Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2023.40.0015 Acta Polytechnica CTU Proceedings 40:15–21, 2023 © 2023 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague MEASUREMENT AND EVALUATION OF CEMENT PASTE POROSITY BY ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY Jana Chalupová a, ∗, Jiří Němeček 1,a, Vojtěch Hybášekb, Vojtěch Pommerc, Jiří Němeček 2,a a Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech Republic b University of Chemistry and Technology, Department of Metals and Corrosion Engineering, Technická 5, 166 28 Prague 6, Czech Republic c Czech Technical University in Prague, Faculty of Civil Engineering, Department of Material Engineering and Chemistry, Thákurova 7, 166 29 Prague 6, Czech Republic ∗ corresponding author: jana.chalupova@fsv.cvut.cz Abstract. Porosity is an important part of cement paste microstructure, which significantly influences the mechanical properties (especially durability and strength) of cement-based materials. Electrochemical impedance spectroscopy (EIS) is a non-destructive method used to measure the pore system utilizing a range of frequencies of electric current, which is fed to the cement paste by stainless steel electrodes. The pore volume is obtained from the pore resistance and the matrix capacitance measured by EIS. This paper deals with the evaluation of porosity based on resistance values from EIS on a sample of pure CEM I 42.5R Portland cement paste at 3 different hydration times (age 7, 14, 28 days). Keywords: Electrochemical impedance spectroscopy, cement paste, porosity. 1. Introduction Cement is one of the most consumed materials in the world. Therefore, many scientists are working on researching, developing, and improving cement-based materials. Porosity is one of the observed proper- ties at the micro-scale that influences strength and durability [1]. Generally, three types of pores can be found in hydrated cement paste – capillary pores, gel pores, and interlayer space. The pore characteristics differ in size, shape, and distribution in the solid matrix. Porosity measurement depends on all these characteristics [2]. The porosity of cement-based material can be ac- cessed either by direct or indirect methods. Direct methods are able to measure the pore sizes from the largest pores in the order of a few millimeters to hun- dreds or tens of nanometers. Direct methods analyze pore structure from 2D or 3D images of the sample. Therefore, these methods depend on the resolution of an image (pixel size). These methods include 2D images of scanning electron microscopy (SEM), 3D images of X-ray microtomography or X-ray nanoto- mography, and laser scanning confocal microscopy (LSCM) [3]. Indirect methods use liquid (such as water, gas, mercury, helium, etc.) inside cement paste as a probe. 1Ph.D. at Czech Technical University in Prague, Orcid: 0000-0002-5635-695X. 2Professor at Czech Technical University in Prague, Orcid: 0000-0002-3565-8182. The size of the measurable pores is limited by the lower (tens of nanometers) and upper boundary (hundred of micrometers). Indirect methods of measuring open porosity include mercury intrusion porosimetry (MIP), water saturation, and pycnometry [3–5]. Electrochemical impedance spectroscopy (EIS) can be ranked as the indirect method because a liquid conduct an electric current and thus is involved in the measurement. Using EIS not only detects the porosity and microstructure of concrete [6–9], but also the hydration and shrinkage process [10], corrosion process of reinforced concrete [11, 12], the diffusion of chloride in concrete [13, 14] and the influence of mineral admixtures on cement-based material [15]. Despite some efforts of porosity characterization by EIS [6–9] the methodology is still limited by many un- certainties. Thus, this paper deals with the EIS mea- surement on pure cement paste samples, evaluation of porosity, and comparison with porosity determined by helium pycnometry. 