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Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations., Comment: Accepted for publication in the Biophysical Journal

Cells can sense and respond to mechanical signals over relatively long distances across fibrous extracellular matrices. Here, we explore all of the key factors that influence long range force transmission in cell-populated collagen matrices: alignment of collagen fibers, responses to applied force, strain stiffening properties of the aligned fibers, aspect ratios of the cells, and the polarization of cellular contraction. A constitutive law accounting for mechanically-driven collagen fiber reorientation is proposed. We systematically investigate the range of collagen fiber alignment using both finite element simulations and analytical calculations. Our results show that tension-driven collagen fiber alignment plays a crucial role in force transmission. Small critical stretch for fiber alignment, large fiber stiffness and fiber strain hardening behavior enable long-range interaction. Furthermore, the range of collagen fiber alignment for elliptical cells with polarized contraction is much larger than that for spherical cells with diagonal contraction. A phase diagram showing the range of force transmission as a function of cell shape and polarization and matrix properties is presented. Our results are in good agreement with recent experiments, and highlight the factors that influence long-range force transmission, in particular tension-driven alignment of fibers. Our work has important relevance to biological processes including development, cancer metastasis and wound healing, suggesting conditions whereby cells communicate over long distances., Comment: Accepted for publication in the Biophysical Journal

This paper presents constant-time and near-constant-time distributed algorithms for a variety of problems in the congested clique model. We show how to compute a 3-ruling set in expected $O(\log \log \log n)$ rounds and using this, we obtain a constant-approximation to metric facility location, also in expected $O(\log \log \log n)$ rounds. In addition, assuming an input metric space of constant doubling dimension, we obtain constant-round algorithms to compute constant-factor approximations to the minimum spanning tree and the metric facility location problems. These results significantly improve on the running time of the fastest known algorithms for these problems in the congested clique setting., Comment: Full version of DISC 2014 paper. Updated Sep 2018 to reflect the fact that using the Ghaffari et al. congested clique MIS algorithm from PODC 2018, it is possible to compute a 2-ruling set in the congested clique in O(logloglog n) rounds with high probability

Two-dimensional (2D) materials can have an excellent capability to handle high rates of charge in ion batteries since metal ions need not diffuse in a 3D lattice structure. However graphene, which is the most important 2D material, is known to have no Li capacity. Herein, adsorption of Li, as well as Na, K, and Ca on Ti$_3$C$_2$, one representative MXene, is predicted by first-principles density functional calculations. In our study, we observed that these alkali ions exhibit different adsorption energy depending on the coverage. The adsorption energies of Na, K and Ca decrease as coverage increases, while Li shows little sensitivity to variance in coverage. This observed relationship between adsorption energies and coverage of alkali ions on Ti$_3$C$_2$ can be explained by their effective ionic radii. A larger effective ionic radius increases interaction between alkali atoms, thus lower capacity and coverage are obtained. Our calculated capacity values for Li, Na, K and Ca on Ti$_3$C$_2$ are 639.5, 319.8, 191.8 and 159.9 mAh g$^{-1}$, respectively. Compared to materials currently used in Li ion battery anodes, MXene shows great promise in increasing overall battery performance., Comment: This paper has been withdrawn by the author due to some mistakes in the figures

We have investigated adsorption of Na and Ca on graphene with divacancy (DV) and Stone-Wales (SW) defect. Our results show that adsorption is not possible on pristine graphene. However, their adsorption on defective sheet is energetically favorable. The enhanced adsorption can be attributed to the increased charge transfer between adatoms and underlying defective sheet. With the increase in defect density until certain possible limit, maximum percentage of adsorption also increases giving higher battery capacity. For maximum possible DV defect, we can achieve maximum capacity of 1459 mAh/g for Na-ion batteries (NIBs) and 2900 mAh/g for Ca-ion batteries (CIBs). For graphene full of SW defect, we find the maximum capacity of NIBs and CIBs is around 1071 mAh/g and 2142 mAh/g respectively. Our results will help create better anode materials with much higher capacity and better cycling performance for NIBs and CIBs., Comment: 7 figures

