Particle Rotation in Colloidal Processing under a Strong Rotating

Subscriber access provided by Kaohsiung Medical University

Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Particle rotation in colloidal processing under a strong rotating magnetic field Shoko Baba, and Satoshi Tanaka Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b04344 • Publication Date (Web): 03 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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

Langmuir

Particle rotation in colloidal processing under a strong rotating magnetic field Shoko Baba and Satoshi Tanaka* Department of Materials Science and Technology, Nagaoka University of Technology 1603-1, Kamitomioka Nagaoka, Niigata 9402188, Japan

ABSTRACT: Functional ceramics with oriented crystals prepared by colloidal processing in a strong magnetic field are expected to show improved functionality. In this study, the orientation rate of particles with low magnetic susceptibility in a concentrated slurry under a strong rotating magnetic field was experimentally demonstrated using a fast photopolymerization reaction. A slurry of (Sr,Ca)2NaNd5O15 particles dispersed in an ultraviolet curable resin with a catalyst was consolidated using UV irradiation under a strong rotating magnetic field. The degree of particle orientation increased with increasing processing time and became saturated after 20 s. The orientation time was observed experimentally; the period required to achieve particle orientation was proportional to the measured viscosity of the slurry and the inverse of the square of the magnetic flux density.

Introduction Optimizing the crystal orientation of functional polycrystalline ceramics is an effective method for improving their properties.1-9 Polycrystalline ceramics are attractive as they are highly

ACS Paragon Plus Environment

1

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

Page 2 of 40

malleable during fabrication and their composition can be easily controlled. Modifying the crystal orientation in ceramics using electrical, magnetic, or mechanical stress fields has been undertaken using several different methods. Mechanical stress fields were used to orient elongated particles prepared by doctor blade and hot forging processes.8-11 Electrical or magnetic fields were also applied to form oriented structures.12-16 Among these techniques, colloidal processing in a strong magnetic field has attracted much research interest as a promising method for preparing alumina ceramics with oriented crystals.17,18 This method takes advantage of the rotational behavior of each crystalline particle caused by their slightly anisotropic magnetic susceptibility in a strong magnetic field.19 Notably, this method is not dependent on the shape of the particles. Hence, conventional fine (submicron) particles, which are desirable for easy densification of bulk samples, can be processed using this method. Colloidal processing in a strong magnetic field has been applied to fabricate various textured ceramics, including titania, zinc oxide, and bismuth titanate.20-27 We recently applied this technique to prepare c-axis-oriented (Sr,Ca)2NaNd5O15 (SCNN) with tetragonal tungsten-bronzestructured ferroelectrics.28,29 SCNN is a multi-functional material with great potential as a leadfree piezoelectric and optical material.28-32 It is desirable to have c-axis-orientation because good piezoelectric performance is limited to the c-axis direction on account of its polarizability. When a rotating magnetic field is applied to a slurry of SCNN particles, the c-axis with the largest diamagnetic susceptibility

is aligned in the direction of the rotational axis.

For colloidal processing in a strong magnetic field, a green body or sheet with oriented particles is typically prepared by conventional processing (e.g., slip or tape casting).20,25 Although particles may orient quickly in a slurry set in a magnetic field, such techniques require long consolidation or drying times; consequently, the sample must remain within the magnetic


2

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

Langmuir

field for a period from several tens of minutes to hours. We recently reported the preparation of a slurry of SCNN dispersed in an ultraviolet (UV)-curable resin and succeeded in fabricating a particle-oriented green sheet by UV irradiation in a magnetic field.33,34 Photopolymerization reactions are fast and controllable, and the processing time was reduced to just 30 s, which is extremely short compared with conventional processing techniques. In practical processing applications, the oriented microstructures in a green body or sheet are enhanced by grain-growth during sintering. This means that a high degree of orientation is not immediately necessary in a green body or sheet, because particle orientation progresses during the sintering process. It is thus important that the degree of orientation in a green body or sheet can be controlled under optimized conditions. Although the theoretical dependence of the parameters was estimated for colloidal processing in a magnetic field for these processing routes,35-38 the dependence of the experimental parameters on the orientation behavior of fine particles in concentrated slurry has not yet been investigated. In previous experimental studies, sub-mm rod-like particles in a dilute suspension were investigated.35-37 While such a model is suitable for investigating theoretical considerations from an experimental perspective, more practical conditions are needed to more fully explore the theory of colloidal processing in a magnetic field. To this end, the objective of this experimental study was to clarify the particle orientation behavior of fine particles in a concentrated slurry under a strong rotating magnetic field. It is expected that understanding the behavior of particle orientation and controlling the degree of orientation is necessary for further development and industrial applications of this field.


3

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

Page 4 of 40

Theory In order to analyze the orientation behavior of the particles, we applied the fundamental theory of particle motion in a concentrated slurry in a rotating magnetic field. Kimura et al. proposed a theoretical description of the behavior of polymer fibers in a rotating magnetic field.15,35,36 Figure 1 shows a Figure 1 Schematic view of a particle in a rotating magnetic field.

schematic diagram of a spherical single particle in a magnetic field. The energy of magnetization U of

the magnetic field applied to the particle depends on the angle between the crystal axis and the magnetic field. It is calculated from the following expression:15,35 1 2 where

//

1 2

∆

∙

is the largest diamagnetic susceptibility

//

//

anisotropy of the diamagnetic susceptibility,

1 , ∆

// // ,

is a unit vector parallel to

is the

B is a unit vector

for a magnetic field acting on a particle rotating on the x-y plane, V is the volume of a particle, and

is the magnetic permeability in vacuum. Here, θ is the angle between the magnetization

vector of a particle and the z-axis, φ is the angle between the projection of the magnetization vector on the x-y plane and the x-axis, and % is the angle between n and B. The particle should be aligned in the direction of the z-axis as n is influenced by the magnetic field. A particle subjected to magnetic torque M in a magnetic field can be described by Eq. (2).36 ∆

∙

∆

os sin !

