Comparative Energy Modeling of Multiwalled Mg3Si2O5(OH)4 and

Article pubs.acs.org/JPCC

Comparative Energy Modeling of Multiwalled Mg3Si2O5(OH)4 and Ni3Si2O5(OH)4 Nanoscroll Growth Andrei A. Krasilin,*,†,‡ Vladimir N. Nevedomsky,† and Victor V. Gusarov*,† †

Ioffe Institute, 26 Politekhnicheskaya st., St. Petersburg 194021, Russia ITMO University, 49A Kronverkskiy pr., St. Petersburg 197101, Russia

‡

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S Supporting Information *

ABSTRACT: Spontaneously scrolling hydrosilicate nanotubes raise additional attention due to their sorption, catalytic, and other functional properties. Layered hydrosilicates like chrysotile and pecoraite form primarily multiwalled nanotubes and nanoscrolls with relatively wide diameter and length distributions. To understand the reasons behind these issues we propose here an energy model of multiwalled nanoscroll formation and growth that accounts for strain, surface, and adhesion energy changes. Objects of comparison are chrysotile and pecoraite nanoscrolls, obtained by hydrothermal synthesis and characterized by X-ray diffraction and microscopic techniques. Energy modeling reveals a preferable nanoscroll cross-section consisting of 12 to 13 chrysotile layers or 25 to 26 pecoraite layers. The energy effect of scrolling is relatively low (3−5 kJ/mol), and the energy minimum becomes broader during growth.

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Quantum-chemistry calculations for single-walled chrysotile53 and halloysite54 showed that these tubes probably have preferable radius of curvature much larger than that of imogolite. In particular, the value of 8.8 nm has been recently approved for chrysotile (compared with ∼1 nm for imogolite) involving a large-scale simulation.55 As for the multiwalled hydrosilicate nanoscrolls, the situation gets even more complicated due to adhesion between the layers and significant increase in a number of atoms in the cell. To date, there are calculations that take up to three to four layers into the account.56 Second, the above-mentioned chrysotile 8.8 nm radius of curvature leaves the question, “Why does it form only multiwalled nanotubes and nanoscrolls?” without answer. Third, a vast majority of models omit nanotubes and nanoscrolls length distributions observed experimentally. To meet this challenge we would like to propose a continuous layer energy model of scrolling that allows us to take a look at the growth process of finite-size multiwalled nanoscrolls.57,58 Here we apply this model to investigate size correlations of Mg3Si2O5(OH)4 chrysotile and Ni3Si2O5(OH)4 pecoraite nanoscrolls, obtained by hydrothermal synthesis.

INTRODUCTION A wide range of single-1,2 and polycrystalline3,4 layered compounds undergo spontaneous curving to form tubes and scrolls, hollow spheres, and onions.5−7 Bilayered hydrosilicate minerals like chrysotile,8−11 pecoraite,12−16 halloysite,17,18 and imogolite19−21 stand at the origins of tubular compounds. Discovery of carbon22 and chalcogenide23 nanotubes encouraged a new wave of research in this area due to their remarkable mechanical,24 rheological,25 and electronic26,27 properties. These findings revealed not only new types of tubular compounds but also new functional properties of the already known tubes. Nowadays, hydrosilicate nanotubes and nanoscrolls occupy a niches of catalyst materials,28−30 sorbents and containers,31,32 drug deliverers,33 polymer membranes fillers,34−36 precursors, and templates for the synthesis of new functional materials.37−39 Nanoscroll growth mechanism and preferable curvature radius remain one of the main topics of study. Starting from Pauling’s predictions40 and Whittaker’s X-ray diffraction studies41,42 the research moved toward phenomenological modeling,43−46 molecular dynamics, and quantum chemistry calculations.47−49 The last showed good coincidence of theory and experiment in the case of single-walled carbon50 and imogolite51,52 nanotubes. Internal strain and surface energy difference on the opposite sides of the layer are considered to be principal reasons of scrolling. Guimarães et al.51 proposed an energy approximation curve E(R) = a/R2 + b/R, where R is nanotube radius, parameter a accounts strain, and parameter b accounts surface energy difference. Thill et al.46 extended this equation to the case of double- and triple-walled Ge-imogolites. © 2017 American Chemical Society

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METHODS

Energy Model of Scrolling. The energy effect of scrolling includes three principal components,57,58 eq 1 Received: April 21, 2017 Revised: May 23, 2017 Published: May 23, 2017 12495

