Effect of temperature on the capillary transport of sodium sulfate solution in calcium silicate hydrate nanopore: A molecular dynamics study

Construction and Building Materials 231 (2020) 117111

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Effect of temperature on the capillary transport of sodium sulfate solution in calcium silicate hydrate nanopore: A molecular dynamics study Fengjuan Wang a, Yu Zhang a,b,⇑, Jinyang Jiang a, Bing Yin b, Zongjin Li c a b c

School of Materials Science and Engineering, Southeast University, Nanjing 211189, China Department of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

h i g h l i g h t s
Elevated temperature promotes the transport of water in the nanometer CSH channel.
Transport rate of sodium and sulfate ions is reduced under raised temperature.
Reduced transport rate of ions is due to formation and adsorption of ionic clusters.
It is related to three types of physiochemical behaviors caused by temperature.

a r t i c l e

i n f o

Article history: Received 8 June 2019 Received in revised form 14 September 2019 Accepted 27 September 2019

Keywords: Calcium silicate hydrate Capillary absorption Molecular dynamics Sodium sulfate Elevated temperature

a b s t r a c t This paper gives a new sight into the effect of raised temperature on the capillary transport and interaction of sodium sulfate with calcium silicate hydrate (C-S-H). Molecular dynamics is utilized and temperature parameters are set as 300, 330, 360, and 390 K, respectively. Elevated temperature promotes the transport of water in the nanometer C-S-H channel, however, the transport rate of sodium and sulfate ions in the channel is significantly reduced as a result of the formation and adsorption of ionic clusters on C-S-H channel. This unexpected phenomenon can be explained by three factors. Under elevated temperature, first, hydration shell of ions is weakened and thus increasing the probability of ion-ion and ionsubstrate contact. Second, more calcium is dissociated from C-S-H channel and resulting in the formation and precipitation of calcium sulfate, the precursor of gypsum. Third, the local structure of C-S-H channel is changed under elevated temperature, such as the dissociation of calcium from C-S-H channel, the strong stretching vibration of Si-Os bond and surficial hydroxyls, and increases in mean bond length of surficial hydroxyls. All of these increase the chemical activity of partial oxygen sites on C-S-H channel surface, contributing to more aqueous sodium ions adsorbed on C-S-H surface by electrostatic attraction from surficial oxygen. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Calcium silicate hydrate (C-S-H) gel, the main hydrated products of Portland cement (PC), is a porous material containing gel pores with diameter of 5–100 Å and capillary pores with diameter of 100–1000 Å [1]. These pores can act as capillary channels for the transport of water and aggressive ions in cement-based materials, and leading to a durability damage [2–4]. In particular, sulfate

⇑ Corresponding author at: School of Materials Science and Engineering, Southeast University, Nanjing 211189, China. E-mail address: [email protected] (Y. Zhang). https://doi.org/10.1016/j.conbuildmat.2019.117111 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

attack is an important durability concern as result of the reactions between cement hydration products and sulfate-bearing solution [5–7]. Ettringite and gypsum can be formed by these reactions, leading to the expansion and cracking of hardened cement [5,6]. Engineering application of cement-based materials is often accompanied by temperature variation such as in the case of fire, uses as nuclear power plants/wastes storage structure, serving as infrastructures in the saline land and marine environment with the land surface temperature fluctuating largely, and so forth. As temperature rises, thermal energy has an important influence on the state of flux of the ionic movement. Jooss et al. [4] and Reinhardt et al. [8] conducted tests of permeability of PC concrete

