Supplementary material
Molecular distribution
The average fraction of molecules x(i) belonging to the states of monomers (i=0), linear
chain (i=1), branched linear chain (i=2), cyclic cluster (i=3), and branched cyclic cluster
(i=4) is presented as a function of temperature T at several pressures in Figure S.1. The
different “curves” are identified with a specific coloured symbol in order to facilitate
distinction. Firstly, an analysis of the behaviour with increasing T at a fixed pressure
(p=25 MPa) follows. Monomers are virtually absent at the lowest temperatures, but
above 300 K x(0) exhibits an increasing behaviour as T is raised and they represent the
most probable state at high levels. As regards associated molecules, the fraction of them
belonging to linear chains, either branched or not, is a function with a maximum
whereas the curves corresponding to cyclic aggregates exhibit a regular decreasing
behaviour. More specifically for each type of cluster, the fraction of molecules taking
part of branched linear aggregates x(2) is maximum at around 300 K and then decreases
to negligible values above 600 K. The temperature at which the fraction of molecules in
non-branched linear chains x(1) reaches its maximum is higher, around 500 K, and it
represents a certain percentage at high temperatures. On the other hand, the fraction of
molecules in isolated rings x(3) is insignificant throughout the temperature range
whereas that of molecules in branched cyclic clusters x(4) is important only at the
lowest temperatures. Once the individual behaviour of each curve is described, the
variation in the relative importance among them along the temperature interval follows.
At 250 K, most molecules belong to branched structures, either linear or cyclic with
similar probabilities. From 250 K to 300 K, the branched linear chains are the most
occupied state, the fraction of molecules in linear chains increases but it still has a minor
contribution in relation to branched cyclic clusters, and the occupation of the rest of
states, monomers and isolated rings, is virtually negligible. About 300 K is the
temperature at which x(2) reaches its highest values and starts decreasing, as well as that
from which molecules in linear chains prevail over those in branched cyclic clusters.
Molecules in linear chains continues gaining importance and x(1) > x(2) above 400 K
approximately. Thus, linear chains represent the most probable state for molecules from
that temperature to around 600 K, above which the dissociated state dominates. At the
highest temperatures, almost all the molecules are monomers. On the other hand,
increasing pressure favours slightly the occupation of branched structures at low
temperatures and considerably that of linear aggregates in the detriment of monomers at
higher ones, as it is clearly apparent from figures; in fact, at the highest pressure
considered, 500 MPa, the temperature above which monomers prevail over molecules in
linear chains is quite highest, around 800 K, and the mole fractions corresponding to
both states are about 0.6 and 0.4 respectively at the highest temperatures.
Unlike Figure S.1, Figures S.2 and S.3 provide information about the molecular
size distribution. Particularly, Figure S.2 shows the variation with s of the average
fraction of molecules in the different states of a certain size x(i,s) at several
temperatures for the fixed pressure of 25 MPa. At the lowest temperature, 250 K,
molecules can occupy aggregates of any size. The behaviour of the different curves is
similar: they reach their highest values at low sizes and then decrease. The size at which
a maximum occurs for non-branched structures, either linear or cyclic, corresponds to 5
units (pentamer); as for branched clusters, it corresponds to 20 units approximately for
linear aggregates and between 10 and 20 for cyclic ones. The variation in the relative
importance among the different curves follows. At low sizes, molecules prefer to form
part of non-branched clusters whereas they are mainly in branched ones at higher sizes.
More specifically, linear clusters represent the most occupied state at s<20 whereas in
the size intervals (20-150) and beyond 150, it corresponds to branched linear clusters
and to both branched linear and cyclic ones, respectively. Increasing temperature (up to
300 K) tends to reduce the probability of occupying long-length clusters and so
increases the fraction of short ones, especially for linear chains, either branched or not,
which are unquestionably the most occupied as it is apparent from figures. Above 300
K, the situation changes considerably. The occupation of aggregates composed by more
than 30 units is negligible. Molecules in cyclic clusters virtually disappear and they are
either associated forming basically short linear structures or dissociated as monomers,
which dominate from that temperature approximately. The curve corresponding to
molecules in linear clusters shows a decreasing behaviour; thus, the dimer is the most
occupied associated state. As for the fraction of molecules in branched linear
aggregates, it follows the previously described behaviour: it is highest at low sizes and
then decreases; increasing temperature makes this maximum decrease and shifts it to
lower sizes. At the highest temperatures, almost all molecules are monomers and only a
small percentage corresponds to associated ones, which form low-sized linear chains,
especially dimers. To sum up, increasing temperature favours the formation of
monomers and the occupation of short linear clusters in the detriment of higher order
clusters. On the other hand, the influence of pressure p on the molecular size
distribution of each state is shown in Figure S.3 for determined temperatures.