Molecular dynamics (MD) simulations have been performed to investigate the mechanical properties of hydrogen functionalized graphene allotropes (GAs) for H-coverage spanning the entire range (0-100%). Four allotropes (graphyne, cyclic graphene, octagonal graphene, and biphenylene) with larger unit lattice size than graphene are considered. The effect of the degree of functionalization and molecular structure on the Young's modulus and strength are investigated, and the failure processes of some new GAs are reported for the first time. We show that the mechanical properties of the hydrogenated GAs deteriorate drastically with increasing H-coverage within the sensitive threshold, beyond which the mechanical properties remain insensitive to the increase in H-coverage. This drastic deterioration arises both from the conversion of sp2 to sp3 bonding and easy rotation of unsupported sp3 bonds. Allotropes with different lattice structures correspond to different sensitive thresholds. The Young's moduli deterioration of fully hydrogenated allotropes can be up to 70% smaller than that of the corresponding pristine structure. Moreover the tensile strength shows an even larger drop of about 90% and higher sensitivity to H-coverage even if it is small. Our results suggest that the unique coverage-dependent deterioration of the mechanical properties must be taken into account when analyzing the performance characteristics of nanodevices fabricated from functionalized GAs., Comment: 11 pages, 4 figures

We report real-time average stress measurements on composite silicon electrodes made with two different binders [Carboxymethyl cellulose (CMC), and polyvinylidene fluoride (PVDF)] during electrochemical lithiation and delithiation. During galvanostatic lithiation at very slow rates, the stress in a CMC-based electrode becomes compressive and increases to 70 MPa, where it reaches a plateau and increases slowly thereafter with capacity. The PVDF-based electrode exhibits similar behavior, although with lower peak compressive stress of about 12 MPa. These initial experiments indicate that the stress evolution in a Si composite electrode depends strongly on the mechanical properties of the binder. Stress data obtained from a series of lithiation/delithiation cycles suggests plasticity induced irreversible shape changes in contacting Si particles, and as a result, the stress response of the system during any given lithiation/delithiation cycle depends on the cycling history of the electrode. While these results constitute the first in-situ stress measurements on composite Si electrodes during electrochemical cycling, the diagnostic technique described herein can be used to assess the mechanical response of a composite electrode made with other active material/binder combinations., Comment: 22 pages, 8 figures

Two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs) can withstand a large deformation without fracture or inelastic relaxation, making them attractive for application in novel strain-engineered and flexible electronic and optoelectronic devices. In this study, we characterize the mechanical response of monolayer group VI TMDs to large elastic deformation using first-principles density functional theory calculations. We find that the ultimate strength and the overall stress response of these 2D materials is strongly influenced by their chemical composition and loading direction. We demonstrate that differences in the observed mechanical behavior can be attributed to the spatial redistribution of the occupied hybridized electronic states in the region between the transition metal atom and the chalcogens. In spite of the strong covalent bonding between the transition metal and the chalcogens, we find that a simple linear relationship can be established to describe the dependence of the mechanical strength on the charge transfer from the transition metal atom to the chalcogens.

Charge lost per unit surface area of a silicon electrode due to the formation of solid-electrolyte-interphase (SEI) layer during initial lithiation was quantified, and the species that constitute this layer were identified. Coin cells made with Si thin-film electrodes were subjected to a combination of galvanostatic and potentiostatic lithiation and delithiation cycles to accurately measure the capacity lost to SEI-layer formation. While the planar geometry of amorphous thin films allows accurate calculation of surface area, creation of additional surface by cracking was prevented by minimizing the thickness of the Si film. The cycled electrodes were analyzed with X-ray photoelectron spectroscopy to characterize the composition of the SEI layer. The charge lost due to SEI formation measured from coin cell experiments was found to be in good agreement with the first-cycle capacity loss during the initial lithiation of a Si (100) crystal with planar geometry. The methodology presented in this work is expected to provide a useful practical tool for battery-material developers in estimating the expected capacity loss due to first cycle SEI-layer formation and in choosing an appropriate particle size distribution that balances mechanical integrity and the first cycle capacity loss in large volume expansion electrodes for lithium-ion batteries., Comment: 15 pages, 9 figures; Journal of Power Sources, 2012