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as a function of temperature between 20 and 80 °C. The results showed a considerable increase of water transport with temperature. However, it is quite different for sulfate attack. Fevziye et al. [9] reported that the amount of sulfate ions penetrating into mortar sample at 20 °C was more than that at 40 °C, even though the water absorption amounts for both samples were similar. Besides, raising temperature from 20 °C to 40 °C was found to improve partial performances of the mortars exposed to sodium sulfate solution, such as an increase in mechanical strength [9]. Skaropoulou et al. [10] reported that the deterioration of the concrete samples exposed to 1.8% MgSO4 solution at 25 °C for 36 months was much lower than that at 5 °C, due to the formation of thaumasite at low temperature. It can be seen that temperature not only controls physical transport, but also influences chemical reactions between sulfate ions and cement hydrates. Another important example is that ettringite, the main reaction product during sulfate attack, is able to maintain stable at low temperature, but can be partially or completely decomposed under thermal environment [11]. Above experimental phenomena elucidate the extremely complicated mechanisms of sulfate attack to PC concrete, which is controlled by physical transport process and chemical reactions, especially in the environment with large temperature fluctuations. Overall, this is because that the thermal energy caused by temperature fluctuating has a great impact on the local structure of C-S-H gel and the dynamics of aqueous ions in C-S-H channel [12]. Unfortunately, detailed mechanism is far from being explained. It seems that it is difficult to make it clear by current experimental technologies alone. At present, there are a great many studies on mesoscopic and microscopic numerical simulations [13–17], which can successfully model the transport of water and ions in cement-based materials. But their concerns are limited by scale, usually porosity and transition zone, etc. The modelling of chemical reactions generally requires the introduction of other related theoretical model and empirical parameters, so the intrinsic mechanisms cannot be achieved. Molecular dynamics (MD) have the potential to give such explanations. With force field parameters derived from quantum mechanics, MD is able to provide a quantitative intrinsic illustration on the structure, reactivity, dynamics, and energy of the system on the molecular level. Based on MD, the model of the interface between C-S-H and solution was reported in the previously papers to be utilized to study the interaction of C-S-H with water and ions [18–22]. The results showed that the properties of water molecules confined in nanometer pore were dramatically different from that in bulk water, e.g., mobility, ionic hydration structure, and hydrogenbond network, due to the electrostatic and geometric restrictions from C-S-H surface. The adsorption of aggressive ions and leaching of cations have been quantitatively investigated by the MD method. Currently, Hou et al. [23–25] first proposed a two-dimensional capillary model, giving an accurate description of the process of water capillary absorption and explained the discrepancy of transport mechanism between ions and water molecules. The study provides molecular insights on the migration of ions and it is valuable for understanding durability problem in cement-based material. This paper gives a new sight into the capillary transport of sodium sulfate in C-S-H nano channel under a series of temperature gradient by means of molecular dynamics. Also, the physical and chemical interaction of sodium sulfate with C-S-H gel were directly probed on the molecular level. Detailedly, we investigated the dynamics, distribution, and local structure of water and ions at 300, 330, 360, and 390 K. Some experimental phenomena mentioned above can be well explained here on the molecular level. Hopefully, this work can promote the understanding on the sulfate attack to the cement-based materials exposed to the environment with large temperature fluctuation.

2. Methodology 2.1. Model construction The model of sulfate solution penetrating into C-S-H nanometer channel was built as shown in Fig. 1. It consists of two parts: C-S-H channel and 1 mol/L sodium sulfate solution. Two C-S-H sheets were placed above the solution and perpendicular to it. Tobermorite11Å crystal was utilized to model the C-S-H sheet in this study due to they had similar layered structure and chemical composition, and same exposed surface to water. Such utilizations of Tobermorite11Å in the problem of transport and interface is extensively accepted and achieved good results in many published articles [20,24–28]. Sodium sulfate solution contains 5196 water molecules, 180 sodium ions and 90 sulfate ions, and its construction used Grand Canonical Monte Carlo (GCMC) method, employed GCMC package on LAMMPS [29], to introduce water molecules into the box. First, ions were irregularly placed in the region of solution. Then GCMC method was utilized to distribute 5196 water molecules over the solution region (10 nm  7 nm  2.22 nm) to reach the density of 1 g/cm3. Every 10 steps, water molecules can be inserted, deleted, and rotated in the solution region. When a water molecule was inserted, its coordinate was chosen randomly within the solution region, and its velocity was randomly assigned based on specified temperature. The maximum rotation angle of inserted water molecules is set as 180 degrees. Periodic boundary was set in both  and z direction. Vacuum space was set on the top and bottom of the box to avoid water molecules escaping along y direction. 2.2. Force field and simulation process C-S-H channel and sulfate solution were simulated under ClayFF force field [30], which is based on a rigorous analysis of experimental

Fig. 1. Model construction of sulfate solution penetrating into C-S-H channel.