2. Electrochemical impedance spectroscopy 2.1. Equivalent circuit models for concrete Electrochemical impedance spectroscopy (EIS) or oth- erwise known as alternating current impedance spec- troscopy (ACIS), is a non-destructive method used to measure the resistance of materials, including cement 15 https://doi.org/10.14311/APP.2023.40.0015 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en J. Chalupová, J. Němeček, V. Hybášek et al. Acta Polytechnica CTU Proceedings paste and concrete. Electric current (usually alternat- ing current AC) is applied to the samples by a pair of electrodes embedded in the material or attached to their opposite surfaces. The transmitted current with the periodic alternating signal can be decomposed into a series of harmonic signals of sinusoidal shape with different frequencies due to fast Fourier trans- form [16, 17]. The measurement is taken from the highest frequencies to the lowest, and the impedance is recorded [6, 12]. Cement paste cannot be considered as a single elec- trical resistor in EIS measurements because the mate- rial consists of a bulk matrix and pores. Pores have different shapes, sizes, and distributions in the ce- ment paste structure. For example, capillary pores are connected and with an oblong shape in contrast to a spherical enclosed pores [2]. Electrochemical impedance spectroscopy allows measuring only the capillary pores, and three conductive paths are distin- guished as shown in the Figure 1 [6]: • Continuous conductive path (CCP) – A series of capillary pores connected by pore necks form CCP. The impedance of this path Z CCP equals the resis- tance of interconnected capillary pores RCCP: Z CCP = RCCP. (1) • Discontinuous conductive path (DCP) – The conti- nuity of a capillary path is disturbed by a discontin- uous point (DP) formed by a thin layer of cement paste. DP is considered to be a double parallel capacitor with electric capacitance C DP. The resis- tance of the capillary path is labeled as RCP. The impedance of the path Z DCP is composed of C DP and RCP connected in series as shown the following equation: Z DCP = RCP + C DP. (2) • Insulator conductive path (ICP) – The pores and voids do not form the largest part of cement paste. It is made up of a bulk matrix that acts as an electric insulator. The matrix becomes charged as a result of the current passing through the sample. Therefore it is considered a double parallel capacitor with capacitance C mat. Although cement paste is not a perfect insulator, its resistance Rmat can be neglected if the sample is not frozen or dried. Thus, the impedance of this path Z ICP is just equal to the C mat: Z ICP = C mat. (3) According to the typical Nyquist diagram (plot of real versus imaginary part of impedance), capacitive loops occur in cement-based materials as shown in Figure 2b. These loops can be replaced by a parallel series of resistors (R) and capacitors (C ). An equiv- alent electric circle containing R and C is necessary to use in order to evaluate the results of EIS mea- surement [18, 19]. Many equivalent circuits have been published and are summarized in [19]. DISCONTINUOUS CONDUCTIVE PATH (DCP) CONTINUOUS CONDUCTIVE PATH (CCP) INSULATOR PATH (ICP) DISCONTINUOUS POINT (DP) PORE SOLUTION CEMENT PASTE CONDUCTIVE PATH Figure 1. Simplified microstructure of cement paste with illustrated conductive paths. In this paper, two different models of equivalent electric circuits published by Guangling Song in [6] were used. The first option is the equivalent circuit model (EC), which is composed of all above mentioned paths, as shown in Figure 2a. The capacitance of the solid matrix of the cement paste is relatively low. Therefore the second option assumes the simplification that C mat does not have to be considered in the second equivalent model, as shown in Figure 3. Furthermore, the electric circuit can be simplified into the simplified equivalent circuit model (SEC) as shown in Figure 2c. Comparing the equivalent models in Figures 2c and 3, the following relations can be deduced [6]: R0 = RCP · RCCP/(RCP + RCCP), (4) R1 = RCCP2/(RCP + RCCP), (5) C1 = (1 + RCP/RCCP)2 · C DP, (6) where R1 is resistance of (continuous and discontinuous) pores, C1 is a capacitance of bulk cement (including C DP), R0 is an offset resistance from the