A Review of the Electrical Conductivity Test Methods for Conductive Fabrics

Abstract

With the substantial growth of the smart textiles market, electrical properties are becoming a basic requirement for most of the advanced textiles used in the development of wearable solutions and other textile-based smart applications. Depending on the textile substrate, the test method to determine the electrical properties can be different. Unlike smart fibers and yarns, the characterization of the electrical properties of fabrics cannot be tested between two connection points because the result would not represent the behavior of the entire fabric, so the electrical properties must be related to an area. The parameters used to characterize the electrical properties of the fabrics include resistance, resistivity, and conductivity. Although all of them can be used to indicate electrical performance, there are significant differences between them and different methods available for their determination, whose suitability will depend on the function and the textile substrate. This paper revises the main parameters used to characterize the electrical properties of conductive fabrics and summarizes the most common methods used to test them. It also discusses the suitability of each method according to several intervening factors, such as the type of conductive fabric (intrinsically or extrinsically conductive), its conductivity range, other fabric parameters, or the final intended application. For intrinsically conductive woven fabrics, all the methods are suitable, but depending on the requirements of conductivity accuracy, the contact resistance from the measuring system should be determined. For intrinsically conductive knitted fabrics, two-point probe, Van der Pauw, and eddy current methods are the most suitable. And for intrinsically conductive nonwoven fabrics, two-point probe and four-point probe methods are the most appropriate. In the case of extrinsically conductive fabrics, the applied method should depend on the substrate and the properties of the conductive layer.

1. Introduction

Smart textiles are textiles that can sense and react to environmental changes. They can be divided into three categories [1,2,3]: (a) passive smart, which means they can only sense the stimuli; (b) active smart, which means they can sense and respond to the stimuli; and (c) very smart, which means they can self-adjust to adapt their response to the stimuli. The stimuli can be electrical, thermal, chemical, magnetic, or of other origin [4]. Conductive smart textiles (which include fibers, yarns, and fabrics that sense the electrical signals as stimuli) can be obtained by introducing conductive particles, fibers, or yarns into textiles, allowing the achievement of certain functions [5].

Regarding smart fabrics, conductivity is achieved by integrating conductive fibers or yarns into the structure of woven, knitted, or nonwoven fabrics or by depositing conductive layers by some physicochemical methods [6,7]. Depending on the methodology employed and the type and content of conductive materials used, different electrical conductivity values can be reached. By incorporating conductive materials, nonconductive fabrics can be modified to display even good conductivity values similar to those of semiconductors and conductors. Figure 1 summarizes the range of electrical conductivity values of fabrics made from different conductive materials and designed for different functions. Although for most applications (like heating, sensors, signal transportation, etc.), relatively high conductivity is required, for other functions (like antistatic), the conductivity requirements are less demanding.

As conductivity is a key property of these materials, choosing the right method to evaluate their electrical behavior is crucial. Nonetheless, the hierarchical structure of textiles, their flexibility, and the different ways to impart conductivity impede an accurate determination of their conductivity. In this sense, some studies have discussed the methods used to test the electrical properties of the fabric [23,24,25,26,27,28,29,30,31,32,33,34,35]. In these studies, the researchers discussed the advantages or limitations of one or a limited number of electrical characterization methods and some influencing factors, mainly for specific fabrics.

However, to the knowledge of the authors, there is still a lack of literature analyzing and summarizing all the testing methods aimed at all kinds of fabrics in a relatively comprehensive way. In order to fill this gap, this study aimed to provide a reference for testing the electrical conductivity of different fabrics. For this purpose, this paper revised basic concepts about the electrical conductivity of materials and then summarized and reviewed the methods currently available to test fabrics according to the International Standards Organization (ISO), the American Society of Testing and Materials (ASTM), the American Association of Textile Chemists and Colorists (AATCC), Semi’s Mission & Vision (SEMI), the European Standard (EN), the International Electrochemical Commission (IEC), and some variations of these methods found in some papers. Finally, based on different types of fabrics and their final function, a discussion about the factors that affect the conductivity and the applicability of various test methods is provided.

2. Electrical Properties of Fabrics

2.1. Key Concepts about Electrical Conductivity

The terms used to describe the electrical properties of fabrics include surface resistance (R_s in Ω), sheet resistance (R_sh in Ω/□ or Ω/sq), surface resistivity (ρ_s in Ω/sq), volume resistance (R_v in Ω), volume resistivity (ρ_v in Ω·m), and conductivity (σ in S/m). Therefore, these terms correspond to three concepts.

The first concept is resistance, which indicates the obstruction of current by a conductor and depends on the geometrical parameters of the specimen tested. It can be measured directly by a multimeter.

The second concept is resistivity, an intrinsic property that can be calculated via Equation (1),

$$\rho =R·k$$

(1)

where ρ is the resistivity, R is resistance, and k is a factor that depends on both the geometry of the specimen and the methodology used to perform the resistance measurements. In this case, resistivity depends on the textile material itself, but the physical strain and other environmental factors also affect it. On the one hand, physical strain (including stretching [36], compression [37,38], and bending [39,40]) affects the resistivity of fabrics, the latter decreasing with the increase in the former forces. However, fabrics with different structures are affected differently by these forces. From a macroscopic point of view, these forces change the arrangement of fibers or yarns, affecting the conductive network and, hence, changing the resistivity. Moreover, from a microscopic point of view, these forces can also change the atomic structure, affecting the resistivity. On the other hand, the environmental factors that affect the resistivity include humidity [41,42], temperature [43], and magnetic fields [44]. First, moisture can provide a conduction path in fabrics, thus reducing the resistivity. Concerning the effect of temperature, it depends mainly on the material; the resistivity of metallic materials increases, while the resistivity of semiconductor materials decreases with increasing temperature [45]. Finally, magnetic fields affect the movement of electrons through the material, resulting in a change in resistivity [46].

The third concept is conductivity, which can be calculated via Equation (2) and is the reciprocal of resistivity,

$$\sigma =\frac{1}{\rho }$$

(2)

where σ is conductivity and ρ is resistivity, as defined before.

2.2. Resistance and Resistivity in Conductive Textiles

For textile materials such as fabrics, it is important to distinguish between surface (2D) and volume (3D) resistance. Simply speaking, surface resistance (R_s) is the obstruction to the current that flows across the surface of the fabric (from one end to another), while volume resistance (R_v) is the obstruction to the current that passes through the fabric (from one side to another). Regarding R_s, the general system for its measurement is shown in Figure 2a.

