Supplementary Material: Melting point trends and solid phase behaviors of
model salts with ion size asymmetry and distributed cation charge
E. K. Lindenberg and G. N. Pateya)
Department of Chemistry, University of British Columbia, Vancouver BC, Canada,
V6T 1Z1
BAROSTAT PARAMETERS
The simulations in the cooling traces use an isotropic
Parrinello-Rahman barostat with a relaxation time of 5.0
ps and compressibility of 3.0×10−5 bar−1 . The same
barostat is used for the heating simulations of the spontaneously crystallized configurations. The pressure is maintained at P = 1.0 bar with an anisotropic ParrinelloRahman barostat when the prepared crystal is heated.
The relaxation time is 5.0 ps along the three primary axes
and zero otherwise and the compressibility is 3.0×10−5
bar−1 . For the two-phase simulations, an anisotropic
Parrinello-Rahman barostat is employed with a relaxation time of 50.0 ps along the three primary axes and
zero otherwise, and a compressibility of 3.0×10−5 bar−1 .
For the simulations that use an anisotropic barostat
(heating the prepared crystals and the two-phase simulations), sometimes the minimum image convention is violated, and Gromacs will abort the simulation. The violations occur when the liquid cell shape fluctuates after the
superheated crystals have melted. When this happens,
the system should be a liquid. To have a complete set
of simulation results, the simulation is restarted from the
initial configuration using an isotropic barostat with the
same relaxation time and compressibility. The change in
barostat type does not have any significant effect on the
results.
SHORT-RANGE CUTOFF DISTANCES
The short-range cutoffs vary with the size ratios and
are near 3.2σ+ . Long-range corrections are applied to
the energies and pressures. The shifted and truncated
form of the potential used for the short-range interactions
neglects contributions beyond Rcut . The correction terms
for the energy and pressure take the form of integrals
from Rcut to infinity, and are evaluated by assuming a
uniform density of LJ particles [g(r) = 1 beyond Rcut ].
a) Electronic
mail: [email protected]
Table SI. The short range interaction cutoff values.
Size Ratio
Label
A100
A133
A167
A200
A233
A267
A300
σ+
(nm)
0.500
0.571
0.625
0.667
0.700
0.727
0.750
Rcut
(nm)
1.70
1.83
2.00
2.14
2.24
2.33
2.40
B133
B167
B200
B233
B267
B300
0.667
0.833
1.000
1.167
1.333
1.500
2.14
2.67
3.20
3.73
4.27
4.80
ION MASSES
Table SII gives the masses placed at each interaction
site on the cations. The mass distribution was determined to keep the moments of inertia approximately constant while keeping the total cation mass at 120 amu.
Table SII. The mass distribution for the cations with two
interaction sites. The total mass of each ion is 120 amu
(1.993 × 10−25 kg), and the mass distribution over the interaction sites varies with the separation distance d (defined
in the main text).
d
(0.01 nm)
0
6
10
14
18
22
26
30
≥ 34
Ion Center Mass
(amu)
120.00
70.00
102.00
112.00
115.00
116.75
117.75
118.25
118.70
Off-center Site Mass
(amu)
50.00
18.00
8.00
5.00
3.25
2.25
1.75
1.30
2
CRYSTAL STRUCTURES
Var-CsCl
For all snapshots shown, the cation centers (CM) are
drawn in blue, the off-center cation charge sites (CC) in
white, and the anion centers (AM) in red. The spheres
are not drawn to scale; the off-center sites on the cations
are embedded within the cation volume. The blue cation
spheres are drawn smaller to expose the locations of the
white off-center charge sites.
The crystal structure labeled Var-CsCl in Table II of
the main text is so labeled because it is a variation on
the CsCl structure. The cations are orientationally ordered such that the crystal structure can maintain ion
pairs. The unit cell of the Var-CsCl is shown in isolation in Fig. S2, and the entire simulation box in Fig. S3.
The unit cell is approximate insofar as the ion positions
have not been refined from the final configuration of the
simulation.
CsCl
An example of the CsCl crystal is shown in Fig. S1.
The snapshot is the final configuration at T = 400 K for
the A133 2L67-10 - 1C salt during the heating trace of the
prepared CsCl structure. The cations are orientationally
disordered, as shown by the variation in the directions
that the off-center cation charge sites point (white).
