Early-age Hydration Process Research Articles

Effect of fly ash on properties and hydration of calcium sulphoaluminate cement-based materials with high water content

Abstract In this study, the effects of fly ash (FA) on the setting time, compressive strength, and hydration evolution of calcium sulphoaluminate (CSA) cement-based materials with high water content were investigated, targeting the design of a modified high-water material to delay excessively rapid setting time and enhance later-age strength. This was investigated using a combination of X-ray diffraction (XRD), Fourier transform infrared resonance (FTIR) spectroscopy, and Thermogravimetric Analysis (TGA). The results showed that the setting time of the high-water materials was delayed by increasing the FA content, with 15% being the optimal dosage for the setting time. A 5–10% content of FA is conducive to the development of later-age compressive strength and has a slight adverse effect on the early-age compressive strength of high-water materials. The microscopic test results show that FA mainly acts as a microaggregate in the early-age hydration process, whereas in the later-age hydration process, it promotes gypsum consumption and C2S hydration to form ettringite. The incorporation of FA effectively promotes ettringite formation in CSA cement-based materials with high water content. Therefore, the addition of FA can enhance the overall performance of high-water materials to a certain extent, and the long-term strength development of the material can satisfy engineering requirements.

Understanding the role of natural pozzolana in regulating the early hydration reaction process and microstructure of Portland cement

The present study examines the regulatory role of natural pozzolana (NP) on the early-age hydration process and microstructural development of Portland cement. Through a series of experiments, including low-field nuclear magnetic resonance (NMR), X-ray diffraction (XRD), thermogravimetric (TG) analysis and scanning electron microscopy (SEM), it was found that NP significantly influences the hydration kinetics and chemical shrinkage of cement paste. The addition of NP was shown to reduce the early-age chemical shrinkage and refine the microstructure by decreasing the quantity of harmful pores and increasing harmless pores, as evidenced by the bimodal distribution observed in pore size distribution (PSD) analysis. XRD and TG results indicate that NP reacts with calcium hydroxide to form additional calcium silicate hydrate (C-S-H) gel, thus improving the interfacial transition zone and resistance to carbonation. SEM micrographs further confirm the improved microstructure with fewer microcracks. The findings suggest that NP can be effectively utilized to optimize the early-age performance of concrete, offering a sustainable approach to improving its durability and long-term structural integrity.

Fractal evolution model of proton spatial distribution in low water/binder cement-based composites (LW/B-CC) during early-age hydration process

This study establishes the fractal evolution model of proton spatial distribution in low water/binder cement-based composites (LW/B-CC) based on fractal theory and low field nuclear magnetic resonance (LF NMR) technology. The results show that the fractal evolution process of gel water, capillary water and surface water distributions in LW/B-CC presents three stages: the first 4–6 h after the beginning of hydration, 4–6 h to 12 h, and 12 h to long-term stage. In the first and second stages, the fractal dimensions of gel and capillary water increase linearly with hydration time, while the fractal dimension of surface water decreases linearly. The boundary is a sudden change of fractal dimensions after about 4–6 h of hydration. The third stage starts after about 12 h of hydration, at which time the fractal dimensions begin to converge to fixed values. Besides, this study reveals the mathematical relationship between fractal dimension (Df) and particle size distribution modulus (q), which is conducive to achieve the full-cycle regulation of LW/B-CC.

Early-age inhomogeneous deformation of 3D printed concrete: Characteristics and influences of superplasticizer and water-binder ratio

3D printed concrete (3DPC) commonly experiences significant shrinkage along the printing direction (x-direction) at the early-age for its high cementitious material content, low water-binder ratio and formwork-free manufacturing process. This shrinkage with gradient along the vertical direction (z-direction) can cause interlayer slippage and further deformation within each filament. To investigate these early-age deformations and their dependence on materials, digital image correlation (DIC) was used to monitor the inhomogeneous deformation of 3DPC at the age of 0.5–6.5 h. It was found x-direction inhomogeneous shrinkage pattern is correlated with early-age hydration process and elastic modulus. After conducting mechanic analysis, it was found that an individual filament could be treated as a Winkler foundation beam with frictional moment, which can provide a semi-quantitative explanation of the phenomenon that the bottom filament shows significant downward deflection, while other layers show minimal upward deflection or almost no deflection. Additionally, the influence of superplasticizer and water-binder ratio on early-age inhomogeneous deformation was monitored. There exists an optimal dosage range for superplasticizer that ensures both better printing quality and lower x-direction shrinkage, shrinkage gradient as well as bottom layer deflection. With the same printing quality, early-age shrinkage, shrinkage gradient and the bottom layer deflection were reduced by adopting higher water-binder ratio. The influence of materials on the moisture evaporation rate and early-age strength was also measured and correlated with early-age x-direction shrinkage, shrinkage gradient of 3DPC and the extent of early-age bottom layer deflection.

