Temperature dependence of photoluminescence spectra from a suspended single-walled carbon nanotube with water adsorption layer

Measurements at low temperature are important in investigating the intrinsic physical properties of materials because the contribution of, or disturbance by, thermal energy is reduced at low temperature. Such measurements are also effective in elucidating the optical properties of single-walled carbon nanotubes (SWCNTs). Spectroscopic measurements of SWCNTs at low temperatures have been reported, and photoluminescence (PL) spectra from SWCNTs with various morphologies at low temperatures have been investigated.^1–3 Although PL emission cannot be obtained from metallic SWCNTs, PL spectroscopy allows us to determine the optical transition energy, $Eii$⁠, which is dependent on chirality $(n,m)$⁠.⁴ Thus, it is an important tool for the investigation of SWCNTs. At low temperatures, PL spectra exhibit a shift in the optical transition energy, sharpening of PL peaks, long decay lifetime of excitons,^3,5 appearance of multiple subbands,^3,5–9 depression of additional peaks assisted by phonons,¹⁰ and thermal strain effects.¹¹ 

PL measurement of SWCNTs requires a dispersion in liquid with wrapping materials¹² or a suspended structure.² In the case of SWCNTs dispersed in water, the temperature dependence of $Eii$ is strongly affected by the strain between SWCNTs and the solution medium.¹¹ The axial strain causes a shift in $Eii$⁠, which depends on $(n,m)$⁠. In particular, this shift shows type dependence,¹³ where type I SWCNTs (⁠$mod(n−m,3)=1$⁠) and type-II SWCNTs (⁠$mod(n−m,3)=2$⁠) show an increase and decrease in $E11$ under tensile strain, respectively.

On the other hand, suspended SWCNTs exhibit a sharp peak at low temperature, which makes it possible to discuss the details of their optical properties.^2,14 Although the temperature dependence of $Eii$ has been reported, the number of measured $(n,m)$ is limited, and the temperature dependence with different $(n,m)$ is unclear.^2,15 Additionally, water molecules adsorb on the outer surface of suspended SWCNTs, forming a stable adsorption layer. The adsorption layer decreases $Eii$^16,17 because it enhances the dielectric constant surrounding SWCNTs.¹⁸ Although the interaction between the SWCNT and water molecules is weak and the SWCNT surface is regarded as hydrophobic, the adsorption layer is stable even at low water vapor pressure or high temperature.¹⁶ The water adsorption layer on a hydrophobic SWCNT surface, which consists of two monolayers of water molecules with lateral hydrogen bonding, is one of the attractive states of water. Such double water layers also exist on the graphene surface.¹⁹ However, their stability and physical properties are unclear. In order to elucidate the physical properties of both SWCNTs and water adsorption layers at low temperature, the temperature dependence of PL spectra from SWCNTs with a water adsorption layer is important.

Recently, the temperature dependence of the $Eii$ of SWCNTs with no water adsorption layer above room temperature and measurements of thermal conductivity on the basis of this temperature dependence have been reported.²⁰ The temperature dependence is independent of $(n,m)$⁠, and it is possible to determine SWCNT temperature. In the present study, PL spectra were measured from SWCNTs with water adsorption layers, and the temperature dependence was determined. The $E11$ of these SWCNTs exhibited a more complex temperature dependence than SWCNTs without adsorption layers. The temperature dependence was governed by the changes in the bandgap, the dielectric constant of the adsorption layer, and the strain due to the temperature change.

SWCNTs suspended between pairs of silica pillars were grown directly by using chemical vapor deposition (CVD). The silica pillar structure was fabricated on silica substrates by a lithographic technique, and a silicon layer with a thickness of $40nm$ was deposited except in the pillar top area.²¹ Cobalt with a nominal thickness of $0.01nm$ was then deposited on the substrates by using a vacuum evaporator. The substrate was heated in an $Ar/H2$ mixed gas (⁠$H2$ $3%$ by volume). During the heating process, the cobalt on the silicon layer formed $CoSi2$⁠, which was commensurate to the silicon lattice,²² and cobalt nanoparticles that served as a catalyst were formed only at the pillar tops. SWCNTs were synthesized using ethanol as the carbon source.²³ Ethanol was supplied using a bubbling method with $Ar/H2$ mixed gas (⁠$50sccm$ at $93kPa$⁠). The growth temperature was $870°C$⁠, and the growth time was $10min$⁠. SWCNTs grew only from the pillar tops. Some of them grew to reach paired pillars, becoming suspended between them.

