Abstract:
Measurement of the impedance and complex resistivity of a sample is used for measuring parameters resulting from a change in physical or chemical state. A variable frequency signal is provided by a transformer primary coil. A secondary coil of the transformer with a closed loop and electrically coupled said sample is monitored along with a leakage current sensor. Sampling at multiple signal frequencies is performed at the multiple signal frequencies.

Description:
BACKGROUND 
     Field 
     The present disclosure relates to measuring non-contact impedance (complex resistivity) measurement adopting the transformer principle. In particular, the disclosure relates to impedance and complex resistivity measurements in concrete and other materials transformed to a solid phase from a liquid phase. 
     Background 
     A hardened hydraulic cement-based material, such as Portland cement, is produced by the hydration reaction which is a complex chemical, physical and mechanical process that starts as soon as water is mixed with cement particles and turns the water-cement mixes into a stone-like material. This complex process is referred as to the hydration of cementitious materials. The main characteristic of the hydration is the reduction of porosity accompanied by the formation of the hydration products. The continuously evolving network of pores determines the ultimate physical and mechanical properties of the cementitious materials, including strength, permeability and durability. Considerable attention has been focused on the pore structure characterization. Experimental methods to measure pore structure characteristics of such cements include water adsorption, mercury intrusion porosimetry (MIP), helium pycnometry, solvent replacement, nuclear magnetic resonance relaxation (NMR), scanning electronic microscope (SEM), transmission electronic microscope (TEM), X-ray diffraction (XRD), and small angle X-Ray scattering. Among the several techniques that allow investigating the evolution of the microstructure of cement-based materials, those based on monitoring the electrical properties during the cement hydration process have received attention. 
     SUMMARY 
     Impedance of a sample resulting from a change in a physical or chemical state is measured, using signals provided by a signal generator with a frequency synthesizer. A transformer has a primary coil connected to the signal generator, and at least one of the primary and secondary coils is electrically coupled the sample. Multiple signal frequencies are sampled by causing sensing of signals from the signal generator as transmitted through the secondary coil of the transformer at the multiple signal frequencies and sensing of the leakage current. 
     The sampling can be performed by using a sympathetic impedance circuit having at least one of a primary reactive circuit and a secondary reactive circuit electrically coupled to the sample, and sampling the voltage across the secondary reactive circuit and leakage current as a function of the frequency-variable signal at multiple signal frequencies provided to the sympathetic impedance circuit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of non-contact impedance (complex resistivity) measurement for a first example configuration. 
         FIG. 2  is a schematic diagram of non-contact impedance (complex resistivity) measurement for a second example configuration. 
         FIGS. 3A-E  are graphic depictions which demonstrate the complex resistivity of the Cement Paste Example 1. 
         FIG. 3A  shows the modulus of complex resistivity. 
         FIG. 3B  shows the real part of complex resistivity. 
         FIG. 3C  shows the imaginary part of complex resistivity. 
         FIG. 3D  shows the phase lag of complex resistivity. 
         FIG. 3E  is a diagram showing a modulus and differential modulus of complex resistivity. 
         FIGS. 4  A-C are graphic depictions which demonstrate the complex resistivity of the Cement Paste Example 2. 
         FIG. 4A  shows the real part of complex resistivity. 
         FIG. 4B  shows the imaginary part of complex resistivity. 
         FIG. 4C  shows the phase lag of complex resistivity. 