Figure S2. Approximate unit cell of the crystal structure
labeled Var-CsCl. The structure is a variation on the CsCl
structure that accommodates ion pairs. The color scheme is
the same as in Fig. S1.
Figure S1. Snapshot of the CsCl structure for the A133 2L6710 - 1C salt from the heating trace of the prepared CsCl crystal. This particular salt maintains the CsCl structure (with
orientational disorder in the cations) until it melts between
Ts = 1000 K and Tl = 1050 K. The anion centers, cation
centers, and cation off-center charge sites are shown in red,
blue, and white, respectively. The ion centers are not shown
to scale to highlight the crystal packing as well as to expose
the CC sites (white) which are embedded inside the cation
volume.
The unit cell shown in Fig. S2 is similar to two stacked
CsCl-type unit cells if we consider the cation centers
(blue) and anion centers (red) only. The deviation from
the CsCl structure accommodates ion pairs. The structure is a viable crystal structure for the A100 2L67-22
- 1C salt. It is also a candidate structure for the lower
temperature crystal of the A100 2L67-18 - 1C salt.
Figure S3. The final configuration of the A100 2L67-22 - 1C
salt from a simulation at T = 100 K. The color scheme is the
same as in Fig. S1.
3
111n
Var-111n
The crystal structure labeled 111n was discussed at
length in earlier work (See reference 8 in the main text).
The snapshot in Fig. S4 is the A133 2L67-22 - 1C salt at
the end of the simulation at T = 400 K during the heating
of the prepared 111n crystal. The ions are arranged in
layers that maintain strong directional ion pairs.
The unit cell shown in Fig. S6 is taken directly from
the final snapshot of a simulation at T = 200 K of the
B133 2L67-22 - 1C salt. The particle positions have not
been refined. The crystal structure is similar to the 111n
structure reported in earlier work, and therefore labeled
Var-111n . Like the 111n structure, the Var-111n accommodates ion pairs that form electrostatic- and LennardJones-dominated layers. The primary differences between the 111n and Var-111n are the skewing of the ion
pairs and the resulting triclinic unit cell. The Var-111n
structure is a candidate structure for the B133 2L67-22 1C and B133 2L67-26 - 1C salts.
(a)
Figure S4. Snapshot of the 111n structure for the A133 2L6722 - 1C salt from the heating trace of the prepared 111n crystal. The color scheme is the same as in Fig. S1.
A rotated view of the crystal is shown in Fig. S5, which
highlights the similarity to the NaCl structure (shown below in Fig. S9). If the cations become rotationally active
in the solid as the 111n structure is heated, the salt will
rearrange from the 111n crystal, which prevents cation
reorientations, into the NaCl structure, which permits
cation reorientations.
Figure S5. A rotated view of the same snapshot of the 111n
structure shown in Fig. S4. This view highlights the similarities between the 111n structure and the NaCl structure. The
color scheme is the same as in Fig. S1.
(b)
Figure S6. Two faces of the approximate unit cell of the
crystal structure labeled Var-111n . The view in (a) is down
the y-axis into the xz-plane, and the view in (b) is rotated 90◦ ,
looking down the x-axis at the yz-plane. The color scheme is
the same as in Fig. S1.
The whole simulation cell is shown in Fig. S7. The
stacking pattern shown highlights the extra space required by the larger cation centers (blue spheres) compared to the 111n structure.
Figure S7. The final configuration of the B133 2L67-22 - 1C
salt from a simulation at T = 200 K. The particular crystal
shown has a stacking fault in the center. The color scheme is
the same as in Fig. S1.
4
NaCl
NOTE
Example of the NaCl structure are shown in Figs. S8
and S9. The NaCl structure itself is not easily recognized
in Fig. S8. The positions of the white CC sites mark the
cations as orientationally disordered. The NaCl structure
is more easily recognized in the rotated view of Fig. S9,
where the ion centers are stacked by type.
In Figs. 6 and 8 of the main text, the positions of the
dot-dash gray lines do not imply any thermal boundaries.
They are sketched only to group the salts by solid type.
