The Collapse and Expansion of Liquid-Filled Elastic Channels and Cracks.

The rate at which fluid drains from a collapsing channel or crack depends on the interaction between the elastic properties of the solid and the fluid flow. The same interaction controls the rate at which a pressurized fluid can flow into a crack. In this paper, we present an analysis for the interaction between the viscous flow and the elastic field associated with an expanding or collapsing fluid-filled channel. We first examine an axisymmetric problem for which a completely analytical solution can be developed. A thick-walled elastic cylinder is opened by external surface tractions, and its core is filled by a fluid. When the applied tractions are relaxed, a hydrostatic pressure gradient drives the fluid to the mouth of the cylinder. The relationship between the change in dimensions, time, and position along the cylinder is given by the diffusion equation, with the diffusion coefficient being dependent on the modulus of the substrate, the viscosity of the fluid, and the ratio of the core radius to the exterior radius of the cylinder. The second part of the paper examines the collapse of elliptical channels with arbitrary aspect ratios, so as to model the behavior of fluid-filled cracks. The channels are opened by a uniaxial tension parallel to their minor axes, filled with a fluid, and then allowed to collapse. The form of the analysis follows that of the axisymmetric calculations, but is complicated by the fact that the aspect ratio of the ellipse changes in response to the local pressure. Approximate analytical solutions in the form of the diffusion equation can be found for small aspect ratios. Numerical solutions are given for more extreme aspect ratios, such as those appropriate for cracks. Of particular note is that, for a given cross-sectional area, the rate of collapse is slower for larger aspect ratios. With minor modifications to the initial conditions and the boundary conditions, the analysis is also valid for cracks being opened by a pressurized fluid.

Fracture-based fabrication of normally closed, adjustable, and fully reversible microscale fluidic channels.

Adjustable fluidic structures play an important role in microfluidic systems. Fracture of multilayered materials under applied tension has been previously demonstrated as a convenient, simple, and inexpensive approach to fabricate nanoscale adjustable structures; here, it is demonstrated how to extend this concept to the microscale. This is achieved by a novel pairing of materials that leverages fracture mechanics to limit crack formation to a specified region, allowing to create size-controllable and adjustable microfluidic structures. This technique can be used to fabricate "normally closed" microfluidic channels that are completely reversible, a feature that is challenging to achieve in conventional systems without careful engineering controls. The adjustable microfluidic channels are then applied to mechanically lyse single cells, and subsequently manipulate the released nuclear chromatin, creating new possibilities for epigenetic analysis of single cells. This simple, versatile, and robust technology provides an easily accessible pathway to construct adjustable microfluidic structures, which will be useful in developing complex assays and experiments even in resource-limited settings.

Nanoscale squeezing in elastomeric nanochannels for single chromatin linearization.

This paper describes a novel nanofluidic phenomenon where untethered DNA and chromatin are linearized by rapidly narrowing an elastomeric nanochannel filled with solutions of the biopolymers. This nanoscale squeezing procedure generates hydrodynamic flows while also confining the biopolymers into smaller and smaller volumes. The unique features of this technique enable full linearization then trapping of biopolymers such as DNA. The versatility of the method is also demonstrated by analysis of chromatin stretchability and mapping of histone states using single strands of chromatin.

Super-resolution imaging of linearized chromatin in tunable nanochannels.

Nanofluidic linearization and optical mapping of naked DNA have been reported in the research literature, and implemented in commercial instruments. However, the resolution with which DNA features can be resolved is still inherently limited by both Brownian motion and diffraction-limited optics. Direct analysis of native chromatin is further hampered by difficulty in electrophoretic manipulation, which is routinely used for DNA analysis. This paper describes the development of a three-layer, tunable, nanochannel system that enables non-electrophoretic linearization and immobilization of native chromatin. Furthermore, through careful selection of self-blinking fluorescent dyes and the design of the nanochannel system, we achieve direct stochastic optical reconstruction microscopy (dSTORM) super-resolution imaging of the linearized chromatin. As an initial demonstration, rDNA chromatin extracted from Tetrahymena is analyzed by multi-color imaging of total DNA, newly synthesized DNA, and newly synthesized histone H3. Our analysis reveals a relatively even distribution of newly synthesized H3 across two halves of the rDNA chromatin with palindromic symmetry, supporting dispersive nucleosome segregation. As a proof-of-concept study, our work achieves super-resolution imaging of native chromatin fibers linearized and immobilized in tunable nanochannels. It opens up a new avenue for collecting long-range and high-resolution epigenetic information as well as genetic information.

