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Citation: Kato, H.; Nakamura, A.
Novel Colloidal Dispersing Concept
in Aqueous Media for Preparation by
Wet-Jet Milling Dispersing Method.
Nanomaterials 2023,13, 80. https://
doi.org/10.3390/nano13010080
Academic Editor: Giuseppe
Cappelletti
Received: 22 November 2022
Revised: 19 December 2022
Accepted: 21 December 2022
Published: 24 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
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conditions of the Creative Commons
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4.0/).
nanomaterials
Article
Novel Colloidal Dispersing Concept in Aqueous Media for
Preparation by Wet-Jet Milling Dispersing Method
Haruhisa Kato * and Ayako Nakamura
National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and
Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba 305-8565, Ibaraki, Japan
*Correspondence: h-kato@aist.go.jp
Abstract:
Dispersing particles in a liquid phase is significant for producing various functional
nano/bio applications. The wet-jet milling method has been gaining attention as an attractive
dispersing method in the preparation of soft material suspensions. This is because the main driving
force of dispersion by the wet-jet milling method is the shear force, which is weaker than that
it is in the ultrasonication dispersing method. In the wet-jet milling method, the pressure of the
narrow channel which the liquid is passes through and the number of passes are used as the control
parameters for dispersing the particles. However, the values of the pressure depend on the size
(diameter and length) of the narrow channel, thus, it is not a commonly used dispersing parameter in
dispersing by wet-jet milling to set the dispersing condition by various wet-jet milling instruments.
In addition, wet-jet milling users must optimize the dispersing conditions such as the pressure and
number of passes in the narrow channel, therefore, a simple prediction/optimization method of the
dispersing size by the wet-jet milling method is desired. In this study, we established a novel colloidal
dispersing concept, the dispersing energy input based on a calorimetric idea, for particle suspension
preparation using the wet-jet milling method. The dispersing energy input by wet-jet milling was
quantitatively calculated under various conditions during the dispersing by wet-jet milling, and then,
the dispersing size of the particles was easily predicted/optimized. We demonstrated the usability of
the concept by preparing aqueous suspensions of calcium carbonate (CaCO
3
) particles with various
surfactants using the wet-jet milling method. Based on the established concept, in a case study on
dispersing CaCO
3
, we found that changes in the micelle sizes of the surfactants played a role in
wet-jet milling. The novel idea of the representation of energy input makes it possible to estimate the
appropriate condition of the dispersing process by wet-jet milling to control the size of particles.
Keywords:
wet-jet milling; dynamic light scattering; dispersing energy input; zeta potential; DLVO
theory; calcium carbonate
1. Introduction
There are various material dispersion applications, such as in paint preparation,
cosmetics, drug delivery systems, photo resists, detergents, coating materials, glues, and
food processing. For the preparation of these applications, suspending various materials
in liquid media is a crucial processing stage because this process is the first step in the
manufacturing stage [
1
–
5
]. There are various methods for suspending materials in the
liquid phase, such as vortex mixing, jet milling [
6
–
8
], and using an ultrasonic bath [
9
,
10
] or
an ultrasonic homogenizer [
11
,
12
]. The wet-jet milling method has been recently utilized as
an attractive dispersing method in preparing soft material suspensions because it involves
a weaker destructive force compared with that in the ultrasonication dispersing method.
The wet-jet milling method is a wet-type milling method that is used to disintegrate
agglomerates of powder/polymer samples in a liquid phase. In this method, which is
also called high-pressure homogenization, the particles dispersed in a liquid are passed
through a narrowed channel at a high pressure. Subsequently, the dispersion of particles is
Nanomaterials 2023,13, 80. https://doi.org/10.3390/nano13010080 https://www.mdpi.com/journal/nanomaterials
Nanomaterials 2023,13, 80 2 of 14
enhanced by the complexed shear force arising from the turbulent flow in the channel. The
advantage of this dispersing technique is that it yields suspensions with low contamination,
unlike the ultrasonic homogenizer method, inducing the contamination of the sonication
tip. Weak destructive forces, such as the shear force, are also attractive to disperse soft
materials in a liquid phase, therefore, the wet-jet milling method has been used to disperse
carbon nanotubes, cellulose, and polymeric materials in a liquid phase. This method is
fundamentally utilized in food processing because the shear force does not induce the
denaturization of food materials. This method has also been used to disperse hard materials,
such as graphene and metal oxide particles.
