Analysis of the microstructure of carbon fibre reinforced cement pastes by impedance spectroscopy

Construction and Building Materials 243 (2020) 118207

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Analysis of the microstructure of carbon fibre reinforced cement pastes by impedance spectroscopy B. Díaz ⇑, B. Guitián, X.R. Nóvoa, C. Pérez ENCOMAT Group, EEI, Campus Universitario Lagoas-Marcosende, 36310 Vigo, Spain

h i g h l i g h t s
The higher the fibre amount, the higher the porosity.
Impedance provides microstructural information in carbon fibre reinforced cement.
The fibres polarization must be included in the equivalent model.
Impedance provides information concerning the fibre dispersion ability.
The fibres functionalization helps to an improved dispersion.

a r t i c l e

i n f o

Article history: Received 27 August 2019 Received in revised form 29 December 2019 Accepted 16 January 2020

Keywords: Conductive fibre Cement paste Microstructure Impedance spectroscopy Mercury intrusion porosimetry

a b s t r a c t The purpose of this study is the identification of the changes produced in cementitious matrices by the incorporation of carbon fibres. The characterization was completed by impedance spectroscopy and mercury intrusion porosimetry on specimens with increasing amounts of carbon fibres. An increased porosity for the higher fibre contents was revealed. The impedance analysis, based on the model used for unreinforced specimens, showed a poor dispersion, even for the lowest contents, and the modifications produced by the fibres could be qualitatively recognized. This preliminary analysis allowed the definition of an innovative electrical equivalent model, which includes the polarization at the fibre surface. The role of two dispersing techniques could be validated, since variations assigned to the fibre active surface available for polarization were detected. Impedance is presented as a promising methodology for the study of the microstructure in carbon fibre reinforced cement composites. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction The number of applications for short carbon fibre reinforced composites, in particular with cementitious matrices, is increasing because they provide an exceptional combination of structural and functional properties [1,2]. These materials exhibit improved tensile strength and flexural toughness as well as decreased drying shrinkage. Carbon fibres are advantageous among other types of fibres since they are electrically conductive, in addition to their chemical inertness, so smart structural elements can be conceived and tailored. Some unique applications include strain or temperature sensing, Joule effect heating, or electromagnetic shielding, among others [2]. Many of the most relevant studies in the field of carbon fibre reinforced composites have been focused on characterization in terms of their conduction performance [3–6]. Basically, several ⇑ Corresponding author. E-mail address: [email protected] (B. Díaz). https://doi.org/10.1016/j.conbuildmat.2020.118207 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

testing methodologies have been discussed, involving AC and DC current methodologies, with two or four electrodes, and factors such as the amount and the size of fibres or the use of dispersants have been treated in those studies. A few authors focused on the characterization of the solid at a microstructural level, being essentially Scanning Electron Microscope (SEM) the conventional technique for that sort of analysis [4,7–9]. Realistic information concerning the fibre dispersion ability or the fibre/matrix adherence can be directly deduced. The major disadvantage of this methodology is that it does not provide an overall perspective of the real state since both the number of samples and the analysis area are restricted. Additional drawbacks are the tediousness of the experimental procedure in terms of samples’ preparation, the poor representativeness of the samples, the overall high timeconsuming and the costly procedure involved. Mercury Intrusion Porosimetry (MIP) has been often employed for the structural characterization of cement-based materials. Few studies were found that include this methodology with carbon fibre reinforced cement studies [10,11], and some publications

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

discuss the influence of carbon nanotubes (CNTs) in cementitious matrices at the microstructural level [9,12–14]. MIP allows characterizing porosity along with the pores diameters, data very useful to understand the macroscopic performance. However, some limitations and disadvantages are inherent to the MIP technique, mainly from the testing point of view, analogous to the SEM procedure. Therefore, neither SEM nor MIP would be the most practical techniques for a general study aimed at easily correlate the material’s composition with specifics requirements. SEM and MIP are adequate for the detailed characterization of a specific specimen, but not for the analysis of a large number of variables in the same study. A non-destructive methodology as the Impedance Spectroscopy (IS) could be a consistent approach for a preliminary inspection, being able to provide rapid and reliable information concerning the modifications in the structure. A number of studies over the last two decades in the field of the characterization of unreinforced cementitious materials have evidenced the possibilities of IS on this field [15–20]. Some important details such as the experimental set-up or the most suitable analytical procedure have been considered in these publications. The key point for a rigorous study using this methodology is sustained in the accurate modelling of the obtained data. Thus, the design of a proper equivalent circuit has been crucial to validate the consistency of this methodology. A recent review has compiled the most important advances in the field of the microstructural characterization of cement-based materials [21]. The inspection of the hardening process, the assessment of the percolating conductivity and the changes produced by the effect of the environmental humidity or by the incorporation of admixtures are some of the most significant applications. Some studies have been already published focusing on the analysis of fibre-reinforced cement by IS [22–27]. Although those studies are significant in terms of the conductivity assessment, no further information concerning the microstructure of the composite is provided. Moreover, some incongruences are detected when trying to identify other matrix properties, as for example the dielectric constant, pointing to incoherencies in the discussed electrical models. Therefore, the main purpose of the present research aims at the analysis of the high-frequency impedance response in carbon fibre reinforced cement pastes. The previous knowledge already acquired by our research group in conventional cementitious samples is helpful and valuable to assume the existing challenge of characterizing reinforced matrices. The key point of this work focuses on the understanding of the influence of the fibres in the cement paste microstructure. The knowledge of the eventual modifications due to the presence of the carbon fibres, beyond a basic conductivity assessment, could contribute in the early production stages. The rapid assessment of design factors, such as the fibre content, the fibre aspect ratio or the type of fibre, would be easily performed if the role of the fibres in the microstructure has been identified. The impedance response could be used as a quality control technique in order to find the most suitable composition for any particular application. The microstructural changes will be also examined by the MIP methodology to confirm the validity of the impedance discussion [17,28,29]. A close connection has been already deduced between the dielectric response of the hardened portion and the porosity. Besides, the assessment of the average pores diameter along with the dispersion of the sizes has found a suitable correlation between both techniques. In order to accomplish with the proposed objective, this study includes, on one hand, the influence of the carbon fibre content into the microstructure of the cement-based material. This preliminary analysis has allowed the identification of the new features in comparison with the unreinforced specimens. Based on these

