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. 2026 Sep 29. Online ahead of print. doi: 10.1039/d6sc05819a

Cu–S bonding regulates polarization loss in ordered Cu-PEDOT networks under an electromagnetic field

Qinglin Zhou a,b, Daohu Sheng a,b, Hao Wang c, Songmao Han c, Lanxin Wang a, Siyao Cheng a,✉, Wei Dong b, Aming Xie a,✉
PMCID: PMC13636764  PMID: 42835673

Abstract

Conductive polymers have emerged as promising lightweight electromagnetic wave (EMW) absorbers because of their low density, high electrical conductivity, and facile synthesis. However, their intrinsically disordered chain packing and excessive charge transport remain key obstacles to polarization loss regulation and impedance matching optimization. Consequently, simultaneously regulating polarization loss and impedance matching remains a central challenge in conductive-polymer-based EMW absorbers. Here, we develop an interchain coordination strategy to construct a layered Cu-PEDOT coordination polymer network (PEDOT = poly(3,4-ethylenedioxythiophene)), in which Cu–S bonding serves as a molecular handle to regulate polarization loss under an electromagnetic field. Thanks to the tunable Cu–S bonding density, such a platform allows the systematic modulation of the local electronic structure, charge transport behavior, and density of polarization centers. Density functional theory calculations reveal coordination-induced charge redistribution and local electronic asymmetry around the Cu2+ sites. Electron paramagnetic resonance analysis further confirms bonding-density-dependent evolution of polaronic states. Together with the ordered layered architecture and abundant interlayer interfaces, these coordination-regulated electronic features strengthen polarization relaxation while maintaining favorable impedance matching. The optimized Cu-PEDOT-2 achieves a minimum reflection loss of −69.53 dB at 2.5 mm and an effective absorption bandwidth of 6.00 GHz. Overall, this study establishes interchain coordination as a powerful molecular design strategy for balancing charge transport and polarization loss in conductive polymers, providing a rational route toward lightweight high-performance EMW absorbers.

Interchain Cu–S coordination forms ordered layered PEDOT networks and regulates charge transport, polaronic states, and polarization loss. Cu-PEDOT-2 delivers −69.53 dB reflection loss and a 6.00 GHz effective absorption bandwidth at 2.5 mm.graphic file with name d6sc05819a-ga.webp

1. Introduction

Electromagnetic (EM) pollution has become an increasingly pressing concern with the rapid development of high-frequency communication technologies, intelligent electronics, and densely integrated devices.1,2 Lightweight electromagnetic-wave absorbers with strong attenuation capability and broad absorption bandwidth are therefore urgently required to suppress undesirable electromagnetic interference and maintain reliable device operation. Among various dielectric absorbers, conductive polymers have attracted considerable attention owing to their low density, high electrical conductivity and facile synthesis.3–5 As a representative conductive polymer, poly(3,4-ethylenedioxythiophene) (PEDOT) has been widely used to enhance conduction loss in EMW absorption systems.6,7 Nevertheless, despite polarization loss being a critical component of dielectric loss, strategies for regulating polarization loss of PEDOT remain underexplored.8,9 In conventional PEDOT, polarization centers originating from defects, impurities, trap states, and localized electronic states are generally structurally disordered and spatially ill-defined.10 Previous studies have attempted to tailor the dielectric response of conductive polymers through defect engineering, heterogeneous-interface construction, and compositional hybridization. These strategies can introduce additional polarization sites, modify charge-transfer pathways, and enhance electromagnetic energy dissipation.9,11,12 However, polarization centers generated by structural disorder or heterogeneous interfaces are often spatially inhomogeneous and difficult to regulate at the molecular level. Therefore, developing structurally well-defined and continuously tunable polarization centers while preserving appropriate charge-transport characteristics is essential for establishing clear structure–polarization–absorption relationships.

Metal ion coordination provides a controllable route to tailor the density and strength of polarization sources.13,14 Recent studies on conductive metal–organic frameworks (c-MOFs) have shown that metal–ligand bonding is critical for regulating charge transfer.15–17 Unlike c-MOFs, in which rigid molecular ligands assemble into periodic coordination networks, conductive polymers feature coordination sites distributed along a flexible long-chain. The intrinsic flexibility of polymer chains, together with chain entanglement, segmental-orientation variations, and conformational distortion, precludes strictly periodic metal–polymer coordination with well-defined distances and angles. Consequently, metal–polymer coordination typically results in localized coordination motifs or short-range order, instead of periodic networks. The realization of crystalline coordination between metal centers and conductive polymers would provide an opportunity to combine the high electrical conductivity with the well-defined coordination environments and programmable charge-transfer pathways.18