Manipulation of the nucleoscaffold potentiates cellular reprogramming kinetics.

Somatic cell fate is an outcome set by the activities of specific transcription factors and the chromatin landscape and is maintained by gene silencing of alternate cell fates through physical interactions with the nuclear scaffold. Here, we evaluate the role of the nuclear scaffold as a guardian of cell fate in human fibroblasts by comparing the effects of transient loss (knockdown) and mutation (progeria) of functional Lamin A/C, a core component of the nuclear scaffold. We observed that Lamin A/C deficiency or mutation disrupts nuclear morphology, heterochromatin levels, and increases access to DNA in lamina-associated domains. Changes in Lamin A/C were also found to impact the mechanical properties of the nucleus when measured by a microfluidic cellular squeezing device. We also show that transient loss of Lamin A/C accelerates the kinetics of cellular reprogramming to pluripotency through opening of previously silenced heterochromatin domains while genetic mutation of Lamin A/C into progerin induces a senescent phenotype that inhibits the induction of reprogramming genes. Our results highlight the physical role of the nuclear scaffold in safeguarding cellular fate.

Periodic cracking of films supported on compliant substrates.

When a tensile strain is applied to a film supported on a compliant substrate, a pattern of parallel cracks can channel through both the film and substrate. A linear-elastic fracture-mechanics model for the phenomenon is presented to extend earlier analyses in which cracking was limited to the film. It is shown how failure of the substrate reduces the critical strain required to initiate fracture of the film. This effect is more pronounced for relatively tough films. However, there is a critical ratio of the film to substrate toughness above which stable cracks do not form in response to an applied load. Instead, catastrophic failure of the substrate occurs simultaneously with the propagation of a single channel crack. This critical toughness ratio increases with the modulus mismatch between the film and substrate, so that periodic crack patterns are more likely to be observed with relatively stiff films. With relatively low values of modulus mismatch, even a film that is more brittle than the substrate can cause catastrophic failure of the substrate. Below the critical toughness ratio, there is a regime in which stable crack arrays can be formed in the film and substrate. The depth of these arrays increases, while the spacing decreases, as the strain is increased. Eventually, the crack array can become deep enough to cause substrate failure.

Instantaneous fabrication of arrays of normally closed, adjustable, and reversible nanochannels by tunnel cracking.

A direct fabrication method capable of producing fully-reversible, tunable nanochannel arrays, without the use of a molding step, is described. It is based on tunnel cracking of a readily-prepared brittle layer constrained between elastomeric substrates. The resulting nanochannels have adjustable cross-sections that can be reversibly opened, closed, widened and narrowed merely by applying and removing tensile strains to the substrate. This permits reversible trapping and release of nanoparticles, and easy priming or unclogging of the nanochannels for user-friendly and robust operations. The ease of fabrication and operation required to open and close the nanochannels is superior to previous approaches.

Influence of the Turing instability on the motion of domain boundaries.

Turing's theory of pattern formation has provided crucial insights into the behavior of various biological, geographical, and chemical systems over the last few decades. Existing studies have focused on moving-boundary Turing systems for which the motion of the boundary is prescribed by an external agent. In this paper, we present an extension of this theory to a class of systems in which the front motion is governed by the physical processes that occur within the domain. Biological systems exhibiting apically dominant growth and corrosion of metals and alloys highlight some of the noteworthy examples of such systems. In this study, we characterize the nature of interaction between the moving front and the Turing-instability for both an activator-inhibitor and an activator-substrate model. Behavioral regimes of periodic, as well as nonperiodic (nonconstant), growth rates are obtained. Furthermore, the trends in the first show striking similarities with the cyclic-boundary-kinetics observed in experimental systems. In general, a stationary, periodic structure is also left behind the moving front. If the periodicity of the boundary kinetics agrees with the allowed range of the stable-periodic solutions, the pattern formed tends to persist. Otherwise, it evolves to a nearby energy-minimum either by peak-splitting, peak-decay, or by settling down to a spatially homogeneous state.