         FIG. 5  is a graphic depiction which demonstrates the modulus of complex resistivity in Cement Paste Example 3. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     Electrical methods have advantages over other methods in terms of sensitivity and fast processing. Electrical conduction through the hydrating cement-based system at the early cure age is almost entirely electrolytic. In addition, the electrical parameters, including the real part and imaginary part of impedance (complex resistivity), reflect the permeability, mobility, concentration and distribution of the charge carriers. Electrical measurements are sensitive to the complex factors affecting the microstructure of cement-based media, such as different water/cement ratios (w/c ratios), the different chemical compositions of cement and its hydration products and the use of particular minerals and other chemicals in the cement mixture. The phenomena that accompany the sol-gel transition, which occurs when water-cement mixes turn into an infinitely connected body, can also be evaluated using electrical methods. Useful information relative to microstructural changes, such as porosity and pore connectivity in hydrating cementitious materials, can also be determined from electrical methods. The impedance or complex resistivity of cement-based media is thus very informative and can be regarded as the fingerprints of cement hydration and its microstructure. Such studies lead to a more profound understanding of the evolution of the microstructure of the cement-based system. Electrical methods also have the advantages of being noninvasive and nondestructive and can be used to test the microstructure in situ. 
     Different electrical approaches exhibit different electro-chemical mechanisms. Previous research on the electrical properties of cement-based materials can be roughly divided into two areas. In the first area, two electrodes are used and connected to a cement-based specimen for direct impedance measurements. Since any direct application of current to a cement or concrete specimen cannot avoid a polarization effect, these methods cannot obtain accurate results for the electrical resistivity of cement and concrete, although these methods have the advantage of being able to utilize a very wide frequency range of electrical stimulus. 
     In the second area, the concept of non-contact resistivity is proposed. A non-contact measurement device utilizes the inductive components to replace the electrodes. Thus, the problem involved in contact between electrodes and fresh cement paste, such as electrochemical reactions and shrinkage gap problems, can be eliminated in the system. This system has high accuracy, good reproducibility, and is useful for the study of microstructure evolution during the hydration process. 
     In one configuration, the inductive components include a transformer and current sensor, which replace electrodes. Alternately, other impedance devices may be used, such as capacitive sensors. It is found that the resistivity or impedance development curves from this kind of apparatus are similar to the curves of heat evolution of cement. 
     Five hydration stages could be identified by characteristic points on the differential resistivity curves, which are: 
     dissolution stage; 
     competition stage; 
     acceleration stage; 
     deceleration stage; and 
     diffusion-controlled stage. 
     The hydration stages can be identified by characteristic points on differential resistivity curves. 
     The non-contact measurement can also determine the setting time of fresh concrete. Furthermore, the effect of type of cement, water/cement ratio (w/c ratio), curing time, chemical and mineral admixtures, and environmental change on hydration of cement-based materials have been investigated using this method. During investigation, it was found that there is a limitation in this system that a fixed frequency (1 kHz) alternating current (AC) is applied for measuring electrical resistivity of the specimen, which mainly reflects the porosity of specimen, and therefore cannot directly demonstrate the pore structure development in real time. 
     The disclosed techniques optimize non-contact measurements of concrete impedance resulting from applying a fixed frequency (1 kHz) alternating current (AC) to measure electrical resistivity of the specimen. The fixed frequency measurement mainly reflects the porosity of the specimen, and therefore cannot directly demonstrate the pore structure development in real time. To achieve an accurate measurement of resistivity for cement-based materials, the disclosed system (non-contact impedance measurement), which combines advantages of two areas mentioned above, applies different electrical parameters to impedance measurement. This system not only continues to implement the transformer principle but also changes the frequency domain of the electrical signal. 
     The disclosed techniques take advantage of an R-L-C (resistor-inductor-capacitor) model of the material under test. This is particularly useful in the case of hydrating cements, because the hydration process significantly affects the electrical conductivity of the material. 
     The non-contact impedance measurement also adopts the transformer principle. This system can apply different frequencies and different amplitudes of electrical stimulus onto materials and utilize an inductive component instead of metallic electrodes. In this system, the input sine wave signal is alternating voltage with amplitude modulation and can sweep the frequency range from about 1 kHz˜100 kHz. The sine wave is applied onto the transformer via a high power amplifier. The secondary coil in the transformer is the cement paste which is cast into the ring-mold. The voltage and current in the cement-based material are measured by a current sensor and voltage detector, respectively. The data is transmitted to an external personal computer. All the data (voltage; current; the phase lag between them; temperature in the internal mold) are saved in a personal computer and are employed to analyze the impedance and complex resistivity of cement-based materials in real time. There are also no electrodes in this set-up; hence the interface problems between the electrodes and matrix are similarly eliminated. Furthermore, the calibration showed that 1 mol KCl electrical resistivity using this set-up was 0.091904 Ω·m at 20° C. The standard electrical resistivity quoted in engineering handbooks for 1 mol KCl is 0.09797 Ω·m at 20° C. The relative errors of the modulus and phase lag of complex resistivity are 6.19% and 4.4°, which demonstrate that this apparatus has a high precision. 
