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Infrared spectra of finite chain molecules—II n-alkyltrimethylammonium bromides
SpectrnchimicaActa, Vol.24A,pp. 1749to 1763. Pergamon Press 1968.
Printed in Northern Ireland
Infrared spectra of finite chain molecules--H n-alkyltrimethylammonium bromides T o Y o z o UNO, KATSUNOSUKE MACHIDA a n d KOICHIRO MIYAJIMA Faculty of Pharmaceutical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan (Received 2 _November 1967)
infrared spectra between 1400 and 700 cm-1 of n-alkyltrimethylammonium bromides with n-alkyl chains including 2 through 18 carbon atoms are reported. The end group frequencies are assigned and the band progression analysed by using the properties of chain length-frequency curves. The result shows that the force field of the chain part of n-alkyltrimethylammonium bromides is practically the same as that of n-paraffins. A vibrational coupling between the chain part and the end group is evidenced by the irregular feature of the CH 2 rocking-twisting band progression. INTRODUCTION Abstract--The
TEE a b s o r p t i o n intensities of t h e infrared b a n d progressions of p o l y m e t h y l e n e chains are o f t e n e n h a n c e d b y introducing polar t e r m i n a l groups. Such e n h a n c e d b a n d progressions h a v e been i n v e s t i g a t e d for n - f a t t y acid salts [1-4] a n d p r o v e d to be useful in determining t h e length of n-alkyl chains in e a r b o x y l a t e anions. T h e r e h a v e been few reports, however, on the b a n d progressions of a m m o n i u m salts containing long n-alkyl chains although t h e y are c o m m o n l y used as cationic surfactants. As a consequence of t h e preceding theoretical t r e a t m e n t of b a n d progressions [5], we r e p o r t in the present p a p e r the infrared spectra of n - a l k y l t r i m e t h y l a m m o n i u m bromides ( a b b r e v i a t e d n - a l k y l - T M A bromides, hereafter) with C 2 t h r o u g h Cls n-alkyl chains a n d give the b a n d progression analysis based on the t r a n s f e r m a t r i x t h e o r y of MATSUDA et al. [6]. T h e analysis was initially p l a n n e d from the necessity of identifying t h e chain length a n d checking the p u r i t y of s t a n d a r d samples in t h e studies on t h e d e t e r m i n a t i o n of cationic s u r f a c t a n t s in this l a b o r a t o r y [7]. I t has been f o u n d t h a t a m o n g t h e four progressions arising between 1400 a n d 700 cm -1, t h e C H 2 r o c k i n g - t w i s t i n g progression is t h e m o s t distinguished a n d is helpful for t h e purpose of identification. The characteristic frequencies of t h e end group, N+(CH3)3, h a v e also been given assignments a n d f o u n d to be correlated closely to t h e f u n d a m e n t a l frequencies of t r i m e t h y l a m i n e h y d r o i o d i d e a n d t e t r a m e t h y l a m m o n i u m iodide r e p o r t e d b y ]~BSV¢ORTH a n d SHEPPARD [8]. [1] D. CHAPMAn,J . Chem. Soc. 784 (1958). [2] R. A. MEIKLEJOHI"~,R. J. MEYER, S. M. ARONOVIC, H. A. SCHUETTEand V. W. MELOCH, Anal. Chem. 29, 329 (1957). [3] T. TAKENAKA,J . Chem. Soc. Japan, Pure Chem. Sect. 84, 392 (1963). [4] E. M. KIRBY, M. J. EVANS-VADER and M. A. BROW'~, J . A m . Oil Chemists' Soc. 42, 437 (1965). [5] T. UNO and K. MACHIDA,Spectrochim. Acta 24A, 1741 (1968). [6] H. MATSUDA, K. OKADA, T. TAKASE and T. YAMAMOTO,J. Chem. Phys. 41, 1527 (1964); H. MATSUDA,Proff. Theor. Phys. (Kyoto), Suppl. 23, 22 (1962). [7] T. UNO, K. MIYAJI~A and I-I. TSVKATANI, Yakugaku Zasshi (Tokyo) 8 0 , 153 (1960). [8] E. A. V. EBSWORTHand •. SHEPPARD,Spectrochim. Acta 13, 261 (1959). 6 1749
1750
ToYozo U~o, KATSUNOSUKE1VIACHIDAand KOIOHIR0MIYA,IIMA ]~XPERIMENTAL
The samples of n-alkyl-TMA bromides, R--N(CHa)aBr (R = n-alkyl), were prepared from the corresponding n-alkyl bromides ( R - - B r ) b y the reactions, R B r + HN(CH3) ~ in sealed tub%. RN(CHs) .HBr RN(CHa)~.HBr + N a O H
~q. soln. _~. RN(CHa)2 + H2 0 + NaBr
RN(CH3)2 + CH3B r in ~ealedtub% RN(CHa)aBr or directly b y the reaction with trimethylamine. They were recrystallized from the mixture of dried ether and ethanol [7]. The homologous impurities in the starting material were checked b y the gas chromatography and found to be less than 1% for each n-alkyl bromide. The infrared spectra between 1400 and 700 cm -1 were recorded on a Koken DS301 infrared spectrophotometer equipped with sodium chloride optics. The samples were measured as l~ujol mulls. For the wavenumber calibration the standard absorptions of polystyrene, indene and ammonia [9] were used and the errors were estimated to be within ± 1 cm -1. The observed infrared spectra are shown in Figs. 1 to 5, and the frequencies in Table 1, together with the assignments to be referred to in the following discussion.
"~ n=2
1300
F i g . 1. I n f r a r e d spectra o f
1200 I100 I000 900 wove number (crn-q
800
700
CHa(CH2)nl~(CI-Ia)aBr,n
= 1-4 ( l ~ u j o ] m u l l ) .
END GROUP FREQUENCIES Although the X-ray crystallographic analysis has not yet been made for any member of the homologous series of n-alkyl-TMA bromides, no ambiguity arises on the mutual conformation of the n-alkyl chain and the axially symmetric terminal group, --N+(CHa)a. Since the n-alkyl chain is usually in the extended trans configuration in the crystalline state, the point group of a whole molecule m a y be taken [9] IUPAC commission on Molecular Structure and Spectroscopy, Tables of Wavenumbers for Calibration of Infrared Spectrometers. Butterworths (1961).
Infrared spectra of finite chain molecules--II
1751
Table 1. Wavenumbers, relative intensities* a n d assignments~ of infrared bands (1350-700 cm -1) of solid n-alkyl-TMA bromides CzHbN(CHa)aBr 713 m 819 m 874 v s 954 1012 1076 1094 1153 1173 1239 1288
vs s m'( wJ m m s vW
WcN(a') r - t (1) 5 P Mec(ap) ( % N ( a p) ~CN (a:) %N(a )
p~ieN(a t, a") s k e l (1) p~eN(a', a") w a g (1)
954 s 977 v s 988 s 1010 w 1029 v w 1050 s 1059 w 1109 m 1155 m 1208 w 1239 v w 1269 m 1294 m 1327 m
CaH~N(CH3)aBr 752 m 892 s 946 v s 966 v s 1038 1079 1099 1154
m w m m
1173 1250 1281 1298 1329 1348
w m w w w w
r - t (1) {p:~) e ') vcIq(a ) ~CN(a ~)
p~ey,(a', a ~) s k e l (2) s k e l (1) S w a g (1) ( PMeN (a', a n) t - r (2) w a g (2)
C4H,N(CHa)aBr 743 m 756 w 776w 800 w 899 s 914 v s 936 s 973 v s 1032 m 1059 m 1076 w 1105 w 1156 m 1174 w 1222 w 1243 m 1274 W 1282 m 1291 w 1315 v w
VCl~(a'' an) PMei~(a~, a '~) s k e l (2) skel (1)
p~e1~(a ~, a n) w a g (2)
s k e l (3) pMeN(a', a n) s k e l (2) s k e l (1)
w a g (2) t--r (3) w a g (3)
C6HIsN(CHa)sBr 725 s 747W 758 v w 805 m 889 m 915 958 964 994 1010 1054 1108 1144 1222 1245
s vs vs m ~¢ m w m w m
1278 v w 1301 w
r - t (1) VCN(a') r--t (2) PMec(a') vc~(a ) r - t (3)
?]cN(a', a n) r - t (4)
r - t (1) r - t (2) VON(a') r--t (3) ~r--t (4) (PMec ( a ' ) vcN(a') VCN(a n) VcN(a ') r--t (5) skel (3 ) s k e l (2) s k e l (1) p ~ e ~ ( a , ' a ~) t - r (3) w a g (3)
CTH15N(CHa)aBr 724 735 755 775 839 916
s vW vw w w s
964 990 1009 1032 1055 1113 1143 1218 1241 1267 1287 1305
vs w w w w w w w m w w w
r - t (1) r - t (2) Ve~ (a') r - t (3) r - t (4) ~VC~ (a') ( r - t (5) YeN (a', a n) r - t (6) skel (3) s k e l (2) s k e l (1) PMeN(a', a n) t - r (3) w a g (3) t - r (4)
CsH11N(CH3)aBr 735 754 770 854 889 927
s w w m s s
r - t (1) YcN(a ~) r - t (2) r - t (3)
p~iec(a') yCN(a t)
CsH~vN(CH3)aBr 723 752 760 804
s m w w
r - t (1, 2) r - t (3) VoN(a') r - t (4)
866 914 933 965 992 1012 1039 1067 1092 1115 1142 1214 1242
m s s vs w w W w vw w m vw m
1258 1270 1289 1312
W w w w
r - t (5) wc~(a') r - t (6) VcN(a p, a n) r - t (7) s k e l (3) P•eN(a p, a H) skel (2) s k e l (1) ~ w a g (2) Lp~feN(a' , a ~) t--r (3) w a g (3) t - r (4) w a g (4)
CgHlaN(CHa)aBr 722 743 756 777 828 888 910 943 964 972 992
s m w w m w s vs vs s m
r - t (1) r - t (3) ycN(a ') r - t (4) r--t (5) r--t (6) VoN(a') r - t (7)
1020 1035 1050 1071
w w w w
r - t (8) s k e l (4)
1089 1116 1142 1235 1247 1258 1282
w w w m vw w w
pMeN(a', a " ) s k e l (2) s k e l (1) w a g (2) t - r (3) w a g (3) t - r (4)
1297 w 1327 w
Vc~ % ~ ( (a') a ~) s k e l (5)
s k e l (3)
w a g (4) w a g (5)
C~°H~IN (CHa)aBr sh r - t (1) vs r - t (2) s r - t (3) w r - t (4) w ~CN(a') m r--t (5) m r - t (6) vw PKec(a') s ~r--t (7) tVcN (a') 950 v s VCN(a") 965 v s YON(a') 978 s r - t (8) 1003 m s k e l (5) 1022 w r - t (9) 1047 w s k e l (4) 1063 w 1077 w s k e l (3) 720 725 740 756 766 804 852 889 910
1752
ToYozo
w W m vvC vw w w
PMeN(a', a") skol (2) s k e l (1)
w a g (2) t - r (3) a 'z ) f'LM.e~--
1268 1289 1300 1315
w m vw w
t - r (4) w a g (4) t - r (5) w a g (5)
CnHzaN (CHa)aBr 720 725 733 748 758 781 820 871 882 911 926 955 964 981 988 999 1016 1029 1049 1059 1079 1089 1120 1141 1228 1234
sh vs m w w m w m vw s s vs vs W
r - t (1) r - t (2) r - t (3) r - t (4) VCN (a') r - t (5) r - t (6) r - t (7) Pl~eC (a') VCN(a') r - t (8) VCN (a:) VCN(a ) s k e l (6)
m
r-~ (9)
vw w w w vw w vw w w w sh
1248 m 1282 w 1302 w 1329 w
skol (5) r - t (10) s k e l (4) skel (3) pMeN(a', a '~) skel (2) s k e l (1) t - r (3) w a g (2) ~t-r (4) '-@MeN (a , a") t - r (5) t - r (6) w a g (5)
C12]~25~(CHa)aBr 719 728 740 757 768 799 842
s vs sh w m m m
891 m 911 937 963 984 995 1018 1030
KOICHIRO MIYAJIMA
1 (cont.)
