Thermal Stability and Flexibility of Hydrogen Terminated Phosphorene

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C: Physical Processes in Nanomaterials and Nanostructures

Thermal Stability and Flexibility of Hydrogen Terminated Phosphorene Nanoflakes Dorina Bódi, and Tibor Höltzl J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11817 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 16, 2018

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The Journal of Physical Chemistry

Thermal Stability and Flexibility of Hydrogen Terminated Phosphorene Nanoflakes Dorina Bódi1, Tibor Höltzl1,2* 1

Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest,

Hungary 2

Furukawa Electric Institute of Technology, Késmárk utca 28/A, H-1158 Budapest, Hungary

Keywords: phosphorene, mechanical properties, nanoflakes, quantum dot, black phosphorus

* Corresponding author: Tibor Höltzl, e-mail: [email protected]

Abstract: Phosphorene nanoflakes are emerging candidates of black phosphorus nanostructures due to their unique, tunable properties like size-dependent band gap, effective synthesis methods and widespread possible applications. While it is apparent that the stability and flexibility of phosphorene nanoflakes is crucial for several applications, there is only few information available. In this article we investigate the stability and flexibility of phosphorene nanoflakes in the gas and liquid phases using quantum chemical and ab-initio molecular dynamics methods as well as the External force Explicitely Included (EFEI) method. Our results show that phosphorene nanoflakes are energetically more stable than white phosphorus, while in the gas 1 ACS Paragon Plus Environment

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phase free energies show opposite trend. However in liquid phase the formation of phosphorene nanoflakes is preferred over white phosphorus. Molecular dynamics simulations show that phosphorene nanoflakes have flat shapes and are stable, while their flexibility depends on their geometry. Surprisingly, despite their flexibility, phosphorene nanoflakes keep their quasi-planar structure up to at least 500K, while at higher temperatures they distort before the decomposition starts.

1. Introduction Phosphorene, the recently discovered 1 2 3 4 5 6 single layer allotrope of phosphorus is one of the most promising candidates for novel electronics applications. phosphorene has a significant direct band gap of 2.5 eV

7 8

Compared to graphene,

, comparable to that of silicon

9 10

11

and

similarly to graphene it has notably high electron and hole mobilities, what make it a promising transistor material.

3 12

The appropriate band gap of phosphorene is also attractive for

photocatalytic applications, especially for water splitting. 13 For practical applications the control and tuning of the properties is important. The band gap can be tuned by the number of the phosphorene layers in a multi-layer structure.

, and also by

14 15

the formal cut of two dimensional phosphorene into quasi one dimensional nanoribbon.

14 16 17

One of the most promising materials derived from phosphorene are the nanoparticles, as for these not only the properties are excellently tunable but also exist facile synthesis methods. 18 19 20 Phosphorene flakes are synthesized and investigated recently and their properties are found to be similar to the bulk phosphorene.

21

It was shown that high quality flakes could be generated 2

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with a lateral dimension ranging from 400 to 600 nm and thickness between 2 and 10 nm.

21

It

was also verified that the dispersion of phosphorene in dimethyl-sulfoxide was stable at room temperature under nitrogen and in the dark for at least one week, while in air the stability was reduced to only a few hours.

. Phosphorene is sensitive not only to air, but also to water.

21

22

However Zhang et al. showed using ab-initio computations that the chemical stability of phosphorene can be greatly enhanced using an external electric field. 23 Also a recent study showed that the stacked black phosphorus flakes can be used in humidity sensing. 24 Recently, phosphorene quantum dots of diameter 2.6 to 15 nm were also synthesized and found to be promising candidates for photothermal therapy of cancer

25 26 27

. Sun et al prepared

28 29

water-soluble and biocompatible polyethylene glycol treated black phosphorus nanoparticles, which have excellent photostability and they can efficiently convert near infrared light into heat. 28 This property makes them suitable for detection and treatment of cancer using by photoacoustic imaging and photothermal therapy, respectively.28 The possible applications of the phosphorene nanoflakes and quantum dots are widespread

30

, they can be applied as visible-light photocatalyst for water splitting

,,

31

, solar cells

32

33 34 35 36

optoelectric applications37, as promising anode materials in lithium or sodium ion batteries fluorescent sensing platforms for DNA detection evaluating the acetylcholinesterase.

40

39

, as

38

and fluorescence sensing platforms for

The quantum dots have size-dependent optical properties

32,41

, what is especially important in optoelectronic applications like electrically tunable p–n

diodes.

38

Due to their remarkable optical response

42 43

and the nonlinear optical saturable

absorption properties the phosphorene quantum dots can be used for ultrafast fiber lasers 44 45 and 3 ACS Paragon Plus Environment


UV photonic devices.

46

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Wang et al. showed that the structural defects and oxidation created

during the synthesis have a small effect on the photoabsorption of phosphorene quantum dots until the coordination number of defective P atoms is 3.47 Stability is one of the most important factor for the application of phosphorene-based materials. The 2D phosphorene has a negative cohesive energy.4,48 A recent study shows that the stability of the metal supported phosphorene nanoflakes composed only of phosphorus atoms depend strongly on the interaction strength between the nanoflake and the substrate and the interaction energy in a specific range is crucial for the successful synthesis. 49 Initial steps of the growth mechanism of blue phosphorene on Au(111) surface was explored recently and the interaction energy shows the synthetic potential of phosphorene.

50

Also, the interaction with the

support influences considerably the thermal-mechanical properties of phosphorene nanoflakes51. It is well known that phosphorene is a highly flexible material and its structure can be deformed easily.

52

The energy difference between the black and blue phosphorene is small, so

they can be converted into each other through a moderate potential energy barrier. 53 Based on this it is expected that phosphorene nanoflakes should also be flexible. This is especially important as nanoflakes are small, so it is not clear at what conditions is their structure flat (2D), deformed or coiled. In this paper we investigate several types of hydrogen terminated phosphorene nanoflakes with diameters up to a few nanometers, which have several potential applications. 32,34 The aim of our article is to examine the thermal and kinetic stability and the flexibility of free phosphorene nanoflakes with hydrogen termination and also their dependence on the size and structure. 4 ACS Paragon Plus Environment

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Therefore we studied the structure, stability, and flexibility of phosphorene nanoflakes using quantum chemical methods and molecular dynamics based on density functional theory.

2. Methods and computations Molecular geometries were optimized using the ωB97X-D functional 54 and the 6-31G** basis set,

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which allows to compute large systems and at the same time provides accurate

geometries. The details of the selection and verification of the methods are available in the Supporting Information (see Table 1S, Figure 1S and Figure 2S). Harmonic vibrational frequencies were computed to confirm that the computed stationary points are minima on the Potential Energy Surface. Subsequently more accurate single point energy computations were performed using the M11/cc-pVTZ

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computed

the

using

method. Molecular dynamics simulations were more

economical

ωB97X-D/LANL2DZ method 59, which was confirmed to provide accurate energy differences for the different conformation isomers of the studied nanoflakes. The effect of the time step of the molecular dynamics was tested in the range of 0.121 fs (5 a.u.) to 0.968 fs (40 a.u.). Finally the time step of 0.48 fs (20 a.u.) was used in the molecular dynamics simulations, what was shown to give consistent results with the smaller time steps. Totally 20 ps was simulated in each case, which corresponds to ~41000 Density Functional Theory computations. Solvent effects were estimated using the SM12 model, 60 as it is implemented in the Q-Chem software.

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To estimate the flexibility of phosphorene nanoflakes we used the External Force Explicitely Included (EFEI) computations

, where two selected atoms of the nanoflake are pulled in

61 62

opposite directions by a given external force, while optimizing the geometry by minimization of all other forces. Thus the deformation due to an external forces on different pairs of atoms can be observed, and the flexibility can be characterized in different directions. All computations were performed using the Q-Chem 4.4 software suite

, while the IQmol

63

64

user interface was used for the visualization of the results.

3. Results and discussions Size dependent stability Nanoflakes can be obtained by formal cutting of smaller nanoparticles from the two dimensional phosphorene lattice, similarly to the recently studied phosphorene nanoflakes and quantum dots 32 34

,

and nanoribbons.65,

66, 67

We constructed the geometry of phosphorene nanoflakes by

successively increasing the number of the P6 rings in the structure, as it is shown in Figure 1. The resulting dangling bonds were terminated using hydrogen atoms, as it was reported earlier. 32,34 The hydrogen termination of the dangling bonds leads to trivalent phosphorus atoms, thus the geometric structure does not distort or reconstruct from a phosphorene-like structure in phosphorene nanostructures,32,34,68,69,70 while bare phosphorus nanoflakes tend to reconstruct. 49 It was shown recently that phosphorene nanoribbons without edge termination reconstruct into a configuration, which is even lower in energy than the hydrogen terminated system. 71 However the


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conditions (especially the hydrogen partial pressure) has a great role in the thermodynamic stability and at appropriate conditions the hydrogen terminated edges can also be stabilized.71 Its is well known that phosphorene can exhibit several different conformations, 72,6 similarly to that of cyclohexane. There are two main structural types of phosphorene nanoflakes: black and blue phosphorene,72 as it is shown in Figure 1. It has to be noted that there are several other conformers, as Tománek et al. demonstrated by using a 2D tiling model that there is a one-to-one correspondence between the coloring of a triangular lattice and the three dimensional structure of the different phosphorene conformers. 72 It was shown recently that phosphorene decomposes at ~400 oC (~700K) in vacuum,73 therefore the optimal condition for the stability of phosphorene nanoflakes is an important question. Generally, by definition the most stable allotrope of the different elements has 0 kJ/mol standard enthalpy of formation. However phosphorus is an exception as white phosphorus has 0 kJ/mol standard enthalpy of formation by definition, while black phosphorus is the most stable form. This is due to the lack of accurate data on the heat of formation of black phosphorus.

74

Therefore we have compared the stability of both phosphorene conformations with that of the white phosphorus using the following equations:

n P H 3 =P n H m +

3 n−m H2 2

4 P H 3= P 4+ 6 H 2

(1) (2)



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Figure 1: Side view of black and blue phosphorene and top view of black and blue phosphorene nanoflakes of different ring count

This can be regarded as a possible method to produce phosphorene nanoflakes from phosphine or in the reverse direction the hydrogenation of phosphorene. The computations showed that the reaction energy correlates linearly with the number of the rings. Black phosphorene nanoflake is slightly more stable than the blue phosphorene at higher ring count. The relative reaction energy normal to one phosphorus atom is in the range of +19 and +21 kJ/mol, independently on the conformation and the size of the nanoparticle, while the reaction energy of white phosphorus normal one phosphorus atom is +24 kJ/mol. This shows that the phosphorene nanoflakes are 8 ACS Paragon Plus Environment

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more stable energetically than the commonly available white phosphorus. This supports that phosphorene nanoflakes are important synthetic targets. This is in line with the negative atomization energies of phosphorene quantum dots.32 During a synthesis at typical laboratory conditions (constant pressure and temperature) the free-energy shows the thermodynamic feasibility of a process. The free-energy change of gas phase synthesis reaction from phosphine at different temperatures for various ring counts is similar for both conformations. (Figure 2) The free-energies indicate that white phosphorus is more stable thermodynamically than the phosphorene nanoflakes. This can be explained by the entropy effect as different quantity of molecules are formed in the case of phosphorene nanoflakes or white phosphorus.



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Black-P

Blue-P

Figure 2: Reaction free-energy with respect to temperature of black and blue phosphorene nanoflakes in gas phase at different temperatures and pressure of 1 bar.


1 0

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Equation 2 shows that the formation of for example 4 mol white phosphorus from 16 mol phosphine, yields 24 mol H2, while according to Equation 1, only 19 mol is formed in the case of P16H10 phosphorene nanoflake. However, the free-energy change during the formation of different phosphorene nanoflakes shows that the larger the nanoflake, the larger the temperature dependence of the free-energies. This can be explained again with the larger number of molecules on the right hand side of the reaction equation compared to the left hand side, since more and more H2 dissociates as the nanoflake grows. It is well visible in Figure 2 that larger phosphorene nanoflakes, especially at higher temperature are more stable, however even the formation of the largest nanoflake is suppressed in the gas phase at atmospheric pressure due to the positive Gibbs-free energy change. Nevertheless, the tendency is clear from Figure 2, large flakes are considerably more stable thermodynamically and we expect that the further increase of the phosphorene size and the inclusion of the stabilization effect of the surface makes the process thermodynamically allowed. Also, it was shown by computed phase diagrams that the hydrogen terminated edge state of phosphorene nanoribbons can be stabilized at appropriate temperature and hydrogen partial pressure conditions. 71 Table 3S in the Supporting Information shows that most of the bare phosphorene nanoflakes reconstruct into a lower energy state, while all the hydrogen terminated phosphorene nanoflakes keep their phosphorene-like structures. Also, the already stabilized bare phosphorene nanoflakes can further reconstruct to an even more energetically stable configuration, which does not have phosphorene structure.75,76 Moreover the reconstuction depends considerably on the type and size of the nanoflakes. In order to elucidate the necessary conditions for the thermodynamic stabilization of


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phosphorene nanoflakes we computed the black phosphorene phase diagrams with respect to temperature and pressure, respectively. For the computations we used a similar method to that in reference,71 but computed the free energy of all the involved compounds at different temperatures and pressures.

