Mathematical models of apparent viscosity as a function of water-cement/binder ratio and superplasticizer in cement pastes.

The water-cement/binder ratio and the admixture of water-reducing agents strongly affect the rheological properties of cement pastes. This study develops mathematical models to predict the apparent viscosity of cement pastes with varying water-cement/binder ratios and polycarboxylate-based superplasticizer content by introducing the power law shear stress-shear strain relation of non-Newtonian fluids into the Navier-Stokes motion equations. The developed models are compared with the results of rheological experiments and verified for their accuracy in simulating the apparent viscosity of cement pastes. These models provide insight into the rheological behaviour of cement pastes and could have practical applications in the construction industry.

Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach.

Thermal loading, especially in fire scenarios, challenges the safety and long-term durability of concrete structures. The resulting heat propagation within the structure is governed by the heat conduction equation, which can be difficult to solve analytically because of the nonlinearity related to the thermophysical properties of concrete. A semi-analytical approach for the transient nonlinear heat conduction problem in concrete structures was established in the present work. The nonlinearity related to the temperature-dependent thermal conductivity, mass density, and specific heat capacity of heated concrete was taken into consideration. A Taylor series approximate solution was first established within a small neighborhood, employing the Boltzmann transformation in combination with the mean value theorem. Thereafter, it was extended to the whole domain by utilizing the Bernstein polynomial. The semi-analytical approach was validated by comparing it with the numerical results of two independent Finite Element simulations of nonlinear heat conduction along concrete plates, subjected to either moderate or fierce thermal loading. Absolute values of the relative errors are smaller than 5%. The validated semi-analytical approach was further applied to prediction of the temporal evolution of the temperature field of a scaled model of a subway station, subjected to fire disaster. The nonlinearities, related to the time-dependent surface temperature and the temperature-dependent thermophysical properties of concrete, were taken into consideration. The predictions agree well with the experimental measurements. The established semi-analytical approach exhibits good accuracy and stability, providing insight into the interaction between the thermophysical properties of concrete in the heat conduction process.

Silicate Dissolution Mechanism from Metakaolinite Using Density Functional Theory.

Metakaolin (MK) is a high-quality, reactive nanomaterial that holds promising potential for large-scale use in improving the sustainability of cement and concrete production. It can replace cement due to its pozzolanic reaction with calcium hydroxide and water to form cementitious compounds. Therefore, understanding the dissolution mechanism is crucial to fully comprehending its pozzolanic reactivity. In this study, we present an approach for computing the activation energies required for the dissolution of metakaolin (MK) silicate units at far-from-equilibrium conditions using the improved dimer method (IDM) and the transition-state theory (TST) within density functional theory (DFT). Four different models were prepared to calculate the activation energies required for breaking oxo-bridging bonds between silicate or aluminate units. Our results showed that the activation energy for breaking the oxo-bridging bond to a silicate neighbor is higher than that to an aluminate neighbor due to the ionic interaction. However, for complete silicate tetrahedra dissolution, a higher activation energy is required for breaking the oxo-bridging bond to the aluminate neighbor compared to the silicate neighbor. The findings provide methodology for missing input data to predict the mesoscopic dissolution rate, e.g., by the atomistic kinetic Monte Carlo (KMC) upscaling approach.

3D Off-Lattice Coarse-Grained Monte Carlo Simulations for Nucleation of Alkaline Aluminosilicate Gels.

This work presents a 3D off-lattice coarse-grained Monte Carlo (CGMC) approach to simulate the nucleation of alkaline aluminosilicate gels, their nanostructure particle size, and their pore size distribution. In this model, four monomer species are coarse-grained with different particle sizes. The novelty is extending the previous on-lattice approach from White et al. (2012 and 2020) by implementing a full off-lattice numerical implementation to consider tetrahedral geometrical constraints when aggregating the particles into clusters. Aggregation of the dissolved silicate and aluminate monomers was simulated until reaching the equilibrium condition of 16.46% and 17.04% in particle number, respectively. The cluster size formation was analyzed as a function of iteration step evolution. The obtained equilibrated nano-structure was digitized to obtain the pore size distribution and this was compared with the on-lattice CGMC and measurement results from White et al. The observed difference highlighted the importance of the developed off-lattice CGMC approach to better describe the nanostructure of aluminosilicate gels.

