Block Copolymers Under Shear Flow

The nonequilibrium molecular dynamics computer simulation method was used to study microsegregated block copolymer systems in a selective solvent under a shear flow field. Two polymer concentrations were considered, 0.3 and 0.4, corresponding to the body centered cubic spherical and hexagonal cylindrical zero-shear phases, respectively. As the shear rate increased, both systems exhibited two-stage shear thinning, a peak in the scalar pressure, and normal stress differences. Microscopic connections were investigated by calculating the gyration and bond orientation tensors and the interaction energies per particle. At high shear rates, polymer chains elongate and orient along the direction of shear, and this is accompanied by the breaking-up of domains. The structure-rheology relation was discussed with regard to the morphological changes reported in our last study for the same systems. In particular, the structurally relevant critical values of the shear rate were found to delimit different behaviors of the shear rate-dependencies obtained in this work.

The phase behavior of poly(styrene-block-2-vinylpyridine) copolymer solutions in an imidazolium bis(trifluoromethane)sulfonamide ([Im][TFSI]) ionic liquid has been studied using small-angle X-ray scattering (SAXS) and optical transmission characterization. Through scaling analysis of SAXS data, we demonstrate that the [Im][TFSI] ionic liquid behaves as a selective solvent toward one of the blocks. We observe lyotropic and thermotropic phase transitions that correspond qualitatively to the phase behavior observed in block copolymer melts and block copolymer solutions in molecular solvents. In addition, we have studied the thermal properties of block copolymer solutions in the ionic liquid using differential scanning calorimetry and wide-angle X-ray scattering. We observe distinct composition regimes corresponding to the change in the block copolymer’s glass transition temperature, Tg, with respect to the concentration of polymer in ionic liquid. At high block copolymer concentrations, a “salt-like” regime corresponding to an increase in the block copolymer Tg is observed, while at intermediate block copolymer concentrations, a “solvent-like” regime corresponding to a decrease in the block copolymer Tg is observed. An unusual thermal transition consisting of crystallization and subsequent melting of the ionic liquid is observed at the lowest block copolymer concentration characterized.

Nonequilibrium molecular dynamics (NEMD) simulations play a major role in characterizing the rheological properties of fluids undergoing shear flow. However, all previous studies of flows in molecular fluids either use an “atomic” thermostat which makes incorrect assumptions concerning the streaming velocity of atoms within their constituent molecules, or they employ a center of mass kinetic (COM) thermostat which only controls the temperature of relatively few degrees of freedom (3) in complex high molecular weight compounds. In the present paper we show how recently developed configurational expressions for the thermodynamic temperature can be used to develop thermostatting mechanisms which avoid both of these problems. We propose a thermostat based on a configurational expression for the temperature and apply it to NEMD simulations of decane undergoing Couette flow at constant volume and at constant pressure. The results so obtained are compared with those obtained using a COM kinetic thermostat. At equilibrium the properties of systems thermostatted in the two different ways are of course equivalent. However, we show that the two responses differ far from equilibrium. In particular, we show that the increase in the potential energy of the internal modes with increasing shear is only observed with a Gaussian isokinetic COM thermostat in both NVT and NPT simulations. There is no such increase with the configurational thermostat, which, unlike the Gaussian isokinetic COM thermostat, correctly accounts for the internal degrees of freedom of the molecular fluid.

We examine several aspects of the dynamics of linear polymers under shear and extensional flows. We use nonequilibrium molecular dynamics (NEMD) to simulate systems under planar Couette flow (PCF) and planar extensional flow (PEF). In addition we look at several kinetic models of polymer melts, in particular the Curtiss-Bird model, for which we calculate the predictions of steady-state viscosity under PEF. To the best of our knowledge this is the first time that these results have been presented for this kinetic model. Our simulations under PEF are enabled by the use of Kraynik-Reinelt periodic boundary conditions (pbcs). We include here our observation that these pbcs are closely related to the Arnold cat map, a simple example of a dynamical map with chaotic properties. This observation enhances our understanding of this simulation technique. We compare directly under flow for the first time two commonly used coarse grained models of linear polymers. The first, a bead-spring model which uses the flexible finitely extensible nonlinear elastic potential (FENE) to bond adjacent beads. The second, a bead-rod model which uses a constraint force algorithm to fix the bond length. For this model we use the name freely jointed chain (FJC). The comparison is based on viscometric, structural and dynamical properties. We find that results for FENE and FJC systems are almost identical. Comparing results with predictions of the Curtiss-Bird model under PEF we find that values for the parameters of the Curtiss-Bird model required for a fit with the simulation data fall outside the range allowed by the Curtiss-Bird model and we conclude that assumptions of the Curtiss-Bird model deviate from dynamics observed in liquids under extensional We then focus on the self-diffusion of molecules under PEF and PCF, calculating elements of the diffusion tensor using appropriate mean-squared displacement formulae. Our interpretation of these results incorporate properties from the FENE and FJC comparison and results for the velocity autocorrelation function in these systems. We find anisotropy of diffusion more significant under PEF than under PCF. We conclude that this arises due to the significant enhancement of alignment under PEF. Our simulations represent the widest range of molecular systems under shear flow for which self-diffusion has been calculated. Results for PEF represent the first examination of self-diffusion for molecular systems under an extensional flow.

Block copolymers in dilute and semidilute solutions in selective solvents self associate forming multimolecular spherical micelles, cores of which are formed by insoluble blocks and shells by soluble blocks. Experimental approaches are surveyed concerning structure and hydrodynamic properties of block copolymer micelles, thermodynamics of micelle formation, kinetics of micelle formation and dissociation, and dynamics of micellar equilibria. Some problems of present interest are briefly mentioned, like anomalous micellization or tentacled micelles

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.