results, an equivalent model was proposed. After that, the influence of the fibre dispersion has be studied. Two common chemical techniques have been validated: the incorporation of a surfactant (Tween-20) and the prior functionalization of the fibres. This is, in fact, an innovative point since the studies so far verify the fibre dispersion via conductivity measurements.

2. Experimental design 2.1. Specimens preparation Cement paste samples were prepared with ASTM Type I Portland cement (CEM I 52.5R) and tap water, using a water/cement ratio fixed to 0.45. Un-sized pitch-based carbon fibres (Donacarbo chopped fibre S-232), produced by Osaka Gas Chemicals Co., Ltd. and kindly supplied by Comindex, S.A., were incorporated as reinforcements. The carbon fibre specifications are included in Table 1. The fibre content varied from 0% (blank) to 1% (by weight of cement). Cement paste samples were prepared by incorporating the water, or the fibres-water mixture previously mixed with a stirring rod, into the container with the cement powder. The mixing period was extended a few minutes until a homogeneous slurry was obtained. Then the mixtures were cast in PVC cylindrical moulds (~5.5 cm height and 5.6 cm diameter). After demoulding, the samples were kept in a humid chamber at ambient temperature. The experimental programme was initiated after one month of curing. In order to accomplish a reliable comparison, all the samples were treated to ensure a complete filling of the pores. Specimens were soaked in water under vacuum, following the preconditioning procedure included in standard ASTM C-1202. Thus, information concerning the pores-saturated condition can be obtained. Afterwards, the samples were dried in an oven at 40 °C for one week and periodical measurements were taken throughout this drying period.

2.2. Dispersion of the carbon fibres Two chemical techniques, the fibres functionalization and the incorporation of a surfactant, were used to assist in the dispersion of the carbon fibres. Additional mixtures with 0.2 wt% of carbon fibres were prepared. The methods to improve the dispersion were labelled as T2 and FF. T2 involves the incorporation of a non-ionic standard surfactant, in particular, Tween-20, used in some studies to assist the dispersion of carbon nanotubes in cementitious matrices [14,30]. In this preliminary study, the fibres/dispersant weight ratio was limited to 1:1, to avoid excessive air voids formation that would worsen the mechanical properties of the final composite [14]. The procedure FF refers to the functionalization of the fibres in a mixture of commercially grade sulfuric and nitric acids 3:1 [31,32]. According to previous studies, this pre-treatment helps to the homogenization in aqueous solution and induces an improved interaction between the fibre and the hydrated cement phases due to the formation of carboxylic groups at the carbon fibres’ surface [31,33,34]. The functionalization treatment consisted in the immersion of 1 g of fibres in 200 ml of the acidic solution for 3 h at room temperature with ultrasonic stirring. The fibres were then kept in the same acidic solution for 24 h, without stirring. After that, the fibres were carefully separated and rinsed with deionized water several times until neutral pH in the remaining filtered solution. Finally, they were oven dried at 40 °C. An improved dispersion of the fibres in water, prior to the incorporation to the cement powder, was visually confirmed in both tested procedures. This observation does not validate the further

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207 Table 1 Properties of the carbon fibres used in this study (http://www.ogc.co.jp/e/). Density (g cm3) 1.6

Volumetric resistivity (O cm) 9  10

3

Tensile modulus (GPa)

Carbon content (%)

Average length (mm)

Diameter (mm)

Aspect ratio

Surface

40

97.1

5.5

13

420

untreated

dispersion in the solid matrix, but it is an encouraging indication on the effect of the dispersing methodologies.