     The real part, imaginary part and phase lag of impedance and complex resistivity can be measured and used to interpret the hydration progress, maturity, strength development and porosity in cement-based materials, such as hydraulic cement based materials. In addition, the system can also be used for the electrochemical and dielectric measurement of liquid phase materials (molten glass, molten metal, toxic solution and biological solution), which have a very strong corroding effect on metallic electrodes. The liquid phase materials may be a liquid phase of a hydrating material such as hydrating cement. Alternatively, the liquid phase materials may be molten glass, molten metal, toxic solution, biological solution or other cement-based materials. The impedance data is useful in analyzing the mechanism of chemical reaction in such systems. 
     In the described examples, a transformer is given as an example of a sympathetic impedance device, in which electrical energy applied to a primary reactive circuit evokes a response in a secondary reactive circuit. While a transformer is described by way of example, the techniques described herein can be applied to other types of sympathetic impedance devices using reactive circuits. Such sympathetic impedance devices can include capacitors or active circuits, provided that the sample can be coupled to a secondary reactive device and respond to an electrical signal applied to the secondary or sympathetic reactive device. 
     Configuration 
       FIG. 1  is a schematic of a non-contact impedance (complex resistivity) measurement apparatus having a first example configuration. Shown are transformer  111 , microcomputer  113 , signal generator  115  and sampling circuit  117 . Transformer  111  includes transformer core  123 , primary coil  125  and secondary coil  127 . Secondary coil  127  is mounted to or cast inside specimen ring  131 , with specimen ring  131  provided as a sample. Leakage current sensor  137  surrounds a portion of secondary coil  127 , but is physically separated from secondary coil  127 . 
     In this example configuration, a single arm transformer core  123  is provided, and primary coil  125  is wound round the core  123  of transformer. In this system, secondary coil  127  makes a part of specimen ring  131  by mounting secondary coil  127  to specimen ring  131  or casting secondary coil  127  in specimen ring  131 . Specimen ring  131  can be annular or rectangular according to which is easier to mold. Secondary coil  127  is constructed as a single coil surround on an upper surface of the specimen  131 , and is able to measure the toroidal voltage of specimen ring  131 . 
     Microcomputer  113  uses microcontrollers with integrated peripherals designed for real-time control applications. Microcomputer  113  has a math-optimized core to give designers the means to improve system efficiency, reliability, and flexibility. The amplitude and frequency of the signal can be altered by programming the microcomputer. The user can modify the parameters in the system to determine the required frequency domain, frequency step, frequency point, applied amplitude of the sine wave scanning timing per frequency and sampling interval, respectively. The impedance data of specimen  131  is sent to an external computer  143  by an appropriate data connection. 
     Signal generator  115  includes a Direct Digital Synthesizer (DDS) and a push-pull high power amplifier with amplitude compensation. 
     Transformer core  123  is constructed of manganese zinc ferrite with high amplitude permeability and low power loss. 
     Specimen  131  is cast in a mold, and combined with secondary coil  127 , functions as part of secondary coil  127  in a closed loop. The toroidal voltage of specimen  131  and the current that goes through the specimen  131  can be measured by sampling circuit  117  in the real time. 
     Leakage current sensor  137  is composed of permalloy which has wide frequency response domain, and is commercially available in wide frequency ranges, e.g., 1 kHz˜100 kHz. 
     Sampling circuit  117  contains an instrumentation amplifier, programmable band-pass filter and analog-to-digital conversion circuit affording high precision. 
