4.1. Surface Roughness Profile Analysis
A surface roughness analysis was performed on plain-weave fabric samples using a non-contact optical profilometer. Surface scans were captured and analyzed with dedicated software in accordance with the ISO 4287 standard [
48].
Figure 4,
Figure 5 and
Figure 6 display the results of the surface roughness analysis, while
Table 2 summarizes the corresponding roughness profile values. In the context of surface roughness and profilometry measurements,
Ls (sampling length) and
Lc (cut-off length or filter length) are parameters related to the analysis and filtering of the surface profile data.
Ls refers to the surface length over which the measurement is taken, representing the distance along the surface over which data points are collected to analyze the roughness profile. In this study,
Ls indicates that the measurement was taken over a
Ls = 245.0 µm length of the fabric surface.
Lc, on the other hand, is a filtering parameter that separates the roughness profile from the waviness profile. The cut-off filter (
Lc) was applied to remove the waviness component from the primary profile. By filtering out the long-wavelength elements associated with waviness, a roughness profile was generated, which isolates the finer surface texture details. It determines the threshold between roughness (shorter wavelengths) and waviness (longer wavelengths) on the surface of the fabrics. With
Lc = 0.800 mm, features smaller than
Lc are considered part of the roughness, while more prominent features are classified as waviness. These parameters are essential for accurately characterizing the surface texture and understanding the distinction between fine roughness and broader waviness in the fabric samples. The results of the structural properties and surface roughness analysis were performed according to the plain-weave fabric made from Shieldex
® 117/17 HCB samples using a non-contact optical profilometer. This effect is primarily due to the greater number of yarns per unit length, which enhances surface uniformity by minimizing air gaps and reducing the occurrence of loose or uneven threads. Moreover, higher yarn density typically induces greater yarn tension during the weaving process, promoting more consistent alignment and tighter integration of the yarns, which further contributes to a smoother fabric surface. This denser arrangement minimizes gaps between the yarns, leading to a smoother surface, as the yarns are less likely to protrude. Additionally, the consistent interlacing pattern of the weave creates a uniform texture, further contributing to a reduction in irregularities. The overall effect is a fabric that feels smoother and more refined with higher weft density. The relationship between weft density and the roughness of fabrics differs due to the weave’s unique structure. The divergence in weft and warp density is a more complex interlacing pattern that involves warp and weft yarns with varying thicknesses and spacing. As weft density increases, the weave’s distinctive texture and visual characteristics can become more pronounced, leading to a potential exhibit of unidirectional property. The interplay between thicker and thinner yarns can create irregularities that contribute to surface texture, and higher density does not necessarily result in fabrics with uniform geometrical and electrical properties. The profilometry method is a technique used to measure and analyze the surface profile of fabrics by scanning the surface using a non-contact chromatic white light sensor. This method records height variations (
Y) as a function of distance (
X), generating a detailed profile of the surface’s peaks and valleys. The collected data are then plotted as a 2D graph, with the
X-axis representing the distance along the surface and the
Y-axis representing the height or depth of the surface features. However, the structural complexity of the woven fabrics introduces variations in surface electrical resistance, which are not solely dependent on changes in weft density, as detailed in
Table 1. The surface roughness profiles of the woven structures, measured with a sampling length (
Ls) of 245.00 µm and a cut-off length (
Lc) of 0.80 mm, are shown in
Figure 4,
Figure 5 and
Figure 6. The
X and
Y axes indicate surface dimensions in mm, while the color scale represents the surface height in mm.
In the surface maps (
Figure 4,
Figure 5 and
Figure 6), the color bar shows surface height, ranging from 0.00 mm (blue/green) to 1.358 mm (yellow/red). Sample W19 (
Figure 4) had the highest surface roughness, with red areas and scattered spots indicating peaks or raised regions. Yellow areas correspond to the highest points, approaching the maximum height range. The sample surface in
Figure 5a,b appears to show moderate uniformity, as less dominant red regions suggest the spread of roughness to different directions, with fewer smooth or flat areas. The yellow patches show the highest points distributed across the surface. These peaks indicate raised features such as fibers, yarn intersections, and general surface irregularities of the woven structures.