0.25

2.3. Mercury intrusion porosimetry (MIP)

0.20

-1

Log diff intrusion vol. (mL.g )

Family 2

Ò

An Autopore IV 9500 from Micromeritics was used for the structural analysis, able to apply pressure values between 14 kPa up to 227 MPa. Hence, pore diameters from 300 mm down to 5 nm can be investigated, considering the contact angle and the Hg surface tension as 130° and 485 dyncm1, respectively. The tests were performed at the age of four months after casting, once the impedance measurements had been concluded. The entire samples were oven-dried at 40 °C to ensure a minimum humidity content and then the small fragments (~0.1 g each) were taken from the core of the specimens after splitting them with a hammer. The tests were performed twice for reliability. This technique provides quantitative information concerning not only the porosity or the density of cementitious materials, but also the average pore size and the distribution of the several pores families.

blank (P=20.6%) 0.2 wt.% (P=20.6%) 0.6 wt.% (P=22.3%) 1 wt.% (P=25.7%)

0.15

0.10

Family 3

0.05

Family 1

0.00 1

10

2

10

3

10

4

10

5

10

Pore size diameter (nm) Fig. 1. MIP results for the blank, the 0.2 wt%, the 0.6 wt% and the 1 wt% samples. The porosity is noted as P.

2.4. Impedance spectroscopy (IS) An HP 4294A analyser, that allows capacitance measurements from 10-15 up to 0.1 Farads, was employed for the impedance data acquisition. An AC potential signal of 50 mV was used, and the frequency was swept from 110 MHz to 100 Hz, recording 9 points per decade. The methodology employed here was that used to study the microstructure in unreinforced cement-based materials [16,17]. The two-electrode configuration was selected, with the graphite electrodes firmly attached to both ends of the specimens. The isolation of the specimen from the driving external electrodes is the most adequate procedure to perform this type of measurement [15,16,35]. Thus, two polyethylene sheets (0.20 mm thick) were placed between the cement specimens and the graphite electrodes. This procedure removes the interfacial polarization, which usually partially masks the dielectric response of the material to be tested. Therefore, the influence of the carbon fibres in the cement structure can be more reliably characterized. The impedance of the wiring arrangement (connecting cables, graphite electrodes and polyethylene sheets) has to be mathematically subtracted from each measurement before performing the quantitative analysis of the impedance results. The measurements were performed using the prepared cylinders (~5.5 cm length), after grinding both ends to avoid any air gap between the sample and the electrodes. 3. Results and discussion 3.1. Microstructural analysis: Mercury intrusion porosimetry (MIP) Fig. 1 shows the results of the MIP tests performed for the blank sample and for the samples with 0.2, 0.6 and 1 wt% of carbon fibres. The differential intruded volume (in log scale) is plotted versus the pore diameter. Two pores families can be distinguished, one centred at 110 nm (labelled as Family 2) and the other at sizes around 70 nm (labelled as Family 3). The porosity values (P, %) are also indicated between parentheses. Some small differences appear for the highest fibre contents. Thus, an increase in the porosity was obtained, in agreement with other studies [10,36],

more remarkable for the 1 wt% sample. Moreover, the existence of an additional pores family, above the 100 nm size range (labelled as Family 1), is displayed. For the other samples, most of the pores lie below 100 nm. This increase in the size of the capillary pores could have some influence on the permeability of the solid [37,38] and, consequently, on the ionic conductivity of the sample. The increase in the porosity could be an indication of the inappropriate fibres dispersion, as already stated by other authors [11,39]. The numerical analysis of these data is given in Table 2. The contribution of each single family to the total porosity along with the central value of each pore family were determined by the fitting to Gaussian functions [17]. No differences are revealed when adding 0.2 wt% into the mixture. However, an additional fibre incorporation leads to the development of larger pores. The MIP test also provides density values. The bulk density, BD, defined as the mass divided by the total volume (volume of the solid plus that of the open and close pores) and the apparent density, AD, defined as the mass divided by the volume corresponding to the solid plus that of the close (non-accessible) pores volume, can be obtained. These density values are compared in Table 3. Although no big changes can be detected among the several samples, it is worth to mention the larger difference (established from the AD/BD ratio) observed between the bulk and the apparent density values for the sample with 1 wt% carbon fibres. Taking into account the definition of each density, that discrepancy seems to be linked to the existence of a larger number of open pores. Thus, among the pores developed in the sample prepared with 1 wt% of carbon fibres, a higher number of them, in comparison to the other mixtures, are pores connected to the surface (percolating porosity). The porosity analysis was also performed for the specimens containing dispersant T2 and with the functionalized fibres (FF method), as presented in Fig. 2a. Table 2 includes also the numerical data obtained from the Gaussian fits. Both procedures assist to the development of smaller pores, in comparison with the 0.2 wt% sample prepared with the as-received fibres. These results show that the incorporation of this type of fibres along with a dispersing agent (either the surfactant or the pre-treatment of the fibres) produces a finer and more compact microstructure.

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Table 2 Numerical analysis of the MIP results shown in Fig. 1. The central pore diameter and the single porosity of each family are summarized. Center (nm)

Blank 0.2 wt% 0.6 wt% 1 wt% 0.2 wt%-T2 0.2 wt%-FF

Porosity (%)

Fam. 1

Fam. 2

Fam. 3

Fam. 1

Fam. 2

Fam. 3

— — — 149.9 — —

104.1 107.9 113.4 116.9 41.3 56.3

77.1 74.6 79.7 69.1 <5 17.8

— — — 2 — —

11.39 11.35 13.47 13.99 10.89 12.01

9.21 9.25 8.83 9.71 2.41 6.59

Table 3 Bulk and apparent density values obtained from the MIP analysis. The influence of the dispersion methods using Tween-20 (T2) and functionalized fibres (FF) is also reported. -1

Log diff intrusion vol. (mL.g )