       FIG. 2  is a schematic of a non-contact impedance (complex resistivity) measurement for a second example configuration, in which the transformer is of a double-arm type. Shown are transformer  211 , microcomputer  113 , signal generator  115 , and sampling circuit  117 . Transformer  211  includes transformer core  223 , primary coil  225  and secondary coil  227 . Secondary coil  227  is mounted to or cast inside specimen ring  231 , with specimen ring  231  provided as a sample. Leakage current sensor  237  surrounds a portion of secondary coil  227 , but is physically separated from secondary coil  227 . 
     In this example configuration, a double arm transformer core  223  is provided, and primary coil  225  is wound around a center pole  239  of transformer core  223 . In this system, secondary coil  227  makes a part of specimen ring  231  by mounting secondary coil  227  to specimen ring  231  or casting secondary coil  227  in specimen ring  231 . Specimen ring  231  can be annular or rectangular, according to which is easier to mold. Secondary coil  227  is constructed as a single coil surround on an upper surface of the specimen  231 , and is able to measure the toroidal voltage of specimen ring  231 . 
     The primary coil surrounds the middle of transformer core  223 , while specimen ring  231  and secondary coil  227  pass the windows of the double-arm transformer  211  by extending around center pole  239 . The working principle is similar with the configuration of  FIG. 1 , with microcomputer  113 , signal generator  115 , sampling circuit  117  and leakage current sensor  237 . 
     In use of the example configurations of  FIGS. 1 and 2 , an AC voltage is applied to the primary coil and then a toroidal voltage is induced in the specimen ring  131  or  231 . By measurement of this toroidal voltage and the induced current flowing in the specimen (specimen ring  131  or  231 ), the impedance and complex resistivity of the specimen can be calculated to analysis the microstructure development in the specimen as occurs at specimen ring  131  or  231 . 
     In order to get a comprehensive view of the disclosed working mechanism, the cement-based materials are taken as an example. Assuming that the selected frequency domain is 1 kHz˜30 kHz, the scanning timing per frequency is 8 seconds; the voltage amplitude applied onto the specimen ring  131  or  231  is 0.5V; the scanning frequency is 1 kHz, 3 kHz, 5 kHz, 10 kHz, 15 kHz and 30 kHz. The sampling interval is 1 minute for each test. The test procedure is as follows: 
     1. Prepare specimen ring  131  or  231 
         a. Weigh the raw materials;   b. Mix the raw materials for 2 minutes in planetary-type mixer at 45 revolutions per minute followed by 2 minutes at 90 revolutions per minute.       

     2. Measure impedance or complex resistivity of the specimen ring  131  or  231 .
         a. Cast the mixture into the ring-shaped mold right after mix. In the prototype configuration, the mold joints were sealed with vacuum grease to prevent water leakage. The slurry was vibrated to drive the air bubbles out until satisfactory compaction was achieved. Test specimen ring  131  or  231  was covered with the attached lid and sealed with adhesive tape to prevent evaporation of water in the hydrating system during the whole testing. Since the resistivity measurements are conducted at the early hydration stage (normally within 1 day), the cement specimen  131  or  231  could be assumed to be saturated; that is, all the pores are filled by the conductive pore solution.   b. Start the impedance measurement immediately right after the casting, usually about 15 minutes after the mixing. In the program of microcomputer  113 , the parameter of the system can be altered in accordance with the experimental conditions. In the prototype configuration, these parameters are set as follows: The applied amplitude of the sine wave is 0.5V. Sweep frequencies are 1 kHz, 3 kHz, 5 kHz, 10 kHz, 15 kHz and 30 kHz, respectively. The interval at every frequency is about 8 seconds. Thus, the total time is 48 seconds, and then the apparatus has a 1 minute sampling interval. When the system starts up, microcomputer  113  is the core of the system, and sends particular commands to signal generator  115 . The designed sine wave with specific amplitude and frequency is generated from signal generator  115 , and then applied to the transformer  123  or  223  via a high power amplifier which is part of signal generator  115 . As a consequence a toroidal voltage is induced from the cement-based specimen ring  131  or  231  and this voltage is measured by secondary coil  127  or  227  surrounded on an upper surface of the specimen ring  131  or  231 . Leak current sensor  137  or  237  is provided surrounding a section of the specimen ring  131  or  231  to measure the current flowing in secondary coil  127  or  227  and specimen ring  131  or  231 . Hence, both voltage and current in the specimen ring  131  or  231  are measured by sampling circuit  117 . Finally, the impedance data of the specimen ring  131  or  231  is sent back to the microcomputer  113  again and revealed on external computer  143 . The operation is continuous.   c. Keep a relative stable temperature and humidity during the test environment.   d. Stop the test at any time as needed, and calibrate the resistivity by measuring the height of the specimen ring  131  or  231 .   e. Process impedance data with smoothing for further analysis.       