In the case of W25 and W27 in
Figure 6, the green areas dominate the surface, suggesting the overall surface is relatively flat or uniform in height before reaching 0.6 mm. Blue or darker green areas were not observed in the case of these samples (in
Figure 6a,b), denoting less availability of depressions or valleys on the surface of these samples. The green regions dominate the surface, indicating that most of the surface is relatively flat and uniform in height among the denser fabrics. Small black and blue spots scattered across the surface represent localized valleys. There are very low yellow regions that are minimal, suggesting very few areas approach the maximum height of 1.240 mm. Surface roughness parameters provide critical insights into the texture and functional properties of a surface, which are directly relevant to the electrical resistance of conductive fabrics.
sRa and
sRq, representing the average and root mean square roughness, respectively, indicate the overall smoothness or variability of the fabric surface. Smoother surfaces (lower
sRa and
sRq) typically result in better contact between conductive fibers, reducing electrical resistance.
sRz25, which quantifies peak-to-valley heights, highlights the depth of surface irregularities that can disrupt electrical pathways, increasing resistance
. sRsk (skewness) indicates whether the surface has more peaks or valleys, influencing contact points between fibers. At the same time,
sRku (kurtosis) describes the sharpness of these features, which can impact the uniformity of the current distribution. These parameters are essential for optimizing the design and performance of conductive fabrics in applications like wearable electronics, sensors, and EMI shielding. A summary of typical values for these parameters is presented in
Table 2.
Table 2 presents the surface roughness and electrical properties of conductive fabrics with varying fabric parameters, such as weft densities (from W19 to W27).
Table 2 presents surface roughness parameters (
sRa, sRq, sRz25, sRsk, and
sRku) and electrical resistance measurements (
Rm M,
Rm S,
D%M, and
D%S) for five fabric samples (W19–W27). Regarding surface roughness, the
sRa and
sRq values decrease from W19 to W27, indicating a smoother surface in sample W27. Similarly, the reductions in
sRz25 and
Rmax25 suggest the presence of fewer and less pronounced surface peaks and valleys.
Parameter
sRmax25 shows a notable decrease after the first sample, followed by relatively stable roughness values across the remaining fabrics. The
sRsk values are highly damaging, indicating surfaces dominated by valleys rather than peaks. The
sRku values are very high, especially for W25 and W27, suggesting sharp peaks and extreme surface variations. Regarding electrical resistance,
Rm for both
M and
S electrode arrangements decreases from W19 to W27, correlating with reduced surface roughness.
D%M and
D%S increase, indicating greater structural changes in samples with smoother surfaces. Smoother surfaces (lower roughness values) generally exhibit lower electrical resistance, likely due to better fiber-to-fiber contact and reduced disruptions in conductive pathways. The high
sRku and negative
sRsk values suggest that surface irregularities, though reduced, remain sharp and valley-dominated, which may still impact conductivity. Comparing the surface profiles, the samples (W25 and W27) show lower roughness values and demonstrate improved conductivity and greater electrical anisotropy, as shown in the values provided in
Table 2. These findings are critical for optimizing conductive fabrics for applications in wearable electronics and smart textiles.
The surface roughness through the area of the samples is related to the orientation of the fibers over the surface of the fabrics. The angular distribution of surface roughness profiles was analyzed using a technique that measures the orientation of surface angles (
θ) and their relative prominence (
ps) across four quadrants. This method generates profiles of the dominant surface orientations, highlighting the direction and intensity of surface features. The results are represented in a quadrant-based plot, where angles indicate the direction of surface features and prominence values reflect their relative intensity. In surface roughness analysis, the angle (
θ) represents the dominant orientation of surface features, measured in degrees (°), indicating the direction of peaks and valleys relative to a reference axis. The relative prominence (
ps), expressed as a percentage (%), quantifies the intensity or significance of these features at specific angles, reflecting their contribution to the overall surface texture. These parameters provide valuable insights into the anisotropic behavior of the fabric surface, helping to assess texture uniformity and directional surface properties; the angular distribution of the surface roughness for the samples from W19 to W27 is presented in
Figure 7 and
Figure 8.
In the case of samples W19 (
Figure 7a), W21 (
Figure 7b), and W23 (
Figure 8a), the angles show diagonal orientations close to 45°, 135°, 225°, and 315°, which is typical of the structural consistency of plain-weave fabrics with balanced warp and weft yarns. In contrast, W25 (
Figure 8b) exhibits orientations closer to 0° and 180°, suggesting alignment with the warp and weft directions. Meanwhile, W27 (
Figure 8c) displays orientations closer to 90° and 270°, indicating alignment perpendicular to the reference direction. Regarding relative prominence,
ps has the lowest values across all quadrants, suggesting that its surface features are less pronounced or less aligned than those of the other samples. On the other hand, W19, W21, and W23 show higher
ps values, with W21 being the most prominent.
Table 3 presents the measured values of (
θ) and (
ps), highlighting the predominant orientations and their corresponding prominence levels.