Table 1091 1120 1142 1168 1202 1233 1242
UNO, KATSUI~OSL'KE MACHIDA and
s s vs m In m w
r - t (1) r - t (2, 3) r - t (4)
voN(a') r - t (5) r - t (6) r - t (7) { r - t (8) PM~c (a') Vcs(a') r - t (9) vcN(a', a") skel (6) r - t (10) s k e l (5) r - t (11)
1045 1057 1085 1093 1122 1141 1224 1231 1244 1251 1264 1280 1293 1316 1342
vw w vw vvc w m vw vw m w w w w w w
skol (4) skel (3)
p~eN(a', a u) skel (2) skel (1) w a g (2)
pMeN(a', a") t - r (4) w a g (4) t - r (5) w a g (5) w a g (6) w a g (7)
C1aH27N(CH3)aBr 718 728 753 759 782 818 860 883 900 913 947 965 990 1004 1028 1036 1058 1087
s vs m sh w m w w s s vs vs s m m w w w
1124 1142 1221 1225
w w vw sh
1239 1246 1258 1266 1287 1307
~ sh w vw m w
1331 w
r - t (1) r - t (2-4) r - t (5) vcN(a') r - t (6) r - t (7) r - t (8) pMec(a') r - t (9) ycN(a') r - t (10) ycN(a', a") skel (6) r - t (11) skel (5) r - t (12) skel (4) ( s k e l (3) t PMeN(a', a") skel (2) s k e l (1) w a g (2) t - r (3) . f w a g (3) ( PMeN (a', a") t - r (4) w a g (4) t ~ r (5) w a g (5) w a g (6) w a g (7)
ClaH~aN(CHa)aBr 720s ~ 730 v s ) 747 m 756 v~¢ 770 w 802 m 834 w 875m
r - t (1-4) r - t (5) YON( a ' ) r - t (6) r - t (7) r-% (8) r t (9)
885 911 918 951 964 972
pMec(a') vcN(a') r - t (10) r--t (11) ~cN(a') vcI~(a")
vw s s vs vs vs
986 s h 10O5 m 1033 w 1061 w 1090w
r - t (12) ~ r - t (13) l s k e l (5) s k e l (4) ~skol (3)
1124 1140 1215 1223 1234
w in w sh m
s k e l (2) skol (1) w a g (2) t - r (3) ~ w a g (3)
1241 1251 1282 1299 1320
W w w w w
t--r (4) w a g (4) w a g (5) w a g (6) w a g (7)
(.p~eN(a', a")
(pMes(a', a")
C15HalN(CHa)aBr 717 s "~ 730 v s ) 743 in 755 v w 762 w 786 ra 814 w 850 m 882 v w 890 w 912 s 930s 957 v s 9~5 v s 980 s 1004 m 1014 w 1032 w 1039 w 1042 s h 1062 w 1089 v¢ 1093 sh 1125w 1142 w 1218 v w 1235 w 1249 m 1255 s h 1268 v w 1282w 1293 w 1312 w
r-t (1-4) r - t (5) VCN( a ' ) r - t (6) r - t (7) r - t (8) r - t (9) pMec(a') r - t (10) YcN(a') r - t (11) VcN(a") vcN(a') r - t (12) skel (6) r - t (13) r - t (14) skel (5) s k e l (4) P~IeN (a', a") skel (3) skel (2) skel (1) t - r (3) t - r (4) ~( pwMa egN (4) (a, ' a .) t - r (5) w a g (5) t - r (6) w a g (6) w a g (7)
CleHaaN(CHa)aBr 720 s~ 730s)
r - t (1-4)
739 749 758 772 797 830
r - t (5) r - t (6) VcN(a') r--t (7) r - t (8) r - t (9)
sh sh v~ m w m
Infrared Tablo
l
864 w 885 v w 903 m 912 s 937 s 960 v s 964vs 981 s 985 sh 1012 m 1016 sh 1037 w 1044 w 1056 v w 1067 w 1090 v w 1126 w 1140 w 1208 w 1234 w 1244 w 1267 w 1287 w 1294vw 1303 w 1322 v w 1340vw
spectra
of finite chain molecules--II
1753
(cont.) r - t (10) PMec(a') r - t (11) ~'cN(a') r--t (12) VcN(an) ;PCN(a') r--t (13) skel (7) r--t (14) skel (6) r - t (15) skel (5) skel (4)
pMey,(a', a n) skel (2) skel (1) w a g (2) t - r (4) w a g (4) w a g (5) w a g (6) t - r (7) w a g (7) w a g (8) w a g (9)
CI~HasN(CHa)aBr 718 s ~ 730 v s ) r - t (1-4) 736 sh r - t (5) 757 m r - t (7) 764 m YcN(a') 784 w r - t (8) 812 m r - t (9)
843 879 883 910 914 946 964 973 977 991
w m sh s sh vs vs sh sh m
1006 1019 1022 1042 1052 1063 1070 1089 1098 1127 1141 1211 1227 1231 1242
w m sh w w vw vw w vw w w vw vw vw m
1258 1282 1297 1314 1332
w w w vw vw
r - t (10) r - t (11) PMec(a') ~CN(a') r - t (12) r - t (13) ~'CN(a" an)
752 758 774 801 825 856 890
m vw w m w m w
912 v s 925 m 947 v s 965 v s 968 v s 975 sh 992 sh 998 m 1019 w 1028 w 1040 v w 1052 m 1074 w 1090 w 1102 v w 1127 w 1141 m 1228 v w 1240m
.fr--t (14) t s k e l (7) r - t (15) skel (6) r - t (16) skel (5) skel (4) pMeN(a', a n) skel (3) skel (2) skel (1) t - r (3) w a g (3) t - r (4) ~ w a g (4) ~ (PMeN(a , a ) w a g (5) w a g (6) w a g (7) w a g (8) w a g (9)
1254 1271 1281 1289 1307 1326 1340
C18ttaTN(CHa)aBr 720 s ~ 731 v s ) r - t (1-6)
w sh sh m w w sh
r - t (7) YC~T(a') r - t (8) r--t (9) r - t (10) r - t (11) ~r--t (12) ( VCN(a') r - t (13) r - t (14) yeN(a:) YCN(a )
p~ec(a')
r - t (15) r - t (16) skel (6) r - t (17) skel (5) skel (4)
p~e~(a', a n) skel (3) skel (2) skel (1) t - r (4) ~ w a g (4)t ~pMeN(a, a ) w a g (5) w a g (6) t - r (7) w a g (7) w a g (8) w a g (9) w a g (10)
* vs, v e r y s t r o n g ; s, s t r o n g ; m , m e d i u m ; w, w e a k ; v w , v e r y w e a k ; sh, shoulder. t Chain m o d e s : r - t , CH~ r o c k l n g - t w i s t i n g (vs); skel, C - - C s t r e t c h i n g (v4); t - r , C H z t w i s t i n g - r o c k i n g (VT); wag, C H ! w a g g i n g (va); t h e k v a l u e s are s h o w n in parentheses. E n d g r o u p m o d e s : v c g ' C - - N s t r e t c h i n g ; Pxec' C - - C H a rocking; P]4eN' N - - C H a rocking; t h e s y m m e t r y classes are s h o w n in parentheses.
i
]
1300 1200 I100 I000 900 w a v e number (cm -I)
F i g . 2. I n f r a r e d
spectra
800
of CHa(C}I2)nN(CH3)aBr
700
, n = 5-8
(•ujol
mull).
1754
Tovozo
UNO, KATSUNOSUKE MACHIDA
and KOICHIRO MIYAJIMA
.
1300
1200 I100 I000 9 0 0 wave number (cm -~)
eoo
700
Fig. 3. Infrared spectra of CH3(CH2)nN(CHs)3Br, n = 9-12 (Nujol mull).
o
lm-
E.
.
.
'
.
n--
wave number (cm -I)
Fig. 4. Infrared spectra of CHs(CH2)~N(CH3)3Br, n = 13-16 (Nujol mull).
1300
1200 I100
I 0 0 0 900
800
700
wave number (cm -a)
Fig. 5. Infrared spectrum of CHs(CH2)ITN(CH3)3Br (Nujol mull).
