Introduction

Carbon fibers (CFs) are integral to composite matrices owing to their high modulus, stiffness, lower thermal expansion coefficient, and density compared to other materials1,2,3,4,5,6,7. Incorporating CFs into polymeric matrices significantly enhances composite system strength and modulus8,9,10,11. Applied loads are transferred from the fibers to the surrounding matrix, significantly improving mechanical properties, structural integrity, and resistance to wear and environmental factors12,13,14. Optimizing surface treatments for CFs during continuous processing is crucial to further strengthen fiber–matrix bonding15,16,17,18,19,20.

CF-reinforced composites (CFRPs) have garnered considerable attention for applications in aerospace, automotive manufacturing, construction, marine engineering, and energy storage21,22,23,24. However, the low wettability of untreated CFs limits their bonding capabilities, necessitating surface treatments to improve performance and ensure strong adhesion with the matrix material25,26,27,28,29. In industrial practice, anodic treatment is widely employed in continuous processing lines to address this challenge30,31.

Surface energy, originating from molecular interactions at interfaces, is typically defined as half the energy needed to break surface bonds32,33. Unlike other energy forms, surface energy directly reflects the surface characteristics of a material and it is closely linked to properties such as wettability, solubility, and adhesion34,35,36. Given its importance, research has focused on developing new strategies leveraging surface properties as indicators to meet specific requirements, particularly in the surface treatment of CFs and CFRPs, as their increasing utilization in modern industry.

Contact angle (CA) measurement is a widely adopted traditional strategy for investigating the surface wettability of various materials37,38,39. Its principle is based on Young’s equation to observe the angle formed at the gas–liquid–solid interface when a droplet contacts a solid surface40. Although the CA method efficiently and intuitively reveals the surface properties of materials, it poses the challenges of providing a flat plane for CF measurement. Forcibly creating the corresponding plane leads to substrate-induced heterogeneity, covering the inherent properties of the material41.

Regarding other strategies, X-ray photoelectron spectroscopy (XPS) is used to determine elemental composition and bond energies at the surface of the material, both of which are intrinsically related to surface energy42,43,44. Moreover, atomic force microscopy (AFM) and scanning tunneling microscopy (STM) provide intuitive and precise surface roughness assessment45,46,47. However, these techniques have limitations when applied to powdered or fibrous materials. Similar to CA measurement, AFM and STM require a flat, continuous material surface, limiting their applicability to CFs. The necessary pretreatment process for XPS might affect material integrity, resulting in inaccurate surface energy values35.

Contrary to the disadvantages of the methods mentioned above, inverse gas chromatography (IGC), initially proposed by Davis and Peterson in 196648, offers a convenient and rapid analytical alternative for analyzing surface characteristics across various materials49,50. This technique requires no additional surface sample preparation, making it ideal for evaluating surface properties and energy variations regardless of shape in powders, particulates, fibers, and films51,52,53,54,55. Since its inception, IGC has significantly advanced surface analysis and it is generally categorized into two approaches: infinite dilution and finite concentration. While both yield comparable results, the infinite dilution method (IGC-ID) is faster and remains the most widely adopted. By employing gas-phase probes that interact with the most active sites on the surface of materials, IGC-ID effectively enables the quantification of London dispersive forces and specific acid–base interactions, providing a detailed assessment of surface energetics at the microscopic scale56. Additionally, the IGC process allows precise control over sample temperature and relative humidity, avoiding potential environmental influences and ensuring accurate and reliable measurements49. Thus, IGC-ID is a precise and stable method for determining the surface properties of anodized CFs.

As discussed, IGC is a straightforward, sensitive, and versatile technique that utilizes various solvent probes to rapidly identify the most active sites and functional groups on solid surfaces. However, some conventional methods57,58 are widely acknowledged as foundational in determining surface free energy through IGC. For polar materials, such as silica59 and clay35, these approaches can be accessed the determination of the Gibbs free energy of adsorption. Nonetheless, these approaches have increasingly been scrutinized for their inherent limitations, regarding their accuracy in characterizing a broad range of materials, particularly for nonpolar materials such as carbonaceous materials60,61,62. This study aims to systematically investigate the differences in surface free energy between anodically treated CFs and their untreated counterparts, employing the methodology established by Donnet and Park et al.63,64 and modified to combine both London dispersive and specific components of the surface free energy of a solid with the particular consideration of deformation polarizability (α0) of the probes49,50,65,66. Changes in acid–base properties of CFs were analyzed before and after electrochemical treatments by examining specific components of surface free energy at infinite dilution in Henry’s region. The study findings could provide valuable data to support advancements in CF surface treatment technologies to produce high-performance CF materials.