0.25

Blank 0.2 wt% 0.6 wt% 1 wt% 0.2 wt%-T2 0.2 wt%-FF

Bulk density, BD (g/mL) m/(Vs + Vcp + Vop)

Apparent density, AD (g/mL) m/(Vs + Vcp)

Ratio AD/BD

1.81 1.76 1.81 1.71 1.89 1.78

2.28 2.21 2.33 2.30 2.18 2.18

1.26 1.26 1.29 1.35 1.15 1.22

Note: m is the mass of the sample, Vs is the volume of the solid, Vop is the volume of the pores open to the surface and Vcp is the volume of the close pores, not connected to the surface, occluded porosity).

a

0.2 wt.% (P=20.6%) 0.2 wt.%-T2 (P=13.3%) 0.2 wt.%-FF (P=18.6%)

0.20 0.15 0.10 0.05 0.00 0.01

The porosity reduction is more marked for the sample prepared with the dispersant, being the lowest pores family diameter below the device detection limit. The impact of this type of surfactants in the cement microstructure has been already checked [14]. The polar groups in the surfactant are able to interact with some of the water molecules from the cement/water mixture. Thus, a lower water amount would be available for the cement hydration, giving the obtained reduced porosity. A comparable effect is obtained with the functionalized fibres. The functionalization promotes the development of carboxylic groups, with a hydrophilic nature, at the surface of the acidtreated fibres [31,33,34]. The water reducing effect has been already evidenced by Musso et al. [40]. Additionally, the use of the functionalized fibres helps to an improved interaction between the fibre and the cementitious matrix [31]. This effect agrees with the reduction in the size of the pores detected by MIP. The reduction in the porosity could be also an indication of the enhanced dispersion. The opposite effect (formation of air bubbles and holes) was pointed to be produced by a poor carbon fibre dispersion that caused the deterioration of the composite strength [39,41]. A filler effect produced by the expected improved dispersion of the fibres could explain the development of a denser microstructure [42]. This point concerning the dispersion was evidenced from the impedance analysis (see section 3.4). Additionally, for the samples prepared with the dispersant, the comparison of the density values (AD/BD ratio in Table 3) points to a lower amount of open porosity. This result reflects that most of the pores of this sample are occluded, thus a precise size quantification cannot be completed. Besides, once the samples were split to take the fragments for the PIM analysis, a number of macropores could be seen by the naked eye, as shown in Fig. 2b. These voids are out of the measurable range of the MIP technique. The dispersant produces the formation of large air voids at the specimen preparation stage, producing a less compact composite [43]. This type of structures will offer poorer mechanical performance, in agreement to the results discussed in other publications in presence of these type of dispersants [14]. No such large voids were discernible in any of the other tested specimens. For the specimens

0.1

1

10

100

Pore size diameter (nm)

b

Fig. 2. (a) MIP results for the samples without dispersant, with dispersant (T2: Tween-20) and with functionalized fibres (FF), and (b) Macroscopic optical image of the mixture including dispersant Tween-20 (T2).

prepared with the functionalized fibres, the AD/BD ratio increases and then the percentage of open porosity is more relevant than for the T2-mixture. 3.2. Microstructural analysis by impedance Spectroscopy: Influence of the fibres content Fig. 3a shows the higher frequency Nyquist plot obtained for the soaked sample prepared with 0.2 wt% of carbon fibres, after subtracting the impedance corresponding to the polyethylene sheets. For this type of capacitive response, the analysis through the Cole-Cole representation is more convenient, as shown in Fig. 3b. The data have been normalised according to the sample thickness and cross-section. The equivalent model inserted in Fig. 3b, already validated for unreinforced conventional cement paste specimens [16], was used for the fitting. C1 allows the estimation of the dielec-

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

a

12

9

6

40

R2

1.6

C2

30

1.2

20

0.8

10

C1

R 2(k Ω.cm)

Capacitance (pF.cm-1)

300 kHz

- Z" (kΩ.cm)

2.0

50

15

0.4

1 MHz

3

0 0.0

2 MHz

0.2

0.4

0.6

0.8

0.0 1.0

Fibre content (wt.%)

0 0

3

6

9

12

15

Fig. 4. Best fitting parameters corresponding to the soaked specimens using the equivalent model inserted in Fig. 3b.

Z' (kΩ.cm)

50

b C1

-1

- C" (pF.cm )

40

30

C2

R2

20 10 MHz 10

1 MHz

0 0

10

20

30

40

50

-1

C' (pF.cm ) Fig. 3. (a) Normalised Impedance plot obtained for the soaked sample with 0.2 wt% carbon fibres, and (b) Cole-Cole plot (squared-symbol plot) of the same sample presented in (a). The ionic contact between the sample and the measuring electrodes was avoided by using rigid polyethylene sheets. The fitted data (Xsymbol plot) are included in the Cole-Cole diagram to show the good match with the experimental data.

tric capacitance, assigned to the solid phase, and C2 and R2 have been assigned to the response of the ions in the electrolyte filling the non-percolating pores. A quite good correspondence between the experimental and the fitted results is graphically shown in Fig. 3b. The numerical results obtained from the fitting are presented in Fig. 4, for all the tested compositions. The parameters obtained for the soaked blank specimen are in the expected range [16,17]. The dielectric constant (e) obtained from the C1 parameter (Fig. 4) is 48.9, assuming a flat parallel capacitor, as described in Eq. (1).

