Aaron P. R. Eberle

Dynamical Arrest, Percolation, Gelation, and Glass Formation in Model Nanoparticle Dispersions with Thermoreversible Adhesive Interactions

We report an experimental study of the dynamical arrest transition for a model system consisting of octadecyl coated silica suspended in n-tetradecane from dilute to concentrated conditions spanning the state diagram. The dispersions interparticle potential is tuned by temperature affecting the brush conformation leading to a thermoreversible model system. The critical temperature for dynamical arrest, T*, is determined as a function of dispersion volume fraction by small-amplitude dynamic oscillatory shear rheology. We corroborate this transition temperature by measuring a power-law decay of the autocorrelation function and a loss of ergodicity via fiber-optic quasi-elastic light scattering. The structure at T* is measured using small-angle neutron scattering. The scattering intensity is fit to extract the interparticle pair-potential using the Ornstein-Zernike equation with the Percus-Yevick closure approximation, assuming a square-well interaction potential with a short-range interaction (1% of particle diameter). (1) The strength of attraction is characterized using the Baxter temperature (2) and mapped onto the adhesive hard sphere state diagram. The experiments show a continuous dynamical arrest transition line that follows the predicted dynamical percolation line until ϕ ≈ 0.41 where it subtends the predictions toward the mode coupling theory attractive-driven glass line. An alternative analysis of the phase transition through the reduced second virial coefficient B(2)* shows a change in the functional dependence of B(2)* on particle concentration around ϕ ≈ 0.36. We propose this signifies the location of a gel-to-glass transition. The results presented herein differ from those observed for depletion flocculated dispersion of micrometer-sized particles in polymer solutions, where dynamical arrest is a consequence of multicomponent phase separation, suggesting dynamical arrest is sensitive to the physical mechanism of attraction.

The microstructure and rheology of a model, thixotropic nanoparticle gel under steady shear and large amplitude oscillatory shear (LAOS)

The microstructure-rheology relationship for a model, thermoreversible nanoparticle gel is investigated using a new technique of time-resolved neutron scattering under steady and time-resolved large amplitude oscillatory shear (LAOS) flows. A 21 vol. % gel is tested with varying strength of interparticle attraction. Shear-induced structural anisotropy is observed as butterfly scattering patterns and quantified through an alignment factor. Measurements in the plane of flow show significant, local anisotropy develops with alignment along the compressional axis of flow, providing new insights into how gels flow. The microstructure-rheology relationship is analyzed through a new type of structure-Lissajous plot that shows how the anisotropic microstructure is responsible for the observed LAOS response, which is beyond a response expected for a purely viscous gel with constant structure. The LAOS shear viscosities are observed to follow the “Delaware-Rutgers” rule. Rheological and microstructural data are successfully compared across a broad range of conditions by scaling the shear rate by the strength of attraction, providing a method to compare behavior between steady shear and LAOS experiments. However, important differences remain between the microstructures measured at comparatively high frequency in LAOS experiments and comparable steady shear experiments that illustrate the importance of measuring the microstructure to properly interpret the nonlinear, dynamic rheological response.The microstructure-rheology relationship for a model, thermoreversible nanoparticle gel is investigated using a new technique of time-resolved neutron scattering under steady and time-resolved large amplitude oscillatory shear (LAOS) flows. A 21 vol. % gel is tested with varying strength of interparticle attraction. Shear-induced structural anisotropy is observed as butterfly scattering patterns and quantified through an alignment factor. Measurements in the plane of flow show significant, local anisotropy develops with alignment along the compressional axis of flow, providing new insights into how gels flow. The microstructure-rheology relationship is analyzed through a new type of structure-Lissajous plot that shows how the anisotropic microstructure is responsible for the observed LAOS response, which is beyond a response expected for a purely viscous gel with constant structure. The LAOS shear viscosities are observed to follow the “Delaware-Rutgers” rule. Rheological and microstructural data are succ...

Using transient shear rheology to determine material parameters in fiber suspension theory

Fiber suspension theory model parameters for use in the simulation of fiber orientation in complex flows are, in general, either calculated from theory or fit to experimentally determined fiber orientation generated in processing flows. Transient stress growth measurements in startup of shear flow and flow reversal in the shear rate range, γ=1–10 s−1, were performed on a commercially available short glass fiber-filled polybutylene terephthalate using a novel “donut-shaped” sample in a cone-and-plate geometry. Predictions using the Folgar–Tucker model for fiber orientation, with a “slip” factor, combined with the Lipscomb model for stress were fit to the transient stresses at the startup of shear flow. Model parameters determined by fitting at γ=6 s−1 allowed for reasonable predictions of the transient stresses in flow reversal experiments at all the shear rates tested. Furthermore, fiber orientation model parameters determined by fitting the transient stresses were compared to the experimentally determi...

Obtaining reliable transient rheological data on concentrated short fiber suspensions using a rotational rheometer

The conventional method for obtaining transient rheological data on short glass fiber-filled polymeric fluids is to use the parallel disk (PP) geometry in a rotational rheometer. Using the PP geometry large transient stress overshoot behavior was observed during the startup of flow measurements on a 30 wt % short glass fiber-filled polybutylene terephthalate. A contributing factor to this behavior is believed to be induced fiber collisions caused by the inhomogeneous velocity field (radial varying velocity gradient). A novel approach was taken in which a “donut” shaped sample was used in a cone-and-plate device (CP-D) to maintain a sufficient gap to fiber length ratio. The magnitude of the first normal stress difference was reduced by 70%, and the time to reach steady state was reduced by 100 strain units. The Lipscomb model coupled with the Folgar–Tucker model for the evolution of fiber orientation was fit to the stress growth behavior measured using both the PP geometry and CP-D resulting in different p...

