Substrate Compliance Research Articles

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation.

Deformation and failure of a film/substrate system subjected to spherical indentation: Part II. Prediction of failure modes in a thin TiN film deposited on a compliant elastic substrate

We have demonstrated previously, using nanoindentation, that the film thickness and substrate plasticity, the important two external variables in the film layer, control the failure of the film in a mutually exclusive way. In this work, we used a non-iterative Hankel transform method to analyze the stresses in an elastic film bound to an elastic substrate by a no-slip boundary condition and subjected to a Hertzian traction. We vary the substrate compliance by two orders of magnitude to generate interfacial mismatch stresses, which mimic the corresponding changes found in a real-life elastic film on an elastic-plastic substrate when the hardness of the substrate is changed. The analysis is found to reproduce faithfully the experimental trends, which showed that normal load and interfacial stresses generated by strain mismatch drive different modes of fracture depending on the film thickness in a mutually exclusive way. This validation paves the way for this theoretical technique to be used to design multilayered film structures.

Investigation of silicon-germanium fins fabricated using germanium condensation on vertical compliant structures

We report the formation of defect-free SiGe vertical heterostructures using Ge condensation on vertical SiGe structures. To evaluate the effectiveness of substrate compliance in vertical structures, SiGe fins of various widths were subjected to Ge condensation. This formed vertical fin heterostructures comprising a SiGe core region sandwiched by Ge-rich regions. Using cross-sectional transmission electron microscopy (TEM), wide fins were found to contain more dislocations than narrower fins, in which we observed few or no dislocations. Lattice strain analysis using high-resolution TEM image analysis was used to confirm that strain relaxation has occurred. In the wide fins (noncompliant substrate), strain relaxation was dislocation mediated. In the narrow fins, substrate compliance enabled strain relaxation in the Ge-rich layer with reduced dislocation formation. Hence, we also demonstrated the formation of a strain-relaxed homogeneous SiGe fin (∼90% Ge concentration) with no observable dislocations.

Effects of Chain Length and Heat Treatment on the Nanotribology of Alkylsilane Monolayers Self-Assembled on a Rough Aluminum Surface

The conformational order of alkylsilane monolayers self-assembled on a rough aluminum surface is affected by the molecular chain length and the thermal history of the sample. These monolayers have been characterized by grazing angle FTIR spectroscopy. Tribological mechanisms were explored using initial molecular conformation order, sliding distance, normal load, and substrate compliance as experimental variables. Results indicate that the initial conformational disorder of the molecules determines the level of friction at the commencement of sliding. Adverse changes in dynamic friction and monolayer life during sliding are not thermally induced but are related to substrate roughness and local plasticity. Plastic deformation reduces the spatial density of the alkylsilane monolayer and is accentuated by an increase in the normal load.

Integrin-dependent actomyosin contraction regulates epithelial cell scattering

The scattering of Madin-Darby canine kidney cells in vitro mimics key aspects of epithelial–mesenchymal transitions during development, carcinoma cell invasion, and metastasis. Scattering is induced by hepatocyte growth factor (HGF) and is thought to involve disruption of cadherin-dependent cell–cell junctions. Scattering is enhanced on collagen and fibronectin, as compared with laminin1, suggesting possible cross talk between integrins and cell–cell junctions. We show that HGF does not trigger any detectable decrease in E-cadherin function, but increases integrin-mediated adhesion. Time-lapse imaging suggests that tension on cell–cell junctions may disrupt cell–cell adhesion. Varying the density and type of extracellular matrix proteins shows that scattering correlates with stronger integrin adhesion and increased phosphorylation of the myosin regulatory light chain. To directly test the role of integrin-dependent traction forces, substrate compliance was varied. Rigid substrates that produce high traction forces promoted scattering, in comparison to more compliant substrates. We conclude that integrin-dependent actomyosin traction force mediates the disruption of cell–cell adhesion during epithelial cell scattering.

