Size-Dependent Crystal Transition Thermodynamics of Nano-VO2 (M)

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C: Physical Processes in Nanomaterials and Nanostructures 2

Size-Dependent Crystal Transition Thermodynamics of Nano-VO (M) Meng Wang, Yongqiang Xue, Zixiang Cui, and Rong Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01183 • Publication Date (Web): 22 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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The Journal of Physical Chemistry

Size-Dependent Crystal Transition Thermodynamics of Nano-VO2 (M)

Meng Wang, Yongqiang Xue∗, Zixiang Cui∗, Rong Zhang

Department of Applied Chemistry, Taiyuan University of Technology, Taiyuan, 030024, P. R. China

∗ ∗

Corresponding author. E-mail：[email protected] Tel.：86-0351-6014476 Corresponding author. E-mail：[email protected] Tel.：86-0351-6014476 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Vanadium dioxide exhibits a reversible crystal transition from monoclinic phase to rutile phase, but the quantitative regularity of effect of particle size on crystal transition thermodynamics still remain unclear. Herein, a new core-shell model was proposed and the universal equations for size-dependent crystal transition thermodynamics have been deduced. Experimentally, we researched the crystal transition behaviors of VO2 (M) with different particle sizes. The results indicate that with the particle size of nano-VO2 (M) decreasing, the temperature, enthalpy and entropy of the crystal transition decrease, and these thermodynamic properties are all linearly related with the reciprocal of particle radius, which are consistent with the theoretical formulas. More importantly, using the quantitative influence regularity of particle size on crystal transition temperature, we can obtain the different crystal transition temperatures for different applications by purely controlling the particle sizes.

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1. Introduction Vanadium can form dozens of vanadium oxides such as VO, VO2, V4O9, V2O3, V6O13, V3O7 and V2O5. In particular, VO2 has various polymorphisms including VO2 (A),1 VO2 (B),2 VO2 (M),3,4 VO2 (R),5 and VO2 (D).6 Among them VO2 (M) has been studied widely for metal–insulator transition (MIT) with undergoing a change in crystal structure from a low temperature semiconductor phase to a high temperature metallic phase at about 341K.7 The reversible first-order phase transition has been widely applied in such fields as those of temperature sensor,8 optical storage,9 field-effect,10,11 energy saving device12 and intelligent windows.13-15 From one side a great effort has been devoted to enhance the performances of the vanadium dioxide single layer through the use of optimized VO2 based multilayers,16-19 inverse VO2 opals and Photonic Band Gap structures,20-22 patterned nanostructures or metamaterials23,24 so to obtain optimal switch properties in the visible and/or in the infrared, and to minimize the deterioration of the structure with aging and fatigue cycles as can be revealed non-destructively by ultrafast infrared nanoscopy,25 AFM images,26 picosecond acoustics,27 etc. From another side a considerable interest has been raised in changing the metal-insulator phase transition to a lower temperature. Many researches indicate that doping with different types of elements into the lattice is a viable way to lower the phase transition temperature of VO2 (M).28-32 As an alternative to element doping, crystal transition temperature can be tuned purely by changing VO2 (M) to nanoscale dimensions.33-37 Sihai Chen et al. have lowered the transition temperature of VO2 (M) 3



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successfully by turning microparticles into nanoparticles, which has reduced the phase transition temperature to around 35 °C.34 Whittakeretal et al. also report that the size effect of VO2 (M) nanostructures on phase transition temperature is remarkable, which has been depressed to as low as 32 °C.35 The recent finding by Lei Dai et al. further indicate that the phase transition temperature of the VO2 (M) can be reduced to 5 °C only through regulating the particle size.36 However, the crystal transition temperature should be tuned to apply to different applications, and the quantitative regularity for size-dependent crystal transition should be figured out. Herein, a new core-shell model for crystal transition was proposed and the universal equations of size-dependent crystal transition thermodynamics have also been derived. Furthermore, the crystal transition behaviors of nano-VO2 (M) with different sizes were researched and the experiment results are in good agreement with the theory.