Experimental

Electrochemical treatments

Electrochemical treatments were conducted following the methodology described in a previous study31. The fibers used were ex-PAN type (Toray T-300), with a specific surface area of 0.68 m2 g−1 and linear mass density of 0.198 g m−1. Figure 1 illustrates the oxidation treatment setup, consisting of three main components: a treatment tank (0.475 m in length), washing tank, and a drying system. Oxidation was performed in a sodium hydroxide (NaOH) solution (0.1 N, pH = 13) with a fiber feed rate of 1 m min−1.

Fig. 1
figure 1

Schematic illustration of the oxidation treatment setup, showing the treatment tank, washing tank, and drying system.

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The anode–cathode potential was adjustable between 0.5 and 10 V, with current intensities incrementally set at 0, 10, 30, 90, 300, 600, and 900 mA, corresponding to current densities of 0, 0.16, 0.47, 1.41, 4.69, 9.38, and 14.07 A m−2, respectively.

Inverse gas chromatography

IGC analysis was conducted using a Shimadzu GC-2014 gas chromatograph (Shimadzu Ltd.) equipped with a flame ionization detector. This chromatographic setup was integrated with a Shimadzu data integrator for precise determination of solute retention times by calculating the first-order moment of the chromatographic peak. The chromatographic columns used were constructed from stainless steel, each measuring approximately 0.6 m and 4.4 mm in length and inner diameter, respectively. Prior to sample loading, columns were thoroughly cleaned with a 10% nitric acid solution, and oven dried at 150 °C overnight. Each column was filled with ~6 g of compacted CFs using a metal rod. Helium served as the carrier gas throughout the analysis.

Before taking measurements, the fiber-filled columns were preconditioned by heating to 130 °C under a helium flow condition overnight to remove all volatile impurities, particularly fiber-absorbed water vapor. For IGC analysis, a series of n-alkanes and polar probes with defined acid–base properties were used. To ensure accurate measurements under infinite dilution conditions, injected probe volumes were minimized to prevent lateral interactions between adsorbed molecules. Additionally, methane was used to measure the dead volume of each column in advance, which is assumed to exhibit negligible adsorption on the adsorbent surface.

Results and discussion

Considerations on the acid–base properties of solid surfaces

The surface free energy of a solid typically comprises two key components: the dispersive component, denoted as \({\gamma }_{\rm{{S}}}^{{\rm{L}}}\), reflecting the contribution of London dispersion forces, and the specific (or polar) component,\({\gamma }_{{\rm{S}}}^{{\rm{SP}}}\), accounting for interactions beyond London dispersion forces. While determining \({\gamma }_{{\rm{S}}}^{{\rm{L}}}\) through IGC is relatively straightforward, accurately assessing \({\gamma }_{{\rm{S}}}^{{\rm{SP}}}\) is considerably more challenging. The \({\gamma }_{{\rm{S}}}^{{\rm{SP}}}\) component is influenced by acid–base interactions, as described by Lewis acid–base theory. In this framework, a molecule is classified as acidic if it tends to attract an electronic cloud, even without displacing electron pairs. Quantifying the strength of these acid–base interactions remains challenging, and various semi-empirical scales have been proposed to address this complexity. For instance,

  • Drago’s scale67,68 described the ability of a molecule to form electrostatic bonds based on its dipole moment (u) and covalent bonds linked to its deformation polarizability (α0).

  • Gutmann’s scale69,70 offered a more refined acid–base interaction evaluation by accounting for the amphoteric nature of most molecules.

  • Kamlet–Taft’s scale71,72 focused on solvatochromic parameters, emphasizing acid–base interactions within hydrogen bonding contexts.