To disperse particles by the wet-jet milling method, a particle suspension which is
pressurized by a pressure intensifier is accelerated by a nozzle in the narrow channel so
that the dispersed particles collide with each other to achieve micronization. This operation
is not enough to disperse the particles completely in one attempt, therefore, a continuous
operation is necessary. The required number of repeated continuous collision of the particle
suspension depends on the characteristics of the particles, such as the degree of aggregation
or agglomeration. Although dispersing particles using this method requires the repeated
continuous collision of the suspension through the narrow channel, it is well known that
this method primarily focuses on the pressure in the narrow channel. Typically, the pressure
range of a commercial wet-jet milling system is 80–245 MPa. Specifically, to describe the
condition of dispersing particles in the wet-jet milling method, the pressure in the narrow
channel is one of the main parameters, however, the dispersing tendency is not simply
represented as a function of this pressure. Therefore, the users of wet-jet milling must
optimize the pressure and change the number continuous collisions of the suspension
through the narrow channel by monitoring using a simple sizing method such as dynamic
light scattering (DLS) in each operation. Therefore, an easy estimation of the appropriate
condition of the dispersing process using wet-jet milling to control the size of particles
is desired.
Therefore, the purpose of this study was to solve the difficulty in predicting/optimizing
the dispersing condition in the wet-jet milling method. In this study, we established a novel
concept—the dispersing energy input—in the preparation of a particle suspension using
the wet-jet milling method. The dispersing energy input was evaluated quantitatively, and
we found a close relationship between the dispersing energy input and the particle size of
the suspension.
In this study, we dispersed calcium carbonate (CaCO
3
) particles in aqueous suspen-
sions with various surfactants using wet-jet milling. CaCO
3
is currently being used in
biological and industrial fields, such as in paper coating, paint, polymer molding, food,
and preparation of clay materials, owing to its ease of production, high biocompatibility,
and slow biodegradability [
13
–
22
]. Especially, the preparation of smaller sized CaCO
3
nanoparticles in a liquid phase is becoming essential to produce better functional properties
in various fields since reducing the size of particle induces a larger specific surface area
and a higher surface energy [
23
,
24
]. Therefore, we used CaCO
3
particles as an example in
this study; predicting the appropriate dispersing condition in the wet-jet milling method to
disperse CaCO3particles in the required size is quite useful for their applications.
2. Experimental Section
2.1. Materials
CaCO
3
powders (Hakuenka-CC-R) were gained from Shiraishi Kogyo Kaisha, Ltd.
(Osaka, Japan). Non-pore-structured CaCO
3
particles were used in this study. Sodium
dodecyl sulfate (SDS) was bought from Wako Pure Chemical Industries, Ltd. (Osaka,
Japan). Softanol-70 was gained from Nippon Shokubai Co., Ltd. (Osaka, Japan). Hex-
adecyltrimethylammonium bromide (CTAB) was bought from Tokyo Chemical Industry
Co., Ltd. (TCI; Tokyo, Japan). Triton X-100 was bought from Thermo Fisher Scientific
(Geel, Belgium).
Nanomaterials 2023,13, 80 3 of 14
2.2. Preparation of CaCO3Particle Aqueous Suspensions
Homogeneous aqueous suspensions of CaCO
3
particles were suspended in aqueous
solutions of Triton X-100, SDS, Softanol-70, and CTAB using the wet-jet milling method
(YUH-PA 5-14-E, Yoshida works pro., Tokyo, Japan). The final concentration of CaCO
3
particles were 0.2 mg/mL and the concentration of all of the surfactants were 0.5 mg/mL.
The pressure range of the wet-jet milling system was from 80 MPa to 240 MPa. The prepared
CaCO3particle dispersions were stable for at least one week.
2.3. DLS Measurements
A DLS particle analyzer (DLS8000, Otsuka Electronics Co., Ltd., Kyoto, Japan) was
utilized. The measurements were taken using a 45 mW He–Ne laser. The observed
scattering angle was 90
◦
at 25.0
±
0.1
◦
C. The measurement system was kept at a constant
temperature of 23.0
±
0.3
◦
C, and the humidity was controlled at 40
±
3%. Repeated
measurements were performed at least three times, and the mean values were calculated.
The particle diameter was calculated by the Stokes–Einstein equation.
dl=kBT
3πη D, (1)
where k
B
is the Boltzmann constant, Tis the absolute temperature,
η
is the viscosity of the
medium, and d
l
is the light scattering intensity averaged diameter of the CaCO
3
particles
in the suspensions.
2.4. Pulsed Field Gradient-Nuclear Magnetic Resonance Measurements
The measurements of pulsed field gradient-nuclear magnetic resonance (PFG-NMR)
were taken by a 14.1 T spectrometer (UNITY INOVA 600A, Varian, CA, USA) using a H-
F{X} diffusion probe (DSI-V218, Doty Scientific, CA, USA) capable of magnetic field pulse
gradients of 2500 G cm
−1
in the z direction. The observed temperature was at 25.0
±
0.1
◦
C.
