Fluctuation-based fracture mechanics of heterogeneous materials.

We present results of a hybrid analytical-simulation investigation of the fracture resistance of heterogeneous materials. We show that bond-energy fluctuations sampled by Monte Carlo simulations in the semigrand canonical ensemble provide a means to rationalize the complexity of heterogeneous fracture processes, encompassing probability and percolation theories of fracture. For a number of random and textured model materials, we derive upper and lower bounds of fracture resistance and link bond fracture fluctuations to statistical descriptors of heterogeneity, such as two-point correlation functions, to identify the origin of toughening mechanisms. This includes a shift from short- to long-range interactions of bond fracture processes in random systems to the transition from critical to subcritical bond fracture percolation in textured materials and the activation of toughness reserves at compliant interfaces. Induced by elastic mismatch, they connect to a number of disparate experimental observations, including toughening of brittle solids by deformable polymers or organics in, e.g., gas shale, nacre; stress-induced transformational toughening in ceramics; and toughening of sparse elastic networks in hydrogels, to name a few.

Phase diagram of brittle fracture in the semi-grand-canonical ensemble.

We present a simulation method to assess the quasistatic fracture resistance of materials. Set within a semi-grand-canonical Monte Carlo (SGCMC) simulation environment, an auxiliary field-the bond rupture potential-is introduced to generate a sufficiently large number of possible microstates in the semi-grand-canonical ensemble, and associated energy and bond fluctuations. The SGCMC approach permits identifying the full phase diagram of brittle fracture for harmonic and nonharmonic bond potentials, analogous to the gas-liquid phase diagram, with the equivalent of a liquidus line ending in a critical point. The phase diagram delineates a solid phase, a fractured phase, and a gas phase, and provides clear evidence of a first-order phase transition intrinsic to fracture. Moreover, energy and bond fluctuations generated with the SGCMC approach permit determination of the maximum energy dissipation associated with bond rupture, and hence of the fracture resistance of a widespread range of materials that can be described by bond potentials.

Multiscale poromechanics of wet cement paste.

Capillary effects, such as imbibition drying cycles, impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, which is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidity is obtained using a lattice gas density functional method together with a realistic nanogranular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well with nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Second, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nanograins assembly were identified due to liquid-solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nanometers. Third, the Love-Weber method provided the homogenized liquid stress at the micrometer scale. The homogenization length coincided with the spatial correlation length of nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micrometer-scale texture is not affected by mild drying, while nanoscale irreversible deformations still occur. These results pave the way for understanding capillary phenomena-induced stresses in heterogeneous porous media ranging from construction materials to hydrogels and living systems.

Role of City Texture in Urban Heat Islands at Nighttime.

An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture-measured by a building distribution function and the sky view factor-explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

Combinatorial molecular optimization of cement hydrates.

Despite its ubiquitous presence in the built environment, concrete's molecular-level properties are only recently being explored using experimental and simulation studies. Increasing societal concerns about concrete's environmental footprint have provided strong motivation to develop new concrete with greater specific stiffness or strength (for structures with less material). Herein, a combinatorial approach is described to optimize properties of cement hydrates. The method entails screening a computationally generated database of atomic structures of calcium-silicate-hydrate, the binding phase of concrete, against a set of three defect attributes: calcium-to-silicon ratio as compositional index and two correlation distances describing medium-range silicon-oxygen and calcium-oxygen environments. Although structural and mechanical properties correlate well with calcium-to-silicon ratio, the cross-correlation between all three defect attributes reveals an indentation modulus-to-hardness ratio extremum, analogous to identifying optimum network connectivity in glass rheology. We also comment on implications of the present findings for a novel route to optimize the nanoscale mechanical properties of cement hydrate.

Order and disorder in calcium-silicate-hydrate.