Coarse-Grained Monte Carlo Simulations with Octree Cells for Geopolymer Nucleation at Different pH Values.

Geopolymers offer a potential alternative to ordinary Portland cement owing to their performance in mechanical and thermal properties, as well as environmental benefits stemming from a reduced carbon footprint. This paper endeavors to build upon prior atomistic computational work delving deeper into the intricate relationship between pH levels and the resulting material's properties, including pore size distribution, geopolymer nucleate cluster dimensions, total system energy, and monomer poly-condensation behavior. Coarse-grained Monte Carlo (CGMC) simulation inputs include tetrahedral geometry and binding energy parameters derived from DFT simulations for aluminate and silicate monomers. Elevated pH values may can alter reactivity and phase stability, or, in the structural concrete application, may passivate the embedded steel reinforcement. Thus, we examine the effects of pH values set at 11, 12, and 13 (based on silicate speciation chemistry), investigating their respective contributions to the nucleation of geopolymers. To simulate a larger system to obtain representative results, we propose the numerical implementation of an Octree cell. Finally, we further digitize the resulting expanded structure to ascertain pore size distribution, facilitating a comparative analysis. The novelty of this study is underscored by its expansion in both system size, more accurate monomer representation, and pH range when compared to previous CGMC simulation approaches. The results unveil a discernible correlation between the number of clusters and pores under specific pH levels. This links geopolymerization mechanisms under varying pH conditions to the resulting chemical properties and final structural state.

Thermodynamic Modeling and Experimental Validation of Acetic Acid Attack on Hardened Cement Paste: Effect of Silica Fume.

Concrete structures are increasingly becoming exposed to organic acid attack conditions, such as those found in agriculture and food-related industries. This paper aims to experimentally verify the thermodynamic modeling of cement pastes under acetic acid attack. For this, a modeling approach implemented in IPHREEQC via Matlab is described, and results are compared with measured pH and compositions of equilibrated solutions (MP-AES) as well as unreacted/precipitated solids (XRF, XRD and STA) for a wide range of acid concentrations. The 11% replacement of cement by silica fume (SF) led to a 60 or 70% reduction (measured or modeled, respectively) of Portlandite content in the hardened cement paste due to the pozzolanic reaction resulting in higher content of CSH phases, which has effects on the progression of dissolution processes and a resulting pH with increased acid concentrations. Considering that no fitting parameter was used, the model predictions showed good agreement with measured values of pH, dissolved ion concentrations and composition of the remaining (degraded) solids overall. The discrepancies here were more pronounced at very high acid concentrations (equilibrium pH < ~4), i.e., after the full dissolution of hydrate phases due to limitations in the model used to describe Al-, Si- and Fe-gel phases and/or identified experimental challenges in precipitation of calcium and aluminum acetate hydrates.

Dissolution of ß-C2S Cement Clinker: Part 2 Atomistic Kinetic Monte Carlo (KMC) Upscaling Approach.

Cement clinkers containing mainly belite (ß-C2S as a model crystal), replacing alite, offer a promising solution for the development of environmentally friendly solutions to reduce the high level of CO2 emissions in the production of Portland cement. However, the much lower reactivity of belite compared to alite limits the widespread use of belite cements. Therefore, this work presents a fundamental atomistic computational approach for comprehending and quantifying the mesoscopic forward dissolution rate of ß-C2S, applied to two reactive crystal facets of (100) and (1¯00). For this, an atomistic kinetic Monte Carlo (KMC) upscaling approach for cement clinker was developed. It was based on the calculated activation energies (ΔG*) under far-from-equilibrium conditions obtained by a molecular dynamic simulation using the combined approach of ReaxFF and metadynamics, as described in the Part 1 paper in this Special Issue. Thus, the individual atomistic dissolution rates were used as input parameters for implementing the KMC upscaling approach coded in MATLAB to study the dissolution time and morphology changes at the mesoscopic scale. Four different cases and 21 event scenarios were considered for the dissolution of calcium atoms (Ca) and silicate monomers. For this purpose, the (100) and (1¯00) facets of a ß-C2S crystal were considered using periodic boundary conditions (PBCs). In order to demonstrate the statistical nature of the KMC approach, 40 numerical realizations were presented. The major findings showed a striking layer-by-layer dissolution mechanism in the case of an ideal crystal, where the total dissolution rate was limited by the much slower dissolution of the silicate monomer compared to Ca. The introduction of crystal defects, namely cutting the edges at two crystal boundaries, increased the overall average dissolution rate by a factor of 519.