Effects of nano-silica modification on early age hydration process in winter construction of tunnel engineering

Fast hardening and high early strength are crucial factors for concrete used in tunnel construction in cold regions. The incorporation of nano-silicate has been found to be an effective method for improving the properties of cement-based materials at an early age. Thus, the objective of this paper is to investigate the nano-modification effects of different nano-silica contents on the hydration process, mechanical properties, and hydration products of cement cured in a low-temperature environment. The effects of various nano-silica concentrations, including 1%, 2%, 3%, and a high dose of 6%, on the properties of the concrete were investigated. According to the test results, the optimal quantity of nano-silica plays a crucial role in determining the properties of concrete. The effects of nano-silica on the hydration of C3A were found to dominate the cement hydration process at an early age. The incorporation of nano-silica led to a significant improvement in the dissolution rate of anhydrite and the reaction rate of the C3A renewal, which may be responsible for the gain in early strength of concrete. However, an excessive amount of nano-silica could negatively affect the hydration process of the alite and C3A, as evidenced by the total heat generated during the silica and aluminate reactions. The XRD patterns further confirmed these results.

Early hydration studies of cementitious materials incorporating nanoalumina

Concrete technologists use different types of additives such as fly ash, slag, natural pozzolans and nanomaterials toenhance concrete performance and durability. However, a detailed explanation of the early-age hydration process and microstructural modification of concrete in the presence of nanomaterials remains to be presented and extensive research is required for strategic modification of cementitious systems. This study focused on the precise monitoring of early-age hydration with the incorporation of nanoalumina (nAl) in tricalcium silicate (C3S) and Portland cement paste and mortar. The dosage of nAl was varied from 1 to 5% (by weight) in C3S and from 0.1 to 1.0% in Portland cement, with a water/cement ratio of 0.4. The hydration studies showed that the nAl increased the cross-linkage in calcium silicate hydrate gel through substitution of aluminium by silicon, which was responsible for the enhancement of the modulus of elasticity (by 40%) with 1.0% nAl) after 7 days of hydration. In summary, the incorporation of nAl modified the concrete microstructure in the initial days of hydration, leading to higher concrete performance and longer service lives of concrete structures.

The Influence of Alkali Content on the Hydration of the Slag-Based Geopolymer: Relationships between Resistivity, Setting, and Strength Development.

This study investigated the influence of alkali content on the early-age hydration process of slag-based geopolymer and the feasibility of non-destructive resistivity. Results showed that there existed a threshold of alkali content in adjusting the early-age hydration. Initially, increasing the alkali content tended to accelerate the dissolution period (detected by resistivity and heat release rate) and resulted in a denser microstructure (detected by TEM). When the alkali content surpassed 6 wt%, the increasing alkali content mitigated the structural development of a slag-based geopolymer, as it lowered the liquid water content and caused local precipitation, which trapped the early-age ions transmission and, therefore, the later-age mechanical development was inhibited. It was proven that the resistivity acted as a linkage among the reaction degree, workability, and strength development.

Effect of phosphates on early-age hydration process and products of calcium aluminate cement at −10 °C