Particularly, the results presented correspond to 25 MPa, 100 MPa and 500 MPa as
representative values of the pressure effect and to temperatures at which different
structural situations were found: 275 K, 400 K and 700 K. From a qualitative point of
view, the curves at each temperature remain virtually invariant with p. However, it can
be seen that pressure implies slight changes as for the relative importance among them;
contrary to temperature, increasing pressure favours the occupation of long-length
branched clusters in relation to monomers and short linear chains. The cluster sizes at
which the fractions of molecules belonging to the different types of aggregates exhibit
their maximum values are shown in Table S.I at several temperature and pressure
conditions.
Figure S.4 shows the fraction of molecules belonging to clusters of a certain size
x(s) as a function of size s in order to observe the molecular size distribution regardless
of the type of aggregate. Particularly, these curves are presented at several temperatures
for the fixed pressure of 25 MPa in Fig. S.4(a) and at several pressures for determined
temperatures in Fig. S.4(b) in order to clearly appreciate the effect provoked by each
magnitude. As it is apparent from Fig. S.4(a), increasing temperature favours the
occupation of short aggregates in such a way that the fraction of molecules in clusters
formed by more than 10 units is insignificant from 600 K approximately. Besides, a
change in the shape of the curve as a consequence of increasing T can be appreciated:
below 400 K, it exhibits a maximum and the higher the temperature is, the narrower the
maximum is; above this level, the maximum disappears and so the curve shows a
decreasing behaviour throughout the size range. Thus, whereas at room temperature,
around 300 K, the maximum of occupation corresponds to a pentamer, the most
probable state for molecules at high temperatures is the dimer. The variation with
pressure is opposite and quite less notable as it can be observed in Fig. S.4(b); the
fraction of molecules in long-length clusters increases as p is raised, which is basically
appreciable at high temperatures.
To sum up, the number of associated molecules increases with decreasing
temperature and increasing pressure. The influence of these magnitudes on the
occupation of the different hydrogen-bonding states follows. At the lowest supercritical
pressure 25 MPa and at the lowest temperatures, between 250 K and 300 K, methanol
molecules prefer to belong to the following clusters (in the order cited): branched linear
chain, branched cyclic cluster, and linear chain; the probability of occupying the rest of
states is insignificant. From 300 K, the situation changes considerably. At 400 K, the
highest fractions correspond to linear chains, either branched or not. At 500 K, the
fraction of molecules belonging to branched linear clusters is, however, quite low and
takes negligible values at higher temperatures; linear aggregates are the most probable
state for molecules at this temperature but it looses significance quickly in relation to
monomers and the vast majority of molecules are dissociated at high temperatures. On
the other hand, the most relevant phenomena as a consequence of increasing pressure is
the notable decrease of monomers in favour to the occupation of linear chains beyond
400 K; at lower temperatures, the influence of pressure is virtually negligible. As
regards the molecular size distribution, at the fixed pressure of 25 MPa and at 250 K,
almost all the molecules are associated forming aggregates of any size. The fractions of
occupying each type of cluster are curves with a maximum at low sizes for linear and
cyclic aggregates and at higher ones for branched structures. Thus, at low sizes,
molecules prefer to form part of non-branched aggregates and the opposite holding for
higher s values. Increasing temperature favours the occupation of linear chains in
relation to cyclic ones and shifts the position of the maximum to lower sizes. Contrary
to the temperature effect, pressure favours the occupation of long-length aggregates, but
its influence is quite less notable.
Figure captions
FIG. S.1. Fraction of molecules belonging to the i-type cluster, x(i), as a function of
temperature T at several pressures. ( ) monomers (i=0), (●) linear chains (i=1), (●)
branched linear chains (i=2), (■) cyclic clusters (i=3), and (■) branched cyclic clusters
(i=4).
