Microstructure models of cement: their importance, utility, and current limitations

Microstructure models seek to explain or predict various material properties in terms of the structure or chemical composition at scales of several hundred nanometres to several hundred micrometres. Such models therefore bridge the scaling gap between atomistic models and continuum methods, and consequently can help establish and validate scaling relations across those scales. Microstructure models have been applied to cementitious materials for at least four decades to help understand setting, strength development, rheological properties, mechanical behavior, and transport properties. This letter describes the current state of cement microstructure modelling in several areas that are important for engineering.  It is not meant to be an exhaustive review, instead highlighting the kinds of models that can now be applied to different aspects of cement binder behaviour. Special attention is paid to challenges or limitations of each kind of model. This is done to promote the judicious use and interpretation of models and especially to indicate where future research could make inroads on problems that are currently inaccessible to microstructure models.

A Critical Comparison of 3D Experiments and Simulations of Tricalcium Silicate Hydration

Advances in nano-computed X-ray tomography (nCT), nano X-ray fluorescence spectrometry (nXRF), and high-performance computing have enabled the first direct comparison between observations of three-dimensional nanoscale microstructure evolution during cement hydration and computer simulations of the same microstructure using HydratiCA. nCT observations of a collection of triclinic tricalcium silicate (Ca3SiO5) particles reacting in a calcium hydroxide solution are reported and compared to simulations that duplicate, as nearly as possible, the thermal and chemical conditions of those experiments. Particular points of comparison are the time dependence of the solid phase volume fractions, spatial distributions, and morphologies. Comparisons made at 7 h of reaction indicate that the simulated and observed volumes of Ca3SiO5 consumed by hydration agree to within the measurement uncertainty. The location of simulated hydration product is qualitatively consistent with the observations, but the outer envelope of hydration product observed by nCT encloses more than twice the volume of hydration product in the simulations at the same time. Simultaneous nXRF measurements of the same observation volume imply calcium and silicon concentrations within the observed hydration product envelope that are consistent with Ca(OH)2 embedded in a sparse network of calcium silicate hydrate (C-S-H) that contains about 70 % occluded porosity in addition to the amount usually accounted as gel porosity. An anomalously large volume of Ca(OH)2 near the particles is observed both in the experiments and in the simulations, and can be explained as originating from the hydration of additional particles outside the field of view. Possible origins of the unusually large amount of observed occluded porosity are discussed.

Simulation of the Influence of Intrinsic C-S-H Aging on Time-Dependent Relaxation of Hydrating Cement Paste

The viscoelastic/viscoplastic behavior of cement paste may occur due to intrinsic calcium silicate hydrate (C-S-H) viscoelasticity/viscoplasticity and cement grain dissolution during the hydration process. A numerical model that combines a microstructure model and a finite element calculation model has been developed to predict the time-dependent behavior of cementitious materials based on these two mechanisms, while incorporating C-S-H intrinsic aging. The simulation results from the model suggest that when considering C-S-H aging, the time-dependent properties of C-S-H are capable of generating the aging effect of cement paste, and can become a significant mechanism leading to the overall relaxation of cement paste.

Dissolution Kinetics of Cubic Tricalcium Aluminate Measured by Digital Holographic Microscopy

In situ digital holographic microscopy is used to characterize the dissolution flux of polycrystalline cubic tricalcium aluminate (C₃A-c). The surface dissolves at rates that vary considerably with time and spatial location. This implies a statistical distribution of fluxes, but an approximately steady-state median rate was obtained by using flowing solutions and by reducing the water activity in the solution. The dissolution flux from highly crystalline C₃A-c depends on the water activity raised to an empirically derived exponent of 5.2 and extrapolates to a median flux of - 2.1 μmol m^-2 s^-1 in pure water with an interquartile range of 3.2 μmol m^-2 s^-1. The flux from a less crystalline source of C₃A-c has an empirical water activity exponent of 4.6 and an extrapolated median flux of only -1.4 μmol m^-2 s^-1 in pure water with an interquartile range of 1.9 μmol m^-2 s^-1. These data suggest that the bulk dissolution rate of C₃A-c can vary by at least 30% from one source to another and that variability in the local rate within a single material is even greater because of the heterogeneous spatial distribution of structural characteristics (i.e., degree of crystallinity, chemical impurities, and defects).