2


4

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

Langmuir

where e is a unit vector parallel to n ™ B. The hydrodynamic torque N is caused by the interaction between a particle and the surrounding liquid acting on the particle, where it is rotating at an angular velocity

. The motion of the particle is also influenced by interactions

with surrounding particles. Therefore, this torque can be related to the viscosity of the concentrated slurry η and the angular velocity of a particle ": 36 #

$%&

'

where L is a tensor that is dependent on the particle shape. For a spherical particle of radius r, L is diagonal and its components are equivalent to L. The equation describing particle rotation in a concentrated slurry in a rotating magnetic field is written as a balance of the magnetic torque and the hydrodynamic torque under a stable state:36 1

& where V/L=(4π/3)* + /,-* +

where 5

( $

∆

∙

)

1/(. Using the relation dn/./ 0 01

∙ 5 65

22 34

&

∙5 7

, we deduce 8

/9 and the intrinsic magnetic response rate of a particle, 2 34 , exposed to the

rotating field is defined as:15,16,35-38 2 34 Here, b is expressed as

1 ∆ 12 $

os :1 ; sin :1 ;

(

, where < is the rotational angle velocity of the

magnetic field and n is indicated as sin = os > ; sin = sin > ; os = .16,36-38


5

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

0= 01

Page 6 of 40

2 34 sin 2= ?@A >

0> 01

2 34 sin 2 >

:1

B

:1

,

According to Eqs. (7) and (8), the particle rotates synchronously with the applied magnetic field rotation as .>/.1

: in the case of stationary state conditions, where C is defined as D

:1.16,36,37 From Eq. (8), sin 2D

2: is obtained by using the relation 0D/01

>

.

Accordingly, this stationary state is possible only if |2:| F 1, which describes the conditions for particle alignment under a static magnetic field. However, when the value of |2:| is G 1, such as when the magnetic field has a rapid angular velocity, the particle cannot follow the rotation of the magnetic field. Because it is assumed that > 0= 01

, Eqs. (7) and (8) can be written as follows:

2 34 sin 2= ?@A 0> 01

:1

H

1

Therefore, the following equation can be deduced: 16,36-38 In

/ n= / n=

1 2

1 sin 2:2

2:1

11

When the second term on the right hand side is very small compared with the first term, that is J

4

KL

sin

2:1 J

1, the orientation time t is obtained as: 16,37-38 1

2 In

/ n= / n=

12


6

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

Langmuir

According to Eqs. (6) and (12), the intrinsic magnetic response rate of a particle τ-1 and the orientation time t depend on the inverse of the slurry viscosity and on the square of the magnetic flux density ηB-2. Figure 2 shows τ-1 and t calculated by Eqs. (6) and (12) with the anisotropy of the diamagnetic susceptibility M (1.0 × 10-6, 5.0 × 10-7, 1.0 × 10-7). For the boundary conditions, the particle direction N0 is assumed to be 45º as the average value at t = 0 and the oriented direction of the particle N is 5º at t = t. As shown in Figure 2, the intrinsic magnetic response rate of a particle τ-1 is inversely proportional to ηB-2, and the orientation time t is proportional to ηB-2. In this study, the influences of the magnetic flux density, slurry viscosity, and processing time on the degree of orientation in a green sheet were examined. The viscosity of the slurry decreases with

increasing

temperature;

hence,

the

Figure 2 The intrinsic rate of magnetic response of a particle exposed to the rotating field τ-1 and the orientation time t plotted against the viscosity of the slurry divided by the square of the magnetic flux density.

orientation behavior can be investigated by changing the temperature of the slurry.

Experimental Methods Slurry preparation and characterization SCNN powder synthesized by a conventional solid-state reaction was used in this study. Detailed information regarding this SCNN powder and its synthesis was published


7

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

Page 8 of 40

previously.28,29 Before preparing the slurry, the SCNN powder was de-agglomerated by ball milling with an azeotropic solvent mixture consisting of methyl ethyl ketone (MEK) and ethanol (EtOH) (60/40 vol.%).33,34 The powder was then dried in an oven at 45 °C for 3 h. The morphology of the powder was examined by scanning electron microscopy (SEM, JSM5310LVB, JEOL Tokyo, Japan). The particle size distribution was determined by the sedimentation method (Sedigraph 5100, Micrometrics, USA). The powder was dispersed in deionized water with sodium hexametaphosphate as the dispersing agent. The slurry for forming the green sheets was prepared as follows.33.34 UV-curable resin was used as the dispersion medium and contained polyether acrylate monomer diluted in hydroxyethyl methacrylate (Ebecryl 770, Daicel-Allnex Ltd. Japan) with 2 wt.% of the photoinitiator 2-hydroxy-2-methyl-1-phenylpropan-1-one (Darocur 1173, Ciba, Japan), which absorbs in the emission range of the UV lamp. A phosphate ester (1.2 wt.%; Disperbyk-110, BYK-Chemie, Japan) was used as the dispersant, which acts by both electrostatic and steric repulsion. First, the photoinitiator and the dispersant were completely dissolved in a UV-curable binder. Then, the de-agglomerated SCNN powder was added to the binder mixture. The volume fraction of the SCNN powder was 45 vol.%. The slurry was stirred using a planetary centrifugal mixer (Are310, Thinky, Japan) in the deforming mode at 2000 rpm for 30 s, followed by a thinfilm spin system high-speed mixer (Filmix, Primix, Japan) at 2000 rpm for 5 min. Both mixing steps were repeated twice. Finally, the slurry was de-aired using the planetary centrifugal mixer in the deforming mode at 2000 rpm for 30 s. The viscosity of the slurry was measured using a rheometer (Physica MCR301, Anton Paar, Austria) using a cone and plate apparatus (CP25-2; diameter: 25 mm; angle: 2.003°; truncation: 52 µm) in the stress-controlled mode. The shear rate was varied from 0.01 s-1 to 100 s-1. The


