Linear Polymer Melts Research Articles

Structure and dynamics of polymer melt confined between two solid surfaces: A molecular dynamics study.

Using large scale molecular dynamics simulations we investigate the static and dynamic properties of a linear polymer melt confined between two solid surfaces. One of the walls is repulsive and the other is attractive wall. The bottom attractive wall is characterized by different degrees of roughness which is tuned by an array of short perpendicular rigid pillars with variable grafting density. We demonstrate that the conformations of polymers at the interfaces do not depend on substrate-polymer interactions, rather they show similar conformations of a single end-grafted chain under critical adsorption condition, consistent with the Silberberg's hypothesis. This observation is found to be in a good agreement with the analysis of the size distributions of trains, loops, and tails of melt chains at the walls known from the theoretical prediction of the end-grafted single chains at critical adsorption. Furthermore, we find that the pressure of the melt PN decreases as PN - P∞ ∝ N-1 with growing length of the chains N (where P∞ is the extrapolated pressure for N → ∞). Moreover, the surface tension γ near both walls is found to follow γN∝N(-2/3). Eventually, the lateral dynamics near rough surface drops suddenly when the separation between the neighboring pillars becomes smaller than 2Rg, where Rg is the bulk radius of gyration.

Entry flows of polylactides with slip

The entry capillary flow of four different polylactides (previously characterized by Othman et al. (2012)) has been modeled with both a viscous (Cross) and a viscoelastic (K-BKZ) model. The modeling takes into account slip-at-the-wall, which was found to increase with decrease of molecular weight. The flow through different capillary dies and apparent shear rates show the excess pressure losses (ends correction), which are smaller than those for other similar linear polymer melts. The viscous simulations capture well the ends correction, while the viscoelastic simulations improve these predictions, as they also account for the viscoelastic nature of the polymer melts. It is concluded that solely viscous modeling can capture their flow behavior satisfactorily.

Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics.

The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate γ, expressed by n ~ γ(-n), exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates γ < τ0(-1) (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (γ > τ0(-1)) the shear dependence of viscosity exhibits a crossover at a critical shear rate γc dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (τ0(-1) < γ < γc), the exponent n increases with increasing chain length N, while in the ST-II regime (γ > γc) a universal power law n ~ γ(-0.37) is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which γc will be equal to τ0(-1), lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of N1 ~ γ(2/3) and N2 ~ γ(0.82), respectively; the orientation resistance parameter mG follows the relation mG ~ γ(0.75) and the tumbling frequency ftb follows ftb ~ γ(0.75). These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.

Wall Slip of Bidisperse Linear Polymer Melts

We have characterized the effect of molecular weight distribution on slip of linear 1,4-polybutadiene samples sandwiched between cover glass and silicon wafer. Monodisperse polybutadiene samples with molecular weights in the range of 4–195 kg/mol and their binary mixtures were examined at steady state in planar Couette flow using tracer particle velocimetry. Slip velocity was measured at shear rates over the range of ∼0.1–15 s–1. Our results revealed that weakly entangled short chains play a crucial role in wall slip and flow dynamics of linear polymer melts. It was found that the critical shear stress for the onset of the transition to the strong slip regime is significantly reduced when a small amount of weakly entangled chains is added to a sample of highly entangled polymer. Within the same range of shear stresses, binary mixtures of long and short chains exhibit significantly enhanced slip compared to the moderate slip of the individual long chains. This is attributed to the reduced friction coeffici...

Nonisothermal analysis of extrusion film casting process using molecular constitutive equations

Extrusion film casting (EFC) is a commercially important process that is used to produce several thousand tons of polymer films and coatings. In a recent work, we demonstrated the influence of polymer chain architecture on the extent of necking in an isothermal film casting operation (Pol et al., J Rheol 57:559–583, 2013). In the present research, we have explored experimentally and theoretically the effects of long-chain branching on the extent of necking during nonisothermal film casting conditions. Polyethylenes of linear and long-chain branched architectures were used for experimental studies. The EFC process was analyzed using the 1-D flow model of Silagy et al. (Polym Eng Sci 36:2614–2625, 1996) in which the energy equation was introduced to model nonisothermal effects, and two multimode constitutive equations, namely the “extended pom-pom” (XPP, for long-chain branched polymer melts) equation and the “Rolie-Poly stretch version” (RP-S, for linear polymer melts) equation, were incorporated to account for the effects of polymer chain architecture. We show that the model does a better job of capturing the qualitative features of the experimental data, thereby elucidating the role of chain architecture and nonisothermal conditions on the extent of necking.