The temperature calibration was completed with pure methanol. The Stejskal–Tanner
diffusion equation was used for the determination of the diffusion coefficients.
ln(I/I0) = −Dγ2G2δ2(∆−δ/3), (2)
where only the data for which the correlation coefficient of ln(I/I
0
) vs.
γ2G2δ2(∆−δ/3)
was higher than 0.99 for the first decay were utilized. In this study, a PFG-stimulated echo
sequence was utilized [
25
]. Rectangular gradients of 1 ms were gradually increased from
0 to approximately 600 G cm
−1
at approximately 100–500 averaged transients. The other
parameters are follows: the
π
/2 pulse width was 12.90
µ
s, the relaxation delay was 10 s,
and the acquisition time was 2.0 s. The diffusion time (
∆
) was set to 50 ms. Pure water was
used to ensure the linearity of the gradient strength. A value of 2.299
×
10
−9
m
2
s
−1
was
utilized as the water diffusion coefficient [26].
2.5. Electrophoretic Mobility Measurements
The electrophoretic mobility measurements were taken using a zeta potential analyzer
(Otsuka Electronics Co., Ltd., Osaka, Japan). The values were calculated using the Smolu-
chowski assumption. The assumption might overestimate an actual zeta potential by up to
approximately 20% [27].
2.6. Viscosity Measurements
The viscosity of aqueous solution of each surfactant was measured using an Uberode
viscometer. The observed temperature was at 25.0
±
0.1
◦
C. The all of the surfactant
solutions had a same viscosities of approximately 0.89 cP, which is equal to that of water
(0.89 cP) [28].
Nanomaterials 2023,13, 80 4 of 14
3. Results and Discussion
3.1. Determination of Dispersing Energy Input by Wet-Jet Milling Method
To determine the dispersing energy input by the wet-jet milling method, we used a
calorimetric idea to measure, directly, the effective energy delivered to a liquid by the wet-
jet milling method. This idea is based on the measurement of the increasing temperature
in a liquid by the wet-jet milling method in relation to the dispersing energy input of the
liquid that is passed through the narrowed channel at a high pressure. Although the heat
transfer from the material tank of a wet-jet milling system is known, in this study, we
assumed the heat transfer to be zero to ensure thermal equilibration while we were passing
the liquid through the channel of the wet-jet milling system. Moreover, we defined the start
temperature of the water as 25
◦
C, following which we started wet-jet milling and recorded
the temperature vs. time in the material tank of the wet-jet milling system to determine
direct calorimetric curves. We evaluated the initial slope of the temperature increase after
obtaining the best linear fit for each curve using least squares regression (data not shown).
The delivered wet-jet milling power is expressed as:
Pcal =cp,water ×mwater ×dT
dt, (3)
where
Pcal
is the delivered wet-jet milling power (W) in one pass, T and t are the temperature
(K) and the passing time (s), respectively,
cp,water
is the specific heat of water (4180 J/gK),
and m is the mass of the liquid (one pass is 30 g in our instrument). In this study, we changed
the dispersing condition by the wet-jet milling method using four different pressures
(80, 120, 180, and 240 MPa) in the narrow channel and pass time in the wet-jet milling
system. In our wet-jet milling instrument, the observed values of
dT
dt
were 3.8, 6.3, 11.6, and
17.4 K/s at the four different pressures (80, 120, 180, and 240 MPa), respectively. Therefore,
using Equation (3), the evaluated values of
Pcal
were 4.75
×
10
6
, 7.89
×
10
6
, 1.45
×
10
7
, and
2.18
×
10
7
W at the four different pressures (80, 120, 180, and 240 MPa), respectively. Using
the evaluated
Pcal
at the different pressures in the narrow channel of the wet-jet milling
instrument, the dispersing energy input (J) was calculated by considering the operating
time (s) of one pass. Finally, the dispersing energy inputs at the four different pressures
(80, 120, 180, and 240 MPa) in the narrow channels were calculated, and the results are
shown in Figure 1. We used the calculated dispersing energy input as the only parameter
based on the measurement of the increasing temperature in the liquid in the wet-jet milling
method. The objective was to examine the relationship between the dispersing energy
input and the particle size in the dispersing process of the particles in the liquid phase
using wet-jet milling.
Figure 1. Cont.
Nanomaterials 2023,13, 80 5 of 14
Figure 1.
Plots of the calculated dispersing energy input as a function of the number of passes in the
wet-jet milling system. The values of the dispersing energy input were evaluated at four different
pressures in the narrow channel and pass time in the wet-jet milling system: (
a
) 80 MPa, (
b
) 120 MPa,
(c) 180 MPa, and (d) 240 MPa, respectively.
