Small-Angle Neutron Scattering Study of the Structural Relaxation of Elongationally Oriented, Moderately Stretched Three-Arm Star Polymers.

We present structural relaxation studies of a polystyrene star polymer after cessation of high-rate extensional flow. During the steady-state flow, the scattering pattern shows two sets of independent correlations peaks, reflecting the structure of a polymer confined in a fully oriented three-armed tube. Upon cessation of flow, the relaxation constitutes three distinct regimes. In a first regime, the perpendicular correlation peaks disappear, signifying disruption of the virtual tube. In a second regime, broad scattering arcs emerge, reflecting relaxation from highly aligned chains to more relaxed, still anisotropic form. New entanglements dominate the last relaxation regime where the scattering pattern evolves to a successively elliptical and circular pattern, reflecting relaxation via reptation.

Threading-Unthreading Transition of Linear-Ring Polymer Blends in Extensional Flow.

Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown to be driven by a transient threading-unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.

Structural Studies of Three-Arm Star Block Copolymers Exposed to Extreme Stretch Suggests a Persistent Polymer Tube.

We present structural small-angle neutron scattering studies of a three-armed polystyrene star polymer with short deuterated segments at the end of each arm. We show that the form factor of the three-armed star molecules in the relaxed state agrees with that of the random phase approximation of Gaussian chains. Upon exposure to large extensional flow conditions, the star polymers change conformation resulting in a highly stretched structure that mimics a fully extended three-armed tube model. All three arms are parallel to the flow, one arm being either in positive or negative stretching direction, while the two other arms are oriented parallel, right next to each other in the direction opposite to the first arm.

Highly Anisotropic Glassy Polystyrenes Are Flexible.

We show that stretching polystyrene melts at a rate faster than the inverse Rouse time, followed by rapid quenching below the glass transition temperature, results in a material that is flexible and remains so for at least six months. Oriented micro/nanofibers are observed in the flexible samples after the mechanical tests. The fibers are probably related to the highly aligned molecules in melt stretching. At room temperature, a tensile strength over 300 MPa has been achieved for the flexible polystyrenes.

Polymer liquids fracture like solids.

While fracture in brittle solids has been studied for centuries until today, there are few studies on fracture in polymer liquids. Recent developments in experimental techniques, especially the combination of controlled filament stretching rheometry and high speed imaging, have opened new windows into the detailed study of fracture processes for polymer liquids. High speed imaging shows that polymer liquids fracture like solids with initiation and propagation of an edge fracture. However, remarkable features such as highly reproducible critical stress, independent appearance of multiple fractures, and trumpet crack profiles, reveal mechanisms which are significantly different from solids.

Rheological Link Between Polymer Melts with a High Molecular Weight Tail and Enhanced Formation of Shish-Kebabs.

Presence of an ultra high molecular weight (UHMw) fraction in flowing polymer melts is known to facilitate formation of oriented crystalline structures significantly. The UHMw fraction manifests itself as a minor tail in the molar mass distribution and is hardly detectable in the canonical characterization methods. In this study, alternatively, we demonstrate how the nonlinear extensional rheology reveals to be a very sensitive characterization tool for investigating the effect of the UHMw-tail on the structural ordering mechanism. Samples containing a UHMw-tail relative to samples without, exhibit a clear increase in extensional stress that is directly correlated with the crystalline orientation of the quenched samples. Extensional rheology, particularly, in combination with linear creep measurements, thus, enables the conformational evolution of the UHMw-tail to be studied and linked to the enhanced formation of oriented structures.

Nematic effects and strain coupling in entangled polymer melts under strong flow.

We use small-angle neutron scattering (SANS) to study labeled short chains with and without the influence of an entangled and highly stretched surrounding environment of longer chains. We find unequivocal evidence of nematic effects as the blend chains in steady state flow are stretched a factor ∼1.5 more from the presence of the long chain nematic field. In the pure melt we confirm that the nonaffine mean-field result ν=0.5 for the strain coupling is still valid for very fast flows, while in the nematic system our analysis predicts an increased coupling constant. We provide a structural explanation for the two first regimes of the nonlinear relaxation, particularly a transition regime where the long chains are relaxing in a sea of reptating short chains.

Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension.

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation.

Brittle fracture in associative polymers: the case of ionomer melts.

Ionomers are interesting due to their applications in coatings, adhesives, films and packaging materials. A study of the underlying mechanisms for fracture in ionomers is consequently of both practical as well as theoretical interest. In this study, we employ high speed imaging coupled with uniaxial extensional rheometry to delineate the mechanics leading to the brittle fracture of ionomer melts. When these ionomers are elongated at a rate higher than the inverse relaxation time of physical crosslinks, an edge fracture occurs at a critical stress. Parabolic fracture profiles provide evidence that the phenomenon is purely elastic and bulk dissipation has little impact on the crack profile. Experimental results are interpreted within the Griffiths theory for linear elastic materials and the de Gennes theory for viscoelastic materials.