Nanoheteroepitaxial growth of GaN on Si nanopillar arrays

Nanoheteroepitaxial growth of GaN by metal-organic chemical-vapor deposition on dense arrays of (111) Si nanopillars has been investigated. Scanning electron microscopy, cross-sectional transmission electron microscopy, and electron-diffraction analysis of 0.15-μm-thick GaN layers indicate single-crystal films. Most of the mismatch defects were in-plane stacking faults and the threading dislocation concentration was <108cm−2 at the interface and decreased away from the interface. High-resolution transmission electron microscopy indicated that grain-boundary defects could heal and were followed by high quality, single-crystal GaN. Facetted voids were also present at the GaN∕Si interface and are believed to be an additional strain-energy reduction mechanism. The unusual defect behavior in these samples appears to be related to the high compliance of the nanopillar silicon substrate.

Cell type-specific response to growth on soft materials

Many cell types respond to forces as acutely as they do to chemical stimuli, but the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular structure and function in vivo are far less explored than those triggered by chemical ligands. Forces arise both from effects outside the cell and from mechanochemical reactions within the cell that generate stresses on the surface to which the cells adhere. Several recent reviews have summarized how externally applied forces may trigger a cellular response (Silver FH and Siperko LM. Crit Rev Biomed Eng 31: 255-331, 2003; Estes BT, Gimble JM, and Guilak F. Curr Top Dev Biol 60: 91-126, 2004; Janmey PA and Weitz DA. Trends Biochem Sci 29: 364-370, 2004). The purpose of this review is to examine the information available in the current literature describing the relationship between a cell and the rigidity of the matrix on which it resides. We will review recent studies and techniques that focus on substrate compliance as a major variable in cell culture studies. We will discuss the specificity of cell response to stiffness and discuss how this may be important in particular tissue systems. We will attempt to link the mechanoresponse to real pathological states and speculate on the possible biological significance of mechanosensing.

Fabrication of Biofunctionalized Quasi-Three-Dimensional Microstructures of a Nonfouling Comb Polymer Using Soft Lithography

This paper describes a simple set of patterning methods that are applicable to diverse substrates and allow the routine and rapid fabrication of protein patterns embedded within a background that consists of quasi-three-dimensional microstructures of a cell-resistant polymer. The ensemble of methods reported here utilizes three components to create topographically nonfouling polymeric structures that present cell-adhesive protein patterns in the regions between the microstructures: the first component is an amphiphilic comb polymer that is comprised of a methyl methacrylate backbone and pendant oligo(ethylene glycol) moieties along the side chain, physically deposited films of which are protein- and cell-resistant. The second component of the fabrication methodology involves the use of different variants of soft lithography, such as microcontact printing to create nonfouling topographical features of the comb polymer that demarcate cell-adhesive regions of the third component: a cell-adhesive extracellular protein or peptide. The ensemble of methods reported in this paper was used to fabricate quasi-three-dimensional patterns that present topographical and biochemical cues on a variety of substrates, and was shown to successfully maintain cellular patterns for up to two months in serum-containing medium. We believe that this, and other such methods under development that allow independent and systematic control of chemistry, topography and substrate compliance will provide versatile “test-beds” for fundamental studies in cell biology as well as allow the discovery of rational design principles for the development of biomaterials and tissue-engineering scaffolds.

Extracellular matrix rigidity governs smooth muscle cell motility in a biphasic fashion

Increasing evidence suggests that mechanical cues inherent to the extracellular matrix (ECM) may be equally as critical as its chemical identity in regulating cell behavior. We hypothesized that the mechanical properties of the ECM directly regulate the motility of vascular smooth muscle cells (SMCs) and tested this hypothesis using polyacrylamide substrates with tunable mechanical properties. Quantification of the migration speed on uniformly compliant hydrogels spanning a range of stiffnesses (Young's moduli values from 1.0 to 308 kPa for acrylamide/bisacrylamide ratios between 5/0.1% and 15/1.2%, respectively) revealed a biphasic dependence on substrate compliance, suggesting the existence of an optimal substrate stiffness capable of supporting maximal migration. The value of this optimal stiffness shifted depending on the concentration of ECM protein covalently attached to the substrate. Specifically, on substrates presenting a theoretical density of 0.8 microg/cm(2) fibronectin, the maximum speed of 0.74 +/- 0.09 microm/min was achieved on a 51.9 kPa gel; on substrates presenting a theoretical density of 8.0 microg/cm(2) fibronectin, the maximum speed of 0.72 +/- 0.06 microm/min occurred on a softer 21.6 kPa gel. Pre-treatment of cells with Y27632, an inhibitor of the Rho/Rho-kinase (ROCK) pathway, reduced these observed maxima to values comparable to those on non-optimal stiffnesses. In parallel, quantification of TritonX-insoluble vinculin via Western blotting, coupled with qualitative fluorescent microscopy, revealed that the formation of focal adhesions and actin stress fibers also depends on ECM stiffness. Combined, these data suggest that the mechanical properties of the underlying ECM regulate Rho-mediated contractility in SMCs by disrupting a presumptive cell-ECM force balance, which in turn regulates cytoskeletal assembly and ultimately, cell migration.

