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Dissolution kinetics of cubic tricalcium aluminate measured by digital holographic microscopy Alexander Sebastian Brand, and Jeffery W. Bullard Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02400 • Publication Date (Web): 25 Aug 2017 Downloaded from http://pubs.acs.org on September 4, 2017

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Dissolution kinetics of cubic tricalcium aluminate measured by digital

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holographic microscopy

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Alexander S. Brand1* and Jeffrey W. Bullard1

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Materials and Structural Systems Division, National Institute of Standards and Technology, Gaithersburg,

Maryland 20899, USA; Electronic addresses: [email protected] and [email protected] *

Corresponding author

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ABSTRACT

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In situ digital holographic microscopy is used to characterize the dissolution flux of

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polycrystalline cubic tricalcium aluminate (C3A-c). The surface dissolves at rates that vary

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considerably with time and spatial location. This implies a statistical distribution of fluxes, but an

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approximately steady-state median rate was obtained by using flowing solutions and by reducing

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the water activity in the solution. The dissolution flux from highly crystalline C3A-c depends on

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the water activity raised to an empirically-derived exponent of 5.2, and extrapolates to a median

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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

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from a less crystalline source of C3A-c has an empirical water activity exponent of 4.6 and an

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extrapolated median flux of only −1.4 µmol m−2 s−1 in pure water with an interquartile range of

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1.9 µmol m−2 s−1. These data suggest that the bulk dissolution rate of C3A-c can vary by at least

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30 % from one source to another and that variability in the local rate within a single material is

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even greater because of the heterogeneous spatial distribution of structural characteristics (i.e.,

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degree of crystallinity, chemical impurities, and defects).

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Keywords: digital holographic microscopy, tricalcium aluminate, dissolution, rate spectra,

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surface reactivity

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1. INTRODUCTION The ability to predict the rate of hydration and development of properties in cement

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binders is a long-standing goal of concrete research. Computational materials science models of

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cement hydration have demonstrated the ability to provide accurate calculations of engineering

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properties based on the microstructural state of the binder. However, accurately predicting the

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rate of change in microstructure has proven to be extremely difficult, in part because the initial 1

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binder material is inherently variable in its composition and reactivity, but primarily because

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there are significant gaps in a quantitative understanding of the basic mechanisms that govern the

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reactions of the solid binder components with water. Any microstructural model rooted in the

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basic physics and chemistry of materials will require input of the details of the binder’s starting

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mineralogical composition, particle size distribution, and basic thermodynamic and kinetic

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properties of the reactions being simulated, including the dissolution rate laws and constants of

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individual cementitious minerals.1,2

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Substantial progress has been made in characterizing the fundamental dissolution rates

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and mechanisms of some minerals, especially calcite and gypsum, which are minority

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components of portland cement. Much of the recent progress has involved monitoring nanoscale

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changes in surface topography with vertical scanning interferometry (VSI) and atomic force

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microscopy (AFM).3 Measurements of the dissolution rates of tricalcium silicate (Ca3SiO5, or

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C3S)4 and dicalcium silicate (Ca2SiO4, or C2S)4 in various aqueous solutions also have been

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reported in the last several years using bulk powder methods,5–8 and VSI observations of surface

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topography changes have characterized the dissolution behavior of C3S9,10 and calcium silicate

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hydrate (C–S–H).11 AFM has also been used to observe C–S–H growth on alite12 and to

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characterize cement clinker hydration.13,14 Scanning electron microscopy (SEM) has also been

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used to infer a dissolution rate of C3S via ex situ measurement of the dissolved surface area.15

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More recently, holographic interferometry techniques have been used to study the dissolution

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kinetics of hardened cement paste under acid attack,16 while digital holographic microscopy

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(DHM) has been used to examine minerals important to cements.17,18

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Tricalcium aluminate (Ca3Al2O6, or C3A)4 is a key component of portland cement clinker

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and is commonly found in cubic form (C3A-c).19 It is usually present in much smaller

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proportions than C3S and C2S, but it nevertheless has an important influence on early hydration

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reactions, enthalpy release, and strength development. The reactivity of C3A with water is so

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great that it can induce rapid precipitation of calcium aluminate hydrates that lead to flash setting

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unless calcium sulfate is added to mitigate the rate of reaction.19 In fact, an important part of

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concrete mixture design is the determination of the optimum mass fraction of calcium sulfate to

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include to properly regulate C3A hydration.20 A wide range of techniques have been used to

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characterize the C3A reactions in water, such as environmental scanning electron microscopy,21

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X-ray transmission microscopy,22,23 in situ synchrotron X-ray diffraction,24–26 X-ray adsorption 2


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spectroscopy,27 nuclear magnetic resonance,28 and solution ionic concentration measurement,29,30

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but no measurements have reported the net dissolution flux from C3A in aqueous solutions.

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Therefore, the objective of this study is to experimentally characterize the dissolution flux of

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C3A and to estimate the form of the dissolution rate equation by in situ monitoring of the

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nanoscale surface topography evolution in real time.