3.2. Particle Size Analysis of Various Aqueous CaCO3Particle Dispersions
Using the wet-jet milling system, the particles were dispersed as small aggregates/
agglomerates or constituent particles. In this study, DLS assessments were performed
for all of the aqueous CaCO
3
particle suspensions to obtain the ensemble particle size
in the liquid phase. Although simple assumptions were used (e.g., a monomodal size
distribution and a spherical shape) in the DLS characterization of the CaCO
3
particles in
the aqueous suspensions, the DLS method is helpful for examining the differences in the
hydrodynamic sizes of the various aqueous CaCO
3
particle suspensions. We applied the
cumulant method for the auto correlation function data analysis because the fitting data
by cumulant method agreed with the raw photon correlation function. The uncertainties
of the measured diameters were calculated from the repeatability of the observed values,
which were obtained from at least three separate measurements. During the wet-jet milling
dispersing process, we performed particle size characterization by DLS to monitor the
change in the size as a function of the number of passes. In this study, we monitored
the sizes of at least five different number of passes from 0 to 30 passes in one dispersing
shear force condition. In addition, we used four dispersing shear forces (80 MPa, 120 MPa,
180 MPa, and 240 MPa), therefore, we obtained at least 20 different energy input conditions
for one sample. Four different samples were examined under these different conditions.
The results are plotted in Figure 2a–d. Additionally, the polydispersity indices (PDIs) at
different times are shown in Figure 3a–d. All of the figures are plotted as functions of the
dispersing energy input.
Figure 2. Cont.
Nanomaterials 2023,13, 80 6 of 14
Figure 2.
Plots of the mean sizes of CaCO
3
particles in various aqueous media as functions of
the dispersing energy input, as determined by DLS. (
a
) Triton X-100, (
b
) SDS, (
c
) Softanol-70, and
(
d
) CTAB were used as surfactants. The plots are for different pressures in the narrow channel
(80 MPa: black, 120 MPa: red, 180 MPa: green, and 240 MPa: blue). The uncertainties were calculated
from the repeatability of the measured sizes, which were obtained from three separate measurements.
The dotted curves were calculated using Equations (4)–(6), respectively.
Figure 3.
Plots of the PDIs of CaCO
3
particles in various aqueous media as functions of the dispersing
energy input, as determined by DLS. The used surfactants are (
a
) Triton X-100, (
b
) SDS, (
c
) Softanol-70,
and (
d
) CTAB. The plots are for different pressures in the narrow channel (80 MPa: black, 120 MPa:
red, 180 MPa: green, and 240 MPa: blue). The uncertainties were calculated from the repeatability of
the observed sizes, which were obtained from three separate measurements.
According to the DLS analysis, the mean particle sizes of the CaCO
3
particles dispersed
by wet-jet milling became clearly smaller with the increase in the dispersing energy input
values, except for the samples using CTAB as the surfactant. The relationship between
Nanomaterials 2023,13, 80 7 of 14
the mean particle size of the CaCO
3
particles and the dispersing energy input value was
unrelated to the pressure in the narrow channel from 80 to 240 MPa. To the best of our
knowledge, studies using the wet-jet milling method have used the pressure in the narrow
channel and the number of passes (dispersing passes in the narrow channel) as the main
parameters to describe the condition of the dispersing particles. However, a serious problem
is that the dispersing tendencies of the particles using the wet-jet milling method are not
simply represented as functions of pressure. Thus, even under the same experimental
conditions, such as the pressure in the narrow channel and the number of passes, wet
milling users cannot reproduce their experimental results. Therefore, the finding of the
close relationship between the particle size and dispersing energy input value is quite
significant because the condition of dispersing particles using the wet-jet milling method is
represented/evaluated by just one parameter. In addition, the most significant impact of
this finding on the process of dispersing CaCO
3
particles using the wet-jet milling method
is the easy estimation of the appropriate condition of the dispersing process using wet-jet
milling. This will enable us to control the required mean size of CaCO3 particles based on
the idea of dispersing energy input. In Figure 2a–c, the relationships between the mean
particle size and the dispersing energy input for different surfactants are represented by
Equations (4)–(6), respectively.
d=139.71 +31.68 ×e(−E
43.01×104)+130.27 ×e(−E
91.33×106)(4)
d=115.38 +45.15 ×e(−E
51.51×106)+148.05 ×e(−E
17.79×107)(5)
d=164.88 +63.05 ×e(−E
23.44×105)+54.25 ×e(−E
80.20×106)(6)
In the equations, d is the estimated mean size (nm), and E is the dispersing energy
input (J). For example, using Equation (6), it is predicted that the mean size of the CaCO
3
particles in the Softanol-70 aqueous phase can be controlled at approximately 200 nm
at a dispersing energy input of 3.5
×
10
7
J. Based on Figure 1, the dispersing condition
to produce approximately 200 nm CaCO
3
particles in the Softanol-70 aqueous phase is
accomplished with twenty passes (80 MPa), fifteen passes (120 MPa), ten passes (180 MPa),
and five passes (240 MPa). This finding solves the difficulty in predicting/optimizing the
dispersing condition in the wet-jet milling method.
