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Interfacial wetting mechanisms of Al liquid on cathode carbon blocks of aluminum reduction cell for developing wettable cathode materials
Journal Pre-proof Interfacial wetting mechanisms of Al liquid on cathode carbon blocks of aluminum reduction cell for developing wettable cathode materials Xiaojun Lv, Chaohong Guan, Zexun Han, Chang Chen PII:
S0167-7322(19)35023-8
DOI:
https://doi.org/10.1016/j.molliq.2019.112017
Reference:
MOLLIQ 112017
To appear in:
Journal of Molecular Liquids
Received Date: 7 September 2019 Revised Date:
20 October 2019
Accepted Date: 24 October 2019
Please cite this article as: X. Lv, C. Guan, Z. Han, C. Chen, Interfacial wetting mechanisms of Al liquid on cathode carbon blocks of aluminum reduction cell for developing wettable cathode materials, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.112017. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Interfacial Wetting Mechanisms of Al liquid on Cathode Carbon Blocks of
2
aluminum reduction cell for developing wettable cathode materials
3 4
Xiaojun Lv, Chaohong Guan, Zexun Han*, Chang Chen
5
School of Metallurgy and Environment, Central South University, Changsha 410083, China
6 7
Abstract: Molecular dynamics simulation had been performed to investigate the wetting
8
properties of Al droplets on amorphous carbon surfaces and graphite surfaces. The effects of
9
temperature, graphitization of substrate and roughness were considered. Our results show that
10
the contact angles can be improved effectively with the increased temperature. Furthermore,
11
the Al droplet on graphite surface has a better wettability than that on amorphous carbon
12
surface. Similarly, the contact angle will also reduce with the increased degree of
13
graphitization and the wetting state will change from the transition wetting state to the Cassie
14
state when the roughness increases. In addition to the contact angles on the rough surface, the
15
remaining contact angles are less than 90°, which is different from the previous reports. The
16
free energy and thermodynamic properties analysis were applied to character the solid-liquid
17
interface properties and explain the wettability. Another interesting finding is that the study
18
reveals the reason of the poor wettability between Al liquid and cathode carbon blocks of
19
aluminum electrolytic cell. These findings improve our understandings of the wetting
20
behaviors of Al droplets on cathode carbon block surfaces at the atomistic level, which is
21
profitable to develop the wettable cathode materials for aluminum electrolysis. *
Corresponding author. E-mail address: [email protected] (Zexun Han), School of Metallurgy and Environment, Central South University, No. 932, South Road Lushan, Changsha, Hunan, 410083, China
22
Keywords: Wettability; Al droplets; Temperature; Graphitization; Roughness
23 24
1. Introduction
25
The industrial aluminum production is carried out by the Hall-Héroult molten salt
26
electrolysis, which was invented by Hall and Héroult in 1886. Since then, this technology has
27
been gradually improved in order to realize a better energy efficiency and environment
28
improvement. But the high energy consumption still exists until now. One of the important
29
reasons is the bad wettability between Al liquid and cathode carbon blocks. It is interesting
30
that the better wettability of aluminum liquid on cathode can reduce energy consumption
31
effectively, so that the wettable cathode materials have attracted a great deal of attention in the
32
scientific community. However, for the studies of wettable cathode materials, how to evaluate
33
the wettability is the most important subject.
34
Usually, the contact angle is used for evaluating wettability during the high-temperature
35
wetting process. In the past years, great efforts have been paid to character the wettability
36
between Al droplets and ceramics through the sessile drop technique at temperatures of
37
interest. In general, the contact angles have a tendency to decrease with the increase of
38
temperature, but which are rather scattered. For instance, the contact angles of molten
39
aluminum on ceramic substrates at 700 were measured by different authors, which were in
40
the range of 88°- 167°. 1-4 This situation may be due to the differences of droplet and substrate
41
compositions, temperature, atmospheric composition, and other factors. But in experiment,
42
it’s difficult to control these factors same. Collecting data about specific high-temperature
43
wetting mechanisms is challenging because the obtained data may represent a convolution of
44
many atomic phenomena. To our knowledge, the Al droplets will be oxidized easily if they
45
are exposed to atmosphere with the oxygen partial pressure of 10-49pa at high temperature
46
environment, which results the Al sessile droplets are always covered by alumina layers. This
47
also leads to the poor and different wettability of Al droplets. 5
48
With the development of computer, molecular dynamic (MD) simulation is used for the
49
researches of molten salt structure 6, interface behaviors 7, transport properties 8, etc. The MD
50
simulation has shown to be an ideal tool in the research of high-temperature wetting.
51
Compared with the sessile drop technique, MD simulation provides some specific advantages,
52
such as observing the wetting process at atomic level and maintaining the conditions of high
53
temperature and vacuum. Moreover, the MD simulation can avoid the oxidation of Al liquid
54
to obtain the more accurate data. The detailed description of atomic level in MD simulation
55
has allowed studies of the structural properties of droplets spreading on substrate surface 9-12,
56
such as radial distribution function (RDF), mean squared displacement (MSD), contact angle
57
and so on. In recent years, the MD simulation has been used to research the properties of Al
58
nanocomposites by a few researchers
59
strength, stability of nanocomposites etc. An investigation to model Al droplet on graphene
60
surface was conducted by Sunil Kumar 18. In his study, a wetting phenomenon of Al atoms
61
spreading fully can be observed. The effects of grain boundaries on the high temperature
62
wetting of the spreading of Al droplets on polycrystalline NiAl had been studied by MD 19. To
63
date, there is no systematic comparison of the microscopic wetting behaviors of Al droplet on
64
cathode carbon blocks surfaces with different degree of graphitization.
65
13-17
. These studies focus on the compressive/tensile
As demonstrated in the previous studies 20-21, the surface morphology of solid substrates
66
will strongly impact the wettability state of droplet. Usually, the rough surface is created by
67
adding, removing (form grooves or pillars on the surface) or rearranging the atoms of
68
substrates and moreover, the roughness can be control by crystallization control
69
phase-separation 23, laser micromachining
70
surface roughness resulting in the decreased wettability
71
angle increases. In addition, the orientation of roughness will cause the anisotropic liquid
72
spreading on the rough surface as the studies of Xin et al. 26, which indicates that it is much
73
easier for the liquid to wet inside the grooves and induce more spreading in the direction that
74
is parallel to the grooves. On the contrary, it also slows down the spreading in the direction
75
that is perpendicular to the grooves. Other studies
76
roughness promotes the transition of wetting state (Cassie-Baxter and Wenzel states), as
77
shown in the study of Xin et al. 26, they concluded the wetting state transition from Cassie to
78
partial wetting state when the width of grooves increases.
24
22
,
and so on. On the whole, the increased graphite 25
26-28
and correspondingly, the contact
have shown that the variety of
79
To the best of our knowledge, the present work is the first MD simulation of Al droplet
80
in contact with cathode carbon blocks of aluminum electrolytic cell. It is preformed to
81
investigate the effects of temperature, graphitization of substrate and roughness on the high
82
temperature wetting of the spreading of Al droplets on amorphous carbon (Al-AC) and
83
graphite by MD simulations. And then, providing a reliable method of characterizing
84
wettability for aluminum electrolysis industry, which is beneficial to the development of
85
wettable cathode materials for aluminum electrolysis.
86 87
2. Methodology:
88
2.1 Model and simulation details
89
Molecular dynamics (MD) simulations were performed to study the wettability of
90
amorphous carbon and graphite based on the large-scale atomic/molecular massively parallel
91
simulator (LAMMPS)
92
970K-1373K by the Nose-Hoover thermostat
93
calculating the time integration of Newton’s equation of motion with a time step of 1.0 fs 32.
94
In the MD simulation, the adaptive intermolecular reactive empirical bond order (AIREBO)
95
potential was selected to calculate the atomic interaction of graphite 33. The Tersoff potential
96
was used to describe the C-C interaction of amorphous carbon 34, which can be defined as
97
below:
98
29
in the NVT ensemble. The temperature was held at the range of 30, 31
. Velocity Verlet algorithm was used for
E = ∑ ∑
(1)
= +
(2)
99 100 101
102
103 104
1 ≤ − # $% = − sin " ' − < < +
&
0 ≥ +
= +,-. −/
= −0,-. −/
(3)
(4) (5)
105 106 107 108 109
According to the reference 34, E is the total energy, which is the sum of . The functions
and represent a repulsive and an attractive potentials. The function represents a
smooth cutoff function. The parameters R, D, / , / , A and B equal 1.95Å, 0.15Å, 3.4879Å-1, 2.2119Å-1, 1393.6eV and 346.74eV. Besides, represents a bond angle term,
110
which can be determined by the bond angle between atoms and the coordination of the atoms.