From the R_s value, ρ_s can be calculated using Equation (3) [47],

$${\rho }_s=R_s\frac{W}{L}$$

(3)

where W and L are the width and the length of the specimen, respectively.

The surface resistivity (ρ_s) represents the surface electrical property of the material, and it should be noted that in some cases it cannot be measured accurately since some current can flow from the surface to the interior, it involves a part of ρ_v. Moreover, the value is affected by surface contamination, electrostatics, and even strain from interfacial tension [48]. Therefore, ensuring clean surfaces and discharging static electricity is necessary before testing the ρ_s.

In addition, for thin materials such as fabrics, when the size of linear electrodes equals the distance between them and the thickness and composition across the surface of the material is uniform, the measured area is a square. Then, ρ_s can be called sheet resistance (R_sh) [49], which is a special case of ρ_s [45] used to characterize thin or sheet materials. In this sense, R_sh is numerically equal to the ρ_s, but it is not a property of the material. Although independent of the material size (in area), it is affected by the material’s resistivity and the specimen’s thickness.

R_sh can be used to calculate volume resistivity (ρ_v) (Equation (4)),

$${\rho }_v=R_{sh}\frac{Wt}{L}=R_{sh}t$$

(4)

where W, L, and t are the width, length, and thickness of the tested specimen, respectively.

Volume resistance (R_v) is used to indicate the ability of an electric current to pass through the material. To measure R_v, the electrodes are placed on opposite sections of the specimen, and the current passes through the specimen from one section to the other, as can be seen in Figure 2b.

The volume resistivity (ρ_v) can be calculated from the R_sh by means of Equation (4) (as previously mentioned) or from R_v value by means of Equation (5) [49],

$${\rho }_v=R_v\frac{A}{L}=R_v\frac{Wt}{L}$$

(5)

where A corresponds to the area of the electrode, and W, L, and t are the width, length, and thickness of the tested specimen, respectively. It is worth mentioning that ρ_v corresponds to the general definition of resistivity, hence, very often, it is just mentioned as resistivity.

The measurement of R_s, R_sh, and R_v should be selected according to the final applications. R_s is important in situations where electrical interactions occur on a thin outer layer. For some functions such as strain sensors [50], electrochromic fabrics [51], electrodes [52], heating [53], electromagnetic interference (EMI) shielding [54], and antistatic function [55], and for fabrics that need to form conductive networks [56], R_s will decide the effectiveness, and its measurement helps improve the design.

For fabrics with a conductive coating layer, R_sh becomes more relevant [57,58,59] because electrical conductivity relies heavily on the thin conductive coating formed primarily on the surface. Here, as a special case of ρ_s, it is better to use R_sh to evaluate the functions. In applications including touch sensors [44], heating devices [45], and EMI shielding devices [60], the measurement of R_sh is very important to ensure the uniformity of the conductivity since it affects their function.

Furthermore, R_v is used to evaluate the overall electrical properties of a material. R_v needs to be measured when the desired properties are related to the electrical properties of the whole fabric. In fabrics intended for protection purposes [61], R_v indicates the ability of the fabric to resist electrical current passing through its thickness, whereas, for some fabric sensors (especially pressure sensors [62]), R_v affects the fabric’s response to stimuli.

3. Revision of Current Methods Used to Test Electrical Properties of Fabrics

Since the conductivity of textiles is similar to that of semiconductors [63], test methods to measure the electrical properties of textiles in the form of fabrics are based on the test methods of semiconductors. These methods can be divided into contact methods and noncontact methods. Generally speaking, the principle of contact methods is based on Ohm’s law, which measures the resistance through physical contact between the probes and the tested material under a certain current or voltage. On the contrary, noncontact methods are based on Faraday’s law, and there is no physical contact with the tested material since the resistance is inferred indirectly through electromagnetic induction. The main difference between the two systems is that the contact method may risk damaging the sample or probe during testing due to physical contact, whereas the noncontact method does not have such a risk as no contact with the sample is required. For textiles, the contact methods include a two-point probe, a four-point probe, and the Van der Pauw method. In the case of the noncontact method, only the eddy current method is available. These methods present advantages and disadvantages and can be more or less appropriate depending on the application, as detailed in the following sections.

3.1. Contact Methods

3.1.1. Two-Point Probe Method

The two-point probe method involves simple equipment and measuring procedures. Hence, it is the most convenient method to test the electrical properties of textiles. Figure 3 indicates the general system for testing the 3D material using the two-point probe method. When applying the voltage to the two probes, the current can flow through the specimen and be detected by an ammeter, and then the resistance can be calculated via Ohm’s law (Figure 3a) [64] or measured by the multimeter directly (Figure 3b).

However, the shape of textile materials (fabrics) is in sheet form, and testing only the resistance between two points does not represent the resistance of the entire fabric. It would be necessary to test it between the cross-section of a textile to characterize the resistance of the whole fabric [65]. Thus, the shape of the electrodes needs to be changed to match the test requirements. There are several standards that use the two-point probe method to test the resistance of fabrics, including AATCC-76 [65], AATCC EP13 [66], EN 1149-1 [67], EN 1149-2 [68], ASTM D257 [48], IEC 62899-201-2 [69], IEC 62631-3-1 [70], and IEC 62631-3-2 [71]. According to these standards, two types of electrodes are widely used for the measurements: parallel rectangular probe electrodes (Figure 4a) and concentric ring probe electrodes (Figure 4b).

In AATCC-76 [65], both the parallel rectangular and the concentric ring probe are used to test the R_s of the fabrics. In the first case (rectangular probe, Figure 4a), the tested specimen should be adjusted to fit the size of the probe, and the width of the specimen should not exceed the width of the probe. Both the length and the width direction have to be measured, and the average value can be used as the resistance of the fabric. Then, ρ_s can be calculated via Equation (3). For the second case (concentric ring probe, Figure 4b), the measurements in the length and width directions are carried out simultaneously. The size of the specimens should be at least as large as the outer ring to fit the probe. Then ρ_s can be calculated, in this case, by means of Equation (6),

$${\rho }_s=R_S\frac{2.73}{lg\frac{r_2}{r_1}}$$

(6)

where r₁ is the radius of the inner electrode, r₂ is the inner radius of the outer electrode, and R_s is surface resistance.

