Electrostatic Interactions Between Barium Hexaferrite

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C: Physical Processes in Nanomaterials and Nanostructures

Electrostatic Interactions Between Barium Hexaferrite Nanoplatelets in Alcohol Suspensions Patricija Hribar Bostjancic, Matija Tomsic, Andrej Jamnik, Darja Lisjak, and Alenka Mertelj J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b07455 • Publication Date (Web): 30 Aug 2019 Downloaded from pubs.acs.org on August 30, 2019

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The Journal of Physical Chemistry

Electrostatic Interactions between Barium Hexaferrite Nanoplatelets in Alcohol Suspensions Patricija Hribar Boštjančič,*,†,§ Matija Tomšič,‡ Andrej Jamnik,‡ Darja Lisjak,† Alenka Mertelj† †

§

‡

Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia

Jožef Stefan International Postgraduate School, Jamova cesta 39, 1000 Ljubljana, Slovenia

University of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, 1000 Ljubljana, Slovenia

*Patricija Hribar Boštjančič | Department of Complex Matter, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia | Phone: 00386 1 477 3937 | E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT: In a room–temperature liquid magnet, barium hexaferrite (BHF) nanoplatelets suspended in 1-butanol spontaneously order and form a ferromagnetic nematic phase. In such concentrated suspension, the nanoplatelets align in large macroscopic regions, forming magnetic domains. The key parameter for the suspension stability and the formation of the ferromagnetic nematic phase is electrostatic interaction, which can be influenced by the solvent and the concentration of surfactant, i.e., dodecylbenzenesulfonic acid (DBSA). In this study, we investigated electrostatic interactions of the DBSA-functionalized nanoplatelets’ suspensions in different alcohols. We prepared suspensions in tert-butanol, 1-hexanol, 1-butanol, 2-propanol and measured conductivity, small-angle X-ray scattering (SAXS), dynamic light scattering (DLS) and electrophoretic mobility. SAXS results and electrophoretic mobility measurements confirmed the colloidal stability of the suspensions, which was not affected by the variation in concentration of added DBSA of the order of 1.3 mM. We showed that the dielectric constant of the solvent affects the surface charge, the strength of the electrostatic repulsion between the nanoplatelets and the Debye screening length. The balance between the magnetic dipolar attraction and electrostatic repulsion were proven to be essential for the ferromagnetic nematic phase formation.


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1.

INTRODUCTION

It was shown recently that a special kind of ferrofluids, made of magnetic nanoplatelets suspended in 1-butanol, at high enough concentrations forms a room-temperature liquid magnet.1,2 In such suspensions, the magnetic interaction in combination with the platelets’ shape leads to a spontaneous orientational magnetic order, resulting in a macroscopic ferromagnetic state. The key constituents of the suspensions are BHF nanoplatelets. BHF is a hexagonal ferrite, that preferentially grows in the ab-plane, causing that the BHF nanoparticles have a platelet-like shape. The BHF nanoplatelets are ferrimagnetic, having the magnetic easy axis perpendicular to the basal plane.3 Ferrofluids are colloidal suspensions of ferro or ferrimagnetic nanoparticles, which can be magnetized.4 For the stability of any ferrofluid, it is crucial to tune the size, size distribution and surface properties of the nanoparticles. Surfactants, which provide for steric stabilization of the suspension, can be used when magnetic moments of the particles are relatively small. In this case, in the absence of a magnetic field, the average magnetic interaction between the nanoparticles at contact is weaker than the thermal energy. However, under an applied magnetic field the magnetic interaction becomes stronger than the thermal energy, causing the formation of chain-like structures, which, for example, results in the increased viscosity of the suspension.5–7 In the suspensions from particles with larger magnetic moments, for which average contact magnetic interaction between the particles exceeds thermal energy significantly, long chain-like aggregates form already in the absence of the magnetic field, and electrostatic stabilization is necessary for their colloidal stability. In ferrofluids, in addition to attractive van der Waals interactions, also attractive magnetic dipolar interactions can cause aggregation. In the case of BHF nanoplatelets, the aggregates are