origin on real axis of Nyquist diagram. The theoretical Nyquist spectrum of the EIS con- sists of arcs. The most important arc of the SEC model is the arc of diameter R1, see Figure 2d. The position of the center of the arc on the real axis Z is ensured by rotation by the depression angle (α) [20], which is related to the pore size distribution and the others imperfection of the sample [12]. R0 can be neglected because of high-frequency measurement (nearly to the origin on the real axis of the Nyquist plot) is negatively influenced by surrounding phenomena and the accuracy limitation of most electrochemical equip- ment [6, 20, 21]. 16 vol. 40/2023 Measurement and evaluation of cement paste porosity . . . RCP CDP CMAT RCCP BULK MATRIX CONNECTED PORES DISCONNECTED PORES ZICP ZDCP ZCCP Re Z [Ω] -I m Z [Ω ] b) Nyquist spectrum based on EC Impedance R0 R1 a) Equivalent circuit (EC) R0 C1 R1 [Ω] d) Nyquist spectrum based on SEC Impedance R0 R1 c) Simplified equivalent circuit (SEC) Re Z -I m Z [Ω ] Figure 2. Equivalent circuit model (EC), theoretical Nyquist EIS spectrum based on a equivalent model EC, simplified equivalent circuit model (SEC) and theoretical Nyquist EIS spectrum based on a equivalent model SEC [6]. RCP CDP RCCP CONNECTED PORES DISCONNECTED PORESZDCP ZCCP Figure 3. Simplified equivalent circuit model for cement paste used to measure of EIS [6]. 2.2. Porosity calculation from EIS measurements Archie’s law is the most widely used relationship be- tween the resistivity and porosity of porous mate- rial. The relationship was originally derived on the sandstone filled with brine [22] and is defined by the equation: F = A · ϕ−m0 , (7) where F is formation factor, A is a coefficient, ϕ0 is the capillary porosity, m is Archie’s index. In cement-based materials, the resistivity is depen- dent on sample dimensions and electrode positions. Thus, it is more convenient to convert the resistance to effective electrical conductivity σeff as a function of electrode size and position: σeff = l/(R · S), (8) where l is the distance between the electrodes in the direc- tion of current, S is the cross-sectional area of the electrode embed- ded in the cement paste. σeff = C · σ0 · ϕ0m , (9) where σ0 is the conductivity of conducting medium, C is a constant depending on the saturation of the sample (assumed to be 1.0 for fully saturated sam- ples), ϕ0 is the pore volume fraction, m is Archie’s index. The exponent m reflects pore complexity and tortuos- ity and has been found in the range 1.5–4.0 [13, 18]. 3. Materials and Methods 3.1. Sample preparation Cement paste samples were made from CEM I 42.5R with a water to cement ratio of 0.4. A fresh mixture was poured into a silicone-lubricated formwork with dimensions of 54×30×11.7 mm (length, width, height). Additionally, a pair of electrodes from a stainless steel plate was put longitudinally into the formwork. Elec- trodes were inserted 3 mm above the formwork bot- tom and 1 mm from formwork edges. The distance between electrodes was set to 10 mm. The scheme of sample setup for EIS measurement is shown in Figure 4. Moreover, the same samples without elec- trodes were prepared for porosity measurement. The samples were demoulded after 24 hours and placed in 0.5 % limewater solution where retained until the measurement. 17 J. Chalupová, J. Němeček, V. Hybášek et al. Acta Polytechnica CTU Proceedings 11 .7 15 9. 7 3 R E F E R E N C E E L . W O R K IN G E L . C O U N T R E L . W O R K IN G E L . 52 54 1 1 10 10 10 30 [mm] EMBEDDED ELECTRODE CEMENT PASTE Figure 4. An illustration of the sample with embed- ded and connected electrodes. 