C¼

ee0 S d

ð1Þ

where e0 represents the vacuum permittivity (8.85  10-14 F cm1), S is the cross-section (cm2) and d is the sample’s thickness (cm). The e value is higher than that expected for a cementitious material, in the range 10–15, according to previous studies [15–17], but corresponds well to a soaked cement paste specimen [44]. However,

unexpected variations were recorded as a function of the carbon fibre amount. As shown in Fig. 4, the dielectric capacitance increases up to the 0.4 wt% fibre content, with a less marked increase above that fibre amount. No changes would be expected in the hydration products formed in the presence of this type of fibres [31,36]. Therefore, variations in the dielectric capacitance produced by a hypothetical cement-fibre chemical interaction could be discarded. The above-discussed enlargement in the pores size as the fibre amount increases (Table 2) is not related to this increase in the capacitance. Actually, an increase in the porosity, and thus a smaller fraction of solid, should translate into smaller C1 values. Additionally, the sample containing 0.2 wt% did not reveal changes in the pore structure, whereas a significant increase in the capacitance was verified for this specimen in comparison to the blank sample. Then, the C1 changes are apparently linked to an effect of the own fibres rather than to mere modifications in the overall porosity. An analogous influence of the carbon fibres in the solid phase dielectric properties had been already detected in presence of a certain amount of carbon fibres [45]. The most likely explanation is the assumption of another capacitance parallel to the dielectric solid phase, not included in the current equivalent model inserted in Fig. 3b, so that the whole measured capacitance, C1, results abnormally high. It can be hypothesised that the incorporation of the conductive fibres into the humidified matrix develops a double layer whose high specific capacitance adds to that of the cement paste. As the amount of fibres increases, a proportional capacitance rise (due to the contribution of that double layer) would be expected according to the increase in the active surface. A nonlinear increase was obtained instead. This observation suggests an inappropriate fibres dispersion and the formation of heterogeneously distributed groups of fibres. The less marked increase in C1 above 0.4 wt% could be also influenced by the modifications in the pore network for those samples with the highest fibre amounts (section 3.1). For these mixtures, the two mentioned factors, porosity rise and fibre interfacial capacitance, although with opposed consequences, need to be taken into account to understand the observed deviations. Firstly, the response at the fibres/electrolyte interface will produce the rise in the capacitance, but above a certain fibre amount, the increased porosity will compete with that variation, leading to the observed minor changes. The parameters of the second time constant (R2C2) are presented in Fig. 4. They have been correlated with the arrangement and motion of ions in the electrolyte filling the pores, under the

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

influence of the electric field. Previous publications point to the use of these parameters as a good approximation to the pores size [35,46]. Thus, the average pore size (d, in cm) can be calculated, using Eq. (2),

d¼

pffiffiffiffiffiffiffiffiffi s2 D

ð2Þ

where s2 (in s) accounts for the value of the second time constant (s2 ¼ R2 C 2 ) and D refers to the ionic diffusivity (105 cm2 s1). For the blank specimen an average pore size around 10 nm was obtained, that is slightly underestimated in comparison to the results provided by MIP but corresponds well to the smallest capillary cavities [38]. For the reinforced specimens, taking into account the changes in R2 (that decreases in comparison to the blank) and C2 (that remains in the same order of magnitude as the blank), then the pore size calculation according to Eq. (2) would result in a reduced pore diameter. Thus, for the 1 wt% sample the pore diameter would drop to around 3 nm. This is completely in contradiction with the results of the MIP study, where an evident increase in the average pores size had been revealed for the samples with the larger fibres amount (see Table 2). Therefore, some other effect, as well as the ionic activity inside the occluded pores, is influencing this second time constant in the carbon fibre reinforced samples. This inaccuracy suggests that the model commonly used for the simulation of plain cement paste is not valid for the case of the carbon fibre reinforced matrices. The following sections will show a model proposal for these type of specimens. The observed resistance decrease follows just a variation opposite to C1 capacitance, and the evident effect of the fibres must be again recognized. Besides, the variations are more important (one order of magnitude) for the parameter R2 (Fig. 4), whereas less remarkable changes (barely a factor of two) are measured in the capacitance C2 (Fig. 4). This non-symmetrical variation leads to changes in the time constant, s2, that moves from 3 MHz, characteristic frequency for the blank specimen, to 20 MHz, for the sample with the highest fibre content. The only influence of the nonpercolating pores in the R2 and C2 values, in the presence of carbon fibres, must be discarded, since in this situation the characteristic frequencies should move in the opposite direction to validate the MIP measurements. Then, an additional phenomenon is playing a role in the values assigned to the current model parameters. The polarization at the fibres/electrolyte interfase could be responsible for the modifications recorded in this second time constant. The fibres, occupying a fraction of the occluded pore’s volume, will represent active sites for redox reactions of species present in the electrolyte. The associated charge transfer resistance will represent an additional parallel contribution to the resistance included in the original model (R2 inserted in Fig. 3b). Then, the whole resistance will decrease. The higher the fibre content, the higher the available active area. Thus, more marked reduction in the whole resistance. This phenomenon of polarization has been already identified in the high-frequency domain in the presence of conductive fibres, in previous studies by other authors [23]. Additionally, the detected increase in the porosity could contribute to the variations recorded in R2, in particular above 0.4 wt% of fibres. Therefore, the obtained R2 value, according to the model in Fig. 3b, is under the influence of the fibres polarization. It is not a suitable parameter for the pore size determination in conductive fibres reinforced cement specimens. A detailed analysis of the variation observed in the R2 values allows making some suggestions about the fibres distribution in the composite mixture. The number of fibres incorporated into each mixture and their total external surface can be estimated, on the basis of the fibres dimensions and density presented in Table 1. Thus, in the 0.2 wt% specimen, one gets 3x105 fibres with