Herein, we introduce an interchain coordination strategy that enables molecular-level regulation of polarization loss in PEDOT-based absorbers by tuning the Cu–S coordination density through the amount of Cu precursor used during oxidative polymerization. Unlike conventional PEDOT synthesis, where oxidants mainly serve to initiate EDOT polymerization, the Cu-PEDOT strategy utilizes Cu2+ as a multifunctional species that simultaneously drives oxidative polymerization and establishes Cu–S coordination with thiophene sulfur atoms during chain growth. The interchain coordination between Cu2+ ions and sulfur atoms serves as a molecular handle to direct the ordered assembly of PEDOT chains into a layered structure. Given the strong coupling between the π-electron cloud and the conjugated polymer backbone, charges introduced through Cu2+ coordination induce local structural relaxation. Meanwhile, d–p orbital hybridization at Cu–S coordination sites further perturbs the local electronic environment of the PEDOT backbone and promotes charge redistribution. Such coordination-induced electronic redistribution facilitates the formation of polaronic/bipolaronic states and reshapes charge-transport pathways by regulating carrier localization within the conjugated polymer network. The tunable Cu–S coordination density further enables systematic regulation of the local electronic structure, charge-transport behavior, and spatial distribution of polarization centers within the conjugated polymer network. By combining structural and spectroscopic characterization, electromagnetic measurements, electron paramagnetic resonance analysis, and density functional theory calculations, we elucidate the relationship among Cu–S coordination, local electronic structure, polaronic state evolution, polarization relaxation, and electromagnetic wave attenuation. The optimized Cu-PEDOT-2 absorber achieves a minimum reflection loss of −69.53 dB at a matching thickness of 2.5 mm and an effective absorption bandwidth of 6.00 GHz. Overall, this study establishes Cu–S coordination as an effective molecular handle for regulating polarization loss in conductive polymer absorbers, thereby providing an interchain coordination strategy for the rational design of lightweight, high-performance microwave absorbers.

2. Results and discussion

2.1. Construction of an ordered Cu-PEDOT network via Cu–S bonding

Conventionally, PEDOT is synthesized through oxidative polymerization of EDOT using external oxidants, where the resulting polymer chains are mainly governed by oxidative doping and chain-growth processes. In contrast, the Cu-PEDOT system developed herein utilizes mildly oxidizing Cu2+ ions as dual-function species, serving both as oxidants to initiate EDOT polymerization and as coordination nodes to link thiophene sulfur atoms.19 This reaction pathway enables Cu–S coordination to proceed concurrently with polymer growth, thereby circumventing the inherent challenge of anchoring metal ions onto insoluble PEDOT chains. Consequently, the PEDOT chains assemble into an ordered layered coordination network rather than disordered aggregates (Fig. 1a). By varying the molar ratio of the copper precursor to EDOT, a series of Cu-PEDOT samples with systematically tuned Cu–S coordination-site densities were synthesized and designated as Cu-PEDOT-1, Cu-PEDOT-1.5, and Cu-PEDOT-2, thereby enabling molecular-level regulation of dielectric polarization behavior.

Fig. 1. Schematic illustration of the Cu-PEDOT system (a). PXRD patterns of Cu-PEDOT and PEDOT (b). Cu K-edge XANES spectrum (c) and R-space fitting of the Cu K-edge EXAFS spectrum (d) for Cu-PEDOT-2. TEM image and corresponding EDS mapping images of C, O, S and Cu of Cu-PEDOT-2 (e). Elemental content of the samples (f).

Fig. 1

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The coordination-induced structure was examined by powder X-ray diffraction (PXRD). As shown in Fig. 1b, Cu-PEDOT-2 exhibits three pronounced peaks at 16.09°, 32.17°, and 39.58°, together with the characteristic diffraction feature of PEDOT at 25.52°. The nearly periodic peaks suggest the formation of a layered network, and the peak at 2θ = 16.09° corresponds to an interlayer spacing of approximately 5.5 Å.20 From Cu-PEDOT-1 to Cu-PEDOT-2, the characteristic diffraction peaks become stronger and better resolved, suggesting that increasing the Cu precursor dosage promotes the formation of a more ordered layered structure. It should be noted that PXRD primarily provides evidence for the formation of a crystalline lattice and enhanced structural order, whereas the increase in the Cu–S bonding density is corroborated by the spectroscopic analyses presented below.

The local coordination environment of Cu2+ in Cu-PEDOT was further probed by X-ray absorption fine structure (XAFS) spectroscopy (Fig. 1c and S10). In the Fourier-transformed EXAFS spectrum, Cu-PEDOT shows a dominant first-shell peak at an apparent radial distance of approximately 1.48 Å, which is clearly different from the Cu–Cu scattering in Cu foil and the Cu–O scattering in Cu oxides. No discernible Cu–Cu scattering contribution was observed, indicating the absence of metallic Cu clusters or extended Cu-containing crystalline domains.21 Quantitative EXAFS fitting based on a CuS-derived coordination model identifies Cu–S scattering as the dominant contribution to the first coordination shell, with an average coordination number of 2.4 and an average Cu–S interatomic distance of 2.13 Å (Fig. 1d and Table S1). These results demonstrate that the Cu species are predominantly stabilized as sulfur-coordinated centers, providing direct structural evidence for Cu–S bonding rather than the presence of physically admixed metallic Cu particles or Cu oxide phases.