111
And the embedded atom method (EAM) potential was used for the aluminum atoms35, 36,
112 113 114 115 116
which formula is as below (Eq. (6)): 1 = 23 "∑ 45 ' + ∑ ∅35
(6)
In addition, we utilized the Lennard-Jones (L-J) potential to describe the Al-C interaction with the cutoff parameter of 12.0Å, which can be written as: =>?@A ' $
178 = 4:;% <"
=>?@A B ' C $
−"
(7)
117
Where the parameters of :;% = 0.0309, , G;% = 3.422Å represent the energy (or
118
well-depth) and the equilibrium interatomic distance 37.
119
Fig.1 shows the initial configurations of the MD simulation boxes. The models of Al
120
droplets with 3430 atoms contact with AC/graphite were built. The AC surface consists of
121
79772 carbon atoms with thickness of 21.314Å. The graphite surface consists of six layers of
122
carbon atoms and the distance between the layers is 3.354Å. And the size of simulation box
123
is 149.54Å × 149.54Å × 270Å so that the interaction of periodic image of the droplet can be
124
avoided effectively, the periodic boundary conditions were applied in the x and y directions,
125
an open boundary condition was used in the z direction. The atoms of substrates were fixed
126
during the process of simulation to represent an inert wall 38.
127
The simulations are described as below. First, energy minimization was used for the
128
reasonable initial configurations. Second, the systems were relaxed in the NVT ensemble for
129
1 ns, another 400ps for the data analysis. Third, focused on the effects of temperature,
130
morphology of AC surface and graphitization to the wetting properties.
131 132
Fig. 1. Initial configurations of the AC (a)/graphite (b) and Al cube. Atoms marked in blue are Al, and marked in red are C.
133 134 135
2.2 The measure of contact angle
136
The contact angle is used to evaluate the wettability, which is determined by establishing
137
a balance between the solid-vapor, liquid-vapor, solid-liquid surface tensions, as described by
138
the Young equation 39,40:
139
MNO = MN7 + M7O cos R
(8)
140
Where R represents the contact angle, MNO , MN7 , and M7O represent the surface tensions of
141
solid-vapor, solid-liquid, liquid-vapor. Usually, we can obtain the contact angle by the method
142
of Fan and Cagin 41 or a method of circular fit of the profile 42,43. Comparing the two methods,
143
the slight difference of the contact angle was found. Therefore, the contact angle was
144
determined by using the method of the best circular fit in this work.
145
In order to obtain the isochore profiles and the density profiles of the droplets, the
146
cylindrical coordinate(r, z) was introduced. The z-axis was determined as the axis through the
147
center of mass of the aluminum liquid and normal to xy-plane, r represents the radial distance
148
from the z-axis. The simulation box was meshed into bins with ∆r=0.5Å, ∆z=0.5Å, so that we
149
can calculate the density distribution of each bin as the average over time and then the
150
profiles could be obtained. To extract the contour line of the vapor-liquid interface, the two
151
steps described by Ruijter et al 44 should be followed. Firstly, we extracted the cylindrical
152
coordinate of the bins where ρ= 47 + 4O . Secondly, the contact angle was measured by a
153
circular best fit through the extracted points, as shown in Fig. 2. It is worth noting that the
154
vapor-liquid interface points below a height of 5 Å were not taken into account for the fit in
155
order to avoid the effect from density fluctuations at the aluminum-substrate interface.
156
According to the tangent line of the circle, we could obtain the contact angle.
157
Fig. 2. Circular fit of Al droplet interface
158 159 160 161
2.3 Free energy calculation The free energy and potential of mean force (PMF) analysis were employed to
162
investigate solid-liquid adhesion. In the present study, the solid-liquid adhesion free energy
163
was calculated by means of free energy perturbation (FEP) method 45. During the process of
164
calculation, the interaction between droplet and substrate was reduced gradually until the
165
droplet was separated from substrate surface. The variation of interaction was realized by
166
introducing a coupling parameter (λ), which was altered between 1 and 0 in 20 steps. λ=1
167
represents the complete solid-liquid interaction, λ=0 represents the droplet separates from the
168
substrate surface. The free energy difference between the initial and perturbed systems can be
169
calculated as follows: ∆T + = −UV ∑d% eT WX 〈,-. "−
170
Z[\]^ %Z[\ _` a
'〉c\
（9）
171
U is the potential energy, n represents the number of intermediate states to reach the final
172
state.
173
The steered molecular dynamics (SMD) simulations based on Jarzynski equlity 46 were
174
applied to calculate PMF for removing the droplet from the substrate surface. During the
175
simulation process, the PMF was defined as follows: PMF = − _
176
`
log 〈, a
%
k l` m
〉
（10）
177
Where UV , n and 〈… 〉 are the Boltzmann constant, environmental temperature and
178
ensemble average, the w represents the work done to remove the nanodroplet from the solid
179
surface.
180 181
3． ．Results and discussions:
182
To make sure reliability of our simulations, several simulations containing 3430, 4631
183
and 6084 Al atoms on the graphite substrates were carried out at 970K. The balanced contact
184
angle of these systems are 48.12±2.1°, 48.84±1.84° and 48.54±1.9°, which indicates that the
185
wetting behaviors have not shown a significant difference between Al nanodroplets of
186
different sizes. Accordingly, the effect of line tension on wettability has been ignored in our
187
works.
188
3.1. Dependence of the wettability on the temperature
189
In our research, the dependence of the contact angles on the different temperature
190
(970K, 1100K, 1200K, 1300K, 1373K) of the aluminum-AC system and the aluminum
191
-graphite system were studied. As shown in Fig.3 (a), the aluminum atoms in contact with the
192
substrate of AC have a tendency to become a circle after a relaxation of 1ns at all
193
temperatures. As the temperature increases, more atoms break free from the shackles of
194
droplets then into the vacuum layer, which is because the increase in atomic kinetic energy
195
reduces the aggregation of Al atoms. This situation is consistent with the experiments of Chai9.
196
To study the movement of Al atoms in detail, we introduced the MSD curve 8 which can
197
indicate the diffusion ability. As seen in Fig. 4(a), the slopes of MSD curves become bigger
198
and bigger with the elevated temperature, which illustrates that the aluminum atoms have the
199
stronger diffusion ability in high temperature. In the x and y directions, the two MSD curves
200
are similar in shape, which reveals the isotropic spreading and the aluminum atoms can
201
spread along the two directions with the similar diffusion speed. Therefore, the Al drop
202
remains a nearly circular shape during the wetting process, shown as Fig. 4(b). The two
203
phenomena also can be found during the structure of Al –graphite (Fig. 3b), and which have a
204
bigger contact diameter of the Al atoms at different temperatures than the Al-AC structure.
205
We can also know that from Fig. 4(b), the MSD curves of Al-graphite have a larger slope in
206
the x-y directions, which shows the Al atoms on the graphite surface will spread with stronger
207
diffusion ability so that a bigger contact circle will be formed in the interface.
208
To quantify the wettability, we computed the contact angles with the method described
209
above. Fig .4(c) shows the various contact angles and their error bars of Al droplets on the
210
two surfaces, AC and graphite, for different temperatures. The contact angles were obtained
211
by averaging the contact angle of several values. The error bars were obtained by taking the
212
standard deviation of the same values which refer to the difference in the calculated contact
213
angle, and the standard deviation is between 1° and 2°. As appears in Fig. 4(c), the contact
214
angle has a decreasing trend with the increased temperature, which illustrates that it can
215
improve wettability effectively by increasing temperature. This is consistent with the
216
simulation results of Rapaport 47 and Kandlikar 48. Additionally, the contact angles of Al-AC
217
systems are approximately twice that of the Al-graphite systems at different temperatures,
218
indicating the Al atoms on the graphite surface have better wettability than AC. The linear
219
relation between contact angles and temperature was fitted, from which we can observe that
220
the slope of graphite system is larger than AC system. This phenomenon indicates the Al
221
droplet on the graphite surface is more sensitive to temperature than that on the AC surface.
