Unique rheological behavior of detonation nanodiamond hydrosols: The nature of sol-gel transition

Journal Pre-proof Unique rheological behavior of detonation nanodiamond hydrosols: The nature of solgel transition Nikita M. Kuznetsov, Sergey I. Belousov, Artem V. Bakirov, Sergei N. Chvalun, Roman A. Kamyshinsky, Alexey A. Mikhutkin, Alexander L. Vasiliev, Peter M. Tolstoy, Anton S. Mazur, Eugeny D. Eidelman, Elena B. Yudina, Alexander Ya Vul PII:

S0008-6223(20)30061-0

DOI:

https://doi.org/10.1016/j.carbon.2020.01.054

Reference:

CARBON 14989

To appear in:

Carbon

Received Date: 31 October 2019 Revised Date:

15 January 2020

Accepted Date: 17 January 2020

Please cite this article as: N.M. Kuznetsov, S.I. Belousov, A.V. Bakirov, S.N. Chvalun, R.A. Kamyshinsky, A.A. Mikhutkin, A.L. Vasiliev, P.M. Tolstoy, A.S. Mazur, E.D. Eidelman, E.B. Yudina, A.Y. Vul, Unique rheological behavior of detonation nanodiamond hydrosols: The nature of sol-gel transition, Carbon (2020), doi: https://doi.org/10.1016/j.carbon.2020.01.054. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

1

Unique rheological behavior of detonation

2

nanodiamond hydrosols: the nature of sol-gel

3

transition

4

Nikita M. Kuznetsov 1,*, Sergey I. Belousov 1, Artem V. Bakirov 1,2, Sergei N. Chvalun 1,2, Roman

5

A. Kamyshinsky

6

Anton S. Mazur 5, Eugeny D. Eidelman 6,7, Elena B. Yudina 6, Alexander Ya. Vul' 6,**

7

1

National Research Center “Kurchatov Institute”, Moscow, Russia

8

2

Enikolopov Institute of Synthetic Polymeric Materials of the Russian Academy of Sciences,

9

Moscow, Russia

1,3,4

, Alexey A. Mikhutkin 1, Alexander L. Vasiliev

1,3,4

, Peter M. Tolstoy 5,

10

3

Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia

11

4

Federal Research Centre “Crystallography and Photonics” of Russian Academy of Science,

12

Moscow, Russia

13

5

Center for Magnetic Resonance, St. Petersburg State University, St. Petersburg, Russia

14

6

Ioffe Institute, St. Petersburg, Russia

15

7

St. Petersburg State Chemical Pharmaceutical University, St. Petersburg, Russia

16

KEYWORDS: detonation nanodiamond; sol-gel transition; rheological properties; thixotropy;

17

percolation threshold; hysteresis of viscosity

18

19

ABSTRACT: The paper describes the data on unusual rheological properties of detonation

20

nanodiamonds (DND) hydrosols and presents the fractal model explaining such behavior. The

21

hydrosols of DND with particles size of 4–5 nm and concentration range of 1.1–7.3 wt% with

1

1

negative (ζ < 0) and positive (ζ > 0) electrokinetic potentials have been studied by rotational

2

viscometry, small-angle X-ray scattering, nuclear magnetic resonance and Cryo Electron

3

Tomography. Remarkable hysteresis of viscosity and thixotropic effect demonstrate the sol-gel

4

transition at very low concentrations of the DND: 4–5 wt% for ζ >0 and 5–6 wt% for ζ <0. The

5

transition is accompanied by increase of loss (viscosity) modulus by two orders of magnitude

6

and the storage (elasticity) modulus started to be detected also. The experimental results have

7

been explained in the frame of percolation theory based on the network formation due to faceted

8

DND particles interactions.

9

INTRODUCTION

10

In recent years much more attention has been focused on various applications of

11

nanodiamonds obtained by detonation synthesis of carbon-containing explosives [1–4]. However,

12

the agglomeration of the detonation nanodiamond (DND), prepared by explosive method is the

13

serious drawback for their usage. Ball milling can partly solve this problem [5], but it has serious

14

disadvantage due to DND's surface graphitization [6]. Recently a new method of

15

deagglomeration excluding mechanical grinding has been developed [7–9] based on annealing

16

and subsequent centrifugation. As a result stable hydrosols of faceted DND particles with

17

averaged size of 4–5 nm have been produced. The stability of such hydrosols is determined by

18

non-spherical distribution of electrical potential around DND particles [10,11]. It would be

19

useful to mention that the sol-gel transition is also detected in the case of ball milling

20

deagglomeration method [12], but at higher concentration. The reason is formation of sp2 layer

21

on the surface of DND particles, which probably screened electrostatic interaction.