3.2. EIS measurement EIS measurement was performed using Zahner Zen- nium X device and ThalesXT USB software with a frequency range of 12 MHz–100 Hz and 10 steps per decade. The amplitude of sinusoidal voltage was set to 10 mV. The use of a larger potential amplitude is not recommended due to possible changes in the surfaces of the samples [17]. The cables connected two working electrodes to one of the embedded electrodes. The reference electrode and the counter electrode were connected to the other of the embedded electrode [23]. Short coaxial cables were used to reduce the influ- ence of surrounding phenomena and the measurement noise [17]. To ensure consistent measurement results, it was necessary to prevent the drying of the saturated samples. Thus, samples were partly submerged in the water while simultaneously avoiding contact between electrodes and water. Otherwise, the electric current entering the samples would pass through the water, and the results would not correspond to the cement paste. The samples were measured at 3 different ages of hydration – 7, 14, and 28 days. The EIS mea- surement was taken at five-minute intervals until the values stabilized. 3.3. Porosity measurement The porosity of the cement paste was determined by helium pycnometry and mercury intrusion porosime- try. After a saturation period of 7, 14, and 28 days, the samples were cut into 2 mm thick slices and dried at 50 °C. Subsequently, sample density, ρ was measured by helium pycnometer Thermo Scientific ATC EVO. The bulk density, ρbulk of the samples was determined by the gravimetric method. Further, the porosity of the sample was calculated from the equation: ϕ0,P = (1 − (ρbulk/ρ)) · 100. (10) 4. Results and Discussion The example of the EIS results for the C-14d and C-28d samples is shown in Figure 5 as the Nyquist 150 200 250 300 0 50 100 150 200 Re Z [Ω] -I m Z [Ω ] a) C-14d Exp. data - cem. paste Exp. data - electrode Exp. data - noise EC fit SEC fit 150 200 250 300 0 50 100 150 200 Re Z [Ω] -I m Z [Ω ] b) C-28d Exp. data - cem. paste Exp. data - electrode Exp. data - noise EC fit SEC fit Figure 5. Experimental Nyquist EIS spectrum with calculated EC and SEC model fits for samples C-14d and C-28d. Note that only data corresponding to cement paste (blue marks) were used for fitting. spectrum. Before the resistance and capacitance eval- uation, experimental data were corrected and cut off at both ends. That is because the values at low fre- quencies correspond to the electrodes’ resistance and their contact with the material, and values at high frequencies are inaccurate due to the limitations of the measuring device. Further, the data were fitted by the Simplex algorithm with the application of EC and SEC models [6]. The samples were remeasured over time until the resistance values were stabilized. The stabilization period took between the 15–30 minutes, as illustrated in Figure 6. Table 1 summarizes the resistances and capacities corresponding to the fits based on the EC and SEC models, as well as degree rotation α. The results clearly show almost no differences between resistances RCCP (EC) and R1 (SEC). Therefore, both values correspond to the continuously connected pores, indi- cating that C mat for the pure cement paste 7–28 days old can be neglected as considered by the simplified equivalent model. Also, both RCCP and R1 are increas- ing with samples age. Such a behavior corresponds 18 vol. 40/2023 Measurement and evaluation of cement paste porosity . . . Sample Equivalent circuit – EC Simplified equivalent circuit – SEC RCCP RDCP RDP Cmat R0 R1 C1 α [Ω] [Ω] [pF] [pF] [Ω] [Ω] [pF] [rad] C-7d 201.3 1290 29.1 38.7 0 204.1 41.9 0.81 C-14d 215.2 1577 29.2 40.7 0 217.3 42.0 0.82 C-28d 274.5 1875 21.7 41.6 0 276.8 45.5 0.86 Table 1. Resistance and capacitance of cement paste samples evaluated with different equivalent circuit models: EC, SEC. 0 5 10 15 20 25 30 200 225 250 275 300 325 Time [min] R C C P [Ω ] C-14d C-28d Figure 6. A stabilization period of cement paste resistance at different hydration times. The EC model evaluated RCCP. well to the decreasing porosity due to the ongoing hydration reaction, during which the newly created hydration products occupy space originally formed by capillary pores. Thus, creating more discontinuous paths results in increasing RDCP over time. The density results measured by helium pycnometry and bulk density are summarized in Table 2 along with the values of calculated porosity (ϕ0). Again the decrease in porosity corresponds to the hydration pro- cess. Initially, the porosity from the EIS measurement could not be directly calculated using Equation (9) and porosity obtained from helium pycnomtery was used for calibration. Another expression, the effective electrical conductivity was easily calculated from resis- tances RCCP and R1. The conductivity of the pore so- lution σ0 was calculated by the analytical relationship of Snyder [24], which is dependent on the w/c ratio, degree of hydration (DoH), and the amount of Na+, K+, OH− concentration. The DoH was estimated by Cemhyd3d model [25]. Thus, the only unknown term remains Archie’s index m. It was found that parameter m is almost identical for both equivalent circuit models EC and SEC and also does not vary with hydration time ranging from 7 to 28 samples age. Therefore, it is possible to calculate the average value Sample ρ ρbulk ϕ0,P [kg/m3] [kg/m3] [%] C-7d 2320 1687 27.3 C-14d 2287 1687 26.2 C-28d 2234 1685 24.6 Table 2. Porosity evaluated from helium pycnometry. of m = 3.46 ± 0.02. Lastly, the porosity ϕ0 was calcu- lated with the known mean value of paramete m. All the calculated parameters are summarized in Table 3. 5. Conclusions In this paper, the porosity was measured by electro- chemical impedance spectroscopy (EIS) with the aid of helium pycnometry and evaluated using Archie’s law. The resistivity of continuous conductive paths was evaluated from the impedance spectrum by the equivalent circuit (EC) and simplified equivalent cir- cuit model (SEC). The minimal differences between resistances RCCP and R1 were found. Hence, the ca- pacitance of matrix C mat can be neglected in the SEC model. Thus, only the SEC model is sufficient for evaluating the impedance spectra of pure Portland cement paste. The value of Archie’s index m was found to be al- most identical between both EC and SEC models and also for 7, 14, and 28 samples age. Thus, the m pa- rameter can be assumed as constant, which would allow porosity from EIS measurement without the aid of another porosity measurement method. Neverthe- less, when time changes or supplementary material is added, the porous system also changes. There- fore, further researches on cement-based materials are necessary. Acknowledgements The works were supported by the Czech Science Foundation (project 21-11965S) and the Grant Agency of the Czech Technical University in Prague (SGS22/088/OHK1/2T/11). Their support is gratefully acknowledged. 19 J. Chalupová, J. Němeček, V. Hybášek et al. Acta Polytechnica CTU Proceedings Sample DoH σ0 ϕ0,P RCCP R1 σeff m ϕ0 EC SEC EC SEC EC SEC m = 3.46 [%] [S/m] [%] [Ω] [Ω] [S/m] [S/m] [-] [-] [-] C-7d 65.5 13.08 27.3 201.3 204.1 0.147 0.145 3.459 3.470 27.3 C-14d 71.7 13.52 26.2 215.2 217.3 0.137 0.136 3.427 3.435 26.5 C-28d 76.8 13.90 24.6 274.5 276.8 0.108 0.107 3.467 3.473 24.5 Table 3. The parameters necessary for the porosity calculation by Archie’s law. References [1] Y.-Y. Kim, K.-M. Lee, J.-W. Bang, S.-J. Kwon. Effect of W/C ratio on durability and porosity in cement mortar with constant cement amount. Advances in Materials Science and Engineering 2014:273460, 2014. https://doi.org/10.1155/2014/273460 [2] H. M. Jennings. Refinements to colloid model of C-S-H in cement: CM-II. Cement and Concrete Research 38(3):275–289, 2008. https://doi.org/10.1016/j.cemconres.2007.10.006 [3] A. Aili, I. Maruyama. Review of several experimental methods for characterization of micro-and nano-scale pores in cement-based material. 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Cement and Concrete Research 36(9):1708–1718, 2006. https://doi.org/10.1016/j.cemconres.2006.05.014 21 https://doi.org/10.1680/adcr.2011.23.5.233 https://doi.org/10.1111/j.1151-2916.1994.tb04507.x https://doi.org/10.1111/j.1151-2916.1994.tb04507.x https://doi.org/10.2118/942054-G https://doi.org/10.1016/S0008-8846(02)01068-2 https://doi.org/10.1016/j.cemconres.2006.05.014 Acta Polytechnica CTU Proceedings 40:15–21, 2023 1 Introduction 2 Electrochemical impedance spectroscopy 2.1 Equivalent circuit models for concrete 2.2 Porosity calculation from EIS measurements 3 Materials and Methods 3.1 Sample preparation 3.2 EIS measurement 3.3 Porosity measurement 4 Results and Discussion 5 Conclusions Acknowledgements References