222 223
224 225 226 227 228
229
Fig. 3. Snapshots of Al droplets spreading on (a) AC substrate and (b) graphite substrate at 970K, 1100K, 1200K, 1300K and 1373K after 1.0ns.
230 231
Fig. 4. (a) The MSD curves of Al atoms on the AC surface at different temperatures. (b)
232
The comparison of MSD curves for the Al atoms on the AC and graphite surfaces along the x
233
and y directions at 970K. (c) The contact angles of Al-AC and Al-graphite systems at different
234
temperatures
235 236
The different wettability of Al droplet on different substrates is attributed to the
237
difference of diffusion barriers. To compute the diffusion barriers of Al atom on AC and
238
graphite surfaces, the nudged elastic band (NEB) method 49 was performed in our work. Fig. 5
239
shows the diffusion barriers of Al atom on surfaces along the x-direction. The diffusion
240
barrier of Al atom on graphite substrate is 1.27eV, which is less than that on the AC substrate
241
(2.23eV). Accordingly, the stronger spreading kinetics occurred on the graphite surface with
242
the lower energy barrier. This can well explain the better wettability presents on the graphite
243
surface.
244 245
Fig. 5. The diffusion barrier of Al atom on graphite and AC substrates along x-direction at 970K.
246 247 248
3.2. Dependence of the wettability on the graphitization
249
At present, most of the cathode carbon blocks of aluminum electrolysis cells are
250
semi-graphitic materials. Hence, it is worth to study the effect of graphitization degree on
251
wettability. The degree of graphitization can be characterized by the distance between the
252
layers of carbon atoms, which can be written as below 50:
253
p = 1 − q d = 3.44 − 0.0861 − q （11）
254
Where U is the degree of graphitization, d is the distance between the layers. In order to retain
255
the structures of different degrees of graphitization, the values of d and U are computed, as
256
Table 1 shown. Thus, the models of different graphitization degrees were built by the
257
parameter d.
258
The balanced structures of the five wetting systems were obtained by MD simulation
259
with the NVT ensemble at the temperature of 970K. Similarly, the contact circles will be
260
found due to the similar diffusion ability in the x and y directions of Al atoms. To reveal their
261
spreading properties quantitatively, Fig 6(a) describes the equilibrium spreading diameters D
262
of contact circles for different graphitization degrees. As we increased the degree, the D will
263
increase. The maximum D is 74.5958Å on the fully graphitized substrate, it is larger than the
264
AC systems at 1373K. This phenomenon illustrates that the high degree of graphitization can
265
improve the spreading behavior and wettability of Al atoms. However, the degree of
266
graphitization has a limited effect on wettability. Center-of-mass displacement of the Al drop
267
in the z direction (CMDZ) plotted in Fig. 6(c) can prove this. Obviously, the distances of
268
CMDZ between the five systems are small in equilibrium. The maximum distance is only
269
about 2Å. Though, from Fig. 5(c) we also know that with the increase of the degree of
270
graphitization, the Al droplet has an increased adhesion tendency. On the other hand, the
271
wetting process exhibits two-stage kinetics, with an initial fast spreading stage and a
272
secondary slow spreading stage. The CMDZ curves show larger displacements in the initial
273
200ps than the after time, which explains the D will close to the maximum at 200ps, and then
274
Al atoms undergo small displacements to reach equilibrium in the slow stage.
275
In this work, we also used another measure to describe the wettability characteristics. As
276
shown in Fig. 6(b), the balanced contact angle R(48°-62°) is decreased as the degree of
277
graphitization rises, which further confirms that the graphitization degree is in favor of the
278
spreading kinetics of Al droplet on ceramics surface. Compared with the system of Al droplet
279
on AC surface, the graphitization systems have smaller balanced contact angles and show
280
better wettability.
281
In general, there are many results of contact angles about Al droplet on the surface of
282
cathode substrates by the sessile drop technique. For example, the wettability of Al droplet on
283
graphite has been studied with contact angles from 120° to 160° at 973K 51-54, yet which was
284
measured by BAO Sarina et al 5 with a value of 92°. In their results, the contact angles of Al
285
droplets on the substrates are over 90° and exhibit the non-wetting behavior so that there is a
286
larger deviation between our MD simulation and the experimental reported. The deviation
287
may be due to the reasons below: 1) Al droplet is oxidized during the process of sessile drop
288
technique, resulting in the larger measurement result than MD simulation; 2) the materials in
289
the MD simulation are ideal pure substances, which contain impurities in the sessile drop
290
technique. 3）the substrate surface is rough in the sessile drop technique, but which is smooth
291
in the MD simulation. Experimental researches39,55 have proved that the roughness of surface
292
has a great influence on wetting behaviors. Hence, the effects of roughness could be studied
293
in the following.
294 295
Table 1
296
The degree of graphitization U and the distance between the layers of carbon atoms d
297 298
U
0.1
d/Å
3.42366
0.3 3.39614
0.5
0.7
3.3755
3.36174
1.0 3.354
299
300 301
Fig. 6. (a) The diameter of contact circle, (b) the contact angles of Al droplet in different
302
graphitic degrees with error bars of standard deviation, (c) the CMDZ of Al liquid as a
303
function of time.
304 305 306
3.3. Dependence of the wettability on the surface roughness It is well known that, the wetting behaviors of droplet on rough surface can be described 56
and Cassie states
57
307
by Wenzel
. According to the influences of surface energy and
308
topography, either the Wenzel state can be formed when a droplet in contact with a roughened
309
substrate, where the liquid atoms fully penetrates into the surface grooves, or the Cassie state,
310
where the liquid interface remains suspended at the tips of surface protrusions and small
311
pockets of air become trapped between the surface and the liquid.
312
Because the microstructure of solid surface has an important influence on wettability, it
313
is significant to understand the surface wettability and its influencing factors so that we can
314
control the surface wettability effectively. In this part, some systems with Al atoms and
315
grooved AC surfaces were simulated in the NVT ensemble at 970K. The initial configurations
316
contain an Al cube with 3430 atoms placed above grooved substrates (Fig. 7a). The substrates
317
were prepared with the lateral sizes of 149.54Å×149.54Å and the thickness of the substrates
318
was 21.345Å, there have the same grooves in the x and y directions so that the rough surface
319
can be formed with square matrix shape. According to Cassie-Baxter theory 55, we can use
320
rough factor γ to character the surface roughness, and γ can be obtained by the formula
321
below: vwx
γ = 1 + wyz{
322
（12）
323
The parameters a, h and b represent the width of square column, depth and width of groove.
324
Then, the values of rough factor γ will be set to 2.0(R2), 3.0(R3) and 4.0(R4) in this MD
325
simulation.
326
Fig. 7(b) shows the equilibrium states for the spreading of Al droplets on the surfaces
327
with different roughness. The Al atoms spreading into grooves can be observed on the R2 and
328
R3 surfaces, but the grooves are not filled with Al atoms. Hence, the wetting process will
329
maintain a transition state from the state of Cassie to Wenzel. On the contrary, the Al atoms
330
will not spreading into grooves on the R4, which is a wetting state of Cassie. Because of the
331
stable b, we can know that the wetting state will change from the transition wetting state to
332
Cassie state with the increased h. This also can be proved by CMDZ curves of Fig. 8a, the
333
CMDZ values of Al atoms are larger than that on smooth surface when roughness equals 2 and
334
3, which means that some Al atoms will move into grooves to reach the transition state of
335
wetting. And compared to R3, the Al droplet on R2 surface will be closer to the Wenzel state.
336
Also, the smaller CMDZ of Al droplet explains the form of Cassie state when the roughness
337
equals 4.
