Optimizing multiscale resin flow kinetics and impregnation uniformity in fiber-reinforced polymers composites via hierarchical carbon nanostructures

Microstructure and surface analysis of CFs

The surface morphologies of treated CFs were characterized using field-emission SEM (JSM-7600F, JEOL) operated at an accelerating voltage of 10 kV, following platinum sputter coating. Surface chemical composition was analyzed by XPS (Kratos Axis Supra+, Shimadzu) equipped with a monochromatic aluminum Kα X-ray source (1,486.6 eV). Measurements were recorded using a 300 × 700 μm² spot size under an ultra-high vacuum of < 5 × 10^-9 mbar.

Contact angle for CF/epoxy interface

Contact angle measurements were conducted to quantitatively evaluate the microscale wettability of individual CFs by epoxy resin. Epoxy microdroplets were deposited on the fiber surfaces and subsequently cured at room temperature for 24 h. The droplet profiles were then captured using a 3D super-depth-of-field microscope (EasyZoom5, Motic). For each sample group, ten droplet profiles were analyzed.

Evaluation of surface free energy

Surface free-energy analysis provides critical insight into the wettability of carbon fibers by epoxy resin. Accordingly, the dynamic Wilhelmy method was used to measure the contact angles and determine the surface energies of CF_Received and CF_GO-CNT^[32]. Deionized water and ethylene glycol were used as probe liquids, and the mean diameter of the individual CFs was ~7 μm. The dispersive ($$ \gamma _{l}^{d} $$) and polar ($$ \gamma _{l}^{p} $$) components of the liquid surface tension, along with the interfacial free energy (γ_sl) between the fiber surface and each liquid, were evaluated using the Owens-Wendt-Rabel-Kaelble (OWRK) model^[33], as follows:

where γ_sl, γ_s, and γ_l represent the solid-liquid interfacial free energy, solid surface free energy, and liquid surface free energy, respectively. The surface-tension components of the probe liquids are summarized in Table 1. According to Young’s equation, the relationship between the contact angle (θ) of a liquid on a solid surface and the interfacial free energies among the solid, liquid, and vapor phases is expressed by:

By substituting Equation (1) into Equation (2), the following expression is obtained:

Capillary wicking rate constant for fiber bundles

Fiber bundle infiltration was evaluated by monitoring the evolution of the apparent contact angle. To minimize variations in sample geometry, a constant tensile preload of 0.1 N was applied to each fiber bundle. This preload aligned the filaments, removed slack, and produced uniform, flattened bundle geometry. Subsequently, a ~3 μL droplet of uncured epoxy resin without curing agent was deposited at the center of the flattened fiber bundle. The droplet was rapidly absorbed, accompanied by a sharp decline in contact angle, indicating capillary-driven dynamic wetting. The dynamic wetting process was recorded in real time using a high-speed camera integrated into an optical contact angle system (OCA20, Data-Physics, Germany). The capillary infiltration rate constant, k_b, was determined by fitting the contact angle evolution using^[34]:

where θ_t is the contact angle at time t and θ₀ is the steady-state contact angle. During the initial stage of capillary infiltration, the liquid rapidly penetrates the fiber bundle, causing a sharp decline in θ_t. In the later stage, resin flow becomes increasingly restricted by viscous resistance, resulting in a more gradual decrease in θ_t. The parameter k_b characterizes the kinetics of capillary-driven wicking in the initial rapid stage. It provides a quantitative measure of the ability of the fiber bundle to spontaneously imbibe resin, and complements permeability measurements by capturing the mesoscale capillary contribution to the overall resin transport.

The impregnation of fiber fabrics

The in-plane impregnation capability of fiber fabrics was evaluated by using the vacuum-assisted resin infusion (VARI) method, in which 1D unsaturated resin flow was generated through the fiber preforms. For each sample group, a two-layer fiber preform was placed on a flat glass mold, sealed under a vacuum bag, and evacuated. Subsequently, uncured epoxy resin was introduced, and the entire infusion process was conducted at 20 °C under an applied pressure of 0.095 MPa. A distinct flow front developed as the resin advanced through the preform under the applied vacuum pressure differential (∆P). The relationship between resin flow-front position (x_p) and time (t) was described by the integrated form of Darcy’s law for 1D flow:

where μ is resin viscosity, K permeability, V_f fiber volume fraction, x_p 1D resin flow-front position, and t flow time.

