Supplementary Information
Energy Funnelling and Macromolecular
Conformational Dynamics: A 2D Raman
Correlation Study of Melting PEG
Ashok Zachariah Samuel and Siva Umapathy*
Department of Inorganic and Physical Chemistry
Indian Institute of Science
Bangalore 560012, India.
E-mail: siva.umapathy@gmail.com
Homepage :http://ipc.iisc.ernet.in/~umalab/
Supplementary Information S1
Background: Two-Dimensional Correlation Analysis*
Two dimensional correlation analysis brings out the relationship between the intensity
variation at two different spectral variables, v1 and v2 (e.g. Raman shift), as a function of
~
external perturbation (e.g. temperature, T). Dynamic spectrum ( y ( , t ) ) could be generated,
from the data set over the interval Tmin< t < Tmax, by subtracting suitable reference (e.g. an
average spectrum, y ( ) ) from each spectrum. Let y ( ) be the intensity of Raman band at
wavenumber  , then the dynamic spectrum could be represented as,
 y ( , t )  y ( )
~
y ( , t )  
 0
T min  t  Tmax 

otherwise 
for
Where,
y ( ) 
Tmax
1
 Tmin
Tmax
 y( , t )dt
Tmin
Synchronous correlation analysis reveals the simultaneous changes in the intensity as a
function of the external perturbation. Correlation intensity (cross peak) could be either
positive or negative depending on the relative direction of intensity changes between the
corresponding wavenumbers. The diagonal of the synchronous map gives the autocorrelation
intensity, which will always be positive and represents total magnitude of the intensity
variation under applied perturbation. The synchronous spectrum is defined as,
 (1 , 2 ) 
Tmax
1
 Tmin
Tmax
 y ( , t ). y ( , t )dt
~
~
1
2
Tmin
Asynchronous correlation is used to characterize the out of phase variation response with
respect to the applied perturbation (Oscillatory). The information on the response (for
instance spectral response) which precedes or lags behind the applied perturbation will be
revealed in asynchronous correlation map. Such a comparison of responses between two
different wavenumbers (asynchronous correlation) will reveal the time of occurrence.
Thereby the sequential order of response of different peaks under perturbation could be
derived. For a non-periodic external perturbation Hilbert Noda transformation matrix is
~
~
normally used to obtain orthogonal function of y (i , t ) , viz, z (i , t ) . The asynchronous
correlation spectrum is defined as,
 (1 , 2 ) 
Tmax
1
 Tmin
Tmax
 y ( , t ).~z ( , t )dt
~
1
2
Tmin
Sequential order of peak variation could be derived by applying modified rules proposed by
Noda [36]. According to the modified rules if 1  2 , either (1,2 ) > 0 and (1 ,2 ) > 0
or (1,2 ) < 0 and (1 ,2 ) < 0, the spectral intensity measured at 1 changes before that
measured at  2 . If the asynchronous and synchronous correlation intensities at these
wavenumbers have opposite sign  2 varies before that of 1 .
* Noda, I. J. Am. Chem. Soc.1989, 111, 8116–8118.
Figure S1.The heptamer and tetradecamer models (top) used for the Gaussian calculations
(red - oxygen, gray - carbon and white - hydrogen). The Raman spectrum of crystalline PEG
(blue) and the calculated Raman spectrum (red; using heptamer helix (TGT) model) are
provided in the figure for comparison. Models with varying number of repeat units (n = 3, 5,
7 and 14) were considered for the DFT calculations (Table S1 and Figure S2). A good
correlation, between calculated and experimental Raman spectra, was observed when
heptamer (n=7) and tetradecamer (n=14) models were used for calculations. The heptamer
model represents one helical segment (72 helix) of crystalline PEG and the tetradecamer.
Table S1. Results of PED calculation is given in the table.
Calculated
frequencies
(cm-1)*
Observed
in 2D CoS
(cm-1)
%PED
Approximate character
δ(H-C-H)
821
828
818
822
- 34, υ(C-O) - 30, υ(C-C) - 2, δ(O-C-H) +
CH2 rocking + C-O
δ
δ
δ
δ
(C-C-H) - 19, (C-O-C) - 3, (C-O-H) - 1, (H-C-H) stretching vibration (near
+ δ(O-C-C) - 1
OH terminal)
CH2 rocking + C-O
(H-C-H) - 49, (C-O) - 33, (C-C) - 2, (C-O-C) - 2 stretching vibration (near
CH3 terminal)
δ
υ
υ
δ(H-C-H)
834
842
845
837
--
844
υ
δ
- 41, υ(C-O) - 32,
(C-C) - 2, δ(O-C-H) + δ(C-C-H) - 2
δ(H-C-H)
- 41, υ(C-O) - 32, δ(O-C-H) + δ(C-C-H) - 2,
(C-O-C) - 5, δ(H-C-H) + δ(O-C-C) - 1
δ
δ(H-C-H)
- 23, υ(C-O) - 34, υ(C-C) - 19, δ(C-O-C) - 7,
δ(H-C-H) + δ(O-C-C) - 2
CH2 rocking + C-O
stretching vibration
CH2 rocking + C-O
stretching vibration
CH2 rocking + C-O
stretching vibration
(near CH3 terminal)
848
853
δ(H-C-H)
- 35, υ(C-O) - 35, δ(C-O-C) - 8, δ(H-C-H) +
δ(O-C-C) - 3
CH2 rocking + C-O
stretching vibration
(near CH3 terminal)
848
--
δ(H-C-H)
- 23, υ(C-O) - 33, υ(C-C) - 10, δ(C-O-C) - 6,
δ(H-C-H) + δ(O-C-C) - 3
CH2 rocking + C-O
stretching vibration
(near CH3 terminal)
-----
858
890
863
923
918
υ(C-C)
- 30, υ(C-O) - 27, δ(H-C-H) - 37, δ(C-O-C) - 2
υ(C-C)
- 40, υ(C-O) - 4, δ(H-C-H) - 18, δ(O-C-H)+
δ(C-C-H) - 5
υ
926
935
934
--
944
--
952
--
----C-C + C-O sterching and
CH2 rocking (OH
terminal)
C-C sterching and CH2
rocking
(C-C) - 35,
C-C sterching and CH2
rocking
υ (C-O) - 8, δ(H-C-H) - 32, δ(O-C-H) + δ(C-C-H) - 1
υ(C-C)
- 31, υ(C-O) - 11, δ(H-C-H) - 33, δ(O-C-H) + C-C sterching and CH2
δ(C-C-H) - 3
rocking
υ(C-C)
- 19, υ(C-O) - 9, δ(H-C-H) - 46, δ(O-C-H) +
δ(C-C-H) - 2
υ(C-C)
- 8, υ(C-O) - 8, δ(H-C-H) - 62, δ(O-C-H) +
δ(C-C-H) - 1
Predominantly CH2
rocking (middle of the
chain)
Predominantly CH2
rocking (middle of the
chain)
960
--
υ
δ
994
989
υ
1048
1040
1061
1061
1062
--
1065
--
1067
--
1071
--
1083
--
1096
--
δ
δ
(C-O) - 7, (H-C-H) - 66, (H-C-H) + (O-C-H) - 9
(C-O) - 8, υ(C-C) - 42, δ(H-C-H) - 39, δ(C-O-C) - 2
Predominantly CH2
rocking (middle of the
chain)
C-C sterching and CH2
rocking (CH3 end)
υ
(C-O) - 46, υ(C-C) - 15, δ(H-C-H) - 10, δ(H-C-H) + C-O sterching and CH2
δ(O-C-H) - 8, δ(C-O-H) - 10, δ(O-C-H) - 7
rocking (OH end)
υ
(C-O) - 34, υ(C-C) - 33, δ(H-C-H) - 16, δ(H-C-H) + C-O and C-C stretching
δ
(O-C-H) - 8
(CH3 end)
υ
(C-O) - 33, υ(C-C) - 29, δ(H-C-H) - 18, δ(H-C-H) +
C-O and C-C stretching
δ(O-C-H) - 5
υ(C-O)
υ(C-O)
- 40, υ(C-C) - 41, δ(H-C-H) - 3
C-O and C-C stretching
- 43, υ(C-C) - 31, δ(H-C-H) - 8, δ(O-C-H) +
δ(C-C-H) - 2, δ(C-O-H) - 4
C-O and C-C stretching
(OH end)
υ(C-O)
- 28, υ(C-C) - 17, δ(H-C-H) - 27, δ(H-C-H) + C-O and C-C stretching
δ(O-C-H) - 10, δ(C-O-H) - 2
and CH2 rocking
υ(C-O)
- 25, υ(C-C) - 12, δ(H-C-H) - 35, δ(H-C-H) + C-O and C-C stretching
δ(O-C-H) - 10, δ(O-C-H) - 2
and CH2 rocking
υ(C-O)
- 27, υ(C-C) - 10, δ(H-C-H) - 30, δ(H-C-H) + C-O and C-C stretching
δ
(O-C-H) - 9, δ(O-C-H) - 4, δ(C-O-C) - 2
and CH2 rocking
υ(C-O)
1110
--
1115
--
1122
--
1124
1124
1126
--
1128
--
1133
1132
- 21, δ(H-C-H) - 38, δ(H-C-H) + δ(O-C-H) - 7,
C-O stretching and CH2
δ(O-C-H) + δ(C-C-H) - 18, δ(C-O-H) - 2, Tortionat
rocking (OH end)
OH end - 3
υ(C-O)
- 13, υ(C-C) - 10, δ(H-C-H) - 52, δ(H-C-H) + C-O and C-C stretching
δ(O-C-H) - 6, δ(O-C-H) - 1
and CH2 rocking
υ(C-O)
- 40, υ(C-C) - 3, δ(H-C-H) - 39, δ(H-C-H) +
δ(O-C-H) - 3, δ(C-O-C) - 1
C-O stretching and CH2
rocking
υ(C-O)
- 34, υ(C-C) - 3, δ(H-C-H) - 39, δ(H-C-H) +
δ(O-C-H) - 3, δ(C-O-C) - 1
C-O stretching and CH2
rocking
υ(C-O)
- 30, δ(H-C-H) - 44, δ(H-C-H) + δ(O-C-H) - 7, C-O stretching and CH2
δ(C-O-C) - 3
rocking
υ(C-O)
- 36, δ(H-C-H) - 43, δ(H-C-H) + δ(O-C-H) - 6, C-O stretching and CH2
δ(C-O-C) - 2
rocking
υ(C-O)
- 61, υ(C-C) - 2, δ(H-C-H) - 19, δ(H-C-H) +
δ(O-C-H) - 2
C-O stretching and CH2
rocking
1142
1139
1144
--
1151
1145
1156
--
1157
--
1160
--
1161
--
υ(C-O)
υ
- 47, υ(C-C) - 9, δ(H-C-H) - 22, δ(H-C-H) +
δ
(O-C-H) - 2
C-O stretching and CH2
rocking
(C-O) - 38, υ(C-C) - 16, δ(H-C-H) - 21, δ(H-C-H) + C-O + C-C stretching and
δ
(O-C-H) - 2, δ(O-C-H) - 2, δ(H-C-H) (CH3) - 1
CH2 rocking
υ
(C-O) - 62, υ(C-C) - 7, δ(H-C-H) - 11, δ(H-C-H) +
δ
(O-C-H) - 3
Predominantly C-O
stretching
υ
Predominantly C-O
stretching
(C-O) - 59, υ(C-C) - 8, δ(H-C-H) - 7, δ(H-C-H) +
δ
(O-C-H) - 1, δ(O-C-H) - 13
υ
(C-O) - 26, υ(C-C) - 3, δ(O-C-H) - 58, δ(H-C-H)
(CH3) - 2
υ(C-O)
Terminal CH3 bending
vibration
- 72, υ(C-C) - 13
C-O + C-C stretching
- 55, υ(C-C) - 13, δ(H-C-H) - 6, δ(H-C-H) +
δ(O-C-H) - 1, δ(O-C-H) - 14
C-O + C-C stretching
υ(C-O)
- 16, υ(C-C) - 6, δ(H-C-H) - 9, δ(C-O-C) - 4,
δ(H-C-H) (CH3) - 3, δ(O-C-H) - 58
Terminal
CH3bendingvibration
υ(C-O)
- 8, υ(C-C) - 3, δ(H-C-H) - 52, δ(C-O-C) - 1,
δ(C-O-H) - 25, δ(O-C-H) - 3
Terminal OH
bendingvibration
υ(C-O)
(CH3end)
1205
--
1210
1229
1235
1234
1237
--
1238
--
δ(H-C-H)
- 89
CH2 wagging (middle of
the chain)
1240
--
δ(H-C-H)
- 90
CH2 wagging (middle of
the chain)
1244
--
δ(H-C-H)
- 91
CH2 wagging (middle of
the chain)
1250
--
- 90, δ(C-O-H) - 3, δ(O-C-H) - 2
CH2 wagging (near OH
terminal)
1258
1270
1288
--
δ(H-C-H)
- 88, υ(C-C) - 2
CH2 wagging (middle of
the chain)
1288
1277
δ(H-C-H)
- 88, υ(C-O) - 1
CH2 wagging (middle of
the chain)
δ(H-C-H)
υ(C-O)
δ(H-C-H)
δ(H-C-H)
- 89 (OH end)
CH2 wagging (OH end)
- 1, δ(H-C-H) - 89
CH2 wagging (middle of
the chain)
- 89, υ(C-C) - 3, υ(C-O) - 2
CH2 wagging (near CH3
terminal)
δ
(H-C-H) - 88, υ(C-O) - 1
CH2 wagging (middle of
the chain)
1289
--
1289
1280
1290
--
1313
--
1353
--
1354
--
δ(H-C-H)
- 90
CH2 wagging
1358
--
δ(H-C-H)
- 90
CH2 wagging
1363
--
δ(H-C-H)
- 87
CH2 wagging
1369
--
δ(H-C-H)
- 86
CH2 wagging
1376
1377
δ(H-C-H)
- 82, υ(C-C) - 3
CH2 wagging
1382
1383
δ(H-C-H)
- 81, υ(C-C) - 5
CH2 wagging
(H-C-H) - 88
CH2 wagging (middle of
the chain)
(H-C-H) - 89, υ(C-O) - 4
CH2 wagging (middle of
the chain)
(H-C-H) - 85, δ(O-C-H) - 4, δ(H-C-H) (CH3) - 1
CH2 wagging (near CH3
terminal)
(H-C-H) - 65, υ(C-O) - 2, δ(O-C-H) - 4, δ(C-O-H) 25, δ(H-C-H) + δ(O-C-H) - 2
Bendingnear OH end
δ
δ
δ
δ
δ(H-C-H)
1389
--
- 79, υ(C-C) - 7, υ(C-O) - 1,
δ(H-C-H)
CH2 wagging
- 1(CH3)
δ(H-C-H)
- 74, υ(C-C) - 1, υ(C-O) - 1, δ(C-O-H) - 8,
δ(H-C-H) + δ(O-C-H) - 2
CH2 wagging
δ(H-C-H)
- 75, υ(C-C) - 5, δ(C-O-H) - 4, δ(H-C-H) +
δ(O-C-H) - 2
CH2 wagging
δ(H-C-H)
- 73, υ(C-C) - 9, δ(C-O-H) - 2, δ(H-C-H) +
δ(O-C-H) - 3
CH2 wagging
--
δ(H-C-H)
- 69, υ(C-C) - 14, δ(H-C-H) + δ(O-C-H) - 5
CH2 wagging + C-C
stretching
1434
--
δ(H-C-H)
- 63, υ(C-C) - 17, δ(H-C-H) + δ(O-C-H) - 9
CH2 wagging + C-C
stretching
1443
1441
1449
--
1451
--
1399
1399
1406
--
1414
--
1423
δ(H-C-H)
δ(H-C-H)
- 60, υ(C-C) - 18, δ(H-C-H) + δ(O-C-H) 12
CH2 wagging + C-C
stretching
- 58, υ(C-C) - 19, δ(H-C-H) + δ(O-C-H) - 13
CH2 wagging + C-C
stretching
CH3 δ(H-C-H) + δ(O-C-H) - 52, δ(H-C-H) + δ(C-C-
CH2 scissoring + CH3
O) - 43
bending
δ
(H-C-H) - 44 (CH3), υ(C-O) - 1, δ(H-C-H) + δ(O-CC) - 50, δ(O-C-H) - 2
CH2 scissoring + CH3
bending
δ
CH2 scissoring (CH3
terminal)
1464
--
1469
--
1470
--
δ
1471
--
δ
1471
--
δ
1472
1472
1473
--
1478
--
1479
--
1488
1486
1493
1490
δ(H-C-H)
+ δ(O-C-C) - 79, δ(H-C-H) - 12
CH2 scissoring
1493
--
δ(H-C-H)
+ δ(O-C-C) - 76, δ(H-C-H) - 14
CH2 scissoring
1494
--
δ(H-C-H)
+ δ(O-C-C) - 81, δ(H-C-H) - 9
CH2 scissoring
1494
--
δ(H-C-H)
+ δ(O-C-C) - 85, δ(H-C-H) - 5
CH2 scissoring
1495
--
δ(H-C-H)
+ δ(O-C-C) - 84, δ(H-C-H) - 6
CH2 scissoring
1497
--
(H-C-H) - 48 (CH3), υ(C-O) - 1, δ(H-C-H) + δ(O-CC) 46, δ(O-C-H) - 2
(H-C-H) + δ(O-C-C) - 93
(H-C-H) + δ(O-C-C) - 93
(H-C-H) + δ(O-C-C) - 93
CH2 scissoring (middle of
the chain)
CH2 scissoring (middle of
the chain)
CH2 scissoring (middle of
the chain)
+ δ(O-C-C) - 92
CH2 scissoring (middle of
the chain)
δ((H-C-H)
+ δ(O-C-C) - 92, δ(H-C-H) + δ(C-C-C) - 4
CH2 scissoring (middle of
the chain)
δ(H-C-H)
+ δ(C-C-C) - 92, δ(H-C-H) + δ(O-C-C) - 4
CH2 scissoring (OH
terminal)
δ(H-C-H)
δ(H-C-H)
+ (O-C-C) - 58, δ(H-C-H) (CH3) - 24,
(CH3) δ(H-C-H) + δ(O-C-H) - 12, δ(O-C-H) - 1
δ(H-C-H)
9,
CH2 scissoring (OH
terminal)
(CH3) - 78, (CH3) δ(H-C-H) + δ(O-C-H) Terminal CH3scissoring
- 9, δ(H-C-H) + (O-C-C) - 2
δ(O-C-H)
δ(H-C-H)
+ δ(O-C-C) - 85, δ(H-C-H) - 8, (CH3) CH2 scissoring (near CH3
+ δ(O-C-H) - 2, (CH3) δ(H-C-H) - 2
end)
δ(H-C-H)
* Uniform scaling factor = 0.985.
Figure S2. Raman spectrum calculated for 3 models with different number repeat units, n= 3,
5 and 7. The heptamer model (n=7) suitably represents the crystalline phase of PEG.
Figure S3. Birefringent pattern obtained at different temperatures. The pattern starts to fade
at 30oC.
Supplementary Information S2
The Raman intensity could be expressed as,
2
I scat µ P.E0
2
æ da ö
=ç
.(I 0 )2
è dqi ÷ø 0
a - polarizability
I0 - incident intensity
qi - vibrational (displacement) coordinate of the i
th
normal mode
Hence the intensity of the normal mode depends on the magnitude of the polarizability
change along the coordinate (considering a constant incident intensity). In the experiment
presented 844 cm-1 and 810 cm-1 bands have very different (dα/dqi), as evident from the
Raman spectra recorded at different temperatures. In order to compare their relative intensity
variation these numbers were scaled from zero to one. It could be seen that the reduction in
intensity of one mode corresponds well with the increase in intensity of the other (see the
figure below), indicating the transformation of one conformer to another, which in this case is
the modification of PEG helix (TGT) to the new configuration where C-C-O-C dihedral angle
becomes gauche.
