastic retraction. As the interfacial entanglement network disintegrates, the hairpin-like configuration is dominant during the tumbling motion or elastic retraction of the interfacial copolymer chain.

Combining particle and field-theoretic polymer models with multi-representation simulations

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

Slip and momentum transfer mechanisms mediated by Janus rods at polymer interfaces

As an incipient but preeminent technology for multiphase nanomaterials/fluids, exact compatibilizing mechanisms of Janus particles in polymer blends and the consequent morphology remain unknown. The contributions of Janus nanorods to slip suppression and momentum transfer across the interface have been explored through dissipative particle dynamics simulations under shear flow at unentangled polymer-polymer interfaces. Rods have been then grafted with flexible polymer chains to unveil interfacial structure-property relationships at a molecular level when compared with flexible diblock copolymer surfactants. When Janus rods are sparsely grafted with necessarily longer grafts, they favor a greater degree of graft interpenetration with polymer phases. This yields less effective momentum transfer that impacts droplet coalescence processes; dynamic heterogeneities at complex interfaces; and helps map their efficiency as compatibilizers.

Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts

We measure the center-of-mass diffusion of poly(methyl methacrylate) (PMMA)-grafted nanoparticles (NPs) in unentangled to slightly entangled PMMA melts using Rutherford backscattering spectrometry. These grafted NPs diffuse ∼100 times slower than predicted by the Stokes-Einstein relation assuming a viscosity equal to bulk PMMA and a hydrodynamic NP size equal to the NP core diameter, 2R_core = 4.3 nm. This slow NP diffusion is consistent with an increased effective NP size, 2R_eff ≈ 20 nm, nominally independent of the range of grafting density and matrix molecular weights explored in this study. Comparing these experimental results to a modified Daoud-Cotton scaling estimate for the brush thickness as well as dynamic mean field simulations of polymer-grafted NPs in athermal polymer melts, we find that 2R_eff is in quantitative agreement with the size of the NP core plus the extended grafted chains. Our results suggest that grafted polymer chains of moderate molecular weight and grafting density may alter the NP diffusion mechanism in polymer melts, primarily by increasing the NP effective size.

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations.

Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Directed self assembly of block copolymers using chemical patterns with sidewall guiding lines, backfilled with random copolymer brushes

Recently, alignment of block copolymer domains has been achieved using a topographically patterned substrate with a sidewall preferential to one of the blocks. This strategy has been suggested as an option to overcome the patterning resolution challenges facing chemoepitaxy strategies, which utilize chemical stripes with a width of about half the period of block copolymer to orient the equilibrium morphologies. In this work, single chain in mean field simulation methodology was used to study the self assembly of symmetric block copolymers on topographically patterned substrates with sidewall interactions. Random copolymer brushes grafted to the background region (space between patterns) were modeled explicitly. The effects of changes in pattern width, film thicknesses and strength of sidewall interaction on the resulting morphologies were examined and the conditions which led to perpendicular morphologies required for lithographic applications were identified. A number of density multiplication schemes were studied in order to gauge the efficiency with which the sidewall pattern can guide the self assembly of block copolymers. The results indicate that such a patterning technique can potentially utilize pattern widths of the order of one-two times the period of block copolymer and still be able to guide ordering of the block copolymer domains up to 8X density multiplication.

Interactions and Aggregation of Charged Nanoparticles in Uncharged Polymer Solutions

We employ an extension of the single chain in mean field simulation method to study mixtures of charged particles and uncharged polymers. We examine the effect of particle charge, polymer concentration, and particle volume fraction on the resulting particle aggregates. The structures of aggregates were characterized using particle-particle radial distribution functions and cluster size distributions. We observe that the level of aggregation between particles increases with increasing particle volume fraction and polymer concentration and decreasing particle charge. At intermediate regimes of particle volume fraction and polymer concentrations, we observe the formation of equilibrium clusters with a preferred size. We also examined the influence of manybody effects on the structure of a charged particle-polymer system. Our results indicate that the effective two-body approximation overpredicts the aggregation between particles even at dilute particle concentrations. Such effects are thought to be a consequence of the interplay between the respective manybody effects on the depletion and electrostatic interactions.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Boundary conditions at the liquid-liquid interface in the presence of surfactants