2. Crystal transition thermodynamic theory of nanoparticles The chemical potential of nanoparticles is equal to the sum of bulk chemical potential and surface chemical potential38

 ∂A    ∂n T , p

µ = µb + µs = µb + σ 

(1)

where µ b and µ s are bulk chemical potential and surface chemical potential, respectively (the superscript b and s denote the bulk and surface phases); σ is the surface tension; A and n are surface area and the amount of substance of nanoparticles.

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Throughout this paper the two crystal structures shall be referred to as α and β, respectively. The change of molar Gibbs energy ∆ βα Gm during the crystal transition is given by,  ∂Aβ ∆βα Gm = µβ − µ α = ∆βαGmb + σ β   ∂n  β

  ∂A   − σ α  α  T , p  ∂nα T , p

(2)

where ∆βα Gmb is the change in molar Gibbs energy of the bulk substance. When crystal transition is in equilibrium, namely, ∆ βα Gm = 0 , the Eq. (2) can be rewritten as  ∂Aβ   ∂A  ∆βαGmb = σ α  α  − σ β     ∂nα T , p  ∂nβ T,p

(3)

Under the crystal transition temperature, the molar Gibbs energy change of bulk substance can also be expressed as

∆βαGmb = ∆βα H mb − T ∆βα Smb

(4)

where ∆ βα H mb and ∆ βα S mb are the change in molar enthalpy and entropy of the bulk substance. By combining Eqs. (3) with (4), the expression for crystal transition temperature of nanoparticles will take the form

T=

∆βα H mb 1   ∂Aβ σ β  + ∆βα S mb ∆βα Smb   ∂nβ 

  ∂A    − σ α  α    ∂nα T,p  T,p

(5)

And the change in molar entropy is given by,  ∂Aβ  ∂∆ β G  ∆ βα S m = −  α m  = ∆ βα S mb −    ∂T  p  ∂nβ

  ∂σ β     −σβ T , p ∂T  p

 ∂   ∂T 

 ∂  ∂A    ∂A   ∂σ  + α   α  +σα   α    ∂T  ∂nα T , p  p  ∂nα T , p  ∂T  p

 ∂Aβ   ∂nβ

    T , p  p

(6)

Similarly, the change in molar enthalpy ∆ βα H m can be derived by Gibbs-Helmholtz 5



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equation,  ∂  ∂A    ∂Aβ    ∂  ∆β G   ∂σβ   β ∆βα Hm = −T 2   α m  = ∆βα Hmb +  σβ − T   − Tσβ           ∂ T T ∂ n ∂ T ∂ T ∂ n          p p  β T,p    β T,p  p

 ∂  ∂A    ∂A    ∂σ   −  α  σα − T  α   + Tσα   α    ∂T  p   ∂T  ∂nα T , p  p  ∂nα T , p 

(7)

Note that Eqs.(5), (6) and (7) are the universal equations for crystal transition thermodynamics without any assumptions, which can be applied to various morphologies of nanoparticles in the process of crystal transition. Since the crystal transition starts from outmost surface into interior lattice,39,40 we proposed the new core-shell model for crystal transition of a spherical nanoparticle (see Figure 1). thickness o f crystal trans ition l ayer t

crystal structure β

rα rβ crystal structure α

Figure 1. The core-shell model for crystal transition of a spherical nanoparticle.

When crystal transition is in a state of equilibrium, let us consider a single nanoparticle made up of two crystal structures α and β which are both strictly homogeneous right up to the dividing mathematical boundary. The core (α) with the radius rα is surrounded continuously by shell (β) with a thickness of t ( t = rβ − rα ) and the outside radius of the shell is rβ . The total mass in crystal transition process is consistent,

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4 3 4 4 π rα ρ α + π ( rβ3 − rα3 ) ρ β = π r 3 ρ α 3 3 3

(8)

where r is the radius of nanoparticle before crystal transition beginning; ρα and ρ β are, respectively, the densities of the core (α) and the shell (β) of the nanoparticle. For the core (α),