Coarse-grained simulations of moderately entangled star polyethylene melts

In this paper, a previous coarse-grain model [J. T. Padding and W. J. Briels, J. Chem. Phys. 117, 925 (2002)] to simulate melts of linear polymers has been adapted to simulate polymers with more complex hierarchies. Bond crossings between highly coarse-grained soft particles are prevented by applying an entanglement algorithm. We first test our method on a virtual branch point inside a linear chain to make sure it works effectively when linking two linear arms. Next, we apply our method to study the diffusive and rheological behaviors of a melt of three-armed stars. We find that the diffusive behavior of the three-armed star is very close to that of a linear polymer with the same molecular weight, while its rheological properties are close to those of a linear chain with molecular mass equal to that of the longest linear sub-chain in the star.

Necking in extrusion film casting: The role of macromolecular architecture

Extrusion film casting (EFC) is used on an industrial scale to produce several thousand tons of polymer films and coatings. While significant research has been carried out on necking of films of viscoelastic melts in EFC, the influence of macromolecular chain architecture on the necking behavior is not yet fully understood. In the present research, we have explored experimentally and theoretically the effects of long chain branching and molecular weight distribution on the extent of necking during EFC. Polyethylenes of essentially linear architecture but having narrow and broad molecular weight distributions, and polyethylenes having long chain branching were used for experimental studies. The EFC process was analyzed using the one-dimensional flow model of Silagy et al. [Polym. Eng. Sci. 36(21), 2614–2625 (1996)] in which multimode molecular constitutive equations namely the “extended pom-pom” equation (for long chain branched polymer melts) and the “Rolie–Poly (Rouse linear entangled polymers)” equation (for linear polymer melts) were incorporated. We show that the model qualitatively captures the salient features of the experimental data thereby elucidating the role of chain architecture on the extent of necking.

Experimental validation of a tube based constitutive equation for linear polymer melts with inter-chain tube pressure effect

A polydisperse case of an entangled linear polymer melts constitutive equation was studied. This constitutive equation, proposed by S. Dhole et al. [J. Non-Newtonian Fluid Mech. 161 (2009) 10–18], based on the reptation theory and the tube model, was tested on a polystyrene in shear (capillary rheometry) and planar extension in a complex flow (fieldwise measurements in a contraction flow) for different level of strain rates. A good quantitative prediction of all the set of experiments was obtained, using no adjustable nonlinear parameters.

Segmental Dynamics in Entangled Linear Polymer Melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2...

Stress and neutron scattering measurements on linear polymer melts undergoing steady elongational flow

We use small-angle neutron scattering to measure the molecular stretching in polystyrene melts undergoing steady elongational flow at large stretch rates. The radius of gyration of the central segment of a partly deuterated polystyrene molecule is, in the stretching direction, increasing with the steady stretch rate to a power of about 0.25. This value is about half of the exponent observed for the increase in stress value σ, in agreement with Gaussian behavior. Thus, finite chain extensibility does not seem to play an important role in the strongly non-linear extensional stress behavior exhibited by the linear polystyrene melt.

Understanding the Mechanism of Anomalous Viscosity–Molecular Weight Relationships of Diolic Perfluoropoly (Oxyethylene‐ran‐oxymethylene): What is Missing in the Debye–Bueche Model?

AbstractFor decades, the viscosity (η)–molecular weight (M) relationship of linear polymer melts has been successfully described by the Debye–Bueche model when M is lower than critical molecular weight (Mc). However, recent studies on diolic perfluoropoly (oxyethylene‐ran‐oxymethylene) (DPFPO), a linear polymer with polar endgroups, raise uncertainty on the validity of Debye–Bueche model. Experimental results show that the Debye–Bueche model does not hold for DPFPO, which has been attributed to the fact that the strong intermolecular endgroup–endgroup coupling is not considered in original Debye–Bueche model. A modified molecular‐level model, in which the endgroup–endgroup coupling is taken into consideration, is proposed to interpret the anomalous η–M relationship of DPFPO.

Bethe-Peierls approximation for linear monodisperse polymers re-examined

Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in the literature. An estimation of the configurational contribution to the total liquid's C(p) is presented. We also discuss the relation between the Kauzmann paradox and polymer semiflexibility.