338
The influences of surface structure on wettability includes two aspects: 1) the surface
339
grooves constitute the resistance of the droplet to spread and infiltrate on the solid surface; 2)
340
when the droplet penetrates into grooves, the volume of the droplet above the three-phase
341
contact line is reduced and the height is lowered, this will result in a decrease on the contact
342
angle. And due to the presence of a rough surface pin effect 54, it is difficult for the droplet to
343
spread freely on the rough surface, which reduces the spreading width of the droplet. As seen
344
in Fig. 8b, the variation tendency of the MSDX curves of Al atoms (on the R2 and R3 surfaces)
345
is almost same with larger slopes than that on the R4 surface. In addition, by computing the
346
equilibrium spreading diameter D of the Al droplets, we can quantitatively reveal their
347
spreading properties on the different rough surfaces. On the R2, R3 and R4 surfaces, the D are
348
49.2414Å, 45.1519Å and 45.0097Å, respectively, which are all smaller than that on the AC or
349
graphite surfaces (74.5958Å). These phenomena express that the diffusion ability of Al atoms
350
will reduce due to the increase of roughness. In other words, this is resulted by the energy
351
barriers of rough surface.
352
It is worth mentioning that the calculated contact angles of Al droplet on R2, R3 and R4
353
surfaces are 106°（±2.14°）, 113°（±1.63°） and 120°（±1.87°）. The wettability of Al liquid
354
changes from a wettable state to a non-wettable state when the surface becomes rough. It
355
shows that the roughness can greatly affect the wetting behaviors. The related reference has
356
reported the liquid Al wetting on rough graphene surface by MD simulation 37. The simulation
357
describes that the rough surface reduces the wettability of liquid Al on substrates which is
358
consistent with our work. In addition, our results are also qualitatively consistent with
359
experimental reports, which all exhibit the non-wettable character of Al droplet on cathode
360
carbon blocks surfaces. While, the contact angles measured by our MD simulation are still
361
smaller than experiment (120°-160°), this is because the Al liquid will be easily oxidized and
362
covered with a alumina film during the process of the sessile drop technique at 970K 58. The
363
results also reveal the reason of the bad wettability between Al liquid and cathode carbon
364
blocks in the aluminum electrolysis industry, which is largely determined by the rough
365
surfaces of cathode carbon blocks.
366
367
368 369
Fig. 7. (a) The initial configuration of Al droplet on rough surface. (b) Snapshots of Al
370
droplets spreading on rough surfaces in the balanced state, and roughness equals 2, 3 and 4.
371 372 373
Fig. 8. (a) The MSDX (b) CMDZ curves of Al droplets on the surfaces with different roughness.
374 375
In addition, other models with different width of grooves along x and y directions were
376
built to investigate the effect of grooves’ width on the wetting behavior of Al droplet. As
377
shown in Fig. 9, Al atoms enter the grooves and realize a Wenzel wetting state with the width
378
of grooves increases. Compared with the system of roughness=4 (the depth of grooves is
379
equal to the two systems), it can be concluded that the wetting state will transition from
380
Cassie to Wenzel state with the increased width of grooves, meaning that the enough
381
roughness can improve the wettability of Al liquid.
382 383 384
Fig. 9. The balanced configurations of different width of grooves, the width of left=8Å, the right=11Å.
385 386
3.4 Free energy and thermodynamic properties analysis
387
The free energy difference between the initial balanced state and the perturbed separation
388
systems for Al droplet on different surfaces calculated by the FEP method were presented in
389
Fig. 10. The difference represents the work done to remove Al droplet from initial system to
390
perturbed systems. Results show that the solid-liquid adhesion decreases with the decrease in
391
graphitization of the graphite. Consequently, the interaction of Al atoms with the substrate
392
decreases. The previous studies have reported the Wenzel state is more favorable in terms of
393
energy than the Cassie state 59. In the Wenzel and transition states, the Al atoms contact with
394
the substrate more effectively so that the interactions between them. The Al droplet in the R2
395
and R3 systems are in the Wenzel and transition states. Hence, the solid-liquid adhesion in the
396
R2 and R3 systems are greater compared to that in the R4 system (Cassie state) so that the
397
contact angle of Al droplet increases with the roughness increases.
398
In this work, another 2ns is necessary for the steered molecular dynamics simulation to
399
compute PMF at 970K. Fig. 10 exhibits the PMF versus time for removing Al droplet from
400
the graphite surface, AC surface and rough AC surfaces. In the all systems, the PMF curves
401
monotonic increase firstly, and then maintain a constant after the Al droplet away from the
402
substrate surfaces. The turn point represents the complete solid-liquid separation.
403
Comparisons of the PMF for different substrates reveal that the interactions between Al
404
droplet and substrates follow the sequence: Graphite > AC > R=2 > R=3 > R=4, which mean
405
the Al droplet on graphite surface has the best wettability and the minimum contact angle. In
406
addition, the interactions will decrease with the increase of roughness, resulting in the poor
407
wettability and solid-liquid adhesion.
408
409
Fig. 10. (a) The free energy difference and (b) the PMF of solid-liquid separation for Al
410
droplet on different substrates.
411 412
According to the relation Helmholtz free energy ∆A = ∆U-T∆S, the free energy is further
413
split into entropic and energetic components. ∆U is the internal energy difference, which can
414
be calculated by the sum of the potential energy difference between Al droplet and other
415
components. Accordingly, the entropy ∆S can be obtained and the T is the temperature of
416
system. Fig. 11 shows the free energy ∆A, energy ∆U and entropy ∆S for Al droplet on
417
substrates. Results exhibit that there is greater energetic contributions and ∆S in the
418
Al-graphite system than Al-AC system. The energetic contributions decreases with the
419
roughness increases in the Al-rough AC systems. And the entropic difference ∆S is decreased
420
with the increased roughness, which explained that the less entropy will lose with the
421
increased roughness during the adhesion process. These observations reveal that the energetic
422
contributions are beneficial to the Al droplet adhesion. Conversely, the entropic contributions
423
are not good for adhesion of Al droplet. The result is consistent with the previous study 60. In
424
addition, the Fig. 11 also shows that the system obtain more energy will lose more entropy,
425
which fits perfectly the thermodynamic investigation of the substrate strength dependence of
426
the wettability 60.
427 428
Fig. 11. Changes in free energy, internal energy and entropy of the (a) Al-graphite and Al-AC systems (b) R=2, R=3, R=4 rough AC-Al systems.
429 430 431
4. Conclusions
432
In summary, the wetting behaviors of Al droplet on the AC and graphite have been
433
studied by performing MD simulation. Here, we elaborated key effect of temperature,
434
substrate material, graphitization and surface roughness on the wetting behaviors. The
435
simulation results show that the high temperature can improve the wettability of Al droplet.
436
The Al droplet on the graphite substrate has a smaller contact angle than that on the AC
437
substrate at the same temperature, and both still maintain the state of wetting. The MSD
438
curves explain that the Al atoms on graphite substrate have stronger diffusion ability than
439
which on the AC substrate, so that a larger contact circle can be formed. As for the graphitized
440
surfaces, we can know that the contact angle will increase with the reduced degree of
441
graphitization. Though, the wetting performance of Al droplet on graphitized surface is still
442
better than which on AC substrate. On the rough surface, the maximum contact angle can be
443
found than other systems we researched due to the presence of pinning effect. The wettability
444
will change from the transition wetting state to the Cassie state, so that the wettability of Al
445
droplet will become very poor. The wetting state will transition from Cassie to Wenzel state
446
with the increased width of grooves. In addition, the free energy analysis reveals the
447
solid-liquid adhesion decreases with the graphitization decreases and the roughness increases,
448
then the wettability decreases. The thermodynamic properties analysis shows the energetic
449
contributions are beneficial to the Al droplet adhesion but the entropic contributions are not
450
good for adhesion of Al droplet.
451
In general, our results reveal that there is a good wettability between Al droplet and
452
Al/graphite in an ideal environment, and the roughness of cathode surface maybe the most
453
important factor for the poor wettability of Al liquid. These studies may help shed light on
454
understanding and controlling the wetting behaviors of liquid metals. What’s more, the
455
effective control of wettability is significant for the development of wettable cathode
456
materials for aluminum cells.
457
Acknowledgements
458
We sincerely acknowledge the High Performance Computing Center of Central South
459
University, China. This work was financially supported by the National Natural Science
460
Foundation of China (No. 51674302) and the Innovation-Driven Project of Central South
461
University (No. 2016CX019).
462 463
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Highlights： 1. Molecular dynamics simulation is applied to study the wettability of Al liquid. 2. The degrees of graphitization are considered in this manuscript. 3. Good wettability is found between Al liquid and amorphous carbon/graphite. 4. The roughness will change the wetting state from wetting to non-wetting. 5. Why the Al liquid has the poor wettability on cathode of Aluminum reduction cell?
