I-Kuan Lin

Viscoelastic Characterization and Modeling of Polymer Transducers for Biological Applications

Polydimethylsiloxane (PDMS) is an important polymeric material widely used in bio-MEMS devices such as micropillar arrays for cellular mechanical force measurements. The accuracy of such a measurement relies on choosing an appropriate material constitutive model for converting the measured structural deformations into corresponding reaction forces. However, although PDMS is a well-known viscoelastic material, many researchers in the past have treated it as a linear elastic material, which could result in errors of cellular traction force interpretation. In this paper, the mechanical properties of PDMS were characterized by using uniaxial compression, dynamic mechanical analysis, and nanoindentation tests, as well as finite element analysis (FEA). A generalized Maxwell model with the use of two exponential terms was used to emulate the mechanical behavior of PDMS at room temperature. After we found the viscoelastic constitutive law of PDMS, we used it to develop a more accurate model for converting deflection data to cellular traction forces. Moreover, in situ cellular traction force evolutions of cardiac myocytes were demonstrated by using this new conversion model. The results presented by this paper are believed to be useful for biologists who are interpreting similar physiological processes.

Viscoelastic mechanical behavior of soft microcantilever-based force sensors

Polydimethylsiloxane (PDMS) microcantilevers have been used as force sensors for studying cellular mechanics by converting their displacements to cellular mechanical forces. However, PDMS is an inherently viscoelastic material and its elastic modulus changes with loading rates and elapsed time. Therefore, the traditional approach to calculating cellular mechanical forces based on elastic mechanics can result in errors. This letter reports a more in-depth method for viscoelastic characterization, modeling, and analysis associated with the bending behavior of the PDMS microcantilevers. A viscoelastic force conversion model was developed and validated by proof-of-principle bending tests.

Extension of the beam theory for polymer bio-transducers with low aspect ratios and viscoelastic characteristics

Polydimethylsiloxane (PDMS)-based micropillars (or microcantilevers) have been used as bio-transducers for measuring cellular forces on the order of pN to µN. The measurement accuracy of these sensitive devices depends on appropriate modeling to convert the micropillar deformations into the corresponding reaction forces. The traditional approach to calculating the reaction force is based on the Euler beam theory with consideration of a linear elastic slender beam for the micropillar. However, the low aspect ratio in geometry of PDMS micropillars does not satisfy the slender beam requirement. Consequently, the Timoshenko beam theory, appropriate for a beam with a low aspect ratio, should be used. In addition, the inherently time-dependent behavior in PDMS has to be considered for accurate force conversion. In this paper, the Timoshenko beam theory, along with the consideration of viscoelastic behavior of PDMS, was used to model the mechanical response of micropillars. The viscoelastic behavior of PDMS was characterized by stress relaxation nanoindentation using a circular flat punch. A correction procedure was developed to determine the load–displacement relationship with consideration of ramp loading. The relaxation function was extracted and described by a generalized Maxwell model. The bending of rectangular micropillars was performed by a wedge indenter tip. The viscoelastic Timoshenko beam formula was used to calculate the mechanical response of the micropillar, and the results were compared with measurement data. The calculated reaction forces agreed well with the experimental data at three different loading rates. A parametric study was conducted to evaluate the accuracy of the viscoelastic Timoshenko beam model by comparing the reaction forces calculated from the elastic Euler beam, elastic Timoshenko beam and viscoelastic Euler beam models at various aspect ratios and loading rates. The extension of modeling from the elastic Euler beam theory to the viscoelastic Timoshenko beam theory has improved the accuracy for the conversion of the PDMS micropillar deformations to forces, which will benefit the polymer-based micro bio-transducer applications.

The deformation of microcantilever-based infrared detectors during thermal cycling

Uncooled microcantilever-based infrared (IR) detectors have recently gained interest due to their low noise equivalent temperature difference (NETD), while concurrently maintaining low costs. These properties have made them available for a wider range of applications. However, the curvature induced by residual strain mismatch severely compromises the devices performance. Therefore, to meet performance and reliability requirements, it is important to fully understand the deformation of IR detectors. In this study, bimaterial (SiNx/Al) microcantilever-based IR detectors were fabricated using surface micromachining with polyimide as a sacrificial layer. Thermo-mechanical deformation mechanisms were studied through the use of thermal cycling. A temperature chamber with accurate temperature control and an interferometer microscope were adopted in this study for thermal cycling and full-field curvature measurements. It was found that thermal cycling reduced the residual strain mismatch within the bimaterial structure and thus flattened the microcantilever-based IR detectors. Specifically, thermal cycling with a maximum temperature of 295 ?C resulted in a 97% decrease in curvature of the microcantilever-based IR detectors upon return to room temperature. The thermoelastic deformation of the IR detectors was modeled using both finite element method (FEM) and analytical methods. A modified analytical solution based on plate theory was established to describe the thermoelastic mechanical responses by using a correction factor derived from FEM. Although in the current study Al and SiNx were chosen for the application of microcantilever-based IR detectors, the general experimental protocol and modeling approach can be applied to describe thermoelastic mechanical responses of bimaterial devices with different materials. Toward the end of this paper, we studied the correction factors in the modified analytical solution while varying parameters such as Youngs modulus ratio, thickness ratio and coefficient of thermal expansion (CTE) mismatch to investigate the influences of these parameters.

