Telechelic Melt Polymer's Structure Variation Depending on Shear Deformation

We present the result of molecular dynamics (MD) simulations of bead and spring models of associating polymers at melt-like densities, both in static conditions and when a shear rate is applied. Specifically, we consider the response of telechelic polymers of general formula AB₁₂A to four different values of shear rate. The A terminals tend to associate with each other and in bulk conditions form clusters or micelles. A reversible network or physical gel is formed by a large fraction of bridging chains that interconnect different clusters. The micelles assume different form depending on the interaction strengths. When a shear rate is applied, the clusters are broken and the chains tend to stretch.     

Elastic properties of polymer networks with sliding junctions

This paper proposes simple models of polymer networks with sliding junctions for molecular simulation and reports the main results obtained by Brownian dynamics on the elastic properties of networks with tri-functional sliding junctions. The stress-strain relation for isotropic swelling and uniaxial deformation are obtained and compared with those of the conventional chemical gels. We find that mobility and distribution of sliding junctions along the polymer chains drastically change with deformation, and lead to new profiles of the stress. We also find that sliding junctions aggregate by deformation, resulting in the decrease in the number of elastically effective chains.     

Phase behavior of flowerlike micelles in a SCF cell model

We study the interactions between flowerlike micelles, self-assembled from telechelic associative polymers, using a molecular self-consistent field (SCF) theory and discuss the corresponding phase behavior. In these calculations we do not impose properties such as aggregation number, micellar structure and number of bridging chains. Adopting a SCF cell model, we calculate the free energy of interaction between a central micelle surrounded by others. Based on these results, we predict the binodal for coexistence of dilute and dense liquid phases, as a function of the length of the hydrophobic and hydrophilic blocks. In the same cell model we compute the number of bridges between micelles, allowing us to predict the network transition. Several quantitative trends obtained from the numerical results can be rationalized in terms of transparent scaling arguments.     

Size and viscoelasticity of spatially confined multilamellar vesicles

We studied viscoelastic properties and scaling behavior of multilamellar vesicles (MLVs) confined between two parallel plates as a function of the shear rate and sample thickness (gap size between parallel plates). The rheological properties are classified into two regimes; the shear-thinning regime at high shear rates and the shear-thickening regime at low shear rates. In the former, the MLV radius results from the mechanical balance between the effective surface tension σ_eff and viscous stress force. The MLV radius is independent of the gap size. σ_eff estimated by van der Linden model is 2.1 ±0.15 ×10^-4 Nm^-1 corresponding to the same value obtained by SANS measurement. Power law exponents for the steady state viscosity and yield stress against pre-shear rate ( , ) well agree with prediction based on the layering of membranes. Therefore, viscoelastic properties in this regime could be modeled by assuming that the dynamics of MLVs are driven by layering of MLV polydomains, which could be accompanied by the viscous dissipation, i.e., the stress relaxation on the MLV, induced by continuous sequence of yields of MLVs. The flow curve is empirically explained by the assumption of a relaxation time for the MLV shape. In the latter, however, scaling laws observed in the shear-thinning regime break down. The MLV radius increases when the gap size is reduced below the threshold value and MLV is no longer formed at very small gap sizes. Different dynamics from the shear-thinning regime seem to dominate the viscoelasticity.     

Microscopic relationship between colloid–colloid interactions and the rheological behaviour of suspensions: a molecular dynamics-stochastic rotation dynamics investigation

ABSTRACT

We investigate the dependence of the shear viscosity of suspensions of spherical colloids as a function of the volume fraction of the suspension, the colloid–colloid interactions and the shear rate. We couple molecular dynamics to describe the motion of the colloids with stochastic rotation dynamics (MD–SRD) for the fluid environment by means of stochastic collisions, in order to incorporate hydrodynamics effects leading to non-newtonian responses. The shear viscosity is computed using non-equilibrium simulations by imposing explicit velocity gradients. The impact of the colloid–colloid interactions is examined by modelling the inter-colloid pair potential with a repulsive power law, that allows interpolating different degrees of colloidal softness. The general rheological behaviour of our suspensions can be described with a Krieger–Dougherty like equation, which must be corrected to account for the variations in the maximum packing fraction and non-equilibrium effects arising from the flux of momentum imposed to the suspension, which appear when varying the softness of the inter-colloidal interactions. We further show evidence for non-newtonian behaviour at high Péclet numbers, characterised both by shear thinning and shear thickening, and thus demonstrate these effects can be successfully captured using MD–SRD methods.     

Single-chain dynamics of linear polyethylene liquids under shear flow

Molecular dynamics simulations of linear C₇₈H₁₅₈ were conducted to investigate the dynamics of individual chains under shear. The distribution of the end-to-end vector exhibited Gaussian behavior at low shear rates; however, it displayed a bimodal form at high shear rates as rotational motion of the individual chains effectively lowered the vector's magnitude. Correlations between the components of the end-to-end vector revealed multiple time scales associated with the fluid response: the Rouse time, and several that were associated with the deformation and rotational dynamics of the fluid.     

Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids

We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup.     