Despite the utility of these scales, none provided a completely satisfactory solution. For practical purposes, and owing to the abundance of available data, Park et al.73 adopted Gutmann’s scale, which accounts for the amphoteric nature of solid surfaces. They refined it by replacing the Gibbs free energy change −∆G) with the specific contribution to free adsorption energy (\({-\Delta G}_{{\rm{A}}}^{{{\rm{SP}}}}\)) for amphoteric molecules:

$${-\Delta G}_{{\rm{A}}}^{{{\rm{SP}}}}={({{\rm{AN}}})}_{{\rm{p}}}\cdot {({{\rm{DN}}})}_{{\rm{s}}}+{({{\rm{DN}}})}_{{\rm{p}}}\cdot {({{\rm{AN}}})}_{{\rm{s}}}$$
(1)

where DN and AN represent the electron donor and acceptor numbers, respectively, as defined by Gutmann. The subscripts s and p refer to the solid surface and volatile probe injected into the GC, respectively.

Subsequently, Lindsay et al.25 modified Eq. (1) by applying the Lewis acid–base principle, incorporating the parameters KA (acid) and KD (base), resulting in the following:

$$\frac{{-\Delta G}_{{\rm{A}}}^{{{\rm{SP}}}}}{{AN}}={\rm{K}}_{{\rm{A}}}\cdot \frac{{{{DN}}}}{{{{AN}}}}+{\rm{K}}_{{\rm{D}}}$$
(2)

Study of free adsorption energy (−∆G A)

IGC provides a direct method for determining the standard Gibbs free energy of adsorption (\({-\Delta G}_{{\rm{A}}}^{0}\)) under thermodynamic equilibrium conditions, expressed using the following equation:

$${-\Delta G}_{{\rm{A}}}^{0}={\rm{RT}}{\mathrm{ln}}{Vn}+{C}$$
(3)

where Vn represents the retention volume, R is the universal gas constant, T denotes the absolute temperature, and C is a constant dependent on the specific surface area of the column-filling material (e.g., fibers) and reference state of the adsorbed molecule, typically defined at 0 °C and 1 atm74.

The free adsorption energy (−∆GA), is the sum of the dispersive contribution of London (\({-\Delta G}_{{\rm{A}}}^{{\rm{L}}}\)) and specific contribution (\({-\Delta G}_{{\rm{A}}}^{{{\rm{SP}}}}\)). A method has been proposed49,50 to determine −∆GA based on the deformation polarizability (α0) and dipole moment (μ) of molecular probes at a specified temperature:

$$\left[-\Delta {\rm{G}}_{{\rm{A}}}\right]=\left[{-\Delta G}_{{\rm{A}}}^{{{L}}}\right]+[{-\Delta G}_{{{A}}}^{{{{SP}}}}]$$
(4)
$$\left[-\Delta {{G}}_{{{A}}}\right]={\rm{K}}\cdot {\left({\rm{h}}{{v}}_{{\rm{S}}}\right)}^{\frac{1}{2}}\cdot {{\upalpha }}_{0,{\rm{S}}}\cdot {\left({\rm{h}}{{v}}_{{\rm{L}}}\right)}^{\frac{1}{2}}\cdot {{\alpha }}_{0,{\rm{L}}}+[{-\Delta G}_{{{A}}}^{{{{SP}}}}]$$
(5)
$$\left[-\Delta {\rm{G}}_{{\rm{A}}}\right]={\rm{f}}({\rm{RT}}{{\mathrm{ln}}}{\rm{Vn}})$$
(6)

where

$$K=\frac{3}{4}\frac{{N}_{{\rm{A}}}}{{(4\pi {\varepsilon }_{0})}^{2}}\frac{1}{{({r}_{{{S,L}}})}^{6}}$$
(7)

S and L indices denote the solid and probe (or liquid), respectively,where Vn: retention volume [m3],

   α0: deformation polarizability [C m2 V−1],

   ε0: vacuum permittivity [C2 N−1 m−2],

   h: Planck constant [J s],

   K: chromatographic process constant [V2 C−2 m−4 mol−1],

   NA: Avogadro number,

   rS, L: distance between two molecules [m].