the total area about 700 cm2. In case this enormous surface becomes effective for that interfacial polarization, affecting to the R2 parameter, the total resistance should decrease to a value, at least, two orders of magnitude lower than that obtained for the blank specimen. However, the reduction presented in Fig. 4 is less important. The explanation to that incoherence agrees with the proposed hypothesis of a heterogeneous distribution of the fibres and the formation of bundles, even when adding the amount of 0.2 wt%. Thus, the increase in the fibre amount does not mean, for this study, a proportional increase in the fibre surface area. The subsequent nonlinear decay observed as increasing the fibre content shows that just some of them contribute to that interfacial effect. Most of the added fibres will incorporate into bundles without important contribution to that interfacial polarization. Above a certain level, 0.4 wt%, the decrease is hardly relevant, pointing to the poor ability of the as-prepared cement paste samples to accept such an amount of fibres. It is important to mention that all the samples were prepared with the same water amount, independently on the fibre content, and the possible drying effect in the cement matrix by the fibres incorporation could produce some increase in the capacitance C1. However, according to the discussion concerning the variation in the R2, their effect, if any, is negligible. Thus, this drying effect should oppose to the reduction in the resistance. The hypothetical drying effect would diminish the number of pores, and then the R2 value should increase along with the corresponding capacitance C2 decrease. Concerning the C2 values, no noticeable differences are identified. The interfacial polarization could have some effect on this capacitance, but the expected increase is not noticeable. This capacitance has been traditionally a difficult parameter, with an arduous interpretation by itself [16,35]. In this study, besides, their values remain in the same order than the C1 values, which impedes a precise distinction between them in the testing conditions. Some percentage of the increase observed in the C1 values is likely associated with the non-quantifiable increment expected for the capacitance C2 in relation to the fibres polarization. 3.3. Impedance spectroscopy measurements: The influence of drying With the purpose of validating the previous discussion concerning the influence of the fibres in the matrix microstructure, the cement paste specimens were dried out over a period of 8 days and their impedance was periodically recorded. The Cole-Cole transformations obtained for the 0.4 wt% specimen are compared in Fig. 5. An evident feature after the graphical analysis refers to the significant decrease in the characteristic frequency as the drying progresses. The equivalent model previously introduced in Fig. 3b has been again used for the analysis. Fig. 6 shows the fitting values obtained for all the tested compositions along the drying period. On one hand, the drying produces a reduction in the capacitance of the dielectric matrix, C1 (Fig. 6a), but the values in the carbon fibrecement composites remain still higher. The influence of the fibres, with its associated interfacial capacitance, must be still taken into account as responsible for the capacitance increase. The apparent dielectric constant for the blank specimen, following Eq. (1), downs to 21, at the eighth day of drying, a value lower than that obtained in the soaked condition. The free water inside the pores has been removed, at least partially, and then its dielectric contribution is not incorporated to that parameter anymore. Analogous variations in the C1 values among the several compositions with the drying time are observed. After the fourth day, less marked changes are detected. This observation means that an excessive humidity inside the porous sample impedes the correct determination of the dielectric characteristic of the solid [44,46].

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

40

a

10

-1

C1 (pF.cm )

8

-1

- C" (pF.cm )

30

blank 0.2 wt.% 0.4 wt.% 0.6 wt.% 0.8 wt.% 1 wt.%

20

6

4

10

10 MHz 1 MHz

2 0

0 0

10

20

30

1

2

4

5

6

7

8

9

7

8

9

7

8

9

Drying period (days)

40

-1

35

C' (pF.cm ) Fig. 5. Cole-Cole plots for the sample with 0.4 wt% carbon fibres after 1 and 8 days of drying. The ionic contact between the sample and the measuring electrodes was avoided by using rigid polyethene sheets. The fitted data (X-symbol plots) are included in the Cole-Cole diagrams to show the good match with the experimental data.

b

30

blank 0.2 wt.% 0.4 wt.% 0.6 wt.% 0.8 wt.% 1 wt.%

R2 (kΩ.cm)

25 20 15 10 5 0 0

1

2

3

4

5

6

Drying period (days) blank 0.2 wt.% 0.4 wt.% 0.6 wt.% 0.8 wt.% 1 wt.%

c

45 40 35 -1

C2 (pF.cm )