For both configurations, depending on the structure and the end use of the fabric, sometimes both the front and the back of the fabric need to be tested. The electrodes should contact the fabric firmly, and the results should not change with the pressure of the electrodes on the fabric. Moreover, the electrodes should be in contact with the fabric for at least 1 min to allow the current to pass from one electrode to another until the result becomes stable during the test. Then, when log R is less than 0.1 per min, it can be considered as constant. The time required for stabilizing resistance may vary for different samples and voltages. It should be noted that prolonged exposure to high voltage might damage the specimen.

AATCC EP13 [66] is a standard containing both two-point and four-point probe methods to test the resistance of the fabric. For the two-point probe part, the standard does not specify the exact type of electrodes to be used but gives some advice on how to perform the measurements. When magnetic electrodes are employed, the specimen is to be placed directly on the metal plate. In the case of using nonmagnetic electrodes, a constant weight has to be applied. Then, each sample is measured once, recording the resistance and the distance between the measured points until the value stabilizes. If the resistance of the specimen is lower than 1 Ω, in order to eliminate the contact resistance, the four-point probe method should be applied. However, if the resistance of the specimen is higher than 1 Ω, the contact resistance only has a small effect on the measurement results.

EN 1149-1 [67] and EN 1149-2 [68] are standards designed for electrostatic protecting clothes, but many studies use them to measure the R_s and R_v of the fabrics, respectively. In both standards, the electrodes used have concentric rings. The shape of the electrodes, with an overall diameter of 100 mm, is shown in Figure 4b (more detailed data can be found in the standard [67]). In the EN 1149-1 [67] standard, the tested specimen is supported by an insulation flat base plate. This base plate needs to be placed on an earthed conductive surface. The size of the base plate, which requires a specific thickness, should be larger than the size of the electrodes. The test circuit is shown in Figure 5a. A premeasurement taken under a specified voltage is required to set the suitable voltage to apply (see standard for detailed information [67]). The resistance is measured through an ohmmeter or an ammeter and calculated according to Ohm’s law. Then, ρ_s can be calculated via Equation (7),

$${\rho }_s=R_s\frac{2\pi }{In\frac{r_2}{r_1}}$$

(7)

where r₁ is the radius of the inner electrode, r₂ is the inner radius of the outer electrode, and R_s is surface resistance.

In EN 1149-2 [68], this standard provides more detailed information about the electrodes. The total weight of the electrodes is 1020 ± 20 g, including the 460 ± 10 g test electrode and the 560 ± 10 g annular electrode. The contact pressure applied by the whole electrode is 10 N, and the test and annular electrodes apply equal pressure (0.225 N·cm²). The procedure of premeasurement is the same as EN 1149-1 [67], but before it is performed, if ρ_s of the tested specimen is less than 10⁸ Ω, the annular electrode should not be grounded or a fault current may cause the voltage to drop. The circuit of the measured system is shown in Figure 5b. ρ_v can be calculated through Equation (5).

ASTM D257 [48] is a standard developed for insulating materials, but it is also suitable for testing R_s and R_v of fabrics. In this standard, depending on the tested materials, there are many kinds of electrodes and materials made into electrodes. As a flexible sheet material, the resistivity of fabric can be tested using two kinds of electrodes: strip electrodes and concentric ring electrodes.

Strip electrodes, which can be seen as a kind of rectangular electrode, are shown in Figure 6. Such electrodes are used to test the R_s and can generate more precise data for specimens with a width much higher than the thickness. The device mainly consists of three parts: strip electrodes, a plastic insulation layer, and a metal support. The metal support is covered by a plastic insulation module as a guard. The strip electrodes are on the top of the plastic insulation module. The strip electrodes are generally made of brass, copper, and stainless steel.

Concentric ring electrodes present a shape similar to other standards mentioned above but different in size. It can be used to test both R_s and R_v. As shown in Figure 5a, when testing the R_s, electrodes 1, 2, and 3 are guarded, unguarded, and guarded electrodes, respectively. However, when testing R_v, as shown in Figure 5b, 1 and 2 are guarded electrodes, and 3 is an unguarded electrode. The purpose of guarded electrodes is to eliminate the error caused by the surface effect. Depending on the tested specimens, two sizes (50 mm and 100 mm) are available for the testing device, although, in general, larger specimens should be used when possible. ρ_s and ρ_v can be calculated via Equations (8) and (5).

$${\rho }_s=R_s\frac{P}{g}$$

(8)

where P is the effective perimeter of the guarded electrode for the particular arrangement employed, and g is the distance between electrodes 1 and 2.

IEC 62899-201-2 [69] is a standard that defines the resistance test method of conductive layer printed on fabrics. More specifically, the standard derives from IEC 62631-3-1 [70] for volume resistance and from IEC 62631-3-2 [71] for surface resistance. Both IEC 62631-3-1 [70] and IEC 62631-3-2 [71] are standards used to test insulating materials. The electrodes used in IEC 62631-3-1 [70] are the same as Figure 5b, and in IEC 62631-3-2 [71], the same as Figure 5a is used, but they recommend different sizes of electrodes in their standards [70,71]. The applied pressure (such as probe pressure) should be 1 KPa or less, and the change in fabric thickness due to the applied pressure should be less than 1%. ρ_s and ρ_v can be calculated via Equation (3) and Equation (5), respectively.

However, although the two-point probe method is simple and convenient, there are some disadvantages. As mentioned before, a contact resistance exists between the electrodes and the tested material; this contact resistance makes the resistivity of the tested material higher than its real resistivity [49]. Thus, the two-point probe method is only suitable for those materials with high resistance since the effect of contact resistance is small in those cases.

3.1.2. Four-Point Probe Method

In order to avoid this contact resistance in the measurement of R_s or R_sh, the four-point probe method can be used. The principal is that it measures voltage and current separately so that the current does not flow through the voltmeter and the potential drop across the contact resistance can be eliminated. Figure 7 illustrates the general system of the four-point probe method.

The four-probe measuring device consists of four colinearly aligned probes: a pair of outer and a pair of inner probes. As a measuring principle, the defined current is applied to the tested specimen through the outer probes, whereas the generated voltage is measured via the voltmeter connected to the inner probes. The resistance is then calculated via Ohm’s law. Several standards use the four-point probe method to test the resistance, including SEMI MF43 [72], SEMI MF84 [73], ASTM F390-11 [74], AATCC EP13 [66], IEC 63203-201-2 [75], and IEC 62899-202 [76].