Amphiphilic telechelic poly(N-isopropylacrylamide) in water: From micelles to gels<Superscript>⋆</Superscript>

We report the first study of aqueous solutions (0.025 gL^-1 to 46 gL^-1) of a telechelic poly(N-isopropylacrylamide) with octadecyl termini (C₁₈-PNIPAM-C₁₈, M_w: 37000, 320 NIPAM units, M_w/ M_n = 1.07) obtained by reversible addition-fragmentation chain transfer (RAFT) free radical polymerization of N-isopropylacrylamide. Static and dynamic light scattering measurements and fluorescence spectroscopy, using 8-anilino-1-naphthalenesulfonic acid (ANS) as probe, yielded the concentration dependence of the size and aggregation number of C₁₈-PNIPAM-C₁₈ micelles in cold ( 20^°C) dilute aqueous solutions. Concentrated solutions ( c > 20gL^-1) form transient gels exhibiting an oscillatory shear behavior that can be approximated by a single-relaxation Maxwellian model. Aqueous solutions of C₁₈-PNIPAM-C₁₈ undergo a phase transition upon heating to 31.5^°C as determined by microcalorimetry. The heat-induced phase separation of dilute (0.025 gL^-1) C₁₈-PNIPAM-C₁₈ solutions yields a fluid that is colloidally stable at temperatures higher than 33^°C. The overall results are consistent with a model assuming the formation of flowerlike micelles in the dilute regime and a network of micelles connected by telechelic chains in the concentrated regime.     

Local phase transitions in driven colloidal suspensions

Using dynamical density functional theory and Brownian dynamics simulations, we investigate the influence of a driven tracer particle on the density distribution of a colloidal suspension at a thermodynamic state point close to the liquid side of the binodal. In bulk systems, we find that a localised region of the colloid-poor phase, a ‘cavitation bubble’, forms behind the moving tracer. The extent of the cavitation bubble is investigated as a function of both the size and velocity of the tracer. The addition of a confining boundary enables us to investigate the interaction between the local phase instability at the substrate and that at the particle surface. When both the substrate and tracer interact repulsively with the colloids we observe the formation of a colloid-poor bridge between the substrate and the tracer. When a shear flow is applied parallel to the substrate the bridge becomes distorted and, at sufficiently high shear-rates, disconnects from the substrate to form a cavitation bubble.     

Entropic phase separation in polymer-microemulsion networks

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first-order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase behavior of the system is extremely robust and is independent of the detailed properties of either polymers or drops.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Shear thickening and migration in granular suspensions

We study the emergence of shear thickening in dense suspensions of non-Brownian particles. We combine local velocity and concentration measurements using magnetic resonance imaging with macroscopic rheometry experiments. In steady state, we observe that the material is heterogeneous, and we find that the local rheology presents a continuous transition at low shear rate from a viscous to a shear thickening, Bagnoldian, behavior with shear stresses proportional to the shear rate squared, as predicted by a scaling analysis. We show that the heterogeneity results from an unexpectedly fast migration of grains, which we attribute to the emergence of the Bagnoldian rheology. The migration process is observed to be accompanied by macroscopic transient discontinuous shear thickening, which is consequently not an intrinsic property of granular suspensions.     

Multilayer Markov Chains with Applications to Polymers in Shear Flow

We present an analysis of multilayer Markov chains and apply the results to a model of a tethered polymer chain in shear flow. We find that the stationary probability measure in the direction of the flow is nonmonotonic, and has several maxima and minima for sufficiently high shear rates. This is in agreement with the experimental observation of cyclic dynamics for such polymer systems. Estimates for the stationary variance and expectation value were obtained and showed to be in accordance with our numerical results.     

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

Shear localization in a model glass

Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.     

Shear thickening of cornstarch suspensions as a reentrant jamming transition

We study the rheology of cornstarch suspensions, a non-Brownian particle system that exhibits shear thickening. From magnetic resonance imaging velocimetry and classical rheology it follows that as a function of the applied stress the suspension is first solid (yield stress), then liquid, and then solid again when it shear thickens. For the onset of thickening we find that the smaller the gap of the shear cell, the lower the shear rate at which thickening occurs. Shear thickening can then be interpreted as the consequence of dilatancy: the system under flow wants to dilate but instead undergoes a jamming transition because it is confined, as confirmed by measurement of the dilation of the suspension as a function of the shear rate.     

Shear viscosity of a simple fluid over a wide range of strain rates

The shear viscosity of the Weeks—Chandler—Andersen (WCA) fluid at the Lennard-Jones triple point has been calculated over a wide range of strain rates using the transient time correlation function (TTCF) formalism. It has been demonstrated that these calculations can be carried out at arbitrarily low strain rates with the precision of the Green—Kubo calculations. At high strain rates, the calculated data agree within the error bars with more precise data acquired using the computationally less demanding steady state (SS) non-equilibrium molecular dynamics (NEMD) method. The linear variation of viscosity with the square root of the strain rate is discussed.     

Verhulst model with Lévy white noise excitation

The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Lévy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise; (ii) noise with a probability density of increments expressed in terms of Gamma function; and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Lévy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.