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1.1 Dissolution Kinetics of C3A 18-

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The crystal structure of C3A-c features closed rings of six aluminate tetrahedra, Al6 O18 ,

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with the aluminum ions located near the corners of the cubic structure,19,31,32 and each aluminate

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tetrahedron has two nonbridging oxygens (NBOs).31 The high electronegativity of the aluminum

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relative to calcium gives a substantial covalent character to the Al−O bond, while the bonds

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between the nine calcium atoms and the NBOs in the aluminate ring has more significant ionic

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character.

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As in most double oxides, like the other portland cement clinker phases, dissolution of

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C3A involves an initial step of protonation of the apical NBOs of the aluminate tetrahedra.32–34 In

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neutral or basic solutions, the proton can be donated by a water molecule, leaving behind a

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hydroxyl ion. Considering a formula unit as three calcium atoms plus one third of the aluminate

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ring, with the corresponding formula Ca3Al2O6, this elementary protonation step can be written 3Ca Al O + H O → 3Ca Al O OH + .

(1)

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This step occurs repeatedly to protonate the other NBOs, and, on average, releases one calcium

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atom for every two hydroxyls produced: 3Ca Al O OH + H O → 2Ca Al O (OH) + Ca + OH .

(2)

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The fate of the “released” calcium ion is not immediately clear; it likely could be released from

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the solid and immediately directly complexed by a hydration shell of six water molecules,35,36 Ca + 6 H O → Ca(H O)

,

(3)

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which could escape into the bulk solution, remain within the electrical double layer near the

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surface, or be adsorbed as an outer-sphere complex.27,37,38 Alternatively, as proposed by Mishra

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et al.,32 each released calcium may condense with two liberated hydroxyl ions to form an

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amorphous calcium hydroxide layer at the surface, Ca + 2 OH → Ca(OH) (am).

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Any such amorphous layer should be unstable with respect to dissociation, since the adjacent

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solution is significantly undersaturated with respect to even crystalline calcium hydroxide

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(portlandite), with saturation corresponding to about 20 mmol L−1 in pure water at 298 K.19

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However, such a layer might be kinetically favored if the hydroxyls are locally available because

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the full hydration of calcium requires coordination with six additional water molecules.

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When NBOs of the aluminate tetrahedra have been protonated, further attack by the water

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on the bridging oxygens can decouple one or more of the aluminate tetrahedra simultaneously

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from the ring structure. For example, two water molecules could attack each of the two bridging

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oxygens of one aluminate group to produce a fully protonated Al(OH) 4 ion and releasing the

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remaining calcium atom that is ionically bonded to that part of the ring: Ca Al O (OH) + 2 H O → 2 Al(OH) + Ca .

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(5)

As suggested by this discussion, the exact sequence of steps involved in C3A dissolution is

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difficult to determine with certainty, and the ordering of the steps may even be subject to some

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statistical fluctuation. Identifying a rate-controlling step is also difficult, although the superficial

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protonation of the apical NBOs likely can be ruled out as being rate controlling. If one of the

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steps could be identified as rate-controlling, then all the other steps before and after would be

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near equilibrium, and the rate equation for dissolution could be written exactly according to

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transition state theory.39,40

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In the absence of more certain knowledge of the reaction sequence and the ratecontrolling step, the overall reaction for C3A still can be written as Ca Al O + 6 H O → 3 Ca + 2 Al(OH) + 4 OH ,

(6)

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and one must be satisfied with an empirical rate equation for the overall process. Under the

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experimental conditions used in this paper, where rapidly flowing water over the solid surface

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removes the product ions as much as possible, the reaction should proceed almost entirely in the

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forward direction and without precipitation of a secondary or intermediate solid, in which case

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the empirical rate equation far from equilibrium is written as a power function of the reactant

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concentrations or activities.39 For C3A the empirical rate equation is *

= !" # $%&' ( ) ,

(7)

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where JC3A is the dissolution flux (mol m−2 s−1), k′+ is the overall rate constant (mol s−1), CC3A is

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the concentration of reactive sites on the C3A surface (m−2), aH2O is the activity of water at the

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surface, and n is the reaction order, which must be determined empirically. 4


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Writing the rate equation as in (7) presupposes that there is only one type of reactive site

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at the surface and that its reactivity is the same everywhere it is found on the surface. However,

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there are several types of reactive sites on a given crystalline surface. In addition, the actual

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reactivity of a given site depends on its molecular identity, its local structural configuration (i.e.,

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terrace, ledge, or kink site), and the effects of nearby structural defects that introduce lattice

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strain energy, such as dislocation outcroppings, stacking faults, grain boundaries, vacancies, or

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chemical impurities. Therefore, a distribution of site types and reactivity will typically present at

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a surface.41

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These atomic-scale structural details usually are not known in advance, nor can the

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introduction of a single term like CC3A in the overall rate equation capture their influence. As an

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alternative, one often measures the total surface area of the solid and assumes it to be

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proportional to the surface concentration of reaction sites. The variability of sites and their

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reactivities are then contained within a local rate constant. In that case, Eq. (7) is recast as *

= ! $%&' ( ) ,

(8)

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where now k+ has units of molar flux. In bulk dissolution experiments using rotating disks or

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dilute granular suspensions, one generally assumes that dissolution occurs uniformly over the

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entire surface area, so that a globally averaged rate constant in recovered. However, topographic

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methods like VSI, AFM, and DHM can track the surface retreat from point to point on a surface.