DOI: 10.1021/acs.jpcc.7b03785 J. Phys. Chem. C 2017, 121, 12495−12502

Article

The Journal of Physical Chemistry C ΔE =

1 [(Es@ − Es=) + (Σ@ − Σ=) − Ua@] ν

Es= =

(1)

= where E@ s and Es are strain energies of scrolled and flat bilayer (or just “layer”); Σ@ and Σ= are the surface energies of scrolled and flat layer, U@ a is the adhesion energy of the layer in case it scrolls on more than one turn, and ν is the amount of substance. Assuming nanoscroll cross-section in the form of Archimedean spiral, the strain energy of scrolled layer is proportional to squared difference of curvatures,58 eq 2

D Es@ = s L 2 2

∫0

2 1 1⎞ − ⎟ f 2 + r 2(φ) dφ ⎜ r0 ⎠ ⎝ r (φ )

2r02

L1L 2

(3)

Stress-free layer radius depends on the cell sizes of octahedral boct and tetrahedral btet sublayers. Assuming their equal thicknesses are h/2 and the octahedral sublayer is outer, eq 4 r0 =

h boct + btet 4 boct − btet

(4)

Subtracting eq 3 from eq 2, the change of strain energy per 1 mol after transformations (see the Supporting Information) is, eq 5

2π n ⎛

(2)

where Ds = Yh /[12(1 − μ )] is bending stiffness, Y is the Young’s modulus, h is bilayer thickness (Figure 1), μ is the 3

Ds

2

1 @ (Es − Es=) ν

ΔEs,m =

2π n

r − 2r(φ)

∫0 l1(φ) 0r 2(φ)r dφ Yh2M 0 = 2π n 24ρ(1 − μ2 ) ∫0 l1(φ) dφ

(5)

where l1(φ) = f 2 + r 2(φ) . Integration in denominator returns L1, the spiral length. Total surface energy of the flat layer is, eq 6 = = Σ= = σoutL1,out L 2 + σinL1,in L 2 + 2σ1L1h + 2σ2L 2h

(6)

where σout, σin, σ1, and σ2 are specific surface energies of outer, inner, and two lateral surfaces of the layer, accordingly; L=1,out = L=1,in = L1. The same principle is for the scrolled layer, except for @ additional calculation of spiral lengths L@ 1,out and L1,in, eq 7 @ L1,out =

∫0

@ L1,in =

∫0

2π n

2π n

f 2 + (rin + h/2 + fφ)2 dφ f 2 + (rin − h/2 + fφ)2 dφ

(7)

After the subtraction and simplification (see the Supporting Information), the change of surface energy per 1 mol is, eq 8 ΔΣm =

@ 1 @ M L1 − L1,in (Σ − Σ=) ≈ Δσ hρ L1 ν

(8)

where Δσ = σout − σin. Assuming n > 1, the change of adhesion energy per 1 mol is, eq 9 ΔUa,m Figure 1. Structure of hydrosilicate sublayers and modeling concept of scrolling and growth.

where

1 M ∫ = − Ua@ = − ua 0 ν hρ

ua 2

is

specific

2π (n − 1)

la(φ) dφ

L1

adhesion

(9)

energy;

2

la(φ) = f + [rin + (h + t )/2 + fφ] . The last equation in the model is constant mass condition during the scrolling process, eq 10

Poisson’s ratio, n is the number of layers within the wall, r(φ) = rin + fφ is the angle-dependent (φ) radius of the Archimedean spiral, rin is the inner radius of the scroll, f = (h + t)/2π is the spiral constant, t is the interlayer distance, r0 is the radius of

m = L1L 2hρ

(10)

To find energy minimum and whole energy surface of scrolling ΔE = f(n,L2) we solved the system of eqs 1 and 10 by numerically increasing the mass step by step from 1 × 10−17 to 1 × 10−13 g. Synthesis of Hydrosilicate Nanoscrolls. The procedure was carried out through two stages: initial composition synthesis and hydrothermal treatment. First, water solution of 1 M MgCl2 or NiCl2 was added dropwise at constant stirring to

mechanically unstressed (or stress-free) layer, f 2 + r 2(φ) is the length of integration element, and L2 is the nanoscroll length. Equation 2 is valid for the case of small curvature changes. For the flat layer, 1/r(φ) = 0, so the strain energy is, eq 3 12496