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usually columnar due to the magnetic easy axis being oriented perpendicular to the ab-plane. Therefore, for colloidal stability that is essential for any subsequent use, some repulsive interactions must be induced. Long-chain surfactants with dielectric properties corresponding to the surrounding solvent can provide for electrosteric stabilization.8 Magnetic dipolar interaction is a long-range interaction that exceeds the reach of steric stabilization. On the other hand, electrostatic interaction is longer-ranged than steric and provides for stabilization of magnetic nanoparticles. It has been shown that the surface modification of the BHF nanoplatelets with a double layer of DBSA allows for the formation of stable colloidal suspensions in alcohols.8 The first prepared suspensions of DBSA modified BHF nanoplatelets in alcohol8 had short-term stability despite the electrosteric repulsion provided by the DBSA. The reason was the size of nanoplatelets (with diameters of a few hundred nanometers) that aggregated and eventually sedimented.8 However, after narrowing the diameter-distributions including the elimination of the large BHF nanoplatelets by partial substitution of Fe3+ with Sc3+,9 the DBSA provided for sufficient electrostatic stabilization in different alcohols and enabled the preparation of ferromagnetic ferrofluid in 1-butanol.1 An important parameter of electrostatic interaction is the Debye screening length. It represents the distance to where the electrostatic interaction is significant. It depends on the solvent properties, temperature and the ionic strength of the solution.10 In the BHF suspensions, the dissolved DBSA contributes to the suspension's ionic strength and, consequently, affects the Debye screening length value. We studied the parameters that affect the electrostatic interaction between the BHF nanoplatelets in different alcohol suspensions, from which ferromagnetic ferrofluids can be made. At least part of the DBSA molecules are physisorbed to the platelets11, so there is a dynamic equilibrium of adsorption and dissolution of the surfactant molecules. This equilibrium is affected by the total


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fraction of the surfactant, the concentration of the platelets and the properties of the alcohol. The concentration of adsorbed molecules affects the platelet’s charge, while the concentration of dissolved molecules determines the Debye screening length. We evaluated the properties of the suspensions that determine the electrostatic interaction, such as surface charge and the concentration of free ions at different concentrations of DBSA. The measurements were performed in tert-butanol, 1-hexanol, 1-butanol and 2-propanol suspensions to consider also the effect of the solvent’s dielectric constant.

2.

METHODS 2.1 Materials. Barium nitrate (99.95%), iron(III) nitrate nonahydrate (98+%), scandium(III)

nitrate hydrate (99.9%), sodium hydroxide (98%) and DBSA (97%) were obtained from Alfa Aesar. Tert-butanol (99.5%), 1-hexanol (99%), 1-butanol (99.4%) and 2-propanol (99.9%) were obtained from Emsure, Alfa Aesar, Baker Analyzed and Carlo Erba. Nitric acid (65%) was obtained from Sigma-Aldrich. 2.2 Synthesis and Processing of Materials. Sc3+ substituted BHF nanoplatelets were hydrothermally synthesized at 245 °C following the previously established process.9 Briefly, barium, iron(III) and scandium(III) nitrates were dissolved in water in a molar ratio 1:4.5:0.5 and coprecipitated with a surplus of sodium hydroxide (1.13 mol). 0.01 mol DBSA was added to the solution. The mixture was transferred to an autoclave and heated up with rate 3 °C min-1 to 245 °C. The obtained nanoplatelets were washed with water. The subsequent treatment with the surfactant DBSA and additional washing was the same as described previously.8 The particles were dispersed in water and 5 M nitric acid was slowly added to drop the pH to 1.5. The mixture was then stirred at 100 °C for 2 h. The particles were washed with distilled water, acetone and