22

The rheological study of DND hydrosols is of great importance for numerous possible

23

applications in biomedicine [13], development of novel liquid heat carriers [14,15] and magnetic

24

liquids [16].

25

The DND hydrosol was prepared by a method described previously [9]. Two unusual

26

rheological features of DND hydrosols have been recently discovered: the sharp increase in

27

viscosity and the phase sol-gel transition at a relatively low filler concentration [11]. Such

28

behavior has been explained in the frame of the model based on network formation from the

29

chains of faceted DND particles due to electrostatic interaction of facets [10]. The network

30

formation can be detected by rotational viscometry, which is sensitive to changes in the

2

1

composition of a dispersed system and often used for characterization of suspensions filled by

2

various particles [17,18]. In measurements by rotational viscometer the critical value of shear

3

stress is determined by equality of shear energy and electrostatic interaction between the

4

particles within a chain.

5

It is worth to note, that in previous studies the viscosity was measured by other methods:

6

capillary [19], vibration [11] and rotation viscometry [20], only the last one allows to detect a

7

value of the shear stress as well as hysteresis at the thixotropic effect.

8

Moreover, based on rotational viscometry measurements the yield stress in DND

9

hydrosols even at low fillings [20] along with the sol-gel transition was observed. However,

10

some issues on the nature of the transition, the response of suspensions to the shear stress and

11

recovery processes of rheological characteristics in time were beyond the scope of these studies.

12

In particular, it would be important to obtain a direct experimental evidence of existence

13

of chains of DND particles in sol and formation of a network from the chains at the sol-gel

14

transition.

15

recovering of the network. Such direct observation of the network formation has been

16

successfully fulfilled by high resolution transmission electron microscopy (HRTEM), at the same

17

time the process of the network modification by a three interval thixotropic test and

18

demonstration of a hysteresis effect at sol-gel transition.

It would be also useful to reveal experimentally a process of breakdown and

19

The understanding of these processes is especially important for practical applications

20

and can be revealed only by a detailed rheological study of the viscoelastic properties of

21

hydrosols, which also allows to suggest and confirm the corresponding models [10].

22

RESULTS AND DISCUSSION

23

Let us consider rheological behavior of hydrosols. First of all rheological properties of

24

DND hydrosols were studied in shear mode recording flow and viscosity curves. Fig. 1 shows

25

the flow (a) and the viscosity (b) curves at different concentrations of DND with negative ζ-

26

potential obtained in the CSR regime.

27

As can be seen the hydrosol with a negative ζ-potential exhibits Newtonian behavior at

28

concentration lower than 5 wt% – the shear stress (τ) changes linearly with shear rate (γ)

29

increasing (Fig. 1a). At the same time, the viscosity curves show a constant value over a wide

30

range of studied shear rates (Fig. 1b). When the concentration increased higher than 5 wt%, the

3

1

behavior of the DND hydrosols dramatically changes. The flow curves presented in Fig. 1a

2

demonstrate the appearance of yield stress. What is more, the magnitude of stress increases

3

sharply with particle concentration in the hydrosol. According to the theory of sol-gel transition

4

formation of a network is the necessary condition [21]. Similar network can be easily formed in

5

the case of the elongated particles similar to V2O5 [22]. The concentration of DND particles at

6

the sol-gel transition is 5-6 wt% corresponds to about 1.5-2.0 vol%. The unusual effect which

7

attracted our attention is the network formation from the DND particles which do not have

8

elongated form (the aspect ratio is closed to one). The behavior of the DND hydrosol at such

9

concentrations is similar to a solid (elastic) body, in fact, the sol-gel transition is observed [11].

10

It should be emphasized that the viscosity curves at high concentrations decreases linearly

11

with shear rate (Fig. 1b). Such behavior of hydrosols also indicates a phase sol-gel transition.

12

Viscosity values increase with the concentration of diamond nanoparticles in hydrosol. The

13

graphs in Fig. 1 demonstrate transitions from elastic deformation and resistance typical for solids

14

to a viscous flow specific for liquids [23].

15

A similar dependence is observed for samples of DND hydrosols with a positive ζ-

16

potential (Fig. 1c,d). The main difference is in that the yield stress is observed for hydrosols

17

even at low concentrations of less than 1 wt% (Fig. 1c). The contribution of the elastic

18

component becomes more significant with increasing of concentration. The values of the yield

19

stress increase substantially with filler concentration. Viscosity curves show similar behavior to

20

hydrosols with negative ζ-potential at high concentrations (Fig. 1d).

