Comparative Energy Modeling of Multiwalled Mg3Si2O5(OH)4 and

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Comparative Energy Modeling of MultiWalled MgSiO(OH) and NiSiO(OH) Nanoscrolls Growth 3

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical


Andrei A Krasilin, Vladimir N Nevedomsky, and Victor V. Gusarov

J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 23 May 2017 Downloaded from http:// pubs.acs.org on May 24, 2017



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

†

Ioffe Institute, 26 Politekhnicheskaya st., St. Petersburg 194021, Russia

‡

ITMO University, 49A Kronverkskiy pr., St. Petersburg 197101, Russia

*Corresponding author (A. K.): 26 Politekhnicheskaya st., St. Petersburg 194021, Russia, +7-921-387-61-96, [email protected] *Corresponding author (V. G.): 26 Politekhnicheskaya st., St. Petersburg 194021, Russia, +7-911-157-72-31, [email protected]


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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 multi-walled nanotubes and nanoscrolls with relatively wide diameter and length distributions. To understand the reasons behind these issues we propose here an energy model of multi-walled nanoscroll formation and growth, that accounts 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 preferable nanoscroll cross-section consisting of 12-13 chrysotile layers or 25-26 pecoraite layers. Energy effect of scrolling is relatively low (3-5 kJ/mol), and the energy minimum becomes broader during growth.


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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 halloysite17,18 and imogolite19–21 stand at the origins of tubular compounds. Discovery of carbon22 and chalcogenide23 nanotubes encouraged new wave of research in this area due to their remarkable mechanical,24 rheological25 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 synthesis of new functional materials.37–39 Nanoscrolls 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 modeling43–46, molecular dynamics and quantum chemistry calculations.47–49 The last showed good coincidence of theory and experiment in case of single-walled carbon50 and imogolite51,52 nanotubes. Internal strain and surface energy difference on the opposite sides of the layer consider to be principal reasons of scrolling. Guimarães et al.51 proposed energy approximation curve E(R) = a R 2 + 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. Quantum chemistry calculations for single-walled chrysotile53 and halloysite54 showed these tubes probably have preferable radius of curvature much larger than that of imogolite. In particular, the value of 8.8 nm have been recently approved for chrysotile (compare to ~1 nm for imogolite) involving a large-scale simulation.55 As for the multi-walled hydrosilicate nanoscrolls, the situation gets even more complicated due to adhesion between the layers and significant increase of a number of atoms in the cell. To date, there are calculations that take up to 3-4 layers into the account.56 Second, the above mentioned chrysotile


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8.8 nm radius of curvature leaves the question “Why does it form only multi-walled 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 to take a look at growth process of finite-size multi-walled 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. METHODS Energy Model of Scrolling. Energy effect of scrolling includes three principal components,57,58 eq (1): 1 ΔE = ⎡⎢( Es@ − Es= ) + (Σ@ −Σ= ) −U a@ ⎤⎥ ⎦ ν⎣

(1)

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

D E = s L2 ∫ 2 0 @ s

2

⎛ 1 1 ⎞⎟ ⎜⎜ ⎟ − ⎜⎜⎝ r(ϕ) r ⎟⎟⎠

f 2 + r 2 (ϕ) dϕ (2)

0

where Ds = Yh3 [12(1−µ 2 )] is bending stiffness, Y is the Young’s modulus, h is bilayer thickness (Figure 1), µ is the Poisson’s ratio; n is the number of layers within the wall; r(ϕ) = rin + f ϕ is angle ( ϕ ) dependent radius of the Archimedean spiral, rin is inner radius of the scroll,

f = (h + t) 2π is spiral constant, t is interlayer distance; r0 is radius of mechanically unstressed (or stress-free) layer;

f 2 + r 2 (ϕ) is length of integration element; 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):


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Es= =

Ds LL 2r02 1 2

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(3)

Figure 1. Structure of hydrosilicate sublayers and modeling concept of scrolling and growth.

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), change of strain energy per 1 mol after transformations (see Supporting Information) is, eq (5):


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1 @ Es − Es= ) ( ν

ΔEs,m =

2πn 2

Yh M

=

24ρ (1−µ 2 )

∫ l (ϕ) 1

0

r0 − 2r(ϕ) dϕ r 2 (ϕ)r0

(5)

2πn

∫ l (ϕ)dϕ 1

0

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= = σout L=1,out L2 + σin L=1,in L2

(6)

+ 2σ1 L1h + 2σ2 L2 h

where σout , σin , σ1 , 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 additional calculation of spiral lengths L@ and L@ , eq (7): 1,out 1,in 2πn

L@ =∫ 1,out

f 2 + (rin + h 2 + f ϕ) dϕ 2

0

2πn

L@ =∫ 1,in

(7) f 2 + (rin − h 2 + f ϕ) dϕ 2

0

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

ΔΣm =

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

(8)

where Δσ = σout −σin . Assuming n >1 change of adhesion energy per 1 mol is, eq (9): 2π( n−1)

1 M ΔU a,m = − U a@ = − ua ν hρ

∫

la (ϕ)dϕ

0

L1

(9)


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where ua is specific adhesion energy; la (ϕ) =

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2

f 2 + ⎡⎢ rin + ( h + t ) 2 + f ϕ ⎤⎥ . The last equation in the ⎣ ⎦

model is constant mass condition during the scrolling process, eq (10): m = L1 L2 hρ

(10)