Linear and Nonlinear Universality in the Rheology of Polymer Melts and Solutions.

Understanding the dynamics of polymeric liquids has great importance in the design and processing of soft materials. While slow flow dynamics is now resolved, fast flow dynamics is still unsolved, especially due to the lack of experimental evidence. We here manipulate a poly(methyl methacrylate) solution into exhibiting the same flow behavior as a polystyrene melt. Strikingly similar responses of the fluids are seen both in slow and very fast flow. With this discovery we show that dynamics in polymeric liquids can be generalized and captured in one single polymer physics model.

Creep measurements confirm steady flow after stress maximum in extension of branched polymer melts.

We provide conclusive evidence of nonmonotonic mechanical behavior in the extension of long-chain branched polymer melts. While nonmonotonic behavior is known to occur for solids, for the case of polymeric melts, this phenomenon is in direct contrast with current theoretical models. We rule out the possibility of the overshoot being an experimental artifact by confirming the existence of steady flow after a maximum in the ratio of stress to strain rate versus strain under both constant stress and constant strain-rate kinematics. This observation indicates the omission of important physics from current models for these industrially important materials, whose processing properties depend on extreme molecular extension.

The chromatographic separation of particles using optical electric fields.

We introduce a new field-flow fractionation (FFF) technique, whereby molecules are separated based on their differential interaction (dielectrophoresis (DEP)) with optical electric fields, i.e. electric fields with frequencies in the visible and near-infrared range. The results show that a parallel array of axially non-uniform optical fields yielding an attractive potential (positive-DEP-FFF) is advantageous for the separation of polymers, biomolecules, and nanoparticles over very short distances. Furthermore, positive-DEP-FFF yields superior selectivity and resolution compared to conventional separation techniques, which do not lend themselves to miniaturization. A wide range of parameters are considered and the results are presented considering traditional chromatography parameters: the retention ratio and resolution. A simple analytical model is introduced which captures the trends for small normalized decay lengths and will be useful in the design of experimental separation platforms.

Extensional Rheology of Entangled Polystyrene Solutions Suggests Importance of Nematic Interactions.

We compare the linear and nonlinear rheological response of three entangled polystyrene solutions with the same concentration of polymer, but diluted using different solvents. The three solutions have exactly the same physical tube model parameters when normalized to the same time scale. Although the three solutions behave identically in small amplitude oscillatory shear flow, they behave markedly different in large strain extensional flow. The experimental observations presented here directly demonstrate that the tube model and its governing parameters are insufficient to describe the nonlinear rheological behavior of entangled polymer solutions. We introduce a new hypothesis that relates the observed nonlinear behavior of three different polymer solutions to the existence of nematic interactions between polymer-solvent and polymer-polymer molecules.

Transient convection, diffusion, and adsorption in surface-based biosensors.

This paper presents a theoretical and computational investigation of convection, diffusion, and adsorption in surface-based biosensors. In particular, we study the transport dynamics in a model geometry of a surface plasmon resonance (SPR) sensor. The work, however, is equally relevant for other microfluidic surface-based biosensors, operating under flow conditions. A widely adopted approximate quasi-steady theory to capture convective and diffusive mass transport is reviewed, and an analytical solution is presented. An expression of the Damköhler number is derived in terms of the nondimensional adsorption coefficient (Biot number), the nondimensional flow rate (Péclet number), and the model geometry. Transient dynamics is investigated, and we quantify the error of using the quasi-steady-state assumption for experimental data fitting in both kinetically limited and convection-diffusion-limited regimes for irreversible adsorption, in specific. The results clarify the conditions under which the quasi-steady theory is reliable or not. In extension to the well-known fact that the range of validity is altered under convection-diffusion-limited conditions, we show how also the ratio of the inlet concentration to the maximum surface capacity is critical for reliable use of the quasi-steady theory. Finally, our results provide users of surface-based biosensors with a tool for correcting experimentally obtained adsorption rate constants.

A new approach to heart valve tissue engineering: mimicking the heart ventricle with a ventricular assist device in a novel bioreactor.