21

As one can see from Fig. 1d at concentrations less than 5 wt% viscosity decreases with

22

shear rate and reach the plateau at high shear rate, exhibiting Newtonian behavior after the

23

structure destroying (τ = η ). The viscosity leveling occurs at shear rate values of 4–5 s-1 at

24

concentrations of DND c = 1; 2 and 4 wt%. It is noteworthy that this dependence is violated for

25

hydrosols at concentration less than 1 wt%. =

26 27

where

≤

≥

ν ν

– Newtonian viscosity,

≈ 4.5

≈ 4.5 ν–

.

;

(1)

critical shear rate.

28

The decrease in viscosity with shear rate corresponds to the part of the flow curve before

29

yield stress. The sample in these conditions is under elastic (reversible) deformation. After

4

1

overcoming the yield stress, a Newtonian flow of hydrosol with a constant viscosity is observed.

2

It should be noted that the viscosity values increase with the number of DND particles in the

3

hydrosol.

4

The DND electrokinetic potential affects the sol-gel transition of hydrosols. If ζ-potential

5

of DND particles is negative, then in the double layer protons H+ dominate. In case of particles

6

with positive ζ-potential, the hydroxyl ions ОН– predominate in double layer. Along with the

7

same potential value, the double layer formed by the protons should have a larger thickness

8

because of the difference in the effective diameters of the Н+ and ОН– ions. Thus, the effective

9

particle size with the double electrical layer surrounding it is higher in the hydrosol with a

10

positive potential. Obviously, that at the same concentration, the viscosity in the hydrosol with

11

positive ζ-potential should be higher, and the sol-gel transition in such sols occurs at lower

12

concentrations (compare Fig. 1b and Fig. 1d).

13

Indeed, a transition from viscous behavior to elastic (sol-gel transition) for DND

14

hydrosols with a positive ζ-potential observed at concentrations above 5 wt%, sol is viscoelastic

15

fluid, although the yield stress is not high. Meanwhile, hydrosols with negative ζ-potential at 5

16

wt% exhibit Newtonian behavior, proving the difference between hydrosols filled with particles

17

of various ζ-potential.

18

The different rheological behavior of DND hydrosols with opposite ζ-potential are also

19

manifested by frequency dependencies of storage and loss moduli. Preliminary amplitude tests

20

were performed in the oscillation mode at a low frequency of 10 s-1 to determine the strain

21

magnitude for frequency tests. According to obtained results, a deformation value of 0.1% was

22

chosen for further frequency experiments. This value is in the linear range of viscoelastic

23

properties for all samples.

24

The frequency dependences of storage G′ and loss G″ moduli for hydrosols and hydrogels

25

with opposite signs of ζ-potential at various concentrations are presented in Fig. S1. For DND

26

hydrosols with a negative ζ-potential (Fig. S1a) and up to 5 wt% particle concentration, only the

27

loss modulus is detected, whose values increase with frequency. Samples reveal viscous

28

behavior. With further increase of concentration, the storage modulus is also detected and

29

exceeds the loss modulus over the whole investigated frequency range. The values of both

30

modules increase with concentration and weakly depend on the frequency. Thus, with the

5

1

increase in concentration a denser network of DND particles is formed and the samples reveal

2

elastic behavior.

3

For DND hydrosols with a positive ζ-potential (Fig. S1b), the storage modulus is

4

detected even at low concentrations and at low frequencies. The value is higher than the loss

5

modulus and the yield stress is observed pointing to a weak network of interacting particles

6

formation even at such low concentrations. The loss modulus increases with frequency and the

7

storage modulus ceases to be detected. Thus, samples with a positive ζ-potential also reveal

8

viscous behavior at high frequency. At a concentration of 5 wt% the hydrosol exhibits a

9

viscoelastic behavior. Both moduli increase with frequency and the cross over point is observed

10

at the low frequency. With a further increase in concentration, the storage modulus exceeds the

11

loss modulus over the studied frequency range. Their values do not change with frequency and

12

increase with concentration.

13

Samples with various concentrations have different values of G′′ and different

14

dependence on frequency. It can be seen that modulus for hydrosols at low concentrations

15

(before sol-gel transition) demonstrate very similar dependences on frequency ω. Regardless of

16

the sign of the zeta potential, the values of the moduli change weakly at low frequencies and

17

increase at a frequency higher than 4 s-1. The observed dependences confirm the results obtained

18

in shear experiments and already mentioned above – the presence of yield stress and increase in

19

their values.