Despite advances in the characterization and modeling of cement hydrates, the atomic order in Calcium-Silicate-Hydrate (C-S-H), the binding phase of cement, remains an open question. Indeed, in contrast to the former crystalline model, recent molecular models suggest that the nanoscale structure of C-S-H is amorphous. To elucidate this issue, we analyzed the structure of a realistic simulated model of C-S-H, and compared the latter to crystalline tobermorite, a natural analogue of C-S-H, and to an artificial ideal glass. The results clearly indicate that C-S-H appears as amorphous, when averaged on all atoms. However, an analysis of the order around each atomic species reveals that its structure shows an intermediate degree of order, retaining some characteristics of the crystal while acquiring an overall glass-like disorder. Thanks to a detailed quantification of order and disorder, we show that, while C-S-H retains some signatures of a tobermorite-like layered structure, hydrated species are completely amorphous.

Nanostructure and nanomechanics of cement: polydisperse colloidal packing.

Cement setting and cohesion are governed by the precipitation and growth of calcium-silicate-hydrate, through a complex evolution of microstructure. A colloidal model to describe nucleation, packing, and rigidity of calcium-silicate-hydrate aggregates is proposed. Polydispersity and particle size dependent cohesion strength combine to produce a spectrum of packing fractions and of corresponding elastic properties that can be tested against nanoindentation experiments. Implications regarding plastic deformations and reconciling current structural characterizations are discussed.

Thermodynamics of water confined in porous calcium-silicate-hydrates.

Water within pores of cementitious materials plays a crucial role in the damage processes of cement pastes, particularly in the binding material comprising calcium-silicate-hydrates (C-S-H). Here, we employed Grand Canonical Monte Carlo simulations to investigate the properties of water confined at ambient temperature within and between C-S-H nanoparticles or "grains" as a function of the relative humidity (%RH). We address the effect of water on the cohesion of cement pastes by computing fluid internal pressures within and between grains as a function of %RH and intergranular separation distance, from 1 to 10 Å. We found that, within a C-S-H grain and between C-S-H grains, pores are completely filled with water for %RH larger than 20%. While the cohesion of the cement paste is mainly driven by the calcium ions in the C-S-H, water facilitates a disjoining behavior inside a C-S-H grain. Between C-S-H grains, confined water diminishes or enhances the cohesion of the material depending on the intergranular distance. At very low %RH, the loss of water increases the cohesion within a C-S-H grain and reduces the cohesion between C-S-H grains. These findings provide insights into the behavior of C-S-H in dry or high-temperature environments, with a loss of cohesion between C-S-H grains due to the loss of water content. Such quantification provides the necessary baseline to understand cement paste damaging upon extreme thermal, mechanical, and salt-rich environments.

Molecular simulation of nitrogen adsorption in nanoporous silica.

This article reports on a molecular simulation study of nitrogen adsorption and condensation at 77 K in atomistic silica cylindrical nanopores (MCM-41). Two models are considered for the nitrogen molecule and its interaction with the silica substrate. In the "pea" model, the nitrogen molecule is described as a single Lennard-Jones sphere and only Lennard-Jones interactions between the nitrogen molecule and the oxygens atoms of the silica substrate are taken into account. In the "bean" model (TraPPE force field), the nitrogen molecule is composed of two Lennard-Jones sites and a linear array of three charges on the atomic positions and at the center of the nitrogen-nitrogen bond. In the bean model, the interactions between the sites on the nitrogen molecule and the Si, O, and H atoms of the substrate are the sum of the Coulombic and dispersion interactions with a repulsive short-range contribution. The data obtained with the pea and bean models in silica nanopores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical MCM-41 nanopores; the adsorbed amount increases continuously in the multilayer adsorption regime until an irreversible jump occurs because of capillary condensation and evaporation of the fluid within the pore. Our results suggest that the pea model can be used for characterization purposes where one is interested in capturing the global experimental behavior upon adsorption and desorption in silica nanopores. However, the bean model is more suitable to investigating the details of the interaction with the surface because this model, which accounts for the partial charges located on the nitrogen atoms of the molecule (quadrupole), allows a description of the specific interactions between this adsorbate and silica surfaces (silanol groups and siloxane bridges) or grafted silica surfaces. In particular, the bean model provides a more realistic picture of nitrogen adsorption in the vicinity of silica surfaces or confined in silica nanopores, where the isosteric heat of adsorption curves show that the nitrogen molecule in this model is sensitive to the surface heterogeneity.