Morphological evolution provides further insight into the coordination-mediated organization of the polymer network. Pristine PEDOT exhibits irregular aggregates composed of disordered and wrinkled sheet-like structures with curled and interwoven edges (Fig. S1). Upon Cu2+ coordination, Cu-PEDOT-1 and Cu-PEDOT-1.5 exhibit more continuous polymer networks containing interconnected quasi-spherical or short rod-like polymeric domains, together with a more homogeneous spatial distribution. As the Cu2+ content is increased further, Cu-PEDOT-2 develops a more compact and uniform polymer network with progressively less distinct boundaries between neighboring polymeric domains. This morphological evolution is consistent with strengthened interchain interactions and the formation of a more integrated polymer network. HRTEM images further reveal enhanced local structural regularity in the Cu-coordinated samples (Fig. 1e, S2 and S3). Well-resolved lattice fringes with spacings of approximately 0.55 and 0.221 nm are observed (Fig. S4), consistent with the diffraction features at 16.09° and 39.58°, respectively. Collectively, these observations support the formation of crystalline domains within the layered Cu-PEDOT network.

Energy-dispersive X-ray spectroscopy (EDS) elemental mapping reveals homogeneous spatial distributions of Cu and S throughout the Cu-PEDOT samples, with no discernible Cu-rich regions or elemental segregation (Fig. 1e and S5). The Cu/S atomic ratios estimated from the EDS data are 1 : 2.00, 1 : 1.55, and 1 : 1.17 for Cu-PEDOT-1, Cu-PEDOT-1.5, and Cu-PEDOT-2, respectively, consistent with the intended Cu incorporation (Fig. S6). Bulk compositional analysis by inductively coupled plasma mass spectrometry (ICP-MS) yields corresponding Cu/S atomic ratios of 1 : 2.10, 1 : 1.70, and 1 : 1.00, respectively (Fig. 1f), further corroborating the systematic increase in Cu content across the series. The close agreement between the local EDS-derived and bulk ICP-MS-derived compositions demonstrates that Cu incorporation can be systematically controlled by varying the Cu precursor dosage, providing a compositional basis for tuning the density of Cu–S coordination sites.

X-ray Photoelectron Spectroscopy (XPS) and Fourier Transform Infrared (FTIR) Spectroscopy analyses further confirm the chemical coupling between Cu species and the PEDOT backbone. In the S 2p XPS spectrum, Cu-PEDOT exhibits the characteristic spin–orbit doublet at 165.10 and 163.93 eV, assigned to S 2p1/2 and S 2p3/2 of thiophene sulfur, respectively (Fig. S8). More importantly, a new component appears at 161.71 eV after Cu incorporation, which is attributed to Cu–S bonding (Fig. 2a).22 This low-bonding-energy sulfur species indicates coordination between Cu ions and thiophene sulfur atoms, consistent with the EXAFS results. FTIR spectra of all samples retain the characteristic vibrational features of PEDOT (Fig. 2e), confirming that the conjugated polymer chain is preserved after coordination.23 Notably, the C–S–C-related vibration at 824 cm−1 gradually shifts to lower wavenumbers with increasing Cu2+ content, reaching the largest shift in Cu-PEDOT-2. This red shift can be attributed to the participation of sulfur lone-pair electrons in Cu–S coordination, which redistributes the local electron density around the C–S bond and weakens the corresponding bond force constant.24 Therefore, the progressive red shift provides spectroscopic evidence for strengthened Cu–S coordination and coordination-mediated electronic coupling.

Fig. 2. S 2p spectra of Cu-PEDOT and PEDOT (a). Schematic of the coordination strategy for “mounting” metal atoms onto the thiophene S of PEDOT (b). Calculated PDOS for the d orbital of Cu-PEDOT (c). Electron localization function of PEDOT (i) and Cu-PEDOT (ii) (d). The FTIR spectra of Cu-PEDOT and PEDOT (e). Diffuse reflectance UV-vis-NIR spectra of Cu-PEDOT and PEDOT (f). EPR spectra of Cu-PEDOT (g). The Nyquist plots of Cu-PEDOT and PEDOT (h). Cole–Cole plots of Cu-PEDOT-1 (i), Cu-PEDOT-1.5 (ii), and Cu-PEDOT-2 (iii) (i). Schematic representation of polarons and bipolarons (j).

Fig. 2

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The high-wavenumber region of the FTIR spectra provides additional information on the local chemical environments of the Cu-PEDOT samples. Cu-PEDOT-1 displays obvious C–H stretching bands at 2874, 2984, and 3118 cm−1, which can be associated with C–H-containing terminal or residual EDOT-related species. In comparison, these features are markedly weakened in Cu-PEDOT-1.5 and Cu-PEDOT-2, indicating a reduced contribution from these C–H-containing environments as the Cu precursor content increases.25 They are considered complementary evidence for the evolution of the local chemical environment accompanying the formation of the Cu-PEDOT coordination network. Raman spectroscopy further supports this conclusion. Cu-PEDOT retains the main Raman fingerprint of PEDOT, including the intense band at 1436 cm−1 and shoulder bands at 1504 and 1554 cm−1, which are assigned to the symmetric and asymmetric Cα = Cβ stretching vibrations of the PEDOT backbone (Fig. S11).26 Compared with pristine PEDOT, the coordinated samples exhibit subtle peak shifts and line-shape variations, indicating that Cu incorporation perturbs the local electronic structure of the conjugated backbone without destroying the PEDOT framework.27 Together with PXRD, XAFS, XPS, and FTIR results, Raman analysis confirms that Cu is incorporated mainly through coordination with sulfur sites rather than through the formation of separate copper oxide or metallic copper phases.

