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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A new electrochemical model has been carefully established to explain the carbonation behavior of cement mortar, and the model has been validated by the experimental results. In fact, it is shown by this study that the electrochemical impedance behavior of mortars varies in the process of carbonation. With the cement/sand ratio reduced, the carbonation rate reveals more remarkable. The carbonation process can be quantitatively accessed by a parameter, which can be obtained by means of the electrochemical impedance spectroscopy (EIS)-based electrochemical model. It has been found that the parameter is a function of carbonation depth and of carbonation time. Thereby, prediction of carbonation depth can be achieved.

Mortar has always found wide application in the construction industry, which plays a bonding, padding and protective role in concrete structures. Due to its high strength, low cost and convenient fabrication, mortars have been used as isolating lining materials in cisterns, wells, aqueducts, shafts and duct drains, as well as supporting materials for pavement sand mosaics, plasters on external and internal walls, supporting materials for frescoes, and as joint mortars of masonry structures [_{2} dissolved in the pore water, the highly alkaline components in concrete like Ca(OH)_{2}, hydrated calcium silicate (C-S-H), _{3} [

One of the traditional ways of determining carbonation depth is to spray phenolphthalein indicator onto the surface of a split concrete prism [

As a sort of nondestructive testing, the electrochemical impedance spectroscopy (EIS) method is able to reflect the micro-structural changes in the cementitious materials under variously natural exposure environments, which has been viewed as a promising way to study the physical and chemical properties of cementitious materials [

The objective of this paper is firstly to obtain the electrochemical impedance data of the carbonated mortar then, to apply the electrochemical model to describe the carbonation behavior of mortar. Finally, obtaining the functional relationship between the fitted parameter of the model and the carbonation time, the prediction of carbonation depth is thought to be achieved.

Cement: P.O 52.5 Portland cement, a product of the Starfish Onoda cement limited company of Shenzhen.

Water: normal tap water.

Sand: The standard sand derived from Xiamen ISO Stand Sand Company, China.

Mortar specimens with dimensions of 160 mm (length) × 40 mm (height) × 40 mm (thickness) were prepared with a cement/sand ratio of 1:2, 1:3 and 1:4 at the room temperature 20 °C as well as 95% of relative humidity. All specimens were water-cured for 28 days.

Before exposing the mortars to accelerating carbonation, they were sealed with wax, with both ends of the specimens left open to carbonation (see _{2} concentration. Regarding temperature and humidity, the carbonation test is set as 29–31 °C and 65%–70%, respectively.

EIS measurement was carried out by Princeton Applied Research Co. (PAR, Oak Ridge, TN, USA) Potentiostat/Galvanostat 283 with a frequency range of 0.01 Hz–1 MHz. The test was performed at 0, 3, 7, 14, 28, 36, 60 days, respectively. The mold for electrochemical impedance measurement is shown in

The carbonation depth was measured according to Chinese Standard (GBJ820-85) “

Generally, a simple electrochemical system can be simulated as a typical equivalent circuit shown in _{s}(_{ct}_{s} is the solution resistance, _{F} stands for the impedance of the Faraday’s procedure that occurs on the surface of the electrodes. Faraday’s procedure includes charge transfer procedure and charge diffusion procedure. As a result, Faraday impedance is represented by a serious connection of _{ct} and _{ct} stands for charge transfer resistance of the electrodes/electrolyte interface and

As far as _{s}(_{ct}_{ct}). In this sense, other reactions are overlooked except the electrode reaction. However, the microstructure of cement-based materials is very complex [

In view of the mechanism, Gu Ping, _{s}(_{1}_{ct1})(_{2}_{ct2}) system (shown in _{s} represents the resistance of the electrolyte solution, _{1} corresponds to the double layer capacitance between the solid/liquid phases, _{ct1} stands for the resistance caused by ion transfer procedure inside the cement mortar sample, _{2} stands for the double layer capacitance between cement mortar and electrodes; _{ct2} stands for the resistance caused by the charge transfer procedure on the surface of the electrodes.