SEMI MF43 [72] and SEMI MF84 [73] are the standards used to test semiconductor materials, although many researchers have applied the device mentioned in the older version of these standards to test the fabric [77,78]. SEMI MF43 [72] is suitable for specimens where both the thickness and the distance from any probe to the nearest edge are at least four times the probe spacing. The arrangement of the testing system of four probes is shown in Figure 8. The probes, made of hardened tool steel, tungsten carbide, or other metals, are point probes. During the measurement, a certain force should be applied to the probes. The space between probes (determined according to the method given in SEMI MF84 [73]) should be uniform since an uneven space will make the measurement results inaccurate [79]. In practice, frequent checks are required of the spacing and state (shape) of the probes since worn probes should be resharpened or replaced in order to maintain this required spacing. A current is applied to the outer two probes, and the generated voltage is measured by the inner two probes. The resistivity (ρ_v) can be calculated via Equation (9),

$${\rho }_v=FRt$$

(9)

where F is the correction factor, R is the resistance, and t is the thickness. Considering the deviations from ideal conditions, both the thickness and probe spacing correction factors are needed to ensure accuracy. Specific values of the correction factors can be found in the standard [72].

SEMI MF84 [73] is used to measure silicon circular wafers with a diameter greater than 16 mm and a thickness less than 1.6 mm. In this standard, the shape, arrangement, and diameter of probes are the same as those of SEMI MF43 [72], but they provide more information about the probes, and some of the requirements are different from those of SEMI MF43 [72]. They provide more information about the probe tip angle, the force applied to the probes, and the distance between probes. Moreover, the current applied to the outer probes should depend on the thickness and resistivity of the specimen. When the thickness is 0.5 mm, the current between 0.1 μA and 100 mA can cover the resistivity from 5 × 10⁻⁵ to 100 Ω·cm. Due to the risk of Joule heating the probe, the applied current should not exceed 100 mA. Then, the resistivity can be calculated via Equation (9); the thickness and probe spacing correction factors (F) should also be considered [73].

ASTM F390-11 is used to test the R_sh of rectangular metallic films and coatings formed by the deposition or thinning process over an insulating substrate. Metallic films and coatings with 0.01 to 100 μm thickness and 10⁻² to 10⁴ Ω/sq, R_sh are suitable to apply this standard. In this case, the electrodes used are also four collinear electrodes. The probes with a conical tip are the same as in SEMI MF43 [72]. In order to protect the film from puncturing, it is recommended that a certain load be applied to the probes. The insulating resistance between the probes should be at least 10⁵ times greater than the resistance of the tested specimen. The appropriate distance between the probes is usually 0.64 to 1 mm. More information to determine the distance of probes can be found in the standard [74]. Moreover, the recommended current for the outer probes ranges from 0.01 to 100 mA. R_sh can be calculated via Equation (9), with the correction factors (for thickness, probe spacing, and lateral) available in the standard [74].

As mentioned previously, another part of AATCC EP13 [66] uses a four-point probe method. It is a standard aimed at textiles. The requirements of samples, the type of electrodes, and the test procedure are the same as the part of the two-point probe method explained in Section 3.1.1. The difference is the requirement for the electrodes.

IEC 63203-201-2 [75] is another standard that uses a four-point probe method to test the R_sh of the fabric. The specimen and test procedure requirements are referred to UN-EN 16812 [80]. The current is applied to the outer probes, and the voltage is measured five times within 1 min at a fixed time interval; each specimen is measured twice. Then, the resistance in the longitudinal direction is calculated using Ohm’s law. It is noted that in order to protect the specimen and ensure test security, they provide the method to find the fusing current in this case. The fusing current is fundamental to determining the safety current that can pass through the conductive fabric without melting or igniting via Joule heat. The detailed test procedure is described in the standard [75].

IEC 62899-202 [76] is a standard aimed at conductive layers obtained by applying conductive inks on substrates. On the one hand, for the measurement of R_v, appropriate pressure must be applied to the probes, these being semi-spherical or flat-tip metal pins of a small diameter (0.5–0.8 mm). The distance between probes (typically 1.5 mm) and the current to be applied to the outer probes (dependent on the range of resistance) is defined in the standard [76]. Thus, ρ_v is calculated via Equation (9). On the other hand, for the measurement of R_s, the same four collinear electrodes are used. ρ_s is obtained by dividing R_v by the thickness. However, a study proposes different equations for the resistivity determination in rectangular (Equation (10)) and circular (Equation (11)) samples [81].

$${\rho }_s=R_s\frac{W}{s}$$

(10)

$${\rho }_s=\frac{R_s\pi }{In2+In(\frac{{\left(\frac{d}{s}\right)}^2+3}{{\left(\frac{d}{s}\right)}^2-3})}$$

(11)

where d is the diameter of the sample, s is the space between two probes, W is the width of the specimen, and R_s is surface resistance.

As the contact resistance can be eliminated, the four-point probe method is suitable for measuring materials with low resistance, thus ensuring measurement accuracy. Although the four-point probe method can avoid contact resistance, there are also some disadvantages. Due to their collinear probes, this method cannot detect the anisotropy of textiles [29]. Moreover, for some fragile or easy-to-break materials, the contact of the probes may damage the specimen.

3.1.3. Van der Pauw Method

The application of the Van der Pauw method can compensate for the shortcomings of the two-point and four-point probe methods [33,82]. The Van der Pauw method differs from the four-point probe since the probes are not collinear; the four probes are connected on the corners of the specimen. The current is measured by one ammeter on one side, and the generated voltage is measured on the opposite side by one voltmeter, following the connections scheme shown in Figure 9. Finally, ρ_v can be calculated from the measured resistance values R_AB,CD and R_BC,DA through Equation (12) [83],

$${\rho }_v=\frac{\pi t}{ln2}\frac{(R_{AB,CD}+R_{BC,DA})}{2}F$$

(12)

where R_AB,CD is the resistance of one direction, R_BC,DA is the resistance of another direction, t is the thickness of the specimen, and F is the correction factor.