 ∂Aα  2Vα   =  ∂nα T , p rα

(9)

For the shell (β), by substituting Eq. (9) into Eq. (8) leads to  ∂Aβ  ∂n  β

 2Vβ  = T , p rβ

 ρβ  1 −   ρα 

(10)

where Vα and Vβ denote the molar volumes of the core (α) and the shell (β), respectively. Differentiating Eq. (9) and Eq. (10) with respect to temperature T we obtain  ∂  ∂A   4Vαγ α α     = 3rα  ∂ T  ∂ nα  T , p  p

 ∂  ∂A    1  ∂r   1 γ  1  1 γ   β   = −2M  2  β   −  +  α − β        ∂T  ∂nβ T,p   rβ  ∂T   ρβ ρα  rβ  ρα ρβ    p

(11)

(12)

where γ is the molar volume thermal expansion coefficient. By combining Eqs. (9), (10) with Eq. (5), one may obtain the precise equation for crystal transition temperature of sphere nanoparticles. Similarly, substituting Eqs. (9), (10), (11), (12) into Eq. (6) and Eq. (7), respectively, the precise equations for molar entropy and entropy crystal transition of sphere nanoparticles are also obtained. For VO2 polymorphs, the density of VO2 (M) is the same as VO2 (R),41 that is to say,

ρα = ρ β , so

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 ∂Aβ   ∂nβ

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 =0  T,p

(13)

 ∂  ∂A     β   =0  ∂T  ∂nβ T,p   p

(14)

By substituting Eqs. (9) and (13) into Eq. (5), we find an equation for particle radius dependency of the crystal transition temperature: T=

∆ βα H mb 2V α σ α − ∆βα S mb ∆βα S mb rα

(15)

Since the heat capacity is same for VO2 (M) and VO2 (R), we can obtain

∆βα H mb (T ) ∆ βα H mb (T0 ) = ∆ βα S mb (T ) ∆βα S mb (T0 )

(16)

where T0 is the crystal transition temperature of the corresponding bulk substance. So, we can simplify Eq. (15) as follows

T = T0 −

2σ αVα ∆βα Smb rα

(17)

Only when the rα >10 nm, the effect of size on σα is not significant, and the σα can be approximately regarded as a constant.42 Then, it can be seen from Eq. (17) that there is a linear relation between the crystal transition temperature and the reciprocal of particle radius. To study the particle radius dependency of the crystal transition entropy, one may substitute Eqs. (9), (11), (13) and (14) into Eq. (6) ∆ βα S m = ∆βα Smb +

2Vα rα

  ∂σ α  2    + σα γ    ∂T  P 3 

(18)

Similarly, by substituting Eqs. (9), (11), (13) and (14) into Eq. (7), we can obtain the Eq. (7) in an alternative form 8


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∆ βα H m = ∆ βα H mb −

2Vα rα

   ∂σ α    2 σ α − T    + σ αγ     ∂T  P 3   

For most substances, the order of γ, σα are, respectively, 10-5 K-1

(19) 43,44

and 10-1~100

N·m-1.45 ( ∂σα ∂T ) p is a negative quantity of the order of 10-4 J·m-2·K-1.46 So it is obvious that both equations above provide a linear relation, with reciprocal of particle radius increasing, the crystal transition entropy and enthalpy decrease. We should note that Eqs (17), (18) and (19) can also be applied to crystal transition of other spherical nanoparticles as long as the both crystal structure phases have identical density.

