Time Evolution of CO 2 Di ﬀ usivity of Carbonated Concrete

: Carbonation of cementitious materials is one of main causes of reinforcement corrosion and CO 2 di ﬀ usivity inﬂuenced by microstructural characteristics of the cementitious materials is a decisive parameter for the carbonation rate. This study focused on establishing a multifactor functional model to calculate the CO 2 di ﬀ usivity of carbonated cementitious materials. Because CO 2 gas ﬂows through carbonated zone, it is necessary to estimate CO 2 di ﬀ usivity of carbonated concrete. Many factors on the CO 2 di ﬀ usivity, such as the di ﬀ usivity in vapor, tortuosity, microstructural characteristics of cement paste, contribution of aggregate, and reduction of porosity due to carbonation, were considered. Apparent and e ﬀ ective CO 2 di ﬀ usivity were calculated according to the absence or presence of moisture in the pore system of concrete, and the results were compared with previous research.


Introduction
Concrete contains a lot of calcium hydroxide in pores because the hydration reaction of C 3 S (3CaO·SiO 2 ) and C 2 S (2CaO·SiO 2 ) abundantly in cement. This can help maintain a strong alkaline environment with pH 12.5 to 13.0 in pore solution and thus reinforcement embedded in the concrete can be well protected from corrosion. If CO 2 gas in the atmosphere diffuses into concrete, however, all the available calcium hydroxide is consumed due to the reaction of the carbonation. Calcium carbonate is produced from this reaction and causes a decrease in pH of pore solution to a level where the passive layer of reinforcement embedded in concrete breaks down. Carbonation may not be harmful for the concrete itself, however, reinforcement corrosion can occur immediately if the pH of the pore water drops below 11.5. As a result, carbonation can precipitate reinforcement corrosion, which ultimately reduces long-term durability performance of concrete. Thus, calculating carbonation rate is very important for predicting service life of the reinforced concrete and CO 2 diffusivity is a crucial parameter for the carbonation rate.
By the way, molecular diffusion and advection through porous media are the main driving force on the penetration of harmful substances such as chloride ions, CO 2 or O 2 gas, and so on [1][2][3]. For carbonation of concrete, once CO 2 gas flow through pore of the materials, CO 2 gas is dissolved in pore solution and reacts with cement hydrates. Diffusivity stands for flow rate of harmful substances and CO 2 diffusivity of cementitious material must be defined for predicting long-term durability. Most studies have obtained only chloride diffusivity of cementitious materials [4][5][6]. From decades of practical experience and theoretical considerations, however, it is well known that carbonation of concrete is one of main causes of deterioration of concrete [7]. Since the long-term performance of concrete structure is greatly dependent on reaction and the migration rate of CO 2 gas in concrete, the CO 2 diffusivity plays a key part in designing and estimating concrete structures under crowded urban area with high CO 2 gas. Figure 1. Importance of CO2 diffusivity as a decisive parameter for controlling carbonation rate of concrete. In this figure, the degree of carbonation of concrete is expressed as the hydroxyl concentration of cement hydrates. In the carbonated area, the pH of the pore solution is greatly reduced, and the rate depends on CO2 concentration in the atmosphere as an environment response. For noncarbonated area, it has an original pH value. The border between the two areas can be determined by spraying a phenolphthalein-alcohol indicator and this also can be influenced by OHcontent. The CO2 diffusivity is a material parameter that can make all these decisions.

Formulation of CO2 Diffusivity of Concrete
Among the models for estimating chloride diffusivity of concrete, practical multifunctional approaches have been proposed [9,10]. However, the solutions could not clearly provide the mutual interference effect between the diffusivity and affecting factors on element function. This study was Figure 1. Importance of CO 2 diffusivity as a decisive parameter for controlling carbonation rate of concrete. In this figure, the degree of carbonation of concrete is expressed as the hydroxyl concentration of cement hydrates. In the carbonated area, the pH of the pore solution is greatly reduced, and the rate depends on CO 2 concentration in the atmosphere as an environment response. For noncarbonated area, it has an original pH value. The border between the two areas can be determined by spraying a phenolphthalein-alcohol indicator and this also can be influenced by OH − content. The CO 2 diffusivity is a material parameter that can make all these decisions.
This study suggests a comprehensive model for the apparent and the effective CO 2 diffusivity of concrete, based on the previous research [4]. It was investigated how much pore solution in the concrete reduces the CO 2 diffusivity due to pore blocking at each stage of cement hydration. In particular, the difference in the CO 2 diffusivity between carbonated concrete and noncarbonated concrete was examined. The approach of this study is expected to be useful in the development of integrated carbonation model at each hydration stage of cement in the future.

Formulation of CO 2 Diffusivity of Concrete
Among the models for estimating chloride diffusivity of concrete, practical multifunctional approaches have been proposed [9,10]. However, the solutions could not clearly provide the mutual interference effect between the diffusivity and affecting factors on element function. This study was conducted as an applied study essential for predicting carbonation, based on the author's previous work [4]. Model for oxygen diffusivity was established with the approach [11].
Concrete is a random composite material composed of two phases, cement paste and aggregate. Thus, diffusivity of concrete (D conc ) can be expressed as a contribution function of cement paste (D cp ) and aggregate (D agg ), respectively: Main functions of diffusivity of cement paste consists of diffusivity in vapor, F(D o (T)), microstructure characteristics, F(St micro ), tortuosity, F(τ 2 T ), disturbed diffusion, F(H). The combination of these factors can be described in Equation (2) and theoretical formulation of CO 2 diffusivity was constructed with the approach as a reference [4]. The schematic diagram was elaborated in Figure 2.

CO2 Diffusivity in Vapor
The first term of Equation (2), (a) F(Do), means CO2 diffusivity in vapor. CO2 gas can flow through bulk pore which is not filled with solution. Diffusion theory on gases is theoretically established from kinetic molecular theory [12]. Fuller et al. suggested the diffusivity D in vapor has a function of both temperature and pressure [13]. They suggested gaseous diffusivity in vapor:

CO 2 Diffusivity in Vapor
The first term of Equation (2), (a) F(Do), means CO 2 diffusivity in vapor. CO 2 gas can flow through bulk pore which is not filled with solution. Diffusion theory on gases is theoretically established from kinetic molecular theory [12]. Fuller et al. suggested the diffusivity D in vapor has a function of both temperature and pressure [13]. They suggested gaseous diffusivity in vapor: in which, D v : vapor diffusivity, T: temperature, M a , M b : molecular weight of components a and b, P: total pressure. According to this equation, the value of CO 2 diffusivity is approximately 0.16 cm 2 /s in the air pore system of concrete.

Pore Structural Properties in Cement Paste
The second term of Equation (2), (a) F(St micro ), means microstructure effect of cement paste. Pore volume and the size distribution are the main factors to characterize fluid transportation through porous media in terms of microstructural characteristics. Porosity distribution function was suggested by Maekawa et al. [14]: where, V p : volumetric fraction of pore with distribution up to pore radius, r, B: a peak point of porosity distribution on a logarithmic scale.
If ln r replaces x, r is substituted for exp(x). Equation (4) is derived as: With increasing degree of hydration, the pore volume decreases, mainly at the cost of the volume of the larger pores. Thus, total porosity (V p ) was calculated by HYMOSTRUC [15] for each hydration step, numerical simulation program for cement hydration. A peak point of porosity distribution B was back calculated from Equation (5).

Tortuosity
To account of the winding streamline of CO 2 gas, tortuosity factor was suggested in previous work of author [4]. Although it makes sense to regard the morphology of cement core as a circular shape, it is assumed to be a square to simplify the fluid streamline [16]. The difference is reflected with shape functional ratio between circle and square and thus, average streamline of tortuosity was depicted as: For depicting flow complexity through cement paste, CO 2 diffusivity has a function with τ T 2 , as shown in Equation (2).

Pore Blocking Due to Moisture
Diffusivity is significantly influenced by relative humidity in cementitious materials [17]. Because gas cannot penetrate through pore water, amount of capillary water should be reflected in estimating effective diffusivity. During the hydration process, capillary pores are gradually emptied until a thermodynamic equilibrium is reached. The effective pore volume (V e f f p ) of the gaseous inflow is equivalent to the volumetric fraction of vapor, which means the remaining air pore fraction depending on the degree of saturation (S r ) in system [18]: The pore system vs. degree of saturation is illustrated in Figure 3. The remaining amount of the pore water and volume of pore system were calculated with hydration process. The pore structure system of the material is filled with vapor and pore water. If concrete is assumed to be an infinite material, moisture from outdoor environment is less easy to mobilize and moisture evaporation due to external heat should be ignored. Thus, the amount of pore water can be regarded as the amount of capillary water.
For depicting flow complexity through cement paste, CO2 diffusivity has a function with T τ 2 , as shown in Equation (2).

Pore Blocking Due to Moisture
Diffusivity is significantly influenced by relative humidity in cementitious materials [17]. Because gas cannot penetrate through pore water, amount of capillary water should be reflected in estimating effective diffusivity. During the hydration process, capillary pores are gradually emptied until a thermodynamic equilibrium is reached. The effective pore volume ( ) of the gaseous inflow is equivalent to the volumetric fraction of vapor, which means the remaining air pore fraction depending on the degree of saturation (Sr) in system [18]: The pore system vs. degree of saturation is illustrated in Figure 3. The remaining amount of the pore water and volume of pore system were calculated with hydration process. The pore structure system of the material is filled with vapor and pore water. If concrete is assumed to be an infinite material, moisture from outdoor environment is less easy to mobilize and moisture evaporation due to external heat should be ignored. Thus, the amount of pore water can be regarded as the amount of capillary water.  Pore system of cementitious materials consists of space filled with pore water (V w ) and remaining space with vapor (V g ): Following capillary water consumed due to ongoing cement hydration [15], amount of pore water also can be expressed as: in which, ρ i : specific mass of i, α: degree of hydration. Therefore, volumetric fraction of gas (V g ) vs. the volume of the cement paste (V cp ) can be expressed as: Therefore, the CO 2 diffusivity can be divided into two diffusivities; (a) apparent diffusivity of the condition described in Figure 3a, ignoring the moisture and considering the total pores; (b) effective diffusivity of the condition described in Figure 3b, considering the effective pores through which moisture is excluded from the total pores and gas can penetrate. The calculation result was shown in Figure 4.
Therefore, the CO2 diffusivity can be divided into two diffusivities; (a) apparent diffusivity of the condition described in Figure 3a, ignoring the moisture and considering the total pores; (b) effective diffusivity of the condition described in Figure 3b, considering the effective pores through which moisture is excluded from the total pores and gas can penetrate. The calculation result was shown in Figure 4.

Disturbed Diffusion
The fourth term of Equation (2), (d) F(H), can express hindered diffusion due to interaction of substance and narrow path between pore walls. As the molecular diameter of the harmful substances approaches the pore wall, the transport of the harmful substances through the pore should be disturbed by the narrow pore wall. The function of the disturbed diffusion is described as [19]: Two correction factors, , are related to the reduced pore diameterϕ : where, ds: kinetic diameter ( ≈ 3.34 × 10 −8 cm for CO2 gas).

Disturbed Diffusion
The fourth term of Equation (2), (d) F(H), can express hindered diffusion due to interaction of substance and narrow path between pore walls. As the molecular diameter of the harmful substances approaches the pore wall, the transport of the harmful substances through the pore should be disturbed by the narrow pore wall. The function of the disturbed diffusion is described as [19]: Two correction factors, f (φ) and f (φ), are related to the reduced pore diameter φ: where, d s : kinetic diameter (≈3.34 × 10 −8 cm for CO 2 gas). d pore : diameter of pore, The first correlation factor, based on geometrical arguments, can be expressed as: in which, t d means a twice thickness of adsorbed layer. The second correlation factor can be expressed as Renkin equation: The effect is effective to depict disturbed diffusion rate due to consequence of narrow pore diameter and collision of CO 2 gaseous molecules to each other.

Effect of Aggregate
The above methods are influencing factors for obtaining the CO 2 diffusivity of the cement paste. Concrete consists of cement paste and aggregate. Effective medium theory (EMT) is used to change diffusivity of composite materials with two phases [20,21]. EMT pertains to analytical modeling that describes the macroscopic properties of composite materials and can be a solution on concentration gradients between phases of the materials. The diffusivity of composite material with two phases can be expressed as: where, D 1 , D 2 : the diffusivities in two phases, V 1 , V 2 : the volumetric fractions of the two phases, : the mass concentrations in the different zones, k = C 1 /C 2 , the distribution of substances between the phases, In EMT theory, the neighborhood region in the multiphase materials is assumed to be a uniform medium. This means that there should exist no correlation between different regions [21]. Diffusivity of cement paste was calculated from multifunctional model described in Sections 2.3 and 2.4, depending hydration stage of cement. The CO 2 diffusivity of aggregate was regarded as a constant to be 1 × 10 −11 cm 2 /s [22].

Porosity Reduction Due to Carbonation
Carbonation of concrete greatly affects changes of pore structure system, which is inevitably connected to the rate of CO 2 diffusion through carbonated concrete. The change of pore structure system in concrete due to carbonation was limited to OPC concrete, in this study. Papadakis et al. proposed the following equation, based on the ratio of the volume of Ca(OH) 2 and CSH in concrete before carbonation to calcium carbonate after carbonation [23]: where, V c : porosity of concrete after carbonation, V p : porosity of concrete before carbonation.
Decreased porosity due to carbonation (∆V c ) is approximately equal to: in which, ∆V CH and ∆V CSH are equivalent to 3.85 × 10 −6 m 3 /mol, 15.39 × 10 −6 m 3 /mol, respectively. Although the concrete is carbonated, the pores of the aggregate remain the same and the pores of the cement paste change. Therefore, changed pores, calculated by Equation (16), was reinputted into Equation (5) to characterize the pore system of carbonated cement paste. Based on the above analysis, the CO 2 diffusivity of concrete before and after carbonation was calculated, and the mixing conditions of concrete used in the calculation are shown in Table 1.  Figure 5 represents apparent and effective CO 2 diffusivity of noncarbonated concrete with time and the difference means the effect of moisture content on CO 2 diffusivity. Three points should be discussed. Firstly, for concrete with a high w/c ratio, the diffusivity was high, and the difference between apparent diffusivity and effective diffusivity was also large. This is coincided with experiment study of Nokken et al. [24]. This would be because high degree of cement hydration and high densification due to microstructure development with elapsed time for cement paste with a high w/c ratio. Secondly, all concrete showed that the CO 2 diffusivity decreased significantly until 28 days because the microstructural densification of the concrete is greatly developed until 28 days. The trend continued because of the ongoing reaction of cement hydration. The trend of the reduction lasted even at long term; however, the reduction rate has become modest. Thirdly, the effective CO 2 diffusivity was considerably smaller than the apparent diffusivity. It can be seen that pore closing due to moisture has great influence on the CO 2 diffusivity. The work has good agreement with Yoon's work that carbonation rate of concrete exposed to the outdoor environment was greatly decreased due to raining [25].

CO 2 Diffusivity of Concrete before Carbonation
The CO 2 diffusivity is a material parameter that directly reflects the carbonation rate. If concrete is exposed to high CO 2 concentrations at early ages, carbonation can threaten concrete significantly. Therefore, extending the curing period could be a good solution in controlling the carbonation rate effectively.  Figure 6 illustrates the ratio of the effective diffusivity and the apparent diffusivity of concrete with w/c ratio. The apparent diffusivity decreases with time because of only development of microstructure of cement paste, while the effective diffusivity decreases with time because of remained amount of pore water after consumption due to cement hydration as well as the microstructural development. For this reason, the difference between two diffusivities was not significant at the beginning of age; however, the difference was obvious with elapsed time. The ratio had decreased significantly to the level of 0.1 to 0.2 after 28 days. At early ages, the difference between two diffusivities was not high because cement was not sufficiently unhydrated and pore was highly filled with water. However, the difference between two diffusivities was clearly noticed with elapsed time because water was continuously consumed by the hydration reaction of cement as it became hydrated. Therefore, it is very important to consider water content in estimating gaseous diffusivity of cementitious materials.    Figure 7 shows the result of estimating CO 2 diffusivity of carbonated concrete with w/c ratio. The result reflected the reduction of pore due to carbonation. Among the four main functions of Equation (2), (a) CO 2 diffusivity in bulk fluid is constant because it has nothing to do with cementitious material. However, (b) pore structural characterization; (c) tortuosity of streamline, and (d) disturbed effect are influenced by carbonation. That is, the carbonation of concrete can make the flow characteristics of the fluid more complicated by reducing the pore system of the concrete. In particular, the CO 2 diffusivity of early carbonated concrete decreased significantly. However, carbonation leaded to the reduction of CO 2 diffusivity of concrete regardless of age, and this tendency was obvious for all concrete.

CO 2 Diffusivity of Concrete after Carbonation
Saeki et al. suggested that chloride diffusivity of OPC concrete was significantly decreased after carbonation, while blended concrete showed different results depended on admixture type or the replacement ratio [26]. That is, chloride diffusivity of concrete with fly ash decreased, while that of concrete with granulated blast furnace slag increased. As Ca(OH) 2 is transferred to CaCO 3 due to carbonation, the microstructure characteristics of the concrete is bound to change because of the difference in molar volumetric expansion of the two materials [27]. However, this is not the case for all concrete and pore of carbonated concrete with blast furnace slag rather increased [28]. carbonation, while blended concrete showed different results depended on admixture type or the replacement ratio [26]. That is, chloride diffusivity of concrete with fly ash decreased, while that of concrete with granulated blast furnace slag increased. As Ca(OH)2 is transferred to CaCO3 due to carbonation, the microstructure characteristics of the concrete is bound to change because of the difference in molar volumetric expansion of the two materials [27]. However, this is not the case for all concrete and pore of carbonated concrete with blast furnace slag rather increased [28].  Figure 8 illustrates the difference between effective CO2 diffusivity and apparent diffusivity of concrete after carbonation. Like the comparative ratio in Figure 5, the ratio of carbonated concrete showed a similar trend. Figure 9 shows the result of comparing the diffusivity concrete before and after carbonation. The ratio of the two diffusivities decreased as time passed. and the width of the w/c ratio decreased with elapsed time. In concrete with a high w/c ratio, the trend of decreasing the diffusivity due to carbonation with time was pronounced. Carbonation led to reducing the effective diffusivity of concrete to the level of 47~69%. This reduction ratio tended to decrease as w/c ratio of concrete was low and time elapsed.
Based on all results above, this study is believed to be useful in expressing the CO2 diffusivity as a function of the mixing conditions of concrete and degree of cement hydration. As a material parameter plays a decisive role in the accuracy of durability design system for concrete structures, CO2 diffusivity with time is very important to calculate the service life of the concrete in detail. This work will be combined with the system in the future.  Figure 8 illustrates the difference between effective CO 2 diffusivity and apparent diffusivity of concrete after carbonation. Like the comparative ratio in Figure 5, the ratio of carbonated concrete showed a similar trend.   Figure 9 shows the result of comparing the diffusivity concrete before and after carbonation. The ratio of the two diffusivities decreased as time passed. and the width of the w/c ratio decreased with elapsed time. In concrete with a high w/c ratio, the trend of decreasing the diffusivity due to carbonation with time was pronounced. Carbonation led to reducing the effective diffusivity of concrete to the level of 47~69%. This reduction ratio tended to decrease as w/c ratio of concrete was low and time elapsed.

Comparison with Previous Research
The rate of gas penetration depends largely on the saturation of concrete. The rate of gas penetration decreased if concrete is more than 50% RH [17]. The diffusivity was constant if concrete is exposed to condition with less than 60% RH. That is, the diffusivity decreased significantly when RH exceeded 60% [16]. The result was similar to the experiment of Martin et al. [29]. They studied the CO2 diffusivity of porous media, not concrete, and the diffusivity greatly decreased as RH exceeded around 55%. The apparent and the effective CO2 diffusivity of concrete cured for 28 days was calculated to be in the range of 3.5 × 10 −3 to 6.1 × 10 −3 cm 2 /s, 2.1 × 10 −4 to 8.3 × 10 −4 cm 2 /s, respectively. In particular, the effective diffusivity of carbonated concrete matched with the limit suggested by CEB 1990 Model Code [30].
In this study, the diffusivity of concrete was estimated from the individual diffusivities of cement and aggregate. The effect of Interfacial Transition Zone (ITZ) at aggregate surface on gas diffusion was not considered. Although the effect of ITZ on the durability of concrete is well known, research on the effect of the CO2 diffusivity is rare. In the future, it is necessary to study the CO2 diffusivity of concrete with three phases, cement paste, aggregate, and ITZ and the influence of carbonation on the porosity of ITZ.  Based on all results above, this study is believed to be useful in expressing the CO 2 diffusivity as a function of the mixing conditions of concrete and degree of cement hydration. As a material parameter plays a decisive role in the accuracy of durability design system for concrete structures, CO 2 diffusivity with time is very important to calculate the service life of the concrete in detail. This work will be combined with the system in the future.

Comparison with Previous Research
The rate of gas penetration depends largely on the saturation of concrete. The rate of gas penetration decreased if concrete is more than 50% RH [17]. The diffusivity was constant if concrete is exposed to condition with less than 60% RH. That is, the diffusivity decreased significantly when RH exceeded 60% [16]. The result was similar to the experiment of Martin et al. [29]. They studied the CO 2 diffusivity of porous media, not concrete, and the diffusivity greatly decreased as RH exceeded around 55%. The apparent and the effective CO 2 diffusivity of concrete cured for 28 days was calculated to be in the range of 3.5 × 10 −3 to 6.1 × 10 −3 cm 2 /s, 2.1 × 10 −4 to 8.3 × 10 −4 cm 2 /s, respectively. In particular, the effective diffusivity of carbonated concrete matched with the limit suggested by CEB 1990 Model Code [30].
In this study, the diffusivity of concrete was estimated from the individual diffusivities of cement and aggregate. The effect of Interfacial Transition Zone (ITZ) at aggregate surface on gas diffusion was not considered. Although the effect of ITZ on the durability of concrete is well known, research on the effect of the CO 2 diffusivity is rare. In the future, it is necessary to study the CO 2 diffusivity of concrete with three phases, cement paste, aggregate, and ITZ and the influence of carbonation on the porosity of ITZ.

Conclusions
CO 2 diffusivity is a decisive material parameter for estimating a carbonation rate of concrete and quantifying durability performance of infrastructure. A comprehensive model with multifunctional factors such as diffusivity bulk fluid, pore structural characteristics, streamline of tortuosity in the pore system, hindrance effect, and volumetric contribution of cement paste and aggregate, was modified to estimate the diffusivity. Apparent and effective CO 2 diffusivities were suggested in terms of the effect of pore water on diffusivity. Because CO 2 diffusivity is a material parameter in the area from surface concrete to carbonation depth, the CO 2 diffusivity of concrete was calculated after carbonation.
(1) For concrete before carbonation, CO 2 diffusivity did not have a constant value, and it continuously decreased with the degree of cement hydration. The trend also maintained a clear trend depending on w/c ratio of concrete. Above all, the trend of decreasing CO 2 diffusivity was more pronounced until 28 days. The reduction rate gradually became more modest over time. The decreasing trend of the diffusivity of concrete with w/c ratio over time also showed the same. The difference between apparent and effective diffusivity was not significant at beginning of age, however, the difference was obvious with elapsed time.
(2) As a result of comparing the CO 2 diffusivity of carbonated concrete and noncarbonated concrete, carbonation significantly reduced CO 2 diffusivity at the early age. Since carbonation of concrete greatly reduced the pore structural system, it resulted in a significant reduction in the CO 2 diffusivity to the level of 47~69% compared to that of noncarbonated concrete. However, this reduction ratio showed a trend of decreasing over time as well.