The influence of Cu–S coordination on the electronic structure was further elucidated by first-principles calculations. The calculated projected density of states (PDOS) reveals substantial overlap between the Cu 3d and S 3p states, indicating strong d–p orbital hybridization. As the Cu–S bonding density increases, the Cu-derived electronic states shift closer to the Fermi level, consistent with enhanced electronic coupling between the Cu 3d orbitals and the S 3p orbitals (Fig. 2c and S14).28 Such orbital hybridization facilitates charge redistribution around the Cu–S coordination sites and perturbs the local electronic environment of the PEDOT backbone. Meanwhile, the coordination-induced charge transfer strongly coupled with the conjugated π-electron system drives local structural relaxation. Electron localization function (ELF) analysis further reveals pronounced electron-density distortion and localized electronic domains near the Cu-PEDOT coordination sites, in sharp contrast to the more uniform electronic distribution in pristine PEDOT (Fig. 2d and S15).29,30 These results demonstrate that Cu–S coordination produces localized electronic heterogeneity and charge asymmetry around the coordination sites. Under an alternating electromagnetic field, these charge-asymmetric regions provide a structurally defined basis for field-induced polarization and subsequent dielectric relaxation.31

Thermogravimetric analysis further reveals that the Cu-PEDOT series exhibits improved thermal robustness compared with pristine PEDOT, as reflected by the increased decomposition temperature and higher residual mass at elevated temperatures (Fig. S12). This improvement can be attributed to the reinforced coordination interactions between Cu species and the PEDOT backbone, together with the presence of Cu-containing residues after thermal treatment.32

2.2. Cu–S bonding regulates polaronic states, charge localization, and dielectric relaxation

The UV-vis-NIR absorption spectra of the Cu-PEDOT samples (Fig. 2f) exhibit the characteristic spectral signatures of PEDOT, including the π–π* transition of neutral PEDOT segments and the near-infrared absorption bands associated with polaronic and bipolaronic states.33 As the [Cu2+]/[EDOT] molar ratio increases, the π–π* absorption band undergoes a progressive red shift from 421 to 502 nm, reflecting coordination-induced modulation of the conjugation length and local electronic environment of the PEDOT backbone.34

Compared with pristine PEDOT, the Cu-PEDOT samples exhibit markedly enhanced polaronic and bipolaronic absorption bands, consistent with an increased doping level. Notably, the polaronic absorption intensity initially increases and then decreases with increasing Cu2+ content, whereas the bipolaronic absorption progressively intensifies. This spectral evolution suggests a coordination-dependent transformation of the dominant charge carriers from neutral segments to polaron-rich states and, at a higher Cu–S bonding density, toward an increased bipolaronic contribution.35

The optical bandgaps were further estimated from Tauc plots (Fig. S16). Pristine PEDOT shows an apparent bandgap of 2.04 eV, whereas Cu-PEDOT-1, Cu-PEDOT-1.5, and Cu-PEDOT-2 exhibit values of 2.35, 2.17, and 2.25 eV, respectively. At low Cu content, the limited degree of polymerization and the spatial isolation of Cu–S coordination sites interrupt the effective conjugation of the PEDOT backbone and favor carrier localization, accounting for the larger apparent optical bandgap of Cu-PEDOT-1.36 At an intermediate Cu–S bonding density, the increased degree of polymerization and higher density of accessible electronic states reduce the average separation between neighboring charge-transport sites and enhance intersegment electronic coupling.37 These effects facilitate short-range charge delocalization across the conjugated domains, resulting in a reduced apparent optical bandgap for Cu-PEDOT-1.5. At a higher coordination density, pronounced local charge accumulation and coordination-induced structural distortion enhance carrier localization and perturb the effective conjugation of the PEDOT backbone. The accompanying increase in the bipolaronic contribution reflects the higher oxidation level and enhanced charge accumulation, while the competing localization and structural-distortion effects lead to a slight increase in the apparent optical bandgap of Cu-PEDOT-2.38 These results reveal that Cu–S coordination regulates not only the oxidation state of PEDOT but also the localization and relaxation characteristics of charge carriers.39

Zeta-potential analysis further supports the coordination-induced reconstruction of the surface charge environment (Fig. S13). Pristine PEDOT exhibits a positive zeta potential of +4.28 mV, whereas Cu-PEDOT-1 displays a negative value of −0.975 mV. As the Cu–S bonding density increases, the zeta potential shifts toward more negative values, reaching −12.9 and −17.0 mV for Cu-PEDOT-1.5 and Cu-PEDOT-2, respectively. This sign reversal and gradual negative shift indicate that Cu–S coordination substantially changes the surface chemical environment of PEDOT. The negatively shifted zeta potential is consistent with coordination-induced charge redistribution, enhanced counterion retention, and increased surface polarity in the ordered Cu-PEDOT framework.40 Although the zeta potential alone cannot directly quantify the internal carrier distribution, it provides useful evidence that Cu incorporation alters the electrostatic environment of the polymer surface.