Conflict of interest statement： The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
S0167-7322(19)35023-8
DOI:
https://doi.org/10.1016/j.molliq.2019.112017
Reference:
MOLLIQ 112017
To appear in:
Journal of Molecular Liquids
Received Date: 7 September 2019 Revised Date:
20 October 2019
Accepted Date: 24 October 2019
Please cite this article as: X. Lv, C. Guan, Z. Han, C. Chen, Interfacial wetting mechanisms of Al liquid on cathode carbon blocks of aluminum reduction cell for developing wettable cathode materials, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.112017. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Interfacial Wetting Mechanisms of Al liquid on Cathode Carbon Blocks of
2
aluminum reduction cell for developing wettable cathode materials
3 4
Xiaojun Lv, Chaohong Guan, Zexun Han*, Chang Chen
5
School of Metallurgy and Environment, Central South University, Changsha 410083, China
6 7
Abstract: Molecular dynamics simulation had been performed to investigate the wetting
8
properties of Al droplets on amorphous carbon surfaces and graphite surfaces. The effects of
9
temperature, graphitization of substrate and roughness were considered. Our results show that
10
the contact angles can be improved effectively with the increased temperature. Furthermore,
11
the Al droplet on graphite surface has a better wettability than that on amorphous carbon
12
surface. Similarly, the contact angle will also reduce with the increased degree of
13
graphitization and the wetting state will change from the transition wetting state to the Cassie
14
state when the roughness increases. In addition to the contact angles on the rough surface, the
15
remaining contact angles are less than 90°, which is different from the previous reports. The
16
free energy and thermodynamic properties analysis were applied to character the solid-liquid
17
interface properties and explain the wettability. Another interesting finding is that the study
18
reveals the reason of the poor wettability between Al liquid and cathode carbon blocks of
19
aluminum electrolytic cell. These findings improve our understandings of the wetting
20
behaviors of Al droplets on cathode carbon block surfaces at the atomistic level, which is
21
profitable to develop the wettable cathode materials for aluminum electrolysis. *
Corresponding author. E-mail address: [email protected] (Zexun Han), School of Metallurgy and Environment, Central South University, No. 932, South Road Lushan, Changsha, Hunan, 410083, China
22
Keywords: Wettability; Al droplets; Temperature; Graphitization; Roughness
23 24
1. Introduction
25
The industrial aluminum production is carried out by the Hall-Héroult molten salt
26
electrolysis, which was invented by Hall and Héroult in 1886. Since then, this technology has
27
been gradually improved in order to realize a better energy efficiency and environment
28
improvement. But the high energy consumption still exists until now. One of the important
29
reasons is the bad wettability between Al liquid and cathode carbon blocks. It is interesting
30
that the better wettability of aluminum liquid on cathode can reduce energy consumption
31
effectively, so that the wettable cathode materials have attracted a great deal of attention in the
32
scientific community. However, for the studies of wettable cathode materials, how to evaluate
33
the wettability is the most important subject.
34
Usually, the contact angle is used for evaluating wettability during the high-temperature
35
wetting process. In the past years, great efforts have been paid to character the wettability
36
between Al droplets and ceramics through the sessile drop technique at temperatures of
37
interest. In general, the contact angles have a tendency to decrease with the increase of
38
temperature, but which are rather scattered. For instance, the contact angles of molten
39
aluminum on ceramic substrates at 700 were measured by different authors, which were in
40
the range of 88°- 167°. 1-4 This situation may be due to the differences of droplet and substrate
41
compositions, temperature, atmospheric composition, and other factors. But in experiment,
42
it’s difficult to control these factors same. Collecting data about specific high-temperature
43
wetting mechanisms is challenging because the obtained data may represent a convolution of
44
many atomic phenomena. To our knowledge, the Al droplets will be oxidized easily if they
45
are exposed to atmosphere with the oxygen partial pressure of 10-49pa at high temperature
46
environment, which results the Al sessile droplets are always covered by alumina layers. This
47
also leads to the poor and different wettability of Al droplets. 5
48
With the development of computer, molecular dynamic (MD) simulation is used for the
49
researches of molten salt structure 6, interface behaviors 7, transport properties 8, etc. The MD
50
simulation has shown to be an ideal tool in the research of high-temperature wetting.
51
Compared with the sessile drop technique, MD simulation provides some specific advantages,
52
such as observing the wetting process at atomic level and maintaining the conditions of high
53
temperature and vacuum. Moreover, the MD simulation can avoid the oxidation of Al liquid
54
to obtain the more accurate data. The detailed description of atomic level in MD simulation
55
has allowed studies of the structural properties of droplets spreading on substrate surface 9-12,
56
such as radial distribution function (RDF), mean squared displacement (MSD), contact angle
57
and so on. In recent years, the MD simulation has been used to research the properties of Al
58
nanocomposites by a few researchers
59
strength, stability of nanocomposites etc. An investigation to model Al droplet on graphene
60
surface was conducted by Sunil Kumar 18. In his study, a wetting phenomenon of Al atoms
61
spreading fully can be observed. The effects of grain boundaries on the high temperature
62
wetting of the spreading of Al droplets on polycrystalline NiAl had been studied by MD 19. To
63
date, there is no systematic comparison of the microscopic wetting behaviors of Al droplet on
64
cathode carbon blocks surfaces with different degree of graphitization.
65
13-17
. These studies focus on the compressive/tensile
As demonstrated in the previous studies 20-21, the surface morphology of solid substrates
66
will strongly impact the wettability state of droplet. Usually, the rough surface is created by
67
adding, removing (form grooves or pillars on the surface) or rearranging the atoms of
68
substrates and moreover, the roughness can be control by crystallization control
69
phase-separation 23, laser micromachining
70
surface roughness resulting in the decreased wettability
71
angle increases. In addition, the orientation of roughness will cause the anisotropic liquid
72
spreading on the rough surface as the studies of Xin et al. 26, which indicates that it is much
73
easier for the liquid to wet inside the grooves and induce more spreading in the direction that
74
is parallel to the grooves. On the contrary, it also slows down the spreading in the direction
75
that is perpendicular to the grooves. Other studies
76
roughness promotes the transition of wetting state (Cassie-Baxter and Wenzel states), as
77
shown in the study of Xin et al. 26, they concluded the wetting state transition from Cassie to
78
partial wetting state when the width of grooves increases.
24
22
,
and so on. On the whole, the increased graphite 25
26-28
and correspondingly, the contact
have shown that the variety of
79
To the best of our knowledge, the present work is the first MD simulation of Al droplet
80
in contact with cathode carbon blocks of aluminum electrolytic cell. It is preformed to
81
investigate the effects of temperature, graphitization of substrate and roughness on the high
82
temperature wetting of the spreading of Al droplets on amorphous carbon (Al-AC) and
83
graphite by MD simulations. And then, providing a reliable method of characterizing
84
wettability for aluminum electrolysis industry, which is beneficial to the development of
85
wettable cathode materials for aluminum electrolysis.
86 87
2. Methodology:
88
2.1 Model and simulation details
89
Molecular dynamics (MD) simulations were performed to study the wettability of
90
amorphous carbon and graphite based on the large-scale atomic/molecular massively parallel
91
simulator (LAMMPS)
92
970K-1373K by the Nose-Hoover thermostat
93
calculating the time integration of Newton’s equation of motion with a time step of 1.0 fs 32.
94
In the MD simulation, the adaptive intermolecular reactive empirical bond order (AIREBO)
95
potential was selected to calculate the atomic interaction of graphite 33. The Tersoff potential
96
was used to describe the C-C interaction of amorphous carbon 34, which can be defined as
97
below:
98
29
in the NVT ensemble. The temperature was held at the range of 30, 31
. Velocity Verlet algorithm was used for
E = ∑ ∑
(1)
= +
(2)
99 100 101
102
103 104
1 ≤ − # $% = − sin " ' − < < +
&
0 ≥ +
= +,-. −/
= −0,-. −/
(3)
(4) (5)
105 106 107 108 109
According to the reference 34, E is the total energy, which is the sum of . The functions
and represent a repulsive and an attractive potentials. The function represents a
smooth cutoff function. The parameters R, D, / , / , A and B equal 1.95Å, 0.15Å, 3.4879Å-1, 2.2119Å-1, 1393.6eV and 346.74eV. Besides, represents a bond angle term,
110
which can be determined by the bond angle between atoms and the coordination of the atoms.
