Non-steady state migration of chloride ions in cement pastes at early age

Abstract

This paper proposes preliminary work to study the diffusion and migration of chloride ions in cement pastes at early age. The non-steady state ion migration coefficients of cement pastes are evaluated from three aspects: (1) electrical rapid ion migration test; (2) non-contact impedance measurement (NCIM) based on a fractal model; and (3) a corresponding simulation of an “I” shape fractal network. The experimental results from electrical rapid ion migration tests and NCIM have good agreement. The influences of water to cement ratio, curing hydration age and addition of mineral admixtures on the performance of ion diffusion/migration in cement pastes are investigated.

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1. Introduction

The durability of cement-based materials, the most used artificial material, is a fundamental topic in many construction engineering fields; it is imperative to understand the durability characteristics of cement-based materials in order to facilitate their use in all kinds of aggressive environments.¹ One of the key evaluation indices of durability is referred to as ion diffusion/migration resistance in cement-based materials. Ion diffusion/migration is considerably significant for the heat and mass transfer in cement-based materials.¹ In general, there are several diffusion/migration coefficients frequently mentioned for the study of transportation performance in cement-based materials,^2,3 i.e. D_ssd the steady state diffusion coefficient; D_ssm the steady state migration coefficient; D_nssd the non-steady state diffusion coefficient; D_nssm the non-steady state migration coefficient. Until now, the key relation between D_ssd and D_nssm is not yet completely developed in cement-based materials at early age. D_ssd may be the most important parameter for characterization of transportation, which is primarily influenced by intrinsic pore structure of cement-based materials; the steady state diffusion takes place at a constant rate and is independent of flow diffusion distance and time. Nevertheless, the steady-state tests are always not preferred from the practical view as they are extremely time consuming and laborious.⁴ Instead, the electrical rapid ion migration test has been developed to overcome these drawbacks. The rapid ion migration method performed in this work is an accelerated method which assesses the ion penetration resistance according to the electrical charge passing through cement-based materials in the first several hours of the test.⁵

On the other hand, some recent studies demonstrate that electrical impedance approaches coupled with sophisticated circuits modeling have the potential to study the evolution of steady state ion diffusion, pore structure and permeability cement-based materials non-destructively in real time,^6–10 and hence, if ion binding capacity inside the cement-based materials is considered, it is possible to derive the evolution of non-steady state migration coefficients of cement-based materials.

Besides, it has been proved that most of real porous media present fractal performance in nature and a realistic picture of disordered porous system could be provided by a fractal description.¹¹ In particular, it has been found that cement-based materials are such kind of typical fractal porous media as well.⁸ Therefore, another alternative evaluation method for non-steady state ion migration coefficients is recently promoted fractal network simulation, apart from electrical migration test and impedance measurement;^12–14 such simulation is likely to intuitively study the influence of all kinds of pore parameters on non-steady state ion migration of cement-based materials.

In this work, the aggressive ion in this work is considered as chloride ion commonly-available in a marine environment.¹ The influence of water to cement ratio, hydration age and mineral admixture (fly ash, slag and silica fume) of cement pastes on the performance of ion diffusion/migration are clarified. The non-steady state migration coefficients (D_nssm) of cement pastes are determined by electrical rapid ion migration method and a newly-proposed non-contact impedance measurement (NCIM) based on a fractal model; exact relation between pore structure and non-steady state chloride migration property in fractal saturated cement pastes is well established. A corresponding simulation of “I” shape fractal network is further proposed to study the influence of porosity and pore size of network on non-steady state ion migration of fractal cement pastes.

2. Experiments and methods

2.1 Materials and mix proportion

In this work, ordinary Portland cement meeting the requirement of ASTM Type I and de-air and de-ion water were used. Cement pastes with water to cement ratios (w/c) 0.3, 0.4 and 0.5 by mass were prepared and marked as P3, P4 and P5. Cement pastes with notations of F10, F20, F30 and F40 were also prepared. F10, F20, F30 and F40 represented pastes with water to binder (cement + mineral admixture) ratio (w/b) of 0.4, in which 10, 20, 30 and 40% of cement were replaced by fly ash by mass. Similar, S10, S30, S50 and S70 denoted that 10, 30, 50 and 70% of cement were replaced by slag and w/b ratios were 0.4. SF5 and SF10 with w/b ratio 0.4 meant that 5% and 10% of cement were replaced by silica fume, respectively. These fresh pastes were prepared in a planetary-type mixer at 45 rpm for 2 minutes first and then at 90 rpm for 2 minutes. The chemical compositions of the cement, fly ash, slag and silica fume are given in Table 1. The morphology of cement, fly ash, slag and silica fume observed by a JEOL 6300 scanning electron microscope (SEM) is shown in Fig. 1.

Table 1 The chemical composition of cement, fly ash, slag and silica fume (wt%)

Cement	CaO	SiO4	Fe2O3	Al2O3	SO4	MgO	K2O	TiO2	LOI
wt%	61.12	18.71	6.11	5.92	3.55	3.08	0.22	0.09	1.2

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Fly ash	SiO2	Al2O3	TiO2	CaO	Fe2O3	Na2O	P2O5	SO4	K2O	MgO	MnO	LOI
wt%	50.26	30.11	3.82	3.26	3.17	2.11	1.72	1.25	1.02	1.01	0.06	2.12

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Slag	SiO2	CaO	Al2O3	MgO	SO4	TiO2	K2O	MnO	Fe2O3	LOI
wt%	38.47	36.92	10.02	5.52	4.63	1.01	0.52	0.38	0.19	2.34

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Silica fume	SiO2	K2O	CaO	SO4	MgO	MnO	Fe2O3	LOI
wt%	92.39	2.63	1.21	0.99	0.61	0.19	0.16	1.82

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Fig. 1 Morphology of cement, fly ash, slag and silica fume.

2.2 Experimental tests

2.2.1 Non-contact impedance measurement. NCIM without electrodes can record the electrical impedance of cement pastes non-destructively in situ during the whole hydration process.⁸ A series of resistor-capacitor and resistor-inductor series circuits have been used to inspect the accuracy of NCIM: the measured impedance response can be perfectly coincident with the ones calculated by corresponding nominal values. The working mechanism and corresponding test procedure of NCIM can be consulted in ref. 8. The tests were implemented in the environmental chamber with temperature (20 °C) and humidity (100%) for 3 days.

2.2.2 Compressive strength test. The fresh cement pastes were cast into 4 cm × 4 cm × 4 cm moulds for compressive strength tests at 1 day and 3 days. The tests were undertaken with a loading rate 1 kN s⁻¹.

2.2.3 Electrical rapid ion migration. In the present study, the electrical rapid ion migration (ERIM) test and procedure similar to those described in ASTM 1202-05 were employed, as shown in Fig. 2. The cement pastes at hydration age 1 and 3 days were in cylindrical shape (100 mm in diameter and 50 mm in thickness).⁶ The tests were performed onto cement pastes through mesh brass at a voltage of 4 V for four hours to avoiding the excessive temperature increase. After ERIM test, the cylindrical cement pastes were split into two halves. Colorimetric method was applied to find the depth of chloride penetration (x) by spraying a 0.1 N AgNO₃ solution on the exposed surface.⁶ Three identical cement pastes were prepared in order to gain the average value of non-steady state migration coefficient. The non-steady state migration coefficient (D_nssm) for each cement paste is determined by this test from eqn (1):where z is the electrical charge of ion which is equal to −1 for chloride; F is the Faraday constant (=96 480 coulomb per mole); E is the strength of electric field, which is the voltage per unit length between anode and cathode; R is the universal gas constant, 8.314 J (mol⁻¹ K⁻¹); T is absolute temperature in the environment, 293.15 K; erf⁻¹(x) is the inverse error function; C_d is the concentration of ion at distance x from the surface, is taken as 0.07 N; C₀ is the ion concentration at the surface of the cement paste and taken to be 0.5 N; t is test time.

Fig. 2 Illustration of electrical rapid ion migration test.

3. Non-steady state migration coefficient predicted by NCIM

In this work, a fractal model with the aid of NCIM is developed to study the non-steady state migration coefficient of fractal saturated cement pastes. First of all, the effective diffusion coefficient (D_s) in the pore solution of saturated cement paste is given as:^3,15where D₋₀ is the diffusion coefficient of anions in the infinite dilute solution, equal to 2.03 × 10⁻⁹ m² s⁻¹;¹⁵ K_τ0 is the difference in transference number in the external source solution, whose typical value is −0.207 × 10⁻⁸ m² s V;¹⁵ γ is the activity coefficient of ions in pore solution; c is the free chloride concentration of ions in the pore solution; ∂ln γ/∂ln c is determined as −0.025 L mol⁻¹;¹⁵ c₀ is the solvent concentration, approximately equal to 56.45 mol L⁻¹;¹⁶ f is the friction coefficient which reflects the ionic interaction in the pore solution, predicted as 15 000 by Tang et al.¹⁶ β_v is the ratio of cation velocity to anion velocity and equal to 0.427.¹⁶

The mass flow rate of ion diffusion (q(d)) in a single tortuous pore path for fractal cement pastes is derived as:¹⁷

q(d) = D_sA(d)Δc/L_t(d) = D_sA(d)Δc/(d^1−D_tL₀^D_t) (3)

where A(d) is the cross sectional area of pore channels with diameter d; Δc is the concentration difference between two ends of pore channels; L_t(d) is the actual length of pore channel, which is satisfied with classical fractal law;⁹ L₀ is the measured length of cement paste; D_t is the fractal dimension associated with pore tortuosity.

Meanwhile, the number of pore size (δN) between d and (d + δd) in fractal cement paste and cross-section area of the saturated cement paste (A_t) are:^9,17

−δN = D_fd_max^D_fd^−D_f−1δd (4)

where D_f is the fractal dimension fore pore space; d_max and d_min are maximal and minimal pore diameters in saturated cement paste; ϕ is the porosity of a cement paste.

The total mass flow rate (Q(d)) and steady state diffusion coefficient (D_ssd) predicted by NCIM are expressed as:¹⁷

With respect to eqn (7), L₀ can be measured when the NCIM test is completed; d_min is predicted as 6.2 nm from electrical double layers model;⁸ ϕ, D_f, D_t and d_max can be determined from NCIM.^8,9

With the purpose of verification, the predicted D_ssd of fractal saturated cement paste from a fractal model by means of NCIM will further transfer to D_nssm in order to compare the relevant result from ERIM. The transformation relation between D_ssd and D_nssm is studied by Tang et al. through transformation ratio, T_r:^3,15,16

where C_b is the bound chlorides with the dimension of kg Cl⁻ m⁻³; the term ∂C_b/c mainly reflects chloride binding capacity in the fractal cement paste and can be derived from eqn (10) and (11) ref.18 and 19 although Spiesz and Brouwers considered that this binding capacity may be low to some extent.⁴where α(t) is hydration degree of cement pastes; k^m_h is the total mass of the hydration products as 1 gram of cement is totally hydrated, taken as 2.06 g g⁻¹;¹⁹ w/b is water to binder ratio of cement pastes; D_w, D_c and D_h are density of water (1.01 g cm⁻³), cement (3.15 g cm⁻³) and hydrated products (1.529 g cm⁻³);¹⁸ V_total the total volume of cement pastes, which can be measured after NCIM test is completed.¹⁸

Actually, it is also worth pointing out that the application of this fractal model to predict the non-steady state ion migration coefficient is not only restricted for the case of fractal saturated cement paste. This model may be possibly used in other cases of fractal porous media, such as melt crystallization of porous crystal layer,²⁰ diffusion-controlled reaction of fractal porous electrodes,²¹ if the fractal dimensions, ion binding capacity, minimal and maximal pore diameters are determined from either simulation or experimental techniques.

4. Non-steady state migration simulation

In this work, a fractal simulation based on an “I” shape network is also developed to analyze non-steady state migration coefficients in fractal saturated cement pastes. Fig. 3 is the two dimensional configuration of fractal “I” shape network in the cuboid of saturated cement paste. This figure only lists this network to Step 2 with the purpose of simplicity.

Fig. 3 Configuration of “I” shape network in the cuboid of saturated cement paste.

This “I” shape network proposed originates from the largest mother “I” channel with circular cross section. This mother channel extends four symmetrical “I” channels further in subsequent step. The similar construction procedure is then implemented continuously to each new “I” channel ad infinitum. This network echoes actual pore size distribution in cement pastes since the fraction of number of small pores in entire pore range usually takes a great portion in the media and vice versa.⁹ First of all, the basic assumptions of “I” shape network are described as:²² (1) each channel in the network is straight and smooth; and (2) the thickness of electrical double layers of pores, approximately 2.18 nm, is not taken into account.⁸

As illustrated in Fig. 3, the size of largest mother “I” channel in Step 0 has width w₀, diameter d₀ and vertical length l₀. w_k, w_k−1, d_k, d_k−1l_k and l_k−1 are accordingly width, diameter and vertical length of “I” channel in Step k and k − 1. The relations of these dimensional parameters in adjacent steps are defined by several scale factors α, β and γ as:¹²

α = w_k/w_k−1 (12)

β = d_k/d_k−1 (13)

γ = l_k/l_k−1 (14)

It should be noted that the “I” shape network is embedded in particular cuboid which represents a saturated cement paste. The red dash line box shown in Fig. 3 stands for such cuboid, which has width w_c, length l_c and thickness d₀. w_c and l_c can be determined from eqn (15) and (16), respectively; the effective porosity (ϕ_c) of cuboid can be also deduced further when the step of “I” shape network is equal to k:¹²

w_c = w₀ + w₁ + w₂ + … + w_k = w₀(1 − α^k+1)/(1 − α) (k ≥ 0) (15)

l_c = l₀ + l₁ + l₂ + … +l_k + 2d_k = l₀(1 − γ^k+1)/(1 − γ) + 2d₀β^k(k ≥ 0) (16)

The number of “I” channel, whose diameter is not less than d_k, can be calculated from key fractal scale law as:⁸

1 + 4 + 4² + … + 4^k = (d₀/d_k)^Df = β^−kDf = (4^k+1 − 1)/3 (k ≥ 0) (18)

In addition, the chloride penetration direction to the cuboid is demonstrated in Fig. 3. The effective concentration gradient per unit length (Δc_u) along the penetration direction is defined as:

With regard to steady state diffusion case, the total mass flow rate through the saturated cement paste (Q_t) is equal to that through “I” shape network, as shown in eqn (20); thereupon, the formula of steady state diffusion coefficient of “I” shape network (D^net_ssd) is also presented as:¹⁷

When the ion binding capacity is taken into account, eventually, non-steady state migration coefficient of “I” shape network (D^net_nssm) is given as:

D^net_nssm = D^net_ssd/〈T_r〉 (22)

where 〈T_r〉 is average experimental transformation ratio among cement pastes.

In this work, the influences of porosity and pore size on non-steady state ion migration in fractal saturated cement paste are evaluated by a simulation based on “I” shape network. The algorithm for this simulation is concluded as follows:

(1) Determine the diffusion coefficient of ion (D_s) in the infinite dilute solution from Tang's work.¹⁵

(2) Set the average transformation ratio (〈T_r〉) from experiments.

(3) Select the appropriate porosity of the cuboid, sizes of largest mother channel and step number of “I” shape network, viz., ϕ_c, d₀, w₀, l₀ and k.

(4) A set of D_f between 1 and 2 is produced randomly.⁹

(5) Calculate the average value of non-steady state migration coefficient of “I” shape network (〈D^net_nssm〉) and corresponding variance (σ) using eqn (21)–(23).

where 〈D^net_nssm²〉 is the average of square of non-steady state migration coefficient of “I” shape network.

5. Results and discussion

5.1 Electrical rapid ion migration

Fig. 4 is non-steady state migration coefficient of cement pastes at hydration age 1 day and 3 days measured by electrical rapid ion migration. In this figure, pastes with higher water to cement ratio, dosage of fly ash or slag usually exhibit larger values of non-steady state chloride migration coefficient. In the case of higher water to cement ratio, less solid phases exist in the paste, volume of the pore space or channels for ion transportation in cement pastes can be thus larger, which can bring about larger ion migration value to great extent.¹ Pozzolanic reaction of fly ash or slag does not occur until the certain amount of calcium hydroxide is generated in blended cement pastes, early hydration and formation of pore structure skeleton will be retarded when fly ash or slag are added into cement pastes,^1,23 and hence, the resistances to ion transportation of fly ash/slag blended pastes are smaller than those of pure pastes at early hydration stage. With regard to silica fume case, pastes with higher silica fume dosage in turn exhibit lower values of non-steady state chloride migration coefficient. As silica fume composed of small particles is mixed with water and immediately covered by a gel-like layer,²³ this may result in a rapid percolation of solid phase and formation of initial pore skeleton. Longer hydration age is also beneficial to reduction of non-steady state chloride migration coefficient since more hydrated products are filled into pore space.²⁴

Fig. 4 Non-steady state migration coefficient measured by electrical rapid ion migration.

For further validation, compressive strength values of cement pastes at hydration age 1 and 3 days are presented in Fig. 5. Strength development in cement pastes primarily depends on the increase of hydration degree or decrease of pore volume.¹⁸ In principle, cement pastes with low ion diffusion/migration ability usually exhibit superior high compressive strength values,¹ it is confirmed that results in Fig. 5 correspond to ones presented in Fig. 4.

Fig. 5 Compressive strength of cement pastes at hydration age 1 day and 3 days.

5.2 Comparison of non-steady state migration coefficients

It may be instructive to compare results either measured from ERIM test in this work or previous literatures, or predicted from the fractal model mentioned above to check merits inherent with the application of each method. It is unfortunate few of experimental electrical migration results for young cement pastes in previous literatures are found since considerably long test time of electrical migration measurement is indispensable.⁶ The comparison of measured and predicted non-steady state migration coefficients of saturated cement pastes from ERIM test and fractal model is shown in Fig. 6. On the whole, it can be clearly seen that most of data sets of saturated cement paste have good agreement at hydration age 1 and 3 days, respectively. The minor differences between measured and predicted results in Fig. 6 may be rooted in several factors: (1) of particular note is that the mobility of ion migration may be accelerated since a high temperature is inevitably generated during the ERIM test when an electrical voltage is applied on sides of cement pastes;²⁵ moreover, the replacement of Na⁺ and OH⁻ ions with Cl⁻ in the pore solution of cement pastes may induce some microstructural changes by formation of new amorphous solid products either within the pores or as electrochemical double layers along the pore walls during ERIM test;⁶ (2) the derivation of non-steady state migration coefficient from the proposed fractal model based on NCIM is a bit complex and involves so many parameters; although how to derive these parameters has been already explained in detail by Tang et al. through a pure solution system or solution-concrete system,^3,15,16 the pore solution in cement pastes is not actual pure solution, and proved as mixed-solvent electrolyte solution.⁴ The contribution of individual species and interactions between pairs of species to ion transportation may be seriously considered in the prediction of non-steady state migration coefficient via fractal model.⁴ However, it may be somewhat difficult to determine these actual contributions of ions constrained by pore structure to the effective diffusion coefficient (D_s) in the complex interconnected pore network of cement pastes with hydration until now;^4,8 (3) hydration and microstructure of fresh cement pastes develop quickly and necessary test time is usually required in ERIM test;¹ for these cases, test timings between ERIM and NCIM may not coincide completely; and (4) assumptions inherent with the application of different techniques for ion migration, for instance, neglected diffusion flux during ERIM test⁴ and the empirical prediction of minimal and maximal pore diameters in the fractal model,^8,9 may be one of sources of scattered results in Fig. 6.^9,24

Fig. 6 Comparison of measured and predicted non-steady state migration coefficients from ERIM and NCIM.

5.3 Non-steady state migration simulation based on “I” shape network

5.3.1 Influence of porosity. Fig. 7 shows the comparison of simulated and predicted non-steady state migration coefficients development with porosity. In this simulation case, sizes of largest mother channel are fixed as: d₀ = w₀ = l₀ = 1 μm, and step number (k) is equal to 10 according to ref. 12. The variance values obtained from this simulation are smaller than migration values in Fig. 7; this implies that stable migration values are yielded. It is also found that the ion migration value increases with increase of the porosity.⁷ This case may be explained as the increase of pore space which provides transportation channels for ions.¹⁷ A paste with longer hydration age usually has smaller porosity and thus presents lower ion diffusion/migration value. Besides, simulated results are generally consistent with ones predicted from fractal model, as illustrated in Fig. 7.

Fig. 7 Comparison of simulated and predicted non-steady state migration coefficients development with porosity.