As shown in Figure 2a–c, the size reduction tendencies were different depending on
the type of the surfactant. This indicates that the best surfactant for dispersing CaCO
3
particles in an aqueous phase is Softanol-70 because the weak dispersing energy input
induces smaller sizes of CaCO
3
particles in the aqueous phase compared with those in the
other two surfactants (Triton X-100 and SDS). As shown in Figure 3a–c, the values of the
PDI also provide important information. The PDI value of the CaCO
3
particles dispersed
using Softanol-70 was smaller than those when they were dispersed using the other two
surfactants (Triton X-100 and SDS) at the same dispersing energy input. This indicates
that the best surfactant for dispersing CaCO3particles in an aqueous phase is Softanol-70.
Comparing Figure 3a,b, at the same dispersing energy input, the PDI values in Figure 3b are
slightly smaller than those in Figure 3a. These results indicate that SDS is a more effective
surfactant in dispersing of CaCO
3
particles in an aqueous phase than Triton X-100 is. This
is because SDS induces a narrower size distribution of CaCO
3
particles in the aqueous
phase than Triton X-100 does, even though the mean sizes of CaCO
3
particles at the same
dispersing energy input are similar.
As shown in Figure 2d, the CaCO
3
particles dispersed by wet-jet milling using CTAB
as the surfactant were smaller for a weak dispersing energy input compared with those
using Triton X-100 and SDS. For example, at a dispersing energy input of 1.0
×
10
7
J, the
CaCO
3
particles were approximately 250 nm in size when they were dispersed using Triton
X-100 and SDS, whereas the size was approximately 200 nm when they were dispersed
using CTAB. Interestingly, in the case of CaCO
3
particles dispersed using CTAB, the CaCO
3
particles at such a weak dispersing energy input (e.g., 1.0
×
10
7
J) were similar in size to
Nanomaterials 2023,13, 80 8 of 14
those that were dispersed when Softanol-70 was used as the surfactant (approximately
200 nm). This is despite the PDI values of the CaCO
3
particles dispersed by CTAB being
larger than those of the CaCO
3
particles dispersed by Softanol-70, as shown in Figure 3c,d.
These phenomena indicate that CTAB endows a higher dispersibility to CaCO
3
particles
in an aqueous phase than Triton X-100 and SDS do. Although the mean particle size of
the CaCO
3
particles dispersed using CTAB was close to that which was achieved using
Softanol-70 at a relatively weak dispersing energy input, Softanol-70 has a higher dispersing
capability for CaCO
3
particles in an aqueous phase than CTAB does. This is because the
size distribution of particles dispersed by Softanol-70 is clearly narrower than that of the
particles dispersed by CTAB, as shown in Figure 3c,d.
However, at a relatively strong dispersing energy input, the mean sizes of the CaCO
3
particles using CTAB as the surfactant increased with the increase in the dispersing energy
input, as shown in Figure 2d. This tendency is completely different from those of the
CaCO
3
particles produced using the other surfactants. In this study, we determined that the
size enlargement of the CaCO
3
particles at a stronger dispersing energy input in the case
of CaCO
3
particles dispersed using CTAB may be caused by the change in the surfactant
micelles. Therefore, to assess the change in the surfactant micelles, we used PFG-NMR.
3.3. PFG-NMR Characterization of the Micellar Sizes of Various Surfactants in the Aqueous
CaCO3Particle Suspensions
Figure 4shows the
1
H spectra of the respective surfactants in the CaCO
3
particle sus-
pensions measured using the PFGSTE pulse sequence at a gradient strength of 65 G cm
−1
.
The peak at 3.6 ppm was assigned to the methoxy group, the carbonyl peaks appeared
at 3.0–2.5 ppm, and other alkyl protons appeared at 1.5–0.5 ppm, such as CH
2
CH
3
and
CH
2
CH
2
. Because the peaks at these chemical shifts for all of the surfactant molecules were
sufficiently strong enough for the PFG-NMR measurements to be performed, we utilized
these peaks for characterizations.