Molecular models

Four all-atom microchannel (MC) models were constructed to evaluate the resin flow behavior [Figure 2]: MC_CG (smooth CF surface), MC_CNT, MC_GO and MC_GO-CNT. Each model comprised CF substrates arranged symmetrically along the z-axis and a microchannel containing 330 diglycidyl ether of bisphenol A (DGEBA) molecules. To isolate flow characteristics, crosslinkers were excluded. The target density of each system was set to 1.17 g/cm³. To eliminate high initial potential energy, each system underwent energy minimization followed by 500 ps relaxation under the canonical ensemble (NVT) (300 K, ∆t = 1 fs). The CF substrates were modeled as three parallel graphite layers (hexagonal closed-packed structure, 0.34 nm spacing). CNTs (1.8 nm length, 0.4 nm diameter) and GO sheets (25% surface oxidation) were incorporated as follows: GO was aligned parallel to the CF surface, whereas the CNTs were oriented normal to the surface and covalently bonded either to GO or directly to the CF surface, depending on the model used. To simplify the system, CF surface roughness and nanomaterial agglomeration were neglected. The effective microchannel dimensions were 10.1 × 3.9 × 5.3 nm³ (y × x × z). To maintain uniform channel geometry, the outermost graphite layers were replaced with GO or GO-CNT surface layers in the modified models.

Figure 2. Schematic representation of all-atom models and corresponding boundary conditions, designed to simulate fluid flow in porous media representative of CF bundle interiors. CF: Carbon fiber; GO-CNT: graphene oxide-carbon nanotube; MC: microchannel; DGEBA: diglycidyl ether of bisphenol A; HCP: hexagonal closed-packed.

Force field

The consistent valence force field (CVFF) was employed to model both bonded and non-bonded interactions in the composite systems. The bonded terms included bond stretching, angle bending, and torsional potentials, while non-bonded interactions were described by the sum of Coulombic and van der Waals forces, represented by the Lennard-Jones 12-6 potential with a cutoff distance of 1.25 nm. Newton’s equations of motion were solved with the velocity-Verlet integration algorithm. All molecular dynamics simulations were conducted using the open-source large-scale atomic/molecular massively parallel simulator (LAMMPS), developed by Sandia National Laboratories, Livermore, CA, USA^[35].

Calculation methods

Initial atomic velocities were assigned according to the Maxwell-Boltzmann distribution at 300 K. Before initiating infiltration, the DGEBA clusters were equilibrated under the NVT ensemble for 10 ps to relax local conformations while preserving structural tension. To prevent premature flow, a van der Waals energy barrier (1.25 nm in height) was applied at the channel entrance. After the barrier was removed, spontaneous capillary-driven resin infiltration was simulated for 30 ps with a time step of ∆t = 1 fs. No external forces were applied during this stage. Free boundary conditions were imposed in all directions, while energy walls were implemented to constrain the polymer within the simulation domain (as illustrated in Figure 2).

Wettability of CF/epoxy interface

The static microscale wetting behavior of epoxy droplets on individual carbon fibers is shown in Figure 4. As shown in Figure 4A, epoxy resin droplets exhibit pronounced convex profiles on untreated fiber surfaces. In contrast, after modification with carbon nanomaterials, the droplet profile changes from convex to concave, forming a hydrodynamic curvature near the triple-phase contact line. This morphological transition indicates improved resin spreading over the modified fiber surface.

Figure 4. Wettability analysis of epoxy resin on CF monofilaments: (A) optical micrographs (OM) schematic representations of the droplet profiles and surface curvature; (B) static contact angles measured by the tangent method, with data presented as mean ± standard deviation (ten droplet profiles for each sample group); (C) droplets height versus length for contact-angle determination; (D) quantitative evaluation of wettability through functional correlation analysis. CF: Carbon fiber; GO-CNT: graphene oxide-carbon nanotube; CA: contact angle.

The contact angle of an individual fiber is typically evaluated using two main approaches: (a) direct measurement of the tangent angle at the three-phase contact line, and (b) geometric estimation based on the droplet height-to-length ratio. Direct measurements show that the static contact angle decreases from 50.65° to a minimum of 34.95° after surface modification [Figure 4B]. Consistent with this result, the droplet height-to-length ratio also decreases after surface modification [Figure 4C]. Based on these two measurements, a functional relationship was established between the tangent angle and the height-to-length ratio [Figure 4D]. A larger slope (> 1) with larger deviation from linearity indicates limited droplet spreading and relatively poor wettability, while a smaller slope suggests improved spreading behavior. Additionally, consistent slope values and closer proximity to the origin denote superior wetting performance. The tangent-angle measurements, geometric-ratio analysis, and functional fitting consistently indicate that the 3D nanostructures markedly improve the wettability of the CF/epoxy interface.