Molecular simulation of water confined in nanoporous silica.

This paper reports on a molecular simulation study of the thermodynamics, structure and dynamics of water confined at ambient temperature in hydroxylated silica nanopores of a width H = 10 and 20 Å. The adsorption isotherms for water in these nanopores resemble those observed for experimental samples; the adsorbed amount increases continuously in the multilayer adsorption regime until a jump occurs due to capillary condensation of the fluid within the pore. Strong layering of water in the vicinity of the silica surfaces is observed as marked density oscillations are observed up to 8 Å from the surface in the density profiles for confined water. Our results indicate that water molecules within the first adsorbed layer tend to adopt a H-down orientation with respect to the silica substrate. For all pore sizes and adsorbed amounts, the self-diffusivity of confined water is lower than the bulk, due to the hydrophilic interaction between the water molecules and the hydroxylated silica surface. Our results also suggest that the self-diffusivity of confined water is sensitive to the adsorbed amount.

Zinc oxide nanostructures confined in porous silicas.

We report on molecular simulations of zinc oxide nanostructures obtained within silica nanopores of diameter D = 1.6 nm and D = 3.2 nm. Both the effects of confinement (by varying the pore size) and degree of pore filling on the structure of the nanomaterial are addressed. Two complementary approaches are adopted: 1) the stability of the three crystalline phases of ZnO (wurtzite, rocksalt, and blende) in the silica nanopores is studied, and 2) ZnO nanostructures are obtained by slowly cooling down a homogeneous liquid phase confined in the silica pores. None of the ideal nanostructures (wurtzite, rocksalt, blende) retains the ideal structure of the initial crystal when confined within the silica pores. Only the structure starting from the ideal wurtzite nanocrystal remains significantly crystalline after relaxation, as revealed by the marked peaks in the pair correlation functions for this system. The morphology and degree of cristallinity of the structures are found to depend on the parameters involved in the synthesis (pore size, filling density). Nanograin boundaries are observed between domains of different crystal structures. Reminiscent features of the bulk behavior, such as faceting of the nanostructures, are also observed when the system size becomes large. We show that the use of nanopores as a template imposes that the confined particles exhibit neutral (basal) surfaces. These predictions provide a guide to experiments on semiconductor nanoparticles.

Thermodynamic and neutron scattering study of hydrogen adsorption in two mesoporous ordered carbons.

Two mesoporous ordered carbon materials (MOCs) have been synthesized from silica templates by using sucrose as the carbon precursor. The textural characterization using Ar, N2, and CO2 adsorption combined with neutron diffraction showed that the two samples exhibit a significant microporous volume close to 0.5 cm3/g and an ordered network of mesopores. For both MCM48 and SBA15 templated carbons, adsorption first proceeds with the filling of micropores and then by the filling of mesopores with an adsorption energy close to the enthalpy of vaporization of bulk hydrogen. The hydrogen isosteric heat of adsorption in the micropores (6-8 kJ/mol) is significantly larger than that on the graphite surface (approximately 4 kJ/mol) but still too small for a reasonable use of these MOCs as hydrogen adsorbents for storage at room temperature. The neutron scattering study showed that the structure at 10 K of the adsorbed deuterium phase is poorly organized; it exhibits short and medium range orders of about 13 angstroms in micropores and about 20 angstroms in mesopores, respectively. The average distance between adsorbed molecules decreases with coverage by about 10%. In the mesopores, the diffracted line is consistent with a pseudohexagonal packing.

A search for a strong physisorption site for H2 in Li-doped porous carbons.