This method can be applied regardless of the shape of the specimen, even for irregular shapes. However, the specimens must meet a lot of requirements [33]. (1) The surface should be flat, and the thickness should be small and uniform. (2) The surface is singly connected, which means the sample does not have isolated holes. (3) All four contacts must be located at the edges of the sample. (4) The distance between two probes should be much higher than the thickness. (5) The contact area of the electrodes should be smaller than the distance between electrodes, and the contact resistance should be much lower than the resistance of the sample. Moreover, some studies found that anisotropy textile materials have different properties in different directions, so using the Van der Pauw method to test the resistance can cause inaccuracy [23,84]. Therefore, some modifications might be required when using the Van der Pauw method in fabrics. In this sense, some researchers have focused on mathematical methods to modify it. For instance, Kazani et al. measured the electrical properties of anisotropic textiles by deforming the formulae [28], whereas other authors achieved measurement via optimized test methodologies [22,34]. For instance, Tokarska Magdalena [34] improved the Van der Pauw method by changing the distance between probes in order to minimize the resistance difference between the horizontal and vertical directions as much as possible.

To summarize, although the Van der Pauw method can be applied to fabrics of any shape, it still needs contact with the specimens, which makes it possible to damage them. In addition, the measurement is difficult for fabrics where only one side is electrically conductive or for materials whose conductive parts have been encapsulated.

3.2. Noncontact Methods

Eddy Current Method

The eddy current method does not need to contact the specimens, so it can both avoid contact resistance and protect the specimen from breaking or damaging, thus compensating for the disadvantages of contact methods. This nondestructive testing was first applied in 1976 by Miller et al. [46] to test the R_sh of semiconductors, and nowadays is widely used in metals [85] and has been accepted as the noncontact method to test the resistance of conductors and semiconductors.

The eddy current method is based on Faraday’s law of induction. The general system is shown in Figure 10a, and the principle is shown in Figure 10b. By applying an alternating current (AC) to a coil, the coil generates an electromagnetic field (dotted black lines) and produces an induced current (dotted blue lines) in the material. The induced current operates at the same AC frequency as the coil, thus producing an electromagnetic field (dotted orange lines) opposite the coils. R_sh is obtained from addition or difference of these two electromagnetic fields. A few standards use eddy current principles, including ISO 24584 [85] and IEC 62899-202-3 [86]. Based on the eddy currents principle, they can be used not only to measure the single conductive layer but also to measure multilayer structures containing conductive and insulating layers. This type of measurement is important for conductive fabrics that are already encapsulated.

The measuring stage used in ISO 24584 [85] is shown in Figure 11. The sensor probe, consisting of excitation and receiving elements, is installed vertically on the surface of the measuring stage (a 5 mm insulation plate). Since the eddy current varies with the distance between the sensor probe and the specimen, a constant distance must be maintained during the measurement. The tested specimen is placed flat on the measuring stage, free of wrinkles and tension, and then R_sh is measured. As the fabric has a rough surface, high thickness, or bulky structure, a pressure plate (made of insulating material) should be used to apply a suitable pressure depending on the type of fabric (often around 100 Pa). In this case, R_sh can be measured after 10 s of applying the pressure.

The standard IEC 62899-202-3 [86] is designed to test R_sh of printed conductive films between 0.01 Ω/sq to 1000 Ω/sq. The eddy current sensor probe consists, indeed, of a coil wound on a ferrite core. As shown in Figure 12, two kinds of sensor systems can be employed: a dual probe (Figure 12a) or a single probe (Figure 12b). For the dual probes, the specimen is placed between a top probe and a bottom probe, and the magnetic flux flows between both probes. Whereas for the single probe, the specimen is placed on an insulating stage, and the magnetic flux flows from the inner core to the outer ring of the same probe. More details about the configuration can be found in the standard [86]. In any case, R_sh can be obtained after correctly placing the specimen.

4. Revision of the Test Methods for Different Types of Fabrics

According to the conductive principle of fabrics, they can be divided into intrinsically conductive and extrinsically conductive. Intrinsically conductive fabrics are those made of conductive fibers or yarns by weaving, knitting, or nonwoven methods, whereas extrinsically conductive fabrics are those fabrics obtained by weaving, knitting, or nonwoven methods as substrates and then endowed with conductive properties through surface treatments like dipping, printing, coating, and deposition, among others. To analyze the situation more deeply, Figure 13 summarizes the composition of intrinsically and extrinsically conductive fabrics described in the literature. As shown, the majority of the conductive fabrics found in the literature are extrinsic, and coating is the most widely used method within this category. For intrinsically conductive fabrics, woven fabric is popular due to its stable structure and easy production.

The different types of fabrics (intrinsically or extrinsically conductive woven, knitted, or nonwoven fabrics) vary greatly in their properties and structure and, therefore, so does the most appropriate testing method for the characterization of their electrical properties. Thus, the application of the testing methods is revised according to this classification as follows.

4.1. Intrinsically Conductive Fabrics

4.1.1. Woven Fabrics

The woven fabrics are formed by the interlacing of warp and weft yarns following a certain regularity (weave structure) [87]. There are various structures of woven fabrics being the most basic and widely used the plain, twill, and satin weaves [88], including the substrates for conductive fabrics [88,89].

The conductivity of a fabric depends on the conductivity of its yarns and on its own fabric structure since different weave structures result in fabrics with different yarn arrangements and yarn densities. Indeed, yarn density is the main factor affecting the electrical conductivity of woven fabrics. The higher the yarn density, the tighter the yarn arrangement, the shorter the conductive path, the smoother the current flow, and thus the higher the conductivity. Depending on the final demands, different woven structures can be chosen.

Table 1. Studies review regarding the measurement of electrical properties of intrinsically-conductive woven fabrics. (Note: results were obtained via the search on the Web of Science: “Conductive woven fabric” (All Fields) from 2015 to 2024).