8

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

Langmuir

measurement temperature was set to 20–50 °C to correspond with a previous study.34 The viscosity behavior was characterized with the Cross model as follows:39 $O P Q

$

$O $ U 1 P RST

1'

where D is the shear rate, $ is the viscosity at zero shear rate, $O is the viscosity at infinite shear rate, and α and n are fitting parameters. The values of $ , α, and n were estimated by fitting the viscosity curves with Eq. (13) using the nonlinear least-squares method. Fabrication and characterization of the green sheet After keeping the slurry in a thermostatic bath at 20–50 °C, it was cast on a poly(ethylene terephthalate) (PET) sheet, where the slurry thickness was adjusted to approximately 0.3 mm. The cast slurry was placed on a stage within a lateral magnetic field of 0–10 T induced by a superconducting magnet (Toshiba, TM-10VH10). The stage set at a temperature between 20 and 50 °C was rotated horizontally in the magnetic field with a rotation speed of 30 rpm. The exposure time was varied from 1 to 300 s. Then, the green sheet was solidified by

Figure 3 Schematic illustration of experimental setting. Rotation apparatus and quartz fiber placed in the unidirectional strong magnetic field of a superconducting magnet.

applying UV radiation emitted from a lamp (MUV-250U-L, Moritex Co., Japan) set above the cast sheet for 30 s, as shown in Figure 3. The UV power and energy for each irradiation step were measured using a UV radiometer (UIT-250, Ushio Inc. Japan). The wavelength output


9

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

Page 10 of 40

spectra of the lamp ranged from 200 to 450 nm with a peak intensity at 365 nm. The average UV energy concentrated on the green sheet was ~360 mW/cm2. The UV radiation was absorbed by the photoinitiator, which in turn generated free radicals to initiate the photochemical reaction. For comparison with a randomly oriented green sheet, control samples were also fabricated by irradiating UV light outside of the magnetic field. The sheet thickness after polymerization was calculated to be approximately 0.14 mm. After exposure, the liquid non-polymerized areas were removed using ethanol. The crystal orientations of the surfaces of the green sheets were evaluated using X-ray diffraction (XRD, Ultima-IV, RIGAKU, Japan) with CuKα/ radiation for a 2θ range of 20–70r . The degree of c-axis orientation was readily evaluated in terms of the Lotgering factor, LF, of the [001] orientation; WX

Y

Y / 1

Y , where Y

∑[

\ / ∑ [ ]^\ , Y

Y for

randomly oriented ceramic samples, and ∑ [ ]^\ is the sum of the XRD peak intensities.40 Rocking curves of the 002 reflections for some samples were also measured in order to confirm the orientation distribution and to relate the LF value with the orientation degree. The measurement conditions of the rocking curves include a step angle of 0.02° at a step speed of 1° min-1. The multiple of a random distribution (MRD) was calculated by a measured rocking curve of the oriented sample divided by that of the random sample. The MRD was characterized by fitting with the March–Dollase function containing a texture volume fraction f as follows: 41-43 _ `;a;b

cd* ?@A = P * 34 Aef =g3+/ P 1

c

(14)


10

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

Langmuir

where r is a parameter that quantifies the alignment quality. When all particles are aligned to a preferred direction, f and r are 1 and 0, respectively. When the sample has a random structure, however, f and r are 0 and 1, respectively. Fitting the MRD with Eq. (14), the parameters f and r were calculated using the nonlinear least-squares method. Results and discussion SCNN powder and slurry Figure 4 shows an SEM image of the deagglomerated SCNN powder. As seen, the particles have irregular shapes; in particular, large particles have tabular shapes. Figure 5 shows a particle size distribution of the sample

Figure 4 SCNN particles. (Mean particle size = 0.85 µm).

measured by the sedimentation method, where the particle size is shown to vary from 0.1 to 2.5 µm. The median particle size D50 of the deagglomerated powder was 0.85 µm. The results show that the synthesized raw particles are typical to those used in industrial ceramics. Here, we estimated the particle size limit for orientation in a magnetic field in terms of balancing the particle magnetic energy and the thermal energy kT. The estimated minimum

Figure 5 Particle size distribution of de-agglomerated SCNN particles.

particle size dmin can be expressed as follows: 16


11

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

0hiT

Page 12 of 40

12 ^j k/∆ -

4/+

(15)

where kB is Boltzmann’s constant and T is the absolute temperature. Figure 6 shows the minimum particle sizes of magnetic orientation at a temperature of 293 K in terms of the anisotropy of the diamagnetic susceptibility M (1.0 × 10-6, 5.0 × 10-7, 1.0 × 10-7) and the magnetic flux density B (0–10 T). We found that dmin = 0.09 µm at T = 293 K, M =5.0 × 10-7, and B = 10 T, and that a magnetic field of 6 T is sufficient to orient all particles if M = 1.0 × 10-7.

Figure 6 A minimum particle size required for the orientation of particles plotted against the magnetic flux density.

Figure 7 shows the viscosity of slurries with a solid content of 45 vol.% at each temperature between 20 and 50 °C.34 The slurry viscosity decreased considerably with increasing temperature, consistent with the behavior of the solvent. The viscosity decreased abruptly with increasing shear rate. The solid lines are the curves fitted with the Cross model represented in Eq. (13). The values of $ , α, and n at each temperature determined by fitting with the Cross model are shown in Table 1. The parameter n is

Figure 7 Shear viscosity of a slurry consisting of 45vol% SCNN powder, UV curable resin, dispersant, and photoinitiator at each temperature. The solid lines are the fitted curves with Cross model Eq. (13).


12

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

Langmuir

in the range of 0.77o0.80 for all slurries and indicates the shear-thinning behavior of the slurry. For the highly concentrated slurry, high shear viscosity at low shear rate is caused by

Table 1 Parameters for the Cross model

interactions among the particles, and weakening of such interactions as a result of the applied shear caused the shear-thinning behavior. Orientation of the consolidated green sheets Figure 8 shows XRD patterns of the consolidated green sheets with 45 vol.% solids prepared with processing times of 1 and 10 s with and without the application of a magnetic field. For all samples prepared with a magnetic field, the intensity of the c-planes (i.e., 001 and 002) was enhanced relative to that of the samples prepared without the magnetic field. The longer the sample was exposed to the magnetic field before consolidation with UV irradiation, the higher the intensities of the c-plane peaks. In contrast, the XRD patterns of the samples produced without the magnetic field were equivalent to those of the International Centre for Diffraction Data (ICDD) card No. 00-034-0429 for Sr2NaNb5O15. The LF

Figure 8 X-ray diffraction patterns obtained from green sheets with a solid concentration of 45vol% for various durations of (a) 10 s, (b) 3 s, (c) 2 s and (d) 1 s (a, b, c and d) with and (e) without a 10T rotating magnetic field at 20 l.


13

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

Page 14 of 40

of the oriented samples (i.e., the degree of orientation) increased gradually with increasing processing time under the magnetic field. The rocking curves MRD of the 002 peak for these samples are shown as points in Figure 9; the solid curves fitted by Eq. (14) are also shown. The peak intensity increased with increasing processing time and its full-width at halfmaximum (FWHM) was less than 10°, indicating that the oriented distribution was narrow. Table 2 shows the LF, FWHM, the r parameter, and the textured fraction f for these samples. The r parameter decreased and the textured fraction f increased as the processing time increased. This

Figure 9 Rocking curves, MRD of particle-oriented SCNN samples with a solid concentration of 45vol% for various durations with a 10T rotating magnetic field at 20 l. The solid lines are fitted curves with March-Dollase function Eq. (14).

relationship between r and f shows that particle orientation varied with the textured fraction. Figure 10 shows the correlation of LF

Table 2 Full-width at half-maximum (FWHM), Lotgering factor (LF), Orientation parameter r and textured fraction f for each processing time

versus the FWHM of the rocking curves and the r parameters. We observed that LF is distributed throughout the range of 0.2 to 0.9, whereas the FWHM and r are distributed in a narrow range. Therefore, FWHM and r are sensitive to higher orientation. An important aspect of these data is the linear correlation between the LF range of 0.2–0.9 and the FWHM and parameter r. Although LF is an


14

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

Langmuir

ambiguous parameter, this correlation indicates that it is nevertheless suitable to quantitatively evaluate the degree of SCNN orientation.41 Furthermore, bearing in mind the development of the orientation structure in a green body or sheet during sintering, the degree of orientation is suitable in the LF range of 0.4 to 0.6. Time dependence of particle orientation in a rotating magnetic field Figure 11 (a) shows the relationship between the exposure time of the sample in the magnetic field and the degree of orientation, LF, of the green sheets prepared under various magnetic flux densities (0–10 T). It is clear that the degree

Figure 10 The correlation between LF calculated from the X-ray diffraction (XRD) pattern and parameters r determined by fitting the MarchDollase function to the MRD, and the full width at half maximum (FWHM) of the rocking curves in the particleoriented SCNN sheet with a solid concentration of 45vol%.

of orientation depends on the duration of exposure to the magnetic field. The saturation values decreased with increased magnetic flux density. The degree of orientation of slurries exposed to 8 and 10 T showed saturation, even after a short exposure time, while the degree of orientation was extremely high (~0.95). Meanwhile, for the green sheets made from slurries exposed to magnetic flux densities of 2–6 T, the degree of orientation gradually increased with exposure time. Thus, the time required for saturation of the degree of orientation decreased with an increase in magnetic flux density. In other words, the time required for orienting the particles in a concentrated slurry decreased with increasing magnetic flux density.


15

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

Page 16 of 40

Figure 11 (b) shows the relationship between the exposure time of the sample in the magnetic field and the degree of orientation of the green sheets prepared from the slurry at various temperatures. As seen, the degree of orientation depended on the exposure time to the magnetic field, and the degree of orientation of the green sheets was affected the viscosity of the slurries. The saturation values decreased with decreased temperature (i.e., increased viscosity). The degree of orientation of the slurries at 40 and 50 °C showed saturation, even after a short exposure time, and the degree of orientation was high (~0.85). By comparison, for the green sheets made from slurries at 20 °C or 30 °C, the orientation time was two to three times that at 50 °C. The time required to orient the particles in a

Figure 11 The orientation degree of prepared by various duration times in rotating magnetic field (a) of each magnetic flux density at 20l and (b) of 6T at each temperature, solid lines are fitted curves by using Eq. (16).

concentrated slurry at 40 and 50 °C became short. This shows that the time required for orienting the particle in a concentrated slurry decreased with decreasing slurry viscosity. Let us consider the effect of the magnetic flux density and slurry viscosity on the intrinsic magnetic response rate τ-1 and the orientation time t, which, according to Eq. (6), may be proportional to ηB-2 as shown in Fig. 2. Regarding Figure 11 and Eq. (12), the intrinsic magnetic response rate τ-1 can be calculated by fitting the data in Figure 11 with the following function:


16

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

Langmuir

WX m

WXhno p1

qrY s

1 tu 2

1(

where LFmax is assumed to be the maximum LF value for each condition. If the particle size satisfies Eq. (15), LFmax is 1. However, in practice, experimental values of LF cannot achieve 1 due to agglomeration, even in a strong magnetic field of 10 T.42 The intrinsic magnetic response rate τ-1 for each condition was calculated using the nonlinear least-squares method. The fitted curves using Eq. (16) are shown as solid lines in Figure 11. Here, regarding the condition of magnetic flux density 2 and 4 T, these results are not contained in the calculation due to lower orientation.

Figure 12 The intrinsic magnetic response rate of a particle exposed to the rotating field plotted to the viscosity of slurry divided by the square magnetic flux density. The solid line is a fitted curve using Eq. (6).

Figure 12 shows the intrinsic magnetic response rate τ-1 plotted against the slurry viscosity divided by the square of the magnetic flux density. Here, the zero shear viscosity η0 calculated from the experimental data shown in Table 1 was used as the viscosity value η along the horizontal axis. In principle, the viscosity described in the model equations is that of the liquid around a particle. However, a given particle in the slurry is actually surrounded with several particles in a concentrated slurry, which is why the viscosity at zero shear rate $ was used. Here, the experimental value of τ-1 is fitted using Eq. (6) with the nonlinear least-squares method. The fitted line is shown in Fig. 12. Thus, the result shows that the experimental values of τ-1 depend on both the viscosity and the inverse of the magnetic flux density squared according to Eq. (6). Furthermore, the anisotropy of the magnetic


17

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

Page 18 of 40

susceptibility of SCNN, ∆χ can be estimated to be 5.5 ™ 10-7. Figure 13 shows the orientation time t plotted against the slurry viscosity divided by the magnetic flux density squared ηB-2. The orientation time t was obtained by Eq. (12) using experimental values of τ-1. The solid line is the line calculated by Eq. (12) with ∆χ of 5.5 ™ 10-7. As shown in Figure 13, the orientation time is proportional to ηB-2. Thus, it is demonstrated that the intrinsic magnetic response rate and orientation time can be estimated accurately from slurry viscosity and magnetic flux density. However, when the ηB2

value is larger than 0.4, that is, at low

magnetic flux density and high slurry viscosity, the experimental data of τ-1 and t differ slightly from those calculated using Eqs.

Figure 13 Time required for particle orientation calculated with Eq. (12) plotted against the viscosity of slurry divided by the square magnetic flux density. Solid line is a calculated line by using Eqs. (6) and (12).

(6) and (12). There is also the possibility of other effects of experimental conditions. These data indicate that it took a certain time to complete particle orientation under so low a magnetic field and so high a viscosity. This may imply a change in particle dispersion state during orientation. The highly precise prediction of the orientation with the real slurry change can be investigated in future work.

Conclusion


18

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

Langmuir

The particle orientation behavior during colloidal processing in a magnetic field was examined experimentally. An increase in the magnetic flux density and a decrease in the viscosity of the slurry led to a significant increase in orientation time. In the case of a low slurry viscosity at 30–50 °C under a magnetic flux density of 6 T, the degree of orientation reached 0.85 and became saturated within several seconds. For a magnetic flux density of 6 T, several tens of seconds were required to saturate the degree of orientation (~0.85). The orientation time calculated using the measured viscosity of the slurry was less than 80 s at 6–10 T. The orientation time calculated using the model equations was 15–30 s and was of the same order as the experimental data. This indicates that the orientation behavior was explained by the applied theory and that a particle in a slurry with a high solid content is affected by both the surrounding liquid and the neighboring particles. Hence, we were able to predict the time required for particle orientation using the measured viscosity of the slurry.

AUTHOR INFORMATION Corresponding Author * Satoshi Tanaka E-mail: [email protected] Fax: +81-258-47-9300

Author Contributions The manuscript was written through contributions from all authors. All authors have given approval to the final version of the manuscript.


19

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

Page 20 of 40

Funding Sources This work was supported by JSPS KAKENHI grant numbers JP16K14383 and JP17H03125. ACKNOWLEDGMENT We sincerely thank Dr. Doshida, Dr. Shimizu, and Dr. Harada from the Taiyo Yuden Co. for supplying the raw powder and for fruitful discussions. REFERENCES (1) Inoue, Y.; Kimura, T.; Yamaguchi, T. Sintering of Plate-Like Bi4Ti3O12 Powders, Am. Ceram. Soc. Bull., 1983, 62, 704-706. (2) Farrell, D. E.; Chandrasekhar, B. S.; DeGuire, M. R.; Fang, M. M.; Kogan, V. G.; Clem, J. R.; Finnemore, D. K. Superconducting Properties of Aligned Crystalline Grains of Y1Ba2Cu3O7δ,

Physical Rev. B, 1987, 36, 4025-4027.