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When these methods are used, the range of local dissolution fluxes can be measured, both in

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terms of point to point flux variability on a given surface,17,18,41–48 and in terms of temporal flux

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variability at a given point on a surface17,18 as defects are annihilated or uncovered by the

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dissolution process.

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This paper assumes that Eq. (8) empirically describes the dissolution flux from several

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polycrystalline C3A surfaces prepared by solid state sintering. Local in situ dissolution rates are

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tracked in real time by DHM using flowing solutions in which the water activity is

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systematically varied by ethanol additions. The statistical distribution of local rate constants is

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measured and related to the presence and evolution of surface defects. Both the spatially

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averaged rate constant, k+, and the activity exponent, n, are estimated by regression of the flux

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data to quantitatively determine the empirical rate equation.

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2. EXPERIMENTAL SECTION

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2.1 Materials

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Two sources of laboratory-synthesized C3A, varying primarily in the abundance of

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amorphous material, were evaluated in this study. The first source, termed hereafter “C3A #1”, in

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this study was produced by Mineral Research Processing (Meyzieu, France).49 Elemental

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analysis by inductively coupled plasma optical emission spectroscopy (ICP-OES) yielded mass

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fractions (with standard deviations) of 64.6 % ± 1.2 % CaO and 35.4 % ± 0.6 % Al2O3, so the

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molar ratio CaO:Al2O3 is 3.3. C3A #1 was provided as nodules, which were ground and

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micronized prior to sample preparation.

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The second source, termed hereafter “C3A #2”, was produced by Construction

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Technology Laboratories (Skokie, Illinois, USA).49 This source was provided as a powder and

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exhibited evidence of some prehydration (i.e., hydrogarnet and portlandite), so the powder was

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heated to 500 °C to dehydrate prior to micronizing for sample preparation. Elemental analysis by

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ICP-OES yielded mass fractions of 64.4 % ± 1.1 % CaO and 35.6 % ± 1.0 % Al2O3,

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corresponding to the molar ratio CaO:Al2O3 = 3.3.

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In keeping with some other topographic analyses of mineral surfaces,50 the nominally flat

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sample surface required for DHM examination was produced by solid state sintering and

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polishing of a cylindrical powder compact. The pellets were 13 mm in diameter and uniaxially

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compressed at approximately 170 MPa, with a small volume of ethanol mixed in to act as a

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compaction aid. The samples were sintered by heating at 10 °C min−1 to 1500 °C, holding

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constant at 1500 °C for 8 h, and finally cooling at 2 °C min−1 to 30 °C. The sintered samples

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were mounted onto titanium stubs and the surface was polished using silicon carbide (grits of

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400, 600, 800, and 1200), diamond paste (3 µm and 0.25 µm), and alumina (0.05 µm) with

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propylene glycol as lubricant.

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Powder samples before and after sintering were micronized and examined with X-ray

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diffraction (XRD) using rutile as an internal standard. Phase abundances determined by Rietveld

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refinement are shown in Table 1. The compositions are consistent with other reports of synthetic

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C3A,51,52 which typically contains 1 % to 2.5 % free lime and some amorphous content. The

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calcite content of C3A #2 before sintering could have been produced by initial heat treatment at

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500 °C to remove its prehydration products, which transformed the free lime content to calcite by

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reaction with ambient CO2 in the furnace atmosphere. A stoichiometric balance implies that C3A 6


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#2 had a free lime content of about 2.2 % before sintering. The higher-temperature sintering

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treatment caused all the calcite to decompose back to free lime. Some mayenite (C12A7) was

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found in both C3A sources but was either totally or substantially transformed by sintering in C3A

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#1 and C3A #2, respectively. C3A #2 has more than twice the amorphous content of C3A #1 both

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before and after sintering. No other crystalline calcium aluminate phases (e.g., orthorhombic

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C3A, monocalcium aluminate) were detected by XRD.