     3. Analyze data
         a. Obtain the real, imaginary and phase lag of complex resistivity or impedance curves to identify hydration stages;   b. Interpret the hydration process and microstructure development.       

     In the three examples below, Portland cement meeting the requirement of ASTM Type I was used for all specimens. All specimens were tested at room temperature (25° C.). 
     Cement Paste Example 1 
       FIGS. 3A-D  are graphic depictions which demonstrate the complex resistivity of the cement paste Example 1. In Example 1, water/cement (w/c) ratio is 0.4 and applied voltage is 0.6V. The modulus, real part, imaginary part, phase lag of complex resistivity are shown, in which: 
       FIG. 3A  shows the modulus of complex resistivity. The plots for 3, 5 and 10 kHz appear near the top and approximately coincide. The plot for 15 kHz is slightly below the plots for 3, 5 and 10 kHz. The plot for 30 kHz is below the other plots. 
       FIG. 3B  shows the real part of complex resistivity. The plots are, in order from top to bottom, 3, 5, 10, 15 and 30 kHz. 
       FIG. 3C  shows the imaginary part of complex resistivity. In the center of the chart, the plots are, in order from bottom to top p, 3, 5, 10, 15 and 30 kHz. On the right, the plot for 30 kHz can be seen dipping below the plots for 15 and 10 kHz. 
       FIG. 3D  shows the phase lag of complex resistivity. The plots are, in order from bottom to top, 3, 5, 10, 15 and 30 kHz. 
     The paste with water/cement (w/c) ratio 0.4 is evaluated, and the applied voltage onto the paste is 0.6V. The test procedure is as follows:
         Prepare specimen by weighing the raw materials and mixing the raw materials for 2 minutes in a vertical-axis pan mixer at low rotational speed and for a further 2 minutes at high speed.   Measure the complex resistivity of the specimen.       

     The measurement is performed with the mixture cast into a ring-shaped mold immediately after mixing. The resistivity measurement started right after casting and the data were automatically recorded by a computer. Sweep frequencies are 3 kHz, 5 kHz, 10 kHz, 15 kHz and 30 kHz, respectively. The interval at every frequency is about 8 seconds. Thus, the total time is 40 seconds, and the apparatus automatically recorded with 1 minute sampling interval. The operation was continuous. Data in one day from casting were processed with smoothing. 
     The modulus and phase lag of complex resistivity in the testing specimen can be obtained from raw data sets.
 
ρ c   / =|ρ c |×cos θ
 
and
 
ρ c   // =|ρ c |×sin θ
         where |ρ c | is the modulus of the complex resistivity;   ρ c   /  is real part of the complex resistivity and ρ c   //  is the imaginary part of the complex resistivity; and   θ is the phase lag between the real part and imaginary part.       

     These parameters are employed to analyze the hydration process in real time. The real part and imaginary part of complex resistivity, phase lag between the real part and imaginary part for different frequencies are demonstrated in  FIGS. 3B, 3C and 3D . 
     The real part of complex resistivity is referred to as the resistive property of liquid and solid phase in cement-based materials. It can be seen from  FIG. 3B  that curves from different frequencies are almost identical before 300 minutes, and then show an obvious difference afterwards. This is due to the different peculation characters of the solid hydration product under different frequencies. Hence, the separation point can be used to identify the hydration stage. 