These findings from
Table 3 show that the variations in surface texture and alignment across the samples reflect differences in their structural and surface roughness properties. The analysis of angle distributions and relative prominence (
ps) reveals the variations in surface texture and alignment across the fabric samples (W19, W21, W23, W25, and W27). These variations reflect differences in their structural properties and surface roughness, which are closely connected to fabric thickness, surface mass, and the weft density of the fabrics. Samples with higher prominence values (e.g., W19 and W21) exhibit more pronounced surface features, indicating rougher textures. This roughness creates air gaps and discontinuities in the conductive pathways, leading to higher electrical resistance. Samples with lower prominence values (e.g., W25 and W27) have smoother surfaces, resulting in better fiber contact and lower electrical resistance.
4.2. Electrical Resistance Analysis
The electrical resistance measurements obtained using the Van der Pauw method revealed electrical anisotropic properties in the two electrode arrangements,
M and
S. Rougher fabric surfaces, such as W19, W21, and W23, exhibited higher electrical resistance compared to denser fabrics like W25 and W27. This increase in resistance for the rougher fabrics is attributed to the creation of air gaps, which reduce the quality of contact between yarns and hinder the flow of electric current. The electrical anisotropy of woven fabrics is influenced by their structural orientations and the quality of yarn contacts within the direction of the fabric surface. Electrical conductivity varies depending on the direction of current flow relative to the weave patterns, resulting in different resistance values along the warp and weft directions. Additionally, the diagonal and other surface directions of the fabrics contribute to the variability in current flow. The warp and weft densities further explain these observations. The warp density ranges from 19.8 to 20.7 threads/cm, while the weft density varies from 20.5 to 27.6 threads/cm. The variation in weft density, while maintaining a relatively constant warp density (as shown in
Table 1), underscores the influence of fabric structure on electrical properties. The anisotropic curve exhibits variability across the plane, whereas the isotropic curve remains constant from 0° to 315° in the electrode configuration represented in the radar charts (
Figure 9,
Figure 10 and
Figure 11). The greater variability of the anisotropic curve compared to the isotropic curve in both
M and
S electrode arrangements indicates a higher anisotropic behavior of the fabrics in electrical resistance. The isotropic and anisotropic properties of the fabrics W19–W27 are presented in
Figure 9,
Figure 10 and
Figure 11.
Figure 9 presents a comparison of electrical resistance (
Rm) and anisotropy coefficients (
D%) for fabric sample W19 in both (
M) and (
S) electrode arrangements. The isotropic and anisotropic measurements indicate that sample W19 behaves as an isotropic fabric, exhibiting electrical resistance values of 190.51 mΩ in the isotropic direction (
Diso) and 191.67 mΩ in the anisotropic direction (
Daniso). The minimal difference between these curves, encompassing total resistance values of isotropic and anisotropic resistances across the complete electrode configuration (0° to 315°), suggests that the fabric exhibits negligible anisotropic properties. The anisotropy coefficient (
D%) is 0.6% for
M and 0.2% for the
S electrode arrangement, respectively, indicating that sample W19 has lower anisotropic properties. Additionally, the smaller fabric area within the four electrodes (
S) shows fewer directional dependencies.
Figure 10a compares the resistance of W21 for the
M and
S electrode arrangements. In this sample, the isotropy and anisotropy curves show greater variability than W19. The anisotropy coefficient (
D%) increases to 3.6% for the
M electrode arrangement and 1.2% for the
S electrode arrangement. Additionally, the electrical resistance (
Rm) decreases from 31.11 mΩ to 29.19 mΩ for the
M electrode arrangement and from 22.68 mΩ to 21.19 mΩ for the
S electrode arrangement. The anisotropy coefficient (
D%) and electrical resistance Rm continued to decrease in sample W23 (as shown in
Figure 10b for the transition from
M to
S electrode arrangement). This trend was continued across all samples, from W19 to W27. The highest anisotropy coefficient (
D%) was observed in W27, with values of 29.9% for the
M (medium) electrode arrangement and 13.7% for the
S (small) electrode arrangement. Additionally, as shown in
Figure 11a,b, the variability between the anisotropy and isotropy curves is also observed to increase, with the curves diverging further apart from each other (
Table 4). Min–max normalization was applied to calculate the normalized electrical resistance (
Rm) values for both
M and
S electrode arrangements. The values of the anisotropic and isotropic resistance are presented in
Table 4. Min–max normalization was applied to calculate the normalized electrical resistance (
Rm) values for both
M and
S electrode configurations.