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Table 1. Mass Fraction Composition (%) of C3A by Rietveld Analysis with an Internal Standard C3A #1 C3A #2 Before Sintering After Sintering Before Sintering After Sintering C3A-c 89.7 ± 0.3 94.2 ± 0.3 74.5 ± 0.4 84.3 ± 0.3 Free Lime 2.2 ± 0.2 2.0 ± 0.2 N/A 1.0 ± 0.2 Calcite N/A N/A 4.0 ± 0.3 N/A Mayenite 4.3 ± 0.3 N/A 5.0 ± 0.3 4.6 ± 0.3 Amorphous Content 3.8 ± 0.7 3.8 ± 0.7 16.5 ± 0.7 10.1 ± 0.6 Note: the uncertainty represents the average standard error of regression from Rietveld refinement Phase

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2.2 Digital Holographic Microscopy (DHM) The DHM utilized in this study was a Lyncée Tec Model R-2203 (Lausanne,

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Switzerland).49 Additional instrument details are reported elsewhere,17,53 but briefly: A

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monochromatic coherent light source (665.5651 nm wavelength) is split into two beams known

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as the reference and object beams. The object beam is sent through an objective lens to the

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specimen surface, reflects into the instrument, and is recombined with the reference beam. The

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interference pattern of the recombined beams is recorded as a hologram for the entire field of

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view. The holograms are collected at frame rates up to 25 s−1, thus allowing full-field, in situ data

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to be collected in real time. Numerical reconstruction of each hologram yields amplitude and

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phase data at every pixel.54–56 The reconstructed phase data are converted to surface elevation at

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each image pixel, so this configuration and procedure enable the quantitative tracking of in situ

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surface topography evolution. Similar approaches have already been reported in studies of

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mineral dissolution17,18 and metal electrodeposition.57 Local dissolution (or growth) fluxes can be

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computed by tracking the change in pixel height with time. The surface normal flux, ks (mol m−2

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s−1), is determined3,58 by the quotient of the surface normal velocity, vs (m s−1), which is the per

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pixel measured change in height over change in time, ∆h/∆t, and the known molar volume of the

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sample, Vm (m3 mol−1):

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!+ =

,+ ∆ℎ 1 = . -. ∆1 -.

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(9)

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The surface normal flux, ks, in Eq. (9) is measured at each pixel and can then be equated to the

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net dissolution flux, JC3A, in Eq. (8), thus linking the measured surface topography changes to the

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unknown k+ and n. For sign convention, dissolution will be denoted as negative vs and negative

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ks, while precipitation will be regarded as positive vs and positive ks. The molar volume of C3A-c

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is 8.91×10−5 m3 mol−1.59 For this configuration, uncertainty in the phase measurement results in

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approximately 0.41 nm (mean value) uncertainty in the height for data averaged from 20

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holograms and a water flow rate of 33 mL min−1.53

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DHM measurements of absolute height changes require a flat and inert surface reference

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plane that remains at constant elevation during the experiment. For this purpose, a thin film of

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chromium was introduced by physical vapor deposition to a typical thickness of about 70 nm to

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100 nm, as shown in Figure 1a. The figure shows some residual porosity at the C3A surface that

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survived the sintering treatment. The depth and poor reflectivity of the larger pores produce

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locally noisy phase data, so they are digitally removed during DHM post-processing (Figure 1b)

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using an image gradient thresholding. Note that only the large pores are removed by this method;

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the smaller, shallower pores provide sufficient signal to permit their numerical reconstruction. In

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general, sintered C3A #2 had lower surface porosity than C3A #1, which might be attributed to

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the mayenite phase, which melts at 1400 °C and therefore could act as a liquid phase sintering

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aid.

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(b)

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Figure 1. (a) Greyscale phase map of a polished C3A #1 surface showing the selected area for

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reference surface (red rectangle) and measurement area (blue rectangle). The pores appear as

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sudden phase jumps and noisy data. (b) In post-processing, the pores are digitally removed from

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the measurement area.

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The reaction of C3A in pure water, either static or rapidly flowing across the surface,

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caused extremely rapid and fine-scale surface roughening. Within seconds the surface became so

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rough that light no longer reflected into the lens with sufficient intensity to enable a

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measurement. The rate of these surface changes at each pixel was reduced by decreasing the

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water activity by mixing deionized water (> 0.18 MΩ m) with 200 proof ethanol. The water

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activity in the ethanol-water mixture was determined using the non-random two-liquid (NRTL)

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model,60 which provides the activity coefficient (γ, mole fraction basis) as a function of the mole

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fraction of each liquid phase (x, mol mol−1). The interaction energy parameters and the non-

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randomness parameter in the NRTL model were estimated as recommended by Gmehling et al.61

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The activity, % = 45, was then calculated for use in Eq. (8). Binary mixtures with ethanol

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volume fractions of 80 % (aH2O = 0.689), 70 % (aH2O = 0.777), 60 % (aH2O = 0.824), and 50 %

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(aH2O = 0.857) were used for this purpose.

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All experiments were performed by affixing the polished C3A specimen to a titanium stub, which was locked into a chemically inert flow-through reaction cell that has been described 9


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previously.17,18,53 A 20× immersion lens was used for all experiments. Unless otherwise noted,

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every 10 s to 30 s sets of 15 to 20 holograms were collected at a rate of 12.5 s−1. The sets of 15 to

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20 holograms were averaged to be representative of that time step in order to reduce the effects

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of noise.53,62 The temperature of the solution at the inlet was (23 ± 1) °C.