• The effect of different phosphates on the setting behavior of CAC at −10℃ was analyzed. • The mechanism of sodium pyrophosphate modification of CAC was described. • New crystal products of phosphate-modified CAC were found. • A kind of cement system which can set and harden well at negative temperature is presented. Phosphates can effectively enhance the hydration rate of calcium aluminate cement (CAC). In order to explore the application potential of phosphates modified CAC at negative temperature, this study investigates the hardening and hydration characteristics of CAC modified with four kinds of sodium phosphates (Na 3 PO 4 , Na 4 P 2 O 7 , Na 5 P 3 O 10 , and ((NaPO 3 ) n ) at −10 ℃. Among those four different systems, the mechanism of the CAC modified by Na 4 P 2 O 7 with the best setting and mechanical performance is discussed. The results indicates that, the increase of the content of Na 4 P 2 O 7 increases the production of canaphite (CaNa 2 P 2 O 7 ·4H 2 O) at the early stage of hydration which makes the paste harden and set more rapidly at −10 ℃. However, in the following hydration process the content of CAH 10 decreases, resulting in the loose and defective microstructure, and the insufficient compressive strength development. The CAP2 system with 10% Na 4 P 2 O 7 content has good setting performance and strength development. The final setting time of cement is 130 min, and the compressive strength of cement reaches 47 MPa at 7d.

Rheological Properties and Early-Age Microstructure of Cement Pastes with Limestone Powder, Redispersible Polymer Powder and Cellulose Ether.

In order to study the synergistic effects of organic and inorganic thickening agents on the rheological properties of cement paste, the rheological parameters, thixotropy cement-paste containing limestone powder (LP), re-dispersible polymer powder (RPP), and hydroxypropyl methylcellulose ether (HPMC) were investigated using the Anton Paar MCR 102 rheometer at different resting times. The early-age hydration process, hydration products, and microstructure were also analyzed with scanning electron microscopy (SEM) and thermogravimetry analyses (TGA). The results showed that the addition of LP, RPP, and HPMC affected the rheological properties of cement paste, but the thickening mechanism between organic and inorganic thickening agents was different. The small amount of LP increased the plastic viscosity but decreased the yield stress of cement paste due to its dense filling effect. Adding 1% of RPP improved the thixotropic property of cement paste by 50%; prolonging the standing time could improve the thixotropic performance by as much as two times. Only 0.035% HPMC added to the cement paste increased the plastic viscosity by 20%, while the yield stress increased nearly twice. The more HPMC added, the more significant effect it showed. Cement paste compounds with LP, RPP, and HPMC balanced the yield stress and plastic viscosity and improved the thixotropy. The C-L6-R1.0-H0.035 paste presented as a pseudoplastic, its rheological indexes were close to one, and it was hardly affected by the resting time. The composite superposition effect of organic and inorganic thickening agents reduced the impact of resting time for all pastes. As the organic thickening component inhibited the hydration more than the LP promoted the hydration of the cement paste, indicating that the C-L6-R1.0-H0.035 paste remained in the particle fusion stage after curing for three days, as shown by the SEM images.

Analysis of Early-Age Hydration Behavior and Micro-Mechanism of Coral Sand Cement Mortar.

Coral sand cement (CSC) mortar is increasingly used in reef projects, which is prepared by mixing coral sand with cement and water in certain proportions. Considering that early-age hydration behavior is closely related to the strength and durability of the mortar, the early-age hydration process and micro-morphology of CSC mortars with various water–cement ratios (W/C) and sand–cement ratios (S/C) were studied. A monitoring system based on FBG is proposed in this paper, which uses the high sensitivity and conformability of optical fiber to measure the hydration temperature and internal shrinkage strain simultaneously and continuously. The standard sand cement (SSC) mortar with the same sand gradation and mix proportion is also prepared for comparison. The micro-morphology is observed by a scanning electron microscope (SEM) for measurement results’ explanation. The results show that the variation of the hydration temperature and shrinkage strain with hydration time of both CSC mortars and SSC mortars follow a unimodal function. Differently, the peak hydration temperature for CSC is obviously lower than that of SSC. The peak temperature of CSC mortar decreases linearly with the increase in S/C, and the decrease rate of the peak temperature is higher for CSC with small W/C than that with higher W/C. For mortars with lower W/C, the peak shrinkage strain of CSC is larger than that of SSC. Meanwhile, for mortars with higher W/C, the peak shrinkage strain of CSC changes to be lower than that of SSC, which is attributed to the significant water absorption characteristic of CSC. Therefore, as an eco-friendly lightweight aggregate, CS is more suitable than SS for the design of high W/C and alleviating the hydration heat of mass concrete under the meeting of strength.

