Advances in biomimetic collagen mineralisation and future approaches to bone tissue engineering.

With an ageing world population and ~20% of adults in Europe being affected by bone diseases, there is an urgent need to develop advanced regenerative approaches and biomaterials capable to facilitate tissue regeneration while providing an adequate microenvironment for cells to thrive. As the main components of bone are collagen and apatite mineral, scientists in the tissue engineering field have attempted in combining these materials by using different biomimetic approaches to favour bone repair. Still, an ideal bone analogue capable of mimicking the distinct properties (i.e., mechanical properties, degradation rate, porosity, etc.) of cancellous bone is to be developed. This review seeks to sum up the current understanding of bone tissue mineralisation and structure while providing a critical outlook on the existing biomimetic strategies of mineralising collagen for bone tissue engineering applications, highlighting where gaps in knowledge exist.

Coarse graining in time with the functional renormalization group: Relaxation in Brownian motion.

We apply the functional renormalization group (fRG) to study relaxation in a stochastic process governed by an overdamped Langevin equation with one degree of freedom, exploiting the connection with supersymmetric quantum mechanics in imaginary time. After reviewing the functional integral formulation of the system and its underlying symmetries, including the resulting Ward-Takahashi identities for arbitrary initial conditions, we compute the effective action Γ from the fRG, approximated in terms of the leading and subleading terms in the gradient expansion: the local potential approximation and wave-function renormalization, respectively. This is achieved by coarse graining the thermal fluctuations in time resulting in, e.g., an effective potential incorporating fluctuations at all timescales. We then use the resulting effective equations of motion to describe the decay of the covariance and the relaxation of the average position and variance toward their equilibrium values at different temperatures. We use as examples a simple polynomial potential, an unequal Lennard-Jones type potential, and a more complex potential with multiple trapping wells and barriers. We find that these are all handled well, with the accuracy of the approximations improving as the relaxation's spectral representation shifts to lower eigenvalues, in line with expectations about the validity of the gradient expansion. The spectral representation's range also correlates with temperature, leading to the conclusion that the gradient expansion works better for higher temperatures than lower ones. This paper demonstrates the ability of the fRG to expedite the computation of statistical objects in otherwise long-timescale simulations, acting as a first step to more complicated systems.

Long-term creep deformations in colloidal calcium-silicate-hydrate gels by accelerated aging simulations.

When subjected to a sustained load, jammed colloidal gels can feature some delayed viscoplastic creep deformations. However, due to the long timescale of creep (up to several years), its modeling and, thereby, prediction has remained challenging. Here, based on mesoscale simulations of calcium-silicate-hydrate gels (CSH, the binding phase of concrete), we present an accelerated simulation method-based on stress perturbations and overaging-to model creep deformations in CSH. Our simulations yield a very good agreement with nanoindentation creep tests, which suggests that concrete creep occurs through the reorganization of CSH grains at the mesoscale. We show that the creep of CSH exhibits a logarithmic dependence on time-in agreement with the free-volume theory of granular physics. Further, we demonstrate the existence of a linear regime, i.e., wherein creep linearly depends on the applied load-which establishes the creep modulus as a material constant. These results could offer a new physics-based basis for nanoengineering colloidal gels featuring minimal creep.

Capillary Stress and Structural Relaxation in Moist Granular Materials.

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

Atomistic Simulations of Geopolymer Models: The Impact of Disorder on Structure and Mechanics.

Geopolymers are hydrated aluminosilicates with excellent binding properties. Geopolymers appeal to the construction sector as a more sustainable alternative to traditional cements, but their exploitation is limited by a poor understanding of the linkage between chemical composition and macroscopic properties. Molecular simulations can help clarify this linkage, but existing models based on amorphous or crystalline aluminosilicate structures provide only a partial explanation of experimental data on the nanoscale. This paper presents a new model for the molecular structure of geopolymers, in particular for nanoscale interfacial zones between crystalline and amorphous nanodomains, which are crucial for the overall mechanical properties of the material. For a range of Si-Al molar ratios and water contents, the proposed structures are analyzed in terms of skeletal density, ring structure, pore structure, bond-angle distribution, bond length distribution, X-ray diffraction, X-ray pair distribution function, elastic moduli, and large-strain mechanics. Results are compared with experimental data and with other simulation results for amorphous and crystalline molecular models, showing that the newly proposed structures better capture important structural features with an impact on mechanical properties. This offers a new starting point for the multiscale modeling of geopolymers.

Topological Control on the Structural Relaxation of Atomic Networks under Stress.

Upon loading, atomic networks can feature delayed irreversible relaxation. However, the effect of composition and structure on relaxation remains poorly understood. Herein, relying on accelerated molecular dynamics simulations and topological constraint theory, we investigate the relationship between atomic topology and stress-induced structural relaxation, by taking the example of creep deformations in calcium silicate hydrates (C─S─H), the binding phase of concrete. Under constant shear stress, C─S─H is found to feature delayed logarithmic shear deformations. We demonstrate that the propensity for relaxation is minimum for isostatic atomic networks, which are characterized by the simultaneous absence of floppy internal modes of relaxation and eigenstress. This suggests that topological nanoengineering could lead to the discovery of nonaging materials.

Mesoscale texture of cement hydrates.

Strength and other mechanical properties of cement and concrete rely upon the formation of calcium-silicate-hydrates (C-S-H) during cement hydration. Controlling structure and properties of the C-S-H phase is a challenge, due to the complexity of this hydration product and of the mechanisms that drive its precipitation from the ionic solution upon dissolution of cement grains in water. Departing from traditional models mostly focused on length scales above the micrometer, recent research addressed the molecular structure of C-S-H. However, small-angle neutron scattering, electron-microscopy imaging, and nanoindentation experiments suggest that its mesoscale organization, extending over hundreds of nanometers, may be more important. Here we unveil the C-S-H mesoscale texture, a crucial step to connect the fundamental scales to the macroscale of engineering properties. We use simulations that combine information of the nanoscale building units of C-S-H and their effective interactions, obtained from atomistic simulations and experiments, into a statistical physics framework for aggregating nanoparticles. We compute small-angle scattering intensities, pore size distributions, specific surface area, local densities, indentation modulus, and hardness of the material, providing quantitative understanding of different experimental investigations. Our results provide insight into how the heterogeneities developed during the early stages of hydration persist in the structure of C-S-H and impact the mechanical performance of the hardened cement paste. Unraveling such links in cement hydrates can be groundbreaking and controlling them can be the key to smarter mix designs of cementitious materials.

Nano-scale mechanics of colloidal C-S-H gels.

Gels of calcium-silicate-hydrates (C-S-H) are the glue that is largely responsible for the mechanical properties of cement. Despite their practical relevance, their nano-scale structure and mechanics are still mainly unexplored, because of the difficulties in characterizing them in a complex material like cement. We propose a colloidal model to investigate the gel mechanics emerging in the critical range of length-scales from several tens to hundreds of nanometers. We show that the size polydispersity of the hydrates and size-dependent effective interactions can explain the mechanical heterogeneities detected in nano-indentation experiments. We also show how these features control the arising of irreversible structural rearrangements under deformation, which are good candidates as nano-scale mechanisms underlying mechanical aging and slow structural relaxation in the gels.