Figure S8. The final configuration of the A233 2L67-10 - 1C
salt during the heating trace of the prepared NaCl crystal at
T = 400 K. The NaCl structure permits cation reorientations,
and the orientational disorder is apparent from the positions
of the CC sites (white). The color scheme is the same as in
Fig. S1.
Figure S9. A rotated view of the configuration shown in
Fig. S8 that shows the cation centers (blue) and anion centers
(red) in the expected NaCl structure of interpenetrating face
centered cubic (fcc) lattices. The color scheme is the same as
in Fig. S1.
5
Table SIII: (Continued)
SET B AVERAGE REDUCED DENSITIES AT Ts
Table SIII: Average reduced densities of the Set B salts.
Each salt is identified by the size ratio and cation charge
displacement distance d (listed in units of 0.01 nm). The
crystal structure is that of the last stable solid before melting, where fcc(+) indicates a fcc lattice of cations. The
highest temperature where the solid persists in the twophase simulations is Ts . The average reduced densities,
3
3
ρ̄∗ = (N+ σ+
+N− σ−
)/V̄ , of both phases are given at Ts . At
each size ratio, the d = 0 entry refers to the charge-centered
1C - 1C salt.
0
6
10
14
18
22
26
Crystal
Structure
CsCl
CsCl
CsCl
CsCl
CsCl
var-111n
var-111n
Ts
(K)
1050
1050
1000
900
750
600
600
ρ̄∗ (s)
—
1.08
1.07
1.08
1.09
1.11
1.12
1.08
ρ̄∗ (l)
—
0.83
0.83
0.85
0.89
0.95
1.00
0.97
B167
0
6
10
14
18
22
26
30
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
111n
111n
1000
950
950
900
800
700
600
550
0.99
1.01
1.00
1.01
1.03
1.05
1.08
1.09
0.83
0.86
0.86
0.88
0.92
0.95
0.98
0.98
B200
0
6
10
14
18
22
26
30
34
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
950
950
900
900
850
800
700
600
550
1.05
1.05
1.06
1.06
1.07
1.07
1.08
1.08
1.08
0.84
0.84
0.87
0.86
0.89
0.90
0.94
0.97
0.97
0
6
10
14
18
22
26
30
34
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
900
900
900
850
800
800
700
650
600
1.08
1.08
1.08
1.09
1.10
1.09
1.11
1.10
1.08
0.85
0.85
0.85
0.87
0.89
0.89
0.93
0.94
0.95
Size
Ratio
B133
B233
d
Continued. . .
Size
Ratio
B267
0
6
10
14
18
22
26
30
34
42
50
Crystal
Structure
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
fcc(+)
fcc(+)
Ts
(K)
800
800
800
800
750
750
700
650
600
500
450
ρ̄∗ (s)
—
1.11
1.11
1.11
1.11
1.12
1.11
1.11
1.11
1.10
1.08
1.04
ρ̄∗ (l)
—
0.88
0.88
0.88
0.88
0.90
0.90
0.92
0.94
0.95
0.97
0.97
0
6
10
14
18
22
26
30
34
42
50
58
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
fcc(+)
fcc(+)
fcc(+)
750
750
750
700
700
700
650
650
600
550
450
450
1.11
1.11
1.11
1.13
1.12
1.11
1.12
1.09
1.09
1.02
1.04
1.02
0.89
0.89
0.89
0.91
0.91
0.91
0.93
0.93
0.95
0.95
0.97
0.95
d
B300
PROPERTIES OF THE SET B SALTS WITH d = 6 AND
d = 10
Table SIV. Properties of the Set B salts with d = 6. These
values were omitted from main text to limit Table III to a
single column. The quantities are defined in the caption for
Table II in the main text.
Size
Ratio
B133
B167
B200
d
6
6
6
10
B233 6
10
B267 6
10
B300 6
10
IP
Crystal
Ts
Ūs ŪsIP /Uiso
∆fus H̄
Structure (K) kJ/mol
(kJ/mol)
CsCl
1050
-426
1.61
31
NaCl
950
-374
1.64
27
NaCl
950
-334
1.67
30
NaCl
900
-337
1.61
28
NaCl
900
-301
1.69
29
NaCl
900
-301
1.63
28
NaCl
800
-275
1.72
25
NaCl
800
-275
1.66
25
NaCl
750
-250
1.71
21
NaCl
750
-250
1.66
21