Table 4 presents the contact angles of individual CFs measured with two probe liquids and corresponding calculated surface free energies. Compared with CF_Received, CF_GO-CNT exhibits markedly lower contact angles with both probe liquids. This trend is consistent with the static contact angle measurements and further supports the improvements in CF surface wettability induced by GO-CNT modification. Meanwhile, the total surface free energy of CF_GO-CNT increases substantially, with a decrease in the dispersive component and a pronounced increase in the polar component. The polar component accounts for 88.6% of the total surface free energy. This shift is closely associated with changes in the surface chemistry and morphology of the fibers. On the untreated CF surface, the graphitic sp² carbon structure provides dispersive interactions, while residual oxygen-containing groups contribute to polar interactions, resulting in a slightly higher polar component. Following GO-CNT modification, O-containing functional groups are introduced to the fiber surface, forming a rough 3D nanostructure. The increased surface polarity strengthens interactions between fiber and resin, while the nanoscale roughness increases the effective solid-liquid contact area. The synergistic effect of these chemical and morphological changes significantly increases both the polar component and total surface free energy of the fiber. This provides more favorable thermodynamic conditions for resin spreading, contributing to the transition of the droplet profile from convex to concave and facilitating resin spreading along the fiber surface.

Capillary wicking dynamics in fiber bundles

In fiber bundles, resin transport begins with spontaneous capillary wicking through inter-fiber microchannels, as visualized by the fiber morphology in Figure 3D and E. This wicking process involves two distinct stages: an initial rapid phase (0-5 s) driven by capillary forces [Figure 5A], during which the resin rapidly penetrates along fiber surfaces and through inter-fiber gaps, followed by a slower, viscous-dominated phase where increasing resistance decelerates flow. Saturation is marked by an inflection point in the contact angle evolution (~5 s). Figure 5B and C illustrates the evolution of contact angle and the fitting results based on Equation (4) during the rapid infiltration stage. Using this method, k_b was also obtained for different surface-modification conditions [Supplementary Figure 2]. The results show that k_b is highly sensitive to the modification conditions, indicating that the carbon nanostructures influence capillary flow. Figure 5D compares the k_b values obtained for different treatment groups. Optimized EPD and flame treatments increase k_b by 31.7% and 67.3%, respectively. Notably, the GO-CNT hybrid exhibits the highest k_b (0.186), exceeding the values obtained with either GO or CNT modification alone, and corresponding to a maximum increase of 84.2%. The significant increase in k_b indicates that the GO-CNT nanostructure markedly enhances capillary-driven infiltration at the mesoscale. Here, “wicking” specifically refers to capillary-driven flow via microscale gaps between adjacent fibers, which is distinct from bulk resin infiltration at the fabric (macroscale) level.

Figure 5. Resin infiltration kinetics in fiber bundles: (A) evolution of contact angle with time for different CF bundles; (B) infiltration curves of different CF bundles; (C) fitted curves used to determine k_b values; and (D) comparison of k_b among CF bundles subjected to different surface modifications. CF: Carbon fiber.

Flow assessment of CF woven fabric

The in-plane impregnation behavior of woven CF fabrics was evaluated using VARI. Under the applied vacuum pressure, the resin advanced from the inlet toward the outlet, forming a nonuniform flow front. The shape and velocity of the flow front are governed by factors including inter-bundle channel geometry, fiber wettability, resin viscosity, and capillary interactions at the fiber-resin interface. This macroscopic flow behavior can be described by Darcy flow.

Figure 6A presents the relationship between the squared flow-front position ($$ x_{p}^{2} $$) and time. The results show that the resin advances more rapidly through the surface-modified fabric than through the untreated fabric. Based on the average impregnation velocity, calculated from the resin travel distance over the same time interval, the GO-CNT modified fabric exhibits the fastest resin advance, with an average velocity of 2.47 × 10^-4 m/s. This value is 85.7% higher than that of the untreated fabric (1.33 × 10^-4 m/s), indicating a substantial improvement in macroscopic resin impregnation behavior.