The specific interaction related to the adsorption (or desorption) of free energy (\({-\varDelta G}_{{\rm{A}}}^{{{\rm{SP}}}}\)) is quantified by deviations from the linear reference line representative of n-alkanes (Fig. 2). This relationship is described using the following equation:

$${-\varDelta G}_{A}^{{SP}}={RTLn}\frac{{V}_{n}({polar\; probe})}{{V}_{n}({reference})}$$
(8)
Fig. 2
figure 2

Concept of determining \({\varDelta G}_{\rm{{A}}}^{{{\rm{SP}}}}\) between the adsorbate and adsorbent based on the points of net retention times for polar probes.

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Table 1 summarizes the characteristics of the probes used31,70,75,76.

Table 1 Characteristics of the probes used.
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Selection of probes

In IGC at infinite dilution, nonpolar probes typically produce symmetrical elution peaks, indicating uniform interactions with the adsorbent surface with minimal tailing. However, this symmetry is often disrupted with the usage of polar probes, as they often show tailing owing to stronger and more varied interactions with the adsorbent surface. Nonpolar probes such as benzene, toluene, xylene, and chloroform exhibit higher Gutmann acceptor numbers and IGC data than polar probes such as diethyl ether and acetonitrile (Table 1). Despite their polarity, these probes exhibit symmetrical chromatographic peaks when adsorbed onto carbon-based materials, such as natural graphite and CFs77, which are nonspecific adsorbents.

This behavior is unexpected, as polar probes typically interact strongly with such surfaces. To investigate this phenomenon, probes were categorized into polar and nonpolar groups using the equation of Stockmayer78, which estimates the degree of polarity:

$${\rm{\delta }}=1,94\times {10}^{3}\frac{{{\rm{\mu }}}^{2}}{{{\rm{V}}}_{{\rm{b}}}{{\rm{T}}}_{{\rm{b}}}}$$
(9)

where

μ: dipole moment [Debye],

Vb: molar volume at the boiling point [cm3 (g mol)-1],

Tb: boiling temperature [K].

The degree of polarity, δ, determined from Eq. (9) for polar and weakly polar probes is systematically < 0.07 (0.05–0.1)78,79,80,81 (Table 2).

Table 2 Characteristics of nonpolar, weak polar, and polar probes.
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Parker et al.82 highlighted that Gutmann’s donor-acceptor model is limited when applied to low dielectric constant probes with weak polarity. Mayer83 suggested that the acceptor number of Gutmann (AN) for weakly polar probes primarily reflects London dispersion forces rather than specific donor-acceptor interactions.

Weakly polar probes were excluded from this study, as they failed to provide reliable linear correlations for assessing the acid–base properties of solid surfaces using Eq. (2), as further discussed.

Determination of London dispersive component of surface free energy at infinite dilution

The London dispersive component (\({\gamma }_{{\rm{S}}}^{{\rm{L}}}\)) of solid surface energy was calculated using the equation established by Gray et al.56,57:

$${\gamma }_{{{S}}}^{{{L}}}=\frac{{\left({-\varDelta G}_{{{{{CH}}}}_{2}}\right)}^{2}}{4{N}_{{{A}}}^{2}{{a}_{{{{{CH}}}}_{2}}^{2}\gamma }_{{{{{CH}}}}_{2}}}$$
(10)

The incremental free adsorption (or desorption) energy for the methylene group (CH2), denoted as \({\varDelta G}_{{{\rm{CH}}}_{2}}\), is expressed as follows:

$${-\varDelta G}_{{{{CH}}}_{2}}={RT}\,{{\cdot }}\,{{{Ln}}}\left(\frac{{V}_{n+1}\left({C}_{n+1}{{VH}}_{2n+4}\right)}{{V}_{n}\left({C}_{n}{{VH}}_{2n+2}\right)}\right)$$
(11)

In this expression, NA represents the Avogadro constant (6.022 × 1023 mol–1), \({a}_{{{\rm{CH}}}_{2}}\) denotes the surface area of the CH2 group according to Gray et al., set at 6 Å2, while \({\gamma }_{{{\rm{CH}}}_{2}}\) indicates the surface free energy of a CH2 group50:

$${\gamma }_{{{{CH}}}_{2}}=35.6-0.058\left(t-20\right){\rm{in}}[{\rm{mJ}}\cdot{{\rm{m}}}^{-2}]$$
(12)