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Flowing solutions were used to promote, as much as possible, conditions in which the

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dissolution rate is controlled by a surface reaction step and not by transport of ions away from

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the surface. Flowing solutions also help maintain a high degree of undersaturation near the solid

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surface, with respect to C3A and to any calcium aluminate hydrates, such as C3AH6, C2AH8, or

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C4AH13, that might otherwise precipitate during the experiment. Dissolution rate measurements

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were conducted at progressively increasing flow rates to determine the minimum flow rate above

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which the average dissolution flux remained constant. Figure 2 indicates that (33 ± 0.5) mL

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min−1 is a suitable minimum flow rate at the highest water activities (40 % water solutions). The

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error bars overlap in Figure 2, but the low flow rates (0 mL min−1 and 15 mL min−1) still have a

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lower median dissolution flux than the higher flow rates (33 mL min−1 to 67 mL min−1). This

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suggests that a minimum of 33 mL min−1 is acceptable for preventing mass transport from being

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the rate-controlling mechanism of C3A dissolution. Furthermore, as discussed further in Section

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3 and the Supporting Information, no evidence of precipitated phases was detected when using a

258

flow rate of 33 mL min−1, although precipitated phases were detected at 0 mL min−1. Dissolution

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fluxes at lower water activities are lower, implying that dissolution is even more likely to be

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controlled by surface reaction at those lower activities. Therefore, and because noise and other

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uncertainties in DHM measurements become increasingly significant at higher flow rates,53 33

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mL min-1 was used for all experiments involving flowing solution.

10


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Figure 2. Effect of flow rate on the median dissolution velocity in solutions with 60 % ethanol.

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Error bars represent the interquartile range.

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When C3A is dissolved in water, surface heights primarily should decrease as material is

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removed from the solid (i.e., dissolution). However, the height of any point on the surface may

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infrequently and temporarily appear to increase. Localized surface advances also may be

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produced by inherent noise in the data, thermal effects, vibration effects, or errors in the

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unwrapping algorithm.17 In previous studies, noise and unwrapping errors were minimized by

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averaging the heights of localized groups of pixels,17,18 somewhat like a median filter in image

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processing. However, for C3A dissolution, height increases could be caused by actual nucleation

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and growth of a solid hydrate phase, especially in static solutions that may become progressively

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saturated with respect to such phases. Therefore, spatial averaging techniques could not be used

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in this study. Instead, the surface normal velocity was evaluated at each pixel to separate positive

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and negative surface normal velocities. This pixel-by-pixel analysis was repeated several times

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during a given experiment to evaluate if the measured flux changes with time. Evaluating the

280

velocities at each pixel yields a single histogram (Figure 3a), from which the dissolution and

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apparent precipitation velocities must be deconvoluted. In addition, the data must be processed to

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remove pixels with unchanging height as well as pixels that have a velocity too low to be

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distinguished from noise (e.g., see Ref. 53). This deconvolution was performed using the Pearson

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product-moment correlation coefficient, which is a statistical test to determine the strength of 11


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correlation between two variables. The Pearson coefficient can range from -1 (perfectly linear

286

negative correlation) to +1 (perfectly linear positive correlation). In this instance, the Pearson

287

coefficient was evaluated for height versus time at each pixel. Only velocities that had a Pearson

288

coefficient of at least 0.95 were retained, while all other values were disregarded (Figure 3b).

289

The analysis revealed portions of the surface at which this criterion suggested statistically

290

significant surface height increases, but ultimately no physical evidence of precipitation was

291

found, as discussed in Section 3 and in Supporting Information Section S.2. Therefore, the

292

surface height increases in Figure 3b are likely artefacts of the data processing and have been

293

subsequently disregarded. A more thorough discussion of the validity of retaining only the

294

identified (deconvoluted) “dissolution” rates is given in Supporting Information Section S.3.

295

Unless otherwise noted, all statistical descriptions and graphical representations of the data (i.e.,

296

median, mean, interquartile range, and standard deviation) in this study are made after the

297

deconvolution, such as in Figure 3b.

298

(a)

(b)

299

Figure 3. As-measured surface normal velocity (a) per pixel of the entire measurement area and

300

(b) deconvoluted as “dissolution” and “precipitation” velocities. These data are from a C3A #1

301

experiment with 60 % ethanol solution at a flow rate of 33 mL min−1.

302 303 304

2.3 Surface Analysis The surfaces of the C3A specimens were examined by SEM and Raman spectroscopy

305

after the dissolution experiments to search for evidence of solid hydrate precipitation. Field

306

emission scanning electron microscopy (SEM) with secondary and backscattered electron 12


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307

imaging was used to search for signs of precipitates on the surface. Raman spectroscopy was

308

performed with a Raman microscope using a 20× objective lens and a 532 nm laser with output

309

power between 10 mW and 20 mW. The Raman microscope had a spectral range of 4400 cm-1 to

310

50 cm-1 and a nominal resolution of about 12 cm-1. Raman spectroscopy was used because the

311

vibration bands of hydrated C3A solids can potentially be distinguished from those of anhydrous

312

C3A.63–66 A band around 3650 cm−1 is attributable to O-H vibration in hydrated C3A phases;63–66

313

this band is not present in unhydrated C3A.