Engineering hepatocellular morphogenesis and function via ligand-presenting hydrogels with graded mechanical compliance

In order to evaluate the sensitivity of hepatocellular cultures to variations in both substrate stiffness and bioactive ligand presentation, hepatocytes were cultured on differentially compliant polyacrylamide gel discs functionalized with varying amounts of the ECM ligand, fibronectin (FN). Subconfluent cell cultures were established in a multiwell plate format enabling the systematic evaluation of cellular response to both underlying substrate rigidity and substrate ligand concentration. Hepatocellular morphogenesis, regulated by a combination of both ligand density and substrate compliance, resulted in a broad spectrum of patterns of cellular reorganization and assembly ranging from highly two-dimensionally spread cells to highly compact, three-dimensional spheroids. Cell compaction was promoted by increasing levels of substrate mechanical compliance and generally inhibited by increasing concentrations of substrate-bound FN. We identified regimes of substrate compliance in which cells are highly responsive or relatively insensitive to the level of substrate-based ligands. For example, while FN presentation did not have a large impact on cell morphogenesis for cultures on highly compliant gels (G' = 1.9 kPa), hepatocytes on "firm" substrates of intermediate compliance (G' = 5.6 kPa) exhibited approximately a 2-fold increase in cell area between the highest and lowest FN concentrations used in this study. Further, we show that increasing substrate compliance at constant ligand concentration results in increased levels of liver-specific albumin secretion while increasing levels of FN at constant substrate rigidity yield reduced liver-specific functional activity. These substrate-elicited differences in cell function also coincided with analogous changes in the transcript levels of metabolic, growth-related, and liver-specific gene markers. Notably, these results also demonstrated that "firm" gel substrates elicit the most hepatocyte functional sensitivity to substrate-based FN presentation. Overall, our findings indicate that hepatocellular responsiveness to ligand concentration can be acutely regulated by gradation of substrate compliance, suggesting that concerted biochemical and biophysical design strategies may be critical toward the fabrication of hepatospecific biomaterials that effectively support desired levels of liver-specific function.

Photopolymerization in Microfluidic Gradient Generators: Microscale Control of Substrate Compliance to Manipulate Cell Response

Photopolymerization in Microfluidic Gradient Generators: Microscale Control of Substrate Compliance to Manipulate Cell Response

Effect of substrate compliance on the global unilateral post-buckling of coatings: AFM observations and finite element calculations

The post-critical regime of straight-sided wrinkles on compliant substrates of polycarbonate has been observed by atomic force microscope and investigated by means of finite element simulations. The effect of coupling between the film and its substrate has revealed a global buckling phenomenon, characterized by critical loads lower than those found in the case of a rigid substrate. Characteristic shapes of the buckled structure have been also found to spread over a region wider than the delaminated zone itself. A law relating the film deflexion to the stress has finally been established for any film/substrate system.

Adhesion-contractile balance in myocyte differentiation

Tissue cells generally pull on their matrix attachments and balance a quasi-static contractility against adequate adhesion, but any correlation with and/or influence on phenotype are not yet understood. Here, we begin to demonstrate how differentiation state couples to actomyosin-based contractility through adhesion and substrate compliance. Myotubes are differentiated from myoblasts on collagen-patterned coverslips that allow linear fusion but prevent classic myotube branching. Post-fusion, myotubes adhere to the micro-strips but lock into a stress fiber-rich state and do not differentiate significantly further. In contrast, myotubes grown on top of such cells do progress through differentiation, exhibiting actomyosin striations within one week. A compliant adhesion to these lower cells is suggested to couple to contractility and accommodate the reorganization needed for upper cell striation. Contractility is assessed in these adherent cells by mechanically detaching one end of the myotubes. All myotubes, whether striated or not, shorten with an exponential decay. The cell-on-cell myotubes relax more, which implies a greater contractile stress. The non-muscle myosin II inhibitor blebbistatin inhibits relaxation for either case. Myotubes in culture are thus clearly prestressed by myosin II, and this contractility couples to substrate compliance and ultimately influences actomyosin striation.