We have studied lithiation of graphene oxide (GO) as a function of oxygen coverage using first principles calculations. Our results show that the lithiation potentials and capacities in GO can be tuned by controlling the oxygen coverage, or the degree of reduction. We find a range of coverages where the lithiation potentials are above the solid electrolyte interface (SEI) formation threshold, but with capacities comparable to, or larger than graphite. We observe that in highly oxidized and mildly reduced sheets, lithiation occurs through the formation of Li-O bonds, whereas at low coverages that are typical of reduced-GO (rGO) (O:C - 12.5 %), both Li-O bonds and LiC6 configurations are observed. The covalent Li-O bond is much stronger than the bonds formed in the LiC6 ring and the lithiation potentials for epoxides at high and medium coverages are generally large (> 1 eV). For these congifurations, as in the case of Li4Ti5O12 anodes, there will be no formation of SEI, but with the additional advantage of having higher lithium storage capacity than Li4Ti5O12. In reduced GO sheets, the presence of residual oxygen atoms allows for formation of covalent Li-O bonds that lead to storage capacities and lithiation potentials higher than that of graphite. Finally, our calculations show high lithiation potentials for the edges of graphene nanoribbons, which will impede the formation of SEI and hence lead to large reversible capacity., Comment: 18 pages, 8 figure sets

We have carried out first-principles calculations on electronic properties of graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The calculations with density functional theory show that the band gaps of quantum dots are determined by the quantum confinement effects and the hybridization of {\pi} orbitals from B, N and C atoms. The energy states near the Fermi level are found to be strongly localized within and in the vicinity of the quantum dots.

We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which in turn causes to the deformation of the filaments. With increasing applied strain, the filaments further deform leading to a stiffened elastic response. When the crosslinks are incompliant, the contractile forces due to motors do not alter the network morphology in a significant manner and hence only small stiffening is observed., Comment: 4 pages, 5 figures

Using molecular dynamics simulations and first principles calculations, we have studied the structure and mechanical strength of tilt grain boundaries in graphene sheets that arise during CVD growth of graphene on metal substrates. Surprisingly, we find that for tilt boundaries in the vicinity of both the zig-zag and arm-chair orientations, large angle boundaries with a higher density of 5-7 defect pairs are stronger than the low-angle boundaries which are comprised of fewer defects per unit length. Interestingly, the trends in our results cannot be explained by a continuum Griffith-type fracture mechanics criterion, which predicts the opposite trend due to that fact that it does not account for the critical bonds that are responsible for the failure mechanism. We have identified the highly-strained bonds in the 7-member rings that lead to the failure of the sheets, and we have found that large angle boundaries are able to better accommodate the strained 7-rings. Our results provide guidelines for designing growth methods to obtain grain boundary structures that can have strengths close to that of pristine graphene.

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in the "two-fluid" model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can also enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network. The nature of these boundary conditions significantly impacts swimming speeds., Comment: 6 pages, 5 figures, submitted to EPL

In the technique of microrheology, macroscopic rheological parameters as well as information about local structure are deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the relation between macroscopic parameters and the force felt by a particle in response to displacements. We investigate this response function for a spherical particle using the two-fluid model, in which the gel is represented by a polymer network coupled to a surrounding solvent via a drag force. We obtain an analytic solution for the response function in the limit of small volume fraction of the polymer network, and neglecting inertial effects. We use no-slip boundary conditions for the solvent at the surface of the sphere. The boundary condition for the network at the surface of the sphere is a kinetic friction law, for which the tangential stress of the network is proportional to relative velocity of the network and the sphere. This boundary condition encompasses both no-slip and frictionless boundary conditions as limits. Far from the sphere there is no relative motion between the solvent and network due to the coupling between them. However, the different boundary conditions on the solvent and network tend to produce different far-field motions. We show that the far field motion and the force on the sphere are controlled by the solvent boundary conditions at high frequency and by the network boundary conditions at low frequency. At low frequencies compression of the network can also affect the force on the sphere. We find the crossover frequencies at which the effects of sliding of the sphere past the polymer network and compression of the gel become important., Comment: Corrected expressions for crossover frequencies on page 2