The 'biomimetic' approach to tissue engineering usually involves the use of a bioreactor mimicking physiological parameters whilst supplying nutrients to the developing tissue. Here we present a new heart valve bioreactor, having as its centrepiece a ventricular assist device (VAD), which exposes the cell-scaffold constructs to a wider array of mechanical forces. The pump of the VAD has two chambers: a blood and a pneumatic chamber, separated by an elastic membrane. Pulsatile air-pressure is generated by a piston-type actuator and delivered to the pneumatic chamber, ejecting the fluid in the blood chamber. Subsequently, applied vacuum to the pneumatic chamber causes the blood chamber to fill. A mechanical heart valve was placed in the VAD's inflow position. The tissue engineered (TE) valve was placed in the outflow position. The VAD was coupled in series with a Windkessel compliance chamber, variable throttle and reservoir, connected by silicone tubings. The reservoir sat on an elevated platform, allowing adjustment of ventricular preload between 0 and 11 mmHg. To allow for sterile gaseous exchange between the circuit interior and exterior, a 0.2 µm filter was placed at the reservoir. Pressure and flow were registered downstream of the TE valve. The circuit was filled with culture medium and fitted in a standard 5% CO(2) incubator set at 37 °C. Pressure and flow waveforms were similar to those obtained under physiological conditions for the pulmonary circulation. The 'cardiomimetic' approach presented here represents a new perspective to conventional biomimetic approaches in TE, with potential advantages.

Simulation of elastic rupture in extension of entangled monodisperse polymer melts.

We use a Lagrangian finite element method to simulate experiments on continued and interrupted extensions of a highly entangled monodisperse polymer melt. It is demonstrated that delayed sample necking or rupture may be explained in terms of the original Doi-Edwards model augmented by the mechanism of chain stretching alone.

3D Simulation of Nano-Imprint Lithography.

A proof of concept study of the feasibility of fully three-dimensional (3D) time-dependent simulation of nano-imprint lithography of polymer melt, where the polymer is treated as a structured liquid, has been presented. Considering the flow physics of the polymer as a structured liquid, we have followed the line initiated by de Gennes, using a Molecular Stress Function model of the Doi and Edwards type. We have used a 3D Lagrangian Galerkin finite element methods implemented on a parallel computer architecture. In a Lagrangian techniques, the node point follows the particle movement, allowing for the movement of free surfaces or interfaces. We have extended the method to handle the dynamic movement of the contact line between the polymer melt and stamp during mold filling.

Proof of the identity between the depletion layer thickness and half the average span for an arbitrary polymer chain.

The confinement analysis from bulk structure (CABS) approach [Y. Wang et al., J. Chem. Phys. 128, 124904 (2008)] is extended to determine the depletion profiles of dilute polymer solutions confined to a slit or near an inert wall. We show that the entire spatial density distributions of any reference point in the polymer chain (such as the center of mass, middle segment, and end segments) can be computed as a function of the confinement size solely based on a single sampling of the configuration space of a polymer chain in bulk. Through a simple analysis based on the CABS approach in the case of a single wall, we prove rigorously that (i) the depletion layer thickness delta is the same no matter which reference point is used to describe the depletion profile and (ii) the value of delta equals half the average span (the mean projection onto a line) of the macromolecule in free solution. Both results hold not only for ideal polymers, as has been noticed before, but also for polymers regardless of details in molecular architecture and configuration statistics.

Equilibrium partitioning of macromolecules in confining geometries: improved universality with a new molecular size parameter.

We present a new framework for the description of macromolecules subject to confining geometries. The two main ingredients are a new computational method and the definition of a new molecular size parameter. The computational method, hereafter referred to the confinement analysis from bulk structures (CABS), allows the computation of equilibrium partition coefficients as a function of confinement size solely based on a single sampling of the configuration space of a macromolecule in bulk. Superior in computational speed to previous computational methods, CABS is capable of handling slits, channels, and box confining geometries for all molecular architectures. The new molecular size parameter, hereafter referred to the steric exclusion radius R(s), is explicitly defined and computed for a number of rigid objects and flexible polymers. We suggest that R(s) is the relevant molecular size parameter for characterization of spatial confinement effects on macromolecules. Results for the equilibrium partition coefficient in the weak confinement regime depend only on the ratio of R(s) to the confinement size regardless of molecular details.

Constitutive equation for polymer networks with phonon fluctuations.

Recent research by Xing [Phys. Rev. Lett. 98, 075502 (2007)] has provided an expression for the Helmholtz free energy related to phonon fluctuations in polymer networks. We extend this result by constructing the corresponding nonlinear constitutive equation, usable for entirely general, volume conserving deformation fields. Constitutive equations for the sliplink model and the tube model are derived and the three models are examined by comparison with each other and with data from Xu and Mark [Rubber Chem. Technol. 63, 276 (1990)] and Wang and Mark [J. Polym. Sci., Part B: Polym. Phys. 30, 801 (1992)]. Elastic moduli are derived for the three models and compared with the moduli determined from the chemical stoichiometry. We conclude that the sliplink model and the phonon fluctuation model are relatively consistent with each other and with the data. The tube model seems consistent neither with the other models nor with the data.