The electrical conductivity of the Cu-PEDOT series shows a nonmonotonic dependence on Cu2+ coordination, while remaining lower than that of pristine PEDOT (Fig. S22). This behavior indicates that Cu–S coordination does not simply increase the number of carriers but also restricts their long-range transport. Upon Cu–S coordination, the extended π-electron delocalization of PEDOT is partially interrupted by coordination sites, and charge transport shifts from continuous delocalized conduction to hopping-dominated transport involving localized polaronic or bipolaronic states.41 At the low Cu–S bonding density, Cu2+ can increase the carrier concentration through oxidative doping, thereby improving conductivity within the Cu-PEDOT series.42 However, at a higher Cu–S bonding density, the increased population of coordination sites and their associated counterions may generate local electrostatic potential barriers and carrier-trapping sites. The resulting electrostatic disorder impedes carrier transport, thereby reducing carrier mobility despite the increased carrier concentration.43 Hall effect measurements provide additional support for the reduced carrier mobility in Cu-PEDOT-2 (Table S2). Therefore, Cu-PEDOT-1.5 can be identified as the carrier transport-favored composition within the Cu-PEDOT series, whereas the higher Cu–S coordination-site density of Cu-PEDOT-2 promotes carrier trapping and localization. This distinction provides the basis for the different conduction-loss contributions discussed below.

Electron paramagnetic resonance (EPR) spectroscopy provides direct information on EPR-active polaronic species (Fig. 2g and S17). In conducting polymers, polarons usually possess unpaired spins and are EPR-active, whereas bipolarons are spin-paired and generally EPR-silent.44 All Cu-PEDOT samples exhibit a characteristic signal at g = 2.004, which can be assigned mainly to polaronic radical species on the PEDOT backbone. Under identical measurement conditions, Cu-PEDOT-1.5 shows a stronger EPR response than Cu-PEDOT-1, indicating an increased concentration of polaronic states at intermediate Cu–S bonding density.45 In contrast, Cu-PEDOT-2 exhibits a weakened EPR signal, suggesting a reduced amount of EPR-active polarons. This decrease is consistent with the enhanced bipolaronic absorption observed in the UV-vis-NIR spectra, indicating that a higher Cu–S bonding density promotes the transformation of polaronic states into spinless bipolaronic states. Given the intrinsic paramagnetism of Cu2+ species, the EPR response should be interpreted as reflecting a Cu–S-coordination-dependent evolution of the overall spin environment, rather than as an exclusive quantitative probe of PEDOT-derived polarons. Nevertheless, the combined UV-vis-NIR and EPR results provide converging evidence for the Cu–S-banding-mediated evolution of charge-carrier states.

Electrochemical impedance spectroscopy (EIS) further reveals the coordination-density-dependent evolution of interfacial charge-transfer behavior in the Cu-PEDOT series (Fig. 2h).46 The Nyquist plots of the Cu-PEDOT series exhibit distinct semicircular capacitive features, with their apparent diameters following the order of Cu-PEDOT-1 > Cu-PEDOT-2 > Cu-PEDOT-1.5. The smallest semicircle observed for Cu-PEDOT-1.5 indicates that an intermediate Cu–S coordination density facilitates interfacial charge transfer. By contrast, the increased semicircle diameter of Cu-PEDOT-2 may originate from local electrostatic potential fluctuations and carrier-trapping sites introduced at a high coordination density, thereby enhancing carrier localization and restricting long-range carrier transport. These findings are consistent with the trends in electrical conductivity and Hall mobility, as well as with the UV-vis-NIR and EPR results, collectively indicating that Cu–S coordination regulates the interplay between the charge-carrier concentration and localization.

The dielectric relaxation behavior was further evaluated using Cole–Cole plots constructed on the basis of Debye relaxation theory (Fig. 2i).47 The Cu-PEDOT samples exhibit depressed or semicircular arcs accompanied by oblique tails. The semicircular arcs indicate non-Debye relaxation behavior associated with a distribution of relaxation times,48,49 whereas the oblique tails reveal a non-negligible contribution from charge-carrier conduction. Therefore, the Cole–Cole plots qualitatively demonstrate the coexistence of polarization relaxation and conduction loss but do not independently quantify their relative contributions. The characteristic relaxation frequencies of Cu-PEDOT-1, Cu-PEDOT-1.5, and Cu-PEDOT-2 are 11.32, 13.60, and 12.68 GHz, respectively. The corresponding relaxation times, calculated using τ = 1/2πf, are 14.06, 11.70, and 12.55 ps, respectively. The nonmonotonic variation in relaxation time is consistent with the Cu–S-coordination-dependent evolution of the charge states. At an intermediate coordination density, Cu-PEDOT-1.5 possesses abundant polaronic states and an optimal degree of carrier localization, providing dynamically responsive polarization centers and thus the shortest relaxation time. In contrast, the increased bipolaronic contribution and denser coordination sites in Cu-PEDOT-2 enhance local charge accumulation, carrier localization, and carrier–lattice coupling, thereby slowing the polarization response and increasing the relaxation time.50,51 Therefore, Cu–S bonding macroscopically manifests as tunable dielectric relaxation behavior.