Table 4 presents the electrical resistance (
Rm), isotropic resistance over the total length of the curve (
Figure 9,
Figure 10 and
Figure 11) (
Diso), anisotropic resistance (
Daniso), and anisotropy coefficient (
D%) for five fabric variants (W19, W21, W23, W25, and W27) under two electrode arrangements (
M and
S). As shown in
Table 4, sample W19 exhibits the highest normalized
Rm under both configurations, while W25 has the lowest, reflecting relative resistance behavior independent of absolute values. These data highlight the influence of fabric parameters such as weft density on electrical properties and anisotropy. In all samples, the anisotropy coefficient (
D%) increases as the fabric parameters, particularly weft density, change from W19 to W27. This trend indicates that structural modifications in the fabric, such as increased weft density, significantly impact electrical anisotropy. The observed electrical isotropy in W19 fabric samples can be attributed to the nearly identical warp and weft densities as well as the use of the same yarn type in both directions. This symmetric construction results in uniform electrical pathways, minimizing directional dependence on resistance. Notably, electrical resistance (
Rm) and anisotropy (
D%) show a decreasing trend when transitioning from the
M to the
S electrode arrangements. These values were measured along multiple directions, from 0° to 315°, following predetermined angular intervals. While the intrinsic electrical properties of the material remain unchanged, these measurements reflect how variations in fabric sizes and positioning relative to the predetermined configuration, such as weft, warp, or diagonal direction, can influence the observed resistance values. This is particularly relevant for anisotropic and inhomogeneous materials, where directional sensitivity plays a significant role. The behavior observed in sample W27, which exhibits a higher degree of anisotropy, further illustrates this effect. While an increase in weft yarn density generally leads to reduced electrical resistance and potentially higher anisotropy due to structural directionality, the observed variations suggest that other factors, such as yarn twist, evenness, and contact quality, also influence electrical behavior. Future studies will consider these aspects to clarify their role in anisotropic performance further.
A detailed analysis revealed that a 35% increase in weft density (from W19 to W27) resulted in a 13–15% reduction in electrical resistance, demonstrating that denser fabrics promote better current flow. This improvement in conductivity is likely due to the enhanced contact between fibers and the more uniform distribution of conductive pathways in denser fabrics. Furthermore, the anisotropic property (D%) for both M and S arrangements shows a significant surge from W19 to W27. Specifically, D% increases by +4900% for the M arrangement and +6750% for the S arrangement. This substantial amplification of the anisotropy ratio indicates that higher weft density not only improves conductivity but also intensifies the directional dependence of electrical properties. The S arrangement exhibits a more pronounced increase in anisotropy, suggesting that this configuration is more sensitive to changes in fabric structure. These findings underscore the intricate relationship between electrical properties and physical parameters such as weft density. Because of the weft density increments, the surface mass (SM, g·m−2) of the fabrics is pronounced, and it also affects the parameters Rm and D%. As SM increases, Rm M generally decreases, indicating better conductivity. For sample W19 with a surface mass of 60 g· m2, the electrical resistance (Rm) for the M electrode arrangement is 31.11 mΩ. In comparison, sample W27, with a surface mass of 75 g·m−2, shows an Rm value of 26.42 mΩ for the same electrode configuration. This suggests that higher surface mass improves conductivity, likely due to increased material availability for charge transport. D% increases significantly with SM, indicating greater directional dependence (anisotropy) in electrical properties. Sample W19, with a surface mass of 60 g· m2, exhibits a directional difference (D%) of 0.6%, indicating low anisotropy. In contrast, sample W27, with a surface mass of 75 g·m2, shows a D% of 29.9%, reflecting high anisotropy. This implies that higher SM leads to more pronounced differences in electrical resistance directional dependencies, which are due to an imbalance of fiber alignment or uneven material distribution on the fabric surface.
The overall trends are visually summarized in
Figure 12, which illustrates how changes in fabric dimensions under the varying electrode configurations from
M to
S influence electrical resistance and anisotropy. This analysis provides valuable insights into the design and optimization of conductive fabrics for applications requiring specific electrical properties.
A consistent and gradual decrease in electrical resistance (
Rm) was observed for both
M and
S configurations (
Figure 12a). While a similar decreasing trend is evident in the degree of isotropy, i.e.,
Diso (
Figure 12b), the variations are more pronounced when comparing
Diso values across different fabric samples. Conversely, the extent of electrical anisotropy (
Daniso) exhibits an increasing trend across all electrode arrangements, both within individual fabrics and between different groups of fabrics (
Figure 12c). A significant disparity is observed in the degree of anisotropy (
D%) (
Figure 12d), indicating a substantial influence of anisotropic properties on the observed changes. Additionally, the fabric parameters and surface profile of the woven fabrics were analyzed as factors influencing their conductivity. A correlation analysis was conducted to determine if there is a direct relationship between the selected roughness profiles and electrical resistance (
Rm) and
D%. Pearson’s correlation coefficients, which were analyzed using PQStat software (version 1.8.6, 2023), are presented in
Table 5. Coefficients with a significance level of the
p-value < 0.05 are marked in bold.
