Dynamics in entangled polyethylene melts

Polymer dynamics creates distinctive viscoelastic behavior as a result of a coupled interplay of motion at the atomic length scale and motion of the entire macromolecule. Capturing the broad time and length scales of polymeric motion however, remains a challenge. Using linear polyethylene as a model system, we probe the effects of the degree of coarse graining on polymer dynamics. Coarse-grained (CG) potentials are derived using iterative Boltzmann inversion with λ methylene groups per CG bead (denoted CGλ) with λ = 2,3,4 and 6 from a fully-atomistic polyethylene melt simulation. By rescaling time in the CG models by a factor α, the chain mobility for the atomistic and CG models match. We show that independent of the degree of coarse graining, all measured static and dynamic properties are essentially the same once the dynamic scaling factor α and a non-crossing constraint for the CG6 model are included. The speedup of the CG4 model is about 3 times that of the CG3 model and is comparable to that of the CG6 model. Using these CG models we were able to reach times of over 500 μs, allowing us to measure a number of quantities, including the stress relaxation function, plateau modulus and shear viscosity, and compare directly to experiment.     

The stress tensor in entangled polymers

In entangled polymeric liquids, a subchain connecting two entanglements is an open system which can exchange particles (Kuhn segments) with its neighboring subchains along the polymer chain. We present a calculation of the subchain mechanical behavior as determined from the grand canonical formalism of statistical mechanics, with different subchains in the same chain sharing the same chemical potential. It is shown that the linear monomer density is a constant, as originally inferred by Doi and Edwards, but the tension is generally different from one subchain to another. Accounting for the latter effect leads to a new tensorial strain measure, somewhat different from that proposed by Doi and Edwards.     

Elastic breakup in uniaxial extension of entangled polymer melts

Five entangled melts, with the number of entanglements per chain ranging from 25 to 160, have been studied to illustrate how cohesive strength can be overcome in either continuous or interrupted extension (i.e., during or after uniaxial stretching). The internal elastic stress due to chain deformation from imposed strain appears to be the cause of the observed yielding behavior that reveals scaling laws. The visual signature of the elastic breakup is the occurrence of nonuniform extension. The yield phenomena may be understood at a force level.     

Melt fracture of entangled polymers*

We construct a model for a slippage plane in a sheared melt, based on a balance between reptation bridging and shear debonding. The resulting state could show up at rather low shear rates and be locally stable. But it is not easy to nucleate: the conventional entangled state is also locally stable. We propose that slippage occurs on solid walls: either at the container surface, or on dust particles floating in the melt. Slippage at solid/melt interfaces was studied (experimentally and theoretically) long ago. There is a critical stress for slippage: our estimate (for strong adsorption of melt chains on the solid) gives (plateau modulus) for typical cases. Thus, melt fracture is expected at moderate stresses, in agreement with observations by S.Q. Wang and coworkers.     

On relaxation of entangled states in a collective thermostat

A kinetic equation describing collective relaxation process in the dispersion limit is derived for an ensemble of two-level atoms placed in a cavity and interacting with one cavity mode. Multiatom entangled states belonging to the set of Dicke states and insensitive to collective decay are found. A scheme for recording, storing, and reading these states with participation of spatially multimode light is reported.     

Nonquiescent relaxation in entangled polymer liquids after step shear

Large step shear experiments revealed through particle tracking velocimetry that entangled polymeric liquids display either internal macroscopic movements upon shear cessation or rupturelike behavior during shear. Visible inhomogeneous motions were detected in five samples with the number of entanglements per chain ranging from 20 to 130 at amplitudes of step strain as low as 135%.     

Hypersonic relaxation in amorphous polymers

In order to more fully understand the viscoelastic properties of amorphous polymers, it is desireable to have dynamic mechanical data over as wide a range in frequency as possible. One useful technique for studying the high-frequency behavior of polymers is to measure the velocity and attenuation of sound waves in the polymer fluid. When the frequency exceeds 109Hz. the sound waves are called hypersonic acoustic phonons. The present review examines the dynamic data obtained in the GHz frequency range for amorphous polymers.     