Infrared spectra of finite chain molecules--II
1755
Table 2. The C--N stretching and the CH 3 rocking frequencies (cm-1) of n-alkyl-TMA bromides and related compounds CH a (CH2)nN+(CH3)a.BrFrequency Assignment~ 1234-1253 1087-1093++ 954-972 963-965++ 910-916 + 882-899 + 754-766 +
pMeN(a', a ~)
p~eN(a',a") %~(a") ~'c~(a') %~(a')
ItN +(CHa)a.I-* Frequency Assignment~ 1256
p~eN(al)
1241
PMeN(e)
1052
p~e~(e)
N+ (CHa)4.I-* Frequency Assignment~ 1294
VcN(f2)
1047
p~e~(e)
980
~'c~(e)
946
P~¢c(f2)
810
rcs (al)
752 §
~'cN(al)
PMec(a') %~(a')
* See Ref. [8]. For descriptions, see footnote ~, Table 1. ++Frequencies of shorter molecules deviate markedly from this range. § Raman frequency in aqueous solution. as C8. T h e end group vibrations are t h e n classified into two classes, the in-plane (a') a n d t h e out-of-plane (a") modes, with respect to t h e plane of t h e n-alkyl skeleton. The end group frequencies n e a r 1240, 1090, 965, 910, 890 a n d 760 cm -1 are identified readily for t h e long chain n - a l k y l - T M A bromides since their positions are v i r t u a l l y i n d e p e n d n e n t of the chain length. T h e b a n d n e a r 890 cm -1 is i m m e d i a t e l y assigned to the a' rocking mode of t h e t e r m i n a l C - - C H 3 group b y analogy to t h e d a t a on m a n y n-alkyl c o m p o u n d s [4, 10-12]. T h e o t h e r b a n d s are u n d o u b t e d l y due to the v i b r a t i o n s of t h e --N+(CH3)3 group at the opposite end, a n d t h e i r f r e q u e n c y range suggests t h a t only t h e C - - N stretching a n d t h e CH 3 rocking modes are concerned with. T h e assignments of these end group absorptions are s u m m a r i z e d in Table 2, t o g e t h e r with those of the reference compounds, t r i m e t h y l a m i n e h y d r o iodide a n d t e t r a m e t h y l a m m o n i u m iodide, due to EBSWORTH a n d SHEPP~a~D [8]. The assignments of the weak bands n e a r 760 a n d 1090 cm -1 are given consistently with b o t h the reference compounds, whereas the strong bands between 975 a n d 910 cm -1 ~nd t h e m e d i u m b a n d n e a r 1240 cm -1 are assigned inversely to the corresponding frequencies, 946 a n d 1296 cm -1, of t e t r a m e t h y l a m m o n i u m iodide. T h e present choice is based on t h e assignments for t r i m e t h y l a m i n e h y d r o i o d i d e from analogy in the n u m b e r of t h e N - - C H 3 groups. One m u s t note, however, t h a t t h e separate assignments to t h e C - - N stretching a n d to the CHa rocking modes are r a t h e r conventional, since the coupling b e t w e e n these two modes is v e r y likely to t a k e place. T h e e x t e n s i v e n o r m a l co-ordinate analysis of b r a n c h e d h y d r o c a r b o n s due to S~YDER a n d SCm~C~TSCK~EIDER [13] suggests t h e occurrence o f such a coupling in tri- a n d t e t r a m e t h y l a m m o n i u m ions a n d in n - a l k y l - T M A ions. According to these a u t h o r s the C - - C stretching a n d the C H 3 rocking modes couple with each o t h e r considerably in the f2 class of n e o p e n t a n e a n d in t h e e class of iso-butane. I t [I0] [11] [12] [13]
R. G. S3]'YDER,J. Mol. Spectry 4, 411 (1960). 1~. G. S)~-YDERand J. i . SC~C~rSCH~rEIDER, Spectrochim. Acta 19~ 85 (1963). M. TAsu~I, T. SHIMA~rOUCHI,A. WATANABEand R. GOTO,Spectrochim. Acta ~0, 629 (1964). R. G. S~YDER and J. I-I. SCHACHTSCH~rEIDER,Spectrochim. Acta 21, 169 (1965).
1756
ToYOZO UNo, K~_TSUNOSUKE MACHIDA and KOICHIRO I~IYAJIMA
seems probable that the strong bands between 975 and 910 cm -1 of long chain n-alkyl-TMA bromides are due to an a" and two a' modes which are correlated to the triply degenerate f~. mode of tetramethylammonium ion, although the relative magnitudes of contributions of the C - - N stretching and the CH a rocking modes may change on the replacement of a methyl b y an n-alkyl group. The two strong bands near 964 and 910 cm -1 are assigned to the a' modes since their positions are almost independent of the overlapping CH 2 rocking-twisting band progressions of the a" class. Around 960 cm -1, some of n-alkyl-TMA bromides show another band due certainly to the a" end group mode interacting with the CH 2 rocking-twisting modes. An evidence of this interaction is shown in the following section in relation to an anomalous feature of the CH2 rocking-twisting band progression. CHAIN VIBRATION FREQUENCIES
For any chain vibration, the amplitudes of the successive oscillators are determined b y the phase difference which, according to the transfer matrix theory [6], is given by = k~/(n ÷ 1) + ~l(n + 1),
(1)
where n is the number of the oscillators, k is an integer such that 1 ~ k =< n, and is the phase shift, a function of frequency determined b y the nature of the end groups b u t independent of n. The second term in the right-hand side of equation (1) m a y be neglected for sufficiently long chain molecules, and the approximate phase difference ~' = k~/(n + 1) (2) may be used. Usually, the band progression analysis starts with the assignment of the k values to each absorption frequency. The phase differences are then calculated from equation (2), and the frequencies plotted against ~ to yield the frequencyphase difference diagram. One must be careful in applying this method to such short chain molecules as dealt with in the present study, since any shift in the progression frequencies on the terminal substitution results in the shift of the frequency-phase difference curve. This shift m a y lead to an overestimation of the change in the force field of the chain part. The present analysis of band progressions is mainly concerned with the properties of the chain length-frequency curves which relate the chain length (n) to the progression frequency (v). As shown previously [5], the transfer matrix theory leads to two rules governing the shift of the chain length-frequency curves on a terminal substitution which leaves the force field of the chain part invariant. Let n and v be taken on the ordinate and abscissa, respectively, then Rule 1 states that the vertical shift at a fixed frequency is independent of the k value and Rule 2 that the horizontal shift in a small frequency range is inversely proportional to n ÷ 1. Rule 1 is due to the relation q~ ----- 7 r / A N , (3) where AN is the increment in n on adding unity to ]c, that is, the spacing between adjacent chain length-frequency curves along the ordinate. Equation (3) can be used to draw the correct frequency-phase difference curve from the data for shorter
Infrared spectra of finite chain molecules--II
1757
chain molecules. In the following discussion on the individual band progressions, we adopt the designation of the vibrational modes of polymethylene chain due to TAsu~II et al. [14]. T h e v a a n d v~ modes
The complicated series of weak absorptions between 1360 and 1200 cm -1 are attributed to the CH 2 wagging (va) and the CH 2 twisting-rocking (v~) modes. The plot of absorption frequencies against the chain length discloses the presence of two progressions, one of which is distributed between 1360 and 1230 cm -1 and the other between 1300 and 1220 cm -1. These frequency regions suggest t h a t the former and the latter correspond to the va and the v~ progressions, respectively. Above 1300 c m -1, the ~a absorptions are distributed regularly for longer molecules but are mostly missing for shorter molecules. Between 1300 and 1230 cm -1, the frequency distribution of both the ~a and the vv progressions seems to be disturbed by the interaction of the chain modes with the CHa-N rocking modes of the a' and the a" classes. Most of the expected absorptions below 1220 cm -~ are too weak to be observed. I t is therefore difficult to correlate these progression frequencies with the chain length accurately, and the assignment of the k values included in Table 1 must be regarded as tentative. A n y detailed analysis of the chain length-frequency curves was not made for these progressions. T h e ~a m o d e
I t has been known t h a t the frequency-phase difference curve for the C--C stretching (v4) progression has a minimum near 960 cm-L SNYDER and SC~CHTSCHNEIDER have divided the curve at the minimum into the phase regions A and B [11]. Each n-alkyl-TMA bromide shows a number of weak or medium bands between 1150 and 970 cm -1 attributable to the ~4 modes. The absorption frequencies above 1060 cm -1 arise only from the phase region A and are given the straightforward assignment of the lc values. The band distribution below 1060 cm -1 is quite complicated, however, because of the overlap of the phase regions A and B. B y referring to the data above 1060 cm -1, the k value assignment was made only for the frequencies belonging to the phase region A between 1060 and 980 cm -1. The resulting chain length-frequency curves are shown in Fig. 6, and are compared with those of nparaffins [6, 11]. The curves of n-paraffins and n-alkyl-TMA bromides for k ---- 1 practically coincide with each other, converging with the increase of the chain length into the common frequency for the phase difference ~ of an infinite chain. For k ~- 2 and 3, however, the curves of n-alkyl-TMA bromides deviate appreciably to higher frequencies from those of n-paraffins, possibly because the C--N stretching modes of the a' class interact with the va modes and accordingly push up the va frequencies. The vibrations for which k --~ 1 are infrared inactive for n-paraffins with even carbon atoms. Correspondingly, an even-odd alternation of the intensity ratio of the two highest v4 bands is clearly observed for n-alkyl-TMA bromides in Figs. 2-5. Figure 7 shows a part of the frequency-phase difference diagrams for the phase region A obtained from the v4 frequencies of n-paraffins [11] and n-alkyl-TMA [14] M. TAsu~I, T. SHIMA~OUC~Iand T. MIYAZAWA, J . !1Iol. Spectry 9, 261 (1962).