Table 5 presents the Pearson correlation coefficients (
r) between the surface roughness parameters (
sRa (mm),
sRq (mm),
sRz25 (mm), and
sRmax25 (mm),
sRsk, sRku) and the electrical resistance measurements (
Rm (mΩ) and
D% (%), for both
M and
S electrode arrangements). Statistical analysis was performed using PQStat software (version 1.8.6, 2023). Correlations with statistical significance (
p-value < 0.05) are highlighted in bold. Effect sizes were interpreted based on the criterion ∣
r∣ ≥ 0.85, indicating a strong and statistically significant correlation. The arithmetic mean roughness (
sRa) and root mean square roughness
(sRq) show substantial positive correlations with electrical resistance (
Rm M and
Rm S). For instance,
sRa and
Rm M have a correlation coefficient of 0.9654, while s
Rq and
Rm M show an even stronger correlation of 0.9847. The observed trend indicating that increased surface roughness (
sRa and
sRq) corresponds to higher electrical resistance is based on the specific yarn and fabric configurations used in this study. This relationship is likely influenced by the amount and distribution of conductive yarn, which may vary with the different physical properties of the yarns and fabric parameters. As such, this analysis should not be generalized beyond the scope of the materials tested, which are plain-weave fabrics produced from Shieldex
® 117/17 HCB. Further research involving a broader range of conductive yarns and fabric structures is necessary to validate the general applicability of these findings.
The increased resistance is attributed to the loose structure, air gaps, and poor fiber-to-fiber contact caused by surface irregularities, which hinder the flow of electric current. Conversely, smoother surfaces (lower sRa and sRq) exhibit lower resistance, as they provide better contact between conductive fibers and more uniform current flow. The anisotropy coefficient (D%), which measures the directional dependence of electrical properties, shows extensive negative correlations with surface roughness parameters. For example, sRa and D%M have a correlation coefficient of −0.9835, and sRq and D%M show a correlation of −0.9670. This means that increasing roughness leads to decreasing anisotropy. Rougher surfaces introduce less variability in current flow, reducing the directional dependence of electrical properties. In contrast, smoother surfaces (lower sRa and sRq) exhibit higher anisotropy, as they allow for a more uniform and directional flow of electric current. Correlation analysis revealed that sRmax25 significantly affects electrical resistance only under the S electrode arrangement, while other surface parameters, such as Rm M and D%, show no notable impact in either configuration. These findings suggest that sRmax25, due to its shorter scan length and localized measurement scope, is less sensitive to surface anisotropy and more relevant for small-scale resistance measurements. The study underscores the importance of targeted surface analysis in predicting the electrical performance of textile-based conductors.
The electrode arrangement was changed from
M to
S, reducing the surface area of the fabrics. This adjustment resulted in less roughness due to smaller irregularities, while the number of warp and weft yarns, their interlacing, and the looseness of the threads were also reduced. This narrowing of the fabric’s structure impacted the electrical resistance (
Rm). This was due to fewer threads and thread contacts, which maintained the fabric’s smoothness and allowed for a uniform flow of electric current across the surface of the fabric. The fabric’s surface area increased, allowing for the growth of rough surface deviations. This led to a high value of the electrical anisotropy coefficient
D% of the fabrics. Plain-weave fabrics are constructed in a textile weave where warp and weft threads are interlaced in a crisscross pattern, resembling the deviation structure to create surface irregularity that can affect the current flow. The Mann–Whitney U (M-W.U) test in
Table 6 was used to compare two groups of the electrode arrangement
M-
S to the electrical resistance
Rm and anisotropy coefficient
D%. To test the null hypothesis, a
p-value < 0.05 was adopted for significant differences in the electrode arrangement and electrical properties.
The Mann–Whitney U test examines the statistical significance of electrode arrangement
M-
S to the electrical resistance (
Rm) across the five conductive fabrics. In the case of W19 and W21, the highest
Z statistics were demonstrated (3.310 and 3.308, respectively). This was also shown by highly significant results, with
p-values far below the standard threshold of 0.05. In contrast, samples W25 and W27 exhibit weaker statistical significance, with effect sizes and
p-values reflecting less pronounced differences. The key fabric parameters, which are presented in
Table 6, namely weft density, mass per unit area, and fabric thickness, significantly influence electrical resistance (
Rm) and anisotropic properties (
D%). A significant difference was observed in the
Rm values of W19, W21, and W23, indicating that the electrode arrangement (
M-
S) influenced the resistance values of the respective samples. Their relationship with the electrical resistance between samples was also examined in the
r-Pearson correlation analysis. The significant correlation coefficients and their significance level are marked in bold and presented in
Table 7. The two groups of electrode arrangements are represented in
M and
S in the box plot graph (
Figure 13 and
Figure 14). The greater spread in group
M indicates that the electrical resistance within this group is more diverse than in group
S.