F. Wang et al. / Construction and Building Materials 231 (2020) 117111

X-ray diffraction data and charge assignment from quantum mechanics calculations. Mixing rule of arithmetic mix is utilized to calculate interatomic parameters. ClayFF has been confirmed to be accurate to describe the interaction between calcium, silicate, oxygen, and hydrogen of C-S-H [19,31] by using Lennard-Jones function and Coulomb formula. Classic single point charge (SPC) model was employed to model water molecules. In the previously published paper, ClayFF was extensively used to model the clay materials with silicon and aluminum species, behavior of water and ions in both bulk and confined solution, and the interaction of water/ions with clay materials [19,20,32–34]. The simulation was conducted on LAMMPS [29], a large-scale atomic/molecular massively parallel simulator. Simulated environment was set as 300, 330, 360, and 390 K, respectively, to research the effect of temperature on the capillary absorption of C-S-H gel. The pressure was 1 atm and time step was 0.002 ps. Thermodynamic information such as pressure, temperature and energy was monitored and modified at regular intervals by using NoseHoover thermostat to ensure stability of the system. Verlet algorithm was utilized to compute the trajectory of atoms of each time unit. Simulation process was divided into two steps. First, C-S-H sheets and solution were relaxed under NVT run, and yet an invisible wall was placed between them to avoid the penetration of solution into the C-S-H channel. This step ran for 500 ps to obtain a well equilibrated C-S-H sheets and sulfate solution. Second, the invisible wall was removed to allow the solution to penetrate into C-S-H channel. This step ran for 2000 ps under NVT resemble, during which the trajectory of atoms were recorded every 0.1 ps for statistical analysis.

3. Results and discussions 3.1. Water and ions penetrating into C-S-H channel Snapshots of water and ion imbibed into C-S-H channel is shown in Fig. 2. An advancing meniscus of water can be observed inside the nanometer channel, which is the typical feature of capillary absorption of water. Also, the contact angle of water is less than 90 degrees, indicating the hydrophilicity of C-S-H channel surface. As the temperature rises from 300 K to 390 K, the imbibition rate of water increases. Besides, more Na+/SO24 clusters can be observed in elevated system, especially at 390 K. Variation of penetration depth of water and ions with simulation time is plotted as shown in Fig. 3a. The penetration depth of

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water is computed based on the bottom of the capillary meniscus of water (see Fig. 2). The penetration rate of the species in the solution can be ranked as follows: water > Na+ > SO2 4 , indicating the selectivity of C-S-H nanometer channel and asynchronous transport, It matches well with the experimental results in the published paper that the nanopores of hardened cement paste act like a molecular filter and hinder the transport of ions [35]. It has been reported [23] that this is related to the electrostatic interaction of ions with C-S-H gel pore, resulting in the adsorption of ions on C-S-H channel and further blocking the channel. As shown in Fig. 3a, the profiles of penetration depth of water follows a visco-inertia regime that is defined by the classic Lucas-Washburn equation [36], Eq. (1). It described the capillary transport process to be a square root dependent on time, which is governed by capillary force and viscous force. On the molecular level, they are derived from the attraction force of electrostatic and van der Waal force from the hydrophilic channel surface and the hydrogen-bonding between water molecules and channel, respectively, which are modeled by ClayFF force field algorithm. Fig. 3b shows sulfate concentrate profiles and it follows Fick‘s second law as determined by Eq. (2). Also, the diffusion coefficient D obtained decreases as diffusion time increases. Both of them confirm the accuracy of MD simulation using ClayFF force field predicting capillary absorption.

yðtÞ ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r rtcosh 2l

ð1Þ

where y represents penetration depth; r is nanopore radius; r is the surface tension of water molecules; l is the viscosity of water; and h is contact angle.

x Cðx; tÞ ¼ C 0 þ ðCS  C 0 Þð1  erfð1  pffiffiffiffiffiffiÞÞ 2 Dt

ð2Þ

where C is sulfate concentration; x stands for the distance along the channel; t represents the duration of exposure to sulfate solution; C0 is the initial sulfate content in the channel, which is zero; Cs is the sulfate concentration at the beginning of the channel; and D is apparent chloride diffusion coefficient, while erf(z) is error function. Penetration depth of each species in the solution as function of time is shown in Fig. 4. As temperature is elevated, the kinetic energy of water molecules increases and water penetrates more quickly. Taking the 800th ps as an example, the penetration depth of water is 52, 61, 78, 86 Å for the sample at 300, 330, 360, and

Fig. 2. Snapshots of capillary flow of water and ions in C-S-H channel.

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Fig. 3. (a) Penetration depth of water and ions variation with simulation time at 300 K; (b) sulfate concentration variation as function of penetrated depth at 300 K. The fitting function is based on Fick‘s second law, where Cs is the concentration at the entrance of the channel; t is the simulation time; and D is diffusion coefficient.

