Electric‑Field‑Induced Alignment of Nanocarbon Fillers in Epoxy Composites: Impact on Electrical Conductivity

Abstract

We report on the alignment of carbon nanoparticles—graphite nanoplatelets (GNPs) and multi‑wall carbon nanotubes (MWCNTs)—in a low‑viscosity epoxy matrix using an alternating current (AC) electric field. Optical microscopy, electrical measurements, and analytical modeling were combined to assess how field strength, geometry, filler morphology, and aspect ratio influence alignment kinetics and percolation behavior. Alignment of GNPs was achieved in seconds at electric field strengths as low as 36 kV m⁻¹, while MWCNTs required several minutes. The aligned GNP composites exhibited a dynamic percolation threshold of 0.84 wt %, nearly a quarter of the 2.0 wt % threshold observed for randomly dispersed fillers. Our findings demonstrate that electric‑field‑assisted alignment can significantly lower the percolation threshold and enhance conductivity in nanocarbon‑filled polymers.

Background

Conductive carbon composites are indispensable in microelectronics, electromagnetic shielding, aerospace structures, and more. They combine corrosion resistance, high strength, low density, and tunable conductivity by varying filler type, loading, and dispersion. Non‑spherical fillers such as CNTs and GNPs are especially effective because their high aspect ratios reduce the packing factor and accelerate percolation, as predicted by statistical percolation models.

However, random dispersion often leaves many high‑aspect‑ratio fillers trapped in “dead‑end” branches of the conductive network, limiting performance at low loadings. Aligning fillers under external stimuli—electric, magnetic, or mechanical—can form continuous pathways and lower the percolation threshold. Mechanical alignment can damage delicate nanocarbon structures; magnetic alignment requires added magnetic components. Electric‑field alignment is therefore attractive: it is non‑contact, operates on the intrinsic polarizability of the fillers, and does not require additives.

Most studies on electric‑field alignment have focused on CNTs; the influence of filler morphology on alignment kinetics and conductivity remains poorly understood. This work investigates how GNPs and MWCNTs behave under AC electric fields, quantifies alignment times via an effective‑medium model, and correlates these findings with measured conductivity.

Methods

Materials

Epoxy resin Larit 285 (Lange Ritter GmbH) was used in its two‑component form (liquid epoxy + hardener H 285). The resin (600–900 mPa s) and hardener (50–100 mPa s) viscosity at 25 °C permitted uniform electric‑field treatment. Fillers were:

• Multi‑wall CNTs (Cheap Tubes Ins, USA)
• Graphite nanoplatelets (GNPs) produced by ultrasonic dispersion of thermally exfoliated graphite in acetone for 3 h (see [22]).

Table 1 lists filler dimensions (obtained by AFM, SEM, optical microscopy) and densities (ρ (CNT) = 1.8 g cm⁻³; ρ (GNP) = 2.23 g cm⁻³).

Composite Fabrication

Filler loadings ranged from 0.05 to 5 wt %. For each loading, one set was mixed mechanically and sonicated (Vaku‑9050, 40 kHz, 50 W, 30 min) before adding hardener at a 100/40 mass ratio to epoxy. A second set was subjected to AC electric field (15 kHz, 2000 V peak‑to‑peak) while the mixture was poured into a mold positioned between capacitor plates. The field magnitude was monitored with a V7‑16A voltmeter. The field was applied for the time required to reach epoxy cross‑linking (~10 min). Samples were then cured by stepwise heating from 40 to 80 °C (10 °C h⁻¹).

Optical Microscopy

Real‑time imaging of 0.05 wt % composites was performed with a stereoscopic microscope (MBS‑1) and digital camera (Etrek DCM‑510). The liquid epoxy and dispersed fillers were observed under both AC (15 kHz) and DC fields while varying field strength.

Electrical Conductivity Measurement

Two‑probe DC measurements were performed at room temperature. Samples (5 × 4 × 4 mm³) were tested; resistances >10¹⁰ Ω were measured with a tera‑ohm meter (E6‑13). Conductivity σ was calculated from measured resistance and sample geometry.

Modeling

Alignment dynamics were modeled by solving the rotational equation:

\[ I\frac{d^2\Theta}{dt^2}+T_{\eta}+T_{\text{align}}=0 \]

where I is the moment of inertia, T_η the viscous torque, and T_align the electric‑field torque. The polarizability \(\alpha^*\) and depolarization factors L_x (ellipsoid) and L_R (spheroid) were computed from particle geometry (see equations (2)–(5)). Numerical integration was performed in Maple 13 using parameters: η = 0.75 Pa s, ε_m = 2.8ε_0, σ_m = 10⁻⁶ S m⁻¹, f = 15 kHz, ε_p(CNT) = 62.2, ε_p(GNP) = 34.3, σ_p = 10⁵ S m⁻¹.

Results and Discussion

Optical Observations

Under AC field, composites became increasingly transparent as fillers migrated along field lines, forming chains. In the capacitor configuration (no current path), GNP chains grew rapidly within seconds, whereas MWCNT chains required minutes. Alignment was more pronounced at lower field strengths for GNPs due to their larger aspect ratio and higher polarizability. DC fields failed to produce aligned networks, confirming the necessity of AC stimulation.

Figures 1–4 illustrate the progressive alignment for GNPs and MWCNTs at various field strengths (36, 167, 83.3, 50 kV m⁻¹). The rapid chain formation in GNP composites correlates with the short rotation time predicted by the model.

Modeling of Alignment Kinetics

Calculated inclination angles vs. time (Fig. 6) show that alignment time scales inversely with aspect ratio. GNP_max and CNT_max align in comparable times, whereas GNP_min aligns slowest. Depolarization factors (Fig. 7) confirm that L_x increases with decreasing aspect ratio, slowing rotation. When the field aligns with the GNP’s long axis (L_R case, Fig. 8), rotation times lengthen further, underscoring the importance of field orientation.

The model indicates that MWCNTs, owing to their cylindrical geometry and higher viscosity, experience longer alignment times than GNPs, consistent with experimental observations.

Electrical Properties of Solid Composites

Figure 10 displays the conductivity vs. filler loading for aligned and random GNP composites. The percolation threshold drops from 2.0 wt % (random) to 0.84 wt % (aligned). Figure 11 shows the distinct σ(c) behavior for MWCNTs (plateau‑then‑rise) versus GNPs (monotonic increase), reflecting different network topologies: crossed frameworks for CNTs and chained structures for GNPs.

These results confirm that electric‑field alignment induces a dynamic percolation transition, lowering the critical loading and enhancing conductivity. The dynamic threshold can be tuned by field parameters, filler morphology, and matrix viscosity.

Conclusions

1. High‑voltage AC electric field aligns GNPs in epoxy, forming continuous chains observable by optical microscopy.
2. Alignment reduces the percolation threshold by ~60 % compared to random dispersion and introduces a dynamic percolation transition.
3. The alignment time depends on filler aspect ratio via the depolarization factor; GNPs align faster than MWCNTs under identical conditions.
4. Aligned GNP composites achieve percolation at 0.84 wt %, while random composites require 2.0 wt % loading.

Abbreviations

AC

Alternating current

AFM

Atomic force microscopy

CNTs

Carbon nanotubes

DC

Direct current

GNPs

Graphite nanoplatelets

MWCNTs

Multi‑wall carbon nanotubes

SEM

Scanning electron microscopy