(3) Lusnikov, A.; Miller, L. L.; McCallum, R. W.; Mitra, S.; Lee, W. C.; Johnston, D. C. Mechanical and High-temperature (920 ºC) Magnetic Field Grain Alignment of Polysrystalline (Ho,Y)Ba2Cu3O7- , J. Appl. Phys., 1989, 65, 3136-3141. (4) Hirao, K.; Nagaoka, T.; Brito, M. E.; Kanzaki, S. Microstructure Control of Silicon Nitride by Seeding with Rodlike β:Silicon Nitride Particles, J. Am. Ceram. Soc., 1994, 77, 1857-1862. (5) Seabaugh, M. W.; Kerscht, I. H.; Messing, G. L. Texture Development by Templated Grain Growth in Liquid-Phase-Sintered α-Alumina, J. Am. Ceram. Soc., 1997, 80, 1181-1188. (6) Suvaci, E.; Ozer, I. O. Processing of Textured Zinc Oxide Varistors via Templated Grain Growth, J. Eur. Ceram. Soc., 2005, 25, 1663-1673. (7) Takenaka, T.; Sakata, K. Grain Orientation and Electrical Properties of Hot-Forged Bi4Ti3O12 Ceramics, Jpn. J. Appl. Phys., 1980, 19, 31-39.


20

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

Langmuir

(8) Messing, G. L.; Trolier-McKinstry, S.; Sabolsky, E. M.; Duran, C.; Kwon, S.; Brahmaroutu, B.; Park, P., Yilmaz, H., Rehrig, P. W.; Eitel, K. B.; Suvaci, E.; Seabaugh, M.; Oh, K. S. Templated Grain Growth of Textured Piezoelectric Ceramics, Solid State Mater. Sci., 2004, 29, 45-96. (9) Messing, G. L.; Poterala, S.; Chang, Y.; Frueh, T.; Kupp, E. R.; Watson, B. H.; Walton, R. L.; Brova, M. J.; Hofer, A. K.; Bermejo, R.; Meyer, R. J. Texture-engineered ceramics – Property enhancements through crystallographic tailoring, J. Mater. Res., 2017, 32, 3219-3241. (10) Kimura, T. Application of Texture Engineering to Piezoelectric Ceramics, J. Ceram. Soc. Jpn., 2006, 114, 15-25. (11) Watanabe, H.; Kimura, T.; Yamaguchi, T. Particle Orientation during Tape Casting in the Fabrication of Grain-Oriented Bismuth Titanate, J. Am. Ceram. Soc., 1989, 72, 289-293. (12) Fujiwara, M.; Chidiwa, T.; Tokunaga, R; Tanimoto, Y. Crystal Growth of Transazobenzene in a Magnetic Field of 80 kOe, J. Phys. Chem. B., 1998, 102, 3417-3419. (13) Yamagishi, A.; Nagao, E.; Date, M. High Field Diamagnetic Susceptibility and the CurieWeiss Law in Organic Liquid, J. Phys. Soc. Jpn., 53 (1984) 928-931. (14) Kawai, T; Iijima, R; Yamamoto, K.; Kimura, T. Crystal Orientation of. N,N'-Dicyclohexyl2,6-Naphthalenedicarboxamide in High Magnetic Field, J. Phys. Chem. B, 2001, 105, 8077-8080. (15) Kimura, T. Study on the Effect of Magnetic Fields on Polymeric Materials and its Application, Polym. J., 2003, 35, 823-843. (16) Kimura, T.; Yoshino, M. Three-Dimensional Crystal Alignment Using a Time-Dependent Elliptic Magnetic Field, Langumuir, 2005, 21, 4805-4808. (17) Makiya, A; Shoji, D.; Tanaka, S.; Uchida, N.; Kimura, T.; Uematsu, K. Grain Oriented Microstructure Made in High Magnetic Field, Key Eng. Mater., 2001, 206-213, 445-448.


21

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

Page 22 of 40

(18) Suzuki, T. S.; Sakka, Y.; Kitazawa, K. Orientation Amplification of Alumina by Colloidal Filtration in a Strong Magnetic Field and Sintering, Adv. Eng. Mater., 2001, 3 [7] 490-492. (19) Uyeda, C.; Sugiyama, K.; Date, M. High Field Magnetization of Solid Oxygen, J. Phys. Soc. Jpn., 1985 54[3] (1985) 1107-1115 (20) Suzuki, T. S.; Sakka, Y. Control of Texture in ZnO by Slip Casting in a Strong Magnetic Field and Heating, Chem. Lett., 2002, 31, 1204-1205. (21) Makiya, A.; Kusano, D.; Tanaka, S.; Uchida, N., Uematsu, K.; Kimura, T.; Kitazawa, K.; Doshida, Y. Particle Oriented Bismuth Titanate Ceramics Made in High Magnetic Field, J. Ceram. Soc. Jpn., 2003, 111, 702-704. (22) Sakka, Y.; Suzuki, T. S. Textured Development of Feeble Magnetic Ceramics by Colloidal Processing under High Magnetic Field, J. Ceram. Soc. Jpn., 2005, 113, 26-36. (23) Chen, W.; Kinemuchi, Y.; Watari, K.; Tamura, T.; Miwa, K. Thick Nb-Doped Bismuth Titanate Film with Controllable Grain Orientation, J. Am. Ceram. Soc., 2006, 89, 2645-2648. (24) Tabara, K.; Makiya, A.; Tanaka, S.; Uematsu, K.; Doshida, Y. Particle Oriented Strontium Bismuth Titanate Ceramics Prepared by Using High Magnetic Field and Subsequent Reaction Sintering, J. Ceram. Soc. Jpn., 2007, 115, 237-240. (25) Tanaka, S.; Makiya, A.; Kato, Z.; Uchida, N.; Uematsu, K.; Kimura, T. Fabrication of cAxis Oriented Polycrystalline ZnO by Using a Rotating Magnetic Field and Following Sintering, J. Mater. Res., 2006, 21, 703-707. (26) Tanaka, S.; Makiya, A.; Okada, T.; Kawase, T.; Kato, Z.; Uematsu, K. C-Axis Orientation of KSr2Nb5O15 Using a Rotating Magnetic Field, J. Am. Ceram. Soc., 2007, 90, 3503-3506.