Fig. 4. Penetration depth of (a) water, (b) sodium, and (c) sulfate as function of simulation time.

390 K, respectively. It is well known that the surface tension and contact angle of water decrease with temperature rising, which increases capillary force and thus promotes water penetrating into capillary pore. However, the penetration of ions does not follow it, and its penetration rate drops sharply at 390 K. The penetration depth of sulfate ions at 390 K only reach 41 Å at the simulation time of 1400 ps, which is equal to that at 300 K. In addition, a great decline of penetration rate of ions occurring at 300 ps can be observed in all samples. The phenomenon above is due to the formation of ionic clusters. Intensity distribution of ions along z direction is shown in Fig. 5. As shown in Fig. 5a, peaks 1, 2, and 3 of Na and S are

orderly located near the C-S-H substrate, meaning the layered packing of sodium and sulfate ions on C-S-H substrate. As shown in Fig. 5d, C-S-H channel with negative charge electrostatically attracts sodium ions and repulses sulfate ions. However, sulfate ions can be indirectly adsorbed on the channel by the formation of ionic pairs with sodium ions. As a result, the anion and cation layers are orderly distributed on the channel. When the temperature rises to 390 K the peak intensity increases significantly. Numerous ionic clusters are formed and adsorbed on C-S-H channel, and there is almost no ion remaining in the center of the channel. Meanwhile, the ordered distribution of anion and cation layer is distorted.

F. Wang et al. / Construction and Building Materials 231 (2020) 117111

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Fig. 5. Intensity distribution of Na and S along z direction when the temperature of whole system is set as (a) 300 K, (b) 360 K, and (c) 390 K; (d) schematic diagram of ionic pairs adsorbed on channel surface at 300 K.

The kinetic energy of the solution increases with temperature, however, more and more ionic clusters are formed and adsorbed on C-S-H channel. This strange phenomenon can be explained by the following three aspects: the weakening of hydration shell of Na+ and SO24 , the precipitation of calcium sulfate, and chemical activity enhancement of oxygen site on C-S-H channel, which are discussed below in detail. 3.2. Weakening of the hydration shell of Na+ and SO2 4 Radial distribution function (RDF) and coordination number of Na and S are listed in Fig. 6 and Table 1, respectively. They describe variations on local structure of aqueous sodium and sulfate ions with temperature and reflect the hydration structure of ions. Cutoff distance for calculating coordination number is based on the first minimum of RDF. For sodium ions, hydration number of the first hydration shell is 4.47 and total coordination number is 5.5 at 300 K. Na-H2O bond length in the first hydration shell is round 245 pm, and distance from the second hydration shell is around 450 pm. According to diffraction studies the hydration number of aqueous sodium ions in the first hydration shell was distributed over the range 4–8 [37,38], and its radius of the first hydration shell fell in a range of 240–250 pm [37,38]. The radius of the second hydration shell calculated by simulation was ranged from 441 to 480 pm [39]. With respect to sulfate ion, it can strongly combine with water molecules and still keeps some water molecules even in crystals of metal sulfates. According to the results by X-ray diffraction studies of sulfate aqueous solutions, an sulfate ion was surrounded by about 7–12 water molecules with S-Ow bond length of

370–393 pm [40,41]. The simulation with ClayFF force field yields the number of Ow surrounding sulfate ions of 11.62 and the radius of hydration shell (S-Ow) of around 375 pm, matching well with the above diffraction studies, confirming the accuracy of molecular dynamics simulating aqueous species. As shown in Fig. 6a and b, short-range and medium-range spatial correlation gradually reduces with temperature rising, implying a reduction of hydration number of the first and second hydration shell of aqueous sodium and sulfate ions. In Table 1, the hydration number in the first hydration shell decreases by 1.63 and 3.3 for sodium and sulfate ions, respectively when the temperature rises from 300 K to 390 K. It is related to a significant increase in the mobility of water molecules caused by temperature rising that encourages some water molecules to break away from the hydration shell of ions. We carried out another simulation test (Supporting Information), in which only one sodium or sulfate ion is mixed with water molecules, and the weakening of hydration shell has been confirmed. It can also be found in the previously published MD study [12] that the H-bond network between water molecules becomes loose with elevating temperature, and some Hbonds even breaks as a result of thermal damage. The weakening of hydration shell weakens the hydration shell‘s restriction on aqueous ions and increases the chance of cations and anions colliding with each other and forming ionic pairs. As shown in Fig. 6c and Table 1, the spatial correlation between Na and S increases with temperature and the coordination number of both Na-S and S-Na doubles to 2.18 and 4.21, respectively. The Na+/SO2 4 ionic clusters can be observed in bulk solution and channel surface in Fig. 2 at 390 K, and Fig. 7 shows an enlarged view. Numerous sulfate and sodium ions gather together by electrostatic

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Fig. 6. Radial distribution function of (a) Na-Ow, (b) S-Ow, and Na-S. Ow is the oxygen in water molecules.