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dried at 60 °C. The dried nanoplatelets were dispersed in tert-butanol, 1-hexanol, 1-butanol and 2propanol using an ultrasonic probe (Sonics Vibra-cell) with pulse 1s on, 1s off at power of 150 W. The suspensions were additionally diluted to get concentrations of 5, 15 and 30 g L-1. 2.3 Characterization of Materials. The BHF nanoplatelets were analyzed using a transmission electron microscope (TEM) (Jeol 2100). The diluted suspensions were drop-deposited on a Cugrid-supported, perforated, transparent carbon foil. The nanoplatelets’ diameter was estimated from TEM images (Figure 1a) using DigitalMicrograph™ Gatan Inc. software. At least 250 particles were measured to determine the average diameter of 55 nm with a standard deviation of 20 nm (Figure 1b). The magnetic properties of dried nanoplatelets were conducted with a vibrating-sample magnetometer (VSM, Lakeshore 7407). The nanoplatelets exhibit typical hard magnetic ferrimagnetic behavior and have a room-temperature saturated mass magnetization of 39 A m2 kg-1 (Figure 1c).

Figure 1. a) TEM image of as-synthesized BHF nanoplatelets. b) The particle-size distribution. c) Magnetic hysteresis, typical for hard magnetic materials. The mass fraction of the DBSA in the sample of as-prepared nanoplatelets was determined thermogravimetrically and is 13.6%. The nanoplatelets that were previously washed and dried at 60 °C were subsequently heated up to 700 °C with a heating rate of 5 °C min-1. At this temperature, the DBSA is quantitatively decomposed. The molar concentration of dissolved DBSA (c-dis) was


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determined with conductivity (  ) measurements (Conductometer Knick – Portamess) for the suspensions in all four alcohols with suspension concentrations 5, 15 and 30 g L-1 at 27 °C. The molar concentrations of the dissolved and adsorbed DBSA (c-ads) were determined by a standard addition method. To the BHF suspensions in alcohols, a solution of DBSA was added. The conductivity linearly increases with the increase of the c-dis. The latter was calculated from the linear line graph equation   a  (b  (c  dis )) , as a quotient of a and b. The c-ads was calculated from the difference between the total molar concentration of DBSA (c-tot) and c-dis. The dissociation degree of the DBSA was estimated from the conductivity measurements in the suspensions and water with increasing concentration of DBSA. The conductivity depends linearly on the concentration of the DBSA ions and is inversely proportional to the viscosity of the solvent. The value of the linear line inclination coefficients was used for the calculation of the dissociation degree of the DBSA in suspensions with an assumption that the DBSA is totally dissociated in water. The number density of DBSA obtained from conductivity measurements, where we considered also the dissociation degree of DBSA was used for the calculation of Debye screening length that can be written as10:

 0 k BT

 1 

2 0

e

n Z i

(1) 2 i

i

where  1 is the Debye screening length,  the dielectric constant of the solvent,  0 the vacuum permittivity = 8.854  10-12 As V-1 m-1, kB the Boltzmann constant with the value of 1.38  10-23 J K-1, T the absolute temperature, e0 the elementary electron charge with the value of 1.6022  10-19 A s, ni the number density and Zi the charge of the i-th ion species in the suspension.


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For the calculations of the Debye screening length in the 200 g L-1 suspensions, the assumption that the value of c-dis is 5 mM was made, because the c-ads is at 30 g L-1 almost saturated and cdis/c-tot is ~ 7%. At this value the c-dis in 200 g L-1 suspensions is ~ 5 mM. The electrophoretic mobility and zeta-potential values of suspensions with concentration of 1 g L-1 were determined on a Litesizer™ 500 using an Univette measurement cell and applied voltage 40 V. For conversion of the particles’ net electrophoretic mobility to zeta potential, the Henry equation was used (2)12, where  is the zeta potential,  is the electrophoretic mobility of the particles,  is the viscosity of the solvent and f(  a) the Debye factor, respectively. We used the Hückel approximation. Therefore, the Debye factor was set to 1.0.

