Efficient liquid exfoliation of KP15 nanowires aided by Hansen's empirical theory

The KP15 nanowires with one-dimensional properties has a defect-free surface, high anisotropy, and carrier mobility which is desirable for the development of novel nanodevices. However, the preparation of nanoscale KP15 is still inefficient. In this work, the Hansen solubility parameters of KP15 were first obtained. Based on the Hansen's empirical theory, the concentration of liquid-exfoliated KP15 nanowires was improved to 0.0458 mg·mL−1 by a solution containing 50% water and 50% acetone. Approximately 79% of the KP15 nanowires had a thickness value below 50 nm and 60.9% of them had a width value below 100 nm. The thinnest KP15 nanowires reached 5.1 nm and had smooth boundaries. Meanwhile, strong temperature-dependent Raman response in exfoliated KP15 nanowires has been observed, which indicates a strong phonon–phonon coupling in those nanowires. This is helpful for non-invasive temperature measurements of KP15 nanodevices.


Introduction
Low-dimensional materials have drawn significant attention in recent years. So far, not only new composite materials with excellent properties have been obtained by the synthesis of dif-ferent materials, but also low-dimensional materials with different properties than those of bulk materials have been synthesized by physical and chemical methods. For instance, Bingjun Yang used one-dimensional graphene nanoscroll-wrapped MnO nanoparticles as anode materials to promote the rapid diffusion and electron transfer of lithium, and Rongjun Zhao prepared n-butanol gas sensors with one-dimensional In 2 O 3 nanorods [1,2]. Different from 2D materials, 1D materials generally have a chain-like crystal structure and are easily exfoliated due to a weak interaction between these chains [3,4]. Therefore, those 1D materials have defect-free surfaces, high anisotropy, and carrier mobility. For example, TiS 3 nanowires obtained by mechanical stripping have a large carrier mobility of about 10000 cm 2 ·V −1 ·s −1 [5][6][7]. Fibrous phosphorus is also a new one-dimensional material with high carrier mobility (308 cm 2 ·V −1 ·s −1 ) and rapid response time [8][9][10]. These onedimensional materials are ideal for photovoltaic and photocatalytic applications.
The KP 15 is considered to be a novel low-dimensional material with layered structure, high hole carrier mobility (1000 cm 2 ·V −1 ·s −1 ), and highly anisotropic properties [11]. The photodetectors prepared with KP 15 have a fast response time and are ideal materials for photovoltaic applications [12]. Based on our previous studies, KP 15 is also a one-dimensional material with a defect-free surface [13,14]. This is beneficial for the development of high-performance nanodevices. Searching effective synthesis routes for nanoscale KP 15 has become an urgent issue. Liquid-phase exfoliation is one of the most straightforward methods to prepare low-dimensional materials at a low cost and with simple processes and high flexibility. In this case, the surface of bulk materials is peeled off or corroded by physical or chemical reactions in a liquid medium, and finally low-dimensional materials are obtained. Based on the Hansen's empirical theory, the exfoliation efficiency of lowdimensional materials can be improved by adjusting the composition and type of solutions used in the liquid-phase exfoliation [15][16][17]. This theory has been successfully used for improving the exfoliation efficiency in several low-dimensional materials, such as carbon, graphene, metal oxides, and fibrous phosphorus. [18].
In a previous study, we exfoliated KP 15 in alcohol; however, this method was still inefficient [13]. Herein, the Hansen's empirical theory was firstly introduced to improve the liquidphase exfoliation efficiency of KP 15 nanowires. In addition, Hansen solubility parameters (HSPs) for KP 15 were also obtained in this work. By using a solution containing 50% water and 50% acetone, the exfoliation efficiency of KP 15 was effectively improved. Our results show that 79% of the KP 15 nanowires had thickness values below 50 nm and 60.9% of these nanowires had width values below 100 nm. The thinnest KP 15 nanowires reached 5.1 nm and had smooth boundaries. Meanwhile, a strong temperature-dependent Raman response was found in exfoliated KP 15 nanowires. This indicates a strong phonon-phonon coupling in KP 15 nanowires, which favors non-invasive temperature measurements of KP 15 nanodevices.

Synthesis of KP 15 bulks
The KP 15 bulks were prepared by the gas-phase transfer method. High-purity red phosphorus (1.370 g, 99.9999%) and metallic potassium (0.130 g, 97%) were mixed in a quartz tube. The temperature gradient in the quartz tube was 650 °C/400 °C and the heat treatment time was 12 h. After annealed, dark-red KP 15 bulks were finally obtained.

Liquid exfoliation
For the liquid-exfoliation process, 1 mg of KP 15 was mixed in 20 mL of solvent and ultrasonically processed at a power of 80 W in an ice bath for 6 h, followed by centrifugation at 2000 rpm for 20 min. For the samples with predetermined concentration, centrifugation was not used.

Measurement equipment
UV−visible spectrophotometry was performed by using a Shimadzu UV-3101PC system. Atomic force microscopy (AFM) tests were performed in a Multimode 8 system. The Raman tests were performed on a WITec alpha300 RA confocal Raman microscopy system. For the Raman tests, KP 15 samples were spun on SiO 2 (300 nm)/Si substrates. The excitation wavelength used was 532 nm, the spot size was approx. 1 μm, and the laser power was kept below 20 μW. For low-temperature Raman measurements, a Linkam THMS600 cryostat cooled by liquid nitrogen was used to control the temperature. To prevent sample drift, SiO 2 (300 nm)/Si substrates with tested KP 15 samples were attached by fixtures to the Linkam THMS600 cryostat.

Results and Discussion
KP 15 bulks, prepared by the gas-phase-transfer method, had a flat and smooth surface shown in Figure 1a. The X-ray diffraction patterns of the synthesized KP 15 were both theoretically calculated and experimentally measured. The consistency between the two patterns shows that there is no impurity phase (Figure 1b), which confirms an excellent crystallization quality of the KP 15 bulks.