111
And the embedded atom method (EAM) potential was used for the aluminum atoms35, 36,
112 113 114 115 116
which formula is as below (Eq. (6)): 1 = 23 "∑ 45 ' + ∑ ∅35
(6)
In addition, we utilized the Lennard-Jones (L-J) potential to describe the Al-C interaction with the cutoff parameter of 12.0Å, which can be written as: =>?@A ' $
178 = 4:;% <"
=>?@A B ' C $
−"
(7)
117
Where the parameters of :;% = 0.0309, , G;% = 3.422Å represent the energy (or
118
well-depth) and the equilibrium interatomic distance 37.
119
Fig.1 shows the initial configurations of the MD simulation boxes. The models of Al
120
droplets with 3430 atoms contact with AC/graphite were built. The AC surface consists of
121
79772 carbon atoms with thickness of 21.314Å. The graphite surface consists of six layers of
122
carbon atoms and the distance between the layers is 3.354Å. And the size of simulation box
123
is 149.54Å × 149.54Å × 270Å so that the interaction of periodic image of the droplet can be
124
avoided effectively, the periodic boundary conditions were applied in the x and y directions,
125
an open boundary condition was used in the z direction. The atoms of substrates were fixed
126
during the process of simulation to represent an inert wall 38.
127
The simulations are described as below. First, energy minimization was used for the
128
reasonable initial configurations. Second, the systems were relaxed in the NVT ensemble for
129
1 ns, another 400ps for the data analysis. Third, focused on the effects of temperature,
130
morphology of AC surface and graphitization to the wetting properties.
131 132
Fig. 1. Initial configurations of the AC (a)/graphite (b) and Al cube. Atoms marked in blue are Al, and marked in red are C.
133 134 135
2.2 The measure of contact angle
136
The contact angle is used to evaluate the wettability, which is determined by establishing
137
a balance between the solid-vapor, liquid-vapor, solid-liquid surface tensions, as described by
138
the Young equation 39,40:
139
MNO = MN7 + M7O cos R
(8)
140
Where R represents the contact angle, MNO , MN7 , and M7O represent the surface tensions of
141
solid-vapor, solid-liquid, liquid-vapor. Usually, we can obtain the contact angle by the method
142
of Fan and Cagin 41 or a method of circular fit of the profile 42,43. Comparing the two methods,
143
the slight difference of the contact angle was found. Therefore, the contact angle was
144
determined by using the method of the best circular fit in this work.
145
In order to obtain the isochore profiles and the density profiles of the droplets, the
146
cylindrical coordinate(r, z) was introduced. The z-axis was determined as the axis through the
147
center of mass of the aluminum liquid and normal to xy-plane, r represents the radial distance
148
from the z-axis. The simulation box was meshed into bins with ∆r=0.5Å, ∆z=0.5Å, so that we
149
can calculate the density distribution of each bin as the average over time and then the
150
profiles could be obtained. To extract the contour line of the vapor-liquid interface, the two
151
steps described by Ruijter et al 44 should be followed. Firstly, we extracted the cylindrical
152
coordinate of the bins where ρ= 47 + 4O . Secondly, the contact angle was measured by a
153
circular best fit through the extracted points, as shown in Fig. 2. It is worth noting that the
154
vapor-liquid interface points below a height of 5 Å were not taken into account for the fit in
155
order to avoid the effect from density fluctuations at the aluminum-substrate interface.
156
According to the tangent line of the circle, we could obtain the contact angle.
157
Fig. 2. Circular fit of Al droplet interface
158 159 160 161
2.3 Free energy calculation The free energy and potential of mean force (PMF) analysis were employed to
162
investigate solid-liquid adhesion. In the present study, the solid-liquid adhesion free energy
163
was calculated by means of free energy perturbation (FEP) method 45. During the process of
164
calculation, the interaction between droplet and substrate was reduced gradually until the
165
droplet was separated from substrate surface. The variation of interaction was realized by
166
introducing a coupling parameter (λ), which was altered between 1 and 0 in 20 steps. λ=1
167
represents the complete solid-liquid interaction, λ=0 represents the droplet separates from the
168
substrate surface. The free energy difference between the initial and perturbed systems can be
169
calculated as follows: ∆T + = −UV ∑d% eT WX 〈,-. "−
170
Z[\]^ %Z[\ _` a
'〉c\
（9）
171
U is the potential energy, n represents the number of intermediate states to reach the final
172
state.
173
The steered molecular dynamics (SMD) simulations based on Jarzynski equlity 46 were
174
applied to calculate PMF for removing the droplet from the substrate surface. During the
175
simulation process, the PMF was defined as follows: PMF = − _
176
`
log 〈, a
%
k l` m
〉
（10）
177
Where UV , n and 〈… 〉 are the Boltzmann constant, environmental temperature and
178
ensemble average, the w represents the work done to remove the nanodroplet from the solid
179
surface.
180 181
3． ．Results and discussions:
182
To make sure reliability of our simulations, several simulations containing 3430, 4631
183
and 6084 Al atoms on the graphite substrates were carried out at 970K. The balanced contact
184
angle of these systems are 48.12±2.1°, 48.84±1.84° and 48.54±1.9°, which indicates that the
185
wetting behaviors have not shown a significant difference between Al nanodroplets of
186
different sizes. Accordingly, the effect of line tension on wettability has been ignored in our
187
works.
188
3.1. Dependence of the wettability on the temperature
189
In our research, the dependence of the contact angles on the different temperature
190
(970K, 1100K, 1200K, 1300K, 1373K) of the aluminum-AC system and the aluminum
191
-graphite system were studied. As shown in Fig.3 (a), the aluminum atoms in contact with the
192
substrate of AC have a tendency to become a circle after a relaxation of 1ns at all
193
temperatures. As the temperature increases, more atoms break free from the shackles of
194
droplets then into the vacuum layer, which is because the increase in atomic kinetic energy
195
reduces the aggregation of Al atoms. This situation is consistent with the experiments of Chai9.
196
To study the movement of Al atoms in detail, we introduced the MSD curve 8 which can
197
indicate the diffusion ability. As seen in Fig. 4(a), the slopes of MSD curves become bigger
198
and bigger with the elevated temperature, which illustrates that the aluminum atoms have the
199
stronger diffusion ability in high temperature. In the x and y directions, the two MSD curves
200
are similar in shape, which reveals the isotropic spreading and the aluminum atoms can
201
spread along the two directions with the similar diffusion speed. Therefore, the Al drop
202
remains a nearly circular shape during the wetting process, shown as Fig. 4(b). The two
203
phenomena also can be found during the structure of Al –graphite (Fig. 3b), and which have a
204
bigger contact diameter of the Al atoms at different temperatures than the Al-AC structure.
205
We can also know that from Fig. 4(b), the MSD curves of Al-graphite have a larger slope in
206
the x-y directions, which shows the Al atoms on the graphite surface will spread with stronger
207
diffusion ability so that a bigger contact circle will be formed in the interface.
208
To quantify the wettability, we computed the contact angles with the method described
209
above. Fig .4(c) shows the various contact angles and their error bars of Al droplets on the
210
two surfaces, AC and graphite, for different temperatures. The contact angles were obtained
211
by averaging the contact angle of several values. The error bars were obtained by taking the
212
standard deviation of the same values which refer to the difference in the calculated contact
213
angle, and the standard deviation is between 1° and 2°. As appears in Fig. 4(c), the contact
214
angle has a decreasing trend with the increased temperature, which illustrates that it can
215
improve wettability effectively by increasing temperature. This is consistent with the
216
simulation results of Rapaport 47 and Kandlikar 48. Additionally, the contact angles of Al-AC
217
systems are approximately twice that of the Al-graphite systems at different temperatures,
218
indicating the Al atoms on the graphite surface have better wettability than AC. The linear
219
relation between contact angles and temperature was fitted, from which we can observe that
220
the slope of graphite system is larger than AC system. This phenomenon indicates the Al
221
droplet on the graphite surface is more sensitive to temperature than that on the AC surface.