The electrical resistance in the sample in
Figure 13a, i.e., W19, with
M to
S arrangement, was characterized by higher variability (reduced by 27.12%) due to the availability of air and looseness of the yarns connected to the low weft density in the
M electrode arrangement, as shown in
Figure 13a. In the case of
Figure 13b, i.e., W21, there is less variability in
Rm for the
M-
S configuration, indicating more consistent and fewer paths for current flow. This trend continued to the denser fabrics, suggesting that the increase in the number of threads and their contact points significantly influences the rising trends of current flow over the fabric surface.
In sample W23 (
Figure 14), a noticeable trend is demonstrated with respect to changes in the fabrics under the four-electrode arrangement from
M to
S. This trend continues in W23, where Rm increases alongside fabric density; as illustrated in
Figure 14, the resistance variability between the two electrodes is reduced by 26.89%. Additionally, fabrics with smaller widths within the four-electrode configuration exhibit reduced electrical resistance and anisotropy coefficient, as discussed previously in
Figure 12a,d. The high weft density fabrics shown in
Figure 15a,b (W25 and W27) exhibit significant electrical resistance; however, no significant variation is observed as a result of the electrode arrangement under the four-electrode (
M-
S) arrangements. This suggests that increasing fabric density may enhance the stability of electrical resistance due to dimensional consistency under defined electrode contact. Nevertheless, the imbalance between warp and weft densities, along with the electrical anisotropy, should be considered as influencing factors in further analysis. The influencing factors of the variability of electrical resistance and anisotropy are discussed in
Table 7.
The variables (WaD), (WeD), (SM), and (Th) represent the warp (WaD) and weft (WeD) densities in threads/cm, surface mass (SM) in g·m−2, and fabric thickness (Th) in mm, respectively. Rm for both M and S indicates the resistance values in mΩ, while D% denotes the coefficient of electrical anisotropy and is expressed in %.
The
r-Pearson correlation matrix (
Table 7) examines the relationships between key parameters, including weft density (
WeD), surface mass (
SM), thickness (
Th), electrical anisotropy coefficient (
D%), and electrical resistance (
Rm). The analysis reveals that weft density (
WeD) is a key parameter influencing changes in electrical resistance and anisotropy (
D%). However, in the case of
Rm S, the magnitude of electrical resistance is less affected by variations in physical parameters. The warp density (
WaD) does not significantly influence electrical resistance in the determined electrode configuration (
M-
S). In contrast, surface mass (
SM) and weft density (
WeD) are positively related to electrical anisotropy (
D%) in both independent electrode arrangements (
M and
S). Notably,
WeD,
SM,
Th,
D%M, and
D%S exhibit strong positive correlations (
r > 0.75), indicating a high degree of interdependence. The governing factor of weft densities influenced other parameters, such as surface mass and fabric thickness, which in turn affected the anisotropic properties of electrical resistance. On the other hand,
Rm M shows strong negative correlations with
WeD,
SM,
Th,
D%M, and
D%S (
r < −0.75), highlighting a significant inverse relationship. These findings provide insights into the influence of
WeD,
SM, and
Th on electrical resistance across the two electrode arrangements (
M and
S). The linear regression analysis between key parameters and their impacts on
Rm and
D% is illustrated in
Figure 16 and
Figure 17, demonstrating how well the data points fit the linear model and indicating the proportion of the variation in the physical parameters explained by the independent variables in
Table 8.
The values of the linear relationship
r2 indicate that the linear model effectively explains both the electrical resistance and its variability based on key parameters (
WeD,
SM, and
Th). All variables exhibit strong linear relationships (
r2 > 0.84), with higher values (closer to 1) suggesting a better fit. The best fits are observed for surface mass and fabric thickness. Notably, fabric thickness shows a strong correlation with electrical anisotropy
D%. Fabric thickness shows the strongest correlation with electrical anisotropy under the
S electrode arrangement (
r2 = 0.9993). This is linked to the production of fabrics with manageable surface irregularities, which play a key role in directional resistance, even within a reduced area of the fabrics limited by four electrodes. The governing factor that greatly affected the electrical resistance was the surface mass of the woven fabrics, i.e.,
r2 = 0.8713, followed by the weft density of the woven samples. All
p-values were statistically significant (
p-value < 0.05), confirming the validity of the observed linear relationships. The most decisive significance is observed for fabric thickness with the anisotropy coefficient, which is the significant level (
p-value = 0.000). The linear relationship and the directions between the electrical properties (
Rm and
D%) and the independent fabric parameters are presented in
Figure 16 and
Figure 17.