Indentation of an elastic half space with material properties varying with depth.

We consider the effect of an elastic modulus that decreases with depth on the load-displacement relation for indentation of a graded half space by a rigid indenter. A closed-form approximation incorporating features of the plate on an elastic substrate and the Hertzian contact theory is compared with finite element results for the case of a uniform stiff layer on a homogeneous substrate. Some general results are presented for the case where the grading has inverse power-law form and the effects of truncation to a finite surface value are investigated numerically. Finally, a more practical error-function grading is considered. In all cases, the load-displacement relation is closer to linear than in the homogeneous case. We conclude that the experimental data can be used to determine parameters in a predetermined form of grading, but that comparative insensitivity to the exact form of the grading would make it difficult to distincguish experimentally between different models based on indentation experiments alone.

Low-interfacial toughness materials for effective large-scale deicing.

Ice accretion has adverse effects on a range of commercial and residential activities. The force required to remove ice from a surface is typically considered to scale with the iced area. This imparts a scalability limit to the use of icephobic coatings for structures with large surface areas, such as power lines or ship hulls. We describe a class of materials that exhibit a low interfacial toughness with ice, resulting in systems for which the forces required to remove large areas of ice (a few square centimeters or greater) are both low and independent of the iced area. We further demonstrate that coatings made of such materials allow ice to be shed readily from large areas (~1 square meter) merely by self-weight.

Enhanced Interfacial Toughness of Thermoplastic-Epoxy Interfaces Using ALD Surface Treatments.

Interfacial fracture and delamination of polymer interfaces can play a critical role in a wide range of applications, including fiber-reinforced composites, flexible electronics, and encapsulation layers for photovoltaics. However, owing to the low surface energy of many thermoplastics, adhesion to dissimilar material surfaces remains a critical challenge. In this work, we demonstrate that surface treatments using atomic layer deposition (ALD) on poly(methyl methacrylate) (PMMA) and fluorinated ethylene propylene (FEP) lead to significant increases in surface energy, without affecting the bulk mechanical response of the thermoplastic. After ALD film growth, the interfacial toughness of the PMMA-epoxy and FEP-epoxy interfaces increased by factors of up to 7 and 60, respectively. These results demonstrate the ability of ALD to engineer the adhesive properties of chemically inert surfaces. However, in the present case, the interfacial toughness was observed to decrease significantly with an increase in humidity. This was attributed to the phenomenon of stress-corrosion cracking associated with the reaction between Al2O3 and water and might have a significant implication for the design of these tailored interfaces.

Surface instability of an elastic half space with material properties varying with depth.

If a body with a stiffer surface layer is loaded in compression, a surface wrinkling instability may be developed. A bifurcation analysis is presented for determining the critical load for the onset of wrinkling and the associated wavelength for materials in which the elastic modulus is an arbitrary function of depth. The analysis leads to an eigenvalue problem involving a pair of linear ordinary differential equations with variable coefficients which are discretized and solved using the finite element method.The method is validated by comparison with classical results for a uniform layer on a dissimilar substrate. Results are then given for materials with exponential and error-function gradation of elastic modulus and for a homogeneous body with thermoelastically-induced compressive stresses.

The mechanical properties of a surface-modified layer on poly(dimethylsiloxane).

Surface-modification of the elastomer poly(dimethylsiloxane) by exposure to oxygen plasma for four minutes creates a thin, stiff film. In this study, the thickness and mechanical properties of this surface-modified layer were determined. Using the phase image capabilities of a tapping-mode atomic-force microscope, the surface-modified region was distinguished from the bulk PDMS; specifically, it suggested a graded surface layer to a depth of about 200 nm. Load-displacement data for elastic indentation using a compliant AFM cantilever was analyzed as a plate bending on an elastic foundation to determine the elastic modulus of the surface (37 MPa). An applied uniaxial strain generated a series of parallel nano-cracks with spacing on the order of a few microns. Numerical analyses of this cracking phenomenon showed that the depth of these cracks was in the range of 300-600 nm and that the surface layer was extremely brittle, with its toughness in the range of 0.1-0.3 J/m(2).