20

It is well known, that the thixotropic effect is a clear manifistation of the sol-gel

21

transition. Shear stress can destroy the DND particle network in gel and transform the gel into a

22

sol [24]. The clear thixotropic effect is shown in Fig. 2. Thixotropic behavior for samples up to 5

23

wt% DND content regardless of the ζ-potential sign cannot be detected. Up to such critical

24

concentration only properties specific for sols are observed.

25

The samples reveal pronounced thixotropic properties at higher concentrations. The

26

processes of viscosity recovery in time are shown on the graphs of the three-interval thixotropic

27

tests (3ITT, see Fig. 2a,b). Three regions can be distinguished on the graphs. The first is

28

measured at low shear rate (1 s-1) and characterizes the initial state of the sample. The second

29

interval is measured at high shear rate (200 s-1) and results in breakdown of the gel structure. In

30

the third region, and at a low shear rate (1 s-1), the structure restoring in time is observed. One

31

can see a sharp decrease in the viscosity of the samples in the second interval with subsequent

6

1

recovery. It is important to note that recovery does not occur instantly. The value of viscosity just

2

after 3ITT is lower than it was before the test (Fig. 2). Such results indicate that a sol-gel

3

transition occurred and the hydrosols at high concentrations of DND become jelly.

4

It is also interesting to note that sols with positive ζ-potential tend to recover their

5

structure much longer. Based on the proposed model the mechanism for break and recovering of

6

the gel is connected to network DNDs chains reorganization. One may suggest that at the 3ITT

7

the incomplete network destruction occurs resulting in remaining of small chains of several DND

8

particles. It is obvious that recovery of the gel network from the small chains requires time. It

9

can explain why the viscosity does not recover immediately after destruction of the network at

10

the third stage of the 3ITT.

11

It is well known that testing of thixotropy properties is a difficult task, because the

12

structure of the sample under study may be crashed during its loading into the measuring cell.

13

However, the measurements show good reproducibility.

14

We found that the recovery process does not depend on the concentration in the studied

15

range. Table S2 presents quantitative results: the degree of structure recovery over time. For

16

hydrosols with negative ζ-potential at 6.9 wt% filler content the recovery process goes faster

17

than at a concentration of 5.9 wt%. Finally, in all samples the viscosity values return to initial

18

level over time and the structure restores.

19

Another thixotropic test is the measurement of hysteresis loop (Fig. 3). It can be expected

20

that the hysteresis loops cannot be observed in hydrosols with the DND concentrations less than

21

5 wt% independently on ζ-potentials sign. It was confirmed experimentally as well as the results

22

of 3ITT. Increase in the hydrosols’ concentration leads to the hysteresis loop, whereas its area

23

depends on the concentration and ζ-potential sign (Fig. 3). With increase in the concentration,

24

the hysteresis loop area also increases.

25 26 27

The hydrosol density at given concentration allows to estimate the energy of the network per particle using the value of area under curve [25]: !"

=

#∗% &

(2)

28

here A – area, Pa/s; V – volume, ml; N – number of particles. The number of particles in solution

29

can be estimated in the spherical approximation, taking into account the density of a DND

30

particle of 3.5 g/cm3 [26] (traditionally taken as density of a bulk diamond) and concentration.

7

1

The calculated parameter has the power dimension '

&∗( )

*

= )+ and corresponds to the

2

energy that must be spent during shear to break the contact between individual particles or DND

3

chains in the hydrosol structure. The results are shown in Table 1. There is an obvious increase

4

in strength of gel network structure with concentration of DND particles with both positive and

5

negative ζ potential. The approximation allows to compare the energy needed to destroy

6

hydrogel structure. It is clearly seen that even at high shear rate (100 s-1) the energy values are

7

almost several orders of magnitude higher than thermal energy (kT).

8

Thus, DND hydrosols exhibit unique rheological behavior, in particular, sol – gel transition

9

and demonstrate the yield stress and hysteresis at extremely low concentrations. It is important

10

that hydrosols exhibit qualitatively similar, but quantitatively quite different rheological

11

properties depending on the ζ-potential of DNDs. To understood such behavior and identify the

12

reasons and nature of this phenomena, detailed structural studies were carried out.

13

First of all, the origin of DNDs particles ζ-potential different sign was studied by 13С solid-

14

state nuclear magnetic resonance (NMR). The various types of functional groups prevailing on

15

the surface of DND particles with different sign of the ζ-potential was established (Fig. S3). It

16

can be seen in Fig. S3, that the COH groups on the particle surfaces are present only in the

17

hydrosol with a negative ζ-potential, and on particles with ζ are completely absent. On the other

18

hand, the CH and CH2 groups are specific just for the surface of particles with a positive ζ-

19

potential.