1758
TOYOZO
UNo,
K~TSUI~OSUKE
M~kCHIDA
and
MIYAJIMA
KOIOItIRO
i -I
Fig. 6. Chain length-frequency curves for the v 4 progression of CI-I2 (CH 2)nN (CH a) a Br (large circles) and CHa(CH~)nCH a (small circles). cm-'-----L- o II00
~ k-I "i---• (P'-~'T ~" L
/
,/,=Tr/AN
o c6- k-2-n-
g °o
]
I'
Io'ol
o I
i
;e
- - _ _
f
[
I oe
,
J oo
1
#oI
1050
1
~ o °e
_
~
I
"el- o , b o
:000
/'
(a) I 04
i
i 02
o
o
o
o o (b) 0.3
0
I ° r-!--:¢
04
0.2
0.3
~6/~
Fig. 7. Frequency-phase difference diagrams for the region A of the % progression of CI-Ia(CI-I~)nl~(CHa)Br (hollow circles and squares) and CH3(CH2)nCH a (filled circles) with n > 10: (a) and (b) represent equations (2) and (3), respectively. b r o m i d e s w i t h m o r e t h a n 10 m e t h y l e n e units, (a) being b a s e d o n e q u a t i o n (2) in w h i c h n is t h e n u m b e r o f C - - C bonds, a n d (b) o n e q u a t i o n (3). I n a p p l y i n g e q u a t i o n (2) t o n-paraffins, S~TYDER a n d SCHAGHTSCJcINEIDER u s e d k -- 1 i n s t e a d o f k in order to correct t h e effect o f C H a in-plane rocking m o d e s interacting w i t h t h e % m o d e s . W e u s e d trial v a l u e s k - - 1 a n d k -- 2 for n - a l k y l - T M A bromides. F o r t h e frequencies a s s i g n e d t o t h e k v a l u e s greater t h a n 3,/c -- 2 w a s f o u n d better t h a n k -- 1 in fitting t h e f r e q u e n c y - p h a s e difference curve o f n - a l k y l - T M A b r o m i d e s t o t h a t o f n-paraffins. This result s u g g e s t s t h a t n - a l k y l - T M A b r o m i d e s h a v e m o r e e n d g r o u p m o d e s interacting w i t h t h e % m o d e s t h a n n-paraffins. I n order t o e s t i m a t e t h e p h a s e difference
Infrared spectra of finite chain molecules--II
1759
from equation (3), we calculated the AN at each absorption frequency b y a simple modification of the interpolation method described in the preceding paper [5]. I f we specify a polymethylene band progression frequency b y v,k, the first and the second subscript denoting the number of methylene units and the k value, respectively, the AN at vmk' is given b y A2V(~m~,)
=
[m
-
n
-
p(~.~
-
~,)/(~
-
v~+~,~)]/(k'
-
lc),
(4)
where v.~ and v~+~.k are the two reference frequencies such that ~n+~,k ~ "Ymk" ~ 'lJnk"
Equation (4) is obtained from equation (8) in Ref. [5] b y replacing v b y vmk' and k + j b y k'. The phase differences in Fig. 7(b) were calculated b y using such reference frequencies that k is k' -- 1 and p is 1 or 2. From the chain length-frequency curves with constant k values in Fig. 6, AN is not available at the frequencies v~2 and vma of n-alkyl-TMA bromides (except v1~.3) and vm2 of n-paraffins. For these frequencies, the phase difference was calculated b y 9 = ~r(1 -- 1/AN'), where AN'(vm~,)
:
[m
-- n
-- (Vn.k,_ 1 --
Vmld)/(Vn,k,_
1 --
Vn+l,k,)]/(m
--
n
~-
1)
(5)
and n was p u t equM to 7 and 8 for k' = 2 and 3, respectively. This calculation is based on the simple relation 1/AN + 1 ~ A N ' : - 1, AN' being the intervM between the chain length-frequency curves connecting such vn~'s that n -- k is constant. The highest reference frequency v~,1 was chosen b y regarding it as the converged value of vnl on the increase of n. B y comparing Fig. 7(b) with (a), it is seen that the use of equation (3) removes the disagreement in the frequency-phase difference diagrams between n-paraffins and n-alkyl-TMA bromides arising from equation (2). This result reveals an excelent transferability in the force constants governing the v4 frequencies between these two homologous series. I t is noteworthy that we need not use any ambiguous correction to the k value in using equation (3). The
v s mode
The rocking-twisting (vs) band progressions are observed between 1060 and 720 cm -1. Although some of them are overlapped b y the weak v4 absorptions above 970 cm -1 and b y the strong C - - N stretching absorptions between 975 and 910 cm -1, the comparison with the data of n-paraffins [11], n-alcohols [12] and n-fatty acid salts [3, 4] allowed the k value assignment of almost all vs absorptions. They are sharp and fairly strong, and are therefore quite useful for the identification of the chain length of n-alkyl-TMA bromides. The chain length-frequency curves are shown in Fig. 8, where the data for n-paraffins [11] are also plotted for comparison. I t is seen that the vs progression frequencies of n-alkyl-TMA bromides are appreciably higher than the corresponding frequencies of n-paraffins. I f we attribute the higher limit of the vs frequency region to the phase difference 7r according to S~YDER and SOHACHTSCHI~EIDER[11], the frequencies of n-paraffins with even k values become
1760
ToYozo U~o, KATSUI~OSUKEMACHIDA and KOICH~ROMIYAJI~L~ . . . .
I I° s
I000
900
800
C m -I
Fig. 8. Chain length-frequency curves for the ~8progressionof CHa(CH2)nN(CHa)aBr (large circles) and CHa(CH~)nCHa (small circles). Squares represent the frequencies of CHa(CH2)nN(CHa)aBr predicted by Rule 2. infrared inactive, whereas all of the v8 modes are infrared active for n-alkyl-TMA bromides. We have therefore two chain length frequency curves of n-alkyl-TMA bromides between each pair of adjacent n-paraffin curves. As seen clearly in Figs. 2-5, the bands of n-alkyl-TMA bromides associated with even and odd k values are strong and weak, respectively, in accordance with the selection rule for n-paraffins. In the vicinity of the strong C--N stretching bands between 975 and 910 cm -1, however, the intensity alternation is not obvious and quite strong vs absorptions are observed. Furthermore, the smooth chain length-frequency curves drawn for nalkyl-TMA bromides in Fig. 8 do not fit well the observed vs frequencies around 950 cm -1. Such anomalous frequencies are explained by taking account of the vibrational coupling between the ~s modes and the a" C--N stretching mode. In Fig. 9, the C - - N stretching frequencies and the vs frequencies above 800 cm -x are plotted against the chain length. By connecting appropriate a" C--N stretching frequencies with the ~8 frequencies having constant values of n -- k q- 1 (the k value due to TASUMI et al. [14]), we obtain a set of smooth curves which do not intersect one another. I t is well known t h a t non-intersecting curves are obtained by plotting frequencies of vibrational modes having the same symmetry against a given molecular parameter such as an atomic mass [15]. The intersecting broken lines in Fig. 9 represent the unperturbed frequencies which might occur on the absence of coupling terms in the kinetic and potential energies. I n Fig. 9, the unperturbed a" C--N stretching frequency is taken as 964 cm -1, the averaged value for the associated a' frequencies of longer molecules, and the frequency nearest to it is assigned to the a" C--N stretching mode for each n-alkyl-T1VIA bromide. In some cases (e.g. n-decyl-TMA bromide), however, an appreciable coupling is expected from the separation between the observed and the unperturbed frequencies and it is difficult to distinguish the end vibration from the vs modes. Assuming t h a t the vibrational coupling between two [15] G. HERZBERG,Infrared and Raman Spectra of Polyatomic Molecules, p. 200. Van Nostrand (1945).
1761
Infrared spectra of finite chain molecules--II
900
I000
800
c m -~
Fig. 9. The vs progressmn and the C - - N stretching frequencies of CHs(CH2) n~(CHa)aBr. Large circles, Us; small circles, a' C--N stretching; squares, a" C--N stretching.
modes gives rise to the shifts of the corresponding frequencies to the opposite directions by the same amount, we may estimate the unperturbed % frequencies roughly in wave numbers by %(unperturbed) = %(observed) + ~a"C-N -- 964. These unperturbed % frequencies fall closely on the broken lines in Fig. 9. The AN's for the % frequencies of n-paraffins [11] and n-alkyl-TM~ bromides are plotted against v in Fig. 10. They were calculated by inserting the k value of TASUMI et al. [14] into equation (4) in which/c was put equal to k' + 1, and p was to I or 2. For n-alkyl-TMA bromides, the aforementioned interaction between the % modes and the a" C - - N stretching mode gives rise to the large deviation in A/V's around 950 AN 8 •
o
o o
o
i
i
i I
I i
~ o c~ ~ -
I000
!
t •
i
'i
i
:
i
I
i i
'
I
r i I
i i
Ii 900
/ i
,
t 800
J I cm-I
Fig. 10. Plot of A N against the frequency for the us progression. Filled circles, CHa(CHu)nCHa; hollow circles, CHa(CH2)nN(CHa)aBr.
1762
ToYozo U~o, KATSUNOSUKEMAOHID)~and KOrOHIROMXYAJIMA
cm -1. The deviation above 980 cm -1 is due to the zigzagging of chain lengthfrequency curves according to the even-odd alternation in methylene numbers of longer n-alkyl-TMA bromides. Below 940 cm -1, however, the data points for both n-alkyI-TMA bromides and n-paraffins lie closely on a smooth curve, in agreement with the prediction of Rule 1. Figure ll(a) shows the frequency-phase difference diagram obtained by applying equation (2) to the v8 frequencies of n-paraffins [11] and n-alkyl-TMA bromides, and Fig. 11(b) by applying equation (3) to the same data. The data points were taken only from the molecules having 17, 15, 13, 9 and 7 methylene units in order to avoid overcrowding. I n calculating the phase difference for Fig. 11(b), the AN's were averaged by using the smallest n and k for each vmk'in equation (4). The advantage of equation (3) over (2) is obvious in fitting the frequencies taken from different homologous series to a common curve. In Fig. 11 (a), the points for n-alkyl-TMA bromides fall nearly on a smooth curve whereas those for nparaffins do not. This result implies t h a t the phase shift for the % modes is small for crn-D
I000
!%%'
I
I
!
i *:
i ,.,./,o+) .% I
,,
i
i 900
i
i\
o
• ooI
i
ii
t
! I
i
v
.'~
l
i.~
80C
i
i
~(a) ] o o.z
i"~' 0.4
i
~i(b)
0.6
0.8
0
0.2
0.4
0.6
,.o ~ / ~
0.8
Fig. 11. Frequency-phase difference diagrams for the %progression of CHa(CH=)nN(CHa)aBr (hollow circles) and Ctta(CH~)nCHa (filled circles) with n = 17, 15, 13, 9 and 7: (a) and (b) represent equations (2) and (3), respectively. (rf+l)A~ c m -I v17
400
\,
16
_ _
____
~5
200 ]7 15
',oo;
I
,T , , .
.
900
.
.
, , , ,i , , r , . . 800 cm -I
Fig. 12. Plot of (n' + 1)Au against the frequency of CI-Ia(OI-I2)nCHa: n' is indicated for each datum point.
Infrared spectra of finite chain molecules--II
1763
n-alkyl-TMA bromides but is not negligible for n-paraffins. Fortunately, such phase shifts are favourable for the prediction of frequency shifts on the change from n-paraffins to n-aLkyl-TMA bromides b y the empirical method based on Rule 2 described in the preceding paper [5]. In Fig. 12, the observed frequency shift, A~n'k'
----
~,k,(n-alkyl-TMA bromide) -- ~,k,(n-paraffin),
multiplied b y n ' + 1 is plotted against the frequencies of n-paraffins for the molecules with n ' ~ 15, 16 and 17. The data points except a few lie on a fairly smooth curve showing that (n + 1)Av,k is independent of the chain length. B y interpolating the data in Fig. 12, (n + 1)Av~k was evaluated at each frequency of shorter nparaffins and the corresponding frequency of n-alkyl-TMA bromides was estimated. The result is included in Fig. 8, where the estimated and the observed frequencies agree well with each other except the cases when v~k(n-alkyl-TMA bromide) - 950 cm -1 (n ---- 3, 7, 8 and 13) and when ~k(n-paraffin) < 800 em -1 (n ---- 2, 3 and 4). In the former case the deviation is due again to the interaction of the ~s modes and the a" C - - N stretching mode, the chain length-frequency curves being fitted well by the estimated frequencies. The latter deviation is related probably to the fact that the frequency shifts from n-paraffins to n-alkyl-TMA bromides are too large to neglect the curvature of the frequency-phase difference curve. From the present result of applying Rules 1 and 2 to the vs progressions of nparaffins and n-alkyl-TMA bromides, we m a y conclude that the shifts of the ~s frequencies on the substitution of a terminal methyl b y a trimethylammonium group are mostly due to the change in the vibrational coupling between the chain and the end parts of molecules and the effect of the change in force constants governing the vs frequencies is not important. From the standpoint of vibrational potential energy, the n-alkyl group of n-alkyl-TMA bromides is thus suggested to be quite similar to that of n-paraffins even for very short molecules. Acknowledgements--The authors' thanks are due to the helpful suggestions of Professor
TSUI~-EI~OBUYAMAMOTO,Professor I-IIXOTSlIOUMATSUD&and Dr. K~N~ICHI OY~.I)Aof Kyoto University.
Printed in Northern Ireland
Infrared spectra of finite chain molecules--H n-alkyltrimethylammonium bromides T o Y o z o UNO, KATSUNOSUKE MACHIDA a n d KOICHIRO MIYAJIMA Faculty of Pharmaceutical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan (Received 2 _November 1967)
infrared spectra between 1400 and 700 cm-1 of n-alkyltrimethylammonium bromides with n-alkyl chains including 2 through 18 carbon atoms are reported. The end group frequencies are assigned and the band progression analysed by using the properties of chain length-frequency curves. The result shows that the force field of the chain part of n-alkyltrimethylammonium bromides is practically the same as that of n-paraffins. A vibrational coupling between the chain part and the end group is evidenced by the irregular feature of the CH 2 rocking-twisting band progression. INTRODUCTION Abstract--The
TEE a b s o r p t i o n intensities of t h e infrared b a n d progressions of p o l y m e t h y l e n e chains are o f t e n e n h a n c e d b y introducing polar t e r m i n a l groups. Such e n h a n c e d b a n d progressions h a v e been i n v e s t i g a t e d for n - f a t t y acid salts [1-4] a n d p r o v e d to be useful in determining t h e length of n-alkyl chains in e a r b o x y l a t e anions. T h e r e h a v e been few reports, however, on the b a n d progressions of a m m o n i u m salts containing long n-alkyl chains although t h e y are c o m m o n l y used as cationic surfactants. As a consequence of t h e preceding theoretical t r e a t m e n t of b a n d progressions [5], we r e p o r t in the present p a p e r the infrared spectra of n - a l k y l t r i m e t h y l a m m o n i u m bromides ( a b b r e v i a t e d n - a l k y l - T M A bromides, hereafter) with C 2 t h r o u g h Cls n-alkyl chains a n d give the b a n d progression analysis based on the t r a n s f e r m a t r i x t h e o r y of MATSUDA et al. [6]. T h e analysis was initially p l a n n e d from the necessity of identifying t h e chain length a n d checking the p u r i t y of s t a n d a r d samples in t h e studies on t h e d e t e r m i n a t i o n of cationic s u r f a c t a n t s in this l a b o r a t o r y [7]. I t has been f o u n d t h a t a m o n g t h e four progressions arising between 1400 a n d 700 cm -1, t h e C H 2 r o c k i n g - t w i s t i n g progression is t h e m o s t distinguished a n d is helpful for t h e purpose of identification. The characteristic frequencies of t h e end group, N+(CH3)3, h a v e also been given assignments a n d f o u n d to be correlated closely to t h e f u n d a m e n t a l frequencies of t r i m e t h y l a m i n e h y d r o i o d i d e a n d t e t r a m e t h y l a m m o n i u m iodide r e p o r t e d b y ]~BSV¢ORTH a n d SHEPPARD [8]. [1] D. CHAPMAn,J . Chem. Soc. 784 (1958). [2] R. A. MEIKLEJOHI"~,R. J. MEYER, S. M. ARONOVIC, H. A. SCHUETTEand V. W. MELOCH, Anal. Chem. 29, 329 (1957). [3] T. TAKENAKA,J . Chem. Soc. Japan, Pure Chem. Sect. 84, 392 (1963). [4] E. M. KIRBY, M. J. EVANS-VADER and M. A. BROW'~, J . A m . Oil Chemists' Soc. 42, 437 (1965). [5] T. UNO and K. MACHIDA,Spectrochim. Acta 24A, 1741 (1968). [6] H. MATSUDA, K. OKADA, T. TAKASE and T. YAMAMOTO,J. Chem. Phys. 41, 1527 (1964); H. MATSUDA,Proff. Theor. Phys. (Kyoto), Suppl. 23, 22 (1962). [7] T. UNO, K. MIYAJI~A and I-I. TSVKATANI, Yakugaku Zasshi (Tokyo) 8 0 , 153 (1960). [8] E. A. V. EBSWORTHand •. SHEPPARD,Spectrochim. Acta 13, 261 (1959). 6 1749
1750
ToYozo U~o, KATSUNOSUKE1VIACHIDAand KOIOHIR0MIYA,IIMA ]~XPERIMENTAL
The samples of n-alkyl-TMA bromides, R--N(CHa)aBr (R = n-alkyl), were prepared from the corresponding n-alkyl bromides ( R - - B r ) b y the reactions, R B r + HN(CH3) ~ in sealed tub%. RN(CHs) .HBr RN(CHa)~.HBr + N a O H
~q. soln. _~. RN(CHa)2 + H2 0 + NaBr
RN(CH3)2 + CH3B r in ~ealedtub% RN(CHa)aBr or directly b y the reaction with trimethylamine. They were recrystallized from the mixture of dried ether and ethanol [7]. The homologous impurities in the starting material were checked b y the gas chromatography and found to be less than 1% for each n-alkyl bromide. The infrared spectra between 1400 and 700 cm -1 were recorded on a Koken DS301 infrared spectrophotometer equipped with sodium chloride optics. The samples were measured as l~ujol mulls. For the wavenumber calibration the standard absorptions of polystyrene, indene and ammonia [9] were used and the errors were estimated to be within ± 1 cm -1. The observed infrared spectra are shown in Figs. 1 to 5, and the frequencies in Table 1, together with the assignments to be referred to in the following discussion.
"~ n=2
1300
F i g . 1. I n f r a r e d spectra o f
1200 I100 I000 900 wove number (crn-q
800
700
CHa(CH2)nl~(CI-Ia)aBr,n
= 1-4 ( l ~ u j o ] m u l l ) .
END GROUP FREQUENCIES Although the X-ray crystallographic analysis has not yet been made for any member of the homologous series of n-alkyl-TMA bromides, no ambiguity arises on the mutual conformation of the n-alkyl chain and the axially symmetric terminal group, --N+(CHa)a. Since the n-alkyl chain is usually in the extended trans configuration in the crystalline state, the point group of a whole molecule m a y be taken [9] IUPAC commission on Molecular Structure and Spectroscopy, Tables of Wavenumbers for Calibration of Infrared Spectrometers. Butterworths (1961).
Infrared spectra of finite chain molecules--II
1751
Table 1. Wavenumbers, relative intensities* a n d assignments~ of infrared bands (1350-700 cm -1) of solid n-alkyl-TMA bromides CzHbN(CHa)aBr 713 m 819 m 874 v s 954 1012 1076 1094 1153 1173 1239 1288
vs s m'( wJ m m s vW
WcN(a') r - t (1) 5 P Mec(ap) ( % N ( a p) ~CN (a:) %N(a )
p~ieN(a t, a") s k e l (1) p~eN(a', a") w a g (1)
954 s 977 v s 988 s 1010 w 1029 v w 1050 s 1059 w 1109 m 1155 m 1208 w 1239 v w 1269 m 1294 m 1327 m
CaH~N(CH3)aBr 752 m 892 s 946 v s 966 v s 1038 1079 1099 1154
m w m m
1173 1250 1281 1298 1329 1348
w m w w w w
r - t (1) {p:~) e ') vcIq(a ) ~CN(a ~)
p~ey,(a', a ~) s k e l (2) s k e l (1) S w a g (1) ( PMeN (a', a n) t - r (2) w a g (2)
C4H,N(CHa)aBr 743 m 756 w 776w 800 w 899 s 914 v s 936 s 973 v s 1032 m 1059 m 1076 w 1105 w 1156 m 1174 w 1222 w 1243 m 1274 W 1282 m 1291 w 1315 v w
VCl~(a'' an) PMei~(a~, a '~) s k e l (2) skel (1)
p~e1~(a ~, a n) w a g (2)
s k e l (3) pMeN(a', a n) s k e l (2) s k e l (1)
w a g (2) t--r (3) w a g (3)
C6HIsN(CHa)sBr 725 s 747W 758 v w 805 m 889 m 915 958 964 994 1010 1054 1108 1144 1222 1245
s vs vs m ~¢ m w m w m
1278 v w 1301 w
r - t (1) VCN(a') r--t (2) PMec(a') vc~(a ) r - t (3)
?]cN(a', a n) r - t (4)
r - t (1) r - t (2) VON(a') r--t (3) ~r--t (4) (PMec ( a ' ) vcN(a') VCN(a n) VcN(a ') r--t (5) skel (3 ) s k e l (2) s k e l (1) p ~ e ~ ( a , ' a ~) t - r (3) w a g (3)
CTH15N(CHa)aBr 724 735 755 775 839 916
s vW vw w w s
964 990 1009 1032 1055 1113 1143 1218 1241 1267 1287 1305
vs w w w w w w w m w w w
r - t (1) r - t (2) Ve~ (a') r - t (3) r - t (4) ~VC~ (a') ( r - t (5) YeN (a', a n) r - t (6) skel (3) s k e l (2) s k e l (1) PMeN(a', a n) t - r (3) w a g (3) t - r (4)
CsH11N(CH3)aBr 735 754 770 854 889 927
s w w m s s
r - t (1) YcN(a ~) r - t (2) r - t (3)
p~iec(a') yCN(a t)
CsH~vN(CH3)aBr 723 752 760 804
s m w w
r - t (1, 2) r - t (3) VoN(a') r - t (4)
866 914 933 965 992 1012 1039 1067 1092 1115 1142 1214 1242
m s s vs w w W w vw w m vw m
1258 1270 1289 1312
W w w w
r - t (5) wc~(a') r - t (6) VcN(a p, a n) r - t (7) s k e l (3) P•eN(a p, a H) skel (2) s k e l (1) ~ w a g (2) Lp~feN(a' , a ~) t--r (3) w a g (3) t - r (4) w a g (4)
CgHlaN(CHa)aBr 722 743 756 777 828 888 910 943 964 972 992
s m w w m w s vs vs s m
r - t (1) r - t (3) ycN(a ') r - t (4) r--t (5) r--t (6) VoN(a') r - t (7)
1020 1035 1050 1071
w w w w
r - t (8) s k e l (4)
1089 1116 1142 1235 1247 1258 1282
w w w m vw w w
pMeN(a', a " ) s k e l (2) s k e l (1) w a g (2) t - r (3) w a g (3) t - r (4)
1297 w 1327 w
Vc~ % ~ ( (a') a ~) s k e l (5)
s k e l (3)
w a g (4) w a g (5)
C~°H~IN (CHa)aBr sh r - t (1) vs r - t (2) s r - t (3) w r - t (4) w ~CN(a') m r--t (5) m r - t (6) vw PKec(a') s ~r--t (7) tVcN (a') 950 v s VCN(a") 965 v s YON(a') 978 s r - t (8) 1003 m s k e l (5) 1022 w r - t (9) 1047 w s k e l (4) 1063 w 1077 w s k e l (3) 720 725 740 756 766 804 852 889 910
1752
ToYozo
w W m vvC vw w w
PMeN(a', a") skol (2) s k e l (1)
w a g (2) t - r (3) a 'z ) f'LM.e~--
1268 1289 1300 1315
w m vw w
t - r (4) w a g (4) t - r (5) w a g (5)
CnHzaN (CHa)aBr 720 725 733 748 758 781 820 871 882 911 926 955 964 981 988 999 1016 1029 1049 1059 1079 1089 1120 1141 1228 1234
sh vs m w w m w m vw s s vs vs W
r - t (1) r - t (2) r - t (3) r - t (4) VCN (a') r - t (5) r - t (6) r - t (7) Pl~eC (a') VCN(a') r - t (8) VCN (a:) VCN(a ) s k e l (6)
m
r-~ (9)
vw w w w vw w vw w w w sh
1248 m 1282 w 1302 w 1329 w
skol (5) r - t (10) s k e l (4) skel (3) pMeN(a', a '~) skel (2) s k e l (1) t - r (3) w a g (2) ~t-r (4) '-@MeN (a , a") t - r (5) t - r (6) w a g (5)
C12]~25~(CHa)aBr 719 728 740 757 768 799 842
s vs sh w m m m
891 m 911 937 963 984 995 1018 1030
KOICHIRO MIYAJIMA
1 (cont.)