Table 1 Coordination number of Na and S at different temperature. Na

300 K 330 K 360 K 390 K

S

Na-Ow

Na-S

Na-Os

Total

S-Ow

S-Na

S-Ca

Total

4.47 3.86 3.53 2.84

0.90 1.30 1.51 2.18

0.12 0.21 0.24 0.25

5.49 5.37 5.28 5.26

11.62 10.45 9.99 8.32

1.82 2.55 2.89 4.21

0.05 0.14 0.32 0.36

13.49 13.21 13.28 13.02

Note: Ow is the oxygen in water molecule; Os is oxygen in silicate chain of C-S-H substrate.

attraction to form a large ionic cluster. There is also some calcium dissociated from C-S-H channel distributed among the cluster, which is marked by arrow in the figure. 3.3. Precipitation of calcium sulfate on C-S-H channel It can be observed that calcium is dissociated from C-S-H matrix into sulfate solution. Taking the 700th ps as an example, the dissociated number of calcium at different penetration depth is counted as shown in Fig. 8a and b. For easy understanding, C-S-H channel imbibing solution at 700 ps is set as background. As shown in Fig. 8a, the number of dissociated calcium is reduced as penetration depth increases. It decreases to 0 at the end of the channel because the solution has not been transported to this region. It is clear that the dissociated number of calcium is determined by the contact time of C-S-H substrate with water. In addition, temperature is the other influencing factor. The dissociated number of calcium at 390 K is around twice as large as that in the case of 300 K. The temperature elevates the kinetic energy of calcium in C-S-H and reduces the reaction barrier, contributing to the escape of calcium from geometrical restriction of

silicate chains and ionic bond of Ca-Onb (Onb is non-bridging oxygen in silicate chains). Once the calcium is dissociated and comes into contact with water, the dissociated calcium will collide with water molecules strongly and is probably trapped in the solution. According to the statistics, the number of dissociated calcium at 390 K is 9.66, around 174% more than that at 300 K when the simulation time is 700 ps. As more and more calcium ions are dissociated from C-S-H substrate to solution, sulfate ions have more probability to contact them by electrostatic attraction and form slightly soluble product, calcium sulfate. As shown in Table 1, the number of coordinated calcium surrounding sulfate ions increases from 0.05 to 0.36 as temperature rises from 300 K to 390 K. Besides, as shown in Fig. 8c, three Ca-S peaks at the range of 3–4 Å, 5–6 Å, and 8–10 Å become stronger with temperature rising, indicative of the enhancement of the short-, medium-, and long-range spatial correlation between Ca and S with temperature, meaning a stronger interaction between them and more accumulation of calcium and silicate ions. It elucidates the formation and growth of calcium sulfate with temperature rising. It leads to the precipitation of calcium sulfate on C-S-H channel, which further results in the formation of

F. Wang et al. / Construction and Building Materials 231 (2020) 117111

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gypsum and causing partial volume expansion and internal stress generated inside C-S-H gel in the case of engineering applications. Particularly for infrastructures serving in marine environment, sulfate attack is a main factor of cracking cement-based concrete materials, which is related to the formation of ettringite and gypsum [42]. Time correlated function (TCF) of Ca-S chemical bond is investigated to reveal the stability of calcium sulfate cluster at different temperature, and it is calculated by Eq. (3).

CðtÞ ¼

Fig. 7. A snapshot of ionic cluster formed and adsorbed on C-S-H channel.