20

DND hydrosols structure was investigated by small-angle X-ray scattering (SAXS). The

21

samples regardless of the ζ-potential sign shows typical two-level organization, corresponding to

22

a loose aggregate with fractal dimension of 2.3 and a compact DND particle, surface fractal with

23

dimension 1.7 [20]. That was also confirmed previously by light [27] and neutron scattering [28].

24

The particle size distributions obtained from SAXS data reveal that the most of DND particles in

25

hydrosols has an average size of d = 5 nm, however there are a low number of larger structures

26

with sizes up to 50 nm (Fig. S4). This corresponds to the proposed model, according to which

27

particle chains are present in the DND hydrosol along with 4–5 nm particles.

28

Surprisingly, the expansion of the X-ray measurement range to smaller angles down to

29

0.04 nm-1 allows us to observe the Bragg peaks corresponding to scattering on an ordered

30

structure of fractals. Scattering curves for suspensions with negative ζ-potential are shown in

8

1

Fig. 4a as example. The peak is observed even at a concentration of 1 wt%, although it is rather

2

weak and manifests itself as a shoulder. Kratky plot shows the second order of scattering,

3

indicating the scattering on the structure rather than a form factor of particles (Fig. 4b). The

4

position of maximum changes and the interplanar distances (d = 2π/q) decrease with

5

concentration of DNDs in hydrosols. Thus, the formation of denser DND particles network

6

during the gel structure organization is observed (Table 2).

7

At the same time, the interplanar distance reaches a constant value at a concentration of

8

4.1 wt% for suspensions of DNDs with positive ζ-potential. For suspensions with a negative ζ-

9

potential, a decrease in the distance up to concentration of 6.9 wt% is observed. It should be

10

noted that the reliable determination of the distance between the scattering centers in 1.0 wt%

11

DND hydrosol is difficult. This fact may indicate the formation of longer chains in the case of

12

samples with a positive ζ-potential, which correlates with the rheology data.

13

To verify the proposed models Cryo transmission electron microscopy (CryoTEM) and

14

Cryo-Electron Tomography (CET) studies were carried out. The measurement procedure in cryo

15

mode allows to observe the native structure of the sample. Fig. 5 and Fig. 6 show the cryoTEM

16

image and the results of CET for 1 wt% of DND hydrosols with a different sign of ζ-potential.

17

The figures clearly demonstrate the formation of extended fractal structures and chains

18

formed by individual faceted DND particles. It is obvious that DNDs with a negative ζ-potential

19

form a fractal structure by a smaller number of particles in contrast with a positive ζ-potential

20

DNDs. In the latter case, tomography data demonstrate the formation of a percolation network

21

(Fig. 6b,c). This explains the differences in the rheological behavior at low concentrations of

22

samples with different sign of ζ-potential. The fractal dimensions estimated from the CET data

23

are of the order of 2.2, which is in good correlation with the SAXS data for the fractal dimension

24

of a DND cluster [20]. Moreover, interparticle distance distribution (insets Figs. 5a and 6a)

25

show, that the secondary maximum position qualitatively matches the interplanar distance

26

between fractals at 1 wt% contain of DND particles in hydrosol measured by SAXS (see

27

Table 2).

28 29

It is important to note that such structures are permanently dynamically rearranged, otherwise aggregation and sedimentation of particles should be observed.

30

Let's estimate the value of shear stress for chains destruction considering the model [11]

31

based on application of DLVO theory to nanoparticles with non-spherical electric potential.

9

1

According to the DLVO theory [21] stability of sols is determined by a balance between

2

attracting forces and repulsive forces. The latter is consequence of interaction of electrical double

3

layers surrounding every particle. The suggested shape of free DND particles is truncated

4

octahedron and as a result the particles in sol, possess a spherically non-symmetric potential [10].

5

Thus, the electrical double layer around every particle is not spherical also [11,20]. The

6

asymmetry of the potential changes the interaction parameters between DND particles.

7

Eventually, this change leads to formation of the chains and increase in hydrosols viscosity.

8

Consequently, the sol-gel transition in such hydrosols may takes place at low concentration of

9

the particles due to formation of a network.

10

Let us make some estimates. An individual DND particle can be described as a multipole.

11

However, such description is a non-trivial task since it is not clear what type of multipole

12

(dipole, quadrupole, etc.) most adequately corresponds to the interaction of real DND particles.

13

Therefore, in a rough estimate, it is possible to consider the DND particles as point charges.