Here, ‘t’ represents the temperature in Celsius, substituting the calculated value of \({N}_{{\rm{A}}}\,{{\cdot }}\,{a}_{{{\rm{CH}}}_{2}}=36,132\) m2 · mol−1 simplifies Eq. (10) as follows:

$${\gamma }_{{{S}}}^{{{L}}}=\frac{1}{4{\gamma }_{{{{{CH}}}}_{2}}}{\left(\frac{{RT}{{\cdot }}{{{Ln}}}\left(\frac{{V}_{n+1}}{{V}_{n}}\right)}{36,132}\right)}^{2}{\rm{in}}\,[{\rm{mJ}}\cdot {{\rm{m}}}^{-2}]$$
(13)

Based on the methodology outlined by Park et al.49,50,51, the solid surface energy (γS) can be expressed as the arithmetic mean of the two parameters, \({\gamma }_{{{S}}}^{{{L}}}\) and \({\gamma }_{{{{CH}}}_{2}}^{{{L}}}\)51, as follows:

$${\gamma }_{{{S}}}^{{{L}}}=\frac{{-\varDelta G}_{{{{CH}}}_{2}}}{{N}_{{\rm{A}}}{{\cdot }}{a}_{{{{CH}}}_{2}}}{\rm{in}}\left[{\rm{mJ}}\cdot {{\rm{m}}}^{-2}\right]$$
(14)

Using the previously determined value \({N}_{{\rm{A}}}{a}_{{{{\rm{CH}}}}_{2}}=36,132\) m2 · mol-1, Eq. (14) can be simplified as follows50

$${\gamma }_{{{S}}}^{{{L}}}=\frac{{-\varDelta G}_{{{{CH}}}_{2}}}{36,132}{\rm{in}}[{\rm{mJ}}\cdot {{\rm{m}}}^{-2}]$$
(15)

The surface energy of CFs was rigorously assessed using IGC at infinite dilution. The incremental adsorption free energy of the methylene group (–CH2–) was derived from the natural logarithm slope of the net retention volume plotted against the number of carbon atoms in linear n-alkanes (Fig. 2). Subsequently, utilizing these values, the \({\gamma }_{{{S}}}^{{{L}}}\) of CFs was determined through Eq. (15), providing insights into their van der Waals interactions.

Figure 3 and Table 3 show that the London dispersive surface free energy (\({\gamma }_{{{S}}}^{{{L}}}\)) of the fibers significantly increased with rising surface treatment current intensity, followed by a slight decline. The \({\gamma }_{{{S}}}^{{{L}}}\) value increased from 92 mJ m–2 (virgin fibers) to 124 mJ m–2 (modified fiber at 90 mA), then decreased to 95 mJ m–2 (modified fiber at 300 mA), and remained stable at higher current intensities up to 900 mA. These findings suggest that 90 mA is the optimal anodic surface treatment current for enhancing the (\({\gamma }_{{{S}}}^{{{L}}}\)) of CFs.

Fig. 3
figure 3

Linear variations of London dispersive components of sample surface energy as a function of experimental temperature.

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Table 3 London dispersive surface free energy (\({\gamma }_{{\rm{S}}}^{{\rm{L}}}\)) of the samples determined using the proposed method in this study.
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Determination of the acido-basicity of fibers

Plotting [−ΔGA] (or RTlnVn) against [\({\left({hv}\right)}^{1/2}\cdot {\alpha }_{0,{{L}}}\)] for n-alkanes probes yielded a straight line (Fig. 4).

Fig. 4
figure 4

Determination of [\({-\Delta G}_{{\rm{A}}}^{{{\rm{SP}}}}\)] from the graph of [\({-\Delta G}_{{\rm{A}}}\)] as a function of \({\left({hv}\right)}^{1/2}\cdot {\alpha }_{0,{\rm{L}}}\) for virgin fibers at 54.5 °C.