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The Journal of Physical Chemistry C basic (2 M NaOH water solution) suspension of amorphous SiO2 (aerosil A-300) until nominal molar ratio Mg(Ni)/Si 3:2 was satisfied. Precipitates were washed (decantation or vacuum filtering) several times by distilled water to remove excess of OH−, Cl−, and Na+ ions. Washed precipitates were dried on air at 90 °C and ground in an agate mortar. On the second stage, ∼0.2 g of initial composition was sealed in PTFE-lined stainless-steel 16 mL vessel. Water or 0.5 M NaOH water solution (13 mL) was used as hydrothermal medium. Sealed vessels were exposed for 168 h at 240 °C in a furnace. Hydrothermal treatment products were washed several times by distilled water to remove excess of OH− ions and then dried on air at 90 °C. X-ray and Microscopic Characterization. X-ray powder diffraction (XRPD) patterns of 0.02° 2θ resolution were obtained on Shimadzu XRD-7000 powder diffractometer with copper anode (λCuKα = 0.15418 nm). XRPD reflections was identified using ICDD PDF-2 database. Scanning electron microscopy (FEI Quanta 200) and energydispersive X-ray spectrometry (SEM/EDS) were used to determine element content and Mg/Si and Ni/Si molar ratios. Spectra were acquired at three to five areas 0.25 × 0.25 mm each; then, the results were then averaged. Jeol JEM 2100 F was used for transmission electron microscopy (TEM). Nanoscrolls were ultrasonically dispersed in water, then a drop of the dispersion was dried on polymer film on a copper grid. ImageJ open software was used for determination of nanoscrolls size parameters: outer diameter, inner diameter, length, and cone angle (in case of conical scroll). These sizes were measured three times each for every scroll; over 200 of scrolls were measured for each sample.

Figure 2. XRPD patters of hydrothermal treatment products. Cards belong to ICDD PDF-2 database.

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RESULTS AND DISCUSSION Nanoscroll Structure and Morphology. SEM/EDS analysis shows the absence of impurities (NaCl and other possible contaminants) in initial compositions. Molar ratios Mg/Si = 1.42 ± 0.17 and Ni/Si = 1.53 ± 0.06 correspond to 1.5 nominal ratios of chrysotile and pecoraite within error. XRPD patterns on Figure 2 demonstrate the formation of Mg-chrysotile and Ni-pecoraite crystalline phases after hydrothermal treatment both in water and NaOH solution. Sample crystallinity is relatively low because of relatively low treatment temperature: Typically, the temperature of chrysotile synthesis is around 350−400 °C. Pattern comparison clearly reveals an important role of NaOH in facilitating of hydrosilicates recrystallization process due to increase in SiO2 solubility.59 NaOH addition decreases full width of Mg-chrysotile and Nipecoraite diffraction peaks by 10% and 25%, accordingly. Cell parameter (monoclinic cell) calculation on the basis of actual XRPD patterns (synthesis in NaOH water solution) returns a = 0.530 ± 0.002 nm, b = 0.922 ± 0.002 nm, c = 1.476 ± 0.008 nm, β = 91.9 ± 0.8°, and V = 0.722 ± 0.005 nm3 for Mgchrysotile and a = 0.5302 ± 0.005 nm, b = 0.9182 ± 0.0005 nm, c = 1.462 ± 0.002 nm, β = 93.0 ± 0.2°, and V = 0.711 ± 0.001 nm3 for Ni-pecoraite. These values are close to those obtained in recent structural studies.60,61 Parameters decrease (except β angle) during Mg to Ni substitution, followed by smaller Ni2+ ionic radius of 69 pm in comparison with 72 pm of Mg2+.62 Xray densities were estimated according to eq 11 ρX =

1 NAV

∑ NM i i i

where NA is the Avogadro constant, V is the cell volume, and Ni is the number of i atoms of mass Mi. The calculation results 2.55 g/cm3 for Mg-chrysotile and 3.55 g/cm3 for Ni-pecoraite. TEM images on Figure 3 approve Mg3Si2O5(OH)4 and Ni3Si2O5(OH)4 nanoscroll formation. Among 900 of measured nanoscrolls every one is found to be multiwalled, double-walled at least, with the shortest length recognizable around 50 nm. On the contrary, some of the nanoscrolls reach 100 nm in outer diameter and up to 7 μm in length. Mean inner diameter of the nanoscrolls is in the range of 6−12 nm, and 0.7 nm interlayer period remains constant. Conical scrolls are also present: Their content depends on chemical composition of hydrosilicate and hydrothermal medium but does not exceed 14% of total number of measured scrolls within one sample. Usually, but not always,63 conical form is less favorable than the cylindrical one due to excessive strain energy of the layer. In addition to the nanoscrolls of different morphology, TEM reveals a large number of small (20−30 nm) plates or slightly curved particles consisting of two to four hydrosilicate layers (we denote them as “prototubulens”64). These particles probably serve both as a construction material for growing nanoscrolls and as a potential nuclei of new scrolls. Participation of similar particles in the formation of imogolite and pecoraite nanotubes was demonstrated recently.15,46 Long period coexistence of thick and long scrolls together with prototubulens can have some thermodynamic reasons, but it also points to the time stretched and stochastic character of scrolling process. Replacing the real time by the value of nanoscroll mass or nanoscroll length allows us to consider statistical data obtained by TEM images processing in the context of “virtual time” change. This means that