14

Let’s compare energy of electrostatic interaction between two particles in a chain and the energy

15

that is required for motion of the chain as a whole with a given angle velocity. DND particles are

16

considered to be polyhedral. Using known electrokinetic potential values of | ζ | = 40–50 mV [8]

17

one is able to calculate electric charge of a particle Q ≈ 2.0·10-18 C. The Q value has been

18

derived from Coulomb low based on the absolute value of electrokinetic potential, distance

19

between particle and slipping plane (3 – 4 nm) and dielectric constant of water.

20

Note, the crystallographic facets having different indexes, (100) and (111), have opposite

21

signs and values of charge. As consequence, water double layer surrounding the particle in

22

hydrosol is non-symmetric [11].

23

Estimation of energy of electrostatic interaction between the particles allows to determine

24

the distance between particles’ centers to be h = 6 nm, it means that inter-particle distance in

25

chains is very short. Moreover, skeleton analysis of the CET data showed that a continuous

26

percolation network from DNDs with positive ζ-potential forms at a distance between particles

27

of 2.3 nm. The energy required for motion of chain as a whole with angle velocity ≈ 4.5 s-1 is

28

turned out to be an order of the electrostatic interaction energy. Angular velocity of the chains

29

corresponds to shear rate. Therefore, at the shear rate of ≈ 4.5 s-1 the chains should be broken.

30 31

Taking into account the values of viscosity and yield stress we can estimate the energy required for destruction of the chains into free diamond particles [20].

10

1 2 3

Let’s to compare the force causing shearing of DND particles Fsh with electric interaction force Fe: Fsh = 3πτδd

(3)

4

where δ = 1 mm is gap between two cylinders in the rotational viscometer, τ – shear stress, d –

5

diameter of DND particle.

6

Fe = Qζ/h

(4)

7

These two forces will be equal to each other in the case at τ ≈ τ0 corresponding to the

8

concentration of 5 wt% (Fig. 1). At smaller shear stress τ ≤ τ0, electric interaction forces forming

9

the chains dominate. If τ ≥ τ0, the Stokes forces causing the shearing dominate, and thus the

10

chains will be destructed. Note, here and above we base on concepts considering the chain

11

formation from spherically non-symmetric DND particles sized 4–5 nm.

12

Thus, simple estimate shows, that due to the non-sphericity of DND particle ζ-potential,

13

chains are formed, which in turn are organized into fractal structures with dimension of 2.2. Such

14

organization results in the formation of a percolation continuous cluster at very low

15

concentrations.

16 17

CONCLUSION

18

This paper describes for the first time rheological properties of hydrosols consisting of

19

diamond nanoparticles sized 4–5 nm with positive and negative electrokinetic potentials in a

20

wide concentration range (1.1–7.3 wt%). The hydrosols were characterized by SAXS, NMR,

21

TEM and CET. Rheological properties were investigated by rotational viscometry. Sufficient

22

distinction in behavior of hydrosols with negative and positive electrokinetic potentials have

23

been observed. The thixotropic effect and the sol-gel transition were revealed at concentrations

24

of DND particles in hydrosol lower than 6 wt%. Viscosity hysteresis occurring under increasing

25

and subsequent decreasing shear stress is revealed for the first time.

26

The analysis of obtained results allows to explain observed features of the rheological

27

behavior associated with non-sphericity of DND’s electrical double layer leading to the chain

28

formation. The explanation is based on application of the general concepts of DLVO theory to

29

nanoparticles with non-spherical electric potential. The SAXS, cryoTEM and CET data confirm

30

the proposed model.

31

11

1

MATERIALS AND METHODS

2

The study was focused on two types of DND hydrosols with positive and negative

3

electrokinetic ζ-potential in the concentration range from 1.0 to 7.0 wt% corresponding to about

4

1.5-2.0 vol%. The DND hydrosols with positive and negative ζ potentials were produced by the

5

method similar to described in our previous papers [9]. ζ potentials depends on atmosphere in

6

which DND powders are annealed. Molecular hydrogen and air are used for obtaining DND with

7

positive and negative ζ-potential, respectively. ζ-potential is determined from electrophoretic

8

mobility measurements using the Henry equation with the Smoluchowski approximation. The

9

measurements are performed by ZetaSizer ZS (Malvern Instruments). Purification of industrial

10

DND powder was carried out by oxidation process to remove the non-diamond carbon and by

11

subsequent etching in HF and KOH with multiple washing in purified water, by centrifugation

12

and drying in air. The samples with positive and negative potentials were made by annealing in

13

hydrogen and air. Sonication and centrifugation resulted in DND hydrosols consisted of

14

primarily particles ranging of 4-5 nm. Energy dispersive X-ray analysis suggested that metal

15

impurities in samples did not exceed 0.4 wt %

16

The negative charge is reported to be a result of dissociation of surface carboxyl groups in

17

aqueous media: DND-COOH + H2O ↔ DND-COO‾ + H3O+. It was repeatedly confirmed

18

experimentally [29–32].

