The thermal conductivity (k) of graphene-based layered µm-thin structures, termed “paper”, is highly anisotropic, and strongly varies from sample to sample. In addition to k, the thermal anisotropy ratio (Θ = kmax/kmin) is also a critical property reflecting the material’s structure and is of great importance in thermal design. The intrinsic Θ determination requires in-situ measurement of both in-plane k (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$k_{\parallel }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mo stretchy="false">‖</mo> </msub> </math></EquationSource> </InlineEquation>) and out-of-plane k (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$k_{ \bot }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>⊥</mi> </msub> </math></EquationSource> </InlineEquation>) of the same sample. Such intrinsic Θ knowledge is not much available to date. In this work, graphene paper (GP), graphene oxide paper (GOP), and partly reduced graphene paper (PRGP) are investigated, each exhibiting distinct microstructural features arising from different oxidation and reduction states. These structural variations lead to pronounced differences in both the magnitude and anisotropy of k, highlighting the strong influence of oxidation-induced disorder on directional thermal transport. A photothermal approach is employed to measure both <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$k_{\parallel }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mo stretchy="false">‖</mo> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$k_{ \bot }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>⊥</mi> </msub> </math></EquationSource> </InlineEquation> of the same suspended micro-thick samples by tuning the modulation frequency to selectively enhance sensitivity to in-plane or out-of-plane heat conduction. Because both <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$k_{\parallel }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mo stretchy="false">‖</mo> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$k_{ \bot }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>⊥</mi> </msub> </math></EquationSource> </InlineEquation> are obtained from a single specimen and a fixed laser position, structural variation associated with multi-sample preparation is eliminated, enabling reliable determination of the intrinsic Θ. The measured <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$k_{ \bot }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>⊥</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$k_{\parallel }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mo stretchy="false">‖</mo> </msub> </math></EquationSource> </InlineEquation> are 7.28 and 690 W·m−1·K−1 for GP (Θ = 94.8), 0.215 and 0.78 W·m−1·K−1 for GOP (Θ = 3.63), and 0.316 and 2.9 W·m−1·K−1 for PRGP (Θ = 9.18), respectively. The significantly reduced k and Θ of GOP is attributed to enhanced phonon scattering from oxygen-containing functional groups, while GP exhibits the highest k and Θ due to its high crystallinity.

Intrinsic Thermal Anisotropy Ratio of Graphene-Based μm-Thick Films

期刊论文
发表日期：

2026年4月13日

查看全文

Mahya Rahbar,
Amin Karamati,
Jiwen Li,
Lijun Zhang,
Xinwei Wang

摘要

The thermal conductivity (k) of graphene-based layered µm-thin structures, termed “paper”, is highly anisotropic, and strongly varies from sample to sample. In addition to k, the thermal anisotropy ratio (Θ = k_max/k_min) is also a critical property reflecting the material’s structure and is of great importance in thermal design. The intrinsic Θ determination requires in-situ measurement of both in-plane k ( $k_{\parallel }$ $k_{‖}$ ) and out-of-plane k ( $k_{ \bot }$ $k_{⊥}$ ) of the same sample. Such intrinsic Θ knowledge is not much available to date. In this work, graphene paper (GP), graphene oxide paper (GOP), and partly reduced graphene paper (PRGP) are investigated, each exhibiting distinct microstructural features arising from different oxidation and reduction states. These structural variations lead to pronounced differences in both the magnitude and anisotropy of k, highlighting the strong influence of oxidation-induced disorder on directional thermal transport. A photothermal approach is employed to measure both $k_{\parallel }$ $k_{‖}$ and $k_{ \bot }$ $k_{⊥}$ of the same suspended micro-thick samples by tuning the modulation frequency to selectively enhance sensitivity to in-plane or out-of-plane heat conduction. Because both $k_{\parallel }$ $k_{‖}$ and $k_{ \bot }$ $k_{⊥}$ are obtained from a single specimen and a fixed laser position, structural variation associated with multi-sample preparation is eliminated, enabling reliable determination of the intrinsic Θ. The measured $k_{ \bot }$ $k_{⊥}$ and $k_{\parallel }$ $k_{‖}$ are 7.28 and 690 W·m⁻¹·K⁻¹ for GP (Θ = 94.8), 0.215 and 0.78 W·m⁻¹·K⁻¹ for GOP (Θ = 3.63), and 0.316 and 2.9 W·m⁻¹·K⁻¹ for PRGP (Θ = 9.18), respectively. The significantly reduced k and Θ of GOP is attributed to enhanced phonon scattering from oxygen-containing functional groups, while GP exhibits the highest k and Θ due to its high crystallinity.