314 315

3. RESULTS AND DISCUSSION

316

3.1 General Observations

317

In static and flowing solutions with water activity less than 0.83, the primary (initial)

318

topographical features that forms during dissolution are etch pits (Figure 4). The etch pits were 3

319

µm to 5 µm wide after 60 min in the solutions with water activities of 0.689 or 0.777. Etch pits

320

are commonly reported to form on a wide range of dissolving crystals, including alite.67 Besides

321

the locally enhanced dissolution fluxes at etch pits, Figure 5 shows significant variation in the

322

extent of material removal. At higher water activities for C3A #1, some regions on the order of

323

50 µm in characteristic dimension showed higher overall dissolution, as etch pits formed quickly

324

and were followed by an extensive surface roughening event (Figure 6). In static solutions, this

325

surface roughening began within 15 min to 20 min when aH2O = 0.824, but only took about 2 min

326

to begin when aH2O = 0.857. The widespread roughening behavior was somewhat delayed in

327

flowing solutions, beginning after about 30 min when aH2O = 0.824. Rapid roughening did not

328

happen at lower water activities, at least not during the observation times used in this study.

329

Larger-scale heterogeneous reactivity in water, as evidenced in Figure 5 and Figure 6, has also

330

been reported for tricalcium silicate and portland cement.10,12,67–72

331

At higher water activities for C3A #2, the primary topographical features are again etch

332

pits (Figure 7), although they are more faceted, are typically wider and deeper, and have steeper

333

walls than the etch pits formed on C3A #1 surfaces. The SEM micrograph in Figure 7 reveals an

334

etching morphology on C3A #2 that is reminiscent of scaffold microstructures produced by

335

leaching of a two-phase composite73,74 and suggests that the crystalline fraction in C3A #2 may

336

be preferentially leaching. The rapid surface roughening exhibited by C3A #1 was not observed

337

on C3A #2 during the time scales investigated. These differences in dissolution morphology 13


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Page 14 of 30

338

imply that C3A #1 and C3A #2 have differing intrinsic variabilities (e.g., differences in defect

339

densities and types, composition and amorphous content, and initial synthesis process).

340

341

10 min

30 min

45 min

60 min

Figure 4. Formation of etch pits over time in C3A #1 in a static solution of 70 % ethanol.

342

14


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343 344

Figure 5. SEM image of C3A#1 after 40 min of exposure to 60 % ethanol solution at 33 mL

345

min−1. In the bottom left, etch pits are seen in a flatter, seemingly less-reacted region with etch

346

pits, while in the top right, the surface has undergone significant dissolution and “roughening.”

347

2 min

8 min

12 min

13 min

15


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14 min

Page 16 of 30

18 min

348

Figure 6. Rapid dissolution behavior of C3A #1 in a static solution of 60 % ethanol. Etch pits

349

initially formed within the first 10 min, which was followed by a rapid dissolution of the entire

350

surface, starting at 12 min.

351

(a)

(b)

352

Figure 7. Dissolution morphology (etch pits) of C3A #2 after 40 min of exposure to 60 % ethanol

353

solution at 33 mL min−1: (a) surface topography from DHM and (b) SEM image (note the

354

chromium mask on the right side of the image). See Supporting Information for a time-lapse

355

video of this sample surface.

356 357 358

3.2 Dissolution in Static and Flowing Solutions The dissolution velocity increased with water activity, as expected. The 80 % ethanol and

359

70 % ethanol experiments yielded a somewhat “steady state” flux as etch pits formed and grew.

360

In contrast, dissolution in the 60 % ethanol solution gave rise to two phenomena: stable behavior

361

etch pit formation and dissolution up to 60 min, and rapid dissolution events within the first 20

362

min to 30 min (e.g., Figure 6). In static 60 % ethanol solution, the stable regime exhibited a 16


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363

median dissolution velocity of about 0.03 nm s−1 to 0.05 nm s−1, while the fastest velocity during

364

the rapid dissolution event was up to ten times greater (0.32 nm s−1 to 0.37 nm s−1). The 50 %

365

ethanol solutions, with the highest water activity, induced only the rapid dissolution events, with

366

the fastest velocity being about 1.5 nm s−1. Figure 8 compares the results from the various water

367

activities in static solution conditions. As expected, the figure shows that the dissolution velocity

368

increases with increasing water activity (decreasing ethanol proportion). The stable dissolution

369

for the 80 % ethanol, 70 % ethanol, and 60 % ethanol experiments all exhibit similar temporal

370

behaviors, having similar slopes in the log-log format of Figure 8. Similarly, the rapid

371

dissolution events for the 60 % ethanol and 50 % ethanol experiments exhibit similar behavior

372

(e.g., slope) prior to the sudden rapid dissolution event. However, Figure 8 also suggests that the

373

dissolution velocity is decreasing with time, since the ionic saturation of the solution is

374

increasing with time in the static solution and suppressing dissolution. It is therefore necessary to

375

replicate these experiments under flowing solution conditions to provide a nominally

376

undersaturated condition to agree with the assumptions in Eq. (8).