 

3 2 0 f ( a )

(2)

The electrophoretic mobility measurements were performed at 25 °C for suspensions in 1-hexanol, 1-butanol, 2-propanol and at 26 °C for the suspensions in tert-butanol at applied voltage 40 V. Measurements with increasing molar concentration of DBSA were performed on the suspensions in tert-butanol at 27 °C and 1-butanol at 25 °C at applied voltage 30 V. The DLS measurements were performed on Litesizer™ 500 on suspensions with nanoplatelets’ concentration of 1 g L-1. The suspensions in tert-butanol are undercooled at ambient conditions, affecting the value of viscosity ( ). To determine the exact  of tert-butanol at 26 °C and 27 °C, the correlation functions from DLS measurements were obtained. A series of DLS measurements was performed from 20 to 28 °C for tert-butanol suspension and at 25 °C for 1-butanol suspension. The difference in the DLS measurements is the characteristic decay rate f1 of the autocorrelation function, which is inversely proportional to the  . By rescaling time with f1, all autocorrelation


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functions fall into a master curve (Figure S1, see Supporting Information). The  of tert-butanol was then calculated from:

f1 BuOH 25C   t  BuOH ft  BuOH 1 BuOH 25C

(3)

The values of  at different temperatures for tert-butanol calculated from equation (3) are presented in Table T1 and Figure S2 (see Supporting Information). The SAXS measurements were performed in an in-lab-modified Kratky camera (Anton Paar KG, Graz, Austria) attached to a conventional X-ray generator (GE Inspection Technologies, SEIFERT ISO-DEBYEFLEX 3003). The incident beam with the wavelength,  = 0.154 nm was generated utilizing the Cu anode operating at 40 kV and 50 mA. It passed the Göbel mirror and the block-collimation system to result in a line-collimated monochromatic primary beam. The samples were placed in a standard quartz capillary (outer diameter of 1 mm and a wall thickness of 10 μm) and thermostated at 25 °C using a Peltier element. The scattered X-ray intensities were detected with a Mythen 1K microstrip solid-state diode-array detector (Dectris, Baden, Switzerland) in the small-angle regime of scattering vector, q , from 0.065 nm-1 to 7 nm-1. The scattering vector is defined as q 

4



sin(   , where  is the scattering angle. Obtained data

were corrected for X-ray absorption and capillary scattering and were put to the absolute intensity scale using water as a secondary standard.13 The resulting data were still experimentally smeared due to the finite dimensions of the primary beam.14 Therefore, they were further desmeared utilizing the iterative Lake algorhitm15 and put to an absolute scale using water as a secondary standard.13 As such, they could be compared to the calculated theoretical scattering intensities. 2.4 Interplatelets Interaction. The interactions between the magnetic nanoplatelets are longrange interactions, such as magnetic dipole-dipole and electrostatic interaction, and short-range


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Van der Waals interaction. The contribution of the latter can be neglected at the distances relevant in this case. A magnetic platelet can be described as a thin disk with magnetic moment pi, oriented perpendicularly to the platelet’s plane and we denote its orientation by a unit vector ni (Figure 2).

Figure 2. Two thin disks describing magnetic platelets. The magnetic dipolar interaction between two such disks can be written as U dip  

 0 p1 p2  3  n1  r  n 2  r   n1  n 2  3  4 r  r r 

(4)

The expression in the bracket depends on relative orientations of the platelets and has values between -2 and 2. Here, r is a vector connecting the centers of the disks and r is its absolute value. Repulsive electrostatic interaction between two thin disks with charges Z1e0 and Z 2 e0 can be well described by a model similar to Debye Hückel model, in which contribution of the anisotropic shape of the interacting particles is described by the anisotropy function f.16

U el 

Z1Z 2 e02 e  r f  R1 ,  R2 , n1 , n 2  4 0 r

(5)

For two very thin disks with radii R1 and R2, the anisotropy function depends on the radii of the disks and their orientation, and it can be approximated by f  4