2.3. Cu–S bonding regulates polarization loss and microwave absorption performance

The dielectric properties of the Cu-PEDOT series were evaluated over 2–18 GHz to elucidate the role of Cu–S coordination in microwave attenuation. Given the negligible contribution from magnetic loss, electromagnetic attenuation is governed predominantly by dielectric loss (Fig. S19). As shown in Fig. 3a, the real part of the permittivity (ε′) gradually decreases with increasing frequency for all samples, reflecting the typical frequency-dispersion behavior of dielectric materials. The ε′ values follow the order Cu-PEDOT-1.5 > Cu-PEDOT-2 > Cu-PEDOT-1, indicating that the electromagnetic energy-storage ability is modulated by the Cu–S bonding density and the associated evolution of the charge states. Cu-PEDOT-1 possesses the lowest ε′, consistent with its low coordination density and limited population of effective polarization centers.

Fig. 3. Dielectric properties and attenuation ability. The real part (a) and imaginary part (b) of permittivity. Dielectric loss tangent of Cu-PEDOT (c). The fitted mean conduction loss and polarization loss of Cu-PEDOT (d). The polarization loss curves plotted as a function of frequency (e). Calculated hyperpolarizability and polarizability of neutral, polaron, and bipolaron (the illustrations depict the local hyperpolarizability contributions of neutral, polaron, and bipolaron, with red and blue regions representing positive and negative spatial contributions, respectively) (f). 2D RL plots of Cu-PEDOT-1 (i), Cu-PEDOT-1.5 (ii) and Cu-PEDOT-2 (iii) (g). Differential charge density plots of Cu-PEDOT-1 (i), Cu-PEDOT-1.5 (ii) and Cu-PEDOT-2 (iii) (h). The amount of charge transferred from Cu to S, and total absolute change of Cu-PEDOT (i). Absorption efficiency of Cu-PEDOT (j). Comparison of the EMW absorption performance of other metal–organic complex materials (k).

Fig. 3

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By contrast, the highest ε′ of Cu-PEDOT-1.5 may be attributed to its more developed conjugated network, relatively high carrier mobility, and abundant polaronic states, which collectively enhance field-induced charge displacement.52,53 At a higher coordination density, the enhanced contribution from bipolaronic states in Cu-PEDOT-2 promotes local charge accumulation and carrier localization around the coordination sites, limiting the spatial extent of field-induced charge displacement and thereby slightly reducing ε′ relative to Cu-PEDOT-1.5.54–56

The imaginary part of the permittivity (ε″), which characterizes electromagnetic wave energy dissipation, further reveals the Cu–S bonding-dependent loss behavior (Fig. 3b).15 Cu-PEDOT-1.5 shows relatively high ε″ value in the low-frequency region, consistent with its favorable charge transport capability. In the 10–14 GHz range, Cu-PEDOT species display distinct relaxation-associated peaks, with their intensities following the order of Cu-PEDOT-2 > Cu-PEDOT-1.5 > Cu-PEDOT-1. In Cu-PEDOT-2, the dense Cu–S coordination sites and associated counterions promote charge localization, thereby increasing the population and relaxation strength of localized polarization centers. This behavior is also reflected in the dielectric loss tangent (tan δε = ε″/ε′) (Fig. 3c). Cu-PEDOT-2 exhibits a sharp tan δε peak of approximately 0.55 at 13–14 GHz, much higher than those of Cu-PEDOT-1 and Cu-PEDOT-1.5, indicating that its dominant relaxation process falls within the effective microwave energy-dissipation window. The combination of moderate dielectric storage and strong frequency-selective dielectric loss is conducive to balancing impedance matching with attenuation capability (Fig. S23 and S27).57

To distinguish the two major contributions to dielectric loss, the contributions of conductive loss Inline graphic and polarization loss Inline graphic were quantitatively deconvoluted through nonlinear least-squares fitting implemented in Python. Nonlinear least-squares fitting reveals that polarization relaxation makes the dominant contribution to the dielectric loss of the Cu-PEDOT system (Fig. 3d). Across Cu-PEDOT series, Inline graphic progressively increases and reaches its maximum in Cu-PEDOT-2, confirming that the high Cu–S bonding density strengthens relaxation loss associated with localized polarization centers. By contrast, Cu-PEDOT-1.5 shows the largest conduction-loss contribution because of its high carrier mobility and polaron-mediated charge transport. In Cu-PEDOT-2, the conduction-loss component decreases slightly, consistent with its reduced electrical conductivity. This decrease does not suppress the overall dielectric dissipation, because the enhanced polarization loss compensates for the weakened conductive loss.