Calcite dissolution rate spectra measured by in situ digital holographic microscopy

Digital holographic microscopy in reflection mode is used to track in situ, real-time nanoscale topography evolution of cleaved (104) calcite surfaces exposed to flowing or static deionized water. The method captures full-field holograms of the surface at frame rates of up to 12.5 s-1. Numerical reconstruction provides 3D surface topography with vertical resolution of a few nanometers and enables measurement of time-dependent local dissolution fluxes. A statistical distribution, or spectrum, of dissolution rates is generated by sampling multiple area domains on multiple crystals. The data show, as has been demonstrated by Fischer et al. (2012), that dissolution is most fully described by a rate spectrum, although the modal dissolution rate agrees well with published mean dissolution rates (e.g., 0.1 µmol m-2 s-1 to 0.3 µmol m-2 s-1). Rhombohedral etch pits and other morphological features resulting from rapid local dissolution appear at different times and are heterogeneously distributed across the surface and through the depth. This makes the distribution in rates measured on a single crystal dependent both on the sample observation field size and on time, even at nominally constant undersaturation. Statistical analysis of the inherent noise in the DHM measurements indicates that the technique is robust and that it likely can be applied to quantify and interpret rate spectra for the dissolution or growth of other minerals.

Cements in the 21st Century: Challenges, Perspectives, and Opportunities

In a book published in 1906, Richard Meade outlined the history of portland cement up to that point1. Since then there has been great progress in portland cement-based construction materials technologies brought about by advances in the materials science of composites and the development of chemical additives (admixtures) for applications. The resulting functionalities, together with its economy and the sheer abundance of its raw materials, have elevated ordinary portland cement (OPC) concrete to the status of most used synthetic material on Earth. While the 20th century was characterized by the emergence of computer technology, computational science and engineering, and instrumental analysis, the fundamental composition of portland cement has remained surprisingly constant. And, although our understanding of ordinary portland cement (OPC) chemistry has grown tremendously, the intermediate steps in hydration and the nature of calcium silicate hydrate (C-S-H), the major product of OPC hydration, remain clouded in uncertainty. Nonetheless, the century also witnessed great advances in the materials technology of cement despite the uncertain understanding of its most fundamental components. Unfortunately, OPC also has a tremendous consumption-based environmental impact, and concrete made from OPC has a poor strength-to-weight ratio. If these challenges are not addressed, the dominance of OPC could wane over the next 100 years. With this in mind, this paper envisions what the 21st century holds in store for OPC in terms of the driving forces that will shape our continued use of this material. Will a new material replace OPC, and concrete as we know it today, as the preeminent infrastructure construction material?

In situ nanoscale observations of gypsum dissolution by digital holographic microscopy

Recent topography measurements of gypsum dissolution have not reported the absolute dissolution rates, but instead focus on the rates of formation and growth of etch pits. In this study, the in situ absolute retreat rates of gypsum (010) cleavage surfaces at etch pits, at cleavage steps, and at apparently defect-free portions of the surface are measured in flowing water by reflection digital holographic microscopy. Observations made on randomly sampled fields of view on seven different cleavage surfaces reveal a range of local dissolution rates, the local rate being determined by the topographical features at which material is removed. Four characteristic types of topographical activity are observed: 1) smooth regions, free of etch pits or other noticeable defects, where dissolution rates are relatively low; 2) shallow, wide etch pits bounded by faceted walls which grow gradually at rates somewhat greater than in smooth regions; 3) narrow, deep etch pits which form and grow throughout the observation period at rates that exceed those at the shallow etch pits; and 4) relatively few, submicrometer cleavage steps which move in a wave-like manner and yield local dissolution fluxes that are about five times greater than at etch pits. Molar dissolution rates at all topographical features except submicrometer steps can be aggregated into a continuous, mildly bimodal distribution with a mean of 3.0 µmolm-2 s-1 and a standard deviation of 0.7 µmolm-2 s-1.