Dissolution of ß-C2S Cement Clinker: Part 1 Molecular Dynamics (MD) Approach for Different Crystal Facets.

A major concern in the modern cement industry is considering how to minimize the CO2 footprint. Thus, cements based on belite, an impure clinker mineral (CaO)2SiO2 (C2S in cement chemistry notation), which forms at lower temperatures, is a promising solution to develop eco-efficient and sustainable cement-based materials, used in enormous quantities. The slow reactivity of belite plays a critical role, but the dissolution mechanisms and kinetic rates at the atomistic scale are not known completely yet. This work aims to understand the dissolution behavior of different facets of ß-C2S providing missing input data and an upscaling modeling approach to connect the atomistic scale to the sub-micro scale. First, a combined ReaxFF and metadynamics-based molecular dynamic approach are applied to compute the atomistic forward reaction rates (RD) of calcium (Ca) and silicate species of (100) facet of ß-C2S considering the influence of crystal facets and crystal defects. To minimize the huge number of atomistic events possibilities, a generalized approach is proposed, based on the systematic removal of nearest neighbors' crystal sites. This enables us to tabulate data on the forward reaction rates of most important atomistic scenarios, which are needed as input parameters to implement the Kinetic Monte Carlo (KMC) computational upscaling approach. The reason for the higher reactivity of the (100) facet compared to the (010) is explained.

Dissolution of Portlandite in Pure Water: Part 1 Molecular Dynamics (MD) Approach.

The current contribution proposes a multi-scale bridging modeling approach for the dissolution of crystals to connect the atomistic scale to the (sub-) micro-scale. This is demonstrated in the example of dissolution of portlandite, as a relatively simple benchmarking example for cementitious materials. Moreover, dissolution kinetics is also important for other industrial processes, e.g., acid gas absorption and pH control. In this work, the biased molecular dynamics (metadynamics) coupled with reactive force field is employed to calculate the reaction path as a free energy surface of calcium dissolution at 298 K in water from the different crystal facets of portlandite. It is also explained why the reactivity of the (010), (100), and (11¯0) crystal facet is higher compared to the (001) facet. In addition, the influence of neighboring Ca crystal sites arrangements on the atomistic dissolution rates is explained as necessary scenarios for the upscaling. The calculated rate constants of all atomistic reaction scenarios provided an input catalog ready to be used in an upscaling kinetic Monte Carlo (KMC) approach.

Dissolution of Portlandite in Pure Water: Part 2 Atomistic Kinetic Monte Carlo (KMC) Approach.

Portlandite, as a most soluble cement hydration reaction product, affects mechanical and durability properties of cementitious materials. In the present work, an atomistic kinetic Monte Carlo (KMC) upscaling approach is implemented in MATLAB code in order to investigate the dissolution time and morphology changes of a hexagonal platelet portlandite crystal. First, the atomistic rate constants of individual Ca dissolution events are computed by a transition state theory equation based on inputs of the computed activation energies (ΔG*) obtained through the metadynamics computational method (Part 1 of paper). Four different facets (100 or 1¯00, 010 or 01¯0, 1¯10 or 11¯0, and 001 or 001¯) are considered, resulting in a total of 16 different atomistic event scenarios. Results of the upscaled KMC simulations demonstrate that dissolution process initially takes place from edges, sides, and facets of 010 or 01¯0 of the crystal morphology. The steady-state dissolution rate for the most reactive facets (010 or 01¯0) was computed to be 1.0443 mol/(s cm2); however, 0.0032 mol/(s cm2) for 1¯10 or 11¯0, 2.672 × 10-7 mol/(s cm2) for 001 or 001¯, and 0.31 × 10-16 mol/(s cm2) for 100 or 1¯00 were represented in a decreasing order for less reactive facets. Obtained upscaled dissolution rates between each facet resulted in a huge (16 orders of magnitude) difference, reflecting the importance of crystallographic orientation of the exposed facets.