I1  R1 sin 1  I1  R2 sin 2  16 ,  R1 sin 1  R2 sin 2

where ϑi is the angle between the vector connecting the centers of disks r and the i-th disk’s orientation ni and I1(x) is modified Bessel function of the order 1. In the range of possible values of κRi in the suspensions, which is from 0.3 to 2.8, f has values between 1 and 6. The effective charge of an average platelet can be estimated from the zeta potential. Assuming the charge of a


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disk is similar to the charge of a sphere with equivalent volume (with radius Req), which is given by17



Ze0  4 0 Req2 k BT / e0 2sinh  e0 s /  2k BT    4 /  Req  tanh  e0 s / (4k BT 



(6)

and assuming  s   ,18 the charge varies from approximately 14e0 (in t-butanol) to 22e0 (in 2propanol). In the calculation of Req, the volume of the disks was taken to consist of a magnetic part and a surfactant layer of the thickness of 1 nm. The total interaction energy U  U dip  U el depends on the distance between the disks and their orientation. The average interaction at a given position r can be calculated by averaging U / k T U over orientations of disks assuming Boltzmann probability distribution p  n1 , n 2 , r   1A e B ,

where A is the normalization constant A   e U / kBT d 1d  2 , and the integration is performed over all solid angles Ωi.

3.

RESULTS AND DISCUSSION 3.1 Suspensions’ Dissociation Properties. BHF nanoplatelets were synthesized hydrothermally

and functionalized with DBSA. The first layer of DBSA is adsorbed at the positively charged nanoplatelet’s surface. The as-modified nanoplatelets show hydrophobic character and flocculate in a strongly polar medium (like water). The exchange of the water with alcohol causes partial desorption of the DBSA molecules from the surface and a double layer formation (Scheme 1).8 The double layer is formed due to the hydrophobic interactions between the two layers of DBSA molecules at the nanoplatelet’s surface and is in a dynamic equilibrium with the system. The protonated sulfonic groups19, formed by a proton exchange20–22 between the BHF nanoplatelet surface and the DBSA molecule result in the positive charge of the nanoplatelets. A part of the


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desorbed DBSA forms a double layer, while another part is dissolved (c-dis) and partially dissociated in the alcohol suspension. The latter importantly contributes to the ionic strength of the suspensions. The concentration c-ads refers to the adsorbed molecules at the nanoplatelets’ surface, i.e., the first and the second layer of DBSA around the nanoplatelet.

Scheme 1. The DBSA double-layer at the nanoplatelet’s surface. The concentrations of the c-dis and c-ads were determined from the conductivity measurement results and are presented in Table 1. The value of c-dis is lower in more polar 2-propanol and 1butanol suspensions than in less polar 1-hexanol and tert-butanol suspensions. A decrease in the suspension concentration from 30 to 15 and further to 5 g L-1 causes additional desorption of the DBSA from the nanoplatelet’s surface and its dissolution in all studied alcohols. For a proper evaluation of the adsorption of the DBSA at the nanoplatelets’ surface, the value of the c-ads/c-tot was compared. The values of this quotient in the suspensions with concentration 30 g L-1 are similar in all studied samples. Some noticeable changes appear when the suspension concentration was decreased to 15 and further to 5 g L-1 because of the DBSA dissolution. With such decrease of concentration, the dissolution of the DBSA from the nanoplatelets’ surface is stronger in less polar tert-butanol and 1-hexanol than in more polar 1-butanol and 2-propanol. The dissolution of the DBSA molecules from the surface must be therefore more significant in alcohols with lower dielectric constant. In other words, the dissolution of DBSA is higher in less polar alcohols.