Weave Structure	Fabric Composition		Application (Function)	Testing Method	Electrical Properties	Ref.
	Nonconductive Yarns	Conductive Yarns
Plain	PES	SS yarn	Heating	4-P probe	R = 4.42 Ω	[90]
Plain	Modal roving	Metallic/modal core yarns	EMI shielding	2-P probe (parallel electrodes)	ρs = 0.34 × 103 Ω/sq	[91]
Plain	PES/CO roving	Cu wires or SS wires (core)	EMI shielding	2-P probe (parallel electrodes)	ρs = 3.15 or 4.11 log Ω/sq	[92]
Plain	High-strength PES/Bamboo charcoal	SS	EMI shielding	2-P probe (concentric rings)	ρs = 107 Ω/sq	[93]
twill 2/2	PP	SS	EMI shielding	2-P probe	ρs = 105–107 Ω ρv = 104–107 Ω·cm	[94]
Plain	CO/PES	SS	EMI shielding	2-P probe (parallel electrodes)	ρs = 103–106 Ω/sq	[95]
Twill					ρs = 103 Ω/sq
Stain					ρs = 103–106 Ω/sq
Hopsack					ρs = 103–106 Ω/sq
Unspecified	\	(tin, nickel, silver) metalized	Conveying electrical signals	Van der Pauw	Rs = 10−3–10−2 Ω	[22]

Abbreviations: CO: cotton; Cu: copper; EMI shielding: electromagnetic interference shielding; PES: polyester; PP: polypropylene; SS: stainless steel; 2-P: two-point; 4-P: four-point.

summarizes some resistance test methods of conductive woven fabric in the last ten years. Due to the dimensionally stable structure, the woven fabric is nearly suitable for all the resistance measurement methods, although it depends on the range of resistance and functions.

Because of its durability and uniform and stable structure, the intrinsically conductive woven fabric is mainly used to manufacture EMI shielding products. Previous studies have verified the plain weave can provide better EMI shielding properties than other structures [96]. ρ_s of EMI shielding material is lower than 10² Ω/sq, but it is also affected by permittivity, permeability, and thickness [89]. Thus, this value can vary with different electromagnetic frequencies [91,93]. Products with specific EMI shielding properties can be obtained by controlling the density and tightness of the yarns according to the final performance requirements.

Furthermore, according to Table 1, when the woven fabric with EMI shielding properties has a much higher resistivity (10³–10⁷ Ω/sq), the contact resistance hardly affects the accuracy of the data, so the two-point probe method can be used for the resistance measurement. For fabrics with other functions such as heating and signal transmitting (which require a higher conductivity), the four-point probe, Van der Pauw, or eddy current methods are more suitable.

4.1.2. Knitted Fabrics

Knitted fabric is formed by interlocking loops of yarn. Depending on its production technique, knitted fabrics can be divided into weft knitted fabrics, including basic structure plain/jersey, rib, purl, interlock stitch, etc., and warp knitted fabrics, including basic structure pillar, tricot, atlas, and double loop stitch [97] etc.

Similar to woven fabrics, different knitting structures can affect the arrangement of yarns, affecting the conductivity. The structure with the tighter arrangement of the yarn can promote conductivity. Moreover, knitted fabrics present better adaptability, and some physical factors (including stretching [98,99], compression [100,101], and bending [39,40]) can affect the conductivity. When the knitted fabric is stretched, the topography of the fabric changes, which can limit the contact between conductive yarns, changing the conductive path and affecting the conductivity. Furthermore, according to Equation (5), stretching increases the length of the yarn, decreasing the cross-sectional area and thus increasing the resistance. For compression, it can make the conductive yarns closer, increasing the contact between the yarns, which potentially improves the conductive path and decreases the resistance. As for bending, in fact, it is a behavior that combines both stretching and compressing. When the fabric is bending, one side of it is stretched while the other is compressed. This can cause a change in the alignment and distribution of conductive yarns, affecting the fabric’s electrical properties. The stretched side might experience an increase in resistance, while the compressed side might see a decrease. These physical factors affect all three kinds of fabrics (woven, knitted, and nonwoven), but since woven fabrics have more dimensional stability and lower elasticity than knitted fabrics, they have a higher effect on knitted fabrics.

The differences in the structure of knitted fabrics result in different yarn arrangements, which will affect the mechanical and electrical properties. Thus, depending on the requirements for conductivity, different structures should be chosen.

Table 2. Studies review regarding the measurement of electrical properties of intrinsically-conductive knitted fabrics. (Note: results were obtained from the search on the Web of Science for: “Conductive knitted” or “conductive knitting” (All Fields)’ from 2015 to 2024).

Structure	Fabric Composition		Application (Function)	Testing Method	Electrical Properties	Ref.
	Nonconductive Yarns	Conductive Yarns
Interlock stitch	PES	Ag-coated yarn	Heating	2-P probe (parallel electrodes)	ρs = 0.15 Ω/sq	[102]
Half-Milano rib	PA6.6 PU	Ag-coated yarn	Heating	2-P probe (parallel electrodes)	Rs = 0.14 Ω	[103]
Weft-knitted jacquard	Merino WO	Ag-coated yarn	Heating	Two-point probe (parallel electrodes)	Rs = 1.91 Ω	[104]
Knit, knit-and-float, and knit-and-tuck stitches	WO yarn/PES yarn	Ag-coated yarn	Heating	2-P probe	Rs = 5.7–25.5 Ω	[105]
Knit, tuck, and float	WO yarn	Ag-coated yarn	Conductive	2-P probe	Rs = 1–1.5 Ω	[106]
Unspecified	Unspecified	Ag-coated yarn	Conductive	Eddy current	Rsh = 0.40 Ω/sq	[26]
Plain weft knitted	None	Ag-coated yarn	Conductive	Van der Pauw	Rs = 0.03–0.5 Ω	[27]
Unspecified	None	Ag metalized	Conveying electrical signals	Van der Pauw	Rs = 10−1 Ω	[22]
Unspecified	antibacterial PA/crisscross-section PES	SS	Conductive/Antimicrobial	2-P probe (concentric ring)	ρs = 109–1010 Ω/sq	[107]
1 × 1 rib	CO/Bamboo/PES	Ag-coated yarn	EMI shielding	2-P probe	ρs = 107–1010 Ω/sq ρv = 107–109 Ω·cm	[108]
Unspecified	Bamboo charcoal	SS	EMI shielding	2-P probe (concentric ring)	ρs = 107 Ω/sq	[93]
Interlock	CO	SS, Cu, and Ag-coated Cu wires (core)	EMI shielding	2-P probe (concentric ring)	ρs = 104–105 Ω	[109]
Plain jersey	PP	SS	EMI shielding	2-P probe	ρs = 107–108 Ω ρv = 106–108 Ω·cm	[94]

Abbreviations: Ag: silver; CO: cotton; Cu: copper; EMI shielding: electromagnetic interference shielding; PA: polyamide; PES: polyester; PP: polypropylene; PU: polyurethane; SS: stainless steel; WO: wool; 2-P: two-point.

lists some of the test methods that have been studied for measuring the resistance of knitted fabrics in the last decade.