The polarization-loss curves plotted as a function of frequency further support this interpretation (Fig. 3e).58 The ε″ was analyzed using a modified Debye model, in which ε″ is expressed as the sum of a conduction-loss component Inline graphic and a polarization-relaxation component Inline graphic59

2.3. 1

where the conduction-loss component can be expressed as:

2.3. 2
2.3. 3

All samples exhibit characteristic polarization-loss peaks in the 11–13 GHz range, with the peak intensities following the order of Cu-PEDOT-2 > Cu-PEDOT-1.5 > Cu-PEDOT-1. At intermediate coordination densities, the polaron-mediated high carrier mobility of Cu-PEDOT-1.5 favors charge transport, thereby limiting further enhancement of polarization relaxation. By contrast, the higher Cu–S bonding density and increased bipolaronic contribution in Cu-PEDOT-2 enhance local charge accumulation, carrier localization, and electric-field inhomogeneity, resulting in the strongest Inline graphic peak near 12–13 GHz despite its reduced long-range charge transport. These results indicate that Cu–S bonding converts part of the transport-active charge carriers into localized polarization centers.

The hyperpolarizability-density distributions reveal a pronounced evolution of the field-induced electronic response from the neutral to the charged states (Fig. 3f).15 The neutral state exhibits a weak response largely confined to the conjugated backbone. Polaron formation markedly enhances and extends the hyperpolarizability density along the backbone, indicating strengthened intrachain charge redistribution and electronic asymmetry. In the bipolaronic state, the response becomes more intense but concentrated around the conjugated backbone and heteroatom-rich moieties, consistent with a localized double-charge state. Consistently, hyperpolarizability βxxx increases sharply in the polaronic state and then increases more moderately in the bipolaronic state, while the static polarizability gradually approaches a plateau. These results suggest that polaron formation promotes extended electronic redistribution, whereas further evolution toward the bipolaronic state enhances charge localization and stabilizes deeper localized electronic states, thereby favoring a delayed polarization relaxation rather than synchronous displacement polarization.60

The electromagnetic wave absorption performance was evaluated by reflection loss analysis (Fig. 3g). Cu-PEDOT-1 and Cu-PEDOT-1.5 exhibit moderate absorption performance, with minimum reflection loss (RLmin) values of −19.41 and −23.92 dB and maximum effective absorption bandwidth (EAB) values of 4.08 and 4.28 GHz, respectively. In striking contrast, Cu-PEDOT-2 exhibits substantially enhanced electromagnetic wave absorption performance. At a fixed matching thickness of 2.5 mm, it achieves a minimum reflection loss of −69.53 dB and a maximum effective absorption bandwidth of 6.00 GHz, where the EAB is defined as the continuous frequency range satisfying RL ≤ −10 dB at a single thickness. Moreover, when the absorber thickness is varied from 2.00 to 5.00 mm, the combined frequency intervals satisfying RL ≤ −10 dB provide an overall thickness-tunable absorption-frequency coverage of 13.22 GHz, demonstrating the broad frequency tunability of the ordered Cu-PEDOT absorber (Fig. S26d).

The superior absorption performance of Cu-PEDOT-2 originates from the coordination-induced modulation of its local electronic structure. Charge-density-difference analysis reveals enhanced charge redistribution around the Cu–S coordination sites (Fig. 3h, S20 and S21). Bader charge analysis further shows increasing electron depletion at the Cu centers from Cu-PEDOT-1 to Cu-PEDOT-2 (Fig. 3i). This trend is reflected by the increase in Cu electron loss from 1.836 e− to 2.143 e−, and further to 3.193 e− in Cu-PEDOT-2, indicating strengthened metal–ligand electronic coupling and more pronounced local electric-field gradients. These charge-asymmetric regions serve as molecularly defined polarization centers under microwave fields.61 Meanwhile, the polaron-to-bipolaron evolution promotes charge localization and strengthens polarization loss, shifting the dominant energy-dissipation pathway from delocalized carrier transport to localized polarization relaxation. The moderate decrease in conductivity of Cu-PEDOT-2 improves impedance matching by preventing excessive surface reflection. Therefore, the enhanced polarization loss and optimized impedance matching jointly enable Cu-PEDOT-2 to achieve deep reflection loss, a broad effective absorption bandwidth, and thickness-dependent tunability across the X–Ku band.

The absorption efficiency analysis further confirms the frequency-dependent attenuation behavior of Cu-PEDOT-2 (Fig. 3j).61 At a thickness of 2.5 mm, Cu-PEDOT-2 exhibits high absorption efficiency above 11 GHz. With increasing matching thickness, the high-absorption region shifts toward lower frequencies, consistent with the quarter-wavelength cancellation principle commonly observed in microwave absorbers. Compared with representative conductive polymers, metal–organic composites, and coordination-polymer-based absorbers, Cu-PEDOT-2 exhibits competitive or superior absorption performance in terms of RLmin, EAB, and matching thickness (Fig. 3k). These results indicate that Cu–S coordination provides an effective molecular-level strategy for regulating dielectric polarization loss in conductive polymer absorbers.

