Brian M. Erwin

A sequence of physical processes determined and quantified in LAOS: Application to a yield stress fluid

Recently, large-amplitude oscillatory shear has been studied in great detail with emphasis on its impact on the material response. Here we present a conceptually different, robust methodology based on viewing the stress waveforms as representing a sequence of physical processes. This novel approach provides the viscous and elastic contributions while overcoming the problems with infinite series encountered by Fourier transformation. Application to a soft colloidal star glass leads to the unambiguous determination and quantification of rate-dependent static and dynamic yield stresses, the rationalization of the response to strain sweeps and the post-yield regime by introducing the apparent cage modulus, and a connection to the steady-shear stress, all from a single-amplitude experiment. We propose that this approach is generic, but focus in this contribution only on a yield stress material which exhibits repeating cycles of (i) elastic extension, (ii) yielding, (iii) flow, and (iv) reformation. We show tha...

Ageing and yield behaviour in model soft colloidal glasses

We use multi-arm star polymers as model soft colloids with tuneable interactions and explore their behaviour in the glassy state. In particular, we perform a systematic rheological study with a well-defined protocol and address aspects of ageing and shear melting of star glasses. Ageing proceeds in two distinct steps: a fast step of O(103 s) and a slow step of O(104 s). We focus on creep and recovery tests, which reveal a rich, albeit complex response. Although the waiting time, the time between pre-shear (rejuvenation) of the glassy sample and measurement, affects the material’s response, it does not play the same role as in other soft glasses. For stresses below the yield value, the creep curve is divided into three regimes with increasing time: viscoplastic, intermediate steady flow (associated with the first ageing step) and long-time evolving elastic solid. This behaviour reflects the interplay between ageing and shear rejuvenation. The yield behaviour, as investigated with the stress-dependent recoverable strain, indicates a highly nonlinear elastic response intermediate between a low-stress Hookean solid and a high-stress viscoelastic liquid, and exemplifies the distinct characteristics of this class of hairy colloids. It appears that a phenomenological classification of different colloidal glasses based on yielding performance may be possible.

Dynamics and rheology of colloidal star polymers

We attempt to elucidate the dynamics of multiarm star polymer solutions, which are representative of a large class of soft hairy colloids, over a wide range of concentrations. In addition to the usual β-relaxation (in-cage rattling) and α-relaxation (terminal cage escape), the relaxation of stars in the glassy state involves a mode associated with arm interpenetration. From linear and nonlinear rheological measurements, we establish a set of criteria for identifying the colloidal glass transition, including aging, yielding and elastic properties. Linear viscoelasticity and steady-shear measurements merge at low frequencies, indicating that terminal behavior is accessible, albeit at very long times. The transition from linear to nonlinear response is controlled by star elasticity and a balance between Brownian diffusion and flow advection. In the nonlinear regime, the flow curves collapse on a universal flow curve using a scaling that expresses a competition between solvent-mediated interactions and elastic forces. While applied to stars, our framework appears to be a generic tool for fingerprinting liquid-solid transitions in colloidal suspensions.

Rheological fingerprinting of an aging soft colloidal glass

We investigate the complex flow behavior of a well-characterized colloidal star glass using linear and nonlinear rheology. The results are integrated into a generic state diagram which specifies the states of the glass for different initial conditions and mechanical histories: viscoelastic liquid and solid, homogeneous shear-thinned solution, and shear-banded material. Aging takes different forms which can be interpreted as kinetic pathways through the state diagram. Shear-banding appears to be an intrinsic mechanical instability which occurs when the solid state of the glass is shear-melted. Our results provide a straightforward methodology to fingerprint the material behavior of soft glassy materials undergoing rheological transitions which can be used as predictive tool to design systems with a desired rheological response.

Oscillatory yielding of a colloidal star glass

We investigate the response of a well-characterized colloidal star glass to large-amplitude oscillatory stress and strain fields. By combining these measurements with dynamic time sweeps we demonstrate the importance of probing both strain- and stress-induced nonlinear rheology of such complex fluids in order to elucidate the yielding and fluidization behavior. We also show that, due to the strong time dependence, it is essential to perform dynamic time sweeps at different strain and stress amplitudes, which result in different departures of the glass cage from its quiescent quasiequilibrium structure. This allows for steady-state responses to be reached and for nonlinear oscillatory responses to be treated properly while also suggesting that yielding is a gradual process. Further, we use a recently published framework for analyzing nonlinear responses to large-amplitude oscillatory shear [Rogers et al., J. Rheol. 55, 435 (2011)], based on the analysis of the whole stress waveforms as a sequence of physic...

Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials

A strain-rate frequency superposition (SRFS) technique, recently proposed to analyze the low-frequency behavior of soft materials, is evaluated. The application of SRFS to an emulsion and multiarm star polymer solution produces master curves that, while promising in appearance, do not match the anticipated linear response as they seem inconsistent with dynamic frequency sweep data and the Kramers–Kronig relation. While the raw unscaled frequency sweep data are well described using the generalized Maxwell model, strong discrepancies appear when the same procedure is applied to SRFS data. These inconsistencies appear to be generic and are observed in other materials as well. An examination of Lissajous curves obtained from large amplitude oscillatory strain shows that nonlinear contributions, such as solvent-mediated convective flow, strongly affect SRFS master curves. Based on these findings, SRFS should be approached with caution when applied to soft materials.

Probing glassy states in binary mixtures of soft interpenetrable colloids

We present experimental evidence confirming the recently established rich dynamic state diagram of asymmetric binary mixtures of soft colloidal spheres. These mixtures consist of glassy suspensions of large star polymers to which different small stars are added at varying concentrations. Using rheology and dynamic light scattering measurements along with a simple phenomenological analysis, we show the existence of re-entrance and multiple glassy states, which exhibit distinct features. Cooperative diffusion, as a probe for star arm interpenetration, is proven to be sensitive to the formation of the liquid pockets which signal the melting of the large-star-glass upon addition of small stars. These results provide ample opportunities for tailoring the properties of soft colloidal glasses.

MBIR characterization of Photosensitive Polyimide in high volume manufacturing

Using model-based infrared reflectometry (MBIR) technique [1] we have developed a method for in-line process monitoring of polyimide passivation films to support the fabrication of fine pitch flip chip devices. A permanent passivation layer is incorporated in semiconductor wafers before the addition of solder in flip chip interconnects to protect sensitive on-chip components from chip-package interconnection (CPI) stresses, the egress of moisture and chemicals, while providing dielectric isolation. Photosensitive Polyimide (PSPI) [2] is often selected for this application because of its well established track record coupled with thermal and chemical stability, and mechanical strength. With the advent of 3-D integration technologies, new attention has been focused on creating options for reducing controlled collapse chip connection (C4) pitch and solder volumes, a change which causes co-planarity of the interconnect and the passivation layer which supports it to play an increasingly important role. An accurate in-line characterization method is needed to monitor and reduce variability in polyimide passivation layer thickness. We have developed an in-line metrology process utilizing MBIR tools which provide valuable wafer level thickness characterization of PSPI films on bare and processed 300 mm Si wafers.