A Ti:sapphire laser was used as an excitation laser for PL spectroscopy. The wavelength of the excitation laser ranged from $700$ to $830nm$⁠. The diameter and total power of the laser spot were approximately $18.4μm$ and $6.25μW$⁠, respectively. The low power density helped to avoid additional heating of the SWCNTs. PL measurements were performed in a vacuum chamber with a cooling stage. The stage temperature was maintained at around room temperature (between $−40$ and $20°C$⁠) by using a Peltier controller. For the lower temperature range (between $−130$ and $20°C$⁠), the stage was cooled by liquid nitrogen (MicrostatN, Oxford Instruments). The chamber was evacuated with a turbo molecular pump, and the stage temperature was controlled between $−140$ and $20°C$⁠. Some SWCNTs that were bundled with semiconducting SWCNTs showed a redshift in optical transition energy.²⁴ Other SWCNTs exhibiting a satellite peak at energies lower than the main emission peak indicated chemical adsorption of certain species, such as hydrogen atoms.²⁵ From among these SWCNTs, SWCNTs with a sharp and intensive PL emission peak at an appropriate $Eii$²⁶ and free of satellite peaks were selected.

The chirality was determined by $E11$ and $E22$ measured at room temperature,²⁶ and 12 different chiralities were examined. Water vapor was introduced into the chamber at $20°C$⁠, and the water adsorption layer was formed on the outer surface of SWCNTs.¹⁶ Then, the chamber was evacuated, and the temperature dependence of the PL spectra was investigated. We confirmed reproducibility of the chirality dependence by measuring several specimens for each chirality.

PL spectra of SWCNTs with different chiralities were measured at different temperatures. Some of these spectra are shown in Fig. 1. The adsorption layer, which formed before evacuation, persisted at lower temperatures even in vacuum because of the residual water molecules in the chamber. PL peaks changed slightly as the temperature changed. SWCNTs with certain chiralities [$(9,8)$ and $(12,5)$ in Fig. 1] exhibited a blueshift with decreasing temperature, while others showed a red-shift [$(11,6)$ SWCNT in Fig. 1].

Figure 2 plots the temperature dependence of the emission energy, $En,m(T)$⁠, which changed monotonically in the temperature range. The direction and amount of the shift depended on $(n,m)$⁠. In the cases of $(9,8)$ and $(12,5)$ SWCNTs, $En,m(T)$ decreased with increasing temperature, and the shift in $(12,5)$ was larger than that in $(9,8)$⁠. The $En,m(T)$ of the $(11,6)$ SWCNT increased with increasing temperature.

In SWCNTs without a water adsorption layer, $En,m(T)$ exhibited a simple temperature dependence that was unaffected by chirality.²⁰ By contrast, SWCNTs with water adsorption layers showed a complex temperature dependence, as seen in Figs. 1 and 2. It is known that $En,m(T)$ is affected by various factors, such as temperature, dielectric constant around the nanotube, $ϵenv$⁠,¹⁸ and axial strain.¹³ Here, we assumed that the factors that simultaneously contributed to the temperature dependence of $En,m(T)$ were the bandgap variations, environmental conditions, and axial strain due to the difference in thermal expansion between the SWCNTs and the adsorption layer.

In the case of SWCNTs without a water adsorption layer, the simple temperature dependence of $En,m(T)$²⁰ can be expressed by

where $E0n,m$ is the emission energy in vacuum at $0K$ and $ΔEintrinsicn,m(T)$ is the intrinsic temperature dependence of the emission energy shift obtained in vacuum (⁠$a=0.177meV/K$ and $T0=1800K$²⁰). In order to take into account the environmental and strain effects, two terms are added in the case of SWCNTs with an adsorption layer. Thus, the expression for $En,m(T)$ becomes

where $ΔEϵn,m(T)$ and $ΔEstrainn,m(T,Tad)$ are the energy shifts due, respectively, to the change of $ϵenv$ and to the strain induced by the adsorption layer. $Tad$ is the temperature at which the adsorption layer is formed. For simplicity, it is assumed that $ΔEϵn,m(T)$ and $ΔEstrainn,m(T,Tad)$ are proportional to temperature,

and

where $α$ is a constant, $p=1$ (type-I) or $−1$ (type-II), $θ$ is the chiral angle, $ϵ(T)$ is the strain along the tube axis, $t0$ is the graphene tight-binding overlap integral for the nearest-neighbor $π$-bonds (⁠$t0=2.7eV$⁠), and $ν$ is Poisson’s ratio (⁠$ν=0.2$⁠).²⁷ It is also assumed that $ΔEϵ,0n,m$⁠, $Δeϵ$⁠, and $α$ are constants that are independent of $(n,m)$⁠. Equation (2) becomes

where

In Eq. (5), $E0′n,m$⁠, $Δeϵ$⁠, and $α$ are unknown constants. The measured $En,m(T)$ are fitted by Eq. (5) using these variables as the parameters.