FIG. S.2. Fraction of molecules belonging to i-type and s-size clusters, x(i,s), plotted
against s at several temperatures for p=25 MPa. ( ) monomers (i=0), (●) linear chains
(i=1), (●) branched linear chains (i=2), (■) cyclic clusters (i=3), and (■) branched cyclic
clusters (i=4).
FIG. S.3. Fraction of molecules belonging to i-type and s-size clusters, x(i,s), plotted
against s at several pressures for selected temperatures. ( ) monomers (i=0), (●) linear
chains (i=1), (●) branched linear chains (i=2), (■) cyclic clusters (i=3), and (■)
branched cyclic clusters (i=4).
FIG. S.4. Fraction of molecules belonging to s-size clusters, x(s), plotted against s. (a)
(●) 250 K, (●) 275 K, (●) 300 K, (●) 400 K, (●) 500 K, and (●) 600 K for p=25 MPa.
(b) (●) 25 MPa, and (●) 100 MPa for selected temperatures.
1
25 MPa
500 MPa
100 MPa
0.8
x (i)
0.6
0.4
0.2
0
200
400
600
T/K
FIG. S.1.
800
1000 200
400
600
T/K
800
1000 200
400
600
T/K
800
1000
0.016
275 K
250 K
0.006
0.012
0.004
0.008
0.002
0.004
300 K
0.016
0.012
0.012
xi,s
0.008
0.004
0.008
0
0
0
0
4
0
8 12 16 20
4
0
8 12 16 20
4
8 12 16 20
0.004
0
0
50
100
150
200
250 0
50
100
150
s
200
250 0
50
100
s
0.3
150
200
250
8
10
s
0.3
1
400 K
500 K
900 K
0.8
0.2
0.2
xi,s
0.6
0.4
0.1
0.1
0.2
0
0
0
10
20
30
s
FIG. S.2.
40
50
0
0
10
20
30
s
40
50
0
2
4
6
s
T= 275 K
0.01
25 MPa
100 MPa
0.01
0.01
0.008
0.008
0.006
0.006
0.004
0.004
0.002
0.002
0.008
500 MPa
0.008
0.006
0.004
xi,s
0.006
0
0
0.004
0.002
0
4
0
8 12 16 20
4
0
8 12 16 20
0
4
8 12 16 20
0.002
0
0
50
100
150
200
250 0
50
100
s
150
200
250 0
50
100
150
s
200
250
s
T= 400 K
0.1
25 MPa
100 MPa
500 MPa
0.08
xi,s
0.06
0.04
0.02
0
0
10
20
30
40
50 0
10
20
s
30
40
50 0
10
20
s
30
40
50
s
T= 700 K
0.8
25 MPa
100 MPa
500 MPa
xi,s
0.6
0.4
0.2
0
0
4
8
12
s
FIG. S.3.
16
20
0
4
8
12
s
16
20
0
4
8
12
s
16
20
(a)
0.25
0.02
0.2
0.015
0.15
xs
xs
0.025
0.01
0.1
0.005
0.05
0
0
0
64
128
192
0
256
5
10
15
20
25
30
s
s
(b)
0.016
0.1
400 K
275 K
0.08
0.012
xs
xs
0.06
0.008
0.04
0.004
0.02
0
FIG. S.4.
0
64
128
s
192
256
0
0
10
20
30
s
40
50
Table S.I. Cluster size of highest molecular occupation for the different types of
aggregates at several temperature and pressure conditions.
p=25 MPa
p=100 MPa
p=500 MPa
Type of aggregate (i)
T/ K
1
2
3
4
1
2
3
4
1
2
3
4
275
5
26
5
12
6
21
5
26
5
22
5
36
300
5
21
5
13
4
19
5
17
4
23
5
23
400
2
10
5
7
3
11
5
8
3
12
5
9
500
2
6
4
6
2
7
4
6
2
8
4
7
600
2
5
3
5
2
5
4
5
2
6
4
6
700
2
4
3
4
2
5
3
5
2
6
3
5
800
2
4
2
4
2
4
3
4
2
5
3
5
900
2
4
2
3
2
4
3
4
2
5
3
4
1000
2
4
2
3
2
4
2
3
2
4
3
4