19

The issue on the origin of the positive charge remains to be controversial [33]. One can

20

only say that annealing in hydrogen atmosphere and vacuum results in positive electrokinetic

21

potential. In our case heat treatment in hydrogen atmosphere was used as it was described in [9].

22

The types of surface functional groups determining the sign of DND particles ζ-potential,

23

were analyzed for by solid-state 13C NMR spectroscopy. NMR measurements were conducted at

24

the Center for Magnetic Resonance (St. Petersburg State University Research Park) on a Bruker

25

Avance III 400WB spectrometer (100.64 MHz for 13C) equipped with an MAS probe. Samples

26

were placed in 4 mm zirconium oxide rotors and spun at 12.5 kHz. Chemical shifts were

27

calibrated using tetramethylsilane (TMS) as an external standard. One-pulse MAS measurements

28

were performed using 3.8 µs pulses and 90 s relaxation delays. For cross-polarization (CP) MAS

29

measurements the contact time was 5 ms and relaxation delay was 10 s. Number of scans was

30

320 for one-pulse MAS and 4096 for CP MAS experiments.

12

1

Rheological properties were measured by Anton Paar Physica MCR 501 rheometer, its

2

measuring system consists of two coaxial cylinders (measuring cell CC-27 E). The cell volume is

3

20 ml, the gap is 1 mm. All samples before measurements were kept for several minutes in the

4

cell to avoid phenomena related with possible structural changes. The measurements were

5

carried out at various regimes: in control shear rate (CSR) mode providing the flow and viscosity

6

curves, in three interval thixotropy test (3ITT) and hysteresis loop modes and also in oscillation

7

mode – amplitude tests (AS) to determine linear-viscoelastic (LVE) region and frequency tests

8

(FS) for storage, loss moduli. All data were obtained in automatic mode at a temperature of 20°C

9

after thermostating. The data were processed using a computer program package of the

10

instrument Rheoplus 3.40.

11

Small angle X-ray scattering (SAXS) data were recorded on BioMur station of Kurchatov

12

synchrotron radiation source, the used wavelength was λ = 1.445 Å, and the 2 detector Dectris

13

Pilatus 1M. Hydrosols were examined in X-ray capillaries Hilgenberg diameter 1.5 mm, wall

14

thickness of the capillary was 10 µm. Exposure time was 180 s. Silver behenate (d001 = 58.8 Å)

15

was used for reference. The processing of the small-angle X-ray scattering results was performed

16

using a computer program package ATSAS [34]. The fractal dimensions was evaluated from

17

scattering curves in log-log scale [35,36].

18

The spatial distribution of DNDs was revealed by Cryo-Electron Tomography (CET). The

19

portion of hydrosol (3 µl) were applied to the glow discharged (30 s, 25 mA) lacey carbon EM

20

grid, blotted for 1.5 s and then plunge-freezed into a liquid ethane cooled by liquid nitrogen in

21

Vitrobot Mark IV (Thermo Fisher Scientific, USA). This procedure results in the formation of a

22

thin layer of vetrified liquid with DNDs. CET study was carried out with Titan Krios 60-300

23

TEM/STEM (Thermo Fisher Scientific, USA) CryoEM, equipped with direct electron detector

24

Falcon II (Thermo Fisher Scientific, USA) and Cs image corrector (CEOS, Germany), at

25

accelerating voltage of 300 kV. Datasets consisted of 61 images of the sample tilted within the

26

range of -60° to 60° with the step increment of 2°. Tilt series were collected automatically using

27

FEI Tomography software in low-dose mode (to prevent crystallization of liquid) at 18000x

28

magnification with the defocus of ~3 µm. Cross-correlation alignment and tomography

29

restoration by simultaneous iterative reconstruction technique (SIRT) were performed with

30

Inspect3D (FEI, USA) software. For further 3D processing and reconstruction of DNDs surface

31

from binary images, Avizo (FEI, USA) software was used. The processed data was binarized by

13

1

the automatic entropy segmentation method [37,38] and surface models of DNDs were

2

generated. The obtained binary data arrays and surface models were then utilized for numerical

3

analysis. The 2D (separate stack images) and 3D (volumetric data) fractal dimensions were

4

calculated for the mass fractal and surface fractality. The distances between DNDs were

5

estimated after the 3D reconstruction of the specimen volume with the size of 1920 x 1781 x

6

216 pixel3 (737,3 x 683,9 x 82,9 nm3), In order to do the estimation, the space between

7

DNDs were split to a set of parallel equally spread three dimensions rods with the thickness

8

of the 1x1 pixel and with a 3 pixels (1.15 nm) distance between the rods. Thus, the period

9

was four pixels, which is 1.54 nm and that is less than DND dimensions. The lengths of the

10

lines between particles were evaluated and the distribution of distances between DNDs were

11

obtained. More details on this method can be found in [39].