22

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

Langmuir

(27) Tanaka, S.; Takahashi, T.; Uematsu, K. Fabrication of Transparent Crystal-Oriented Polycrystalline Strontium Barium Niobate Ceramics for Electro-Optical Application, J. Euro. Ceram. Soc., 2014, 34, 3723-3728. (28) Shimizu, H.; Doshida, Y.; Tanaka, S.; Uematsu, K. C-Axis-Oriented (Sr,Ca)2NaNb5O15 Multilayer Piezoelectric Ceramics Fabricated Using High-Magnetic-Field Method, Jpn. J. Appl. Phys., 2008, 47, 7693-7697. (29) Shimizu, H.; Doshida, Y.; Mizuno, Y.; Tanaka, S.; Uematsu, K.; Tamura, H. High-Power Piezoelectric Characteristics of c-Axis Crystal-Oriented (Sr,Ca)2NaNb5O15 Ceramics, Jpn. J. Appl. Phys., 2012, 51, 09LD02. (30) Neurgaonkar, R. R.; Ho, W. W.; Cory, W. K.; Hall, W. F.; Cross, L. E. Low and High Frequency Dielectric Properties of Ferroelectric Tungsten Bronze Sr2KNb4O15 Crystals, Ferroelectrics, 1984, 51, 185-191. (31) Neurgaonkar, R. R.; Oliver, J. R.; Cory, W. K.; Cross, L. E.; Viehland, D. Piezoelectricity in Tungsten Bronze Crystals, Ferroelectrics, 1994, 160, 265-276. (32) Xie, R. J.,; Akimune, Y.; Wang, R. P.; Hiroaki N. Spark Plasma Sintering of Tungsten Bronze Sr2-xCaxNaNb5O15 (x=0.1) Piezoelectric Ceramics: ll, Electrical Properties, J. Am. Ceram. Soc., 2002, 85, 2731-2737. (33) Baba, S.; Harada, T.; Shimizu, H.; Doshida, Y.; Tanaka, S. Colloidal processing using UV curable resin under high magnetic field for textured ceramics, J. Euro. Ceram. Soc., 2016, 36, 2739-2743. (34) Baba, S.; Tanaka, S. Effect of Slurry Temperature on Particle Orientation in Magnetic Field Assisted Forming Method, J. Soc. Powder Technol, 2016, 53, 791-796.


23

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

Page 24 of 40

(35) Kimura, T.; Yamato, M.; Koshimizu, W.; Koike, M.; Kawai, T. Magnetic orientation of polymer fibers in suspension, Langmuir, 2000, 16, 858-861. (36) Kimura, T.; Yoshino, M.; Yamane, T.; Yamato, M.; Tobita, M. Uniaxial alignment of the smallest diamagnetic susceptibility axis using time-dependent magnetic fields, Langmuir, 2004, 20, 5669-5672. (37) Kimura, T. Orientation of Feeble Magnetic Particles in Dynamic Magnetic Field, Jpn. J. Appl. Phys., 2009, 48, 020217. (38) Iwai, K. Dynamic Behavior analysis of crystal with magnetic anisotropy under imposition of rotating magnetic field, Jpn. J. Appl. Phys., 2010, 49, 125602. (39) Cross, M. M. Rheology of Non-Newtonian Fluids: A New Flow Equation for Pseudoplastic Systems, J. Colloid Sci., 1965, 20, 417-437. (40) Lotgering, F. K. Topotactical reactions with ferrimagnetic oxides having hexagonal crystal structures- I, J. Inorg. Nucl. Chem., 1959, 9, 113-123. (41) Dollase, W. A. Correction of Intensities for Preferred Orientation in Powder Diffractometry: Application of the March Model, J. Appl. Cryst., 1986, 19, 267-272. (42) Furushima, R.; Kato, Z.; Uematsu, K.; Tanaka, S. Influence of Aggregates in α-A2O3 Slurry on Orientation Degree of Powder Compact Fabricated by Magnetic Forming Method, J. Am. Ceram. Soc., 2013, 96, 2411. (43) Seabaugh, M. M.; Vaudin, M. D.; Cline, J. P.; Messing, G. L. Comparison of Texture Analysis Techniques for Highly Oriented α-Al2O3, J. Am. Ceram. Soc., 2000, 83 [8], 2049-2054


24

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

Langmuir

z

𝜽𝜽

ξ

𝐱𝐱

𝝎𝝎𝒕𝒕

𝒃𝒃

𝒏𝒏

𝝋𝝋

𝐲𝐲

Figure 1 Schematic view of a particle in rotating magnetic field.


Langmuir

0.5

500 Δχ = 1.0×10-7 5.0×10-7 1.0×10-6

0.4

400

0.3

300

0.2

200

0.1

100

0

Orientation time [s]

the intrinsic magnetic response rate τ-1 [s-1]

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

Page 26 of 40

0 0.0

0.2

0.4

0.6

0.8

1.0

η/B2 Figure 2 The intrinsic rate of magnetic response of a particle exposed to the rotating field τ-1 and the orientation time t plotted against the viscosity of the slurry divided by the square of the magnetic flux density.


