Yieldlike constitutive transition in shear flow of entangled polymeric fluids

We describe an unexpected constitutive transition in entangled polymer solutions. At and beyond a critical stress, the initial spatially homogeneous and well-entangled sample transforms from its entangled (coiled) state into a fully disentangled (stretched) state over a period during which the resulting shear rate increases in a spatially inhomogeneous fashion. In the mode of controlled shear rate, the sample exhibits a stress plateau over three decades. Flow birefringence and normal stress observations unravel additional features of these flow phenomena.     

Polymer solutions in co-rotating Taylor-Couette flow without vorticity

We present experimental results of the flow of dilute and semi-dilute polymer solutions in co-rotating Taylor-Couette cylinders. The experimental set-up consists of a modified Mars II rheometer (Thermo Scientific) with two drive units that are mounted opposite each other. The rotational velocities of the inner and outer cylinders are chosen in a way such that the angular velocity has a 1/r profile and the flow is free of vorticity, but the direction of elongation is not constant, but rotates with the flow. Our particle image velocimetry (PIV) measurements show that for polymer solutions without shear thinning the flow is indeed free of vorticity and is equal to a stagnation point flow at a given position and a given instant in time. In contrast, torque measurements reveal that the stresses are identical to the stresses that are present in a plane shear flow. Thus, we find that for polymer solutions a flow with vorticity and a constant direction of elongation is equal to a flow without vorticity in which the direction of elongation is rotating. Finally, we show that for shear thinning solutions the flow velocity becomes non-monotonic through the gap and resembles a pluglike profile which is known from the Poiseuille flow.     

Shear banding in molecular dynamics of polymer melts

In order to establish constitutive equations for a viscoelastic fluid uniform shear flow is usually required. However, in the last 10 years S. Q. Wang and co-workers have demonstrated that some entangled polymers do not flow with the uniform shear rate as usually assumed, but instead choose to separate into fast and slow flowing regions. This phenomenon, known as shear banding, causes flow instabilities and in principle invalidates all rheological measurements when it occurs. In this Letter we report the first observation of shear banding in molecular dynamics simulations of entangled polymer melts. We show that our observations are in a very good agreement with the phenomenology developed by Fielding and Olmsted. Our findings provide a simple way of validating the empirical macroscopic phenomenology of shear banding.     

Anisotropic thermal conduction in a polymer liquid subjected to shear flow

Flow-induced anisotropic thermal conduction in a polymer liquid is studied using force Rayleigh scattering. Time-dependent measurements of the complete thermal diffusivity tensor, which includes one off-diagonal and three diagonal components, are reported on an entangled polymer melt subjected to a uniform shear deformation. These data, in conjunction with mechanical measurements of the stress, provide the first direct evidence that the thermal conductivity tensor and the stress tensor are linearly related in a deformed polymer liquid.     

Microscopic theory for the fast flow of polymer melts

We develop a theory of fast flows of entangled polymer melts incorporating the process of convective constraint release (CCR) as a local rearrangement of the entanglement tubes. Using a new formalism that simultaneously captures reptation, fluctuation motion of the chain, and Rouse motion of its tube, we show that the spurious maximum of shear stress as a function of shear rate, predicted by the original Doi-Edwards theory and other treatments of CCR, may be removed. The single chain (SANS) structure factor in shear flow is also predicted and compared to hitherto unexplained experimental data. The stress maximum is retained in the case of living polymeric micelles.     

Banding in entangled polymer fluids under oscillatory shearing

We report a flow phenomenon in entangled polymer solutions that has never been described in the literature. A large-amplitude oscillatory shear was imposed on the polymer sample at a frequency higher than the overall chain relaxation rate. The resulting chain orientation led to a new environment in which the initially well-entangled chains managed to disentangle inhomogeneously in space. A layer lacking chain entanglement developed to take the load of the imposed strain. As a result of this nonlinearity, the rest of the sample avoided significant deformation and its chain entanglement remained intact.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

Molecular origin and dynamic behavior of slip in sheared polymer films

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N=10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum.     