The mechanism of hydrogen absorption between two coronene molecules has been studied by first principle calculations. Examination of different sites for H(2) molecule confirmed the classical picture of physisorption. We have also considered molecular hydrogen adsorption in a charged carbon structure achieved by doping with lithium at a density corresponding to the intercalate compound LiC(6). We have performed different types of calculations [Hartree-Fock and density functional theory (DFT)] for various atomic basis sets using CRYSTAL98, GAUSSIAN98, and DMOL3 codes. B3LYP-DFT (B3LYP-three-parameter functional of Backe, Lee, Yang and Parr) energy minimization calculations unravel that there is a stable adsorption site for molecular hydrogen in Li-doped sp(2) carbon structure. These calculations also give an insight into the atomic configurations of interlayer species (H(2) and Li) as the interlayer spacing increases. It can be shown that large changes occur in the positions and electronic properties of interlayer species. Hydrogen molecule does not show any tendency for dissociation and adopts a position in the interlayer void that is deeply related to that of lithium ions. We have evidenced a rather large charge transfer from lithium and capping hydrogen species on neighboring slab carbon atoms that induce the stabilization of molecular hydrogen. We have also found that rotating one carbon layer with respect to the other one (at constant interlayer distance) does not change the adsorption energy to a large extent. The best adsorption site is about five times deeper than the physisorption site found in the undoped case and occurs at an interlayer separation of 5.5+/-0.5 A. The corresponding atomic configuration consists in a hydrogen molecule standing (nearly) perpendicular to the plane surface surrounded by the three lithium ions in a configuration close to that of the LiC(6) intercalation compound.

A grand canonical Monte Carlo study of capillary condensation in mesoporous media: effect of the pore morphology and topology.

We study by means of Grand Canonical Monte Carlo simulations the condensation and evaporation of argon at 77 K in nanoporous silica media of different morphology or topology. For each porous material, our results are compared with data obtained for regular cylindrical pores. We show that both the filling and emptying mechanisms are significantly affected by the presence of a constriction. The simulation data for a constricted pore closed at one end reproduces the asymmetrical shape of the hysteresis loop that is observed for many real disordered porous materials. The adsorption process is a quasicontinuous mechanism that corresponds to the filling of the different parts of the porous material, cavity, and constriction. In contrast, the desorption branch for this pore closed at one end is brutal because the evaporation of Ar atoms confined in the largest cavity is triggered by the evaporation of the fluid confined in the constriction (which isolates the cavity from the gas reservoir). This evaporation process conforms to the classical picture of "pore blocking effect" proposed by Everett many years ago. We also simulate Ar adsorption in a disordered porous medium, which mimics a Vycor mesoporous silica glass. The adsorption isotherm for this disordered porous material having both topological and morphological defects presents the same features as that for the constricted pore (quasicontinuous adsorption and steep desorption process). However, the larger degree of disorder of the Vycor surface enhances these main characteristics. Finally, we show that the effect of the disorder, topological and/or morphological, leads to a significant lowering of the capillary condensation pressure compared to that for regular cylindrical nanopores. Also, our results suggest that confined fluids isolated from the bulk reservoir evaporate at a pressure driven by the smallest size of the pore.

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness.

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.

Confinement effect on thermodynamic and structural properties of water in hydrophilic mesoporous silica.

The adsorption of water on porous silica surfaces at 300 K, has been qualitatively reproduced by Grand Canonical Monte Carlo simulations (GCMC) without any adjustment of adsorbate/substrate potential parameter. The simulated adsorption isotherm and isosteric differential enthalpy of adsorption compare well to experimental data for Vycor, showing the ability of the model in describing hydrophilic properties of silica surfaces. The analysis of fluid structure in the mesoporous glass gives detailed insights into confinement and disorder effects on water adsorbed on the hydrophilic surface of a porous glass. It is shown that hydrophilic properties are not simply related to surface hydroxyl density but are also related to local structure of the silica surface.