In the linear relationship analysis between the electrical resistance and weft density shown in
Figure 16a, higher weft density results in a more compact fabric structure with increased conductive paths on the surface and fewer air gaps between yarns. The electrical resistance decreases as the number of conductive yarns increases from 20.5 threads/cm to 27.6 threads/cm due to the enhanced conductive pathways provided by the additional silver-plated material (yarns), facilitating more efficient current flow throughout the fabric. The observed changes are mainly due to variations in weft density, while warp density remains nearly constant, as shown in
Table 1. Increasing the weft density creates structural differences between the warp and weft yarns, which alter the fabric’s electrical properties. Linear regression analysis shows that higher weft density is associated with an increase in the anisotropy coefficient (
D%), highlighting the fabric’s anisotropic structure. This is because the availability of higher weft threads, without a corresponding rise in warp threads, increases the directional dependence of electrical resistance, as shown in
Figure 16b. In denser regions, the conductive area expands, and the resistive path length shortens, resulting in lower electrical resistance. This is due to the increased contact points and conductive pathways, allowing for smoother current flow. Similar to the effect of weft density, the surface mass (
SM) of the fabric significantly influences the electrical parameters
Rm and
D% (
Figure 17a,b). An increase in
SM enhances electrical conductivity by providing more pathways for charge transport. Moreover, higher
SM leads to an increase in the anisotropy coefficient (
D%) due to the preferential alignment of conductive paths along the fabric’s length. This alignment lowers resistance along the lengthwise direction compared to the perpendicular (width) direction, inducing directional dependence in the fabric’s electrical properties.
The increase in anisotropy is a consequence of uneven fiber orientation and material distribution across the surface. Fabric thickness also plays a significant role in influencing electrical resistance, as it is closely related to surface variability and irregularities. The sample W27 is thicker (0.29 mm) than W19 (0.22 mm); it exhibits lower surface roughness (as indicated by lower sRa and sRq values) and a reduced electrical resistance (26.422 mΩ compared to 31.114 mΩ for W19). This apparent contradiction highlights that fabric thickness alone does not dictate surface roughness or electrical resistance. Instead, microstructural factors—such as weft yarn density, the degree of yarn alignment, and the continuity of conductive paths—play a more dominant role. In the case of W27, the higher weft density leads to an increased number of conductive elements per unit area and improved yarn alignment, contributing to both a smoother surface and enhanced conductivity. W27 incorporates more conductive yarns than W19, which enhances the formation of continuous electrical pathways and thus reduces resistance. Therefore, this study’s observed trends are specific to the tested configurations and yarns. It is important to emphasize that these outcomes may vary depending on the type of yarn, the coating material, and the weave structure. Further investigation across different fabric systems is required to generalize these findings.
In this study, the fabrics constructed with silver-plated polyamide yarns, such as sample W27, were observed to have greater surface mass and thickness than sample W19; however, W27 exhibits lower surface roughness (s
Ra and s
Rq) and reduced electrical resistance. This suggests that, within this specific textile material, microstructural characteristics—particularly weft yarn density (
Figure 16a)—play a more decisive role in determining electrical performance. The higher weft density in W27 enhances the fiber integrity and continuity of conductive pathways, resulting in a smoother surface and improved conductivity. While prior studies have established that yarn density and alignment influence conductive textile performance [
45,
52], the results in this study reveal material-specific thresholds and surface profile mechanisms. In comparing samples W19 and W27, a notable reduction in surface roughness (
Ra) was observed, decreasing from 0.051 mm in W19 to 0.027 mm in W27 (
Table 1), representing a 47% decrease. Correspondingly, the mean electrical resistance (
Rm) decreased from 31.11 Ω in W19 to 26.42 Ω in W27 (
Table 4), indicating a 15% reduction. Additionally, the anisotropy coefficient (
D%) increased significantly from 0.6% in W19 to 29.9% in W27. These findings suggest that the smoother surface topology in W27, as evidenced by the lower
Ra value, contributes to enhanced electrical conductivity, likely due to improved contact between conductive elements and reduced electron scattering. The substantial increase in
D% indicates a higher degree of directional dependence in electrical resistance, which may be attributed to the specific alignment and distribution of conductive yarns in W27. This anisotropy underscores the importance of microstructural characteristics, such as yarn orientation and density, in influencing the electrical properties of conductive textiles. The angular distribution of material orientations—categorized explicitly into three primary directions: 0°/180° (warp) straight, 90°/270° (weft), and 45°/135°/225°/315° (bias)—significantly influences the electrical resistance (
Rm) and anisotropy coefficient (
D%) of woven conductive fabrics. The measurements, detailed in
Table 2 and
Table 3, reveal that resistance values vary with the direction of current flow relative to the fabric’s structural orientation. Notably, samples exhibit lower resistance along the weft direction (0°/180°) compared to the weft and bias directions, indicating anisotropic conductive behavior. These findings are consistent with previous studies that have reported directional dependence of electrical resistance in textile materials. The observed variations underscore the importance of considering fabric orientation in the design and application of electro-conductive textiles, particularly for devices where directional conductivity is critical.