377

378 379

Figure 8. Median surface normal dissolution velocities for C3A #1 in a static solutions of varying

380

water activity. The rapid dissolution results (60 % ethanol and 50 % ethanol) are from one

381

experiment while the others represent the median values from the combined results of at least

382

four replicate tests.

383

17


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384

The dissolution behavior under flowing conditions was similar to the behavior in static

385

conditions, albeit at different time scales. As was also seen in the static solutions, under flowing

386

conditions, the rapid surface roughening event occurred with the 60 % ethanol solution, but not

387

with the 70 % ethanol or 80 % ethanol solutions. This rapid dissolution event manifested around

388

25 min to 35 min in flowing solutions (Figure 9). Dissolution fluxes were comparatively constant

389

in 70 % ethanol or 80 % ethanol solutions (Figure 10) within 5 min to 15 min.

390

391 392

Figure 9. Median surface normal dissolution velocities for replicate experiments of C3A #1 in 33

393

mL min−1 60 % ethanol, indicating time intervals of transient, relatively constant, and rapid

394

dissolution behavior. Each of the four colored lines represents the data from one replicate

395

experiment.

396

18


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(a)

(b)

397

Figure 10. Median surface normal dissolution velocities for replicate experiments of C3A #1 in

398

33 mL min−1 solutions with (a) 70 % ethanol and (b) 80 % ethanol. Each of the four colored lines

399

represents the data from one replicate experiment.

400 401 402

3.3 Statistical Analysis of C3A Dissolution Kinetics The data from each experiment were collated from within the relatively constant rate

403

region and yielded the flux data shown in Figure 11. The flux increases with increasing water

404

activity as expected. In addition, Figure 11 indicates that dissolution flux is a spectrum of values,

405

as has been shown for C3S10 and other minerals,17,18,41,43–48 primarily as a result of the intrinsic

406

heterogeneity of crystalline surfaces. The distributions are non-normal and heavy-tailed

407

(skewed), which is similar behavior to the distributions in the literature.

408

Based on Eqs. (8) and (9), the estimated distributions of k+ for water are shown in Figure

409

12, using the method detailed in the Supporting Information Section S.1. Table 2 summarizes the

410

statistics of these distributions, including the mean, median, standard deviation, and interquartile

411

range (IQR). Assuming n is a constant value, from the method detailed in the Supporting

412

Information, n = 5.24 for C3A #1 and n = 4.62 for C3A #2 (see the Supporting Information for a

413

discussion of the uncertainty in n). In Figure 12 the modal value of k+ is −1.94 µmol m−2 s−1 and

414

the median value of k+ is −2.06 µmol m−2 s−1 for C3A #1, both of which agree with the value of

415

−2.07 µmol m−2 s−1 found by linear regression (see Figure S1). This also agrees with the

416

dissolution flux value of dissolution flux is −2.0 µmol m−2 s−1 that was proposed based on

19


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417

simulations.75 For C3A #2, the modal k+ is −1.28 µmol m−2 s−1 with a median k+ of −1.42 µmol

418

m−2 s−1.

419

(a)

(b)

420

Figure 11. Histogram of surface normal dissolution flux as a function of ethanol content for (a)

421

C3A #1 and (b) C3A #2.

422

423 424

Figure 12. Empirical distributions of k+ for C3A #1 and C3A #2, assuming n is constant. These

425

data are available in the Supporting Information.

426

20


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427

Table 2. Surface Normal Dissolution Flux Statistics Solution Ethanol Water Content Activity 60 % 0.824 70 % 0.777 80 % 0.689 Predicted k+ (assuming constant n)

C3A #1 Flux (µmol m-2 s-1) Standard Mean Median Deviation −1.12 −0.754 1.57 −0.608 −0.473 0.545 −0.363 −0.286 0.295

0.741 0.425 0.254

C3A #2 Flux (µmol m-2 s-1) Standard Mean Median IQR Deviation −0.671 −0.502 0.757 0.465 −0.454 −0.369 0.361 0.287 −0.352 −0.305 0.214 0.216

−3.25

3.15

−1.99

−2.06

4.42

IQR

−1.42

2.45

1.87

428 429

The dissolution behaviors of C3A #1 and C3A #2 are different, as is evident by Figure 12,

430

with C3A #2 dissolving more slowly than C3A #1. This may be a function of the crystallinity and

431

purity of the C3A samples, since C3A #1 was 94 % C3A-c while C3A #2 consisted of only 84 %

432

C3A-c, which may indicate preferential etching of crystalline phases (e.g., Ref. 73). C3A #2

433

might have fewer intrinsic crystalline heterogeneities, owing to its lower crystalline content,

434

which can affect the overall reactivity (e.g., see Ref. 67 and references therein).