Dispersible oxygen microsensors map oxygen gradients in three-dimensional cell cultures.

Phase fluorimetry, unlike the more commonly used intensity-based measurement, is not affected by differences in light paths from culture vessels or by optical attenuation through dense 3D cell cultures and hydrogels thereby minimizing dependence on signal intensity for accurate measurements. This work describes the use of phase fluorimetry on oxygen-sensor microbeads to perform oxygen measurements in different microtissue culture environments. In one example, cell spheroids were observed to deplete oxygen from the cell-culture medium filling the bottom of conventional microwells within minutes, whereas oxygen concentrations remained close to ambient levels for several days in hanging-drop cultures. By dispersing multiple oxygen microsensors in cell-laden hydrogels, we also mapped cell-generated oxygen gradients. The spatial oxygen mapping was sufficiently precise to enable the use of computational models of oxygen diffusion and uptake to give estimates of the cellular oxygen uptake rate and the half-saturation constant. The results show the importance of integrated design and analysis of 3D cell cultures from both biomaterial and oxygen supply aspects. While this paper specifically tests spheroids and cell-laden gel cultures, the described methods should be useful for measuring pericellular oxygen concentrations in a variety of biomaterials and culture formats.

Dynamic simulations show repeated narrowing maximizes DNA linearization in elastomeric nanochannels.

This paper uses computer simulations to reveal unprecedented details about linearization of deoxyribonucleic acid (DNA) inside dynamic nanochannels that can be repeatedly widened and narrowed. We first analyze the effect of rate of channel narrowing on DNA linearization dynamics. Quick (∼0.1 s) narrowing of nanoscale channels results in rapid overstretching of the semi-flexible chain followed by a slower (∼0.1-10 s) relaxation to an equilibrium extension. Two phenomena that induce linearization during channel narrowing, namely, elongational-flow and confinement, occur simultaneously, regardless of narrowing speed. Interestingly, although elongational flow is a minimum at the mid-point of the channel and increases towards the two ends, neither the linearization dynamics nor the degree of DNA extension varies significantly with the center-of-mass of the polymer projected on the channel axis. We also noticed that there was a significant difference in time to reach the equilibrium length, as well as the degree of DNA linearization at short times, depending on the initial conformation of the biopolymer. Based on these observations, we tested a novel linearization protocol where the channels are narrowed and widened repeatedly, allowing DNA to explore multiple conformations. Repeated narrowing and widening, something uniquely enabled by the elastomeric nanochannels, significantly decrease the time to reach the equilibrium-level of stretch when performed within periods comparable to the chain relaxation time and more effectively untangle chains into more linearized biopolymers.

Fracture fabrication of a multi-scale channel device that efficiently captures and linearizes DNA from dilute solutions.

This paper describes a simple technique for patterning channels on elastomeric substrates, at two distinct scales of depth, through the use of controlled fracture. Control of channel depth is achieved by the careful use of different layers of PDMS, where the thickness and material properties of each layer, as well as the position of the layers relative to one another, dictate the depth of the channels formed. The system created in this work consists of a single 'deep' channel, whose width can be adjusted between the micron- and the nano-scale by the controlled application or removal of a uniaxial strain, and an array of 'shallow' nano-scale channels oriented perpendicular to the 'deep' channel. The utility of this system is demonstrated through the successful capture and linearization of DNA from a dilute solution by executing a two-step 'concentrate-then-linearize' procedure. When the 'deep' channel is in its open state and a voltage is applied across the channel network, an overlapping electric double layer forms within the 'shallow' channel array. This overlapping electric double layer was used to prevent passage of DNA into the 'shallow' channels when the DNA molecules migrate into the junctional region by electrophoresis. Release of the applied strain then allows the 'deep' channel to return to its closed state, reducing the cross-sectional area of this channel from the micro- to the nano-scale. The resulting hydrodynamic flow and nano-confinement effects then combine to efficiently uncoil and trap the DNA in its linearized form. By adopting this strategy, we were able to overcome the entropic barriers associated with capturing and linearizing DNA derived from a dilute solution.