Viscoelastic response of woven composite substrates

Micromechanical models are developed to predict the time and temperature dependent response of woven composite substrates used in multilayer printed circuit boards. In the first part of this study, the elastic–viscoelastic correspondence principle is applied to previously reported elastic micromechanical models. The time-dependent creep compliance of a particular composite substrate (7628 style fabric) is predicted and compared with experimental measurements. Several deficiencies and possible modifications to the analytical models are identified. In the second part, a finite element model is adopted to examine the influence of boundary conditions and relevant matrix properties on the composite viscoelastic response. Parametric studies reveal the importance of shifts in the relaxation spectrum local to the matrix in the high volume fraction fiber bundles and the need to account for time-dependent Poisson’s ratio of the matrix.

Extracellular matrix controls myosin light chain phosphorylation and cell contractility through modulation of cell shape and cytoskeletal prestress.

The mechanism by which vascular smooth muscle (VSM) cells modulate their contractility in response to structural cues from extracellular matrix remains poorly understood. When pulmonary VSM cells were cultured on increasing densities of immobilized fibronectin (FN), cell spreading, myosin light chain (MLC) phosphorylation, cytoskeletal prestress (isometric tension in the cell before vasoagonist stimulation), and the active contractile response to the vasoconstrictor endothelin-1 all increased in parallel. In contrast, MLC phosphorylation did not increase when suspended cells were allowed to bind FN-coated microbeads (4.5-microm diameter) or cultured on micrometer-sized (30 x 30 microm) FN islands surrounded by nonadhesive regions that support integrin binding but prevent cell spreading. Cell spreading and MLC phosphorylation also both decreased in parallel when the mechanical compliance of flexible FN substrates was raised. MLC phosphorylation was inhibited independently of cell shape when cytoskeletal prestress was dissipated using a myosin ATPase inhibitor in fully spread cells, whereas it increased to maximal levels when microtubules were disrupted using nocodazole in cells adherent to FN but not in suspended cells. These data demonstrate that changes in cell-extracellular matrix (ECM) interactions modulate smooth muscle cell contractility at the level of biochemical signal transduction and suggest that the mechanism underlying this regulation may involve physical interplay between ECM and the cytoskeleton, such that cell spreading and generation of cytoskeletal tension feed back to promote MLC phosphorylation and further increase tension generation.

Substrate Compliance versus Ligand Density in Cell on Gel Responses

Substrate stiffness is emerging as an important physical factor in the response of many cell types. In agreement with findings on other anchorage-dependent cell lineages, aortic smooth muscle cells are found to spread and organize their cytoskeleton and focal adhesions much more so on “rigid” glass or “stiff” gels than on “soft” gels. Whereas these cells generally show maximal spreading on intermediate collagen densities, the limited spreading on soft gels is surprisingly insensitive to adhesive ligand density. Bell-shaped cell spreading curves encompassing all substrates are modeled by simple functions that couple ligand density to substrate stiffness. Although smooth muscle cells spread minimally on soft gels regardless of collagen, GFP-actin gives a slight overexpression of total actin that can override the soft gel response and drive spreading; GFP and GFP-paxillin do not have the same effect. The GFP-actin cells invariably show an organized filamentous cytoskeleton and clearly indicate that the cytoskeleton is at least one structural node in a signaling network that can override spreading limits typically dictated by soft gels. Based on such results, we hypothesize a central structural role for the cytoskeleton in driving the membrane outward during spreading whereas adhesion reinforces the spreading.