435

The regression analysis yielded water activity exponent parameters, n, of 5.2 and 4.6 for

436

C3A #1 and C3A #2, respectively. These values differ from the stoichiometric value of 6 from

437

Eq. (6), which is not surprising since Eq. (6) only applies to elementary reactions and C3A

438

dissolution is almost certainly not elementary. The spatial heterogeneity in dissolution

439

morphology and fluxes suggests that different (i.e., multiple) reaction mechanisms occur,41,47,76,77

440

which are associated with various sources (e.g., defect type and density, crystallographic

441

orientation and exposed surfaces). Furthermore, the value of n computed by this study considers

442

the bulk effect of all morphologies. Further study is needed to link specific surface reaction

443

mechanisms to a given probabilistic dissolution flux (or range of fluxes) and reaction order. That

444

effort is being undertaken for other minerals with the help of kinetic Monte Carlo

445

simulations.35,47,78

446

However, what if n is not assumed to be constant? Kinetically, n can be non-constant for

447

multistep reaction processes,79 and, as already discussed, the dissolution of C3A is a complicated

448

process depending on composition, crystallinity, and structural defects. Performing the least

449

squares optimization (see Supporting Information) for the C3A #1 data under this assumption

450

yields a spectrum of n values with a modal value of 5.3, which is very similar to the value of 5.2

451

obtained if n is assumed constant. The assumption of a non-constant n would imply that n is a

452

different constant value for each specific value of k+, which means that further discretization

453

could yield many values of n. If there are multiple reactions, each with a different reaction order, 21


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454

it would be more reasonable to assume that there are a few constant n values, for example, one

455

value of n associated with each defect type. Further research is needed to confirm this, although

456

kinetic Monte Carlo simulations35,47,78 may offer additional insight.

457

Finally, the preceding analysis assumed that the data were obtained from experiments

458

without the formation of precipitated phases. To confirm this, the surface was examined a

459

posteriori by various techniques to search for evidence of any precipitated phases. XRD was

460

unable to detect any precipitated phase. SEM and Raman spectroscopy demonstrated that

461

precipitated phases could form under static solution conditions (see Figure S4 and Figure S6) but

462

showed no evidence of precipitation under flowing solution conditions (see Figure 5, Figure 7b,

463

and Figure S6). Therefore, the analysis is justified in assuming that the data are unadulterated by

464

precipitation in flowing solution experiments.

465 466 467

4. CONCLUSIONS Reflection digital holographic microscopy (DHM) was used to monitor the in situ, real

468

time nanoscale surface evolution of cubic tricalcium aluminate (C3A) in water in nominally

469

undersaturated conditions. The computed dissolution flux was observed to be a function of the

470

rate constant and the water activity raised to an empirically-derived exponent. Experiments were

471

conducted at multiple water activities to estimate these values.

472

The data and analysis strongly suggest that dissolution is spatially heterogeneous, owing

473

to the intrinsic variability of crystalline surfaces (e.g., defect density and type, crystal orientation,

474

etc.), thereby yielding a probabilistic distribution (histogram) of fluxes. Using least-squares

475

optimization, the shape of the empirical cumulative distribution function was derived to

476

determine the empirical probabilistic distribution of the rate constant. The rate constant

477

distribution was found to have median and interquartile range values of −2.1 µmol m−2 s−1 and

478

3.2 µmol m−2 s−1, respectfully, for highly crystalline C3A (94 % cubic C3A, 4 % amorphous

479

content) with a constant exponent of 5.2 and median and interquartile range values of −1.4 µmol

480

m−2 s−1 and 1.9 µmol m−2 s−1, respectfully, for less crystalline C3A (84 % cubic C3A, 10 %

481

amorphous content) with a constant exponent of 4.6. These data can now be used in

482

computational materials science models (e.g., HydratiCA75) to provide a more accurate

483

prediction of cement hydration.

484 22


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485

SUPPORTING INFORMATION

486

Accompanying supporting information is available free of charge via the Internet at

487

http://pubs.acs.org. This material includes an appendix detailing the analysis methodology and

488

surface examination for precipitated phases, a time-lapse video of Figure 7, and the data from

489

Figure 12. The data from Figure 12 can also be acquired at https://doi.org/10.18434/M3SW2G.

490 491

ACKNOWLEDGMENTS

492

The authors would like to thank Paul Stutzman (National Institute of Standards and Technology,

493

NIST) for his expertise and advice on XRD and SEM analyses, Pan Feng (Southeast University)

494

for discussions on experimental methodology, Adam Pintar (NIST) for suggesting the use of the

495

nonparametric least squares optimization utilized in this study, and LaKesha Perry (NIST) for

496

performing the ICP-OES measurements. ASB would like to acknowledge the National Research

497

Council (NRC) for funding through the NRC Postdoctoral Research Associateship program at

498

NIST.

499 500

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Dissolution Rate at Room Temperature in Conditions close to a Cement Paste: From

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Dissolution Kinetics of Cubic Tricalcium Aluminate ... - ACS Publications

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