Gerrit W. M. Peters

Mechanically induced chemiluminescence from polymers incorporating a 1,2-dioxetane unit in the main chain

Nature uses mechanochemical transduction processes to achieve diverse and vital functions, such as hearing, cellular adhesion and gating of ion channels. One fascinating example of biological mechanotransduction is the emission of light on mechanical stimulation. However, molecular-level transduction of force into luminescence in a synthetic system remains a challenge. Here, we show that bis(adamantyl)-1,2-dioxetane emits visible light when force is applied to a polymer chain or network in which this unit is incorporated. Bright-blue luminescence was observed on sonication of solutions of dioxetane-containing linear polymers and on the straining of polymer networks with dioxetane crosslinkers. Light is emitted from the adamantanone-excited state that forms on opening of the four-membered dioxetane ring. Increased sensitivity and colour tuning were achieved by energy transfer to suitable acceptors. High spatial and temporal resolutions highlight the potential to study the failure of polymeric materials in unprecedented detail.

Differential constitutive equations for polymer melts: The extended Pom-Pom model

The Pom‐Pom model, recently introduced by McLeish and Larson @J. Rheol. 42, 81‐110~1998!#, is a breakthrough in the field of viscoelastic constitutive equations. With this model, a correct nonlinear behavior in both elongation and shear is accomplished. The original differential equations, improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified extended Pom‐Pom model does not show the three problems and is easy for implementation in finite element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxial, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial low density polyethylene ~LDPE! melts and one high density polyethylene ~HDPE! melt. Such a good agreement over a full range of well defined rheometric experiments, i.e., shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional.

Viscoelastic flow past a confined cylinder of a low-density polyethylene melt

The capabilities of the exponential version of the Phan-Thien-Tanner (PTT) model and the Giesekus model to predict stress fields for the viscoelastic flow of a low density polyethylene melt around a confined cylinder are investigated. Computations are based on a newly developed version of the discontinuous Galerkin method. This method gives convergent results up to a Deborah number of 2.5 for the falling sphere in a tube benchmark problem. Moreover, the specific implicit-explicit implementation allows the efficient resolution of problems with multiple relaxation times which are mandatory for polymer melts. Experimentally, stress fields are related to birefringence distributions by means of the stress optical rule. Three different fits, of equal quality, to available viscometric shear data are used: two for the PTT model and one for the Giesekus model. Comparison of computed and measured fringes reveals that neither of the models is capable of describing the full birefringence pattern sufficiently well. In particular it appears difficult to predict both the birefringent tail at the wake of the cylinder that is dominated by elongational effects and the fringe pattern between cylinder and the walls where a combined shear-elongational flow is present.

Modelling of non-isothermal viscoelastic flows

The modelling of non-isothermal flow of viscoelastic materials using differential constitutive equations is investigated. The approach is based on the concept of a slip tensor describing the nonaffine motion of the stress-carrying structure of the fluid. By specifying a slip tensor and the elastic behaviour of the structure, the constitutive model is determined. This slip tensor also appears in the energy equation and thus, for a given constitutive model, the form of the energy equation is known. Besides the partitioning between dissipated and elastically stored energy, also the difference between entropy and energy elasticity is discussed. Numerical simulations are based on a stabilized Discontinuous Galerkin method to solve the mass, momentum and constitutive equations and a Streamline Upwind Petrov-Galerkin formulation to solve the energy equation. Coupling is achieved by a fixed point iteration. The flow around a confined cylinder is investigated, showing differences between viscous and viscoelastic modelling, and between limiting cases of viscoelastic modelling.

In vitro indentation to determine the mechanical properties of epidermis

The lack of understanding of the mechanical behavior of the human skin layers makes the development of drug delivery using microneedles or microjets a challenging task. In particular, the key mechanical properties of the epidermis composed of stratum corneum and viable epidermis should be better understood. Micro-indentation experiments were applied, using a spherical tip with a large diameter to the sample thickness ratio. The Youngs moduli were derived via an analytical and a numerical method. The tests showed that the analytical method was not appropriate to assess the Youngs moduli. That is why a numerical model was used to obtain the correct stiffness. When loaded perpendicularly, the stiffness of both the epidermis and stratum corneum vary between 1 and 2MPa. No significant differences in stiffness between the stratum corneum and viable epidermis were observed.

Viscoelastic analysis of complex polymer melt flows using the eXtended Pom-Pom model

Abstract The ability of the multi-mode eXtended Pom–Pom model to predict inhomogeneous flows of a polyethylene melt is investigated. Two benchmark problems are examined: the confined flow around a cylinder, and the flow through a cross-slot device. Numerical results for the eXtended Pom–Pom model are compared to experimental data, and predictions of the Giesekus and exponential Phan-Thien Tanner (PTT-a) models. Characteristic features observed experimentally in the benchmark flows are described well by all three models. The eXtended Pom–Pom model performs most satisfactorily, both with respect to the rheological data and the inhomogeneous flow data.