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Table 1. The Concentrations of the Dissolved (c-dis) and Adsorbed DBSA (c-ads) in Suspensions in Tert-butanol, 1-hexanol, 1-butanol and 2-propanol with Different Nanoplatelet Concentrations Solvent

*

tert-butanol

12.1 23

1-hexanol

13.1 24

1-butanol

17.3 23

2-propanol

18.9 25

 (g L-1)

c-dis (mM)

c-ads (mM)

c-ads / c-tot

5 15 30 5 15 30 5 15 30 5 15 30

0.71 0.92 0.93 0.31 0.59 0.90 0.27 0.49 0.68 0.25 0.50 0.79

1.38 5.33 11.57 1.77 5.66 11.60 1.81 5.76 11.81 1.84 5.75 11.71

0.66 0.85 0.93 0.85 0.91 0.93 0.87 0.92 0.95 0.88 0.92 0.94

* the values are for 27 °C 3.2 The Debye Screening Length. The obtained results from the conductivity measurements showed that the dissociation of the DBSA is higher in more polar alcohols. The dissociation degree of DBSA increases in the following order: 0.6% in tert-butanol, 2.1% in 1-hexanol, 8.6% in 1butanol and 9.0% in 2-propanol and significantly influences the  1 . Tert-butanol and 1-hexanol suspensions have larger  1 than 1-butanol and 2-propanol suspension (Table 2), meaning that the values of  1 decrease with increasing dielectric constant of a solvent. Less polar alcohols dissociate lower concentrations of the DBSA, making the ionic strength of the suspension lower. The dissociated DBSA molecules weakly shield the nanoplatelet’s charge resulting in stronger electrostatic repulsive forces between the nanoplatelets and therefore larger  1 . The  1 also decreases with increasing concentration of the suspension in all alcohols.


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Table 2. The Debye Screening Length in the Alcohol Suspensions of Different Concentrations 200 g L-1 5 g L-1 15 g L-1 30 g L-1  1 (nm)  1 (nm)  1 (nm)  1 (nm) 29 tert-butanol 78 78 70 16 1-hexanol 70 49 41 9 1-butanol 44 32 26 2-propanol 41 30 25 9 3.3 Zeta Potential and Suspension Stability. The zeta potential of the DBSA-functionalized nanoplatelets is positive due to the protonated sulfonic groups on the second layer of the DBSA.8,19 We performed the electrophoretic mobility measurements, and from those, we obtained the zeta potentials for comparison of the suspension stability in tert-butanol, 1-hexanol, 1-butanol and 2propanol. The measurements were performed in 1 g L-1 suspensions in all alcohols and with the addition of DBSA in 1-butanol and tert-butanol suspensions. Table 3. The Electrophoretic Mobility and Zeta Potential of the Suspensions  (mPas)  Solvent Tmeasurement (°C)  (µm cm V-1 s-1) tert-butanol 12.3 23 4.2 26 0.159 ± 0.005 1-hexanol 13.3 24 4.6 26 25 0.135 ± 0.006 23 27 1-butanol 17.6 2.6 25 0.303 ± 0.009 2-propanol 19.3 25 2.0 28 25 0.406 ± 0.007

 (mV) 92 ± 3 79 ± 4 75 ± 2 70 ± 1

We observe a decrease in the zeta-potential values with an increasing dielectric constant of alcohol (Table 3). These results are similar as previously published, where they showed an obvious connection between the zeta potential and the solvent’s polarity.8 However, we observe higher values of the zeta potential in tert-butanol suspension than it would be expected from its dielectric constant. In order to rule out the change in the suspension stability with minor experimental variations of the c-tot values between different suspensions, the zeta potential was also determined after subsequent additions of the DBSA to the suspensions. The zeta-potential values do not show any correlation with the DBSA additions (Table 4). In general, they remain constant in 1-butanol


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suspension, as well in the tert-butanol suspension, but with an obvious drop at the first addition of the DBSA in the latter. The change in the zeta-potential of tert-butanol suspension is probably attributed to better solubility (Table 1) and lower dissociation degree (see Section 3.2) of DBSA in tert-butanol than in 1-butanol. The fact that the electrophoretic mobility does not change with subsequent additions of DBSA (Table 4) does not exclude the impact of higher additions of DBSA on the suspension stability. We visually observed that very high surplus of DBSA (120 mM) causes sedimentation of the suspensions. Table 4. The Zeta Potential Variation with the DBSA Addition (  c-tot) 1-butanol  c-tot (mM) 0 0.29 0.40 0.79 0.97 1.18