5.3.2 Influence of diameter of largest mother channel. Fig. 8 shows simulated non-steady state migration coefficients development with diameter of largest mother channel (d₀). The determination of actual diameter of largest mother channel in complicated pore network of fractal saturated cement paste is practically somewhat difficult.⁹ It is reported that d₀ in saturated cement paste may be associated with porosity, pore size distribution, solid phase imbibition coefficients and pore solution wetting properties.⁹ As a consequence, for simplicity, d₀ is selected in wide range for this simulation, from 1 to 10 μm with interval of 1 μm, as shown in Fig. 8, when other parameters of “I” shape network are kept as: w₀ = l₀ = 1 μm, k = 10 and ϕ_c = 0.3. It can be clearly observed that the non-steady state migration value doesn't present obvious fluctuation at given d₀ and steadily decreases from 13.09 to 4.81 × 10⁻¹¹ m² s⁻¹ in the selected range of d₀ from 10 to 1 μm. It is expected that the dimension of large capillary pores in saturated cement pastes decreases naturally with hydration time and this will have a positive effect on the reduction of ion migration performance.⁹

Fig. 8 Simulated non-steady state migration coefficients development with diameter of largest mother channel.

5.3.3 Influence of step number. Table 2 shows simulated non-steady state migration coefficients with different step numbers from 3 to 12 when d₀ = w₀ = l₀ = 1 μm and ϕ_c = 0.3. It can be seen that non-steady state ion migration value increases with small variance value as the step number of “I” shape network increases. As expected, the increase of step number will increase beyond doubt the number of small plentiful of transportation channels that is favorable for ion migration. In particular, it is also emphasized that migration coefficients tend to be stable as step number begins to reach to 9 in Table 2; this phenomenon may be explained that migration movements of ions are strongly constrained by pore walls in small pores.²⁴

Table 2 Simulated non-steady state migration coefficients with different step numbers

Step number	Non-steady state migration coefficient (×10^−11 m^2 s^−1)	Variance (×10^−12 m^2 s^−1)
3	4.48	1.67
4	4.62	1.99
5	4.68	2.03
6	4.71	2.41
7	4.75	2.55
8	4.79	2.64
9	4.82	2.73
10	4.82	2.84
11	4.82	2.95
12	4.82	2.95

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6. Conclusion

For the first time, this study presents a preliminary work to evaluate the diffusion and migration of ions in fractal cement pastes at early age. The aggressive ion in this analysis is taken as chloride ion that is widespread species in the marine environment. The traditional migration test, electrical rapid ion migration (ERIM), has been carried out to assess the ability of non-steady state ion migration (D_nssm) in cement pastes at early age. Meanwhile, a newly developed non-contact impedance measurement (NCIM) has been adopted in this work to in situ study the evolution of non-steady state ion migration coefficients in cement pastes through a fractal model when ion binding capacity is considered. The corresponding non-steady state ion migration coefficients predicted from the fractal model have good agreement with ones measured by ERIM. Additionally, the influences of water to cement ratio, curing hydration age, addition of fly ash, slag and silica fume on performance of ion migration in cement paste can be observed obviously. A cement paste with lower water to cement ratio, longer hydration age and addition of silica fume usually exhibits lower values of (D_nssm) due to the reduction of pore space; on the contrary, addition of fly ash and slag is favorable to the gain of values of (D_nssm). NCIM combined with the proposed fractal model may have broad prospects to predict the ion diffusion/migration performance of other porous media if the fractal dimensions, ion binding capacity, minimal and maximal pore diameters can be determined.

Besides, a fractal simulation based on an “I” shape network has been established to provide valuable information of ion migration evolution with pore structure parameters in fractal cement paste. It can be inferred that the simulated non-steady state ion migration coefficient of fractal cement paste is associated with some structural parameters of “I” shape network, such as size of largest mother channel and step number. From simulation results, it is shown that larger porosity, diameter of largest mother channel or more step number of “I” shape network is beneficial to yield larger values of (D_nssm).

Indeed, the contribution of dead or isolated pores to ion diffusion/migration in fractal cement pastes is not taken into consideration in this work since these pores have minor effect on the transportation performance.²⁴ Additionally, some studies have been devoted to the elucidation of the effect of temperature on the ion transportation performance in fractal porous media.^2,26 The resulting output in this work should be further optimized when the effect of temperature on the transportation of ion diffusion/migration of cement pastes is clarified.

Acknowledgements

The support from the Hong Kong Research Grant Council under grant of 615412 and from the China Ministry of Science and Technology under grant of 2009CB623200 is gratefully acknowledged.

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