Some percentage of water remains in the pores after the drying procedure scheduled. It should be completely eliminated to obtain the expected dielectric constant according to the cement paste components [17]. On the other hand, the removal of the electrolyte in the pores also reduces the fraction of pores available to be detected (filled with electrolyte). For the blank specimen, a clear tendency is observed in the R2 parameter (Fig. 6b) whereas no significant changes were identified in the C2 (Fig. 6c). Thus, the characteristic frequency shifts at the end of the drying procedure down to 200 kHz. Comparable changes can be observed for the reinforced specimens, the water removal changes also the characteristic frequencies to lower values, in comparison to the soaked condition. In particular, for 1 wt% sample, it is moved to 1.8 MHz, after eight days of drying, still higher than for the blank. Then, analogously to the discussion in the previous section, the presence of fibres affects the parameters assigned to the second time constant. The polarization phenomenon at the cement/fibres interfaces, although less significant because of the drying, must be taken into account and it is still responsible for the lower R2 values obtained for the reinforced composites, at any of the drying stages considered. Fig. 6b shows remarkable differences in the R2 over the drying period among the different fibre contents and no steady value was reached after one week, contrary to that observed for the C1 values. The rate of R2 increasing (slopes of the plots in Fig. 6b) with drying is smaller for the samples with the highest carbon contents. It is important to mention that the drying process was analogous for all the samples, and an equivalent weight loss was recorded at the several stages (8% after 1 week). One possible explanation to this fact lies in the fibres hydrophobic character that will fix less water molecules at the double layer than the pore’s walls, whose hydrophilic character will lead to higher number of water molecules immobilised. Thus, for the same water content, the fraction of free electrolyte (remaining in the specimen and providing lower resistance) will increase as the fraction of fibre’s surface increases. The variation in the capacitance C2 is again irrelevant, neither among the different compositions nor with the drying period. For the blank specimen, this situation points to a change in the number and size of the detectable pores, being less than in the saturated condition. For the fibre-reinforced samples, it points to that pore

3

30 25 20 15 10 0

1

2

3 4 5 6 Drying period (days)

Fig. 6. Best fitting values through the drying period at 40 °C: (a) parameter C1, (b) parameter R2 and (c) parameter C2.

walls remain hydrated during and at the end of the drying process, since water has been mainly removed from the fibres surrounding areas. 3.4. Proposal of an enhanced electrical equivalent model From the results described in the previous sections, the influence of the carbon fibres in the cement paste impedance response could be recognized. Although the traditional model (in Fig. 3b) has

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B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

allowed a qualitative description of the variations detected in terms of the fibres content, an attempt will be next presented to provide a more accurate quantitative analysis. An innovative approach, where the effective fibres response is independently described, is inserted in Fig. 7. The concept of the Electrically Floating Electrode (EFE) is applicable here [47]. A conductive element, the carbon fibre, which is electrically isolated to the external circuit and is embedded in an electrolyte (cementitious matrix), is polarized when a potential is applied between the two external measuring electrodes. The polarization response, at the fibre/electrolyte interface, is represented by a parallel double layer capacitance (C3) and charge transfer resistance (R3). The polarization of reinforcing conductive fibres has been analogously interpreted in previous studies by Mason et al. [22,23,48]. The new element was incorporated in the same branch as the response of the nonpercolating pores. This is consistent with the scheme where the matrix contains the two distributed elements: pores and fibres. The geometrical factor will be a key point for the discussion, since any change in the fibre active surface available for the electrochemical activity will be reflected in those new parameters. The other parameters have the same physical meaning as referred in section 3.2. The Nyquist plot for the saturated 0.2 wt% specimen along with the fitted results following this model is presented in Fig. 7. The good fitting confirms the validity of the proposed model. The numerical parameters obtained from the fitting are presented in Table 4. The evaluation of the samples with the greater fibre contents is summarized as well. No major differences are obtained in the high and low frequency limits, C1 and C2 respectively, in comparison to the results

50 C1

R3 R2

-1

- C" (pF.cm )

C2

C3

10 MHz 1 MHz

0 0

10

20

30

40

50

-1

C' (pF.cm ) Fig. 7. Impedance plot obtained for the soaked sample with 0.2 wt% carbon fibres with the fitted data (X-symbol plot).

obtained from the original model. The dielectric capacitances (C1) continue being above the expected value for a wet cement paste sample and then the incorporation of the fibres may still create an additional effect. The existence of an extra capacitance, generated by the separation of charges at the fibre/cement matrix interface, is compiled in the current C1 value [25,49]. This point still requires an additional analysis that is not covered in the present research. The characteristic frequency of the second time constant is analogous for all the samples. The determination of the averaged pore size according to Eq. (2) shows values in the same range, around 10 nm, than those measured by MIP (summarized in Table 2). Above the 0.6 wt% content, the reduction in the R2 parameter along with the increment in the C2 agrees with the increased porosity obtained by MIP (Fig. 1). These parameters compile the response of the non-percolating pores considering them as a number of holes placed in parallel. An increase in the number of these holes will result in a whole reduced resistance and increased capacitance, in agreement to the fitted data. The higher the fibre content, the higher the capacitance (C3) and the lower the resistance (R3). Less marked variations were obtained above 0.4 wt%. The increase in the fibre amount provides a larger fibre/electrolyte interfacial area where the polarization is developed. Thus, the predictable resistance reduction along with the capacitance increment is checked up to the 0.4 wt% level. A further increase in the fibre content does not result in these expected modifications. This is consistent with a deficiency in the dispersion of the fibres. For such a high content, and with the followed preparation procedure, the fibres remain mostly entangled. Dense packs of fibres are distributed into the matrix where many fibres are not directly exposed to the electrolyte and then its polarization response is not recorded. Therefore, the impedance technique is able to distinguish important points such as the fibre dispersion, after defining a proper equivalent model. The role of the dispersing methodologies (T2 and FF specimens) was validated with the new model. The fitted parameters are also indicated in Table 4. The above-discussed variations in the elements of the third time constant are again valid here. In both treatments, a reduced resistance and an increased capacitance were obtained (in comparison to the same fibre amount, 0.2 wt%). Thus, both the surfactant and the functionalization are suitable techniques to achieve a more uniform distribution of this type of carbon fibres. The less noticeable variation obtained for the sample prepared with the dispersant (T2) point to a less marked dispersing effect. Taking into account Eq. (2), both treatments assist to the development of smaller pores, in agreement to the information provided by MIP (Fig. 2a and Table 2). The change is more pronounced when using the functionalized fibres (FF specimen), with an average pore diameter around 2 nm. This agrees to the information given by MIP (in Fig. 2a and Table 2) where a larger amount of smaller pores had been detected for the sample prepared with the functionalized fibres.