Early-age hydration process and autogenous shrinkage evolution of high performance cement pastes

This paper presented a comprehensive study on the early-age hydration process and autogenous shrinkage evolution of high performance cement pastes. The early-age hydration process of cement pastes was analyzed by combining 1H nuclear magnetic resonance relaxometry (1H NMR) with isothermal calorimetry. The hydration degree was contrastively analyzed by using 1H NMR and thermogravimetry analyses (TGA). Moreover, the relationship between the free water consumption process and autogenous shrinkage for cement pastes was revealed. Results showed that a magnetism-heat (M − H) model could be established according to the correspondence between free water consumption rate and hydration exothermic rate, which divided the early-age hydration process of cement pastes into four periods. The initial setting time was the onset that free water signal fraction started to drop, after this moment, the consumption rate of free water was increased and more hydration products were generated. After about final setting time, the weighted mean relaxation time of the free water sharply decreased, and the pore structure of cement pastes was gradually refined. The hydration degree (α) of cement calculated by 1H NMR and TGA showed good agreement, with the error of α values less than 2% after initial setting time. Furthermore, cement paste with a lower water/cement ratio showed higher autogenous shrinkage and lower free water signal fraction, but they did not show a good linear correlation with each other throughout the hydration process.

Effects of nano-C-S-H seed crystal on early-age hydration process of Portland cement

Nano-C-S-H seed crystal, as an early strength agent for cement-based materials, has great application prospects. In order to investigate the effect of nano-C-S-H seed crystal on the early-age hydration process of Portland cement, in this article, low-field nuclear magnetic resonance (NMR) technology with 1H as a probe was used to in situ monitor the microstructure evolution of cement paste during the hydration process. Other micro-test methods including mercury intrusion porosimetry (MIP), scanning electron microscope (SEM), and X-ray diffraction (XRD) were also applied to characterize the microstructure of hardened cement paste. The results showed that nano-C-S-H seed crystal can promote the early hydration of cement, and the hydration promotion effect decreased with the hydration time and increased with the content of nano-C-S-H seed crystal. The average hydration rate of C-0.75 paste with addition of 0.75% nano-C-S-H seed crystal was the highest within 1 day of hydration, which was 7.75 times higher than that of pure cement C-0 paste. Nano-C-S-H seed crystal had a great effect on the pore size refinement of cement paste. After 7 days of hydration, the total porosity of all samples decreased to about 5%.

Synergistic effect of carbon nanotube/TiO2 nanotube multi-scale reinforcement on the mechanical properties and hydration process of portland cement paste

The synergistic effect of hybrid carbon nanotube (CNT)/TiO2 nanotube (TNT) multi-scale reinforcement on the mechanical properties, early-age hydration process, and microstructure of Portland cement paste was investigated. In this study, TNT was synthesized via the hydrothermal process. The dispersion of CNT in an aqueous solution was enhanced in the hybrid CNT/TNT. Further, the dispersion state of CNT was modified to a smaller agglomeration of hybrid CNT/TNT. At the optimal CNT/TNT ratio (0.1 wt% CNT/0.5 wt% TNT), an earlier initiation of the acceleration period in the hydration process, an enhanced degree of hydration, and improvements of 29% and 40% in the compressive and splitting tensile strengths of the cement paste, respectively, were observed. Further, the time taken for the occurrence of the calorimetric peak of cement paste was shortened from 3 h (without nanotubes) to 2.3 h and the time taken to achieve maximum peak intensity was shortened from 13.6 h to 11.5 h. Enhancing effect of the hybrid CNT/TNT on the hydration and mechanical properties of cement paste was more apparent than only that of CNT or TNT. The results suggest that using multi-scale hybrid CNT/TNT can be feasible as a new nano-reinforcing method for various cementitious materials.

In situ characterization of early-age hydration process of recycled powder blended cement paste using low-field NMR

The relaxation signal intensity and transverse relaxation time of Portland cement pastes with different dosages of recycled powder at different ages were measured by low-field nuclear magnetic resonance (NMR) technology. Combined with scanning electron microscopy (SEM), the effect of recycled powder on early-age hydration and microstructure of Portland cement was studied. The results show that the hydration process of composite slurry can be divided into four stages, namely, induction period, acceleration period, attenuation period and stable period. As the hydration progressed, the T2 distribution of evaporable water in the composite slurry shifted to short relaxation time, indicating the pores were filled by hydration productions and pore diameter was getting smaller. Recycled powder has high water-adsorption capacity and water slowly-release function, which will lead to the formation of interfacial transition zone (ITZ) and compromise the mechanical property. The transverse relaxation time T2 of samples with higher recycled powder content always maintains obvious bimodal distribution during hydration.