Figure 4. 1
H NMR spectra of various surfactants in aqueous CaCO
3
particle suspensions. Triton
X-100 (black), SDS (red), Softanol-70 (green), and CTAB (blue) were used as surfactants. All of the
spectra were obtained using the PFGSTE pulse sequence at a gradient strength of 65 G cm−1.
The plots of the PFGSTE echo signal attenuation for the aqueous CaCO
3
particle
suspensions using various surfactants are shown in Figure 5. The attenuation plots are
approximately linear, and they do not rely on the diffusion time, suggesting that the
industrial surfactants follow a monomodal size distribution. The diffusion coefficients
of all of the surfactant molecules before wet-jet milling which were calculated by linear
regression (the solid lines in Figure 5) were 1.11
±
0.49
×
10
−10
, 4.28
±
0.22
×
10
−10
,
6.50
±
0.33
×
10
−11
, and 1.60
±
0.06
×
10
−10
m
2
s
−1
for Triton X-100, SDS, softanol-70,
and CTAB, respectively. The uncertainties of the diffusion coefficients were calculated
on the basis of [
29
]. Based on the Stokes–Einstein assumption, the calculated micellar
Nanomaterials 2023,13, 80 9 of 14
surfactant sizes were approximately 1–8 nm, indicating the surfactants were not solved
as individual molecules, and instead they took the micellar structures. However, at
the highest dispersing energy input (approximately 1.4 x 10
7
J) in this study, the cal-
culated diffusion coefficients of all of the surfactant molecules were 1.28
±
0.15
×
10
−10
,
4.39
±
0.16
×
10
−10
, 6.59
±
0.35
×
10
−11
, and 2.69
±
0.16
×
10
−10
m
2
s
−1
for Triton X-100,
SDS, Softanol-70, and CTAB, respectively. As shown in Figure 5, the attenuation plots of
the different surfactant micelles present two different trends. For the first type, the slopes of
the attenuation plots increase with an increasing dispersing energy input, suggesting that
the size of the surfactant micelles decreased with an increasing dispersing energy input,
based on the Stejskal–Tanner diffusion equation (Equation (2)). This tendency can be seen
in Figure 6a,d (TritonX-100 and CTAB, respectively), however, the degree by which the
slopes increased differ relying on the type of surfactant. Specifically, the slope at the highest
dispersing energy input (approximately 1.4
×
10
7
J) in CTAB is changed significantly from
the initial value, whereas this change in Triton X-100 is small. For the second type, it is
observed that there is approximately no change in the slope at the highest dispersing energy
input (approximately 1.4
×
10
7
J) from the initial slope. In contrast to the first tendency, this
observation indicates that there were approximately no changes in the diffusion coefficients
of the surfactant micelles on dispersing using the wet-jet milling method. This trend can be
seen in Figure 6b,c (for SDS and Softanol-70, respectively).
Figure 5.
Examples of PFG-NMR spin-echo signal attenuation plots of respective surfactants in
aqueous CaCO
3
particle suspensions: (
a
) Triton X-100, (
b
) SDS, (
c
) Softanol-70, and (
d
) CTAB at
δ
= 1 ms for diffusion time of
∆
= 50 ms. The solid line represents linear regression. Black circles
and lines are for the samples before wet-jet milling. Red colored circles and lines are for the samples
dispersed at the highest dispersing energy input (approximately 1.4
×
10
7
J). Based on the Stokes–
Einstein assumption, the estimated micellar size of the surfactants is approximately 1–8 nm.
Nanomaterials 2023,13, 80 10 of 14
Figure 6.
Plots of the micellar sizes of various surfactants in aqueous media as functions of the
dispersing energy input, as determined by PFG-NMR. (
a
) Triton X-100, (
b
) SDS, (
c
) Softanol-70,
and (
d
) CTAB were used as surfactants. The plots are for different pressures in the narrow channel
(80 MPa: black, 120 MPa: red, 180 MPa: green, and 240 MPa: blue). The uncertainties of the diffusion
coefficients were calculated according to [29].
To visualize the changes in the micellar sizes of the surfactants in each aqueous CaCO
3
particle suspension, the sizes were calculated from the observed diffusion coefficients
using the Stokes–Einstein equation (Equation (1)). The calculated changes in the micellar
sizes of the surfactants as a function of the dispersing energy input are plotted in Figure 6.