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In contrast, the representative points for polar probes lie above the n-alkane line, while weak polar probes, such as CCl4 and chloroform, are close to it. The distance between these points and the n-alkane line is used to determine [\({-\Delta G}_{{{A}}}^{{{{SP}}}}\)]. However, weak polar probes have δ values close to zero, owing to their similar polarity to n-alkanes (Table 2), making them unreliable for assessing the surface acid–base properties of CFs or epoxy materials. Therefore, weak polar probes (Table 2) were excluded from the analysis of the acid–base properties of pristine and electrochemically treated fibers.

Table 4 shows increased values of \({-\Delta G}_{{{A}}}^{{{L}}}\), \({-\Delta G}_{{{A}}}^{{{{SP}}}}\), and −∆GA for virgin CFs, with a significant increase in interaction strength of the treated fibers with acidic and basic probes. This indicates the amphoteric nature of these carbonaceous surfaces.

Table 4 Gibbs free energy (−ΔGA) of probe adsorption on virgin CFs.
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Figure 5 illustrates a linear relationship between the specific free adsorption energy on virgin fibers and the degree of probe polarity, with a regression coefficient of 0.94, justifying the probe selection.

Fig. 5
figure 5

Relationship between [\({-\Delta G}_{{\rm {A}}}^{{{\rm {SP}}}}\)] and the degree of probe polarity for virgin fibers at 54.5 °C. [\({-\Delta G}_{{\rm {A}}}^{{{\rm {SP}}}}=3.98+7.76\cdot \delta ,{R}=0.94\)].

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The specific free component energy (\({-\Delta G}_{{{A}}}^{{{{SP}}}}\)) of adsorption Gibbs free energy (−ΔGA) between the solid and polar probes can be determined from the reference line points (Fig. 2) using Eq. (8). Figure 4 illustrates the principle underlying this estimation. Figure 6 presents \({-\Delta G}_{{{A}}}^{{{{SP}}}}\) values as functions of the polar probe and temperature, showing that modified fibers exhibit higher \({-\Delta G}_{{{A}}}^{{{{SP}}}}\) values than virgin fibers. This suggests stronger specific interactions between modified fibers and probes, owing to oxygen functional groups generated on anodic electrochemically treated fiber surfaces.

Fig. 6
figure 6

Linear fitting of \({-\Delta G}_{{\rm {A}}}^{{{\rm {SP}}}}\) vs. temperature for virgin and modified “T-300” fibers (acetonitrile, nitromethane, acetone, tetrahydrofuran, ethyl acetate, and diethyl ether).

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According to Eq. (2), the variation of [\({-\Delta G}_{{{A}}}^{{{{SP}}}}/{AN}\)] against [DN/AN] of the polar probes forms a straight line, where the slope represents the acid constant, KA, and the y-intercept indicates the basic constant, KD, of the solid surface. Figure 7 illustrates an example of variation in [\({-\Delta G}_{{{A}}}^{{{{SP}}}}/{AN}\)], against [DN/AN] for the fibers, with the linear regression coefficients exceeding 0.98. Figure 8 presents the KA and KD values for all fibers analyzed.

Fig. 7
figure 7

Determination of KA and KD values for virgin and modified fibers treated at 90 and 900 mA.

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Fig. 8
figure 8

KA and KD values of all explored fibers (arbitrary units).

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Figure 8 illustrates the variation of KA and KD with the electrochemical treatment intensity. The fiber surface acidity and basicity increased significantly with processing current intensity reaching up to ~90 mA. However, at high current intensities (>90 mA), no significant change was observed in the acid–base properties of the fiber surface.

Conclusions

The anodic treatment effectively modifies the surface properties of CFs, enhancing surface acidity and basicity as demonstrated by IGC under infinite dilution conditions. Treatment in a NaOH electrolytic solution significantly enhanced basic CF surface characteristics. Although Gutmann’s weak polar probes were unsuitable for assessing surface acid–base properties, carefully selected polar probes confirmed the amphoteric nature of both virgin and anodized CF surfaces, with a strong basic tendency. This basic polarity increase is significant for improving wettability in acidic matrices, indicating that customized surface treatments can effectively modify chemical reactivity in composite systems through physical or intermolecular acid–base interaction.