Figure 6. Macroscopic resin infiltration in T300 woven fabrics: (A) linearized infiltration kinetics ($$ x_{p}^{2} $$ versus t); (B) evaluation of flow-front uniformity, with the bars representing the flow-front range (left axis) and the lines representing the standard deviation of the flow-front position (right axis); (C) comparison of dual-scale resin flow in untreated and GO-CNT modified fabrics. CF: Carbon fiber; GO-CNT: graphene oxide-carbon nanotube.

To quantify the morphological evolution of the flow front, the flow-front range (the maximum lag behind the leading point) and the standard deviation were extracted [Figure 6B]. For the untreated fabric, the flow-front nonuniformity progressively increases as infiltration proceeds. In contrast, the flow front in the GO-CNT modified fabric remains relatively stable, with only a slight increase in spatial dispersion. This difference in macroscopic uniformity is associated with changes in the multiscale resin transport mechanisms. A clear dual-scale transport phenomenon is observed in the untreated fabric (left photos in Figure 6C): rapid Stokes flow through inter-bundle channels and slower capillary-driven flow within intra-bundle pores. This pronounced difference in flow velocity can cause void entrapment within the fiber bundles. In contrast, after GO-CNT modification (right photos in Figure 6C), the engineered nanostructured wetting layer substantially enhances intra-bundle infiltration. This enhancement reduces the velocity difference between intra-bundle and inter-bundle flows, resulting in a more continuous flow front and more uniform overall resin advancement. Moreover, the dry spots are smaller than those in the untreated fabric and are mainly confined to bundle boundaries, suggesting that they may be more readily filled as infiltration proceeds.

The reduction in final porosity [Supplementary Figure 3] further supports the role of GO-CNT nanostructures in balancing inter-bundle and intra-bundle flows, thereby promoting more coordinated resin transport across multiple scales. The increased surface polarity and roughness enhance the wetting driving force, which increases capillary pressure P_c and facilitates resin penetration into intra-bundle pores. These results indicate that the GO-CNT nanostructures enhance multiscale resin transport without compromising macroscopic flow. Overall, the improvements in interfacial wettability and bundle-scale wicking synergistically contribute to the enhanced resin filling efficiency observed at the fabric scale. Such multiscale regulation of resin transport may also extend beyond LCM to prepreg manufacturing, where improved impregnation could reduce initial air entrapment within the fiber tows, facilitate void removal during subsequent consolidation, and ultimately improve prepreg quality.

Regulation mechanism of fiber/resin interface in porous media

Figure 7A shows the velocity distribution of the resin within the microchannels, revealing that the introduction of nanostructures significantly alters the velocity field. Generally, the flow velocity is higher at the channel center and follows the order MC_GO-CNT > MC_CNT > MC_GO > MC_CG. To further investigate the origin of these differences, the evolution of the imbibition depth over time was fitted. The penetration of epoxy (DGEBA) into the microchannels follows the scaling relationship: L(t) ~ t^0.5 [Figure 7B], indicating a capillary-driven imbibition regime. The slope reflects the combined influence of capillary pressure and resin viscosity. The infiltration efficiency follows the order: MC_GO-CNT ≈ MC_CNT > MC_GO > MC_CG. The stronger effect of CNTs relative to GO may be associated with more extensive π-π stacking with the DGEBA aromatic rings, which enabled multi-dimensional adsorption. In contrast, the interaction with GO is governed primarily by shorter-range hydrogen bonding via its polar groups. It should be noted that the idealized MD models neglect morphological irregularities and local agglomeration in real nanostructures, which may lead to quantitative deviations in the predicted velocity profiles and imbibition depth. Nevertheless, the simulations preserve the intrinsic differences in interfacial interactions among the systems, and the resulting performance rankings remain consistent with the qualitative experimental trends.

Figure 7. MD simulations of epoxy resin flow behavior in microchannels: (A) velocity distribution profiles of the polymer across different microchannels; (B) penetration depth as a function of time; and (C) solid-liquid interaction energy (E_s-l) versus number of resin atoms infiltrating the microchannel. MD: Molecular dynamics; GO-CNT: graphene oxide-carbon nanotube.