     The imaginary part of the complex resistivity, shown in  FIG. 3C , is determined mainly by the electrical double layer of pore and pore connectivity. At the beginning, the solution is connected in all the portions of the specimen and the values of imaginary part are almost equal to zero. Therefore, not much difference in imaginary response for different frequencies appears in  FIG. 3C . With the hydration product development, more solid contents appear and a microstructure with porosity forms. At that time, the imaginary response increases and shows the different values for different frequencies. All of the imaginary part of the complex resistivity is positive due to the inductive behavior of tortuous pores. 
       FIG. 3D  is the phase lag of complex resistivity development. Here, it is assumed that the phase of the applied voltage is always zero. The entire phase lag is positive, which coincides with  FIG. 3C . It is noted that the higher frequency curve reflects a larger value, which corresponds to electromagnetic wave penetration performance in the real part of the complex resistivity. 
       FIG. 3E  is a diagram showing a modulus and differential modulus of complex resistivity. The modulus of complex resistivity is given in Ω·m, on the scale on the left. The differential modulus of complex resistivity is given in (Ω·m)/min, on the scale on the right. 
     From  FIG. 3E  above, five stages of the hydration can be identified from the characteristic points of complex resistivity and its differential curve: the dissolution stage (I), (0˜0.5 h) from the beginning to the minimum modulus point; the competition stage (II), (0.5˜3 h) from minimum modulus point to the end of flat zero stage of differential of modulus; the setting stage (III), (3˜6.5 h) from the end of flat zero stage to the first peak of differential of modulus curves; the hardening stage (IV), (6.5-10 h) from the first peak to the second peak of differential of modulus curves; and the hardening deceleration stage (V), (&gt;10 h) after the second peak of differential of modulus curves. 
     The first four stages (I-IV) are the first four stages at the beginning of hydration in cement-based materials. 
     The dissolution stage (I) occurs from the mixing time to the minimum point time. In this stage, the rate of the modulus curves is less than zero and the dissolution of cement particles is dominant. Ions are rapidly released from the surface of cement grains and dissolved into the solution. At this stage, hydration reactions start to take place. The electrical resistivity decreases due to the increase of ionic concentrations and the mobility of these ions. 
     The competition stage (II) occurs from the minimum point time to the end of flat zero stage. The rate of the modulus curves is very close to zero, which demonstrates the competition of consuming and releasing ions results in a dynamic balance. In this stage, the ions in the solution are gradually absorbed by the formation of hydrated products. Such initial hydration reactions consume a few ions, which reduces ion concentration. Meanwhile, additional ions continue to release from the surface of unhydrated cement grains and are allowed to dissolve in the mixture. 
     The setting stage (III) occurs from the end of flat zero stage to the first peak point of the differential curve. The rate of the modulus curves increases sharply. In this stage, the rapid increase of resistivity is related to a significant decrease in the number of ionic species due to the rapid formation of gel product, ettringite and calcium hydroxide, leading to hardening. This stage always coincides with strong heat generation (exothermic reaction) associated with the hydration process. 
     The hardening stage (IV) occurs from the first peak point time to the second peak of differential of modulus curves. The resistivity development of specimen becomes ion diffusion controlled and presents larger values, because the hydrates have formed an envelope which blocks the way of solution exposure to the unhydrated cement particles. Finally, ion diffusion through the calcium silicate hydrate (C—S—H) layers determines the rate of chemical reaction in the mixture. (C—S—H refers to a cement paste composed of CaO, SiO 2  and H 2 O, but may also include Fe 2 O 3 , Al 2 O 3  and SO 3  and other materials.) 
     Subsequent to hardening stage IV, the hardening deceleration stage (V) occurs. 