Table 1091 1120 1142 1168 1202 1233 1242
UNO, KATSUI~OSL'KE MACHIDA and
s s vs m In m w
r - t (1) r - t (2, 3) r - t (4)
voN(a') r - t (5) r - t (6) r - t (7) { r - t (8) PM~c (a') Vcs(a') r - t (9) vcN(a', a") skel (6) r - t (10) s k e l (5) r - t (11)
1045 1057 1085 1093 1122 1141 1224 1231 1244 1251 1264 1280 1293 1316 1342
vw w vw vvc w m vw vw m w w w w w w
skol (4) skel (3)
p~eN(a', a u) skel (2) skel (1) w a g (2)
pMeN(a', a") t - r (4) w a g (4) t - r (5) w a g (5) w a g (6) w a g (7)
C1aH27N(CH3)aBr 718 728 753 759 782 818 860 883 900 913 947 965 990 1004 1028 1036 1058 1087
s vs m sh w m w w s s vs vs s m m w w w
1124 1142 1221 1225
w w vw sh
1239 1246 1258 1266 1287 1307
~ sh w vw m w
1331 w
r - t (1) r - t (2-4) r - t (5) vcN(a') r - t (6) r - t (7) r - t (8) pMec(a') r - t (9) ycN(a') r - t (10) ycN(a', a") skel (6) r - t (11) skel (5) r - t (12) skel (4) ( s k e l (3) t PMeN(a', a") skel (2) s k e l (1) w a g (2) t - r (3) . f w a g (3) ( PMeN (a', a") t - r (4) w a g (4) t ~ r (5) w a g (5) w a g (6) w a g (7)
ClaH~aN(CHa)aBr 720s ~ 730 v s ) 747 m 756 v~¢ 770 w 802 m 834 w 875m
r - t (1-4) r - t (5) YON( a ' ) r - t (6) r - t (7) r-% (8) r t (9)
885 911 918 951 964 972
pMec(a') vcN(a') r - t (10) r--t (11) ~cN(a') vcI~(a")
vw s s vs vs vs
986 s h 10O5 m 1033 w 1061 w 1090w
r - t (12) ~ r - t (13) l s k e l (5) s k e l (4) ~skol (3)
1124 1140 1215 1223 1234
w in w sh m
s k e l (2) skol (1) w a g (2) t - r (3) ~ w a g (3)
1241 1251 1282 1299 1320
W w w w w
t--r (4) w a g (4) w a g (5) w a g (6) w a g (7)
(.p~eN(a', a")
(pMes(a', a")
C15HalN(CHa)aBr 717 s "~ 730 v s ) 743 in 755 v w 762 w 786 ra 814 w 850 m 882 v w 890 w 912 s 930s 957 v s 9~5 v s 980 s 1004 m 1014 w 1032 w 1039 w 1042 s h 1062 w 1089 v¢ 1093 sh 1125w 1142 w 1218 v w 1235 w 1249 m 1255 s h 1268 v w 1282w 1293 w 1312 w
r-t (1-4) r - t (5) VCN( a ' ) r - t (6) r - t (7) r - t (8) r - t (9) pMec(a') r - t (10) YcN(a') r - t (11) VcN(a") vcN(a') r - t (12) skel (6) r - t (13) r - t (14) skel (5) s k e l (4) P~IeN (a', a") skel (3) skel (2) skel (1) t - r (3) t - r (4) ~( pwMa egN (4) (a, ' a .) t - r (5) w a g (5) t - r (6) w a g (6) w a g (7)
CleHaaN(CHa)aBr 720 s~ 730s)
r - t (1-4)
739 749 758 772 797 830
r - t (5) r - t (6) VcN(a') r--t (7) r - t (8) r - t (9)
sh sh v~ m w m
Infrared Tablo
l
864 w 885 v w 903 m 912 s 937 s 960 v s 964vs 981 s 985 sh 1012 m 1016 sh 1037 w 1044 w 1056 v w 1067 w 1090 v w 1126 w 1140 w 1208 w 1234 w 1244 w 1267 w 1287 w 1294vw 1303 w 1322 v w 1340vw
spectra
of finite chain molecules--II
1753
(cont.) r - t (10) PMec(a') r - t (11) ~'cN(a') r--t (12) VcN(an) ;PCN(a') r--t (13) skel (7) r--t (14) skel (6) r - t (15) skel (5) skel (4)
pMey,(a', a n) skel (2) skel (1) w a g (2) t - r (4) w a g (4) w a g (5) w a g (6) t - r (7) w a g (7) w a g (8) w a g (9)
CI~HasN(CHa)aBr 718 s ~ 730 v s ) r - t (1-4) 736 sh r - t (5) 757 m r - t (7) 764 m YcN(a') 784 w r - t (8) 812 m r - t (9)
843 879 883 910 914 946 964 973 977 991
w m sh s sh vs vs sh sh m
1006 1019 1022 1042 1052 1063 1070 1089 1098 1127 1141 1211 1227 1231 1242
w m sh w w vw vw w vw w w vw vw vw m
1258 1282 1297 1314 1332
w w w vw vw
r - t (10) r - t (11) PMec(a') ~CN(a') r - t (12) r - t (13) ~'CN(a" an)
752 758 774 801 825 856 890
m vw w m w m w
912 v s 925 m 947 v s 965 v s 968 v s 975 sh 992 sh 998 m 1019 w 1028 w 1040 v w 1052 m 1074 w 1090 w 1102 v w 1127 w 1141 m 1228 v w 1240m
.fr--t (14) t s k e l (7) r - t (15) skel (6) r - t (16) skel (5) skel (4) pMeN(a', a n) skel (3) skel (2) skel (1) t - r (3) w a g (3) t - r (4) ~ w a g (4) ~ (PMeN(a , a ) w a g (5) w a g (6) w a g (7) w a g (8) w a g (9)
1254 1271 1281 1289 1307 1326 1340
C18ttaTN(CHa)aBr 720 s ~ 731 v s ) r - t (1-6)
w sh sh m w w sh
r - t (7) YC~T(a') r - t (8) r--t (9) r - t (10) r - t (11) ~r--t (12) ( VCN(a') r - t (13) r - t (14) yeN(a:) YCN(a )
p~ec(a')
r - t (15) r - t (16) skel (6) r - t (17) skel (5) skel (4)
p~e~(a', a n) skel (3) skel (2) skel (1) t - r (4) ~ w a g (4)t ~pMeN(a, a ) w a g (5) w a g (6) t - r (7) w a g (7) w a g (8) w a g (9) w a g (10)
* vs, v e r y s t r o n g ; s, s t r o n g ; m , m e d i u m ; w, w e a k ; v w , v e r y w e a k ; sh, shoulder. t Chain m o d e s : r - t , CH~ r o c k l n g - t w i s t i n g (vs); skel, C - - C s t r e t c h i n g (v4); t - r , C H z t w i s t i n g - r o c k i n g (VT); wag, C H ! w a g g i n g (va); t h e k v a l u e s are s h o w n in parentheses. E n d g r o u p m o d e s : v c g ' C - - N s t r e t c h i n g ; Pxec' C - - C H a rocking; P]4eN' N - - C H a rocking; t h e s y m m e t r y classes are s h o w n in parentheses.
i
]
1300 1200 I100 I000 900 w a v e number (cm -I)
F i g . 2. I n f r a r e d
spectra
800
of CHa(C}I2)nN(CH3)aBr
700
, n = 5-8
(•ujol
mull).
1754
Tovozo
UNO, KATSUNOSUKE MACHIDA
and KOICHIRO MIYAJIMA
.
1300
1200 I100 I000 9 0 0 wave number (cm -~)
eoo
700
Fig. 3. Infrared spectra of CH3(CH2)nN(CHs)3Br, n = 9-12 (Nujol mull).
o
lm-
E.
.
.
'
.
n--
wave number (cm -I)
Fig. 4. Infrared spectra of CHs(CH2)~N(CH3)3Br, n = 13-16 (Nujol mull).
1300
1200 I100
I 0 0 0 900
800
700
wave number (cm -a)
Fig. 5. Infrared spectrum of CHs(CH2)ITN(CH3)3Br (Nujol mull).