< dbðtÞdbð0Þ > < dbð0Þdbð0Þ >

ð3Þ

where db(t) = b(t)  , b(t) is a binary operator that is the value of 1 if the chemical bond is bonded and 0 if not, and is the average value of b over the whole simulation time. Generally, the bond stability can be evaluated by calculating the deviation from value of 1. The lifetime of Ca-S bond is computed by the integration of TCF curves for quantitative analysis. As shown in Fig. 8d, the TCF value of Ca-S bond decays gradually from 1 to around 0.9 during the simulation time of 200 ps, indicating that most of Ca-S bond remains bonded and the minorities are broken. The broken ratio of Ca-S bond is fluctuated with temperature changes, and its lifetime decreases first and then increases as temperature rises. Overall, it is controlled by two factors, the

Fig. 8. Number of dissociated calcium at different penetrated depth at (a) 300 K and (b) 390 K; (c) radial distribution function (RDF) of Ca-S; (d) time correlated function (TCF) of S-Ca bond. The insert is the lifetime of the chemical bond.

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dissolution and growth of calcium sulfate. Elevated temperature increases the kinetic energy of Ca2+ and SO2 4 species and intensifies the collision of water molecules with calcium sulfate. It is well known, however, that temperature variation has a slight effect on the solubility of calcium sulfate. As temperature rises, more and more calcium ions are dissociated from C-S-H matrix and aggregate with sulfate ions forming larger and larger clusters. The chemical bonds inside the Ca2+/SO2 4 cluster is much more stable than the superficial ones. 3.4. Chemical activity enhancement of oxygen site on C-S-H channel Elevated temperature changes the structure of C-S-H substrate. In addition to the dissociation of calcium, thermal stretching vibration of Si-Os bond and surficial hydroxyls (Os-Hs) can also be observed with temperature rising. As shown in Fig. 9a and b, the RDF peaks become wider and weaker, indicating an increase in stretching vibration of Si-Os and Os-Hs (surficial hydroxyls). Also, the mean bond length of Os-Hs increases from 0.985 to 1 Å when temperature rises from 300 K to 390 K, which means an increase in polarity of surficial hydroxyl groups. A slight elongation of SiO bond can also be observed at 390 K. According to the previous experimental results of X-ray absorption fine structure (EXAFS) [43] and neutral diffraction [44], the Si–O bond length was found to be between 1.608 and 1.62 Å. In this study the Si–O bond length obtained is around 1.62 Å at 300 K, consistent with the experimental results. The variation on C-S-H structure mentioned above, dissociation of calcium, strong stretching vibration of Si-Os and Os-Hs (surficial hydroxyl), and thermal elongation of Os-Hs bond length, increase the chemical activity of some oxygen sites on C-S-H surface. As a result, aqueous sodium is more likely to be electrostatically

attracted to C-S-H substrate. As shown in Fig. 9c, the spatial correlation between Na and Os at the range of around 2–3 Å, 4–5 Å, 6– 8 Å is enhanced with temperature rising, implying a stronger interaction between them and more accumulation of sodium ions on the channel with temperature. As listed in Table 1, the number of sodium bound to Os increases from 0.12 to 0.25 as temperature rises from 300 K to 390 K. Time correlated function (TCF) of Na-Os at different temperature is plotted in Fig. 9d. The TCF profile of Na-Os decays progressively from 1 to around 0.6 during the simulation time of 200 ps. Its chemical bond strength is weaker than Ca-S bond in aqueous solution according to the comparison of TCF between them, which also reflects the difference in their solubility. As shown in the insert in Fig. 9d, the lifetime of Na-Os bond decreases from 68 to 62 ps in the range 300–360 K, and then it increases to 71 ps at 390 K. The stability of Na-Os ionic bond is influenced by its chemical environment and temperature. The sodium bound to C-S-H surface is collided by nearby water molecules, resulting in the breakage of some Na-Os ionic bonds (thus the TCF value reduces with time all along). Elevated temperature intensifies the collision between atoms, but also improves the chemical activity of Os on CS-H surface correspondingly. 3.5. Dynamics of ions at different temperature Dynamics is another perspective to study the effect of temperature on water/ions transport, and investigated by means of displacement distribution and self-diffusion coefficient. These two methods are based on mean square displacement (MSD), which are calculated by Eq. (4).

MSDðtÞ ¼< jr i ðt Þ  r i ð0Þj2 >

ð4Þ

Fig. 9. Radial distribution function of (a) Si-Os, (b) Os-Hs (surficial hydroxyls), and (c) Na-Os. Os is the oxygen in silicate tetrahedron on C-S-H channel; Hs is the hydrogen in surficial hydroxyls; (d) time correlated function of Na-Os. The insert is the lifetime of the chemical bond.