 (mV)

 (µm cm V-1 s-1)

75 ± 2 74 ± 2 73 ± 3 75 ± 2 75 ± 2 76 ± 3

0.301 ± 0.007 0.297 ± 0.009 0.29 ± 0.01 0.302 ± 0.006 0.302 ± 0.009 0.31 ± 0.01

tert-butanol  c-tot  (mV) (mM) 0 98 ± 5 0.56 80 ± 4 0.78 80 ± 5 0.90 79 ± 4 1.12 82 ± 4 1.31 81 ± 5

 (µm cm V-1 s-1) 0.174 ± 0.009 0.142 ± 0.007 0.142 ± 0.008 0.141 ± 0.007 0.146 ± 0.006 0.145 ± 0.008

The results of SAXS measurements are presented in Figure S3 (see Supporting Information) in the form of the desmeared SAXS curves on an absolute scale. They do not show any considerable differences between the nanoplatelets in different alcohols and confirm the stable suspensions in all the studied samples. The thickness of the nanoplatelets is determined by the crystal structure, and it has been shown that can only have discrete values.29 Only platelets of 3 different thicknesses were observed. The distance between the centers of the surface Fe3+ ions was measured to be 3.0, 4.1 and 5.3 nm.29 Taking in the account the crystal structure, the nanoplatelets’ thicknesses are estimated to be 3.3, 4.4 and 5.6 nm. We calculated expected SAXS scattering intensity, assuming the platelets are disks with a certain thickness and log-normal distribution of diameters as shown in Figure 1b (see Supporting Information for the details). Then we fitted measured SAXS


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intensities by a sum of calculated intensities corresponding to thicknesses 3.3 nm, 4.4 nm, 5.6 nm and 6.6 nm. We added the platelets with a thickness of 6.6 nm to account for the possible aggregates. The parameters of the fit were the amplitudes of the calculated intensities (Figure 3). From these amplitudes, we estimated that more than 70 vol% of the platelets have a thickness of 3.3 nm.

Figure 3. Desmeared experimental SAXS curve on an absolute scale (black squares). The thick red line is the fit (see text), which consist of a sum of contributions from the platelets with the thicknesses as marked in the graph (thin lines). The fit gives the volume fractions of 76% (1 ± 0.09), 22% (1 ± 0.1), 2% (1 ± 0.7) and 0.008% (1 ± 1.5) for the platelets with a thickness of 3.3 nm, 4.4 nm, 5.6 nm and 6.6 nm, respectively. 3.4 Interplatelets Interaction. Understanding the interaction between the platelets is crucial for the design of stable suspensions. In this section, we discuss the interaction between a pair of platelets theoretically. Prevailing interactions between the nanoplatelets are long-range interactions, such as magnetic dipole and electrostatic interaction. At the distance of short-range interactions, the nanoplatelets would aggregate due to the attractive magnetic dipole interactions. For example, for the platelets with average magnetic moments of ~2  10-18 Am2, the magnitude of


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the dipolar interaction at r = 10 nm is > 700 kBT. This shows that stable suspensions cannot be prepared by steric stabilization alone, so a strong enough repulsive electrostatic interaction between the platelets is needed. In other words, the platelets need to carry a surface charge.

Figure 4. Numerically calculated average interaction between a pair of disks. a) comparison of the average interaction between disks in different solvents with a concentration of 30 g L-1 using  1 from Table 2. b) Contour plot of the interaction in 1- butanol for  1 = 26 nm c) comparison of the interaction in 1-butanol for different  1 . d) Contour plots of the interaction in 1- butanol for  1 = 8 nm. In the calculations orientation of the first disk, n1 was fixed along the x-axis. The side view of the first disk is schematically shown in the middle of b) and d) (dark red). The interaction in the contour plots is shown in the units kBT.