As infiltration progressed, the solid-liquid interfacial interaction energy (E_s-l) increased and eventually plateaued at equilibrium [Figure 7C]. In the absence of covalent bonding, E_s-l is dominated by nonbonded interactions (van der Waals forces and charge transfer), as expressed by:

where E_system, E_epoxy, and E_substrate denote the total energy of the full system, the resin, and the fiber substrate, respectively. It should be noted that a positive E_s-l indicates repulsive atomic interactions, whereas a negative value signifies attractive forces. In all MD simulations, E_s-l values were negative, confirming inherently attractive resin-substrate interactions.

The interfacial energy E_s-l is influenced by channel morphology, the number of resin molecules entering the channel, and their adsorption near channel walls [Figure 7C]. Compared with MC_GO, MC_CNT exhibits lower |E_s-l|, indicating weaker interfacial retention. Nevertheless, the CNT architecture enhances the attraction of fluid molecules, consistent with the higher permeation rate observed in MC_CNT [Figure 7B]. However, even in the idealized MD models, the 3D CNT network increases pathway tortuosity and creates local constrictions, thereby introducing steric hindrance. In real hierarchical coatings, random CNT entanglement and nonuniform surface coverage may further increase this steric hindrance. As infiltration proceeds, DGEBA molecules can accumulate around the CNTs, resulting in local molecular crowding that restricts molecular mobility and limits further penetration. In contrast, MC_GO displays higher |E_s-l| because its polar functional groups promote epoxy-chain adsorption and molecular retention near channel walls. However, without the transport-promoting effect of the CNT architecture, its overall penetration rate remains lower than that of MC_GO-CNT. Over time, the lamellar GO surface facilitates the redistribution of DGEBA molecules along the channel walls, enabling continued resin penetration into the confined channel.

Capillary pressure of resin in porous media

In the MD infiltration simulations, epoxy penetration is driven by a pressure difference, ∆P, which comprises the applied external pressure, P_app, and the intrinsic capillary pressure, P_c. Assuming 2D flow and neglecting gravitational effects, the governing relationship can be expressed as follows^[36,37]:

Here, P_c at the unsaturated flow front can be interpreted as the ratio of the intercept to the slope in the functional relationship between the independent variable P_app and $$ x_{p}^{2} /t $$.

Based on this derivation, P_c in MC_CG and MC_GO-CNT systems are presented in Figure 8A. To construct the $$ P_{app} - x_{p}^{2} /t $$ curve, external pressures of 2.0 × 10⁴, 3.0 × 10⁴, and 4.0 × 10⁴ kPa are applied to the models, simulating Darcy flow under vacuum-driven negative pressure. The pressure applied in MD is substantially higher than those typically used in experiments. This discrepancy arises from the intrinsic limitations of MD, where simulations are confined to femtosecond timescales and nanometer spatial regimes. Consequently, elevated pressures are required to produce measurable infiltration within computationally accessible simulation times. The introduction of the GO-CNT hybrid layer increases the magnitude of the flow-front capillary pressure (|P_c|) by 166.36%. As shown in Figure 8B, interfacial tension induces a curved meniscus that extends toward the low-pressure region during vacuum-assisted infiltration. Under the adopted sign convention, this curvature yields a negative P_c, showing that the capillary-pressure contribution acts opposite to the defined positive flow direction. Viscous forces also influence the evolution of the interfacial curvature via wall-induced flow resistance and internal viscous dissipation within the resin. For capillary-driven transport, the pressure differential across the 2D liquid-gas interface is expressed by:

Figure 8. (A) Plots of ($$ x_{p}^{2} / t $$) versus applied external pressures P_app; (B) concave meniscus flow front during resin infiltration visualized from molecular configuration at 30 ps of the imbibition process. GO-CNT: Graphene oxide-carbon nanotube; MC: microchannel.

where $$ P_{c}^{d} $$ is dynamic capillary pressure (approximated as P_c), R_cc radius of curvature of the meniscus, and γ surface tension, calculated through the MD method in our previous work^[21]. From Equation (8), the theoretical capillary curvature radius R_cc was calculated, whereas the experimental crescent radius R_c was determined directly from the visualized interfacial profile. As shown in Figure 8B, the grass-green dashed arc (representing R_cc) coincides closely with the orange-red solid arc (representing R_c), demonstrating good agreement between theoretical prediction and MD configuration. The MC_GO-CNT system exhibits a more strongly curved meniscus, indicating a greater capillary driving force that facilitates resin transport at the microscale.