Model Structures
Code
Name
a1, b 1
Helix7
a2
1T
a3
2T
a4
4T
b2
a5
6T
b1
a6
7T
b2
2GGG
b3
2GGG-1
b4
4GGG
b5
a6
Number of trans C-C’s
increase
a5
a4
a3
b4
b3
a2
a1
d
c
c4
d4
d3
c2
d2
d1
c1
Gauche C-Os increase
c3
b5
6GGG
c1, d1
Helix14
c2
2IG
c3
4IG
c4
4IG 2T
d2
1GGG14
d3
5GGG14
d4
1GGG14-1
Figure S4. Calculated spectra for different model conformers of PEG are shown in the figure.
a and b are the model conformers generated using with seven ethylene oxide repeat units
(heptamer) while c and d are the model conformers generated using with fourteen ethylene
oxide repeat units (tetradecamer). The table in the right panel lists the names of model
structures. (see S6 for details of the model structures)
Table S2.
The conformational sequence of the model polymer chain, energies of different chain
configurations relative to TGT helical configuration, calculated dipole moment values and
symmetry of the model structure are given in the table below.
Name
Energy
(Kcal/mol)
Dipole
Moment
(D)
Symm.
Conformational Sequence
Model PEG structure with 7 (C-C-O) repeat units
Helix7
0
2.5
C1
-GTTGTTGTTGTTGTTGTTGT
2GGG
1.4
3.8
C1
GGGTGTTGTTGTTGTTGTGG-
2GGG-1
3.4
1.9
C1
-GG’TGTTGTTGTTGTTGTG’GG
4GGG
8.9
3.0
C1
-GG’GGGTGTTGTTGTGGGGGG
6GGG
13.9
3.2
C1
-GGGGGGGGTGTGGGGGGGGG
1T
2.7
2.9
C1
-GTTGTTGTTGTTGTTGTTTT
2T
2.1
2.5
C1
-TTTGTTGTTGTTGTTGTTTT
4T
1.4
3.0
C1
-TTTTTTGTTGTTGTTTTTTT
6T
0.7
2.9
C1
-TTTTTTTTTGTTTTTTTTTT
7T
0.4
0.6
C1
-TTTTTTTTTTTTTTTTTTTT
Model PEG structure with 14 (C-C-O) repeat units
2 IG
0.7
3.3
C1
GGTTGGTGTTGTTGTTGTTG-
4 IG
0.9
5.4
C1
GGTTGGTGG’TGTG’GTTGTTG-
4 IG 2T
2.5
3.6
C1
GGTTTG’TGG’TGTG’TTTGTTG-
Helix14
0
2.6
C1
-GT(TGT)13
1GGG14
3.2
2.4
C1
GGG(TGT)12TG-
5GGG14
9.8
3.6
C1
-GGGGGGGG(TGT)9GGGGGG
‘-‘ The last CH2-CH2-O-H dihedral angle is not mentioned. G – gauche where the dihedral
angle lies in between 50o to 80o in different models. T – trans where the dihedral angle lies in
between 180o and 160o. IG – irregular C-O gauche. G and G’ represents gauche conformation
with opposite angles.
Geometry optimised structures
Supplementary Information S3
Estimation of TransC-O to Gauche C-O ratio from Raman spectroscopy
Peaks at 810 cm-1 and 844 cm-1 are specific to gauche C-O and Trans C-O respectively.
The intensity of these peaks hence should reflect the composition of gauche C-O and Trans
C-O in the sample.
Iscat = f *N* Ii
……………………. (1)
Where, N – is the number density of scatterers
Ii – incident laser intensity
f = is a factor that depends on the scattering solid angle, Raman cross-section and
the temperature dependant spectral width (line shape).
The Raman cross-section for trans and gauche C-Os are found to be different. Later in the
discussion we will show that the Raman bands of the molten PEG has a Gaussian line shape
while that of the crystalline PEG has a Lorentzian line shape. Therefore, the value of “ f ”
depends on the conformations of the C-O bond (gauche or trans) along the polymer chain. In
order to estimate the composition of gauche and trans C-O in the crystalline polymer (at 20°C
in the present case) it is important to know “ f ” for each conformation (fT and fG).
Estimating fT and fG from Raman spectra at different temperatures
We have shown that there is a correspondence between the variation of intensity of Raman
band at 810 cm-1 and 844 cm-1 (see Supplementary Information S4). This suggests that for
each trans C-O that disappears a new gauche C-O appears.