222 223
224 225 226 227 228
229
Fig. 3. Snapshots of Al droplets spreading on (a) AC substrate and (b) graphite substrate at 970K, 1100K, 1200K, 1300K and 1373K after 1.0ns.
230 231
Fig. 4. (a) The MSD curves of Al atoms on the AC surface at different temperatures. (b)
232
The comparison of MSD curves for the Al atoms on the AC and graphite surfaces along the x
233
and y directions at 970K. (c) The contact angles of Al-AC and Al-graphite systems at different
234
temperatures
235 236
The different wettability of Al droplet on different substrates is attributed to the
237
difference of diffusion barriers. To compute the diffusion barriers of Al atom on AC and
238
graphite surfaces, the nudged elastic band (NEB) method 49 was performed in our work. Fig. 5
239
shows the diffusion barriers of Al atom on surfaces along the x-direction. The diffusion
240
barrier of Al atom on graphite substrate is 1.27eV, which is less than that on the AC substrate
241
(2.23eV). Accordingly, the stronger spreading kinetics occurred on the graphite surface with
242
the lower energy barrier. This can well explain the better wettability presents on the graphite
243
surface.
244 245
Fig. 5. The diffusion barrier of Al atom on graphite and AC substrates along x-direction at 970K.
246 247 248
3.2. Dependence of the wettability on the graphitization
249
At present, most of the cathode carbon blocks of aluminum electrolysis cells are
250
semi-graphitic materials. Hence, it is worth to study the effect of graphitization degree on
251
wettability. The degree of graphitization can be characterized by the distance between the
252
layers of carbon atoms, which can be written as below 50:
253
p = 1 − q d = 3.44 − 0.0861 − q （11）
254
Where U is the degree of graphitization, d is the distance between the layers. In order to retain
255
the structures of different degrees of graphitization, the values of d and U are computed, as
256
Table 1 shown. Thus, the models of different graphitization degrees were built by the
257
parameter d.
258
The balanced structures of the five wetting systems were obtained by MD simulation
259
with the NVT ensemble at the temperature of 970K. Similarly, the contact circles will be
260
found due to the similar diffusion ability in the x and y directions of Al atoms. To reveal their
261
spreading properties quantitatively, Fig 6(a) describes the equilibrium spreading diameters D
262
of contact circles for different graphitization degrees. As we increased the degree, the D will
263
increase. The maximum D is 74.5958Å on the fully graphitized substrate, it is larger than the
264
AC systems at 1373K. This phenomenon illustrates that the high degree of graphitization can
265
improve the spreading behavior and wettability of Al atoms. However, the degree of
266
graphitization has a limited effect on wettability. Center-of-mass displacement of the Al drop
267
in the z direction (CMDZ) plotted in Fig. 6(c) can prove this. Obviously, the distances of
268
CMDZ between the five systems are small in equilibrium. The maximum distance is only
269
about 2Å. Though, from Fig. 5(c) we also know that with the increase of the degree of
270
graphitization, the Al droplet has an increased adhesion tendency. On the other hand, the
271
wetting process exhibits two-stage kinetics, with an initial fast spreading stage and a
272
secondary slow spreading stage. The CMDZ curves show larger displacements in the initial
273
200ps than the after time, which explains the D will close to the maximum at 200ps, and then
274
Al atoms undergo small displacements to reach equilibrium in the slow stage.
275
In this work, we also used another measure to describe the wettability characteristics. As
276
shown in Fig. 6(b), the balanced contact angle R(48°-62°) is decreased as the degree of
277
graphitization rises, which further confirms that the graphitization degree is in favor of the
278
spreading kinetics of Al droplet on ceramics surface. Compared with the system of Al droplet
279
on AC surface, the graphitization systems have smaller balanced contact angles and show
280
better wettability.
281
In general, there are many results of contact angles about Al droplet on the surface of
282
cathode substrates by the sessile drop technique. For example, the wettability of Al droplet on
283
graphite has been studied with contact angles from 120° to 160° at 973K 51-54, yet which was
284
measured by BAO Sarina et al 5 with a value of 92°. In their results, the contact angles of Al
285
droplets on the substrates are over 90° and exhibit the non-wetting behavior so that there is a
286
larger deviation between our MD simulation and the experimental reported. The deviation
287
may be due to the reasons below: 1) Al droplet is oxidized during the process of sessile drop
288
technique, resulting in the larger measurement result than MD simulation; 2) the materials in
289
the MD simulation are ideal pure substances, which contain impurities in the sessile drop
290
technique. 3）the substrate surface is rough in the sessile drop technique, but which is smooth
291
in the MD simulation. Experimental researches39,55 have proved that the roughness of surface
292
has a great influence on wetting behaviors. Hence, the effects of roughness could be studied
293
in the following.
294 295
Table 1
296
The degree of graphitization U and the distance between the layers of carbon atoms d
297 298
U
0.1
d/Å
3.42366
0.3 3.39614
0.5
0.7
3.3755
3.36174
1.0 3.354
299
300 301
Fig. 6. (a) The diameter of contact circle, (b) the contact angles of Al droplet in different
302
graphitic degrees with error bars of standard deviation, (c) the CMDZ of Al liquid as a
303
function of time.
304 305 306
3.3. Dependence of the wettability on the surface roughness It is well known that, the wetting behaviors of droplet on rough surface can be described 56
and Cassie states
57
307
by Wenzel
. According to the influences of surface energy and
308
topography, either the Wenzel state can be formed when a droplet in contact with a roughened
309
substrate, where the liquid atoms fully penetrates into the surface grooves, or the Cassie state,
310
where the liquid interface remains suspended at the tips of surface protrusions and small
311
pockets of air become trapped between the surface and the liquid.
312
Because the microstructure of solid surface has an important influence on wettability, it
313
is significant to understand the surface wettability and its influencing factors so that we can
314
control the surface wettability effectively. In this part, some systems with Al atoms and
315
grooved AC surfaces were simulated in the NVT ensemble at 970K. The initial configurations
316
contain an Al cube with 3430 atoms placed above grooved substrates (Fig. 7a). The substrates
317
were prepared with the lateral sizes of 149.54Å×149.54Å and the thickness of the substrates
318
was 21.345Å, there have the same grooves in the x and y directions so that the rough surface
319
can be formed with square matrix shape. According to Cassie-Baxter theory 55, we can use
320
rough factor γ to character the surface roughness, and γ can be obtained by the formula
321
below: vwx
γ = 1 + wyz{
322
（12）
323
The parameters a, h and b represent the width of square column, depth and width of groove.
324
Then, the values of rough factor γ will be set to 2.0(R2), 3.0(R3) and 4.0(R4) in this MD
325
simulation.
326
Fig. 7(b) shows the equilibrium states for the spreading of Al droplets on the surfaces
327
with different roughness. The Al atoms spreading into grooves can be observed on the R2 and
328
R3 surfaces, but the grooves are not filled with Al atoms. Hence, the wetting process will
329
maintain a transition state from the state of Cassie to Wenzel. On the contrary, the Al atoms
330
will not spreading into grooves on the R4, which is a wetting state of Cassie. Because of the
331
stable b, we can know that the wetting state will change from the transition wetting state to
332
Cassie state with the increased h. This also can be proved by CMDZ curves of Fig. 8a, the
333
CMDZ values of Al atoms are larger than that on smooth surface when roughness equals 2 and
334
3, which means that some Al atoms will move into grooves to reach the transition state of
335
wetting. And compared to R3, the Al droplet on R2 surface will be closer to the Wenzel state.
336
Also, the smaller CMDZ of Al droplet explains the form of Cassie state when the roughness
337
equals 4.
338
The influences of surface structure on wettability includes two aspects: 1) the surface
339
grooves constitute the resistance of the droplet to spread and infiltrate on the solid surface; 2)
340
when the droplet penetrates into grooves, the volume of the droplet above the three-phase
341
contact line is reduced and the height is lowered, this will result in a decrease on the contact
342
angle. And due to the presence of a rough surface pin effect 54, it is difficult for the droplet to
343
spread freely on the rough surface, which reduces the spreading width of the droplet. As seen
344
in Fig. 8b, the variation tendency of the MSDX curves of Al atoms (on the R2 and R3 surfaces)
345
is almost same with larger slopes than that on the R4 surface. In addition, by computing the
346
equilibrium spreading diameter D of the Al droplets, we can quantitatively reveal their
347
spreading properties on the different rough surfaces. On the R2, R3 and R4 surfaces, the D are
348
49.2414Å, 45.1519Å and 45.0097Å, respectively, which are all smaller than that on the AC or
349
graphite surfaces (74.5958Å). These phenomena express that the diffusion ability of Al atoms
350
will reduce due to the increase of roughness. In other words, this is resulted by the energy
351
barriers of rough surface.