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We fixed the orientation of the first disk n1 to be along the x-axis and calculated the average interaction of the second disk. Figure 4a shows a comparison of along the direction n1 (x-axis) and perpendicular to it (y-axis) for different solvents for  1 as estimated at the concentration 30 g L-1 (Table 2) and zeta potentials given in Table 3. The effective charge calculated using Eq. 6 was 14e0, 15e0, 22e0 and 22e0 in tert-butanol, 1-hexanol, 1-butanol and 2propanol, respectively. Figure 4b shows numerically calculated for disks in 1-butanol (  1 = 26 nm) in the xy plane. The interaction is repulsive and anisotropic. The anisotropy increases with decreasing Debye length. As expected, the disks can come closer, when oriented face to face (i.e., in the x-direction). In this direction, we observe a finite barrier of the height of a few tens of kBT. If the barrier is smaller than about 10 kBT, the disks irreversibly aggregate. Comparison of the barriers shows that the 1-butanol is the solvent with the best stability. The height of the barrier increases with decreasing  1 (Figure 4c) and for small enough  1 , a minimum in appears on each side of the disk (Figure 4c and d). When these minima become deeper than approximately kBT, the disks start to flocculate, which can either lead to sedimentation or in concentrated suspension to gelation.

4.

CONCLUSIONS

We studied electrostatic interactions between dodecylbenzenesulfonic-acid-functionalized magnetic nanoplatelets in alcohols because the alcohol suspensions allow for the preparation of nematic ferromagnetic ferrofluid. For the stability of such a system, the formation of the double layer around the nanoplatelets is crucial. The volume fraction of the nanoplatelets needed for the ferromagnetic nematic suspension highly depends on the total fraction of dodecylbenzenesulfonic acid,

because

of

the

dynamic

equilibrium

between

the

dissolved

and

adsorbed


18

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dodecylbenzenesulfonic acid. If the concentration of dissolved dodecylbenzenesulfonic acid is too high, the nanoplatelets can aggregate due to a high screening of the charge. The concentration of dissolved

dodecylbenzenesulfonic

acid

also

affects

the

concentration

of

adsorbed

dodecylbenzenesulfonic acid. If the latter is too low, the system does not ensure efficient surface coverage of the nanoplatelets, which also causes their aggregation. According to our results, despite slightly smaller Debye screening length, 1-butanol suspensions showed the highest colloidal stability due to a combination of high enough surface charge and low enough dielectric constant. These results indicate that 1-butanol is the most promising solvent for our future work requiring high colloidal stability of suspensions and prove previously predicted assumptions.8 We showed the presence of a secondary minimum in the interaction between the platelets in concentrated suspensions. This minimum causes an increase of magnetic ordering of the nanoplatelets but can also lead to gelation of the suspension, if it is too deep. Therefore, the next step in our research will be the investigation of the phase diagram and the nematic phase formation of the suspensions in 1-butanol as a function of the concentration of dissolved dodecylbenzenesulfonic acid.

ASSOCIATED CONTENT Supporting Information. Abbreviations, autocorrelation functions, viscosity of tert-butanol, desmeared experimental SAXS curves and calculation of SAXS intensities AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].


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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources This work was financially supported by the Slovenian Research Agency (A. M. research core funding No. P1-0192, M. T. and A. J. No. P1-0201, D. L. No. P2-0089, P. H. B. No. PR-08415, D. L. and A. M. project No. J7-8267). Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors acknowledge the financial support from the Slovenian Research Agency (A. M. research core funding No. P1-0192, M. T. and A. J. No. P1-0201, D. L. No. P2-0089, P. H. B. No. PR-08415, D. L. and A. M. project No. J7-8267). We thank the CENN Nanocenter for the use of the LakeShore 7400 Series VSM vibrating-sample magnetometer and the TEM Jeol 2100. M. T. and A. J. are most grateful also to Prof. Otto Glatter for his generous contribution to the instrumentation of their laboratory of the light-scattering methods. We thank Dr. Nerea Sebastián Ugarteche and Žiga Gregorin for the liquid magnet image that is used in the Table of Contents.


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Table of Contents/Abstract Graphics


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Electrostatic Interactions Between Barium Hexaferrite

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