_{s}(_{1}_{ct1})(_{2}_{ct2}) effectively characterizes the electrochemical impedance spectroscopy when the cement mortars are in dry condition. For dry specimens, as the pore solution in the materials is rather little and the ions scarcely diffuse on a large scale. It is therefore to say that the charge diffusion procedure impedance (Warburg impedance) is insignificant to mention in this case. However, as to the moist mortars (especially the ones that used in the neighborhood of seaside), the interior amount of solution is apparently higher, the Warburg impedance is supposed to be considered.

After consideration of the fact that ions in mortar would transfer on a large scale, a novel electrical circuit model is proposed for investigation of mortar’s carbonation (illustrated in

Where, _{s} stands for the resistance of pore solution in mortar; _{1} stands for the double layer capacitance between the solid/liquid phases; _{ct1} stands for the resistance caused by ions transfer procedure inside the mortar; _{1} stands for Warburg resistance caused by ions diffusion procedure inside the mortar; _{2} stands for the double layer capacitance between mortar and electrodes; _{ct2} stands for the resistance caused by the charge transfer procedure on the surface of the electrodes; _{2} stands for Warburg resistance caused by the ion diffusion procedure on the surface of the electrodes. The CDC (Circuit Description Code) for this new equivalent circuit can then be described as _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})), in which _{ct1} + _{1} = _{F1}, standing for the Faraday impedance caused by the Faraday’s procedure inside the mortar; while _{ct2} + _{2} = _{F2}, standing for the Faraday impedance caused by the Faraday’s procedure between the mortar and electrodes.

As concerning the mentioned-above equivalent electrical circuit model, the total impedance can be stated by the mathematical equation as below:

The real part of

And imaginary part of Z is:

where, σ_{1}: the conductivity of cement mortar; σ_{2}: the conductivity of electrodes;

(1) When

then

Based on

It is an equation standing for a half circle in the first quadrant.

When ω → 0 (Very low frequency);

Based on

This is a linear equation.

Based on the derivation in

_{s}(_{ct}_{s}(_{1}_{ct1})(_{2}_{ct2}), and the model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) in the Nyquist figure. It can see clearly that model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) that considers the charge diffusion procedure impedance (Warburg) in mortar performs the best fit for the impedance spectroscopy data while the Randles model _{s}(_{ct}_{s}(_{ct}_{s}(_{1}_{ct1})(_{2}_{ct2}) makes a good figure, it is inferior to the model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})). The phenomenon is not hard to explain: The samples in the whole experimental work are wettish (cured for 28 days in water and then kept in carbonation chamber of 95% relative humidity). As noted above, Warburg impedance is supposed to be taken into account for those of mortars in wet state. But model _{s}(_{1}_{ct1})(_{2}_{ct2})leaves out the Warburg impedance of the mortar. If the mortar turn dry, the most comprehensive model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) will convert to electrical equivalent circuit of _{s}(_{1}_{ct1})(_{2}_{ct2}) as the “_{1}” and “_{2}” are cleared away.

In the light of the fitting results above, conclusion can naturally be drawn that the new model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) proposed in this paper is able to explore the properties of carbonation of mortar.

_{2} dissolved in the electrolyte solution reacts with OH^{−} ions generated by the hydration of the cement so that the concentration of OH^{−} ions tends to decline. Among all the ions in the cement-based materials, OH^{−} ion is thought of as the most conductive [

With the purpose to investigate the quantized links between the resistance caused by ion transfer procedure inside the mortar sample (_{ct1}) and carbonation depth, the fitting parameter _{ct1} of _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) model at different carbonation time is listed in _{ct1} is an increasingly linear proportion to the carbonation time. In order to explore the quantitatively functional correlation between _{ct1} and carbonation depth, the test of the carbonation depth for the mortar is carried out with the same carbonation cycle. The results shown in

where,

The experimental results are in perfect agreement with other researchers [

Given that _{ct1} value is linear with time while carbonation depth (_{ct1} value:

A comparison between the experimental values and the estimated values of the carbonation depth both at 90 days and 120 days is shown in _{ct1} based on _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) model can be used to predict the cement carbonation depth in an acceptable manner.