12

14

1

FIGURES

Figure 1. Flow (a,c) and viscosity (b,d) curves of hydrosols filled by DND with negative (a,b) and positive (c,d) ζ-potential at various concentrations obtained by control shear rate mode. 2 3

15

Figure 2. The three-interval thixotropic test: (a) – for negative ζ-potential, (b) – for positive ζ1 2

potential. Viscosity as function of time for DND hydrosols.

Figure 3. Hysteresis loop for DND hydrosols with negative (6.9 wt%) and positive (7.3 wt%) ζ-potential. 3

16

Figure 4. (a) –Small-angle X-ray scattering curves for hydrosols filled by DND with negative ζ-potential, (b) – Kratky plot, the inset shows possible model of Bragg scattering.

Figure 5. CryoTEM image of 1.0 wt% DND hydrosol with negative ζ-potential (a). The distribution of interparticle distances are shown in the inset. CET 3D reconstruction of the hydrosol thin layer in different projections (b,c). 1

17

Figure 6. CryoTEM image of 1.0 wt% DND hydrosol with positive ζ-potential (a) with the distribution of interparticle distances in the inset. CET 3D reconstruction of the hydrosol thin layer under study (b,c). 1 2

TABLES

3

Table 1. The area of hysteresis loop for DND hydrosols at various concentrations. Sample, wt%

Ahyst., Pa/s

Enetwork, J/s

5.7 (ζ+)

80.3±3.7

(3.2±0.2)*10-16

7.3 (ζ+)

194.9±13.2

(6.1±0.4)*10-16

5.9 (ζ–)

78.3±10.3

(3.0±0.4)*10-16

6.9 (ζ–)

173.7±2.7

(5.8±0.1)*10-16

4 5

Table 2. Interplanar distances in DND hydrosols determined from SAXS data at various

6

concentrations and ζ-potential sign. ζ-potential negative

Concentration, wt%

Scattering distance (d), nm

1.0

–

2.0

67.5

18

positive

4.2

65.2

5.9

62.9

6.9

57.1

1.1

67.5

2.0

59.0

4.1

57.1

5.7

57.1

7.3

57.1

1 2

ASSOCIATED CONTENT

3

1.

Figure S1, tif.

4

2.

Table S2, text.

5

3.

Figure S3, tif.

6

4.

Figure S4, tif.

7

AUTHOR INFORMATION

8

Corresponding Author

9

*E-mail address: [email protected] (Nikita M. Kuznetsov)

10

**E-mail address: [email protected] (Alexander Ya. Vul')

11

Author Contributions

12

The manuscript was written through contributions of all authors. All authors have given approval

13

to the final version of the manuscript.

14

ACKNOWLEDGMENT

15

Alexander Ya. Vul' and Elena B. Yudina thank the Russian Scientific Foundation (project N 14-

16

13-00795) for support.

17

Nikta M. Kuznetsov and Sergey I. Belousov, thank the RFBR for partial financial support

18

(project 18-29-19117).

19

1

The authors acknowledge support from the resource centers of organic and hybrid materials

2

“Polymer” and X-ray methods “Rentgen” of the National Research Center “Kurchatov Institute”

3

for the possibility of rheological and X-ray structural studies.

4

ABBREVIATIONS

5

DND, detonation nanodiamond; 3ITT, three-interval thixotropic tests; NMR, nuclear magnetic

6

resonance; SAXS, small-angle X-ray scattering; CryoTEM, Cryo transmission electron

7

microscopy; CET, Cryo-Electron Tomography.

8

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CRediT author statement Conceptualization: Alexander Ya. Vul'; Sergei N. Chvalun; Sergey I. Belousov; Writing: Nikita M. Kuznetsov; Resources: Elena B. Yudina; Methodology: Alexander L. Vasiliev; Artem V. Bakirov; Roman A. Kamyshinsky; Peter M. Tolstoy; Anton S. Mazur; Eugeny D. Eidelman: Formal analysis

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: