827
Anal. Chem. 1993, 85, 827-833
Factor Analysis of Phase Transitions and Conformational Changes in Pentaerythritol Tetrastearate Wanjiang Gu' Instrument Analysis & Research Center, Zhejiang University, Hangzhou, People's Republic of China
The phase trandtlonr and conformatlonal changes of pentaorythrltoi tetrastearate (n-C1,HasCOOCHz),C have been studied by appiylng factor analyrls (FA) to the examlnatlon of Fourler transform Infrared spectra (FTIR) at different temporaturer. The FA Indicator the presence of three phase tranrltkns and four conformational changes, which are abstantlated, respecthrdy,by differential scanningcakrlmeky (DSC) and FTIR. The study reveals that FA of the phase trandtkns and conformational changes may be applied to esters and other organic compounds which can be tested by infrared spectroscopy (IR).
Table I. Criteria of Factor Analysis
IND= (2)
RE indicator function (n- P)
INTRODUCTION A multivariate statistical analysis method called factor analysis (FA), originally developed by psychologists and sociologists,1~2 has been found to be useful in the interpretation of data by yielding the number of independently contributing entities, In recent years, this method has been applied to infrared spectra, ultraviolet/visible spectra, Raman spectra, mass spectroscopy, nuclear magnetic resonance, chromatography, polarography, biological activity, solution qualities (equilibriumconstant, stability constant, and thermodynamic parameters), etc. as reviewed by Weiner and He et al.394 In infrared spectroscopy,factor analysis has found application to the spectral identification of unknown mixtures,5 the determination of the number of components contributing to a chemical system,6J the reduction of noise in Fourier transform infrared spectra (FTIR)? the separation of pure component spectra from mixture spectra? and the compression of IR data for storage in spectral libraries.lOJ1 The analyses of these systems have focused on infrared spectra at ambient temperature; however, little attention has been paid to applying factor analysis to infrared spectra at varied temperature.'* In order to understand temperature-induced phase transitions and conformationalchanges of (n-C17H&OOCH2)4C, we are interested in applying factor analysis to its FTIR spectra at different temperatures. Satisfactory results are obtained as shown in this paper.
* Author to whom correspondence should be sent.
Current address: 5, the 8th Hubin Lane, Hangzhou 310006, P. R. China. (1) Thrustone, L. L. Multiple Factor Analysis; University of Chicago: Chicago, 1947. (2) Harman, H. H. Modern Factor Analysis; University of Chicago: Chicago, 1967. (3) Weiner, P. H. CHEMTECH 1977, 7, 321-328. (4) He, X.; Ren, H.; Shi, H. Fenxi Huaxue 1987,15,372-381. (5) Gillette, P. C.; Lando, J. B.; Koenig, J. L. Appl. Spectrosc. 1982, 36. - - ,661-665. - - -~- (6) Antoon, M. K.; DEsposito, L.; Koenig,J. L. Appl. Spectrosc. 1979, 33,351-357. (7) Koenig, J. L.; Tovar Rodriquez, M. J. M. Appl. Spectrosc. 1981, 35, 543-548. (8)Gillette, P. C.; Koenig, J. L. Appl. Spectrosc. 1982, 36, 535-539. (9) Gillette, P. C.; Lando, J. B.; Koenig, J. L. Anal. Chem. 1983,55, 63M3.7. - - - - - -. (10) Hangac, G.; Wiedbolt, R. C.; Lam, R. B.; Isenhour, T. L. Appl. Spectrosc. 1982,366, 40-47. (11) Williams, S . S.; Lam, R. B.; Isenhour, T. L. Anal. Chem. 1983,55, 1117-1121. (12) b o , G.R.; Zerbi, G. Appl. Spectrosc. 1984,38, 795-803. 0003-2700/93/0365-0827$04.00/0
= RE
m m -P )
(E)
l''
imbedded error
x
(4)
ER = 1 eigenvalue ratio A,+,
-
51.7Pbl
IfI
O
am
o m
tom
mm
701
c m
pow
.m
1eww.tur.e I C 1
Flguro 1. The DSC thermogram of (+CI7H3&OOCH2),C.
The theory of factor analysis has been described elsewhere in detai1,5-9J3-16 so only a short summary relating to some criteria is given here. Malinowski14 developed a theory of error in factor analysis that leads to three types of errors: (1) real error (RE), the difference between exact data and raw experimental data, which contain experimental error; (2) imbedded error (E), the differencebetween the factor analysis regenerated data and the exact data, (3)extracted error (XE), the amount of error that is removed by factor analysis regenerated data from the raw data. The first approach developed by Malinowski14utilizes the concept of imbedded error (IE).The second approach,an empiricalfunction called the indicator function (IND), utilizesthe concept of real error (13) Malinowski,E. R.; Howery, D. G.Factor Analysis in Chemistry; Wiley: New York, 1980. (14) Malinowski, E. R. Anal. Chem. 1977,49,606-612. (15) Malinowski, E. R. Anal. Chem. 1977,49,612-617. (16) He, X.;Li, H.; Shi, H. Fenxi H w x u e 1986, 14, 34-40.
0 1993 American Chemical Soclety
828
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6,MARCH 15, 1993
Table 11. Criteria of the FA of ( ~ - C I , H U C O O C H ~in~ C the Frequency Range 1080-1300 cm-l no. T ("0 IND ER I 3 X lo6 no. T ("0 IND Set 1 (62-67 " C ) 6580.291 1 62 0.6413-05" 0.99 4 65 0.1173-04 5 1.973 0.89 2 63 0.7073-05 66 0.459344 0.000E+00 3 64 0.7063-05 0.53 6 5.034 67 1 2 3 4
62 63 64 65
0.4333-05 0.448345 0.4063-05 0.566345
7157.856 1.818 5.037 2.446
Set 2 (62-68" C ) 0.98 5 0.91 6 7 0.58 0.45
1 2 3 4
62 63 64 65
0.4513-05 0.4243-05 0.435345 0.4063-05
3368.285 2.512 1.901 4.681
Set 3 (62-69 O C ) 1.40 5 1.27 6 1.01 7 0.62 8
1 2 3 4 5
62 63 64 65 66
0.3373-05 0.3183-05 0.3223-05 0.2823-05 0.3783-05
3804.085 2.264 1.607 5.417 1.487
Set 4 (62-70" C ) 1.37 6 1.32 7 1.11 8 0.72 9 0.61
1 2 3 4 5
62 63 64 65 66
0.2623-05 0.248345 0.2353-05 0.1953-05 0.2483-05
4238.906 1.860 1.726 6.134 1.334
Set 5 (62-72 " C ) 1.36 6 1.36 7 1.13 8 0.74 9 0.67 10
ER
IEx 105
3.372 1.090 O.OO0
0.37 0.29 0.00
1.651 1.236 O.OO0
0.37 0.27 0.00
0.48 0.38 0.27 0.00
66 67 68
0.113E-04 0.4273-04
66 67 68 69
0.566345 0.113E-04 0.4273-04 0.0003+00
2.442 1.652 1.235 O.OO0
67 68 69 70
0.5633-05 0.112E-04 0.4203-04 0.000E+00
1.869 1.648 1.271 O.OO0
0.49 0.38 0.27 0.00
67 68 69 70 72
0.335345 0.5493-05 0.1083-04 0.3903-04
1.866 1.158 1.594 1.475
0.0003+00
O.OO0
0.57 0.49 0.38 0.25 0.00
IND
ER
I 3 X 105
0.1283-04 0.4083-04
0.40 0.25 0.00
0.0003+00
This is read aa 0.641 X low5. Table 111. Criteria of the FA of (n-Cl,H&OOCHz)& in the Frequency Range 1080-1300 cm-l IND
ER
1 2 3
95 100 120
0.140E-04" 0.1493-04 0.724345
1307.132 1.824 28.598
1 2 3 4 5 6
70 72 75 80 85 90
0.385345 0.1603-05 0.8203-06 0.9043-06 0.106345 0.1343-05
487.386 9.913 16.552 1.636 1.644 1.139
Set 2 (70-150 " C ) 3.01 7 1.39 8 0.68 9 0.64 10 0.60 11 0.57 12
1 2 3 4 5 6 7
69 70 72 75 80 85 90
0.3423-05 0.161345 0.1423-05 0.8203-06 0.902346 0.1063-05 0.1343-05
449.849 11.565 1.340 12.433 1.640 1.640 1.139
Set 3 (69-150 " C ) 3.20 8 1.72 9 1.46 10 0.75 11 0.69 12 0.64 13 0.59
1 2 3 4
68 69 70 72 75 80 85
0.2953-05 0.1323-05 0.116M5 0.6863-06 0.735EX6 0.8313-06 0.1033-05
434.625 12.903 1.278 11.181 1.627 1.927 1.126
Set 4 (68-150 " C ) 3.24 8 1.68 9 1.46 10 0.79 11 0.73 12 0.67 13 0.65 14
5
6 7 0
T ("0
I 3 X 105 no. Set 1 (95-150 "C) 2.16 4 5 1.86 0.54 6
no.
T ("0 130 140 150
O.OO03+00
2.063 2.170 O.OO0
95 100 120 130 140
0.1773-05 0.2553-05 0.4013-05 0.8053-05 0.2983-04
1.355 1.143 1.494 1.515 1.391
150
0.0003+00
O.OO0
0.52 0.46 0.37 0.29 0.20 0.00
95 100 120 130 140 150
0.1763435 0.2543-05 0.400345 0.805345 0.2963-04 0.0003+00
1.351 1.159 1.496 1.513 1.361 O.OO0
0.53 0.46 0.38 0.29 0.20 0.00
90 95 LOO 120 130 140 150
0.1323-05 0.1723-05 0.2483-05 0.3943-05 0.7853-05 0.291344 0.0003+00
1.017 1.417 1.172 1.408 1.601 1.333 O.OO0
0.60 0.53 0.46 0.38 0.28 0.19 0.00
This is read aa 0.140 X
(RE). He e t al.le p u t forward a practical criterion called the which is t h e ratio between two adjacent eigenvalue ratio (ER), eigenvalues. T h e mathematical expressions of the different criteria used in this paper are listed in Table I where n = number of spectra, p = number of pure components, m = number of points/spectrum, a n d X I = eigenvalues.
EXPERIMENTAL SECTION The FTIR spectra of (n-C17H&OOCH2)4C were collected as a function of temperature from 1540 to 650 cm-1 on a Nicolet FTIR-5DX spectrometer using 10 scans of sample and reference at a resolution of 4 cm-'. On the FTIR spectrometer, the heating
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1003
Table IV. Criteria of the FA of (n-C17H&OOCH& in the Frequency Range 1080-1300 cm-l no. T ("C) IND ER IE X 105 no. T ("C) IND Set 1(60-68 "C) 1 2 3 4 5
60 61 62 63 64
0.2503-05a 0.2513-05 0.171E-05 0.210E-05 0.3033-05
7641.472 1.202 9.108 2.072 1.359
1 2 3 4 5
59 60 61 62 63
0.249345 0.1943-05 0.1543-05 0,1703-05 0.2063-05
3437.131 2.945 4.746 1.920 2.082
1 2 3 4 5 6
58 59 60 61 62 63
0.2803-05 0.1623-05 0.1493-05 0.122345 0.1433-05 0.1923-05
1461.834 7.565 1.745 5.221 2.083 1.311
1 2 3 4
57 58 59 60 61 62
0.345345 0.1353-05 0.130345 0.923E-06 0.106E-05 0.1353-05
575.765 20.749 1.616 7.843 2.045 1.321
1.02 1.04 0.59 0.53 0.49
6 7 8 9
829
ER
I3 X 1P
65 66 67 68
0.5033-05 0.9873-05 0.3713-04 0.0003+00
1.064 1.745 1.261 O.OO0
0.44 0.34 0.24 0.00
64 65 66 67 68
0.2953-05 0.4903-05 0.9553-05 0.345344 0.000E+00
1.412 1.066 1.687 1.445
0.50 0.44 0.33 0.23 0.00
64 65 66 67 68
0.283345 0.4583-05 0.9343-05 0.3253-04 0.000E+00
63 64 65 66 67 68
0.1873-05 0.272345 0.4473-05 0.933345 0.324344 0.0003+00
Set 2 (59-68 "C) 1.29 1.06 0.74 0.64 0.56
6 7 8 9 10
O.Oo0
Set 3 (58-68 "C) 1.80 1.14 0.96 0.65 0.58 0.54
7 8 9 10 11
1.079 1.335 1.339 1.636
O.OO0
0.50 0.42 0.33 0.21 0.00
Set 4 (57-68 "C)
5 6 a
2.70 1.18 1.07 0.66 0.60 0.58
7 8 9 10 11 12
1.019 1.232 1.309 1.189 1.651 O.OO0
0.55 0.49 0.42 0.33 0.21 0.00
ER
IE x 105 0.36 0.25 0.00
This reads as 0.25 X
Table V. Criteria of the FA of (n-C17Hs&OOCH2)& in the Frequency Range 1080-1300 cm-' no. T ("0 IND ER IE x 105 no. T ("0 IND Set 1 (51-56 "C) 1 2 3
51 52 53
0.3563-04' 0.114E-04 0.6683-05
127.019 31.285 16.584
1 2
3 4
51 52 53 54
0.2923-04 0.7193-05 0.449345 0.5403-05
1 2 3 4
51 52 53 54
1
4 5 6
54 55 56
0.1143-04 0.3993-04 0.0003+00
2.913 1.596
86.964 45.956 10.371 4.027
Set 2 (51-57 "C) 6.58 5 1.45 6 0.64 7 0.43
55 56 57
0.108E-04 0.3933-04 0.0003+00
1.557 1.400
0.2463-04 0.4973-05 0.325345 0.3113-05
63.846 62.900 5.895 6.804
Set 3 (51-58 "C) 7.62 5 1.48 6 0.75 7 0.48 8
55 56 57 58
0.4943-05 0.1043-04 0.372344 0.0003+00
51 52 53 54 55
0.2083-04 0.355345 0.2263-05 0.1953-05 0.2773-05
51.310 80.710 6.199 6.972 1.386
Set 4 (51-59 8.46 1.47 0.78 0.49 0.45
56 57 58 59
0.454345 0.955345 0.3513-04 0.0003+00
1 2 3 4
51 52 53
5
55 56
0.148FiO4 0.2163-05 0.1483-05 0.1113-05 0.1303-05 0.174345
40.290 106.647 3.949 6.649 2.147 1.353
57 58 59 60 61
0.2583-05 0.437345 0.8983-05 0.347344 0.0003+00
2 3 4 5
6
54
This reads as 0.356
X
5.49 1.43 0.51
"C) 6 7 8 9
Set 5 (51-61 "C) 9.53 7 1.51 8 0.95 9 0.59 10 0.53 11 0.49
O.OO0
O.OO0
1.614 1.180 1.506 O.OO0
1.381 1.238 1.362 O.OO0
1.238 1.038 1.508 1.137 O.OO0
0.35 0.25 0.00
0.41 0.35 0.24 0.00 0.39 0.33 0.23 0.00
0.45 0.40 0.32 0.23 0.00
lo4.
process was continuous at a properly chosen rate. Temperature was continuously measured with a thermistor thermograph and controlled to within hO.1 "C. The spectra were stored by computer. The spectra were manually digitized at 1-cm-1 intervals as described previouely,17 giving a total of 221 data pointa between 1300 and 1080 cm-l for each spectrum. All spectral data were
transferred to a DEC MICRO VAX-I1 computer for factor analysis. Factor analysis was done initially using self-programs at a minimum (or maximum) number of spectra in their corresponding temperature range. Then the procedure was repeated by increasing (or decreasing) the number of spectra (17) Bulmer, J. T.; Shurvell, H.F.Can. Spectrosc. 1971, 16, 94-99.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993
890
Table VI. Criteria of the FA of (n-C17Hs&OOCHz)@ in the Frequency Range 1080-1300 cm-1 no. T ("0 IND ER I 3 X los no. T ("C) IND Set 1 (54-62"C) 1 54 0.1633-04a 82.412 6.65 6 59 0.4543-05 2 55 0.168345 273.782 0.70 7 60 0.9603-05 3 56 0.1433-05 6.500 0.49 8 61 0.3473-04 0.0003+00 4 57 0.1883-05 1.482 0.48 9 62 5 58 0.2753-05 1.193 0.45
a
ER
IEX106
1.346 1.174 1.453 0.000
0.39 0.33 0.22 0.00
46.605 241.I40 8.412 2.129 1.263 1.371
Set 2 (52-62"C) 8.84 7 0.93 8 0.57 9 0.53 10 0.51 11 0.48
58 59 60 61 62
0.2513-05 0.4213-05 0.8643-05 0.3403-04 0.000E+00
1.161 1.124 1.551 1.068 0.000
0.44 0.38 0.30 0.22 0.00
57
0.1373-04 0.1323-05 0.8893-06 0.9973-06 0.1263-05 0.1693-05
51 52 53 54 55 56
0.1243-04 0.171345 0.1183-05 0.8813-06 0.9963-06 0.1263-05
38.692 116.478 3.690 6.526 2.029 1.262
Set 3 (51-62"C) 9.73 7 1.50 8 0.98 9 0.63 10 0.57 11 0.54 12
57 58 59 60 61 62
0.1693-05 0.2513-05 0.4203-05 0.8613-05 0.3383-04
1.369 1.164 1.121 1.564 1.070 0.000
0.49 0.45 0.39 0.31 0.22 0.00
1 2 3 4 5 6
52 53 54 55
1 2 3 4 5 6
56
0.0003+00
This reads as 0.163 X lo4.
Table VII. Criteria of the FA of ( I I - C ~ ~ H J & O O C H in~the )~ Frequency Range 1080-1300 cm-l no. T("C) IND ER no. T(OC) IND ER
1 2 3
33 37 39
Set 1 (33-45 "C) 41 0.2983-04" 222.600 4 0.210E-04 5.787 5 43 45 0.1453-04 10.419 6
1 2 3 4
33 37 39 41
0.3253-04 0.1793-04 0.1543-04 0.1433-04
Set 2 (33-46 "C) 80.817 5 43 9.414 6 45 3.983 7 46 5.002
0.1893-04 4.660 0.5683-04 2.546 0.0003+00 0.000
1 2 3 4
33 37 39 41
0.2963-04 0.1583-04 0.1673-04 0.1043-04
Set 3 (33-47 "C) 50.927 5 43 45 12.020 6 1.401 7 46 47 11.618 8
0.1383-04 0.1783-04 0.5483-04 0.000E+00
1 2 3 4 5
33 37 39 41 43
0.2923-04 0.1243-04 0.126E-04 0.121E-04 0.9523-05
Set 4 (33-48 "C) 28.348 6 45 18.858 7 46 1.747 8 47 2.100 9 48 6.555
1 2 3 4 5
33 37 39 41 43
0.2743-04 0.9363-05 0.9153-05 0.8933-05 0.8493-05
Set 5 (33-49 "C) 18.999 6 45 46 28.208 7 47 1.865 8 48 1.991 9 2.954 10 49
a
46C
0.1953-04 4.694 0.6303-04 2.072 0.0003+00 0.000 45c
43c
40c
1.801 5.109 2.365
37c
O.OO0
0.1233-04 1.965 0.1643-04 4.752 0.5123-04 2.280 0.0003+00 0.000
0.9473-05 0.1223-04 0.1593-04 0.4993-04 0.000E+00
2.398 2.000 4.934 2.268
Y
0.000
Y
e 40.0
This reads as 0.298 X 1o-L.
c
1 h . O
1240.0 lbeo.0 940.00 URVENWERS tCM-11
650.00
Flgwr 2. The FTIR spectra of (~J~,,H~~COOCH~),C from 29 to 47
gradually for factor analysis. A series of error criteria were obtained finally. The calorimetric measurements of (n-C17H&OOCHhC were performed with a Perkin-Elmer DSC 7 differential scanning calorimeter (DSC) equipped with a Perkin-Elmer 3700 data station. The (n-C1,H&OOCH2)& sample was synthesized by a previous method's and purified by column chromatography. pH measurements and hydroxy value titrations gave chemical purity estimated at >99%. (18) Feuge, R. 0. J. Am. Oil Chem. SOC.1962,39,521-528.
OC.
RESULTS AND DISCUSSION A. Solid-Liquid Phase Transition. In the frequency range 1080-1300 cm-l, the factor analysis of (n'C17H35' COOCH2)4C was done initially with six spectra recorded at 62,63,64,65,66, and 67 "C. Later, the number of spectra included in the analysis was increased one a t a time. Five seta of error criteria were obtained in turn, shown in Table 11. It can be seen from this table that (n-C17H35COOCH2)4C is a three-component system for set 1as t h e indicator function
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993 651
e
I
I
1540.0
1380.0
1080.0 940.00 UCIvENuttaERs t m- 11
1240.4
650.00
Rguw 5. The FTIR spectra of (n-Cl7H&X0CH2),C from 48 to 57 OC.
1540.0
I
1300.0
1240.0 1080.0 940.00 UCIVCNUHERS tCH-11
650.00
Flgure 4. The FTIR spectra of (n-C17H&OOCH2)4C from 58 to 150
OC.
(IND) is a minimum at no. = 3. This conclusion is substanTo sum up, when the temperature range is extended from tiated by the eigenvalue ratio (ER) reaching a maximum at 70-150 O C to 64-150 OC, the number of components of (nno. = 3 and by the imbedded error (IE) not decreasing C1,H35COOH~)4Cincreases from 3 to 4. This result agrees substantially with the conclusion of Table 11. appreciably beyond no. = 3. When the spectrum at 68 OC is included in the analysis, the number of components is still It is note worthy that Table I1differs somewhat from Table three (see set 2). For set 3, the IND at no. = 4 reaches a I11 at the temperature of phase transitions; the former is minimum, giving an evidence for four components. The between 68 and 69 OC and the latter between 69 and 70 OC. conclusion is substantiated by the ER reaching a maximum This is explained as in the process of solid-liquid phase at no. = 4 and by the IE not decreasing appreciably beyond transition from 62.3to 69.3OC (see Figure l),where there are no. = 4. This indicates that a fourth independent component both solid and liquid components. During the gradualmelting enters the system between 68 and 69 OC. When the number of the solid, the liquid component is initially minor and not of spectra included in the analysis is increased, (n-Cl7H35' found by factor analysisuntil 68 "C (see Table 11). When the COOCHZ)~C is still a four-componentsystem until 72 "C (see quantity of liquid become measurable above 68OC, the liquid set 4 and set 5). is detected by factor analysis as a component, so the To sum up, when the temperature range is extended from temperature of the phase transition in Table 11is between 68 62-68OC to 62-69 OC, the number of componentsof (d17H35and 69 OC. For Table 111,because there is only a liquid above COOCH2)4C increases from 3 to 4. Namely, a solid-liquid 70O C , no solid component is found by factor analysis, whereas phase transition occurs between 68 and 69 OC. It is in good when solid become measurable at 69 "C or lower, the solid agreementwith the results of differentialscanningcalorimetry component is detected by factor analysis. Therefore, the temperature of the phase transition in Table I11 is between (DSC) of ( ~ - C ~ , H ~ ~ C O O C H (see Z ) Figure ~ C 1). The figure demonstrates that there is a endothermic peak at 68.8 OC, 69 and 70 OC. Though the conclusions of factor analysis are with no other peaks above the temperature. slightly different at two temperature ranges, the same phase In order to confiim the above-mentioned conclusion and transition is substantiated. explore the sensitivity of factor analysis, we change the B. Solid-Solid Phase Transitions. Some error criteria temperature range of factor analysis with results shown in of factor analysisof ( ~ - C ~ ~ H ~ & O O C H areZlisted ) ~ C in Table Table 111. We find from this table that ( ~ - C I ~ H & O O C H ~ ) ~ C IV in the frequency range 1080-1300 cm-l. Table IV shows is a three-component system for set 1 or set 2 because IND H aZthree-component )~C that in set 1 or 2 ( ~ - C ~ , H ~ ~ C O O C is reaches a minimum at no. = 3 and the ER is a maximum at system,as indicated by the minimum data of the IND, further no. = 3 and the IE does not decrease appreciably beyond no. supported by the ER reaching a maximum at no. 3 and by the IE not decreasing obviously beyond no. = 3. When the = 3. When the spectrum at 69 "C is included in the analysis, the number of components become four (see set 3). When spectrum at 58 "C is included in the analysis,the number of the spectrum at 68OC is included in the analysis,the number components become 4for set 3. When the number of spectra of components is still four (see set 4). included in the analysis is increased, ( ~ - C I , H ~ & O O C H ~ ) ~ C
832 ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993 Table VIII. Criteria of the FA of (II-C~~H~&OOCH~)& in the Frequency Range 1080-1300 cm-' no. T ("C) IND ER IE x 105 no. T ("(2) IND Set 1(49-62 "C) 1 2 3 4 5 6 7
49 50 51 52 53 54 55
0.9943-05n 0.136345 0.120345 0.8533-06 0.6563-06 0.780346 0.954346
30.661 159.010 1.419 3.394 8.563 1.199 1.291
10.94 1.74 1.52 0.98 0.65 0.63 0.60
8 9 10 11 12 13 14
50 51 52 53 54 55 56
0.1123-04 0.149345 0.1223-05 0,919346 0.7983-06 0.9823-06 0.124345
33.658 144.258 2.170 3.370 6.214 1.085 1.284
Set 2 (50-62 10.43 1.59 1.25 0.84 0.61 0.59 0.55
"C)
1
51 52 53 54 55 56
0.124344 0.1713-05 0.1183-05 0.8813-06 0.9963-06 0.1263-05
38.692 116.478 3.690 6.526 2.029 1.262
2 3 4 5
53 54 55 56 57
0.150344 0.148345 0.108345 0.134345 0.180E-05
59.883 253.015 9.087 1.508 1.163
1 2 3 4 5
54 55 56 57 58
0.1633-04 0.168345 0.143345 0.188345 0.275345
82.412 273.782 6.500 1.482 1.193
1 2 3 4
55 56 57 58
0.171344 0.1963-05 0.2043-05 0.2943-05
130.422 291.773 4.101 1.252
1
56 57 58 59
0.1823-04 0.2733-05 0.3213-05 0.527345
220.359 201.448 3.305 1.267
2 3 4 5 6 7
8 9 10 11 12 13
ER
IEX106
56 57 58 59 60 61 62
0.1233-05 0.1643-05 0.2463-05 0.4113-05 0.8593-06 0.3383-04 O.OOOE+00
1.066 1.536 1.030 1.210 1.436 1.065 0.000
0.56 0.51 0.46 0.39 0.31 0.23 0.00
57 58 59 60 61 62
0.165345 0.2493-05 0.4173-05 0.8583-05 0.3383-04 0.0003+00
1.528 1.028 1.138 1.550 1.057 0.000
0.50 0.46 0.39 0.31 0.23 0.00
57 58 59 560 61 62
0.169345 0.2513-05 0.420345 0.8613-05 0.3380.0003+00
1.369 1.164 1.121 1.564 1.070 0.000
0.49 0.45 0.39 0.31 0.22 0.00
58 59 60 61 62
0.2593-05 0.4243-05 0.8693-05 0.344344 0.0003+00
1.325 1.271 1.586 1.041 0.000
0.44 0.38 0.30 0.22 0.00
59 60 61 62
0.454345 0.9603-05 0.347344
1.346 1.174 1.453 0.000
0.39 0.33 0.22 0.00
59 60 61 62
0.4803-05 0.1013-04 0.3483-04
0.0003+00
1.398 1.138 1.695 0.000
0.40 0.34 0.22 0.00
60 61 62
0.10834 0.397344 0.0003+00
1.395 1.374
0.35 0.25 0.00
Set 3 (51-62 "C) 1
2 3 4 5 6
9.73 1.50 0.98 0.63 0.57 0.54
7 8 9 10 11
12
Set 4 (53-62 "C) 1
7.80 0.81 0.52 0.51 0.49
6 7 8 9 10
Set 5 (54-62 "C) 6.65 0.70 0.49 0.48 0.45
6 7 8 9
0.0003+00
Set 6 (55-62 "C) 5.30 0.58 0.47 0.45
5 6 7 8
Set 7 (56-62 "C) 2 3 4 a
This reads as 0.994
4.09 0.55 0.46 0.42
5 6 7
0.000
X
Table IX. Summary of the FA of Phase Transitions and Conformational Changes in (a-Cl,Hs&OOCHd& change of temperature change of change of range, OC componentnumber temperature, "C change type' 3to4 33-45 to 33-46 45-46 conformational change 4to5 33-47 to 33-48 47-48 conformational change 4to5 51-62 to 50-62 50-51 conformational change 3to4 52-62 to 51-62 51-52 S-S phase transition 2to3 55-62 to 54-62 54-55 conformational change 3to4 51-57 to 51-58 57-59 S-S phase transition 3to4 59-68 to 58-68 62-68 to 62-69 70-150 to 69-150 0
3to4 3to4
68-70
S-L phase transition
~
substantiation FTIR FTIR FTIR DSC FTIR DSC DSC
S, solid; L, liquid.
is still a four-component system (see set 4). To s u m up, when the temperature range is extended from 59-68 "Cto 58-68 "C,the number of components of (n-Cl,H%COOCH&C increases from 3 to 4. Namely, a solid-solid phase transitionoccurs between 58 and 59 "C as substantiated
by the DSC of (n-C17H&OOCH&C (see Figure 1, indicating an endothermic peak at 58.6 "C). This conclusion is also seen in Table V in that the number of components of (n-C17H&OOCH2)& increases from 3 to 4 when the temperature range is extended from 51-57 "C to
ANALYTICAL CHEMISTRY, VOL. 65, NO. 6, MARCH 15, 1993 888 51-58 "C. Namely, a solid-solid phase transition occurs between 57 and 58 "C. For Tables IV and V, the conclusions of fador analysis are slightly different at two temperature ranges, too. They are similar to Tables I1 and 111. Some results of factor analysis of (n-C17H35COOCH2)4Cin the frequency range 1080-1300 cm-1 are shown in Table VI, which indicates that the number of componentsof bC17H35COOCH2)4Cincreasesfrom 3 to 4 when thetemperature range is extended from 52-62 "C to 51-62 OC. Namely, a solidsolid phase transition occurs between 51 and 52 OC, which is again substantiated by DSC results for (n-C17H&OOCH2)4C. Figure 1 shows a endothermic peak at 51.8 OC. According to the papers of Maroncelli et al.,lQSnyder et al.,20 and Strobl et al.,21 below the melting point the crystals of long-chain n-alkanes showed a remarkable series of solidsolid phase transitions, which were studied by DSC and substantiated by X-ray scattering experiments.21 This suggests that (n-C17H&OOCH2)& passes through three crystal states before melting, which are denoted X, Y, and Z. X crystal exists below 51.8 OC, where a solid-solid phase transition to Y crystal occurs. The second solid-solid phase transition occurs from Y to Z crystal at 58.6 "C, and a solidliquid phase transition occurs at 68.8 "C where Z crystal melts. C. Conformational Changes. Some error criteria of factor analysis of (~-CZ~H&OOCHZ)~C, in the frequency range 108&1300 cm-l, are listed in Table VII. The number of components of (n-C17H35COOCH2)4Cincreases from 3 to 4 when the temperature range is extended from 33-45 "C to 33-46 "C. Namely, a conformational change occurs between 45 and 46 "C and the number of components of (wC17H35COOCH2)4C increasesfrom 4 to 5 when the temperature range is extended from 33-47 OC to 33-48 "C. Namely, the second conformational change occurs between 47 and 48 OC. The above-mentioned conformational changes can be substantiated by Fourier transform infrared spectra (FTIR) of (nC17H35COOCH2)4C in Figures 2 and 3. Figure 2 manifests that the four spectra at 29,37,40, and 43 "C are almost the same. In the spectrum at 45 OC, the right side of the i peaks crooksand so does the left side of the j peak (the oblique lines in the spectra). When the temperature increases to 46 "C, the right side of the i peaks bends obviously,and the j single peak becomes double peaks. This indicates that a conformational change occurs between 45 and 46 OC. The right side of the i peaks bends more, and the j double peaks still exist at 47 "C. (19) Maroncelli, M.; Qi, S. P.; Strauss, H. L.; Snyder, R. G. J. Am.
When the temperature increased from 47 to 48 OC, the i peaks change from triple to quadruplet peaks and the j peaks change from double peaks to a single peak (see Figure 3). This indicates that the second conformationalchange occurs between 47 and 48 OC. T w o conformational changes are in good agreement with the conclusionsof factor analysis about 45.5 and 47.5 "C. Some error criteria of factor analysis of (n'C17H35' COOCHZ)~C in the frequencyrange 1080-1300 cm-1 are shown in Table VI11where the number of components of (n'C17H35' COOCH2)4Cchanges from 5 to4 when the temperature range is decreased from 50-62 OC to 51-62 "C. The third conformational change occurs between 50 and 51 OC. When the temperature range is decreased from 54-62 OC to 55-62 OC, the number of components of (n-C17H&OOCH2)4C changes from 3 to 2. (The ER also reaches a maximum at no. = 3 besides the maximum at no. = 2, and the value at no. = 2 is much more than one at no. = 3, so we infer the number of components on the basis of the IND and the IE. The ER was only a reference.) The fourth conformationalchange occurs between 54 and 55 "C. Because at higher temperature the conformational changes are faster, the latter two conformational changes are not seen clearly in the FTIR, but there are still some changes in the i peaks between 50 and 55 OC (see Figure 3). The above four conformational changes indicate that the energy provided by temperature is not enough to generate conformational changes below 45 OC, where (n'C17H35' COOCH2)4Cexists in a stable, dominant conformation. The energy provided by temperature allows conformations to quickly and freely transform between each other above 55 "C; thus the conformationalchangesof (n-C17H=COOCHz)& are not determined by factor analysis and FTIR (see Figures 3 and 4, Tables 11-VI). So a temperature range where conformationalchangesnot onlyoccur but are also determined by factor analysis and FTIR is limited to between 45 and 55 "C. The conclusionsof factor analysis of phase transitions and conformational changes in ( ~ - C ~ ~ H ~ S C O O Care H Zsum)~C marized in Table IX.
ACKNOWLEDGMENT The author gratefullyacknowledgessupport and help from Mmgxiao Shiand Qing Liu, Instrument Analysisand Research Center of ZhejiangUniversity. This work was also supported by the ZhejiangCommittee of Science and Technology in the People's Republic of China.
Chem. SOC. 1982,104,6237-6241.
(20) Snyder, R. G.; Maroncelli, M.; Qi, S. P.; Strauss, H.L.Science
1981.214. _ . . ~ ,188-190. ~.~ ~ ~ ~ , ~
~
(21) Strobl, G.; Ewen, B.; Fischer, E. W.; Piesczek, W. J. Chem. Phys. 1974,61,5257-5264.
RECEIVED for review April 28, 1992. Accepted November 2, 1992.