F. Wang et al. / Construction and Building Materials 231 (2020) 117111

2DðtÞ ¼

1 MSDðtÞ n

ð5Þ

where ri (t) is the position of atom i at time t. The self-diffusion coefficient (D) is calculated by Eq. (5), and n is the dimension of calculated diffusion coefficient. Displacement distribution of water molecules in YZ plane at 700 ps is shown in Fig. 10. It reflects the mobility of water molecules at each position in the channel and the influence of temperature on water transport. As shown in Fig. 10, a frontier of solution with crescent shape can be observed inside the channel. Water molecules at the frontier moves fastest, where water molecules are driven by capillary force and carries water molecules behind moving upward. The mobility of the water at the entrance of the channel is the lowest. These water molecules are confined by wan der vaals and H-bond restriction from C-S-H surface.

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Therefore, it leads to the narrowing of the channel in the figure of displacement distribution (in Fig. 10). As temperature rises from 300 K to 390 K, the mobility of water molecules at any position of the channel increases progressively. The improved mobility of the water molecules at the frontier and near the channel elucidate the enhanced capillary force and the reduced binding force from the channel. Overall, the mobility of water molecules characterized by self-diffusion coefficient (D) as shown in Fig. 11a also shows an increased trend, such as the D at 600 ps is 0.76, 0.98, 1.2, and 1.79  108 m2/s, respectively. The mobility of water drops sharply during the simulation time from 0 to around 200 ps, and then the downward trend slows down and the mobility tends to be stable. It is related to the balance between capillary force and viscous force, which matches well with the penetration depth variation with time in Fig. 4a.

Fig. 10. Displacement distribution of water molecules in YZ plane. The value of the color bar is taken from mean square displacement.

Fig. 11. Self-diffusion coefficient of (a) water molecule, (b) sodium, and (c) sulfate ions at different temperature.

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With respect to ions, their self-diffusion coefficients have dropped twice during the simulation. The first drop of these four samples is synchronous and caused by the sharp drop of the mobility of water. The second drop is not synchronous. It comes earliest in the model at 390 K when it is about 280 ps, followed by the model at 360 K and 330 K. It cannot be observed in the model at 300 K. Besides, the decreased degree of the self-diffusion coefficients increases with temperature. This is related to the formation of ionic clusters in the C-S-H channel. Under the influences of three factors as mentioned in Sections 3.2, 3.3 and 3.4, elevated temperature promotes the formation and growth of ionic clusters, which is more likely to be adsorbed on C-S-H channel with mobility significantly slower than that of individual ions, and further blocking the passage of other ions. As shown in Fig. 11b and c, the self-diffusion coefficient of ions is almost 0 m2/s after 900 ps for the sample at 360 and 390 K. As shown in Fig. 11c, the self-diffusion coefficient of sulfate ions at the beginning is almost 0.9 times smaller than that of sodium ions. At the later stage, the fluctuation of the self-diffusion coefficient of sulfate ions is almost same as that of sodium ions. It means the strong spatial correlation between them in C-S-H nano channel. 4. Conclusions Elevated temperature promotes the imbibition of water into nanometer C-S-H channel, but reduces the transport rate of sodium sulfate ions as a result of the formation of ionic clusters. There are three factors contributing to more ionic clusters formed and adsorbed on C-S-H channel under elevated temperature: (1) Elevated temperature weakens hydration shell of Na+ and SO24 , increasing the probability of ion-ion and ionsubstrate contact. (2) Elevated temperature promotes the dissociation of calcium from C-S-H matrix, resulting in the formation and precipitation of slightly soluble products, calcium sulfate, in C-S-H channel. (3) Elevated temperature changes the structure of C-S-H channel, such as the dissociation of calcium from C-S-H matrix, the strong stretching vibration of Si-Os bond and surficial hydroxyls, and increases in mean bond length of surficial hydroxyls. Both of them increase the chemical activity of some oxygen sites on C-S-H channel surface, contributing to more aqueous sodium ions adsorbed on C-S-H surface by electrostatic attraction from surficial oxygen.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Financial support from China Postdoctoral Science Foundation under Grant 2018M642630, Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen Durability Center for Civil Engineering, Shenzhen University under Grant GDDCE 18-4, Shandong Provincial Natural Science Foundation of China under Grant ZR2019MEM041. References [1] D.A. Lange, H.M. Jennings, S.P. Shah, Image analysis techniques for characterization of pore structure of cement-based materials, Cem. Concr. Res. 24 (1994) 841–853.

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