3. Experimental section 3.1 Synthesis of VO2 (M) with different sizes VO2 (M) nanoparticles were synthesized by hydrothermal method with vanadium pentoxide (V2O5), ammonium hydroxide (NH3·H2O, 25 wt%) and hydrazine hydrate (N2H4·H2O, 80 wt%) as raw materials. All reagents are analytical grade and need not be further purified. In a typical procedure, 1.5 g V2O5 was dissolved in 160 ml distilled water with stirring at 80 °C for 20 min to make a yellow suspension. Then 7 ml NH3·H2O was slowly added into the above mixture, 30 min later, an appropriate amount of N2H4·H2O was added dropwise until a gray solution was formed. Under adequately stirring, the resulting solution was transferred into a 200 ml autoclave and maintained at 220 °C. Nano-VO2 (M) with different particle sizes can be obtained by changing the hydrothermal reaction time. As the hydrothermal time increased from 24h, 30 h, 36 h to 42 h or 48 h, the particle size increases gradually, one can get a series of different particle size (20.2 nm 29.7 nm 50.1 nm 79.4 nm 110.8 nm) of VO2 9



(M). After cooling to room temperature naturally, the black-blue products were collected by centrifuging and washed with distilled water and ethyl alcohol repeatedly to remove ionic residue, and then dried in air at 100 °C for 2 h. Finally, the nanoparticles were annealed under the protection of high purity nitrogen at 550 °C for 2 h. 3.2 Characterization method Phase identification was performed using X-ray diffraction (XRD Germany Bluker D8 Advance Powder Diffractometer, Cu Kα, λ=1.54178 Å). The morphologies of the prepared nanoparticles were examined by field emission scanning electron microscopy (FE-SEM, JEOL, JSM-7001F). Crystal phase transition behaviors of the samples with different particle sizes were measured by differential scanning calorimetry (DSC, Q2000) at a heating rate of 10 °C /min in nitrogen atmosphere.

4. Results and discussion

55.4 nm

39.7 nm

Intensity (a.u.)

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25.1 nm 14.9 nm 10.1 nm

10

20

30

40

50

60

70

2θ (deg.)

Figure 2. XRD patterns of VO2 (M) nanoparticles with different diameters.

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The XRD patterns of Figure 2 have number of peaks that can be well indexed to VO2 (JCPDS 76-0456) corresponding to monoclinic crystal and the crystallinity is high.

Figure 3. The FE-SEM images of the nano-VO2 (M) with different radius (a 55.4 nm, b 39.7 nm, c 25.1 nm, d 14.9 nm, e 10.1 nm) and EDS spectrum (f) of nanoparticle with radius 25.1 nm.

11



30

30

(a)

(c)

15

10

25

25

20

20

15

10

5

5

0

0

100

110

120

130

140

Percentage (% )

Percentage (% )

20

90

30

(b)

25

Percentage (% )

15

10

5

0 65

70

Particle size (nm)

75

80

85

90

95

40

45

Particle size (nm)

35

50

55

60

Particle size (nm)

30

(d)

(e)

30

25

Percentage (% )

25

P ercentage (% )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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20

15

10

20

15

10

5

5

0

0

25

30

35

40

45

15

Particle size (nm)

20

25

30

35

Particle size (nm)

Figure 4. The particle size distribution of the nano-VO2 (M) with different radius (a 55.4 nm, b 39.7 nm, c 25.1 nm, d 14.9 nm, e 10.1 nm).

As clearly shown in Figure 3 and Figure 4, the morphology and size of the as-prepared VO2 (M) with different radius were sphere-like and relatively uniform. The average particle radii used in this experiment are, respectively, 55.4 nm, 39.7 nm, 25.1 nm, 14.9 nm and 10.1 nm. Figure 3 (f) displays a typical EDS spectrum of VO2 (M) with radius 25.1 nm, which reveals that the sample only consists of O and V elements, and their contents are 66.69 and 33.31 at.% respectively.

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55.4 nm

H eat flow (a.u.)

39.7 nm

25.1 nm 14.9 nm

10.1 nm

Endo

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Heating 315

320

325

330

335

340

345

350

355

360

365

Temperature/K

Figure 5. DSC curves of nano-VO2 (M) with different particle diameters.

Figure 6. Schematic of crystal transition from monoclinic VO2 (M) to tetragonal VO2 (R).