Thermomechanical behavior and microstructural evolution of SiNx/Al bimaterial microcantilevers

Bimaterial microcantilevers are used in numerous applications in microelectromechanical systems (MEMS) for thermal, mechanical, optical, tribological and biological functionalities. Unfortunately, the residual stress-induced curvature and combined effects of creep and stress relaxation in the thin film significantly compromises the performance of these structures. To fully understand the themomechanical deformation and microstructural evolution of such microcantilevers, SiNx/Al bilayer cantilever beams were studied in this work. These microcantilevers were heated and subsequently cooled for five cycles between room temperature and 250 °C, with the peak temperature in each successive cycle increased in increments of 25 °C using a custom-built micro-heating stage. The in situ curvature change was monitored using an interferometric microscope. The general behavior of the bimaterial microcantilever beams can be characterized by linear thermoelastic regimes with (dκ/dT)ave = 0.079 mm−1 °C−1 and inelastic regimes. After thermal cycling with a maximum temperature of 225 °C, upon returning to room temperature, the bimaterial microcantilever beams were flattened and the curvature decreased by 99%. The thermoelastic deformation during thermal cycling was well described by the Kirchhoff plate theory. Deformation of bimaterial microcantilevers during long-term isothermal holding was studied at temperatures of 100 °C, 125 °C and 150 °C with a holding period of 70 h. The curvature of bimaterial microcantilever beams decreased more for higher holding temperatures. Finite element analysis (FEA) with power-law creep in Al was used to simulate the creep and stress relaxation and thus the curvature change of the bimaterial microcantilever beams. The microstructure evolutions due to isothermal holding in SiNx/Al microcantilevers were studied using an atomic force microscope (AFM). The grain growth in both the vertical and lateral directions was present due to isothermal holding. As the isothermal holding temperature increased, the surface roughness of the film increased with more prominent grain structures.

Effect of loading rates on cellular force measurements by polymer micropillar based transducers

Polymeric deformable sensor arrays have been employed to measure cellular forces and offered insights into the study of cellular mechanics. Previous studies have been focused on using transducers in static domain and assumed elastic beam theory as the force conversion model. Neglecting the inherent viscoelastic behavior of polydimethylsiloxane and low aspect ratios of the sensor arrays compromised the accuracy of these devices. In this work, a more in-depth viscoelastic Timoshenko beam model was developed incorporating dynamic cellular forces. We studied chemically stimulated contractions of cardiac myocytes and found that the loading rate has a considerable influence on the sensitivity of the sensor arrays.

Elastic and Viscoelastic Characterization of Polydimethylsiloxane (PDMS) for Cell-Mechanics Applications

The mechanical properties of polydimethylsiloxane (PDMS) were characterized by using uniaxial compression, dynamic mechanical analysis (DMA), and nanoindentation tests as well as finite element simulation methods. A five-parameter linear solid model was used to emulate the behavior of PDMS. The study results indicated that the effect of viscoelasticity affected the PDMS pillar arrays significantly. The traditional approach for calculating the cell force basing on the linear elastic mechanics could result in considerable errors.

Effect of loading rates on polymer micropillar based force transducers

Polymeric sensor arrays have been extensively used to measure cellular forces and offer new insight into the study of cellular mechanics. Previous studies have been focused on using transducers in static domain and assumed elastic beam theory as a force conversion model. Neglecting the inherent viscoelastic behavior of Polydimethylsiloxane (PDMS) and low aspect ratios of micropillars compromised the accuracy of these devices. In this work, a more in-depth viscoelastic Timoshenko beam model was introduced. We studied chemical stimulated contractions of cardiac myocytes and found that the loading rate has a considerable influence on the sensitivity of the sensor arrays.

Suppression of Inelastic Deformation in Multilayer Microcantilevers with Nanoscale Coating

Multilayer microcantilevers present in micro-/nano- electromechanical system (MEMS/NEMS) applications serving passive and active structural roles. The application and commercialization of MEMS devices suffer from reliability problems. Appropriate nanocoatings, such as atomic layer deposition (ALD), have been demonstrated to be promising solutions for these reliability problems in MEMS devices. However, the micro/nano- mechanics within and/or between the microcantilevers and nanocoatings are not fully understood, especially when temperature, time, microstructural evolution and material nonlinearities play significant roles in thermomechanical response. The overall goal of this work is to suppress and understand the inelastic deformation and microstructural evolution in multilayer microcantilevers with nanocoatings. Moreover, to better understand the stress relief and Al 2 O 3 suppression mechanism, scanning electron microscopy (SEM) was employed to explore the microstructural evolution.

Mechanical Characterization of Atomic Layer Deposited (ALD) Alumina for Applications in Corrosive Environments

In this work, thin ALD alumina films were fabricated for evaluating their capabilities as a barrier material for corrosive environments. The fracture toughness and the corrosion-resisting properties after fatigue cycle of these thin ALD alumina films have been characterized. Indentation tests indicate that the ALD alumina/Al structures could enhance both the yield strength of the metal and the effective fracture toughness of the coated ALD alumina films and this result could be useful for designing nanocomposite structures. However, the test results also indicate that the interfacial strength of the ALD/Al structures was prone to degrade under fatigue loading under corrosive environment. This could potentially be a problem for the long term reliability of related devices operated under a harsh environment. In addition, the strong correlation between indentation behavior and fatigue loading for the structure indicate that nanoindentation response could be possibly used to indicate the damage level of microstructures for future reliability evaluations.