Stress relaxation in entangled melts of unlinked ring polymers

Stress relaxation in unlinked ring polymer melts poses an important challenge to our theoretical understanding of entangled polymer dynamics. Recent experiments on entangled unlinked ring melts show power-law stress relaxation with no hint of a rubbery plateau, usually the hallmark of entangled polymers. Here we present a theory for stress relaxation in rings analogous to the successful approach for star polymers. We augment our theory with mesoscale Monte Carlo dynamics simulations of equivalent "lattice animal" configurations. We find a stress relaxation function G(t)～t(-α) with α≈1/2 consistent with experiment, emerging ultimately from the disparate relaxation times of more- and less-central portions of ring conformations.     

High-resolution magnetic resonance flow imaging in a model of porous bone-implant interface

PURPOSE: To evaluate the application of high-resolution MRI methodology for characterizing the fluid velocity field and evaluate fluid shear field within a simplified in vitro model of a bone-implant interface. MATERIALS AND METHODS: The study used a specific micromotion canine bone implant that has been used for over a decade in the experimental evaluation of anatomical, biomaterial, mechanical and surgical factors influencing the quality of the implant interface. To allow its implementation in an MR coil, a nonmagnetic model of the micromotion implant was fabricated. The model consisted of a cylinder of polymethylmethacrylate (PMMA) representing the implant, located within an annular controlled gap into a block of coralline-derived bulk porous hydroxyapatite (HA; Interpore Cross International, Irvine, CA, USA). The assembly was potted in a polycarbonate shell and connected to a gravity-feed flow system consisting of a water fluid reservoir and peristaltic pump. Cross-sectional fluid velocity images through the principal axis of the implant were generated using a phase-encoding MR imaging technique; axial fluid flow was derived, and fluid shear was evaluated using a Newtonian fluid model. RESULTS: Due to the nonuniform gap of the actual experimental construct, a highly nonuniform flow through the annular gap and a secondary flow through the porous HA block were observed. Axial velocity magnitudes in the range 0.04 to 14 mm/s were measured, and the flow velocities within the annular gap and the surrounding bone differed by nearly two orders of magnitude. Image analysis showed that 95% of total flow passed through the annular gap and 5% was transported through the porous HA block. Fluid shear was computed within the porous structure and the annular gap, and they differed by one order of magnitude. CONCLUSION: We demonstrated that high-resolution MR flow imaging has the resolution to measure fluid transport processes noninvasively through a nonmagnetic model bone implant. Gap fluid flow and fluid flow into the permeable skeleton (HA block) were quantified, and these data allowed the noninvasive determination of fluid shear. These promising results are encouraging for applications in biological tissue, artificial bone substitutes, tissue engineering and clinically relevant studies concerning implant fixation.     

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%.     

Rheology of giant micelles

Giant micelles are elongated, polymer-like objects created by the self-assembly of amphiphilic molecules (such as detergents) in solution. Giant micelles are typically flexible, and can become highly entangled even at modest concentrations. The resulting viscoelastic solutions show fascinating flow behaviour (rheology) which we address theoretically in this article at two levels. First, we summarize advances in understanding linear viscoelastic spectra and steady-state nonlinear flows, based on microscopic constitutive models that combine the physics of polymer entanglement with the reversible kinetics of self-assembly. Such models were first introduced two decades ago, and since then have been shown to explain robustly several distinctive features of the rheology in the strongly entangled regime, including extreme shear thinning. We then turn to more complex rheological phenomena, particularly involving spatial heterogeneity, spontaneous oscillation, instability and chaos. Recent understanding of these complex flows is based largely on grossly simplified models which capture in outline just a few pertinent microscopic features, such as coupling between stresses and other order parameters such as concentration. The role of ‘structural memory’ (the dependence of structural parameters such as the micellar length distribution on the flow history) in explaining these highly nonlinear phenomena is addressed. Structural memory also plays an intriguing role in the little-understood shear thickening regime, which occurs in a concentration regime close to but below the onset of strong entanglement, and which is marked by a shear-induced transformation from an inviscid to a gelatinous state.     

多组分纠缠在光子晶体中的存储

研究了激子的多组分纠缠相干态保真度在各向异性光子晶体中的演化行为.结果表明,当激子的跃迁频率处于光子晶体带隙时,保真度随时间变化作周期振荡,这与激子处于真空环境时,保真度振荡衰减的演化行为不同.此外,当激子跃迁频率离光子晶体带边较远时,其多组分纠缠相干态越容易被保存.     