As shown in Figure 6d, the change in the size of CTAB micelles can be clearly observed,
whereas those in the micellar sizes of the surfactants in aqueous CaCO
3
particles suspension
cannot be found in Figure 6a–c. This occurred even though the micellar sizes of Triton
X-100 slightly decreased with the increase in the dispersing energy input. After adding
the highest dispersing energy input (approximately 1.4
×
10
7
J), the micellar sizes of the
two surfactants did not change (SDS: 1.1 nm and Softanol-70: 7.5 nm), whereas those of
the other two surfactants changed (Triton X-100 (4.3 nm to 3.9 nm) and CTAB (3.1 nm to
1.9 nm)). Interestingly, the tendencies of the changes in the micellar sizes were estimated to
be related to the changes in the size of CaCO
3
particles in the aqueous medium. Specifically,
after adding the dispersing energy input by wet-jet milling, the mean sizes of CaCO
3
particles reduced with the increase in the dispersing energy input when the sizes of the
micellar sizes of the surfactants were not changed or slightly changed. Concurrently, in
the case of a large change in the micellar sizes of the surfactant, such as with CTAB, the
reduction in the mean sizes of the CaCO
3
particles was disturbed, and then, the size
of the CaCO
3
particles increased with increasing dispersing energy input. Comparing
Figures 2d and 6d, the CaCO
3
particles increased in size when the relative reduction in
the micellar sizes of CTAB was at approximately 20% (at approximately 5.0
×
10
7
J). In
the case of Triton X-100, the reduction in the micellar sizes was approximately 10% at the
highest dispersing energy input in this study, indicating this degree of the reduction of
Nanomaterials 2023,13, 80 11 of 14
the micellar sizes is not critical in maintaining the stability of the sizes of CaCO
3
particles
in aqueous media. These results suggest that wet-jet milling affects the sizes of CaCO
3
particles and some types of surfactant micelles, resulting in an adverse increase in the size
of the CaCO3particles.
3.4. DLVO Theoretical Assessment for Aqueous CaCO3Particle Suspensions
To explain our observation related to the dispersibility of CaCO
3
particles suspen-
sion under various dispersing conditions, we performed the measurements of the zeta
potentials for all of the samples. The observed zeta potentials of the CaCO
3
particles were
−
16.3
±
0.5 (with Triton X-100 as the surfactant),
−
27.2
±
0.6 mV (with SDS as the surfac-
tant),
−
19.1
±
0.7 mV (with Softanol-70 as the surfactant), and
−
42.8
±
1.0 mV (with CTAB
as the surfactant). The zeta potentials of aqueous CaCO
3
particle suspensions without
any surfactant were also measured. The repeatability of the observed zeta potentials was
used as uncertainties in this study, which were obtained from at least three separate zeta
potential measurements. Depending on the type of surfactant molecules, the observed zeta
potentials of CaCO3particles differed.
According to the Deryaguin–Landau–Verwey–Overbeek (DLVO) theory [
30
,
31
], two
types of interactions are attributed to the dispersibility of CaCO
3
particle dispersion, such
as van der Waals attractive interactions and electrostatic repulsive interactions. With regard
to the electrostatic repulsive energy, it is not equal to the zeta potential. However, the
zeta potential is considered to be the potential for the slip face where a liquid starts to
flow inside the electrical double layer formed on the hydrodynamic surface of a material.
Therefore, the zeta potential is a significant factor for the evaluation of the electrostatic
repulsive interaction between the CaCO3particles in a liquid medium.
In the DLVO theory, the inter-particle van der Waals energy can be represented
as follows:
V(A) = −A
6 2
4B+B2+2
(2+B)2+ln 4B+B2
(2+B)2!! (7)
where Ais the Hamaker constant, B= 2r/d,dis the particle size, and ris the distance
between the interacting two particles. By contrast, the electrostatic repulsive interaction
between the CaCO3particles and surfactant micelles are represented as follows:
V(R) = πε0εdΨ2eκr(8)
and
1
κ=s∑iρ∞ie2z2
i
ε0εkBT, (9)
where
ε0
is the permittivity of vacuum,
ε
is the dielectric constant of the electrolyte solution,
eis the elemental charge, k
B
is the Boltzmann constant, Tis the absolute temperature,
ρ∝i
is
the ion number density in the bulk electrolyte, zis the valence of ion i, and
κ
is the inverse
of the Debye length. Considering the two interaction energies, the total DLVO force, V
total
,
is given as follows:
Vtotal =V(A) + V(R)(10)
In the DLVO theory, V(A) is attributed to the attractive energy between two particles
if their sizes are the same. As shown in Figure 2d, the re-agglomeration of CaCO
3
parti-
cles in the CTAB aqueous solution starts at a dispersing energy input of approximately
7.5
×
10
7
J, and the produced agglomerates never re-disperse after constituent dispersing
by wet-jet milling (with a much higher dispersing energy input). The increase in the size
decreases the attractive interaction energy according to Equation (7), however, redispersion
never occurs, suggesting that the main factor for this dispersing system is not equal to the
van der Waals attractive energies. By contrast, when we assume that the zeta potentials
are equal to the surface potentials of the CaCO
3
particles, as shown in Equation (8), the
electrostatic repulsive energies of the CaCO
3
particles using the various industrial surfac-
Nanomaterials 2023,13, 80 12 of 14
tants as dispersant are different because of the difference in the values of the observed
zeta potentials (from
−
16 mV to
−
43 mV). Specifically, according to the observation of the
zeta potential, the repulsive energy of the CaCO
3
particles in the aqueous CTAB solution
was higher compared with those in the other surfactant aqueous solutions. Nevertheless,
the reaggregation of CaCO
3
particles occurred in the aqueous CTAB solution, as shown
in Figure 2d, whereas no size changes were observed for the CaCO
3
particles in the other
surfactant solutions. In this case, Figure 6suggests that the surfactant micellar sizes have an
important role to induce the sufficient dispersibility of CaCO
3
particles in aqueous media.
