Modeling the Effect of Polymer Chain Stiffness on the Behavior of Polymer Nanocomposites (original) (raw)
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Journal of Non-Newtonian Fluid Mechanics, 2003
We present new results for the low strain rate behavior of the steady-state planar shear and elongational viscometric functions of model polymer melts, computed by non-equilibrium molecular dynamics simulations. The chain lengths in our model polymer melts vary from N = 2 up to N = 100 beads, the maximum value corresponding to approximately 57 Kuhn lengths (approximately equivalent to polyethylene of molar mass 8300 g/mol). The new results allow us to more precisely evaluate the constants in the third-order fluid constitutive relation that we fitted to the results of our previous simulations. We find agreement between the values of the retarded motion expansion coefficients of terms up to second-order in the strain rate obtained from the two types of flow. This indicates that the second-order fluid model self-consistently describes the stress tensor in shear and elongational flow with a single set of material constants if the deformation rate is sufficiently small. However, we find a discrepancy between two different estimates of a third-order term when it is evaluated from the first and second planar elongational viscosities. The second-order retarded motion expansion is extended to apply to compressible fluids and the deformation rate dependence of the pressure in shear and elongational flows is obtained. The predictions are confirmed by the simulation results. The chain length dependencies of the computed zero shear rate viscosity and first normal stress coefficient agree with the predictions of the Rouse model. The second normal stress coefficient varies as the cube of the chain length and the coefficient of the quadratic term in the strain rate dependence of the shear viscosity is proportional to the sixth power of the chain length for unentangled chains. (P.J. Daivis). bead mobility that occur as the concentration [2] and chain length [1] are increased. In the limit of long (strongly entangled) chains, the reptation model incorporates a specific model for anisotropic diffusion. The stress is often (but not always) then obtained by assuming the validity of the linear stress-optical law and averaging the bond-order tensor over the single-molecule configurational distribution function.
Coarse-grained, molecular dynamics ͑MD͒ simulations have been conducted to study the effect of shear flow on polymer nanocomposite systems. In particular, the interactions between different components have been tuned such that the nanoparticle-nanoparticle attraction is stronger than nanoparticle-polymer interaction, and therefore, the final equilibrium state for such systems is one with clustered nanoparticles. In the current study, we focus on how shear flow affects the kinetics of particle aggregation at the very initial stages in systems with polymers of different chain lengths. The particle volume fraction and size are kept fixed at 0.1 and 1.7 MD units, respectively. Through this work, shear has been shown to significantly slow down nanoparticle aggregation, an effect that was found to be a strong function of both polymer chain length and shear rate. To understand our findings, a systematic study on effect of shear on particle diffusion and an analysis of relative time scales of different mechanisms causing particle aggregation have been conducted. The aggregation rate obtained from the time scale analysis is in good agreement with that determined from the aggregation time derived from the pair correlation function monitored during simulations.
Effect of chain stiffness on the entropic segregation of chain ends to the surface of a polymer melt
The Journal of Chemical Physics
Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension are examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, p , is comparable to the width of the surface profile, ξ, but still much smaller than the total contour length of the polymer, c. Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k B T per chain end, which results in the usual N −1 reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N n relative to the bulk. This provides a partial explanation for recent quantitative differences between experiments and SCFT calculations for flexible polymers.
The Journal of Chemical Physics, 2013
In this work, we study the influence of polymer chain length (m), based on Lennard-Jones potential, and nanoparticle (NP)-polymer interaction strength (ɛnp) on aggregation and dispersion of soft repulsive spherically structured NPs in polymer melt using coarse-grain molecular dynamics simulations. A phase diagram is proposed where transitions between different structures in the NP-polymer system are shown to depend on m and ɛnp. At a very weak interaction strength ɛnp = 0.1, a transition from dispersed state to collapsed state of NPs is found with increasing m, due to the polymer's excluded volume effect. NPs are well dispersed at intermediate interaction strengths (0.5 ⩽ ɛnp ⩽ 2.0), independent of m. A transition from dispersion to agglomeration of NPs, at a moderately high NP-polymer interaction strength ɛnp = 5.0, for m = 1–30, is identified by a significant decrease in the second virial coefficient, excess entropy, and potential energy, and a sharp increase in the Kirkwood-B...
A Monte-Carlo study of equilibrium polymers in a shear flow
The European Physical Journal B, 1999
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.
GUJRATI:MODELING POLYMERS O-BK, 2010
Polymer molecules differ from simple fluids in several aspects: they are extremely diverse in structure (they can have a linear, branched, ring-like, or block copolymer structure), they can be characterized by a molecular weight distribution, and they are capable of exhibiting a huge number of configurations implying that a large number of degrees of freedom should be accounted for in any molecular modeling approach. As a result, polymers exhibit properties which are totally distinct from those of the simpler Newtonian liquids. The drag reduction phenomenon (the substantial reduction in pressure drop during the turbulent flow of a Newtonian liquid when a very small amount of a flexible polymer is added), their unique rheological properties (shear thinning and normal stress differences in simple shear, strain hardening in elongation, complex viscosity, anisotropy in thermal conductivity and diffusivity), and a plethora of other phenomena associated with their elastic character are only a few manifestations of the departure of their behavior from the Newtonian one . Of particular importance from a mechanical or fluid dynamics point of view is their viscoelasticity quantifying the irreversible conversion of the work needed for their deformation to heat loss but also their capability to store part of this work as elastic energy. It is a property closely related to the multiplicity of time and length scales characterizing dynamics and structure in these fluids. Thus, even in the viscous regime (Wi ≪ 1, where Wi is the Weissenberg number empirically defined as Wi = τ pγ with τ p being the longest relaxation time anḋ γ the flow rate), the flow can still be strong enough for several degrees of freedom not to be close to equilibrium giving rise to interesting rheological properties also there [2], especially for high molecular weight polymers.
The Journal of Chemical Physics, 2018
Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent beadspring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.
Chain Stiffness Intensifies the Reptation Characteristics of Polymer Dynamics in the Melt
ChemPhysChem, 2001
The reptation concept in polymer dynamics is studied for model chains with added stiffness. The main idea of a chain diffusing inside a tube can be transferred from fully flexible chains although the renormalization onto a flexible chain of fewer Kuhn segments fails. The entanglement length shrinks with increasing persistence length. If entanglement length and persistence length come to the same order of magnitude the picture of a tight tube is better suited, in which chain segments can move only along the contour, any transverse motion being much reduced. Thus, as stiffness increases, the monomers loose their freedom to perform random walks inside the tube, the "Rouse-like" part of their dynamics.
The Journal of Chemical Physics, 2004
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.