P10H8 – P10

P28H14 - P28

P52H18 - P52 Figure 3. Phase diagram of phosphorene nanoflakes at different temperatures and total pressures. Thus, similarly to tha case of phosphorene nanoribbons 71, hydrogen terminated phosphorene nanoflakes can be stabilized thermodynamically at appropriate pressure and temperature conditions.


1 2

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The reaction free-energy change according to Equation 1 in dimethylformamide (DMF) solvent shows that the formation of phosphorene is preferred against the white phosphorus, however the formation free-energy is still positive. As it can be seen in Figure 3, the reaction free-energy depends linearly on the ring number and the free-energies of black phosphorene are slightly lower than those of the blue phosphorene nanoflakes. The reaction free-energy referred to one phosphorus atom in the case of phosphorene nanoflakes is in the range of +22 and +24 kJ/mol independently from the conformation and the size of the nanoparticle, while the reaction freeenergy of the white phosphorus normal to one phosphorus atom is +29 kJ/mol (Figure 4).

Figure 4: Reaction free-energy normal to one phosphorus atom respect to the ring count of hydrogen terminated black and blue phosphorene nanoflakes and white phosphorus in the liquid phase.

This shows that the reaction energy of phosphorene nanoflakes is less positive than that of the white phosphorus, thus energetically these are relatively stable structures. However, the study of the free-energy change of gas phase synthesis from phosphine at different temperatures showed


1 3


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that the formation of white phosphorus is preferred due to the entropy reasons. This indicates, that the synthesis of phosphorene nanoflakes are possible either in a solvent phase or surface preparation methods. Larger nanoflakes may also be synthesized in the gas phase due to their lower Gibbs-free energies. Flexibility It was shown earlier that 2D black phosphorene is a flexible material, indicated by the large maximum tensile strain.52 Also, monolayer black phosphorene has anisotropic mechanical properties, as the deformation is easier in the armchair direction, what is attributed to the stretching of the puckered layer.52 So in the case of monolayer phosphorene flexibility is indicated by the easy mechanical deformation. In the case of phosphorene nanoflakes there are much more possibilities for mechanical deformation, as for the small size, the different conformations (black or blue phosphorene) raise the question about the planarity. Thus we analyze the flexibility of phosphorene nanoflakes by two different point of views: (i) are they quasi-planar at typical laboratory conditions and (ii) how easy is to deform their structures with respect to an external force? We investigated the flexibility of phosphorene nanoflakes at different conditions using molecular dynamics simulations. While currently the maximum attainable time in ab-initio molecular dynamics is typically in the range of a few picoseconds, decomposition in a laboratory often takes place in seconds or minutes. Thus high temperature molecular dynamics is often used to accelerate the chemical reactions in the simulations and to get qualitative information on the


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possible chemical transformations. Therefore we carried out molecular dynamics simulations also at high temperature. We analyzed the time dependent RMSD (root mean square deviation) compared to the initial structure (Figure 5). As it can be seen on the diagrams and associated pictures, both conformations are stable at room temperature and 500K, as there is no significant deformation and the RMSD varies between 0.2 and 0.9 Å. At this condition the atoms vibrate around the equilibrium configuration. This indicates that at ambient conditions phosphorene nanoflakes have flat structure. On the other hand at 1000K the black and blue phosphorene nanoflakes behave differently. While only the backbone of the blue-P nanoflake deforms, in case of the black-P reaction occurs and the bonds begin to dissociate. At 1000K the RMSDs of both conformations show a growing tendency with respect to time instead of oscillation around equilibrium. This is due to the collapse of the rings, as phosphorene nanoflakes start to degrades rapidly at this temperature. At very high temperature of 2000K the degradation is well visible even in short simulation times. This indicates that although phosphorene nanoflakes are flexible, at room temperature and at 500K there is no significant deformation and at laboratory environment the shapes of phosphorene nanoflakes can be considered as flat and stable. At higher temperature the nanoflakes deform and degradation also takes place.


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Figure 5: RMSD with respect to time of black and blue phoshorene nanoflakes at different temperatures. Initial and final geometries are also shown on the figure.


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Since the 2D phosphorene layer has an anisotropic geometric structure, its flexibility depends on the orientation.