An Ideal Solid Solution Model for C-S-H

A model for an ideal solid solution, developed by Nourtier-Mazauric et al. [Oil & Gas Sci. Tech. Rev. IFP, 60 [2] (2005) 401], is applied to calcium-silicate-hydrate (C-S-H). Fitting the model to solubility data reported in the literature for C-S-H yields reasonable values for the compositions of the end-members of the solid solution and for their equilibrium constants. This model will be useful in models of hydration kinetics of tricalcium silicate because it is easier to implement than other solid solution models, it clearly identifies the driving force for growth of the most favorable C-S-H composition, and it still allows the model to accurately capture variations in C-S-H composition as the aqueous solution changes significantly at early hydration times.

Direct Measurements of 3D Structure, Chemistry and Mass Density During the Induction Period of C3S Hydration

The reasons for the start and end of the induction period of cement hydration remain topic of controversy. One long-standing hypothesis is that a thin metastable hydrate forming on the surface of cement grains significantly reduces the particle dissolution rate; the eventual disappearance of this layer re-establishes higher dissolution rates at the beginning of the acceleration period. However, the importance, or even the existence, of this metastable layer has been questioned because it cannot be directly detected in most experiments. In this work, a combined analysis using nano-tomography and nano-X-ray fluorescence makes the direct imaging of early hydration products possible. These novel X-ray imaging techniques provide quantitative measurements of 3D structure, chemical composition, and mass density of the hydration products during the induction period. This work does not observe a low density product on the surface of the particle, but does provide insights into the formation of etch pits and the subsequent hydration products that fill them.

Phase Analysis of Portland Cement by Combined Quantitative X-Ray Powder Diffraction and Scanning Electron Microscopy

X-ray powder diffraction (XRD) has been used for several decades to identify and measure the mass fractions of various crystalline phases in portland cement. More recently, a combination of scanning electron microscopy with X-ray microanalysis (SEM/XMA) and image processing has been shown to enable the quantitative characterization of microstructural features in these materials. Each technique can furnish some information that is not accessible from the other. For example, SEM/XMA can identify the microstructural location and morphology of calcium sulfate minerals, while only XRD can determine the relative abundance of the different forms of calcium sulfate, such as gypsum (CaSO₄ · 2H₂O), bassanite ( CaSO 4 ⋅ 1 2 H 2 O ) , and anhydrite (CaSO₄). This document describes how XRD and SEM/XMA can be used together to establish and validate the portland cement phase composition and microstructure. Particular emphasis is laid on step-by-step procedures and best practices for XRD specimen preparation, data collection, and intepretation. Similar detail has been given recently for SEM/XMA [Stutzman et al., NIST Tech Note 1877, U.S. Department of Commerce, April 2015]. The methods are demonstrated for three portland cement powders, through which apparent discrepancies between the results of the two methods are identified and procedures are described for resolving the discrepancies and quantifying uncertainty.