The measured $En,m(T)$ of SWCNTs with different $12$ chiralities are shown in Fig. 3. The $En,m(T)$ values were well-fitted by Eq. (5) for SWCNTs of all chiralities. The SWCNTs clearly fell into two categories, viz., type-I and type-II, which indicates that the temperature dependence of $En,m(T)$ is strongly affected by the strain. The value of $α$ was $−7.6×10−5K−1$⁠, which means that a tensile strain of $1.4×10−3$ was induced by a temperature decrease of $100K$⁠.²⁷ The tensile strain indicated that the adsorption layer did not have liquidity comparable to bulk water in the liquid phase. The poor liquidity was consistent with the low volatility and high stability observed even under low vapor pressure. Note that the temperature dependence of the PL emission energy of SWCNTs dispersed in water has been explained in terms of only strain effects (⁠$ΔEstrain$⁠)¹¹ because the strain of SWCNTs dispersed in water was larger than that of suspended SWCNTs.

Finally, the environmental effect on the temperature dependence was investigated. $ΔEϵn,m(T)$ was calculated by Eq. (2) with $α=−7.6×10−5K−1$⁠, and the value of $Eϵ,0n,m(T)$ was determined to reproduce the energy shift due to water desorption at room temperature.^28,29 In Fig. 4, the temperature dependence of $ΔEϵn,m(T)$ of some SWCNTs with different chiralities is shown. Data obtained in the lower temperature range (between $−130$ and $20°C$⁠) were shown as well. $ΔEϵn,m(T)$ between $−40$ and $20°C$ were obtained under the assumption that the temperature dependence was linear [Eq. (3)], and they clearly showed the slope of $Δeϵ$ in Fig. 4. On the other hand, although $ΔEϵn,m(T)$ between $−140$ and $−40°C$ were simply calculated by Eq. (5) using $α$⁠, without the assumption of linearity, they showed the same trend as in the higher temperature range.

The contribution of the environmental effect decreased with increasing temperature, which indicated that $ϵenv$ decreased with increasing temperature. Based on the time scale of exciton dynamics, only electronic polarization contributes to $ΔEϵn,m$⁠. The electronic polarization of bulk water in the solid phase slightly increases with increasing temperature.³⁰ Therefore, $ΔEϵn,m(T)$ cannot simply be explained by the temperature dependence of the electronic polarization of water in the solid phase. Furthermore, since $ΔEϵn,m(T)$ changed monotonically, the adsorption layer did not show phase transition behavior in the present temperature range. $ΔEϵn,m(T)$ suggested that the density of the water adsorption layer decreased with increasing temperature.

These features, i.e., the imposition of strain (nonliquidity), dielectric constant decrease with increasing temperature, and the absence of phase transitions from RT down to $140K$⁠, are completely different from bulk water. On the other hand, they can be understood from the molecular dynamics simulation results of double-layered water adsorption on the graphene surface.³¹ The water molecules in the adsorption layer form temporal lateral-polygon clusters. At low temperature (⁠$100K$⁠), the dominant polygons in double-layered water are mainly tetragonal, pentagonal, and hexagonal, while the density of these polygon clusters decreases with increasing temperature (⁠$250K$⁠), indicating a decrease in the areal density of water molecules in the adsorption layer.³¹ The water adsorption layer does not have a crystalline structure but can be regarded as a two-dimensional disordered solid-like phase.

We have investigated the temperature dependence of PL spectra of individual suspended SWCNTs by PL spectroscopy to elucidate the physical properties of water adsorption layers on the surface of SWCNTs. At higher temperatures, the PL emission spectra for SWCNTs without a water adsorption layer only reflected the bandgap change with temperature regardless of SWCNT chirality, while those at lower temperatures for water-adsorbed SWCNT surfaces exhibited chirality-dependent changes even in vacuum: opposite trends for type I and type II SWCNTs and the dependence of the chiral angle. These results were quantitatively explained on the basis of three factors: changes in the bandgap, the dielectric constant of the adsorption layer, and the strain imposed by the adsorption layer, assuming linear temperature dependences for the dielectric constant and strain. The dielectric constant of the adsorption layer obtained experimentally showed no transitional behavior, which indicated the absence of phase transitions. The present findings suggested that the water adsorption layer on the SWCNT surface might be a two-dimensional disordered solid rather than a liquid.

This work was supported in part by a MEXT Grant-in-Aid for Scientific Research on Innovative Areas “Science of hybrid quantum systems” (Grant No. 15H05869) and a Grant-in-Aid for Scientific Research (C) (No. 19K05200). The authors acknowledge support from the Nanocarbon Research Division and the Water Frontier Science & Technology Research Center of the Research Institute of Science & Technology at the Tokyo University of Science.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.