(11) 12497


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The Journal of Physical Chemistry C

Figure 3. TEM images of chrysotile nanoscrolls synthesized (a) in NaOH water solution and (b) in water and of pecoraite nanoscrolls synthesized (c) in NaOH water solution and (d) in water. (e) TEM image of pecoraite nanoscroll layered structure with gray value profile plot along selected line. Additional TEM images of the samples can be found in the Supporting Information.

Table 1. Structural Parameters of Energy Model

a

par.

Mg-chr

Ni-pec

M, g/mol ρ, g/cm3 r0, nm h, nm t, nm Y, GPa μ Δσ, J/m2 ua, J/m2

270.1 2.5 8.8 0.4 0.3 300 0.2 0.1 0.01

380.3 3.5 15 0.4 0.3 300 0.2 0.1 0.01

ref

Figure 4. Energy surface of scrolling of Mg-chrysotile and Ni-pecoraite of m = 1 × 10−15 g. Energy minima for every L2 values are joined by dashed curve.

ps ps55 ps68 ps68

where D̅ is mean outer diameter, d̅ is mean inner diameter, (h + t) is interlayer period, and ρ is the hydrosilicate density. Energy Effect of Scrolling. To model the scrolling process it is first necessary to specify a number of structural parameters such as the Young’s modulus or surface energy difference. Table 1 summarizes these values. Remarkable difference between chrysotile and pecoraite structures consists of r0. Being well confirmed for chrysotile by Whittaker41,42 and Demichelis55 calculations, it is still questionable for pecoraite. The decrease in cell parameters during Mg to Ni substitution is mainly owed to size decrease in the octahedral sublayer (see Figure 1). This process eliminates the size difference between the sublayers and probably increases r0 of Ni3Si2O5(OH)4. We estimate r0 value using a variation of eq 4 assuming constant h during the cation change, eq 14

53,69 42 65−67

ps

ps: present study.

although every nanoscroll during growth (or dissolution) passes its own way in the real time, a group of scrolls can designate specific energy preferable growth trajectories in the virtual time. We model the energy surface of scrolling in the number of layers n versus nanoscroll length L2 coordinates for certain mass m. For this reason we determine the number of layers of individual nanoscrolls, measured by TEM, eq 12 D̅ − d ̅ n= 2(h + t )

r0Ni = (12)

Ni Mg Mg Mg h boct(r0 + h/4) + boct (r0 − h/4) Ni Mg Mg Mg 4 boct (r0 + h/4) − boct (r0 − h/4)

bNi oct

(14)

bMg oct

where and are cell parameters of corresponding hydroxides, Ni(OH)2 and Mg(OH)2. Surface energies of oxides like MgO and NiO (if they contact with air, in{100} and {001} directions) lie within the 1.1 to 1.5

and nanoscroll mass assuming hollow cylindrical form, eq 13 π 2 m = (D̅ 2 − d ̅ )L 2ρ (13) 4 12498


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The Journal of Physical Chemistry C

Figure 5. Growth of Mg-chrysotile and Ni-pecoraite. Points are nanoscrolls measured by TEM, and solid curves are modeling results. Colored areas are 500 J/mol regions (see Figure 4) modeled for nanoscrolls of different mass.

J/m2 range,65,66 whereas surface energy of SiO2 is ∼1.5 J/m2 (in {111} direction).67 In the case of hydroxides, OH groups can lower both of these values, so we decide to not overrate Δσ value as well as specific adhesion energy ua. Figure 4 conjoins calculated energy surfaces of scrolling of 10−15 g Mg3Si2O5(OH)4 and Ni3Si2O5(OH)4 together with experimental points obtained by TEM measurements (with m varying from 1 × 10−15 to 2 × 10−15 g). Mg-chrysotile energy minimum is narrower and deeper (∼4.7 kJ/mol) than that of Ni-pecoraite (3.5 kJ/mol). Moreover, Mg-chrysotile energy minimum position occupies the area of thin and long scrolls formation, whereas Ni-pecoraite of the same mass prefers to form thick and short scrolls. This is because of higher r0 value, which also lowers total energy effect of scrolling. All experimental points are situated in a close energy proximity to calculated minimum. For further discussion we emphasize a curve (dashed line in Figure 4) that passes through the global minimum and all of the local minima with certain (n,L2) and also an energy region 500 J/mol away from the global minimum.