For the CaCO
3
particles in the aqueous CTAB solution, the surfactant micelle sizes were
reduced with the increase in the dispersing energy input, indicating that the electrostatic
repulsive energies induced by the surfactant micelles decreased with a decrease in the
sizes of the surfactant micelles, as expressed in Equation (8). By contrast, the sizes of the
two surfactant micelles (SDS and Softanol-70) did not change by wet-jet milling at any
dispersing energy input, indicating that the electrostatic repulsive energies caused by these
surfactant micelles did not change in their dispersion systems. Although the sizes of the
micelles for Triton X-100 slightly changed, the size changes are estimated to be critical to
reduce the dispersibility of the CaCO
3
particles in aqueous media. This is because the size
change of the micelles of CTAB was 40% at an energy input of approximately 1.4
×
10
7
J,
whereas that of Triton X-100 was 10% at the same energy input. Relatively small changes
in the micelle sizes might not affect the dispersibility of the CaCO
3
particles in aqueous
media. According to the DLVO theory, irregular changes in the dispersibility of CaCO
3
particles in the aqueous CTAB solution can therefore be clearly explained by the change
in the micellar sizes of CTAB. We previously observed similar phenomena (change in the
micelle sizes of the surfactant affected by the dispersibility of particles in liquid media) in
the case of dispersing carbon black particles using ultrasonication [
10
]. Thus, similarly, the
micellar sizes of surfactants are crucial for inducing and maintaining the dispersibility of
CaCO3particles in aqueous media.
4. Conclusions
In this study, we established a new concept—dispersing energy input—in the wet-jet
milling method to disperse materials in a liquid phase. The wet-jet milling method has been
used in the preparation of soft material suspensions. However, the shear forces are the main
driving force of dispersing, and they are weaker than they are in other dispersing methods,
such as the ultrasonication dispersing method. Therefore, the control parameters of the
wet-jet milling method for dispersing are the pressure of the narrow channel that the target
liquid including particles is passed through and the number of passes. The above indicates
that the former one is not a universal parameter to setup the dispersing condition by
various wet-jet milling users because the values of this pressure are dependent on the size
(diameter and length) of the narrow channel. A simple optimization/prediction method of
dispersing desired sizes of target particles by the wet-jet milling method is desired. Using
the idea of the dispersing energy input, it was found that the dispersing size of particles can
be easily optimized/predicted. We demonstrated the usability of the concept by preparing
CaCO
3
particles in aqueous suspensions with various surfactants using the wet-jet milling
method as an example. For instance, it was easy to estimate the dispersing condition to
produce approximately 200 nm CaCO
3
particles in the Softanol-70 aqueous phase, and
this was accomplished with 20 passes (80 MPa), 15 passes (120 MPa), 10 passes (180 MPa),
and 5 passes (240 MPa) using the idea of energy input. This finding solves the difficulty in
predicting/optimizing the dispersing condition in the wet-jet milling method. In addition,
by conducting a PFG-NMR assessment, we also identified the important role played by the
micellar sizes of surfactants in dispersing particles by wet-jet milling. The tendencies of
the changes in the micellar sizes were estimated to be related to the changes in the size of
the CaCO
3
particles in the aqueous medium. It was found that with a large change in the
micellar sizes of the surfactant, such as with CTAB, the reduction in the mean sizes of the
CaCO3particles is disturbed.
Nanomaterials 2023,13, 80 13 of 14
Author Contributions:
Conceptualization, H.K.; methodology, H.K.; validation, H.K. and A.N.;
formal analysis, H.K.; investigation, H.K.; resources, A.N.; data curation, H.K.; writing—original draft
preparation, H.K.; writing—review and editing, A.N.; visualization, H.K.; supervision, H.K.; project
administration, H.K. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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