Enhanced Metakaolin Reactivity in Blended Cement with Additional Calcium Hydroxide.

This study aims to increase the pozzolanic reactivity of metakaolin (MK) in Portland cement (PC) blends by adding additional calcium hydroxide (CH_add) to the initial mixture. Cement paste samples were prepared with PC, MK and water with a water-to-binder ratio of 0.6. Cement replacement ratios were chosen from 5 to 40 wt.% MK. For higher replacement ratios, i.e., 20, 30 and 40 wt.% MK, CH_add was included in the mixture. CH_add-to-MK ratios of 0.1, 0.25 and 0.5 were investigated. Thermogravimetric analysis (TGA) was carried out to study the pozzolanic reactivity after 1, 7, 28 and 56 days of hydration. A modified mass balance approach was used to normalize thermogravimetric data and to calculate the calcium hydroxide (CH) consumption of samples with CH_add. Results showed that, without CH_add, a replacement ratio of 30 wt.% or higher results in the complete consumption of CH after 28 days at the latest. In these samples, the pozzolanic reaction of MK turned out to be restricted by the amount of CH available from the cement hydration. The increased amount of CH in the samples with CH_add resulted in an enhanced pozzolanic reaction of MK as confirmed by CH consumption measurements from TGA.

A Mass Balance Approach for Thermogravimetric Analysis in Pozzolanic Reactivity R3 Test and Effect of Drying Methods.

The reactivity of supplementary cementitious materials (SCMs) is a key issue in the sustainability of cement-based materials. In this study, the effect of drying with isopropanol and acetone as well as the interpretation of thermogravimetric data on the results of an R3 test for evaluation of the SCM pozzolanic reaction were investigated. R3 samples consisting of calcium hydroxide, potassium hydroxide, potassium sulphate, water, and SCM were prepared. Besides silica fume, three different types of calcined clays were investigated as SCMs. These were a relatively pure metakaolin, a quartz-rich metakaolin, and a mixed calcined clay, where the amount of other types of clays was two times higher than the kaolinite content. Thermogravimetric analysis (TGA) was carried out on seven-day-old samples dried with isopropanol and acetone to stop the reaction processes. Additional calorimetric measurement of the R3 samples was carried out for evaluation of the reaction kinetics. Results show that drying with isopropanol is more suitable for analysis of R3 samples compared to acetone. The use of acetone results in increased carbonation and TGA mass losses until 40 (isothermal drying for 30 min) and 105 °C (ramp heating), indicating that parts of the acetone remain in the sample, causing problems in the interpretation of TGA data. A mass balance approach was proposed to calculate calcium hydroxide consumption from TGA data, while also considering the amount of carbonates in the sample and TGA data corrections of original SCMs. With this approach, an improvement of the linear correlation of TGA results and heat release from calorimetric measurement was achieved.

Optimization of Multilayered Walls for Building Envelopes Including PCM-Based Composites.

This work proposes a numerical procedure to simulate and optimize the thermal response of a multilayered wallboard system for building envelopes, where each layer can be possibly made of Phase Change Materials (PCM)-based composites to take advantage of their Thermal-Energy Storage (TES) capacity. The simulation step consists in solving the transient heat conduction equation across the whole wallboard using the enthalpy-based finite element method. The weather is described in detail by the Typical Meteorological Year (TMY) of the building location. Taking the TMY as well as the wall azimuth as inputs, EnergyPlusTM is used to define the convective boundary conditions at the external surface of the wall. For each layer, the material is chosen from a predefined vade mecum, including several PCM-based composites developed at the Institut für Werkstoffe im Bauwesen of TU Darmstadt together with standard insulating materials (i.e., EPS or Rockwool). Finally, the optimization step consists in using genetic algorithms to determine the stacking sequence of materials across the wallboard to minimize the undesired heat loads. The current simulation-based optimization procedure is applied to the design of envelopes for minimal undesired heat losses and gains in two locations with considerably different weather conditions, viz. Sauce Viejo in Argentina and Frankfurt in Germany. In general, for each location and all the considered orientations (north, east, south and west), optimal results consist of EPS walls containing a thin layer made of the PCM-based composite with highest TES capacity, placed near the middle of the wall and closer to the internal surface.