Study on hydration reaction and structure evolution of cemented paste backfill in early-age based on resistivity and hydration heat

In order to reveal the hydration reaction of cemented paste backfill (CPB) more comprehensively, the non-contact electrical resistivity (NER) and microcalorimeter (TAM Air) were used to combine the hydration reaction with microstructure evolution of CPB in the early-age hydration process. The influence of tailings-cement ratio (TCR) on hydration reaction and microstructure evolution of CPB was studied, and the mathematical relationship model of resistivity and hydration heat of CPB was established; the kinetic parameters of CPB in the deceleration period were quantified by using the kinetic model; In combination with CPB’s unconfined compressive strength (UCS), the relationship between resistivity, hydration heat and UCS was established. The results show that the hydration process of resistivity and hydration heat characterization is highly consistent, which can be combined to characterize the hydration reaction and microstructure evolution of the CPB hydration process, and more comprehensively reveal the hydration reaction of CPB from a different perspective. Under different TCRs, the resistivity of CPB is affected by both tailings and cement. The content of tailings determines the overall value of its resistivity. As the content of tailings increases, the resistivity value increases, and the resistivity corresponds to the structural kinetic parameter Kc increases; the hydration heat of CPB is mainly affected by the cement content. The higher the cement content, the higher the hydration heat, and the larger the corresponding hydration kinetic parameter Km. In addition, the hydration reaction process characterized by resistivity and hydration heat is dominated by cement content, the specific manifestation is that as the cement content decreases, the induction period will be prolonged, the acceleration period and the deceleration period will be shortened, and the reaction constants D and D′ increase. The mathematical relation model of resistivity and accumulative heat release of CPB can realize the mutual characterization of resistivity and hydration heat.The resistivity and hydration heat of CPB under different TCR at 24, 36 and 48 h have good corresponding relationship with the UCS; the UCS of different TCRs at 28 days is negatively correlated with its resistivity at 48 h, and positively correlated with the hydration heat of 48 h. Studies have shown that the combination of resistivity and hydration heat can more fully reveal the hydration reaction and microstructure evolution of CPB, which is of great significance to the design of CPB.

Development of mathematical models for predicting the compressive strength and hydration process using the EIS impedance of cementitious materials

Abstract In this study, the early-age hydration process of cement paste is characterized using the rate of change in the impedance measured by electrochemical impedance spectroscopy (EIS). To effectively describe the microstructure variation during the hydration process, specific hydration models corresponding to four related primary hydration stages with variation in the impedance are explained. An impedance evaluation function for the degree of hydration and heat evolution has been proposed and the correlation has been deduced as α t = W n t W total = Q t Q total = D ln k 1 ρ z t ln k 2 ρ total . The hydration degree and heat evolution of cementitious materials with different amounts of w/c ratio and fly-ash (FA) contents are both characterized using the rate of change in the impedance. Early-age impedance can be considered as an equivalent index for the total heat release and offers a promising method of evaluating the cement-hydration degree. Moreover, the impedance can be applied to predict the compressive strength of the FA-blended cement paste. In most cases, the hydration properties of cementitious materials are measured using damaged samples for further analysis. EIS provides additional technical foundations for theoretical and non-destructive testing to investigate the hydration progress and strength estimation, which further aids in achieving improved understanding of the change rate in the electrical impedance of cement-based materials at early ages.

New insights into water dynamics of Portland cement paste with nano-additives using quasielastic neutron scattering

Early-age hydration kinetics of Portland cement with nano-additives such as nano-silica (NS) was examined using quasielastic neutron scattering (QENS). Cement pastes with different ratios of Portland cement to NS were prepared. The concentration of the NS played a major role in controlling the free and bound water during the hydration of the cement paste. Additionally, the effects of metakaolin (MK) with NS in Portland cements revealed that MK acts as a retarder by decreasing the bounding water capacity during the early age of hydration. An increase in the concentration of NS affected the degree of hydration by reducing the amount of free and mobile water in the gel pores when compared to Portland cement paste. Here, we show that the concentration of NS governs the early-age hydration process in Portland cements.