     Cement Paste Example 2 
       FIGS. 4  A-C are graphic depictions which demonstrate the complex resistivity of the cement paste Example 2. The water/cement (w/c) ratio is 0.4 and applied voltage is 0.8V. The real part, imaginary part and phase lag of complex resistivity are shown in  FIG. 4 . 
       FIG. 4A  shows the real part of complex resistivity. The plots are, in order from top to bottom, 3, 5, 10, 15 and 30 kHz. 
       FIG. 4B  shows the imaginary part of complex resistivity. In the center of the chart, the plots are, in order from bottom to top, 3, 5, 10, 15 and 30 kHz. On the right, the plot for 30 kHz can be seen dipping below the plots for 15 and 10 kHz. 
       FIG. 4C  shows the phase lag of complex resistivity. The plots are, in order from bottom to top, 3, 5, 10, 15 and 30 kHz. 
     The paste with water/cement (w/c) ratio 0.4 is evaluated, and the applied voltage onto the paste is 0.8V. The test procedure is as follows:
         Prepare specimen by weighing the raw materials and mixing the raw materials for 2 minutes in a vertical-axis pan mixer at low rotational speed and for a further 2 minutes at high speed.   Measure the complex resistivity of the specimen.       

     The measurement of complex resistivity is performed by casting the mixture into the ring-shaped mold right after mixing. The resistivity measurement started right after casting and the data were automatically recorded by a computer. Sweep frequencies are 3 kHz, 5 kHz, 10 kHz, 15 kHz and 30 kHz, respectively. The interval at every frequency is about 8 seconds. Thus, the total time is 40 seconds, and the apparatus automatically records with 1 minute sampling interval. The operation was continuous. Data in one day from casting were processed with smoothing. 
     Cement Paste Example 3 
       FIG. 5  is a graphic depiction which demonstrates the modulus of complex resistivity in Cement Paste Example 3. The water/cement (w/c) ratio is 0.3 and applied voltage is 0.8V. In the center of the chart, the plots are, in order from bottom to top, 5, 3, 10, 15 and 30 kHz, which places the plot for 3 kHz below that of the plot for 5 kHz. On the right, the plot for 3 kHz can be seen dipping below the plots for 5 and 10 kHz, but is still above the plots for 15 and 30 kHz. 
     The paste with w/c ratio of 0.3 is evaluated according to the test procedure is as follows:
         Prepare specimen by weighing the raw materials and mixing the raw materials for 2 minutes in a vertical-axis pan mixer at low rotational speed and for a further 2 minutes at high speed.   Measure the complex resistivity of the specimen.       

     As with the above examples, the measurement of complex resistivity is performed by casting the mixture into the ring-shaped mold right after mixing. The resistivity measurement started right after casting and the data were automatically recorded by a computer. As indicated, sweep frequencies are 3 kHz, 5 kHz, 10 kHz, 15 kHz and 30 kHz, respectively. The interval at every frequency is about 8 seconds. Thus, the total time is 40 seconds, and so the apparatus automatically recorded with a 1 minute sampling interval. The operation is continuous. Data in one day from casting were processed with smoothing. 
     In the examples of  FIGS. 3-5 , it can be seen that modulus of complex resistivity curves first decrease and then increase after the lowest point is reached. This period corresponds to the dissolving (initial hydrolysis) period in a hydration process. While the real part of complex resistivity is referred to as the resistive property of liquid and solid phase in cement-based materials, which reflects the penetration performance of electromagnetic wave in materials. In addition, the imaginary part of the complex resistivity is determined mainly by the pore heterogeneity and pore connectivity in materials. 
     CONCLUSION 
     It will be understood that many additional changes in the details, materials, steps and arrangement of parts, which have been herein described and illustrated to explain the nature of the subject matter, may be made by those skilled in the art within the principle and scope of the invention as expressed in the appended claims. For example, various configurations for transformers and other sympathetic impedance devices can be used, with the intent of obtaining a response as electrical energy is applied to one reactive circuit and sampled from a reactively coupled reactive circuit. Similarly, while the sample has been described as coupled to the secondary coil, it is possible to construct a testing device with the sample coupled to the primary coil.