Supplemental Material
Supplemental Material for the paper entitled “Charge-Signal Multiplication
Mediated by Urea Wires inside Y-Shaped Carbon Nanotubes” by Mei Lv, Bing He,
Zengrong Liu, Peng Xiu, and Yusong Tu
PS1: Detailed Procedure of System Preparation
The simulation system was prepared as follows. First, we prepared the 1 M urea
solution composed of 79 urea and 4116 water molecules, with box sizes of
4.5×5.6×5.2 nm3. Second, this aqueous urea system was relaxed for 5 ns at the
constant volume and a temperature of 400 K to obtain the dispersive urea solution
(here we used a high temperature for system-relaxation because urea usually
self-aggregates at room temperature1). Third, a Y-SWNT was placed at the central
region of the solvation box with those water/urea molecules removed if the distance
between water oxygen and any Y-SWNT atom was <2.7 Å, and if the distance
between any heavy atom of urea and Y-SWNT atom was <2.4 Ǻ.2 The concentration
of the resulting urea solution is also ~1 M. Fourth, the obtained system was
equilibrated for 5 ns at a constant temperature and pressure (300K, 1 atm), followed
by a 1 ns NVT simulation at 300 K for further relaxation of the system. Last, a single
charge of magnitude 1.0e was introduced and positioned at the center of a fourth
carbon ring of the main tube, with a counterion position restrained at the edge of the
box to keep the system charge-neutral. Then this system was used as the starting
structure for the production run.
PS2: Urea-Induced Drying of Y-SWNTs with A Positive Charge
Fig. S1 shows when q = +e, the number of solvents inside Y-SWNT sub-tubes with
respect to the time. We have performed two independent simulations, namely, case 1
(A-C) and case 2 (D-F). The urea-induced drying process for q = +e is similar to that
for q = -e (see Fig. 1 in the main text), despite longer equilibrium times required
(approximately 500 and 600 ns, for cases 1 and 2, respectively) and a slightly larger
amount of the remaining water.
Fig. S1. Number of solvents (urea/water) within the main tube (MT) and 2 branch
tubes (BT1 and BT2) of the Y-SWNT with a positively external charge (of magnitude
1.0e) as a function of the time. Subfigures A-C and D-F denote cases 1 and 2 (two
independent simulations performed at same conditions), respectively.
Table S1 summarizes the average number of solvents inside Y-SWNT sub-tubes in
equilibrium, together with the corresponding Pperfect, for two cases of the positive
charge. Two independent simulations yield similar results. For both branch tubes, the
tubes are occupied by ~4 urea molecules and the Pperfect are high. Although the Pperfect
is not high for the main tube, as indicated in the main text, the “defective” urea wire
in MT do not impede signal multiplication which is dependent upon urea wires in
branch tubes, rather than the main tube. One may ask that why the data for two branch
tubes are unequal. The reason is that despite the symmetric nature of two branch tubes,
the potential energy profile of urea along the tube is asymmetric due to urea’s
concerted orientations in the confined environment,3 thus breaking the symmetry of
the system within a finite time period.
Table S1: Average number of urea ( N urea ) and water molecules ( N water ) inside
sub-tubes (MT/BT1/BT2) of the Y-SWNT in equilibriuma, as well as the occurrence
probabilities for the “perfect” b urea wire (Pperfect), for two independent simulations
(cases 1 and 2) when q = +e.
Case 1
Case 2
Sub-tubes
a
N urea
N water
Pperfect
N urea
N water
Pperfect
MT
3.87
0.31
71.3%
3.74
0.53
61.4%
BT1
3.95
0.15
85.6%
3.93
0.04
95.7%
BT2
3.94
0.03
97.3%
3.92
0.21
80.2%
The data were averaged over the last 300 ns (500–800 ns and 600–900 ns, for the
case1 and case 2, respectively) in the “drying simulations”.
b
At this time, there is no water inside this sub-tube.
PS3: Statistics for Inner Solvents in Signal-Multiplication Simulations
Table S2 summarizes the average number of inner solvent molecules and the
corresponding Pperfect in signal-multiplication simulations. The results are similar to
those of the “drying simulations (in equilibrium)” (see Tables 1 and S1), indicating
that the nearly perfect Y-shaped urea wires persist in signal-multiplication
simulations.
Table S2: Average number of urea ( N urea ) and water molecules ( N water ) inside
sub-tubes (MT/BT1/BT2) of the Y-SWNT, as well as the occurrence probabilities for
“perfect wire” (Pperfect), in signal-multiplication simulations.
q = -e
q = +e (case 1)
q = +e (case 2)
Sub-tubes
N urea
N water
Pperfect
N urea
N water
Pperfect
N urea
N water
Pperfect
MT
4.00
1.00
0.00%
3.86
0.31
72.95%
3.90
0.24
77.33%
BT1
3.99
0.00
99.99%
3.95
0.14
86.50%
3.95
0.02
98.19%
BT2
3.99
0.00
99.99%
3.94
0.04
96.34%
3.94
0.16
84.59%
PS4: Altering Charge Locations on the Main Tube
In this study, the charges are positioned at the center of a fourth carbon ring of the
main tube. To investigate the influence of charge locations on the signal multiplication,
we performed simulations with the charge located at the center of the second, twelfth,
and fourteenth rings of the MT, respectively. Fig. S2 shows that as the charge position
shifts, the monitored molecule (water and urea, for q = -e and q = +e cases,
respectively) shifts accordingly; however, urea’s structures and orientations at the
Y-junction and in branch tubes are largely unaffected by the alteration of charge
locations, indicating that the urea-mediated signal multiplication is insensitive to the
charge locations (provided that the charge is located on the main tube). It is interesting
to note that when the charge is approaching the Y-junction (i.e., placed at the center of
a fourteenth ring of the MT; see Fig. S2C), the orientations of urea wires in two
branch tubes are modulated by a water molecule (which is just the monitored
molecule).