Overall, the comparative analysis between W19 and W27 highlights the critical role of surface morphology and internal fabric structure in determining the electrical performance of conductive textiles. These insights emphasize the need for precise control over fabric construction parameters to optimize conductivity for specific applications. It is important to note that these observations are specific to the silver-plated polyamide yarns utilized in this study. Other conductive textile technologies, such as surface-coated fabrics or those incorporating blended conductive fibers, may exhibit different relationships between structural parameters and electrical resistance due to their distinct material compositions and fabrication methods. Therefore, for each conductive textile technology, it is essential to conduct comprehensive evaluations using appropriate methodologies to accurately assess their electrical properties. These findings underscore the importance of focusing on internal architectural features to accurately assess and optimize the electrical properties of woven conductive fabrics, especially for sensitive electronic textile applications.
Although the detailed behavior of electric current penetration in textile materials warrants further investigation using advanced methods such as the Van der Pauw (VdP) technique, it is generally recognized that fabrics with higher surface mass enhance the free path for the flow of electric currents in the fabric structures. In anisotropic woven structures, variations in surface mass often correlate with microstructural inconsistencies, such as differential fiber integration and contact quality between conductive yarns, which are directly linked to the surface roughness parameters (e.g.,
sRa, sRq, and
sRz25) presented in
Table 2. The peaks and valleys quantified by these roughness metrics reflect irregularity of vertical compactness and uneven topography, both of which modulate electrical resistance by increasing the effective path length for current flow. In the den’s fabrics, this irregularity contributes to current scattering and deviation from ideal conductive paths, thus enhancing the anisotropic behavior. Additionally, in the loose fabrics, increased air entrapment between yarns—common in samples that are rougher and have less mass, such as W19 to W23—introduces insulating zones that further disrupt conductivity. Given the structural anisotropy and inherent heterogeneity of textile materials, conventional methods such as the VdP technique alone are insufficient to characterize electrical behavior fully. To address these limitations, this study adopted an integrated methodological framework combining the Van der Pauw technique, four-point probe electrical measurements, and three-dimensional surface profilometry to comprehensively characterize the electrical and topographical properties of the conductive fabrics.
This hybrid framework enabled a more robust analysis of directional conductivity and facilitated improved interpretation of complex current distributions in textiles with non-uniform geometries.
The angular distribution of surface features plays a key role in determining the directional dependency of electrical resistance, as shown in
Table 3. Samples with a more uniform angular distribution, such as W19 and W21, display lower anisotropy (
D%). In contrast, samples with irregular distributions, like W25 and W27, exhibit higher anisotropy. Additionally, the anisotropy coefficient (
D%) tends to increase with fabric thickness. This is because thicker fabrics have greater directional variations in yarn distribution and structural compactness along the warp and weft directions. The findings from the analysis of electrical resistance, anisotropic properties, and surface characteristics provide a comprehensive understanding of how fabric structure and surface morphology influence electrical behavior. These results highlight the critical role of surface roughness, yarn orientation, and fabric density in determining the ease of current flow and the directional dependency of electrical resistance. In terms of usability, the observed reduction in electrical resistance could significantly impact applications where electrical performance is critical, such as flexible electronics, sensors, and other conductive textile applications. Although the reduction is relatively modest (13–15%), it may still lead to improved overall performance, particularly in terms of enhanced signal transmission and reduced power loss, which are valuable in high-performance environments. Moreover, the anisotropic properties observed in W27, while contributing to increased variability in electrical resistance, may influence its suitability in applications requiring highly uniform resistance. For example, in medical applications such as heart rate or respiratory monitoring, precise and reliable data transmission is essential. In such cases, the increased resistance variability in W27 could limit its effectiveness, and W19 may be a more appropriate choice due to its stable and isotropic electrical properties, which provide greater consistency in performance. From a cost–benefit perspective, the fabrication process for W27 involves additional costs. These include increased material usage (e.g., more weft threads), higher energy consumption, and longer production times associated with tighter fabrics. As a result, W27 could be more expensive compared to W19. For applications where extreme precision or low electrical resistance is not crucial, the 13–15% reduction in resistance may not justify the additional cost, especially in general textile applications where electrical properties are less critical. Based on these findings, the subsequent discussion examines how these factors influence the anisotropic behavior and overall performance of conductive woven fabrics. By examining the interplay between structural parameters and electrical properties, this study offers a foundation for optimizing fabric design for advanced applications in smart textiles and wearable electronics.