To assess the far-field radar-scattering suppression capability under practical conditions, radar cross-section (RCS) simulations were performed using perfect electric conductor (PEC) substrates coated with the corresponding Cu-PEDOT layers. Compared with bare PEC substrates, all Cu-PEDOT coatings suppress radar scattering in the angular range of −90° to 90°, with Cu-PEDOT-2 exhibiting the greatest RCS reduction (Fig. 4a, b and S29–S31). Moreover, Cu-PEDOT-2 retains effective electromagnetic-wave absorption at incidence angles of up to 85°, demonstrating favorable angular robustness under oblique incidence (Fig. 4c).62 Smith-chart analysis further shows that Cu–S coordination shifts the normalized input impedance toward the free-space impedance. Cu-PEDOT-2 exhibits the largest proportion of impedance loci within the effective absorption region, indicating improved impedance matching at the corresponding matching thicknesses (Fig. 4h).63

Fig. 4. RCS simulation of Cu-PEDOT-2 (i) and PEC (ii) (a). RCS values of Cu-PEDOT and PEC (b). EMW absorption performance of Cu-PEDOT-2 at different angles of incidence of EMW (c). Visual representations of the flexible absorbing patch (d): top view and thickness measurement (i); mechanical flexibility demonstrations: press (ii), bend (iii), fold (iv), and adhesion properties (v and vi). Time evolution of the electric field radiation level before and after patch application (e). Application scenario on a communication device (f). The electromagnetic wave absorption mechanism of Cu-PEDOT (g). Smith chart of Cu-PEDOT (h).

Fig. 4

Open in a new tab

Finally, device-level applicability was assessed by embedding Cu-PEDOT in an elastomer matrix to fabricate flexible composite patches that conform closely to device surfaces (Fig. 4d).64 When applied to a chip in a communication device, the Cu-PEDOT patch reduced the radiated electric-field strength from 736.82 to 5.33 V m−1 under identical testing conditions, representing a reduction of more than two orders of magnitude (Fig. 4e and f). These results connect powder-level EMW absorption with practical radiation mitigation and highlight the potential of Cu-PEDOT for flexible electromagnetic-protection components in integrated electronics.

3. Conclusion

In conclusion, this work demonstrates that Cu–S bonding can serve as an effective molecular handle for regulating dielectric polarization loss in an ordered Cu-PEDOT network. Varying the Cu–S coordination-site density systematically modulates the local electronic structure, polaronic state evolution, and the balance between charge transport and localization. Moreover, Cu–S bonding shifts the dominant contribution to dielectric loss from conduction loss toward polarization relaxation, thereby enabling a favorable balance between impedance matching and attenuation capability. As a result, the optimized Cu-PEDOT-2 absorber achieves a minimum reflection loss of −69.53 dB and an effective absorption bandwidth of 6.00 GHz at a matching thickness of 2.5 mm. This work provides an interchain-coordination strategy for the molecular-level design of conductive-polymer microwave absorbers with tunable dielectric responses and well-defined structure–property relationships.

Author contributions

Conceptualization: Siyao Cheng, Aming Xie and Qinglin Zhou. Methodology: Qinglin Zhou and Siyao Cheng. investigation: Qinglin Zhou and Hao Wang (synthesis, structural and spectroscopic characterization, and electrical and electromagnetic measurements); Daohu Sheng (flexible-patch fabrication and performance evaluation). Formal analysis: Qinglin Zhou, Songmao Han and Daohu Sheng. Data curation: Lanxin Wang and Wei Dong. Visualization: Qinglin Zhou. Writing – original draft: Qinglin Zhou. Writing – review & editing: Siyao Cheng and Aming Xie. Supervision: Aming Xie and Wei Dong. Funding acquisition: Siyao Cheng and Aming Xie.

Conflicts of interest

There are no conflicts to declare.

Supplementary Material

SC-OLF-D6SC05819A-s001

Acknowledgments

This work was supported by the National Natural Science Foundation of China (22505266 to S. Y. C. and 52273267 to A. M. X.). We thank Prof. Weijing Li from Nanjing University of Science and Technology for the fruitful discussions and suggestions.

Data availability

The data supporting the findings of this study are available within the article and its supplementary information (SI). Supplementary information: experimental details, supplementary figures and characterization data. See DOI: https://doi.org/10.1039/d6sc05819a.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

SC-OLF-D6SC05819A-s001
SC-OLF-D6SC05819A-s001.pdf (11.8MB, pdf)

Data Availability Statement

The data supporting the findings of this study are available within the article and its supplementary information (SI). Supplementary information: experimental details, supplementary figures and characterization data. See DOI: https://doi.org/10.1039/d6sc05819a.

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