52

Thus the anisotropic flexibility of phosphorene nanoflakes is an interesting

question. After the dynamics calculations we examined the deformation due to an external force as implemented in the External Force Explicitly Included method of Q-Chem software. This method models the atomic-scale analogue of the macroscopic tensile test and it is able to simulate the atomic-scale mechano-chemical transformations of the materials. 77 We examined the deformation of black and blue phosphorene nanoflakes having 8 rings due to an external force acting at different directions (Figure 5).

Figure 6: Different external force directions of black and blue phosphorene nanoflakes with 8 rings

Figure 7 shows the force-strain curve of phosphorene nanoflakes at different directions. Strain is defined as the distance of the pulled atoms compared to that of the original structure. The anisotropic properties of black-P are well visible, as the slope of the force-strain curve (a quantity analogous to the macroscopic Young modulus) varies from 0.46 to 0.17 Å/nN, depending on the


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force direction. The isotropic properties of blue-P can also be observed, as pulling in either directions cause similar strain as the slope of the force strain curve is 0.18-0.19 Å/nN, irrespectively the force direction. Applying the same force, the strain of black-P is higher than that of the blue-P. This can be explained by the side view pictures in Figure 1, as the small change of bond angles of black-P causes considerable strain unlike in the case of blue-P. There are however other directions (black-P 4 in Figure 8) where the strain is similar to that of the blueP. It is well visible in both conformations that initially the strain depends linearly on the applied force and it is an elastic deformation. Applying stronger forces to the nanoflakes, the structure of phosphorene nanoflakes begin to collapse and small molecules (like P2H2) are separated.

Figure 7: Strain with respect to force diagram by pulling the nanoflakes at different directions (the numbers of the notation corresponding to the numbers of Figure 6)


1 8

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Figure 8: Geometries of strained phosphorene nanoflakes and the direction of external forces in the EFEI computations. The external force is shown by arrows.

The strain-energy curve (Figure 9) shows that at the 8-ring number black phosphorene nanoflakes in some directions (Black-P 1, Black-P 2) do not collapse due to the strain, even if the energy is increased by 500 kJ/mol. It suggests that the phosphorene nanoflakes could be used as structural material in composites.


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Figure 9: Energy with respect to strain for nanoflakes by different directions of black and blue phosphorene

Thus phosphorene nanoflakes are quasi-planar at typical laboratory conditions and their mechanical deformation with respect to an external force is similar to that of the phosphorene monolayer reported in.52

4. Conclusions Geometry, energetic and thermodynamic stability and flexibility of free black and blue phosphorene nanoflakes with hydrogen edge termination were studied using density functional theory methods. Nanoflakes spread from molecular size (0.2-0.6 nm) to nano-size (1-2 nm). While the black phosphorene nanoflakes have an anisotropic structure with anisotropic stressstrain relationship, the blue phoshorene is isotropic, similarly to the macroscopic counterpart.


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The black phosphorene nanoflakes are strong materials, which can tolerate high energy effect without splitting, thus the nanoflakes could be used as structural material in composites. Hydrogen-terminated free phosphorene nanoflakes are energetically more stable than the commonly available white phosphorus, however are higher in energy than the bare phosphorene nanoflakes. However the phase diagrams show that at higher hydrogen partial pressure, hydrogen terminated phosphorene nanoflakes are stable.. During gas phase synthesis from phosphine the formation of white phosphorus is preferred due to the change of the entropy. This highlights the importance of the precursor for the gas phase synthesis. Larger phosphorene nanoflakes may also be synthesized in the gas phase from phosphine. The solvation computations show, that in the liquid phase the formation of phosphorene is preferred over the white phosphorus. This also indicates that either solvent phase or surface preparation methods are more suitable for the synthesis of phosphorene nanoflakes. The molecular dynamics simulations also confirm the stability of the phosphorene nanoflakes at up to 500K, and their shapes can be considered as flat. These provide important information for selecting the right conditions for phosphorene nanoflake synthesis.

Author information: *Corresponding author E-mail: [email protected] Tel: +36-1-417-3257

ORCID


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Tibor Höltzl: 0000-0002-9701-1966 Dorina Bódi: 0000-0003-3000-6211

Acknowledgments The authors thank Prof. Tamás Veszprémi for his support and advices.

Supporting information available: detailed data for method verification and cartesian coordinates of the different structures


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Table of contents graphics


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Thermal Stability and Flexibility of Hydrogen Terminated Phosphorene

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