Combined effects of substrate compliance and film compositional grading on strain relaxation in layer-by-layer semiconductor heteroepitaxy: the case of InAs/In 0.50Ga 0.50As/GaAs(1 1 1)A

A systematic theoretical analysis is presented of the combined effects of substrate compliance and film compositional grading on the relaxation of strain due to lattice mismatch in layer-by-layer semiconductor heteroepitaxy. The analysis is based on a combination of continuum elasticity theory and a novel atomistic simulation approach for modeling structural and compositional relaxation in layer-by-layer heteroepitaxial systems. Results are presented for InAs epitaxy on GaAs(1 1 1)A compliant substrates with some marginal film compositional grading that consists of one monolayer of In 0.50Ga 0.50As grown on the substrate surface prior to InAs growth. A parametric study is carried out over a wide range of substrate thicknesses. Interfacial stability with respect to misfit dislocation formation, the dependence on substrate thickness of a thermodynamic critical film thickness, and the completion of the coherent-to-semicoherent interfacial transition are examined in detail. In addition, the structural characteristics and compositional distribution of the corresponding semicoherent interfaces, the associated strain fields, as well as the film surface morphological characteristics are analyzed. Most importantly, the role of segregation at defects of a semicoherent interface in the thermodynamics of layer-by-layer heteroepitaxial growth is demonstrated. Our study shows that systematic combination of the mechanical behavior of thin compliant substrates with grading of the epitaxial film composition provides a very promising engineering strategy for strain relaxation in heteroepitaxy.

Directed Movement of Vascular Smooth Muscle Cells on Gradient-Compliant Hydrogels

Current solutions in the treatment of cardiovascular disease include angioplasty and the insertion of stents, but a large number of these cases result in restenosis. Biomaterial coatings that control vascular smooth muscle cell migration are therefore desirable. In this study, we describe a novel method to create substrata with defined gradients in mechanical compliance using photopolymerization and patterning. Cell speed was found to be 53 ± 2.6 μm/h on a substrate with a Young's modulus of 15 kPa compared to 40 ± 3.1 μm/h for a 28 kPa substratum (P < 0.005). We demonstrate that vascular smooth muscle cells undergo direct migration on radial-gradient-compliant substrata from soft to stiff regions of the substrate and that cells accumulate in the stiff regions after 24 h. Our results show that the pattern of the compliance gradient is important and that substrate compliance may be a key design parameter for modulation of cell migration for vascular tissue engineering applications.

Influence of substrate compliance on buckling delamination of thin films

A thin film subject to in-plane compressive stress is susceptible to buckling-driven delamination. This paper analyzes a straight-sided delamination buckle with a focus on the effects of substrate compliance, following earlier work by B. Cotterell and Z. Chen. The critical buckling condition, the energy release rate and the mode mix of the interface delamination crack are calculated as a function of the elastic mismatch between the film and substrate. The average energy release rate at the curved end of a tunneling straight-sided blister is also determined. The more compliant the substrate, the easier for the film to buckle and the higher the energy release rates. The effect becomes significant when the modulus of the substrate is appreciably less than that of the film. When the substrate modulus is comparable to that of the film, or higher, the usual assumption is justified to the effect that the film is clamped along its edges. When the substrate is very compliant the energy release rate at the curved front exceeds that along the straight sides.

Nanotribological and Nanomechanical Properties of Ultrathin Amorphous Carbon Films Synthesized by Radio Frequency Sputtering

The dependence of the nanotribological properties of ultrathin amorphous carbon (a-C) films, deposited on Si(100) substrates by radio frequency sputtering, on their nanomechanical properties was investigated using surface force microscopy. The thickness and nanohardness of the a-C films were found to be in the range of 7–95 nm and 9–44 GPa, respectively. Sharp conical diamond tips with a 90 deg included angle and radius of curvature of about 20 μm and 100 nm were used to perform friction and wear experiments, respectively. The effect of the substrate compliance on the nanomechanical and nanotribological properties of the a-C films is interpreted in terms of the indentation depth and the film thickness. The coefficient of friction and wear rate of the a-C films are related to their nanomechanical properties, thickness, and surface roughness. The dependence of the coefficient of friction on contact load and the dominant friction mechanisms of elastically and plastically deformed films are discussed in light of friction force and surface imaging results. High effective hardness-to-elastic modulus ratio and low surface roughness characterize high wear resistance a-C films. Below a critical load, the steady-state removal rate of the film material is insignificantly small, revealing a predominantly elastic behavior.