Measurement of the absorption coefficient and the Hansen solubility parameters for KP 15
According to the Hansen's theory [19], the dispersed concentration C of a KP 15 dispersion prepared by liquid exfoliation can be expressed by Equation 1 as follows. (1) where δ D is the intermolecular dispersion force, δ H is the intermolecular hydrogen bond; δ P is the intermolecular polar force; δ A,D , δ A,P , δ A,H are the Hansen solubility parameters (HSPs) of the solute; and δ B,D , δ B,P , δ B,H are the HSPs of the solvent. Therefore, to get a high concentration of KP 15 in dispersion, the HSPs of the solvent for the exfoliation of KP 15 should be close to those of KP 15 . A weighted average method was used to calculate the HSPs of KP 15 . The concentration of KP 15 was used as a weight factor for each suspension. This way, the HSPs of KP 15 can be expressed according to Equation 2 [19]. (2) where δ i,sol are the HSPs of the solvent and C is the concentration of the KP 15 dispersions. The Lambert-Beer law (Equation 3) was then used to measure the concentration of the KP 15 dispersions: where A is the absorbance, K is the absorption coefficient of the material, b is the absorbing layer thickness (which in this work is the width of the cuvette, i.e., 1 cm), and C is the concentration of the KP 15 dispersions. The absorbance A and the absorption coefficient K are related to the wavelength of the incident light. To determine A and K, it is necessary to choose a specific incident wavelength. The bandgap of bulk KP 15 is approx.
1.75 eV [20]. However, according to our previous study, with thickness reduction of the KP 15 nanowires, a surface-state luminescence at 693 nm gradually dominates in the KP 15 nanowire [14]. This could affect light absorption properties of KP 15 due to its decreased size.
To avoid the generation of concentration error caused by the absorbance influence of the surface state, a wavelength (800 nm) which is far away from the bandgap of KP 15 bulk and surface state in the KP 15 nanowires was chosen. Some dispersions for which we predetermined the concentration were prepared to fit and determine the absorption coefficient K. Solutions of five different concentrations of KP 15 dispersions in butyrolactone were prepared by liquid exfoliation with a predetermined concentration. UV−visible absorption spectra results are shown in Figure 2. The concentration linearly varies with absorbance. The slope of this fitted linear equation is 3.86 ± 0.13. This means that the absorption coefficient of KP 15 is 3.86 ± 0.13 mL·mg −1 ·cm −1 .
We selected 20 common solvents, including benzyl benzoate, toluene, ethyl acetate, acetone, alcohol, butyrolactone, N,N'dimethylpropyleneurea, bromobenzene, cyclopentanone, N-dodecyl-2-pyrrolidone, glycol, vinyl acetate, hexane, isopropyl alcohol, N,N-dimethylformamide, O-phthalic dimethyl ester, dimethyl sulfoxide, N-methylpyrrolidone, water, and cyclohexanone. The HSPs of those solvents are listed in Table 1.     15 and the HSPs of a given solvent is reduced, τ can be reduced with an improved exfoliation efficiency. Figure 5 shows the concentration of KP 15 dispersions as a function of τ. When τ tends to zero, the concentration of the KP 15 dispersion reaches the maximum value, which corresponds to the results of the aforementioned equation.

Liquid exfoliation of one-dimensional KP 15
The HSPs obtained for KP 15   where ϕ i,comp is the volume fraction of the corresponding solvent and δ i,comp is the HSPs of the solvent. The concentration of the KP 15 dispersion can be measured by the Lambert-Beer law (Equation 3). As shown in Figure 6a, by tuning the volume fraction of acetone in the mixed solution, the HSPs of the mixed solution can be close to those of KP 15 , and the exfoliation effi- ciency can be clearly improved. The concentration values of the KP 15 suspension in the solutions were 0.0268 mg·mL −1 (exfoliated in deionized water), 0.0079 mg·mL −1 (acetone), and 0.0236 mg·mL −1 (alcohol), respectively [13]. When the solvent mixture with a 50% volume fraction of acetone is used for stripping, the concentration of the KP 15 dispersion finally increases to 0.0458 mg·mL −1 . At this point, the parameter τ is close to the minimum value.
The Raman result for the KP 15 nanowires exfoliated in water−acetone mixed solution is shown in Figure 7c.  [11]. As shown in Figure 7d, Figure 7e, and Figure 8, the thinnest KP 15 nanowires obtained by liquid exfoliation could reach 5.1 nm and had smooth boundaries. The thicknesses of 79% of the liquid-exfoli-  ated KP 15 nanowires were below 50 nm; the widths of 60.9% of the KP 15 nanowires were below 100 nm. The sizes of the obtained KP 15 nanowires were much smaller than those obtained in our previous studies [13]. Meanwhile, a strong temperaturedependent Raman response in exfoliated KP 15

Conclusion
In summary, based on the Hansen's empirical theory, the liquid phase exfoliation efficiency of KP 15 nanowires has been improved. The HSPs of KP 15 were calculated to be δ D = 17.60 MPa 1/2 , δ P = 11.19 MPa 1/2 , and δ H = 8.95 MPa 1/2 . In addition, based on the Hansen's empirical theory, the exfoliation efficiency was improved by adjusting the ratio of water and acetone. When the mixed solvents had the smallest τ, the thick- nesses of 79% of liquid-exfoliated KP 15 nanowires were below 50 nm and the widths of 60.9% of KP 15 nanowires were below 100 nm. Meanwhile, a strong temperature-dependent Raman response has been found in exfoliated KP 15 , which may help with non-invasive temperature measurements of KP 15 nanodevices.