Infrared spectra of finite chain molecules--II
1755
Table 2. The C--N stretching and the CH 3 rocking frequencies (cm-1) of n-alkyl-TMA bromides and related compounds CH a (CH2)nN+(CH3)a.BrFrequency Assignment~ 1234-1253 1087-1093++ 954-972 963-965++ 910-916 + 882-899 + 754-766 +
pMeN(a', a ~)
p~eN(a',a") %~(a") ~'c~(a') %~(a')
ItN +(CHa)a.I-* Frequency Assignment~ 1256
p~eN(al)
1241
PMeN(e)
1052
p~e~(e)
N+ (CHa)4.I-* Frequency Assignment~ 1294
VcN(f2)
1047
p~e~(e)
980
~'c~(e)
946
P~¢c(f2)
810
rcs (al)
752 §
~'cN(al)
PMec(a') %~(a')
* See Ref. [8]. For descriptions, see footnote ~, Table 1. ++Frequencies of shorter molecules deviate markedly from this range. § Raman frequency in aqueous solution. as C8. T h e end group vibrations are t h e n classified into two classes, the in-plane (a') a n d t h e out-of-plane (a") modes, with respect to t h e plane of t h e n-alkyl skeleton. The end group frequencies n e a r 1240, 1090, 965, 910, 890 a n d 760 cm -1 are identified readily for t h e long chain n - a l k y l - T M A bromides since their positions are v i r t u a l l y i n d e p e n d n e n t of the chain length. T h e b a n d n e a r 890 cm -1 is i m m e d i a t e l y assigned to the a' rocking mode of t h e t e r m i n a l C - - C H 3 group b y analogy to t h e d a t a on m a n y n-alkyl c o m p o u n d s [4, 10-12]. T h e o t h e r b a n d s are u n d o u b t e d l y due to the v i b r a t i o n s of t h e --N+(CH3)3 group at the opposite end, a n d t h e i r f r e q u e n c y range suggests t h a t only t h e C - - N stretching a n d t h e CH 3 rocking modes are concerned with. T h e assignments of these end group absorptions are s u m m a r i z e d in Table 2, t o g e t h e r with those of the reference compounds, t r i m e t h y l a m i n e h y d r o iodide a n d t e t r a m e t h y l a m m o n i u m iodide, due to EBSWORTH a n d SHEPP~a~D [8]. The assignments of the weak bands n e a r 760 a n d 1090 cm -1 are given consistently with b o t h the reference compounds, whereas the strong bands between 975 a n d 910 cm -1 ~nd t h e m e d i u m b a n d n e a r 1240 cm -1 are assigned inversely to the corresponding frequencies, 946 a n d 1296 cm -1, of t e t r a m e t h y l a m m o n i u m iodide. T h e present choice is based on t h e assignments for t r i m e t h y l a m i n e h y d r o i o d i d e from analogy in the n u m b e r of t h e N - - C H 3 groups. One m u s t note, however, t h a t t h e separate assignments to t h e C - - N stretching a n d to the CHa rocking modes are r a t h e r conventional, since the coupling b e t w e e n these two modes is v e r y likely to t a k e place. T h e e x t e n s i v e n o r m a l co-ordinate analysis of b r a n c h e d h y d r o c a r b o n s due to S~YDER a n d SCm~C~TSCK~EIDER [13] suggests t h e occurrence o f such a coupling in tri- a n d t e t r a m e t h y l a m m o n i u m ions a n d in n - a l k y l - T M A ions. According to these a u t h o r s the C - - C stretching a n d the C H 3 rocking modes couple with each o t h e r considerably in the f2 class of n e o p e n t a n e a n d in t h e e class of iso-butane. I t [I0] [11] [12] [13]
R. G. S3]'YDER,J. Mol. Spectry 4, 411 (1960). 1~. G. S)~-YDERand J. i . SC~C~rSCH~rEIDER, Spectrochim. Acta 19~ 85 (1963). M. TAsu~I, T. SHIMA~rOUCHI,A. WATANABEand R. GOTO,Spectrochim. Acta ~0, 629 (1964). R. G. S~YDER and J. I-I. SCHACHTSCH~rEIDER,Spectrochim. Acta 21, 169 (1965).
1756
ToYOZO UNo, K~_TSUNOSUKE MACHIDA and KOICHIRO I~IYAJIMA
seems probable that the strong bands between 975 and 910 cm -1 of long chain n-alkyl-TMA bromides are due to an a" and two a' modes which are correlated to the triply degenerate f~. mode of tetramethylammonium ion, although the relative magnitudes of contributions of the C - - N stretching and the CH a rocking modes may change on the replacement of a methyl b y an n-alkyl group. The two strong bands near 964 and 910 cm -1 are assigned to the a' modes since their positions are almost independent of the overlapping CH 2 rocking-twisting band progressions of the a" class. Around 960 cm -1, some of n-alkyl-TMA bromides show another band due certainly to the a" end group mode interacting with the CH 2 rocking-twisting modes. An evidence of this interaction is shown in the following section in relation to an anomalous feature of the CH2 rocking-twisting band progression. CHAIN VIBRATION FREQUENCIES
For any chain vibration, the amplitudes of the successive oscillators are determined b y the phase difference which, according to the transfer matrix theory [6], is given by = k~/(n ÷ 1) + ~l(n + 1),
(1)
where n is the number of the oscillators, k is an integer such that 1 ~ k =< n, and is the phase shift, a function of frequency determined b y the nature of the end groups b u t independent of n. The second term in the right-hand side of equation (1) m a y be neglected for sufficiently long chain molecules, and the approximate phase difference ~' = k~/(n + 1) (2) may be used. Usually, the band progression analysis starts with the assignment of the k values to each absorption frequency. The phase differences are then calculated from equation (2), and the frequencies plotted against ~ to yield the frequencyphase difference diagram. One must be careful in applying this method to such short chain molecules as dealt with in the present study, since any shift in the progression frequencies on the terminal substitution results in the shift of the frequency-phase difference curve. This shift m a y lead to an overestimation of the change in the force field of the chain part. The present analysis of band progressions is mainly concerned with the properties of the chain length-frequency curves which relate the chain length (n) to the progression frequency (v). As shown previously [5], the transfer matrix theory leads to two rules governing the shift of the chain length-frequency curves on a terminal substitution which leaves the force field of the chain part invariant. Let n and v be taken on the ordinate and abscissa, respectively, then Rule 1 states that the vertical shift at a fixed frequency is independent of the k value and Rule 2 that the horizontal shift in a small frequency range is inversely proportional to n ÷ 1. Rule 1 is due to the relation q~ ----- 7 r / A N , (3) where AN is the increment in n on adding unity to ]c, that is, the spacing between adjacent chain length-frequency curves along the ordinate. Equation (3) can be used to draw the correct frequency-phase difference curve from the data for shorter
Infrared spectra of finite chain molecules--II
1757
chain molecules. In the following discussion on the individual band progressions, we adopt the designation of the vibrational modes of polymethylene chain due to TAsu~II et al. [14]. T h e v a a n d v~ modes
The complicated series of weak absorptions between 1360 and 1200 cm -1 are attributed to the CH 2 wagging (va) and the CH 2 twisting-rocking (v~) modes. The plot of absorption frequencies against the chain length discloses the presence of two progressions, one of which is distributed between 1360 and 1230 cm -1 and the other between 1300 and 1220 cm -1. These frequency regions suggest t h a t the former and the latter correspond to the va and the v~ progressions, respectively. Above 1300 c m -1, the ~a absorptions are distributed regularly for longer molecules but are mostly missing for shorter molecules. Between 1300 and 1230 cm -1, the frequency distribution of both the ~a and the vv progressions seems to be disturbed by the interaction of the chain modes with the CHa-N rocking modes of the a' and the a" classes. Most of the expected absorptions below 1220 cm -~ are too weak to be observed. I t is therefore difficult to correlate these progression frequencies with the chain length accurately, and the assignment of the k values included in Table 1 must be regarded as tentative. A n y detailed analysis of the chain length-frequency curves was not made for these progressions. T h e ~a m o d e
I t has been known t h a t the frequency-phase difference curve for the C--C stretching (v4) progression has a minimum near 960 cm-L SNYDER and SC~CHTSCHNEIDER have divided the curve at the minimum into the phase regions A and B [11]. Each n-alkyl-TMA bromide shows a number of weak or medium bands between 1150 and 970 cm -1 attributable to the ~4 modes. The absorption frequencies above 1060 cm -1 arise only from the phase region A and are given the straightforward assignment of the lc values. The band distribution below 1060 cm -1 is quite complicated, however, because of the overlap of the phase regions A and B. B y referring to the data above 1060 cm -1, the k value assignment was made only for the frequencies belonging to the phase region A between 1060 and 980 cm -1. The resulting chain length-frequency curves are shown in Fig. 6, and are compared with those of nparaffins [6, 11]. The curves of n-paraffins and n-alkyl-TMA bromides for k ---- 1 practically coincide with each other, converging with the increase of the chain length into the common frequency for the phase difference ~ of an infinite chain. For k ~- 2 and 3, however, the curves of n-alkyl-TMA bromides deviate appreciably to higher frequencies from those of n-paraffins, possibly because the C--N stretching modes of the a' class interact with the va modes and accordingly push up the va frequencies. The vibrations for which k --~ 1 are infrared inactive for n-paraffins with even carbon atoms. Correspondingly, an even-odd alternation of the intensity ratio of the two highest v4 bands is clearly observed for n-alkyl-TMA bromides in Figs. 2-5. Figure 7 shows a part of the frequency-phase difference diagrams for the phase region A obtained from the v4 frequencies of n-paraffins [11] and n-alkyl-TMA [14] M. TAsu~I, T. SHIMA~OUC~Iand T. MIYAZAWA, J . !1Iol. Spectry 9, 261 (1962).
1758
TOYOZO
UNo,
K~TSUI~OSUKE
M~kCHIDA
and
MIYAJIMA
KOIOItIRO
i -I
Fig. 6. Chain length-frequency curves for the v 4 progression of CI-I2 (CH 2)nN (CH a) a Br (large circles) and CHa(CH~)nCH a (small circles). cm-'-----L- o II00
~ k-I "i---• (P'-~'T ~" L
/
,/,=Tr/AN
o c6- k-2-n-
g °o
]
I'
Io'ol
o I
i
;e
- - _ _
f
[
I oe
,
J oo
1
#oI
1050
1
~ o °e
_
~
I
"el- o , b o
:000
/'
(a) I 04
i
i 02
o
o
o
o o (b) 0.3
0
I ° r-!--:¢
04
0.2
0.3
~6/~
Fig. 7. Frequency-phase difference diagrams for the region A of the % progression of CI-Ia(CI-I~)nl~(CHa)Br (hollow circles and squares) and CH3(CH2)nCH a (filled circles) with n > 10: (a) and (b) represent equations (2) and (3), respectively. b r o m i d e s w i t h m o r e t h a n 10 m e t h y l e n e units, (a) being b a s e d o n e q u a t i o n (2) in w h i c h n is t h e n u m b e r o f C - - C bonds, a n d (b) o n e q u a t i o n (3). I n a p p l y i n g e q u a t i o n (2) t o n-paraffins, S~TYDER a n d SCHAGHTSCJcINEIDER u s e d k -- 1 i n s t e a d o f k in order to correct t h e effect o f C H a in-plane rocking m o d e s interacting w i t h t h e % m o d e s . W e u s e d trial v a l u e s k - - 1 a n d k -- 2 for n - a l k y l - T M A bromides. F o r t h e frequencies a s s i g n e d t o t h e k v a l u e s greater t h a n 3,/c -- 2 w a s f o u n d better t h a n k -- 1 in fitting t h e f r e q u e n c y - p h a s e difference curve o f n - a l k y l - T M A b r o m i d e s t o t h a t o f n-paraffins. This result s u g g e s t s t h a t n - a l k y l - T M A b r o m i d e s h a v e m o r e e n d g r o u p m o d e s interacting w i t h t h e % m o d e s t h a n n-paraffins. I n order t o e s t i m a t e t h e p h a s e difference
Infrared spectra of finite chain molecules--II
1759
from equation (3), we calculated the AN at each absorption frequency b y a simple modification of the interpolation method described in the preceding paper [5]. I f we specify a polymethylene band progression frequency b y v,k, the first and the second subscript denoting the number of methylene units and the k value, respectively, the AN at vmk' is given b y A2V(~m~,)
=
[m
-
n
-
p(~.~
-
~,)/(~
-
v~+~,~)]/(k'
-
lc),
(4)
where v.~ and v~+~.k are the two reference frequencies such that ~n+~,k ~ "Ymk" ~ 'lJnk"
Equation (4) is obtained from equation (8) in Ref. [5] b y replacing v b y vmk' and k + j b y k'. The phase differences in Fig. 7(b) were calculated b y using such reference frequencies that k is k' -- 1 and p is 1 or 2. From the chain length-frequency curves with constant k values in Fig. 6, AN is not available at the frequencies v~2 and vma of n-alkyl-TMA bromides (except v1~.3) and vm2 of n-paraffins. For these frequencies, the phase difference was calculated b y 9 = ~r(1 -- 1/AN'), where AN'(vm~,)
:
[m
-- n
-- (Vn.k,_ 1 --
Vmld)/(Vn,k,_
1 --
Vn+l,k,)]/(m
--
n
~-
1)
(5)
and n was p u t equM to 7 and 8 for k' = 2 and 3, respectively. This calculation is based on the simple relation 1/AN + 1 ~ A N ' : - 1, AN' being the intervM between the chain length-frequency curves connecting such vn~'s that n -- k is constant. The highest reference frequency v~,1 was chosen b y regarding it as the converged value of vnl on the increase of n. B y comparing Fig. 7(b) with (a), it is seen that the use of equation (3) removes the disagreement in the frequency-phase difference diagrams between n-paraffins and n-alkyl-TMA bromides arising from equation (2). This result reveals an excelent transferability in the force constants governing the v4 frequencies between these two homologous series. I t is noteworthy that we need not use any ambiguous correction to the k value in using equation (3). The
v s mode
The rocking-twisting (vs) band progressions are observed between 1060 and 720 cm -1. Although some of them are overlapped b y the weak v4 absorptions above 970 cm -1 and b y the strong C - - N stretching absorptions between 975 and 910 cm -1, the comparison with the data of n-paraffins [11], n-alcohols [12] and n-fatty acid salts [3, 4] allowed the k value assignment of almost all vs absorptions. They are sharp and fairly strong, and are therefore quite useful for the identification of the chain length of n-alkyl-TMA bromides. The chain length-frequency curves are shown in Fig. 8, where the data for n-paraffins [11] are also plotted for comparison. I t is seen that the vs progression frequencies of n-alkyl-TMA bromides are appreciably higher than the corresponding frequencies of n-paraffins. I f we attribute the higher limit of the vs frequency region to the phase difference 7r according to S~YDER and SOHACHTSCHI~EIDER[11], the frequencies of n-paraffins with even k values become
1760
ToYozo U~o, KATSUI~OSUKEMACHIDA and KOICH~ROMIYAJI~L~ . . . .
I I° s
I000
900
800
C m -I
Fig. 8. Chain length-frequency curves for the ~8progressionof CHa(CH2)nN(CHa)aBr (large circles) and CHa(CH~)nCHa (small circles). Squares represent the frequencies of CHa(CH2)nN(CHa)aBr predicted by Rule 2. infrared inactive, whereas all of the v8 modes are infrared active for n-alkyl-TMA bromides. We have therefore two chain length frequency curves of n-alkyl-TMA bromides between each pair of adjacent n-paraffin curves. As seen clearly in Figs. 2-5, the bands of n-alkyl-TMA bromides associated with even and odd k values are strong and weak, respectively, in accordance with the selection rule for n-paraffins. In the vicinity of the strong C--N stretching bands between 975 and 910 cm -1, however, the intensity alternation is not obvious and quite strong vs absorptions are observed. Furthermore, the smooth chain length-frequency curves drawn for nalkyl-TMA bromides in Fig. 8 do not fit well the observed vs frequencies around 950 cm -1. Such anomalous frequencies are explained by taking account of the vibrational coupling between the ~s modes and the a" C--N stretching mode. In Fig. 9, the C - - N stretching frequencies and the vs frequencies above 800 cm -x are plotted against the chain length. By connecting appropriate a" C--N stretching frequencies with the ~8 frequencies having constant values of n -- k q- 1 (the k value due to TASUMI et al. [14]), we obtain a set of smooth curves which do not intersect one another. I t is well known t h a t non-intersecting curves are obtained by plotting frequencies of vibrational modes having the same symmetry against a given molecular parameter such as an atomic mass [15]. The intersecting broken lines in Fig. 9 represent the unperturbed frequencies which might occur on the absence of coupling terms in the kinetic and potential energies. I n Fig. 9, the unperturbed a" C--N stretching frequency is taken as 964 cm -1, the averaged value for the associated a' frequencies of longer molecules, and the frequency nearest to it is assigned to the a" C--N stretching mode for each n-alkyl-T1VIA bromide. In some cases (e.g. n-decyl-TMA bromide), however, an appreciable coupling is expected from the separation between the observed and the unperturbed frequencies and it is difficult to distinguish the end vibration from the vs modes. Assuming t h a t the vibrational coupling between two [15] G. HERZBERG,Infrared and Raman Spectra of Polyatomic Molecules, p. 200. Van Nostrand (1945).
1761
Infrared spectra of finite chain molecules--II
900
I000
800
c m -~
Fig. 9. The vs progressmn and the C - - N stretching frequencies of CHs(CH2) n~(CHa)aBr. Large circles, Us; small circles, a' C--N stretching; squares, a" C--N stretching.
modes gives rise to the shifts of the corresponding frequencies to the opposite directions by the same amount, we may estimate the unperturbed % frequencies roughly in wave numbers by %(unperturbed) = %(observed) + ~a"C-N -- 964. These unperturbed % frequencies fall closely on the broken lines in Fig. 9. The AN's for the % frequencies of n-paraffins [11] and n-alkyl-TM~ bromides are plotted against v in Fig. 10. They were calculated by inserting the k value of TASUMI et al. [14] into equation (4) in which/c was put equal to k' + 1, and p was to I or 2. For n-alkyl-TMA bromides, the aforementioned interaction between the % modes and the a" C - - N stretching mode gives rise to the large deviation in A/V's around 950 AN 8 •
o
o o
o
i
i
i I
I i
~ o c~ ~ -
I000
!
t •
i
'i
i
:
i
I
i i
'
I
r i I
i i
Ii 900
/ i
,
t 800
J I cm-I
Fig. 10. Plot of A N against the frequency for the us progression. Filled circles, CHa(CHu)nCHa; hollow circles, CHa(CH2)nN(CHa)aBr.
1762
ToYozo U~o, KATSUNOSUKEMAOHID)~and KOrOHIROMXYAJIMA
cm -1. The deviation above 980 cm -1 is due to the zigzagging of chain lengthfrequency curves according to the even-odd alternation in methylene numbers of longer n-alkyl-TMA bromides. Below 940 cm -1, however, the data points for both n-alkyI-TMA bromides and n-paraffins lie closely on a smooth curve, in agreement with the prediction of Rule 1. Figure ll(a) shows the frequency-phase difference diagram obtained by applying equation (2) to the v8 frequencies of n-paraffins [11] and n-alkyl-TMA bromides, and Fig. 11(b) by applying equation (3) to the same data. The data points were taken only from the molecules having 17, 15, 13, 9 and 7 methylene units in order to avoid overcrowding. I n calculating the phase difference for Fig. 11(b), the AN's were averaged by using the smallest n and k for each vmk'in equation (4). The advantage of equation (3) over (2) is obvious in fitting the frequencies taken from different homologous series to a common curve. In Fig. 11 (a), the points for n-alkyl-TMA bromides fall nearly on a smooth curve whereas those for nparaffins do not. This result implies t h a t the phase shift for the % modes is small for crn-D
I000
!%%'
I
I
!
i *:
i ,.,./,o+) .% I
,,
i
i 900
i
i\
o
• ooI
i
ii
t
! I
i
v
.'~
l
i.~
80C
i
i
~(a) ] o o.z
i"~' 0.4
i
~i(b)
0.6
0.8
0
0.2
0.4
0.6
,.o ~ / ~
0.8
Fig. 11. Frequency-phase difference diagrams for the %progression of CHa(CH=)nN(CHa)aBr (hollow circles) and Ctta(CH~)nCHa (filled circles) with n = 17, 15, 13, 9 and 7: (a) and (b) represent equations (2) and (3), respectively. (rf+l)A~ c m -I v17
400
\,
16
_ _
____
~5
200 ]7 15
',oo;
I
,T , , .
.
900
.
.
, , , ,i , , r , . . 800 cm -I
Fig. 12. Plot of (n' + 1)Au against the frequency of CI-Ia(OI-I2)nCHa: n' is indicated for each datum point.
Infrared spectra of finite chain molecules--II
1763
n-alkyl-TMA bromides but is not negligible for n-paraffins. Fortunately, such phase shifts are favourable for the prediction of frequency shifts on the change from n-paraffins to n-aLkyl-TMA bromides b y the empirical method based on Rule 2 described in the preceding paper [5]. In Fig. 12, the observed frequency shift, A~n'k'
----
~,k,(n-alkyl-TMA bromide) -- ~,k,(n-paraffin),
multiplied b y n ' + 1 is plotted against the frequencies of n-paraffins for the molecules with n ' ~ 15, 16 and 17. The data points except a few lie on a fairly smooth curve showing that (n + 1)Av,k is independent of the chain length. B y interpolating the data in Fig. 12, (n + 1)Av~k was evaluated at each frequency of shorter nparaffins and the corresponding frequency of n-alkyl-TMA bromides was estimated. The result is included in Fig. 8, where the estimated and the observed frequencies agree well with each other except the cases when v~k(n-alkyl-TMA bromide) - 950 cm -1 (n ---- 3, 7, 8 and 13) and when ~k(n-paraffin) < 800 em -1 (n ---- 2, 3 and 4). In the former case the deviation is due again to the interaction of the ~s modes and the a" C - - N stretching mode, the chain length-frequency curves being fitted well by the estimated frequencies. The latter deviation is related probably to the fact that the frequency shifts from n-paraffins to n-alkyl-TMA bromides are too large to neglect the curvature of the frequency-phase difference curve. From the present result of applying Rules 1 and 2 to the vs progressions of nparaffins and n-alkyl-TMA bromides, we m a y conclude that the shifts of the ~s frequencies on the substitution of a terminal methyl b y a trimethylammonium group are mostly due to the change in the vibrational coupling between the chain and the end parts of molecules and the effect of the change in force constants governing the vs frequencies is not important. From the standpoint of vibrational potential energy, the n-alkyl group of n-alkyl-TMA bromides is thus suggested to be quite similar to that of n-paraffins even for very short molecules. Acknowledgements--The authors' thanks are due to the helpful suggestions of Professor
TSUI~-EI~OBUYAMAMOTO,Professor I-IIXOTSlIOUMATSUD&and Dr. K~N~ICHI OY~.I)Aof Kyoto University.