Structural relaxation of metallic glass forming melts

The fragility of superheated melts, M, for 13 kinds of metallic alloys has been evaluated from the data of the dynamic viscosity above their liquidus temperatures. The authors find that the glass forming ability of metallic melts depends on the fragility of superheated melts rather than on the value of viscosity. In the present work the value of fragility is less than 1 for good glass-forming melts but more than 1 for the other melts. The variation rate of atomic coordination number with temperature indicat...     

Tight and loose shapes in flat entangled dense polymers

We investigate the effects of topological constraints (entanglements) on two-dimensional polymer loops in the dense phase, and at the collapse transition ( -point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and conditions, the uncontracted-knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.Received: 7 October 2003, Published online: 21 November 2003PACS: 87.15.-v Biomolecules: structure and physical properties - 82.35.-x Polymers: properties; reactions; polymerization - 02.10.Kn Knot theory     

Creation of pure multi-mode entangled states in a ring cavity

Practical schemes for creation of multi-mode squeezed (entangled) states of atomic ensembles located inside a high-Q ring cavity are discussed. It is assumed that the cavity is composed of two degenerate mutually counter-propagating modes that can simultaneously couple to the atomic ensembles with the same coupling strengths. The ensembles are composed of ultra-cold atoms which are modeled as four-level systems driven by two laser fields, both co-propagating with one of the cavity directions. We illustrate a procedure that constructs multi-mode squeezed states from the vacuum by a unitary transformation associated with the collective dynamics of the atomic ensembles subjected to driving lasers of a suitably adjusted amplitudes and phases. The lasers pulses together with the cavity dissipation prepare the collective modes in a desired stationary squeezed state.     

Calculation of second topological moment of two entangled polymers

We set up a field theoretical model based on Abelian Chern-Simons field theories to describe the topological entanglement of two polymers. The topological states of the system are distinguished using the link invariant of Gauss. The second topological moment of the two polymers , where m is the linking number, is exactly computed by field theoretical methods. The result is applied to estimate approximatively the mean square average of the linking number of a polymer P₁ in a dilute solution with other polymers.     

Stress relaxation in crumpled surfaces

The stress relaxation in crumpled surfaces maintained at a fixed compressive strain is investigated. The experiments indicate a slow relaxation of the mechanical stress in these non-equilibrium disordered systems. The experimental data indicate an anomalous stretched exponential decay with exponent β=0.28±0.03 along six decades in the rescaled variable t/τ, for a wide interval of strain. The results are compared with the similar behaviour of glassy materials, among others.     

Nuclear spin relaxation in stoichiometric and thallium-doped thallous halide melts

Relaxation times for ^203,205Tl, ^79,81Br and ^35,37Cl are reported for molten TlBr, TlCl and TlBr : Tl. For Br and Cl, relaxation is predominantly quadrupolar; for Tl the relaxation indicates contact hyperfine interaction with paramagnetic centres produced thermally and by adding Tl.     

Role of the entangled amorphous network in tensile deformation of semicrystalline polymers

Being composed of crystalline lamellae and entangled amorphous polymeric chains in between, semicrystalline polymers always show a complicated deformation behavior under tensile deformation. In recent years, the process of tensile deformation was found to exhibit several regimes: intralamellar slipping of crystalline blocks occurs at small deformation whereas a stress-induced crystalline block disaggregation-recrystallization process occurs at a strain larger than the yield strain. The strain at this transition point is related to the interplay between the amorphous entanglement density and the stability of crystal blocks. We report experimental evidence from true stress-strain experiments that support this argument. It is emphasized that tie molecules, which connect adjacent lamellae, are of lesser importance with respect to the deformational behavior.     

Analytic expressions for the statistics of the primitive-path length in entangled polymers

An analytic expression is proposed for the primitive-path length of entangled polymer chains. The expression is derived from statistical mechanics of a chain that is a random walk with randomly scattered entanglements. The only parameters are the number of Kuhn steps in the chain and a dimensionless parameter beta that contains information about the entanglement density and Kuhn step size. The expression is found to compare very favorably with numerical results recently found from examining topological constraints in microscopic simulations. The comparison also predicts well the plateau modulus of polyethylene, suggesting that the slip-link model is a viable intermediate in the search for true ab initio rheology predictions. Since the expression is analytic, it can be used to make predictions where the simulations cannot reach, and hence is applicable for coarse graining.     

Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts

We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from proportional, variant t(1/2) to proportional, variant t(1/4) is expected and clearly corroborated by the incoherent NSE results.