Evolution of Energy Minimum. Figure 5 shows experimental points, the energy curves, and the 500 J/mol regions of different mass nanoscrolls formation. In all cases growing scrolls of certain mass follow close to their energy minimum curves. Note that the mass increase yields remarkable area increase in the 500 J/mol region; that is, it permits the nanoscroll to have more and more spread size parameters. Considering model eqs 1, 5, and 8−10, (see Methods), it is facile to realize that the most energy effective way for a single nanoscroll that has reached the minimum to grow further is to grow in length. So the number of layers in minimum is independent of mass increase as well as energy effect of scrolling per 1 mol (in current model approximation). That particular situation of growth we observe in the experiment: The longest Mg-chrysotile and Ni-pecoraite nanoscrolls have around 10 and 30 layers, accordingly, but to reach energy minimum, nanoscrolls of different chemical composition have to pass different ways due to r0 difference. TEM images (Figure 3) reveal prototubulens as potential “starting points” of scrolling and growth, so the initial area is 12499


The Journal of Physical Chemistry C situated in the n = 1−3 and L2 ≤ 50 nm region for both Mgchrysotile and Ni-pecoraite. In the case of hydrothermal treatment in the presence of NaOH recrystallization strengthens, so nanoscrolls can occupy energy states below and above energy minimum (in the number of layers scale) with ease. Comparing Mg-chrysotile and Ni-pecoraite nanoscrolls within certain mass region (Figure 5), the latter tend to form thicker and shorter scrolls, but to reach energy minimum and energy preferable states around it, Ni-pecoraite nanoscrolls become heavier than the Mg-chrysotile nanoscrolls. That is why Ni-pecoraite nanoscrolls obtained by hydrothermal treatment in NaOH water solution form the thickest and the longest nanoscrolls and have higher crystallinity (see XRPD patterns on Figure 2) among all samples studied. Without NaOH addition poor solubility complicates recrystallization process, and only Mg-chrysotile nanoscrolls succeed in axial growth because of relative proximity of starting position to energy minimum, whereas Ni-pecoraite ones demonstrate relatively poor growth of the number of layers (Figure 5).

ACKNOWLEDGMENTS

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REFERENCES

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CONCLUSIONS We study the formation and growth of multiwalled Mg3Si2O5(OH)4 chrysotile and Ni3Si2O5(OH)4 pecoraite nanoscrolls experimentally and using continuous layer energy model. The model provides good quantitative explanation of chrysotile and pecoraite growth issues like wide length and diameter distributions and the role of hydrothermal medium in the nanoscroll formation. The energy preferable Mg-chrysotile nanoscroll wall consists of 12 to 13 layers, whereas the Nipecoraite one consists of 25 to 26 layers. The most important task for just formed nanoscrolls is to reach this energy preferable value or be near to it, and the number of layers growth dominates at the start. Considerable axial growth is possible only in the region close to the energy minimum. Chrysotile structure leaves considerable room for Mg and Si cations substitutions (not only by Ni ions), which often are accompanied by change of morphology and appearance of new functional properties. The energy approach proposed in this study can be applied to predict the possibility of scrolling and estimate size parameters of new multiwalled hydrosilicate nanoscrolls. At the same time, it does not tie to chrysotile structure and thus can be used to describe scrolling of other layered compounds. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b03785. Details of derivation of model equations and additional TEM images.(PDF)

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The research was supported by Russian Science Foundation grant 16-13-10252. A.A.K. thanks Anastasia M. Suprun for help with the hydrothermal synthesis.

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AUTHOR INFORMATION

Corresponding Authors

*A.K.: Tel: +7-921-387-61-96. E-mail: [email protected]ffe.ru. *V.G.: Tel: +7-911-157-72-31. E-mail: [email protected]ffe.ru. ORCID

Andrei A. Krasilin: 0000-0002-3938-3024 Victor V. Gusarov: 0000-0003-4375-6388 Notes

The authors declare no competing financial interest. 12500


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Comparative Energy Modeling of Multiwalled Mg3Si2O5(OH)4 and

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