Based on the concerns of impact factors, the two-point probe, eddy current, and Van der Pauw methods seem more suitable for the resistance test of knitted fabrics. The two-point probe uses larger probes (both parallel and concentric ring) than other methods, which can cover more area and help in accommodating the fabric’s texture and irregularities. The Van der Pauw method, when applied to fabrics, assumes a planar surface for accurate measurements. However, fabrics exhibit anisotropic electrical properties (their electrical resistance can vary depending on the measurement direction). Hence, some variations maintained in Section 3.1.3 are required for practical use. For the eddy current method, since it measures resistance contactless via electromagnetic induction, the surface properties of the material have virtually no effect on the measurement results. Thus, it is also suitable for the measurement. For the four-point probe method, the space between probes should be adjusted for different structures. The topography of knitted surfaces will affect the contact between probes and the fabric. Thus, the four-point probe method is not suitable for the measurement of knitted fabrics.

For the applications, conductive knitted fabric is the most suitable for making heating fabrics. Since knitted fabrics are inherently flexible and can conform to complex shapes, this makes them ideal for applications requiring the fabric to fit snugly to various surfaces or body contours, ensuring efficient heat transfer. The looped structure of knitted fabrics creates air pockets that can help retain heat, enhancing heating efficiency.

4.1.3. Nonwoven Fabrics

Normally, nonwoven fabric is made from fibers, staple yarns, and filaments; after the web-forming process, the fibers are bonded together via mechanical, thermal, or chemical methods without the traditional methods of weaving or knitting. The web-forming methods include dry (air-laid and carding), wet (wet-laid), and thermal methods, and the web consolidation methods mainly include mechanical (spin-laid, needle punching, and hydroentangling), thermal (bonding and melt-blown), and chemical methods (wet-laid) [110]. The structure of nonwoven fabrics depends on the production technique, which is of special interest to the web formation, which leads to directionally or randomly orientated fiber arrangement, and the bonding steps. Compared to woven or knitted fabrics, nonwovens present a lighter weight, lower strength, lower elasticity, high porosity and permeability, and a more complex structure with randomly distributed fibers, resulting in anisotropic structure and properties. Consequently, the properties (including conductivity) are different along the machine’s direction (MD) and across the machine’s direction (CD).

Depending on the structure of the nonwoven, the two-point and the four-point probe methods are more suitable for resistance testing. Depending on the final requirements, the test method should be different.

Table 3. Studies review regarding the measurement of electrical properties of intrinsically conductive nonwoven fabrics. (Note: results obtained from the search on the Web of Science for: “Conductive nonwoven” (All Fields)’ from 2015 to 2024).

Nonwoven Fabrication Technique	Fabric Composition		Application (Function)	Testing Method	Electrical Properties	Ref.
	Nonconductive Elements	Conductive Fibers
Wet laid	Xanthan gum	CF	Heating	4-P probe	ρs = 10–27 Ω/sq	[111]
Needle punching	PP/PE core/sheath bicomponent fiber	CF	Unspecified	4-P probe	σ = 13 S/cm	[112]
Needle punching	PP fiber	CF	EMI shielding	2-P probe	ρs = 3.35 kΩ	[113]
Needle punching	None	Ag-coated fibers	EMI shielding	2-P probe	ρs = 1.03 kΩ	[114]
Needle punching	PA6 fiber	Recycled CF	EMI shielding and sound absorption	4-P probe	σ = 33.83 S/m	[115]

Abbreviations: Ag: silver; CF: carbon fiber; EMI shielding: electromagnetic interference shielding; PA: polyamide; PE: polyethylene; PP: polypropylene; 2-P: two-point; 4-P: four-point.

summarizes the resistance test method of some conductive nonwoven fabrics in the last ten years. For the two-point probe method, since the electrodes can cover a larger area, the impact of uneven distribution of conductive fibers on the measurement can be reduced. Moreover, by applying a suitable weight, the electrodes can be in contact firmly with the fabric surface, and in addition, the distance between the conductive fibers can be shortened by pressure, thereby increasing the probability of contact and reducing the effect of fluffiness on the measurement. If the conductive nonwoven fabric has a relatively high resistance, the impact of contact resistance becomes less significant in the total resistance measurement. For nonwovens that require high precision in electrical conductivity properties, the four-point probe method is more suitable. Regarding the Van der Pauw method, since the nonwoven fabrics are porous, they do not fit the requirements for applying such a principle. For the eddy current method, the uneven distribution of fibers can affect the induction of eddy currents, leading to inconsistent eddy current readings and affecting accuracy.

4.2. Extrinsically Conductive Fabrics

The combination of conductive particles with a nonconductive fabric substrate forms the extrinsically conductive fabric. The most common methods used for coating are shown in Figure 13. Conductive particles used to impart conductivity to textiles are categorized into metallic particles, carbon-based materials, and conductive polymers. Metallic particles like silver [116], copper [117], and gold [118] are commonly used, with silver preferred for its high conductivity and antimicrobial properties. MXene (Ti₃C₂T_x) [119], a metal-based material, is also popular due to its excellent conductivity and flexibility. Carbon-based materials such as carbon black [120], carbon nanotubes (CNTs) [121,122], carbon nanofibers (CNFs) [123], graphene [124], and graphene nanoplatelets (GNPs) [125] are valued for their outstanding electrical conductivity, flexibility, and strength. Lastly, conductive polymers, such as polypyrrole (PPy) [126,127], poly(3,4-ethylenedioxythiophene) (PEDOT) [128], and polyaniline (PANI) [129], offer good conductivity, are lightweight, stable, and are compatible with textiles so are widely used. Moreover, in some cases, to improve electrical conductivity and/or to reach a certain multifunctionality, two or more conductive particles are applied [130,131,132,133]. Therefore, the different materials to apply are selected based on the final requirements. In fact, given the range of electrical properties and flexibility exhibited by the different materials, different functions related to conductivity can be achieved [24]. These functions are photothermal [134,135] such as Joule heating [136], signal transportation [120], energy storage [130], and EMI shielding [137], among others.

Table 4. Studies review regarding the measurement of electrical properties of extrinsically conductive fabrics.