A mean-field anisotropic diffusion model for unentangled polymeric liquids and semi-dilute solutions: Model development and comparison with experimental and simulation data

ABSTRACTThe ability to produce block copolymers has led to new materials with unique properties. The chemical connectivity of incompatible blocks forces segregation to occur at distances of the order of the block sizes. In block copolymer melts, the segregated domains form periodic ordered structures called microphases. Most block copolymers are strongly incompatible. In such cases, in order to ensure equilibrium microphase separated samples, the microphases are prepared from solution. Microphase separation in semidilute solutions of block copolymers in nonselective good solvent is analyzed. The solvent effects on the thermodynamics in the weak segregation limit are discussed. The concentration of block copolymer at the transition in good solvents, scales as φtN−.62and in ϑ solvents as N−.5. The transitions between microphase morphologies as a function of block copolymer concentration are studied.

We consider the dynamics of an isolated kink band within an otherwise well-aligned lamellar block copolymer (or other smectic A liquid crystal) subjected to a macroscopic shear flow. We find on geometrical grounds that normal relative motion of the tilt boundaries that delineate such a band, relative to the normal velocity of the fluid, can occur only if there is jump in the tangential component of the fluid velocity across the boundary. We show that such tangential slippage should be negligible for well-developed bands with narrow boundaries. These observations lead to a simple description of the evolution of an idealized kink band, in which the kink bandwidth remains constant after the formation of narrow tilt boundaries, and the tilt boundaries rotate as material surfaces in a shear flow. The resulting prediction for the rate of rotation of the layers within such a band is confirmed by in situ small-angle X-ray scattering (SAXS)-steady shear experiments, which measure the evolution of the distribution of lamellar orientations within kink bands in a predominantly parallel poly(styrene-co-ethylenepropylene) diblock copolymer.

We present a detailed analysis of the general influence of short branches on the structural, topological, and rheological behaviors of entangled short-chain branched (SCB) polyethylene (PE) melt systems under shear flow via direct comparison with the corresponding linear analogs using extensive atomistic nonequilibrium molecular dynamics (NEMD) simulations, for a wide range of flow strengths. In comparison with the linear melt, the SCB systems generally exhibit more compact chain structures and larger dynamic resistance, in response to an imposed flow field at all flow strengths. These features essentially arise from (i) the increased chain stiffness due to the torsional restriction of backbone atoms around the branch points and (ii) the fast random Brownian motion of short branches via their very short characteristic relaxation time. We analyzed various structural and rheological properties, such as anisotropic chain dimension and orientation and their detailed distributions, topological characteristics of the entanglement network, material functions, chain rotation dynamics, and flow birefringence. Distinctive physical characteristics of the entangled SCB systems exposed by these individual properties can be consistently understood based on the fundamental structural and dynamical roles of short branches. These findings are considered informative in our systematic understanding and prediction for the general rheological behaviors of long entangled SCB polymer systems under flow, and in tuning the material properties of SCB polymers in practical applications.

Non-linear responses of the hard-spheroid fluid under shear flow

We present and discuss results obtained by an extensive nonequilibrium molecular dynamics computer simulation study of polymer solutions under shear, where the chain consists of N beads connected by a finitely extendable nonlinear elastic (FENE) spring force and the solvent is explicitly taken into account. Various scaling laws are extracted from the data which allow one to predict the qualitativeand to certain extent also quantitativestructural and rheological behavior of polymer solutions under good solvent conditions. For most quantities, the results drawn from simulation are compared with experimental data and theoretical predictions which are based on similar models (e.g., harmonic bond potentials or Brownian dynamics methods). Specifically, and in contrast to common theoretical approaches, the simulation yield information about a set of different but characteristic relaxation times, which determine the rheological and structural behavior (for example, flow birefringence, structure factor, rotational dynamics) separately, the difference either resulting from the underlying static or dynamic nature or from relaxation processes which act on different length scales.

An algorithm is described which allows Nonequilibrium Molecular Dynamics (NEMD) simulations of a fluid undergoing planar Couette flow (shear flow) to be carried out on a distributed memory parallel processor using a (spatial) domain decomposition technique. Unlike previous algorithms, this algorithm uses a co-moving, or Lagrangian, simulation box. Also, the shape of the simulation box changes throughout the course of the simulation. The algorithm, which can be used for two or three dimensional systems, has been tested on a Fujitsu AP1000 Parallel computer with 128 processors.

A combination of group theory and NEMD computer simulation confirms the existence of new asymmetric cross-current correlation functions excited in a monatomic fluid subjected to couette flow. The structure of these functions is explored and their implications for spectroscopic techniques such as depolarised light scattering and infra-red absorption are discussed.

We present nonequilibrium molecular dynamics (NEMD) simulation results for the miscibility, structural properties, and melt rheological behavior of polymeric blends under shear flow. The polymeric blends consist of chemically identical linear polymer chains (187 monomers per chain) and dendrimer polymers of generations g = 1-4. The number fraction x of the dendrimer species is varied (4%, 8%, and 12%) in the blend melt. The miscibility of blend species is measured, using the pair distribution functions gDL, gLL, and gDD. All the studied systems form miscible blend melts under the conditions investigated. We also study the effect of shear rate γ̇ and dendrimer generation on inter-penetration between blend species for different blend systems. The results reveal that shear flow increases the interpenetration of linear chains toward the core of the dendrimers. We also calculate the shear-rate dependent radius of gyration and ratios of the eigenvalues of the gyration tensor to study the shear-induced deformation of the molecules in the blend. Melt rheological properties including the shear viscosity and first and second normal stress coefficients obtained from NEMD simulations at constant pressure are found to fall into the range between those of pure dendrimer and pure linear polymer melts.