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

Langmuir

Optical fiber Ultraviolet rays

Quartz Cover Sheet

Magnetic Field

Rotation

Water (20-50ºC)

PET film

Timing belt

Water plumbing

Rotation table

Figure 3 Schematic illustration of experimental setting. Rotation apparatus and quartz fiber placed in the unidirectional strong magnetic field of a superconducting magnet.


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

Page 28 of 40

1μm

Figure 4 SCNN particles. (Mean particle size = 0.85 µm).


Page 29 of 40

5

Volume frequency [%]

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

Langmuir

4

3

2

1

0 0.1

1

Particle size [μm] Figure 5 Particle size distribution of de-agglomerated SCNN particles.


10

Langmuir

1

Minimum particle radius [μm]

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

Page 30 of 40

0.8 Δχ = 1.0×10-7 5.0×10-7 1.0×10-6

0.6

0.4

0.2

0 0

2

4

6

8

10

Magnetic flux density [T] Figure 6 A minimum particle size required for the orientation of particles plotted against the magnetic flux density.


Page 31 of 40

16 14

Shear viscosity [Pa・s]

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

Langmuir

20℃

12

30℃

10

40℃

8

50℃

6 4 2 0 0.01

0.1

1

10

100

Shear rate [s-1] Figure 7 Shear viscosity of a slurry consisting of 45vol% SCNN powder, UV curable resin, dispersant, and photoinitiator at each temperature. The solid lines are the fitted curves with Cross model Eq. (13).


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

Page 32 of 40

Table 1 Parameters for the Cross model Temperature of slurry [°C] 20 30 40 50

η∞ [Pa・s] 1.77 0.903 0.537 0.356

η0 [Pa・s] 18.3 16.0 12.7 10.4


α 17.0 18.5 18.7 18.6

n 0.791 0.783 0.795 0.770

Page 33 of 40

002

001

0T or 10T (a)10s LF 0.86 (b)3s LF 0.53

Intensity [-]

(c)2s LF.0.41

20

30

(e)0s Green

002

331 321

221

410

(d)1s LF 0.22 001 320 211

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

Langmuir

40

50

60

70

2θ [°] Figure 8 X-ray diffraction patterns obtained from green sheets with a solid concentration of 45vol% for various duration times of (a) 10s, (b) 3s, (c) 2s and (d) 1s (a, b, c and d) with and (e) without a 10T rotating magnetic field at 20℃.


Langmuir

120

0s 1s 2s 3s 5s 10s 150s

100 80

MRD

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

Page 34 of 40

60 40 20 0 0

5

10

15

Orienration angle θ [°]

20

Figure 9 Rocking curves, MRD of particle-oriented SCNN samples with a solid concentration of 45vol% for various durations with a 10T rotating magnetic field at 20 ℃. The solid lines are fitted curves with March-Dollase function Eq. (14).


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

Langmuir

Table 2 Full-width at half-maximum (FWHM), Lotgering factor (LF), Orientation parameter r and textured fraction f for each processing time Processing time[s] 1 2 3 5 10 150

LF

FWHM[°]

0.22 0.41 0.53 0.65 0.86 0.95

7.70 7.42 6.54 5.48 4.50 3.46

Orientation Textured parameter (r) fraction (f) 0.349 0.248 0.350 0.423 0.312 0.474 0.282 0.614 0.236 0.836 0.201 0.931


Langmuir

0.40

10

0.35

9 8

0.30

7

0.25

6

0.20

5

0.15

4

FWHM r

0.10

3 2

0.05

1

0.00

0

0.0

0.2

0.4 0.6 0.8 Lotgering factor

1.0

Figure 10 The correlation between LF calculated from the X-ray diffraction (XRD) pattern and parameters r determined by fitting the March-Dollase function to the MRD, and the full width at half maximum (FWHM) of the rocking curves in the particle-oriented SCNN sheet with a solid concentration of 45vol%. ACS Paragon Plus Environment

FWHM [°]

r

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

Page 36 of 40

Page 37 of 40

(a)

Lotgering facter

1.0 0.8

2T 6T 10T

0.6 0.4

4T 8T

0.2 0.0 0

100

200

300

Duration time in magnetic field [s] (b) 1.0

Lotgering factor

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

Langmuir

0.8 0.6

20 °C (18.3 Pa・s) 30 °C (16.0 Pa・s) 40 °C (12.7 Pa・s) 50 °C (10.4 Pa・s)

0.4 0.2 0.0 0

100

200

300

Duration time in magnetic field [s] Figure 11 The orientation degree of prepared by various duration times in rotating magnetic field (a) of each magnetic flux density at 20℃ACS and (b) of 6T at each temperature, solid Paragon Plus Environment lines are fitted curves by using Eq. (16).

Langmuir

0.5

the intrinsic magnetic response rate τ-1 [s-1]

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

Page 38 of 40

Magnetic flux density Slurry viscosity

0.4

Fitted curve with Eq. (6)

0.3

0.2

0.1

0 0.0

0.2

0.4

0.6

0.8

1.0

η/B2 Figure 12 The intrinsic magnetic response rate of a particle exposed to the rotating field plotted to the viscosity of slurry divided by the square magnetic flux density. The solid line is a fitted curve using Eq. (6).


Page 39 of 40

200 180

Orientation time t [s]

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

Langmuir

160 140 120

Magnetic flux density Slurry viscosity Calculated values

100 80 60 40 20 0 0.00

0.20

0.40

0.60

η/B2 Figure 13 Time required for particle orientation calculated with Eq. (12) plotted against the viscosity of slurry divided by the square magnetic flux density. Solid line is a calculated line by using Eqs. (6) and (12).


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


Page 40 of 40

Particle Rotation in Colloidal Processing under a Strong Rotating

Recommend Documents