Fig. S2. Representative snapshots to show Y-shaped urea wires inside Y-SWNTs
with different charge locations. Subfigures A, B and C represent the charges located
at the center of the second, twelfth, and fourteenth rings of the MT, respectively. The
imposed charge is represented by a green sphere; some carbon atoms of Y-SWNTs
are omitted for clarity. (Insets) Close-ups for typical configurations of the monitored
molecules and their neighboring molecules.
PS5: Rerunning Simulations Using the OPLS Urea Model
As noted in the main text, OPLS and KBFF models are the most widely used urea
models in simulating aqueous urea systems. However, OPLS urea lacks van der Waals
parameters for the hydrogen, whereas the dispersion interaction of hydrogen atoms
with the nanotube wall is proven to be non-negligible when the nanotube is narrow.4
Therefore, the OPLS model may be less accurate than the KBFF model for the current
study. But in order to investigate the robustness of the urea-mediated
signal-multiplication, we rerun the simulations employing the OPLS urea model.
To accelerate the equilibrating process, the OPLS-urea-model simulations start
from the equilibrium structures obtained from KBFF-urea-model simulations. It has
been found that equilibrium has been reached within 300 ns for both negative and
positive charges. Then we perform 500-ns and 1-μs simulations for q = -e and q = +e,
respectively, to calculate the average number of inner solvents and to study the dipole
orientations of urea wires versus the time (the simulation time for q = +e is larger than
that for q = -e, because we want to capture the flipping events in the positive-charge
simulation). The results are displayed in Table S3 and Fig. S3.
Table S3: Average number of urea ( N urea ) and water molecules ( N water ) inside
sub-tubes (MT/BT1/BT2) in equilibrium of OPLS-urea-model simulations, as well as
the occurrence probabilities for the “perfect” urea wire (Pperfect), with different
external charges.
q = -e
q = +e
Sub-tubes
N urea
N water
Pperfect
N urea
N water
Pperfect
MT
3.76
1.28
0.0%
3.85
0.46
57.3%
BT1
3.63
0.48
60.8%
3.62
0.51
57.1%
BT2
3.49
0.70
46.6%
3.66
0.51
56.4%
After the simulations have reached equilibrium, the Y-SWNT interiors are mostly
filled by urea, with high occurrence probabilities of “perfect” urea wires for branch
tubes (see Table S3). In addition, the monitored molecules are water and urea for q =
-e and q = +e, respectively. These results are similar to those from KBFF-urea-model
simulations. Compared with Table 1 in the main text, the number of remaining water
is slightly larger, and Pperfect is lower. This is due to the lack of vdW parameters on
OPLS-urea’s hydrogen, which underestimates the urea-nanotube interactions (and
yields less accurate results as compared with the KBFF model).
Fig. S3 displays the average dipole orientations [  (t ) ] of urea wires as a function
of times.  (t ) for the MT are stable (unchanged versus times), and are opposite for q
= -e and q = +e. Hence, the charge signal has been readily converted into the
orientation of the urea wire in the MT. For q = -e,  (t ) for two branch tubes are
mostly in the same orientation with small fluctuations [occasionally,  (t ) for BT2
can flip (it seems that the orientations of OPLS urea wires in branch tubes are less
stable than the KBFF one, because of the mixture with the water defects) and thus
 (t ) for two branch tubes are in different orientations, but this state cannot persist for
a long time]; whereas for q = +e,  (t ) for two branch tubes can flip (on average, the
flipping occurs with a time period of ~300 ns) and they are mostly in different
orientations. Thus, we can distinguish the sign of the charge via identifying  (t ) for
two branch tubes. These results are consistent with those of KBFF-urea-model
simulations, indicating that signal conversion and multiplication persist for the OPLS
urea model. In comparison with the KBFF cases (see Fig. 3 in the main text),
OPLS-urea-wires are found to flip more easily than KBFF one. The possible reasons
are as follows: First, as mentioned earlier, the Y-shaped urea wires in OPLS cases are
mixed with more “water defects”, while water flips more easily than urea. Second,
OPLS urea has no vdW parameters on its hydrogen atoms, so it undergoes smaller
steric repulsion in flipping.
Fig. S3. Trajectory of average dipole angle  (t ) of urea orientations in each tube
of the Y-SWNT in OPLS-urea-model simulations, for q = -e (left panel) and q = +e
(right panel). MT, BT1 and BT2 represent the main tube and two branch tubes,
respectively.
In summary, when we employ the OPLS urea model instead of the KBFF model,
the formation of Y-shaped urea wires as well as signal conversion and multiplication
are also available. Thus, the results with the OPLS model are consistent with those of
the KBFF model, in spite of slight differences between them (the KBFF results may
be more accurate, since OPLS urea lacks vdW parameters on the hydrogen, which
underestimates urea-nanotube interactions). We conclude that urea’s capability of
converting and multiplying charge signals is robust, independent of the urea model
used.
References for Supplemental Material:
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105, 16928 (2008).
3
P. Xiu, Y. Tu, X. Tian, H. Fang, and R. Zhou, Nanoscale 4, 652 (2012).
4
X. Tian, Z. Wang, Z. Yang, P. Xiu, and B. Zhou, J. Phys. D: Appl. Phys. 46,
395302 (2013).