Crystallization of an Entangled Ring Polymer: Coexistence of Crystal and Amorphous Regions

We discuss a molecular model of crystallization of a quenched ring polymer of a fixed knot type. Crystallized ring polymers contain not only crystal regions but also amorphous regions consisting of highly entangled chain configurations that could not be obtained simply by folding the polymer chains. In the crystallization process, the growth of a lamella region is accompanied by the reduction of a locally entangled region of the polymer chain. The model should effectively describe the separation and formation processes of amorphous and crystal regions in polymer crystallization. Here, the knot type of an initial configuration of the ring polymer is conserved in time evolution. We find that the average fraction of amorphous regions in the ring chain does not depend on the knot type or the chain length.     

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     

Strain stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model system to investigate the contribution of entanglements to strain stiffening. The chain packings are sheared in uniaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds the scale of the confining pressure, similar to granular packings of unconnected particles. In contrast, packings of chains which are long enough to form loops exhibit strain stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.     

Polymer dynamics in chaotic flows with a strong shear component

We consider the dynamics of a polymer molecule injected into a chaotic flow with a strong mean shear component. The polymer experiences aperiodic tumbling in such flows. We consider a simplified model of the chaotic velocity field given by the superposition of a steady shear flow and a large-scale isotropic short-correlated random component. In the framework of this model, we present a detailed study of the statistical properties of single-polymer dynamics. We obtain the stationary probability distribution function of the polymer orientation, find the distribution of time periods between consequent events of tumbling, and find the tails of the polymer size distribution. The text was submitted by the author in English.     

On the Mechanisms of Recrystallization After Melting in Semicrystalline Polymers: The Effect of the Initial Melt State

The mechanisms of recrystallization after melting during a heating scan of syndiotactic polypropylene (sPP) and isotactic polystyrene (iPS) were studied. This was done by monitoring the structure evolution during the recrystallization process and its changes during a subsequent heating scan via time- and temperature-dependent SAXS measurements, respectively. The results of this study showed that the sPP samples exhibited a recrystallization mechanism similar to the multistage route found upon initial crystallization of semicrystalline polymers from an entangled melt. Meanwhile, a different recrystallization mechanism was shown by the iPS samples. In this case, the recrystallization process proceeded as a direct growth into the melt in a one-step process. This is the first time we observed such a mechanism that resembles the picture presented by the classical models for crystallization from an entangled polymer melt. The reason for such different mechanisms may be related to the initial melt state prior to crystallization. It seems as though when crystallization sets in in an entangled polymer melt, it follows the multistage route, whereas if the melt is locally disentangled, it proceeds by a direct growth mechanism.     

Spatiotemporal dynamics of shear induced bands en route to rheochaos

We show experimentally that the route to rheochaos in shear rate relaxation measurements is via Type-III intermittency and mixed mode oscillations in the shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate in the presence of salt sodium chloride. Depolarised small angle light scattering measurements performed during flow show that scattered intensity temporally follows the shear rate/stress dynamics and portrays the crucial role played by nematic ordering. Direct visualization of the gap of the Couette cell, illuminated by an unpolarised laser sheet, in the (vorticity, velocity gradient) plane shows that the spatiotemporal dynamics of the shear induced structures is closely related to the temporal behaviour of shear rate/stress fluctuations.     

Shear-thickening transition in surfactant solutions: New experimental features from rheology and flow birefringence

We report on the shear-thickening transition observed in dilute aqueous solutions of cetyltrimethylammonium tosylate (CTAT) at concentrations . We have re-examined the kinetics of the shear-thickening transition using start-up experiments at rates above the critical shear rate . Using simple well-defined protocols, we have found that the transient mechanical response depends dramatically on the thermal and on the shear histories. Using the same protocols, flow birefringence experiments were carried out. The gap of a Couette cell containing the sheared solution has been visualized between crossed polarizers in steady shear conditions, as well as in start-up experiments. We show that the birefringent shear-induced phase starts from the inner cylinder and grows along the velocity gradient direction, as in a shear banding situation. However, around we have not observed a regime of phase coexistence (isotropic and birefringent). Received 11 November 1999