In this work, we studied the flow boundary conditions for the interface between two immiscible liquids under the condition of low shear rates in the presence or absence of surfactants. Our simulation results indicate that the boundary conditions are substantially changed by the presence of surfactants. Similar to the liquid-solid boundary, several boundary conditions at immiscible liquid-liquid interfaces, including slip, no-slip, and locking boundary conditions, are observed depending on the interfacial surfactant concentration. The slip boundary condition is achieved only at zero or lower surfactant concentration. The locking boundary condition is observed when the surfactant concentration is large enough to form a fully developed monolayer whereas the no-slip condition occurs for systems with intermediate values of surfactant concentration. The slip, no-slip, and locking boundary conditions yield the positive, zero, and negative slip lengths, respectively. We also investigated the dependence of boundary slip on shear rate at different interfacial surfactant concentrations. Compared to the systems without surfactants, the increase in slip with shear rate slows down because of the presence of surfactants, and consequently, the linear dependence of slip length changes to a nonlinear dependence. Simulation results also indicate that the shear rate also affects the surfactant distribution. In particular, when the surfactant concentration is high enough to form a fully developed monolayer, the higher shear rate would make the monolayer rupture.

Hybrid particle-field molecular dynamics simulations for dense polymer systems

We propose a theoretical scheme for a hybrid simulation technique where self-consistent field theory and molecular dynamics simulation are combined (MD-SCF). We describe the detail of the main implementation issues on the evaluation of a smooth three-dimensional spatial density distribution and its special gradient based on the positions of particles. The treatments of our multiscale model system on an atomic scale or on a specific coarse-grained scale are carefully discussed. We perform a series of test simulations on this hybrid model system and compare the structural correlations on the atomic scale with those of classical MD simulations. The results are very encouraging and open a way to an efficient strategy that possess the main advantages common to the SCF and the atomistic approaches, while avoiding the disadvantages of each of the treatments.

Mesoscopic dynamics of inhomogeneous polymers based on variable cell shape dynamic self-consistent field theory

In this paper, we combine variable cell shape method with dynamic self-consistent field theory and extend to study structure and dynamics under shear for triblock copolymer melts. Due to shear, the calculation cell shape is variable and no longer orthogonal. Pseudospectral method is employed to solve the diffusion equation for chain propagator on the nonorthogonal coordinate and the shear periodical condition can be easily designed in terms of the variable cell shape method. By using this strategy, the shear induced morphology evolution is investigated for topologically complex polymeric systems such as linear and star triblock copolymers; the morphology of linear ABC triblock copolymers is more shear sensitive than that of star triblocks. In particular, once the chain propagator is obtained, the microscopic elastic stress and spatial stress distribution can be derived and thus the dynamic mechanical property can be calculated under shear. By imitating the dynamic storage modulus G' corresponding to any given morphology in the oscillatory shear measurements, we explore the relationship between the morphology and the storage modulus G' and extend to study the mechanism of phase separation dynamics as well as order-disorder transition (ODT) for linear and star triblock copolymers. The results show that the chain architecture can be easily distinguished by investigating the ODT, though the systems such as AB symmetric diblock and ABA triblock copolymers by coupling AB precursors almost exhibit similar microstructures. In addition, the storage modulus G' and loss modulus G" can be simultaneously determined in frequency sweeps of oscillatory shear measurements and the dependence of the moduli on phase separated patterns and the chain topology is investigated. The simulation findings are in qualitatively agreement with the experimental results.

Single chain in mean field simulations: Quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations

The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers.

Morphology of multi-component polymer systems: single chain in mean field simulation studies

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies reconstruction on patterned substrates.

Shear-induced phase transitions in ternary polymer blends

We present a study of flow-induced phase transitions in microemulsion phases of ternary polymer blends. The results match qualitatively with the recent experimental observations on such systems but differ from the behavior expected and observed in the analogous system of surfactants. We rationalize this contrast from a molecular viewpoint suggesting that the interplay between polymer chain conformations and their flow deformations can lead to novel flow effects upon the phase, structural, and rheological behavior of multicomponent polymer systems.