Self-healing of pores in PLGAs.

Self-healing of pores in Poly(lactic-co-glycolic acid)s (PLGA) plays an important role in the encapsulation and controlled release of drugs from PLGA microparticles. Despite the importance of this phenomenon, neither the mechanics of the deformation nor the material properties that control it have been fully studied. In this study, the material properties of PLGA have been characterized using mechanical tests, and a finite-element model has been developed to predict how pores heal. This model assumes that the healing process occurs by viscous flow resulting from the deviatoric stress field induced by the interaction between the surface curvature and the surface tension of the PLGA. The simulations, which incorporate measured material properties, show good agreement with experimental observations. However, annealing processes that occur over prolonged times increase the viscosity and slow the healing times of PLGA films at intermediate temperatures above the glass-transition temperature. These findings may be reasonably applied towards the prediction of healing processes in PLGA and in related biomaterials for important biomedical applications such as drug delivery.

The Control of Crack Arrays in Thin Films.

Thin-film fracture can be used as a nano-fabrication technique but, generally, it is a stochastic process that results in non-uniform patterns. Crack spacings depend on the interaction between intrinsic flaw populations and the fracture mechanics of crack channeling. Geometrical features can be used to trigger cracks at specific locations to generate controlled crack patterns. However, while this basic idea is intuitive, it is not so obvious how to realize the concept in practice, nor what the limitations are. The control of crack arrays depends on the nature of the intrinsic flaw population. If there is a relatively large density of long flaws, as commonly assumed in fracture-mechanics analyses, reliable crack patterns can be obtained fairly robustly using relatively blunt geometrical features to initiate cracks, provided the applied strain is carefully matched to the properties of the system and the desired crack spacing. This process is analyzed both for cracks confined to the thickness of a film and for cracks growing into a substrate. The latter analysis is complicated by the fact that increases in strain can either drive cracks deeper into the substrate or generate new cracks at shallower depths. If the intrinsic flaws are all very short, the geometrical features need to be very sharp to achieve the desired patterns. While careful control of the applied strain is not required, the strain needs to be relatively large compared to that which would be required to propagate a large flaw across the film. This results in an approach that is not robust against the introduction of accidental damage or a few large flaws.

Fracture-based micro- and nanofabrication for biological applications.

While fracture is generally considered to be undesirable in various manufacturing processes, delicate control of fracture can be successfully implemented to generate structures at micro/nano length scales. Fracture-based fabrication techniques can serve as a template-free manufacturing method, and enables highly-ordered patterns or fluidic channels to be formed over large areas in a simple and cost-effective manner. Such technologies can be leveraged to address biologically-relevant problems, such as in the analysis of biomolecules or in the design of culture systems that imitate the cellular or molecular environment. This mini review provides an overview of current fracture-guided fabrication techniques and their biological applications. We first survey the mechanical principles of fracture-based approaches. Then we describe biological applications at the cellular and molecular levels. Finally, we discuss unique advantages of the different system for biological studies.

One-dimensional patterning of cells in silicone wells via compression-induced fracture.

We have adapted our existing compression-induced fracture technology to cell culture studies by generating linear patterns on a complex cell culture well structure rather than on simple solid constructs. We present a simple method to create one-dimensional (1D), submicron, and linear patterns of extracellular matrix on a multilayer silicone material. We identified critical design parameters necessary to optimize compression-induced fracture patterning on the wells, and applied stresses using compression Hoffman clamps. Finite-element analyses show that the incorporation of the well improves stress homogeneity (stress variation = 25%), and, thus, crack uniformity over the patterned region. Notably, a shallow well with a thick base (vs. deeper wells with thinner bases) reduces out-of-plane deflections by greater than a sixth in the cell culture region, improving clarity for optical imaging. The comparison of cellular and nuclear shape indices of a neuroblast line cultured on patterned 1D lines and unpatterned 2D surfaces reveals significant differences in cellular morphology, which could impact many cellular functions. Because 1D cell cultures recapitulate many important phenotypical traits of 3D cell cultures, our culture system offers a simple means to further study the relationship between 1D and 3D cell culture environments, without demanding expensive engineering techniques and expertise.