Factors influencing the stability of AFm and AFt in the Ca-Al-S-O-H system at 25 °C

The stabilities of Al₂O₃-Fe₂O₃-mono (AFm) and -tri (AFt) phases in the Ca-Al-S-O-H system at 25 °C are examined using Gibbs energy minimization as implemented by GEM-Selektor software coupled with the Nagra/PSI thermodynamic database. Equilibrium phase diagrams are constructed and compared to those reported in previous studies. The sensitivity of the calculations to the assumed solid solubility products, highlighted by the example of hydrogarnet, is likely the reason why some studies, including this one, predict a stable SO₄-rich AFm phase while others do not. The majority of the effort is given to calculating the influences on AFm and AFt stability of alkali and carbonate components, both of which are typically present in cementitious binders. Higher alkali content shifts the equilibria of both AFt and AFm to lower Ca but higher Al and S concentrations in solution. More importantly, higher alkali content significantly expands the range of solution compositions in equilibrium with AFm relative to AFt phases. The introduction of carbonates alters not only the stable AFm solid solution compositions, as expected, but also influences the range of solution pH over which SO₄-rich and OH-rich AFm phases are dominant. Some experimental tests are suggested that could provide validation of these calculations, which are all the more important because of the implications for resistance of portland cement binders to external sulfate attack.

Microstructural Origins of Cement Paste Degradation by External Sulfate Attack

A microstructure model has been applied to simulate near-surface degradation of portland cement paste in contact with a sodium sulfate solution. This new model uses thermodynamic equilibrium calculations to guide both compositional and microstructure changes. It predicts localized deformation and the onset of damage by coupling the confined growth of new solids with linear thermoelastic finite element calculations of stress and strain fields. Constrained ettringite growth happens primarily at the expense of calcium monosulfoaluminate, carboaluminate and aluminum-rich hydrotalcite, if any, respectively. Expansion and damage can be mitigated chemically by increasing carbonate and magnesium concentrations or microstructurally by inducing a finer dispersion of monosulfate.

Capillary rise between planar surfaces

Minimization of free energy is used to calculate the equilibrium vertical rise and meniscus shape of a liquid column between two closely spaced, parallel planar surfaces that are inert and immobile. States of minimum free energy are found using standard variational principles, which lead not only to an Euler-Lagrange differential equation for the meniscus shape and elevation, but also to the boundary conditions at the three-phase junction where the liquid meniscus intersects the solid walls. The analysis shows that the classical Young-Dupré equation for the thermodynamic contact angle is valid at the three-phase junction, as already shown for sessile drops with or without the influence of a gravitational field. Integration of the Euler-Lagrange equation shows that a generalized Laplace-Young (LY) equation first proposed by O'Brien, Craig, and Peyton [J. Colloid Interface Sci. 26, 500 (1968)] gives an exact prediction of the mean elevation of the meniscus at any wall separation, whereas the classical LY equation for the elevation of the midpoint of the meniscus is accurate only when the separation approaches zero or infinity. When both walls are identical, the meniscus is symmetric about the midpoint, and the midpoint elevation is a more traditional and convenient measure of capillary rise than the mean elevation. Therefore, for this symmetric system a different equation is fitted to numerical predictions of the midpoint elevation and is shown to give excellent agreement for contact angles between 15 degrees and 160 degrees and wall separations up to 30mm . When the walls have dissimilar surface properties, the meniscus generally assumes an asymmetric shape, and significant elevation of the liquid column can occur even when one of the walls has a contact angle significantly greater than 90 degrees . The height of the capillary rise depends on the spacing between the walls and also on the difference in contact angles at the two surfaces. When the contact angle at one wall is greater than 90 degrees but the contact angle at the other wall is less than 90 degrees , the meniscus can have an inflection point separating a region of positive curvature from a region of negative curvature, the inflection point being pinned at zero height. However, this condition arises only when the spacing between the walls exceeds a threshold value that depends on the difference in contact angles.

A comparison of viscosity-concentration relationships for emulsions

Differential effective medium theory (D-EMT) has been used by a number of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the volume fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concentration expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the volume fraction at which the ratio of each emulsion was experimentally observed to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded volume due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addition, the resulting equations either do not account for the limiting behavior near the critical concentration, that is, the concentration at which the viscosity diverges, or they incorporate this critical behavior in an ad hoc way. We suggest an alternative viscosity-concentration equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J.F. Douglas, D.A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to physical properties of the suspension and (2) it recovers the correct limiting behavior both in the dilute limit and near the critical concentration for rigid particles. In addition, the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.