Stability analysis of polymer shear flows using the extended Pom-Pom constitutive equations

Abstract The stability of polymer melt shear flows is explored using the recently proposed eXtended Pom–Pom (XPP) model of Verbeeten et al. [J. Rheol. 45 (2001) 823]. We show that both the planar Couette and the planar Poiseuille flow are stable for ‘small’ disturbances. From our one-dimensional eigenvalue analysis and two-dimensional finite element calculations, excellent agreement is obtained with respect to the rate of slowest decay. For a single mode of the XPP model, the maximum growth of a perturbation is fully controlled by the rightmost part of the continuous eigenspectrum. We show that the local fourth order ordinary differential equation has three regular singular points that appear in the eigenspectrum of the Couette flow. Two of these spectra are branch cuts and discrete modes move in and out of these continuous spectra as the streamwise wavelength is varied. An important issue that is addressed is the error that is contained in the rightmost set of continuous modes. We observe that the XPP model behaves much better as compared to, for example, the Upper Convected Maxwell (UCM) model in terms of approximating the eigenvalues associated with the singular eigenfunctions. We demonstrate that this feature is extended to the two-dimensional computations of a periodic channel which means that the requirements on the spatial grid are much less restrictive, resulting in the possibility to use multi-mode simulations to perform realistic stability analysis of polymer melts. Also, it is shown that inclusion of a nonzero second normal stress difference has a strong stabilizing effect on the linear stability of both planar shear flows.

Polymer crystallization studies under processing-relevant conditions at the SAXS/WAXS DUBBLE beamline at the ESRF

Recent developments on the experimental infrastructure and the acquisition of new detectors on the Dutch–Belgian beamline BM26B at the ESRF offer novel and promising possibilities for synchrotron X-ray experiments in the field of polymer crystallization under processing-relevant conditions. In this contribution, some of the most recent experiments mimicking conditions similar to those relevant for the plastics processing industry are discussed. Simultaneous thermal analysis and wide-angle X-ray scattering (WAXS) experiments, at the millisecond time-frame level, on β-nucleated isotactic polypropylene (i-PP) samples subjected to ballistic cooling up to 230 K s−1, show that the efficiency of the nucleating agent can be suppressed when quenched cooling rates higher than 130 K s−1 are used. In situ WAXS experiments using small-scale industrial equipment during a real film blowing process reveal the dependence of the onset of crystallinity (the so-called freeze line) and the crystal orientation as a function of different take-up and blow-up ratios. In situ small-angle X-ray scattering (SAXS) experiments during high-flow fields reveal the formation of shish and kebab structures in i-PP as a function of the imposed stress. Quantitative analysis of i-PP flow-induced structures is presented. The beamline specifications required to obtain high quality and industrially relevant results are also briefly reported

On the performance of enhanced constitutive models for polymer melts in a cross-slot flow

Abstract A new class of viscoelastic constitutive equations is proposed that provides enhanced control of shear and elongational properties. Together with the widely used Giesekus and Phan-Thien Tanner model, these enhanced models are evaluated for a polymer melt (LDPE) in a cross-slot flow. This stagnation flow has a strong planar elongational deformation component. The material is characterized, in both viscometric simple shear flow and in uniaxial elongation. Velocities are measured with particle tracking velocimetry while field-wise flow-induced birefringence is used for correlation with stresses. The experimental results are compared with 2D viscoelastic simulations. With equal quality of describing viscometric data, the enhanced models can predict the flow properties of the cross-slot flow significantly better than the well known PTT and Giesekus model.

An adaptive front tracking technique for three-dimensional transient flows

An adaptive technique, based on both surface stretching and surface curvature analysis for tracking strongly deforming fluid volumes in three-dimensional flows is presented. The efficiency and accuracy of the technique are demonstrated for two- and three-dimensional flow simulations. For the two-dimensional test example, the results are compared with results obtained using a different tracking approach based on the advection of a passive scalar. Although for both techniques roughly the same structures are found, the resolution for the front tracking technique is much higher. In the three-dimensional test example, a spherical blob is tracked in a chaotic mixing flow. For this problem, the accuracy of the adaptive tracking is demonstrated by the volume conservation for the advected blob. Adaptive front tracking is suitable for simulation of the initial stages of fluid mixing, where the interfacial area can grow exponentially with time. The efficiency of the algorithm significantly benefits from parallelization of the code