To find energy minimum and whole energy surface of scrolling ΔE = f ( n, L2 ) we solved the system of eqs (1) and (10) numerically increasing the mass step by step from 1⋅10–17 g 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 drop-wise at constant stirring to 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 grinded 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) were used as hydrothermal medium. Sealed vessels were exposed 168 hours 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 energy-dispersive X-ray spectrometry (SEM/EDS) were used to determine elements content, Mg:Si and Ni:Si molar ratios. Spectra were acquired at 3-5 areas 0.25x0.25 mm each, 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


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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 3 times each for every scroll; over 200 of scrolls were measured for each sample. RESULTS AND DISCUSSION Nanoscrolls Structure and Morphology. SEM/EDS analysis show 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 a formation of Mg-chrysotile and Ni-pecoraite crysralline phases after hydrothermal treatment both in water and NaOH solution. Samples crystallinity is relatively low because of relatively low treatment temperature: typically, temperature of chrysotile synthesis is around 350-400 °C. Patterns comparison clearly reveals an important role of NaOH in facilitating of hydrosilicates recrystallization process due to increase of SiO2 solubility.59 To note its addition affects on Ni-pecoraite growth rather than on Mg-chrysotile growth, decreasing mean full width of diffraction peaks on 10% and 25%, accordingly. Cell parameters (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! , V = 0.722 ± 0.005 nm 3 for Mg-chrysotile and a = 0.5302 ± 0.0005 nm , b = 0.9182 ± 0.0005 nm ,

c = 1.462 ± 0.002 nm , β = 93.0 ± 0.2! , V = 0.711± 0.001 nm 3 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 follows by smaller Ni2+ ionic radius of 69 pm in comparison with 72 pm of Mg2+.62 X-ray densities were estimated according to eq (11):

ρX =

1 N AV

∑N M i

i

i

(11)

where N A is the Avogadro constant; V is the cell volume; N i is number of i atoms of mass M i . The calculation results 2.55 g/cm3 for Mg-chrysotile and 3.55 g/cm3 for Ni-pecoraite.


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

TEM images on Figure 3 approve Mg3Si2O5(OH)4 and Ni3Si2O5(OH)4 nanoscrolls formation. Among 900 of measured nanoscrolls every one is found to be multi-walled, double-walled at least, with the shortest length recognizable around 50 nm. On the other hand, 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 2-4 hydrosilicate layers (we denote them as “prototubulens”64). ACS Paragon Plus Environment

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Probably these particles serve both as a construction material for growing nanoscrolls and as a potential nuclei of new scrolls. Participation of similar particles in formation of imogolite and pecoraite nanotubes was demonstrated recently.15,46 Long period co-existence of thick and long scrolls together with prototubulens can have some thermodynamic reasons, but also it points on 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, 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 energy surface of scrolling in the number of layers n vs 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):

n=

D−d 2(h + t)

(12)

and nanoscroll mass assuming hollow cylindrical form, eq (13): m=

π 2 ( D − d 2 ) L2ρ 4

(13)

where D is mean outer diameter, d is mean inner diameter, (h + t) is interlayer period and ρ is the hydrosilicate density.


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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 Supporting Information.


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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 in r0 . Being well confirmed for chrysotile by Whittaker41,42 and Demichelis55 calculations, it is still questionable for pecoraite. Decrease of cell parameters during Mg to Ni substitution mainly owe to size decrease of 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): Ni Mg Mg Mg h boct (r0 + h 4) + boct (r0 − h 4) r = Ni 4 boct (r0Mg + h 4)− boctMg (r0Mg − h 4) Ni 0

(14)

Ni Mg where boct and boct 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 1.1-1.5 J/m2 range,65,66 whereas surface energy of SiO2 is around 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 .

Table 1. Structural parameters of energy model par.

Mg-chr

Ni-pec

ref.

M , g/mol

270.1

380.3

-

ρ , g/cm3

2.5

3.5

ps

r0 , nm

8.8

15

ps,55

h , nm

0.4

0.4

ps,68

t , nm

0.3

0.3

ps,68

Y , GPa

300

300

53,69


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µ

0.2

0.2

42

Δσ , J/m2

0.1

0.1

65–67

ua , J/m2

0.01

0.01

ps

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*ps – present study 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 (around 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 on Figure 4) which passes through the global minimum and all the local minima with certain (n, L2 ) , and also an energy region 500 J/mol away from the global minimum.


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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.

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 of the 500 J/mol region, i.e. permits the nanoscroll to have more and more spread size parameters. Considering model equations (1), (5) and (8)-(10) (see Methods Section) it is facile to realize that the most energy effective way for 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


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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 Nipecoraite 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 initial area is situated in the n = 1..3 and L2 ≤ 50 nm region for both Mg-chrysotile 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 last tend to form thicker and shorter scrolls. But in order 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 Mgchrysotile 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).


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

CONCLUSION We study the formation and growth of multi-walled 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. Energy preferable Mg-chrysotile nanoscroll wall consists of 12-13 layers, whereas the Ni-pecoraite


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one consists of 25-26 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 multi-walled hydrosilicate nanoscrolls. At the same time, it does not tie to chrysotile structure, thus can be used to describe scrolling of other layered compounds. ASSOCIATED CONTENT Supporting Information. Supporting Information contains details on derivation of model equations, and additional TEM images. ACKNOWLEDGEMENTS The research was supported by Russian Science Foundation grant 16-13-10252. Andrei A. Krasilin would like to thank Anastasia M. Suprun for help with the hydrothermal synthesis. REFERENCES (1)

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Comparative Energy Modeling of Multiwalled Mg3Si2O5(OH)4 and

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