Approximate rate constants for nonideal diffusion and their application in a stochastic model

Rate constants are presented for diffusion in dilute nonideal solutions with or without the presence of a spatially varying potential field. Expressions for the rate constants have been derived by earlier workers, and essentially the same derivation is reviewed and expanded in this paper to justify the expressions used for the rate constants. The diffusion rate constants are used in a random walker model to demonstrate how solution nonidealities can be captured accurately using this approach. Examples are presented of ideal solute diffusion as well as nonideal diffusion of nonelectrolytes and simple electrolytes in water. The use of the approach to simulate advection is described, and a possible strategy for extending the approach to more concentrated solutions is briefly discussed.

Stability of voids formed in cavities at liquid–solid interfaces

A thermodynamic model is developed of the free energy of gas-filled voids formed within cavities on solid surfaces covered by a liquid. Capillary effects are assumed to be the only important contributions to the free energy, and expressions are derived for the free energy of the system as a function of the void size, the relative surface free energy densities involved, and the geometry of the cavity. The results of the model are (1) construction of a stability diagram that maps the most stable void configuration versus the wetting properties of the various solid surfaces involved, and (2) rough estimates of the work required to liberate a void of a given size and position. The model can give qualitative insight into the stability of coating defects on uneven surfaces, and also can be used to prescribe possible surface treatments for reducing the work required to remove voids from the system.

Comparison of the effectiveness of several denture sanitizing systems: a clinical study

The purpose of this clinical study was to test the effectiveness of three methods of decontamination on complete dentures. Dentures worn by patients for varying lengths of time were handled aseptically and treated with three different treatment modalities. The dentures were touched and sectioned and then retouched to a variety of microbiological media. The quantity of microbial growth was recorded and predominating microorganisms were identified using standard microbiological techniques. System A was found to consistently decontaminate and sanitize dentures worn by patients. System B and System C showed variable reduction of microorganisms. An unexpected spectrum of both pathogenic and opportunistic microorganisms was found in the dentures examined, including a wide range of gram-negative bacteria, gram-positive bacteria, and yeasts. A wide range of microorganisms must be considered when treating either oral or systemic diseases in denture wearers. Denture hygiene and decontamination are critical to the prevention of oral and systemic disease transmission. The dentures of ill patients must be considered as possible sources of pathogenic microorganisms.

Partial spectrum of microorganisms found in dentures and possible disease implications

While it would appear that denture surfaces alone become colonized by microorganisms, this study showed that the porosity of denture material allows for contamination throughout the entire denture. Further, the numerous opportunistic and pathogenic microorganisms found in this study were unexpected and are known to produce not only substantial oral infections, but also systemic diseases.

Equilibrium Shapes of Solid Particles on Elastically Mismatched Substrates

Small particles or islands bonded to a substrate can be profoundly influenced by both interfacial and elastic driving forces that tend to have opposing influences on the apparent wetting behavior. The superposition of these two driving forces can therefore lead to a rich set of particle properties, most notably their equilibrium shapes. Here we present a variational analysis leading directly to an Euler-Lagrange equation that can be solved to yield the equilibrium shapes of partially wetting particles as a function of their size, interface energy densities, and elastic interaction with a rigid substrate. The solutions are used to gain insight into the variables that most significantly influence the equilibrium morphology, and to derive the approximate driving force for surface area reduction by coarsening among a dispersion of unequally sized particles. The relatively simple analytical model can also form a foundation upon which more realistic numerical simulations may be built and compared. Copyright 1999 Academic Press.

IgG subclass deficiency in children with recurrent respiratory infections

IgG subclass deficiency frequently occurs in children with recurrent otitis media and respiratory infections. IgG subclasses should be included in the diagnostic evaluation of all such children.