Figure 5 shows the DSC curves of spherical VO2 (M) with different radius corresponding to the crystal transition from monoclinic VO2 (M) to rutile tetragonal VO2 (R) (see Figure 6). Notably, the DSC peaks are shifted to lower temperatures relative to the bulk materials during the heating curve. The starting point of the DSC peak was used to characterize the temperature at which the crystal transition begins; the area of the integral of the DSC curve was used to represent the heat absorbed during the crystal transition process. More specifically, the crystal transition thermodynamic data of VO2 (M) were calculated and summarized in Table 1.

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Table 1. Thermodynamic data of crystal transition of nano-VO2 (M) with different radius

∆H / kJ·mol-1

No.

r/nm

r-1/nm-1

T/K

1 2 3 4 5

55.4 39.7 25.1 14.9 10.1

0.0181 0.0252 0.0399 0.0673 0.0990

339.03 338.07 337.60 335.90 335.04

3.81 3.56 3.14 2.25 1.56

∆S /J·mol-1·K-1 7.39 6.62 6.13 5.65 3.83

As can be seen from Figure 5 and Table 1, VO2 (M) nanoparticles with different sizes exhibit different crystal phase transition behaviors, and smaller particle size leads to lower phase transition temperature, both of which consistent with the literature.47 Table 1 also records that smaller particle size leads to a much lower latent heat for phase transition.48 The reason to the results is because nano-VO2 (M) particles have larger external surface, higher surface energy as compared with the bulk materials, which dramatically reduced the energy required for the process of the crystal transition.

339.0 338.5 338.0

Tem perature/K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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337.5 337.0 336.5 336.0 335.5 335.0 334.5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 -1

r /nm

-1

Figure 7. Crystal transition temperature (T) versus the reciprocal particle radius (r-1).

It can be seen from Figure 7 that the crystal transition temperatures decrease linearly with the particle radius decreasing, verifying that smaller nanoparticles show 14


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a more distinct depression in the crystal transition temperature. That is to say, the crystal transition temperatures of the nano-VO2 (M) can be tuned via a size effect rather than the previous doping methods. The intersection point value is 339.52 K which is approximately equal to the crystal transition temperature of bulk materials (341.15 K), when we extend the straight line toward the Y axis. Furthermore, correctness of the theoretical analysis is verified by the above experiment results.

7.5 7.0

∆S (J⋅m ol-1 ⋅K -1 )

6.5 6.0 5.5 5.0 4.5 4.0 3.5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11

r-1/nm-1

Figure 8. Relation between crystal transition entropy and reciprocal particle radius.

4.00 3.75 3.50 3.25 3.00

∆H(kJ⋅m ol -1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.75 2.50 2.25 2.00 1.75 1.50 1.25 0.01

0.02

0.03

0.04

0.05

0.06

-1

r /nm

0.07

0.08

0.09

0.10

-1

Figure 9. Relation between crystal transition enthalpy and reciprocal particle radius. 15



As illustrated in Figure 8 and Figure 9, it is obvious that when the radius of nanoparticles decreases, the crystal transition entropy and enthalpy decrease respectively, which are in agreement with the above-mentioned theoretical equations of Eqs. (18) and (19). The thermal analysis results and the influence rules were identical with those reported in literatures.49-51

5. Conclusions The core-shell model is proposed and we have derived the universal equations for size-dependent crystal transition thermodynamics. The results outlined here indicate that with the particle size of nano-VO2 (M) decreasing, the temperature, entropy and enthalpy of the crystal transition decrease, and there are linear relations between these thermodynamic properties and the reciprocal of particle radius. Furthermore, the universal equations in this paper provide a much deeper understanding of the size-dependent crystal transition. It can be used to better explain and predict the crystal transition behaviors in the preparation and application of other nanomaterials.

Notes The authors declare no competing financial interest.

Acknowledgements The work was financially supported by the National Natural Science Foundation of China (NSFC Nos. 21373147 and 21573157)

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TOC Graphic

thi ckness o f crystal tr ans ition layer t

crystal structure β

rα rβ crystal structure α

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Size-Dependent Crystal Transition Thermodynamics of Nano-VO2 (M)

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