Linear and non-linear dynamics of entangled linear polymer melts by modified tunable coarse-grained level Dissipative Particle Dynamics

Dissipative particle dynamics (DPD) is a well-known simulation method for soft materials and has been applied to a variety of systems. However, doubts have been cast recently on its adequacy because of upper coarse-graining limitations, which could prevent the method from being applicable to the whole mesoscopic range. This paper proposes a modified coarse-grained level tunable DPD method and demonstrates its performance for linear polymeric systems. The method can reproduce both static and dynamic properties of entangled linear polymer systems well. Linear and non-linear viscoelastic properties were predicted and despite being a mesoscale technique, the code is able to capture the transition from the plateau regime to the terminal zone with decreasing angular frequency, the transition from the Rouse to the entangled regime with increasing molecular weight and the overshoots in both shear stress and normal-stress differences upon start-up of steady shear.

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, [linear span]R(g)(2)[linear span], was found to scale as N(4/5) for an intermediate regime and N(2/3) for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with both architectures approximately obeying a D ∼ N(-2.4) scaling law for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the ring extension [linear span]R(g)(2)[linear span], neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers, and the zero-shear viscosity was found to vary as η(0) ∼ N(1.4 ± 0.2) which is much weaker than the N(3.4) behavior of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204904 (2011)].

Structure and dynamics of polymer rings by neutron scattering: breakdown of the Rouse model

We present a static and quasi-elastic neutron scattering study on both the structure and dynamics of a ring polymer in a ring and linear polymer melt, respectively. In the first case, the ring structure proved to be significantly more compact compared to the linear chain with the same molecular weight. In the mixture, the ring molecules swell as was confirmed by small angle neutron scattering (SANS) in accordance with both theory and simulation work. The dynamical behavior of both systems, which for the first time has been explored by neutron spin echo spectroscopy (NSE), shows a surprisingly fast center of mass diffusion as compared to the linear polymer. These results agree qualitatively with the presented atomistic MD simulations. The fast diffusion turned out to be an explicit violation of the Rouse model.

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) \((\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3)\) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (Tgel) characterized with a power–law relationship between the storage and loss moduli, G′ and G″, and frequency ω, \({G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}\), was observed to be 152°C. The elongational viscosity of the gel was measured below the Tgel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the Tgel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.

Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site–site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N − 1 for the small values of N , an exponent predicted by the Rouse theory, whereas in the range of 2.3 ≲ ln N ≲ 4.5 the N dependence smoothly crosses over to N − 2 , which is reminiscent of the exponent by the reptation theory. However, for ln N ≳ 4.5 the N dependence of the self-diffusion coefficient differs from N − 2 , but gives an N dependence, N − 2 − δ ( 0 < δ < 1 ) , consistent with experiment on polymer melts in the range. For polyethylene δ ≈ 0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.

Diffusion of linear polymer melts in shear and extensional flows

We present results from molecular dynamics simulations for the anisotropic self-diffusion tensor and the velocity autocorrelation functions of monodisperse systems of dense linear chain molecules under flow. Two molecular models are used in these simulations: The finitely extensible nonlinear elastic chain and the freely jointed tangent sphere chain. Nonequilibrium molecular dynamics is used to simulate these systems under planar Couette flow and planar extensional flow. Under planar extensional flow, results presented here are the first, from simulation, for diffusion and velocity autocorrelation functions of molecules, while for planar Couette flow, we compare the broadest range of conditions. An explicit derivation is provided of the Green-Kubo expression for the diffusion tensor. This expression is then used to derive the relation involving the mean-squared displacement-an often used alternative method to calculate diffusion coefficients. Velocity autocorrelation functions have been used, in combination with results on the alignment of molecules from a previous paper, to provide some details of the molecular scale dynamics that influence diffusive transport under flow.

Step Shear of Entangled Linear Polymer Melts: New Experimental Evidence for Elastic Yielding

This work studies the most basic and important behavior of entangled linear polymer melts in sudden large shear deformations. In particular, melt elasticity resulting from the large step shear is extensively shown to produce cohesive breakdown. Unlike entangled solutions studied in Macromolecules 2007, 40, 8031, the residual elastic forces in sheared melts struggle quiescently for a significant induction period before bringing down the entanglement network. The induction time for the elastic yielding can be much longer than the longest Rouse relaxation time τR, making it difficult to associate this cohesive failure with a chain retraction process envisioned in the tube theory. The cohesive failure also occurs upon a step strain produced at rates too slow to produce chain stretching, again making it unreasonable to invoke the concept of chain retraction due to chain stretching.