Therefore
ΔNT = ΔNG
where,
ΔNT = [(NT)at temperature1] – [(NT)at temperature2]
ΔNG = [(NG)at temperature1] – [(NG)at temperature2]
NT – number of trans C-Os, NG – number of gauche C-Os
Thus, from equation (1)
ΔIT = ΔNT.fT.Ii
………………(2)
ΔIG = ΔNG.fG.Ii ………………(3)
IT – intensity of 844 cm Raman band
IG – intensity of 810 cm-1 Raman band
-1
Since ΔNT = ΔNG
Estimation of fT/fG from the Raman spectra of PEG
A continuous variation in the Raman spectrum of PEG was observed during its melting. But
no changes were observed after the melting is completed (after 40°C). This indicates that the
trans to gauche transformation is complete at 40°C, which is approximately 2°C above the
melting point of PEG used in the study. So it could be assumed that the Raman spectrum
obtained at 40°C is the Raman spectrum of PEG with no or negligibly small trans C-O
conformation. A minimum of 9 bands were required to fit the broad Raman feature (near 800
cm-1) in the molten PEG Raman spectrum. This region was hence deconvoluted into 9 Raman
bands with a Gaussian line shape. As expected the Lorentzian line shape did not give a
satisfactory fit. On the other hand the Raman bands of crystalline PEG were pure Lorentzian
in character.
o
Intensity (a.u.)
40 C
100% Gauche C-O
Model: Gauss
Chi^2 = 8630.37485
R^2
= 0.99973
600
650
700
750
800
850
900
950
1000
-1
Ramanshift (cm )
In order to extract the Raman spectrum of PEG with only trans C-Os, the Raman
spectrum of PEG recorded at 40°C was subtracted (after appropriate scaling as shown below)
from each Raman spectrum at different temperatures.
400000
Intensity (a.u.)
Y Axis Title
300000
0
20 C
0
40 C
200000
100000
0
900
1200
X Axis Title (cm-1)
Ramanshift
1500
The Raman spectra of PEG with trans C-Os and gauche C-Os thus obtained were
deconvoluted (shown below) to calculate the area under 844 cm-1 and 810 cm-1 bands.
100% Trans C-O
o
844 cm-1
Intensity (a.u.)
Intensity (a.u.)
40 C
100% Gauche C-O
810 cm-1
600
650
700
750
800
850
900
950
1000
760
780
-1
760
780
800
820
840
840
860
880
900
All the plots together
Intensity (a.u.)
Intensity (a.u.)
820
Ramanshift (cm )
100% Trans C-O
100% Gauche C-O
Solid crystalline
o
PEG at 20 C
740
800
-1
Ramanshift (cm )
860
-1
Ramanshift (cm )
880
900
720
740
760
780
800
820
840
-1
Ramanshift (cm )
860
880
900
ΔA810 – Area under the 810 cm-1 band that is specific to C-O gauche conformation
ΔA844 – Area under the 844 cm-1 band that is specific to C-O trans conformation
The average value of ΔfG / ΔfT :
This number is an average of 40 different values calculated from the Raman data set at
different temperatures.
Calculating the Trans C-O and Gauche C-O composition
Percentage trans C-O in the polymer =
From equation (1):
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Ramanshift (cm-1)
Figure S5. 2D correlation map (synchronous right and asynchronous lef) for different regions
of the spectrum is given below. Negative correlation intensity is coded gray and positive
white. Asynchronous 2D correlation analysis improved the spectral resolution as evident
from the plot. The highly resolved spectral information is provided in the table S3 below.
Table S3. The table lists Raman
spectral bands resolved in the 2D CoS
Analysis
785 844 1040 1229 1322 1490
792
853
1044
1234
1377
2835
796
858
1061
1250
1383
2870
802
863
1095
1254
1399
2887
810
886
1105
1270
1441
2903
814
918
1124
1277
1461
2930
818
935
1132
1280
1472
2940
822
981
1139
1294
1472
2959
837
989
1145
1301
1486
Figure S6. The plot shows the broad spectral region from 780 cm-1 to 910 cm-1 and the
corresponding second derivative plot. The table (right) shows the comparison of the resolved
band information obtained after 2D CoS analysis and second derivative analysis. There is a
good agreement between in the resolved spectral information obtained from 2D CoS analysis
and second derivative analysis of the average spectrum.