The early hydration of metakaolin blended cements by non-contact impedance measurement

This paper aims to study the early-age hydration process of metakaolin blended cement pastes. The hydration characteristics of different stages, i.e. first dissolution, acceleration, second dissolution and hardened stage, are analyzed by non-contact impedance measurement (NCIM), X-ray diffraction (XRD), derivative thermogravimetric analysis test (DTG), and Fourier transform infrared spectroscopy (FTIR). Through the comprehensive investigation, the second dissolution stages corresponding to the plateau segments appearing in impedance modulus curves for metakaolin blended cement pastes, seem to be associated with the dissolution behavior of metakaolin in alkaline condition. The larger amount of metakaolin in the paste results in the more distinct plateau or descent segment. Furthermore, 15% metakaolin replacement is most favorable to enhance the hydration rate and broaden the range of pore size distribution of blended cement paste. Meanwhile, the compressive strength, water requirement of normal consistency and setting time of blended pastes are examined to study their macro-physical performances.

Study on the effect of chloride ion on the early age hydration process of concrete by a non-contact monitoring method

The quality of the mixing and curing water for the concrete is essentially important since water is definitely a key factor and component which will determine the mechanical properties of the hydrated structures and members. Normally, we make use of fresh water during mixing and curing since it seldom contains excess dissolved ions. And according to the literature review, various kinds of dissolved ions in sea water solution like Cl−, SO42− etc. is about to induce physical and chemical reactions in the fresh cement-based material mixture. The hydration process of it will exhibit apparently different features from the ordinary hydration process of cement-based material with fresh water. However, fresh water is actually quite difficult to obtain sometimes especially in coastal areas and outlying islands. And if we are not able to provide reliable information and solution on the sea water mixed concrete structures and members, the construction effort of infrastructure in coastal areas and outlying islands will be greatly affected. In this study, the early age hydration processes of concrete mixed with sodium chloride solution using various mixture proportions are accurately monitored and recorded by a non-contact resistivity monitoring method to investigate and discuss the similarities and differences of the microstructure development of them compared to that of paste and mortar with sea water and fresh water. The non-contact resistivity monitoring method is found good at revealing the liquid phase conductive path development during hydration. Many research works have proved that non-contact resistivity monitoring method is quite sensitive to the changes of microstructure of cement-based materials. Thus, it is capable of reflecting the subtle changes and the features of the microstructure percolation and the degree of hydration reaction throughout the early age hydration process. Based on the monitoring results, the active hydration reaction of concrete with sea water in the early age are found prolonged and the percolation time point of it is postponed obviously compared to that of concrete with fresh water. It is similar to the effect of superplasticizer. And the dissolving period is observed completely disappeared when chloride ions are used for mixing. However, when compared to the sea water mixed paste and mortar, it is found that coarse aggregate in concrete will obviously weaken the superplasticizer effect from sea water. All of these phenomena provide new information on the early age hydration behavior of concrete with chloride ions and sodium ions. And it is widely accepted that the early age hydration behavior determines the long term durability and reliability of hydrated cement-based structures. Therefore, the durability and reliability of the concrete infrastructure using sea water in coastal areas and outlying islands is found possible to be studied and controlled by the non-contact resistivity monitoring method.

Characterization of the absolute volume change of cement pastes in early-age hydration process based on helium pycnometry

Based on detection technology of helium pycnometry, this study developed a novel approach for characterizing the absolute volume change of cement pastes in early-age hydration process. This method gives an accurate and continuous surveillance on the absolute volume change of cement pastes excluding all the empty pore space even below nm-scale. Traditional methods, such as chemical shrinkage test (based on ASTM C 1608), isothermal calorimetry test and X-ray diffraction (XRD) analysis, are also adopted for comparison and analyzation. It was found that the data obtained by chemical shrinkage test is discontinuous and inaccurate, the data gotten by isothermal calorimetry test is vague and unspecific, and the data gained by XRD analysis is discontinuous and unspecific. Compared with the traditional methods, the results captured by helium pycnometry are continuous, accurate and specific for describing the hydration process, especially the changing details of the absolute volume change. But at the same time, helium pycnometry has a good correspondence with the traditional methods, whose trends are almost the same. Based on the trends of the absolute volume change and heat flow, the absolute volume change of cement pastes in early-age hydration process was then divided into four periods (dissolution period, induction period, fast reaction period and stable period).