Based on the test and the analytical results, the following conclusions could be drawn:

It is of theoretical and practical significance to characterize the carbonation behavior and to predict the carbonation depth of mortar by EIS measurement. This approach can overcome the inherent constraints of phenolphthalein solution test.

A novel equivalent circuit model with _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) has been proposed to provide detailed insight on the carbonation behavior of mortar, taking into account both the solid/liquid double-phase interaction and the Warburg impedance. The curve fitting results based on the proposed model show a high consistency with the experimental results.

_{ct1} value obtained by fitting calculation of the impedance data with the new electric circuit can be applied to characterize the carbonation behaviors of the mortar. Comparing with the experimental results and with modeling parameters, it is found that carbonation depth is the function of _{ct1}:

The authors would like to acknowledge financial support provided by National Key Basic Research Program funded by MOST (Project No. 2011CB013600; Issue No. 2011CB013604) and National Natural Science Foundation of China (No. 51120185002/51272160); Foundation for technology innovation project in Higher Education of Guangdong, China (No. 2012KJCX0091).

The authors declare no conflict of interest.

_{2}(review article)

^{−}, K

^{+}and Na

^{+}concentrations

(

The Randles equivalent circuit for a general electrochemical system.

The simplified electrical equivalent circuit for hydration measurement of cement mortar.

The equivalent circuit model proposed to investigate the cement mortar with carbonation process.

Curve on the complex plane corresponding to carbonation process of mortar.

(_{s}(_{ct}_{s}(_{1}_{ct1})(_{2}_{ct2}) model, together with the dots which represents the model _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})).

The Nyquist curves measured at different carbonation time for the mortar: (

The experimental result of carbonation depth for mortars with different cement/sand ratio (1:2,1:3,1:4) and its fitting result.

Comparison of the experimental results with fitting results based on for the mortar: (

The fitting result of _{ct1} based on _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) model.

Carbonation time (day) | _{ct1} value calculated from _{s}(_{1}(_{ct1}_{1}))(_{2}(_{ct2}_{2})) model (Ohm)
| ||
---|---|---|---|

0 | 66,200 | 77,330 | 136,200 |

3 | 118,900 | 139,800 | 178,600 |

7 | 211,000 | 185,100 | 201,300 |

14 | 292,000 | 216,600 | 343,300 |

36 | 358,000 | 354,500 | 460,600 |

60 | 467,000 | 534,600 | 697,300 |

90 | 663,200 | 745,800 | 968,100 |

120 | 854,600 | 957,800 | 1,238,900 |

The average carbonation depth for mortars with different cement/sand ratio (1:2,1:3,1:4).

Carbonation time (day) | Carbonation depth (mm)
| ||
---|---|---|---|

C/S = 1:2 | C/S = 1:3 | C/S = 1:4 | |

0 | 0.00 | 0.00 | 0.00 |

3 | 0.89 | 1.80 | 1.02 |

7 | 1.55 | 2.54 | 2.18 |

14 | 1.96 | 2.67 | 3.29 |

36 | 2.60 | 3.68 | 3.94 |

60 | 3.18 | 4.32 | 4.61 |

90 | 3.40 | 5.53 | 5.62 |

120 | 3.60 | 5.80 | 6.46 |

The comparison of average measured carbonation depth for mortars with different cement/sand ratio.

Carbonation Depth | Cement/Sand Ratio
| |||
---|---|---|---|---|

1:2 | 1:3 | 1:4 | ||

90 day | Measured carbonation depth (mm |
3.40 | 5.53 | 5.62 |

Calculated value (mm) | 3.56 | 5.59 | 6.04 | |

Variation (%) | 4.71 | 1.08 | 7.47 | |

| ||||

120 day | Measured carbonation depth (mm) | 3.60 | 5.80 | 6.46 |

Calculated value (mm) | 4.09 | 6.42 | 7.00 | |

Variation (%) | 13.61 | 10.69 | 8.36 |