Table 4 Comparison of the fitting parameters using the equivalent circuit inserted in Fig. 7.

0.2 wt% 0.4 wt% 0.6 wt% 0.8 wt% 1 wt% 0.2 wt%-T2 0.2 wt%-FF

C1 (pFcm1)

R2 (Ocm)

C2 (pFcm1)

R3 (kOcm)

C3 (nFcm1)

7.7 ± 0.1 9.2 ± 0.03 11.0 ± 0.07 12.1 ± 0.4 12.4 ± 0.3 5.9 ± 0.5 6.1 ± 0.2

1767.2 ± 99.8 1718.3 ± 172 1112.4 ± 164 941.5 ± 84.6 1024.6 ± 21.5 1867.4 ± 231 544.7 ± 3.8

28.6 28.5 44.1 29.8 51.6 18.6 12.7

38114.7 ± 1430 4660.9 ± 152 3290.3 ± 165 2086.7 ± 212 3264.1 ± 489 5710.3 ± 248 821.4 ± 90.2

0.16 ± 0.05 1.6 ± 0.4 2.1 ± 0.5 2.3 ± 0.05 2.3 ± 0.7 0.7 ± 0.05 4.9 ± 0.3

Note: T2: Tween-20, FF: functionalized fibres.

± ± ± ± ± ± ±

0.9 0.09 0.4 0.2 3.3 8.8 0.02

B. Díaz et al. / Construction and Building Materials 243 (2020) 118207

4. Conclusions This research was focused on the microstructural characterization of cement paste samples after the incorporation of short carbon fibres. The main remarks can be summarized as follows: - The incorporation of carbon fibres produces more porous cementitious matrices, where larger pores are developed. The use of dispersants, by the contrary, assist in the reduction in both the porosity and the pore diameter. - The model used for the analysis of plain cement pastes was firstly employed for the interpretation of the results obtained from the reinforced specimens. As an initial approach, the composite properties in terms of the carbon content and the humidity level could be evaluated from a qualitative point of view. The fitting parameters, originally correlated to the dielectric matrix and the non-percolating pores activity, revealed a significant influence of the fibres response. In spite of this effect, a poor fibre dispersion was concluded, even for the lowest fibre contents. - The own response of the conductive fibres as a single time constant in the equivalent model was proposed. An improved model with separated elements to describe the role of the fibres in terms of its polarization was presented. This new approach is able to validate both the influence of the amount of fibres incorporated to the mixture and the fibres dispersion ability. Thus, an increase in the fibre/electrolyte interfacial area can be identified as a reduction in the resistance along with an increase in the capacitance in the new time constant. The functionalization of the fibres prior the mixture was verified as a promising process to achieve an improved dispersion. - Impedance is a suitable technique to easily validate the role of the carbon fibres in cementitious matrices. The effect of the amount of fibre and the use of dispersant was checked in this study but the analysis could be extended to any relevant variable. CRediT authorship contribution statement B. Díaz: Conceptualization, Methodology, Formal analysis, Writing - original draft. B. Guitián: Investigation, Formal analysis, Methodology. X.R. Nóvoa: Formal analysis, Supervision, Conceptualization. C. Pérez: Methodology, Formal analysis, Conceptualization. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Authors are grateful to Comindex S.A. for supplying the fibres and, in particular, to Sandra Cunha for her technical support. References [1] D.D.L. Chung, Composite Materials. Science and applications, Second, Springer US, 2010. doi:10.1007/978-1-84882-831-5. [2] Deborah D.L. Chung Multifunctional Cement-Based Materials 1 CRC Press [3] D.D.L. Chung, Cement reinforced with short carbon fibers: A multifunctional material, Compos. Part B Eng. 31 (2000) 511–526, https://doi.org/10.1016/ S1359-8368(99)00071-2. [4] B. Chen, K. Wu, W. Yao, Conductivity of carbon fiber reinforced cement-based composites, Cem. Concr. Compos. 26 (2004) 291–297, https://doi.org/10.1016/ S0958-9465(02)00138-5.

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