Impact of Morphology and Crystal Structure on Titania Nanotube Thermal Conductivity

Background

Miniaturization of electronics and NEMS drives the need to understand thermal transport in nanostructures. By tailoring size, composition, and crystal structure, researchers can dramatically reduce heat dissipation—critical for device longevity and thermoelectric performance.

One‑dimensional (1D) materials such as carbon nanotubes exhibit extraordinary thermal conductivities (~3000 W m⁻¹ K⁻¹) owing to strong covalent bonds and defect‑free lattices. In contrast, semiconductor nanotubes typically show markedly lower conductivities than their bulk counterparts because of phonon mean‑free‑path reductions, grain‑size effects, and boundary scattering.

Silicon nanowires pioneered this field, achieving up to a 100‑fold conductivity reduction relative to bulk silicon through phonon‑boundary scattering. Similar trends appear in Bi₂Te₃, Si/SiGe, Ge/SiGe, ZnTe, GaN, InSb, CdS, PbS, PbSe, InAs, Bi, SrTiO₃, ZnO, and TiO₂ nanowires, all of which benefit thermoelectrics.

TiO₂ nanotubes, synthesized via hydrothermal, anodization, chemical, rapid‑breakdown anodization, and template methods, have shown thermal conductivities ranging from 0.40 to 1.5 W m⁻¹ K⁻¹ depending on crystallinity and wall thickness. Crystalline anatase tubes often exceed amorphous tubes in conductivity, but recent data suggest that size scaling can lower even amorphous conductivities below the amorphous limit, implicating propagons.

The present study extends the size‑dependent thermal conductivity investigation to fourth‑generation TNTs (RBA powders) and provides experimental validation for models predicting wall‑thickness effects and surface‑roughness‑driven phonon scattering.

Methods/Experimental

Synthesis of TNTs

Three TNT variants were produced:

• Multi‑walled, open‑ended TNT_A,T (mixed titanate/anatase) via chemical processing.
• Single‑walled, partially open TNT_Amor (amorphous) via RBA in an organic electrolyte.
• Single‑walled, partially closed TNT_A (anatase) via RBA in a water‑based electrolyte.

Key dimensions: TNT_A,T wall thickness 4–5 nm; TNT_A 7–12 nm; TNT_Amor 15–30 nm. Schematic representation is shown in Figure 1.

Characterization Methods

TEM (Tecnai F‑20 G2 200 kV) revealed morphology and wall layering. XRD (PANalytical X’pert Pro, Cu‑Kα, 40 kV/45 mA) confirmed crystal phases. Powder density was measured by pycnometer; pellets were hydrostatically pressed (5–50 kN) and thickness 2–4 mm. Surface morphology of pellets was examined via FE‑SEM.

Thermal diffusivity was measured by the laser flash method (Netzsch LFA 467). Pellets were coated with graphite spray; a xenon laser pulse heated the rear face while an infrared detector recorded the front‑side temperature rise. Using the relation

$$\alpha = \frac{0.1338\ d^{2}}{t^{1/2}}$$

we obtained diffusivity; thermal conductivity followed from

$$\kappa = \alpha\ c_{p}\ \rho$$

Specific heat (c_p) was taken from Guo et al., matching bulk TiO₂ above 100 K. Density (ρ) was calculated from pellet mass and volume. Experimental uncertainty was 8 %.

Results and Discussion

XRD patterns (Figure 2) confirm the three distinct structures: TNT_Amor shows no peaks, TNT_A,T displays anatase and titanate peaks, and TNT_A presents only anatase reflections.

XRD of crystalline TNTs (TNT_A, TNT_A,T) and amorphous TNT_Amor

TEM images (Figure 3) reveal:

• TNT_A,T as 3–4 layer multi‑walled tubes, 60–hundreds of nm long.
• TNT_A as single‑walled, 18–35 µm long, 7–12 nm walls.
• TNT_Amor as single‑walled, 6–13 µm long, 15–30 nm walls.

Average surface roughness (≈0.3 nm for TNT_A,T, 1.0 nm for TNT_A, 1.5 nm for TNT_Amor) was extracted from TEM profiles.

Pellet porosities (P) were calculated from bulk and pellet densities using

$$P = \frac{\rho_{o}-\rho}{\rho_{o}}$$

Thermal diffusivity and conductivity measurements (Table 2) show conductivity decreasing with porosity. Applying effective‑medium theory for non‑conducting pores yields

$$\kappa_{TNTs} = \frac{\kappa_{eff}}{1-P}$$

Results (Figure 4) give:

• TNT_A,T: 0.44–0.61 W m⁻¹ K⁻¹
• TNT_A: 1.07 W m⁻¹ K⁻¹
• TNT_Amor: 0.98 W m⁻¹ K⁻¹

Fitting the porosity dependence with Bauer’s model (ε = 1.24) corroborates these values.

Effective thermal conductivity vs. porosity (solid lines from Eq. 6, ε = 1.24)

Comparing wall thickness to conductivity (Figure 5) shows a clear decline in both crystalline and amorphous TNTs as walls shrink toward the 2.5 nm phonon mean free path. This size‑dependent behavior, previously unobserved in some studies, suggests propagons contribute significantly even in disordered TiO₂.

Thermal conductivity vs. wall thickness for crystalline and amorphous TNTs

Surface‑roughness effects were quantified using Liang & Li’s expression adapted for nanotubes:

$$\frac{\kappa_{TNT}}{\kappa_{B}} = p\,\exp\left(-\frac{l_{0}}{L}\right)\,\exp\left[\frac{1-\alpha}{\frac{L}{L_{0}}-1}\right]^{3/2}$$

with κ_B = 8.5 W m⁻¹ K⁻¹, l₀ = 2.5 nm. Best fits yield surface‑roughness factors p = 0.26 (TNT_A,T), 0.18 (TNT_A), and 0.65 (TNT_Amor), corresponding to roughness values that match TEM estimates.

Size‑dependent conductivity of crystalline (a) and amorphous (b) TNTs with fitted roughness factors

Conclusions

Three TNT morphologies were synthesized: single‑walled anatase (TNT_A, 7–12 nm), single‑walled amorphous (TNT_Amor, 15–30 nm), and multi‑walled mixed titanate/anatase (TNT_A,T, 4–5 nm). Their room‑temperature conductivities, obtained via an effective‑medium model, are 1.07, 0.98, and 0.75 W m⁻¹ K⁻¹, respectively. The lowest value corresponds to the thinnest walls, confirming that phonon confinement and boundary scattering dominate heat transport in 1D TiO₂ structures. Surface‑roughness‑driven scattering, quantified by p‑factors of 0.26, 0.18, and 0.65, further explains the conductivity disparities. Although amorphous oxides are traditionally considered size‑independent, our data reveal a clear wall‑thickness dependence, likely due to propagons in disordered lattices. These insights refine the design of TiO₂ nanostructures for thermoelectrics and heat‑management applications.

Abbreviations

RBA

Rapid breakdown anodization

SEM

Scanning electron microscopy

TEM

Transmission electron microscopy

TNT_A

Titania nanotubes with anatase crystal structure

TNT_A,T

Titania nanotubes with mixed anatase and titanate phases

TNT_Amor

Titania nanotubes with amorphous structure

TNTs

Titania nanotubes

XRD

X‑ray diffraction