Substrate	Fabric Composition		Application (Function)	Testing Method	Electrical Properties	Ref.
	Conductive Treatment Method	Conductive Material
PES woven fabric	In situ polymerization	Aniline and Py	Supercapacitors	4-P probe	σ = 1.44 × 10−2 S/cm	[129]
CO woven fabric	Electroless plating	Ag	Ultrahigh washability	4-P probe	Rsh = 0.33–2.49 Ω/sq	[116]
CO woven fabric	Dip-coating	MXene (Ti3C2Tx)	Strain sensors	4-P probe	ρv = 1.52 × 10−2 Ω m	[119]
CO woven fabrics	Dip-and-dry	PDA and SWCNTs	EMI shielding	Van der Pauw	Rs = 9 ± 2 Ω/sq	[131]
CO woven fabric	In situ polymerization	PPy/AgNWs	Joule heating/ Photothermal	4-P probe	σ = 1.97 × 104 S/m	[130]
PES warp-knit	In situ polymerization	PPy/Ag	Conductive and antimicrobial	4-P probe	Rsh = 61.54 Ω/sq	[132]
CO knit	In situ polymerization	PPy	Heating	4-P probe	ρs = 59.9 ± 13.6 Ω/sq	[126]
Plain, basket & twill woven Single jersey weft-knit	In situ polymerization	PPy	Conductive	2-P probe	σ = 10−3–10−6 S/sq	[127]
Rib stitch knitted	Spray-drying coating	CNTs and GNs	Heating/strain sensor	2-P probe	σ = 36.5 S/m	[121]
SA/FRV weft-knit	Spray-drying	MXene	EMI shielding/ Joule heating/ Photothermal	4-P probe	Rsh = 2 Ω/sq	[137]
PLA nonwoven	Padding	MWCNTs	Conductive/antimicrobial	4-P probe	Rsh = 77–681 Ω/sq	[122]
PPS needle punching nonwoven	In situ polymerization	PPy	Heating	4-P probe	ρs = 4.5–8.8 Ω/sq	[134]
Aramid nonwoven	Dip-coating	PEDOT: PSS/AgNWs	EMI shielding/Heating	4-P probe	Rsh = 0.92 ± 0.06 Ω/sq	[133]
CO nonwoven	Dipping	Graphene	Heating	2-P probe	ρs = 727.57 Ω/sq	[124]
Aramid spunlaced nonwoven	Spraying–drying	MXene	EMI shielding/ Joule heating/ Photothermal	4-P probe	Rsh = 4.36 Ω/sq	[135]

Abbreviations: AgNWs: silver nanowires; aniline and pyrrole: An and Py; CO: cotton; CNTs: carbon nanotubes; FRV: retardant viscose; GNs: graphene nanosheets; MXene: metal carbide/carbonitride; MWCNTs: multiple-wall carbon nanotubes; PES: polyester; PLA: polylactide; PPS: polyphenylene sulfite; PDA: polydopamine; PPy: polypyrrole; PEDOT:PSS: poly(3,4-ethylene dioxythiophene): poly(styrene sulfonate); SA: sodium alginate; SWCNTs: single-wall carbon nanotubes; 2-P: two-point; 4-P: four-point.

summarizes the conductive particles used, the testing method employed, and the functions reached for some studies developed in the last ten years.

The conductivity of the extrinsically conductive fabrics is affected by the properties of the conductive layer/coating formed by conductive particles and the textile substrate. Depending on these two factors, different electrical resistance test methods were selected. In fabrics with highly resistive conductive layers, the choice of method depends more on the textile substrate, as electrode contact resistance has less impact [49,64]. However, for fabrics with low-resistance conductive layers, methods that minimize or avoid contact resistance (four-point probe [49,79], Van der Pauw [33,82], eddy current [26,85]) are recommended for more accurate measurements. For low resistance and fragile conductive layers, noncontact methods (eddy current method) are preferable since they can prevent contact damage. For different textile substrates, the choice of test method varies with the fabric’s structure. The methods applicable for each substrate can be found in the previous section. Due to the possibility of poor contact between the probe and the fabric surface, the four-point probe method is not the best choice. Nonwoven substrates, characterized by high porosity and a complex structure, are best tested with the two-probe [124] and four-probe [122,124,133,134] methods. The Van der Pauw method is unsuitable for nonwovens due to its porosity, and the eddy current method may yield inconsistent results due to the uneven distribution of fibers.

5. Conclusions and Outlooks

In general, correctly measuring the electrical properties of fabrics has a profound impact on the realization of various intelligent functions. This paper discussed the parameters, test methods, and influencing factors according to different types of fabrics. The conclusions are as follows:

• The parameters used to evaluate the electrical properties of smart textiles (fabric) include surface and volume resistance, sheet resistance, surface and volume resistivity, and conductivity. Depending on the final requirements, different parameters should be measured.
• The electrical resistance test method includes contact (two-point probe, four-point probe, and Van der Pauw) and noncontact (eddy current) methods. Each method has its own advantages and disadvantages.
• Multiple factors affect the conductivity, including the materials’ intrinsic properties, physical strain such as stretching, compression, and bending, and environmental factors such as humidity, temperature, and magnetic fields.
• The method used to test intrinsically conductive fabrics should depend on the properties of the fabric and the final applications. Based on the structure of the fabrics, for woven fabrics, both contact and noncontact resistance test methods are the most suitable; for knitted fabrics, two-point probe, Van der Pauw, and eddy current methods are the most appropriate; and for nonwoven fabrics, both two-point and four-point probe methods can provide more accurate measures. For the applications, it depends on the range of resistance; if the tested specimen has a low resistance, to ensure accuracy, methods that can estimate the contact resistance should be employed.
• The method used to test extrinsically conductive fabric was highly affected by the fabric substrate and conductive layers. The suitable method should be selected based on the properties of the fabrics. If the conductive layers are fragile, the noncontact method should be applied to avoid damage to the specimen.

Nowadays, in order to obtain textiles with desired features, printing and embroidery have become the main techniques to customize circuits [136,138,139]. These methods allow for easier customization of circuits or patterns according to people’s needs than the traditional textile manufacturing methods. Such textiles tend to exhibit high electrical conductivity and they have high requirements for accuracy in resistance testing. Therefore, the development of resistance testing methods with lower errors is necessary.