352
It is worth mentioning that the calculated contact angles of Al droplet on R2, R3 and R4
353
surfaces are 106°（±2.14°）, 113°（±1.63°） and 120°（±1.87°）. The wettability of Al liquid
354
changes from a wettable state to a non-wettable state when the surface becomes rough. It
355
shows that the roughness can greatly affect the wetting behaviors. The related reference has
356
reported the liquid Al wetting on rough graphene surface by MD simulation 37. The simulation
357
describes that the rough surface reduces the wettability of liquid Al on substrates which is
358
consistent with our work. In addition, our results are also qualitatively consistent with
359
experimental reports, which all exhibit the non-wettable character of Al droplet on cathode
360
carbon blocks surfaces. While, the contact angles measured by our MD simulation are still
361
smaller than experiment (120°-160°), this is because the Al liquid will be easily oxidized and
362
covered with a alumina film during the process of the sessile drop technique at 970K 58. The
363
results also reveal the reason of the bad wettability between Al liquid and cathode carbon
364
blocks in the aluminum electrolysis industry, which is largely determined by the rough
365
surfaces of cathode carbon blocks.
366
367
368 369
Fig. 7. (a) The initial configuration of Al droplet on rough surface. (b) Snapshots of Al
370
droplets spreading on rough surfaces in the balanced state, and roughness equals 2, 3 and 4.
371 372 373
Fig. 8. (a) The MSDX (b) CMDZ curves of Al droplets on the surfaces with different roughness.
374 375
In addition, other models with different width of grooves along x and y directions were
376
built to investigate the effect of grooves’ width on the wetting behavior of Al droplet. As
377
shown in Fig. 9, Al atoms enter the grooves and realize a Wenzel wetting state with the width
378
of grooves increases. Compared with the system of roughness=4 (the depth of grooves is
379
equal to the two systems), it can be concluded that the wetting state will transition from
380
Cassie to Wenzel state with the increased width of grooves, meaning that the enough
381
roughness can improve the wettability of Al liquid.
382 383 384
Fig. 9. The balanced configurations of different width of grooves, the width of left=8Å, the right=11Å.
385 386
3.4 Free energy and thermodynamic properties analysis
387
The free energy difference between the initial balanced state and the perturbed separation
388
systems for Al droplet on different surfaces calculated by the FEP method were presented in
389
Fig. 10. The difference represents the work done to remove Al droplet from initial system to
390
perturbed systems. Results show that the solid-liquid adhesion decreases with the decrease in
391
graphitization of the graphite. Consequently, the interaction of Al atoms with the substrate
392
decreases. The previous studies have reported the Wenzel state is more favorable in terms of
393
energy than the Cassie state 59. In the Wenzel and transition states, the Al atoms contact with
394
the substrate more effectively so that the interactions between them. The Al droplet in the R2
395
and R3 systems are in the Wenzel and transition states. Hence, the solid-liquid adhesion in the
396
R2 and R3 systems are greater compared to that in the R4 system (Cassie state) so that the
397
contact angle of Al droplet increases with the roughness increases.
398
In this work, another 2ns is necessary for the steered molecular dynamics simulation to
399
compute PMF at 970K. Fig. 10 exhibits the PMF versus time for removing Al droplet from
400
the graphite surface, AC surface and rough AC surfaces. In the all systems, the PMF curves
401
monotonic increase firstly, and then maintain a constant after the Al droplet away from the
402
substrate surfaces. The turn point represents the complete solid-liquid separation.
403
Comparisons of the PMF for different substrates reveal that the interactions between Al
404
droplet and substrates follow the sequence: Graphite > AC > R=2 > R=3 > R=4, which mean
405
the Al droplet on graphite surface has the best wettability and the minimum contact angle. In
406
addition, the interactions will decrease with the increase of roughness, resulting in the poor
407
wettability and solid-liquid adhesion.
408
409
Fig. 10. (a) The free energy difference and (b) the PMF of solid-liquid separation for Al
410
droplet on different substrates.
411 412
According to the relation Helmholtz free energy ∆A = ∆U-T∆S, the free energy is further
413
split into entropic and energetic components. ∆U is the internal energy difference, which can
414
be calculated by the sum of the potential energy difference between Al droplet and other
415
components. Accordingly, the entropy ∆S can be obtained and the T is the temperature of
416
system. Fig. 11 shows the free energy ∆A, energy ∆U and entropy ∆S for Al droplet on
417
substrates. Results exhibit that there is greater energetic contributions and ∆S in the
418
Al-graphite system than Al-AC system. The energetic contributions decreases with the
419
roughness increases in the Al-rough AC systems. And the entropic difference ∆S is decreased
420
with the increased roughness, which explained that the less entropy will lose with the
421
increased roughness during the adhesion process. These observations reveal that the energetic
422
contributions are beneficial to the Al droplet adhesion. Conversely, the entropic contributions
423
are not good for adhesion of Al droplet. The result is consistent with the previous study 60. In
424
addition, the Fig. 11 also shows that the system obtain more energy will lose more entropy,
425
which fits perfectly the thermodynamic investigation of the substrate strength dependence of
426
the wettability 60.
427 428
Fig. 11. Changes in free energy, internal energy and entropy of the (a) Al-graphite and Al-AC systems (b) R=2, R=3, R=4 rough AC-Al systems.
429 430 431
4. Conclusions
432
In summary, the wetting behaviors of Al droplet on the AC and graphite have been
433
studied by performing MD simulation. Here, we elaborated key effect of temperature,
434
substrate material, graphitization and surface roughness on the wetting behaviors. The
435
simulation results show that the high temperature can improve the wettability of Al droplet.
436
The Al droplet on the graphite substrate has a smaller contact angle than that on the AC
437
substrate at the same temperature, and both still maintain the state of wetting. The MSD
438
curves explain that the Al atoms on graphite substrate have stronger diffusion ability than
439
which on the AC substrate, so that a larger contact circle can be formed. As for the graphitized
440
surfaces, we can know that the contact angle will increase with the reduced degree of
441
graphitization. Though, the wetting performance of Al droplet on graphitized surface is still
442
better than which on AC substrate. On the rough surface, the maximum contact angle can be
443
found than other systems we researched due to the presence of pinning effect. The wettability
444
will change from the transition wetting state to the Cassie state, so that the wettability of Al
445
droplet will become very poor. The wetting state will transition from Cassie to Wenzel state
446
with the increased width of grooves. In addition, the free energy analysis reveals the
447
solid-liquid adhesion decreases with the graphitization decreases and the roughness increases,
448
then the wettability decreases. The thermodynamic properties analysis shows the energetic
449
contributions are beneficial to the Al droplet adhesion but the entropic contributions are not
450
good for adhesion of Al droplet.
451
In general, our results reveal that there is a good wettability between Al droplet and
452
Al/graphite in an ideal environment, and the roughness of cathode surface maybe the most
453
important factor for the poor wettability of Al liquid. These studies may help shed light on
454
understanding and controlling the wetting behaviors of liquid metals. What’s more, the
455
effective control of wettability is significant for the development of wettable cathode
456
materials for aluminum cells.
457
Acknowledgements
458
We sincerely acknowledge the High Performance Computing Center of Central South
459
University, China. This work was financially supported by the National Natural Science
460
Foundation of China (No. 51674302) and the Innovation-Driven Project of Central South
461
University (No. 2016CX019).
462 463
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Highlights： 1. Molecular dynamics simulation is applied to study the wettability of Al liquid. 2. The degrees of graphitization are considered in this manuscript. 3. Good wettability is found between Al liquid and amorphous carbon/graphite. 4. The roughness will change the wetting state from wetting to non-wetting. 5. Why the Al liquid has the poor wettability on cathode of Aluminum reduction cell?
Conflict of interest statement： The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.