Linear rheology and structure of molecular bottlebrushes with short side chains

We investigate the microstructure and linear viscoelasticity of model molecular bottlebrushes (BBs) using rheological and small-angle X-ray and neutron scattering measurements. Our polymers have short atactic polypropylene (aPP) side chains of molecular weight ranging from 119 g/mol to 259 g/mol and narrow molecular weight distribution (Mw/Mn 1.02–1.05). The side chain molecular weights are a small fraction of the entanglement molecular weight of the corresponding linear polymer ( Me,aPP= 7.05 kg/mol), and as such, they are unentangled. The morphology of the aPP BBs is characterized as semiflexible thick chains with small side chain interdigitation. Their dynamic master curves, obtained by time-temperature superposition, reveal two sequential relaxation processes corresponding to the segmental relaxation and the relaxation of the BB backbone. Due to the short length of the side chains, their fast relaxation could not be distinguished from the glassy relaxation. The fractional free volume is an increasing ...

Temperature-dependent nanostructure of an end-tethered octadecane brush in tetradecane and nanoparticle phase behavior.

The phase behavior of a molecular brush-C(18) grafted to the surface of both a silicon wafer and SiO(2) nanoparticles was investigated as a function of temperature using neutron reflectometry (NR) and small-angle neutron scattering (SANS), respectively. The experiments demonstrate a phase change in the brush layer characterized by a straightening of the molecular configuration, increase in shell thickness, and increase in solvent concentration with decreasing temperature that corresponds to gelation in the nanoparticle dispersion.

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is presented. The SANS shear cell consists of a concentric cylinder Couette geometry that is sealed and rotating about a horizontal axis so that the vorticity direction of the flow field is aligned with the neutron beam enabling scattering from the 1-2 plane of shear (velocity-velocity gradient, respectively). This approach is an advance over previous shear cell sample environments as there is a strong coupling between the bulk rheology and microstructural features in the 1-2 plane of shear. Flow-instabilities, such as shear banding, can also be studied by spatially resolved measurements. This is accomplished in this sample environment by using a narrow aperture for the neutron beam and scanning along the velocity gradient direction. Time resolved experiments, such as flow start-ups and large amplitude oscillatory shear flow are also possible by synchronization of the shear motion and time-resolved detection of scattered neutrons. Representative results using the methods outlined here demonstrate the useful nature of spatial resolution for measuring the microstructure of a wormlike micelle solution that exhibits shear banding, a phenomenon that can only be investigated by resolving the structure along the velocity gradient direction. Finally, potential improvements to the current design are discussed along with suggestions for supplementary experiments as motivation for future experiments on a broad range of complex fluids in a variety of shear motions.

Viscoelastic coalescence of thermotropic liquid crystalline polymers: The role of transient rheology

The coalescence in air of two polymeric drops into a single drop (also referred to as sintering) was investigated for two thermotropic liquid crystalline polymers. Initial coalescence via elastic contact was ruled out based on the magnitude of the equilibrium compliance values and the process was, therefore, believed to be driven by surface tension and resisted by means of viscous flow. Remarkably the viscous coalescence model developed for Newtonian fluids (an extension of the Frenkel and Eshelby approach) agreed well under some conditions of temperature with coalescence data (i.e., observation of neck growth under a microscope). On the other hand, the extension of the Newtonian model to the viscoelastic case by incorporating the upper convected Maxwell model (UCM) assuming steady state stresses always underpredicted the rate of coalescence. The viscous neck growth model using the UCM constitutive equation was extended to the transient stress case in order to incorporate the slow growth of viscosity at t...

The Dynamic Behavior of a Concentrated Non-Brownian Glass Fiber Suspension in Simple Shear Flow

The dynamic behavior of a concentrated short glass fiber suspension subject to simple shear flow is investigated. In particular we are interested in determining the relationship between the stress growth functions (shear and first normal stress difference) and the fiber microstructure within the sample. Stress growth experiments, in start up of flow, are performed on a Rheometrics Mechanical Spectrometer (RMS‐800) using a novel approach which deforms the sample in a homogeneous shear field. The 3D fiber orientation is characterized using confocal laser microscopy and experimental results are compared to predictions based on the generalized Jeffery equation. It is found that the theory over predicts the rate at which the fiber orientation evolves.

Simulation of Orientation in Injection Molding of High Aspect Ratio Particle Thermoplastic Composites

A 2D coupled Hele‐Shaw flow approximation for predicting the flow‐induced orientation of high aspect ratio particles in injection molded composite parts is presented. For a highly concentrated short glass fiber PBT suspension, the impact of inter‐particle interactions and the orientation at the gate is investigated for a center‐gated disk using material parameters determined from rheometry. Experimental orientation is determined from confocal laser micrographs using the methods of ellipses. The constitutive equations are discretized using discontinuous Galerkin Finite Elements. Model predictions are significantly improved by using a localized orientation measured experimentally at the gate region instead of random or averaged gapwise measured orientation assumed in previous studies. The predicted profile in different radial positions can be related to the layered structure along the gapwise direction. Model modifications including interactions have lower impact than the initial conditions.