J. Phys. Chem. 1991,95, 4647-4651 be T~ = 44 f 3 mssl). This and off-resonance observations are consistent with the detection of “free” Bi atoms and [Bi...Bi]** transition-state configurations, respectively. Determination of the topologies of the dissociative PESs” and their absolute location in configuration space relative to the ground-state molecular geometry await the outcome of future experiments in which the excess energy above dissociation threshold is varied by means of tuning the pump laser wavelength XI. Such data should further reveal the possible existence and location of conical intersections between the reactive PESs and allow the appropriate interaction matrix element to be elucidated, as has been carried out in the case of predissociation of NaI.I4 A range of experiments involving systematicvariation of XI would be of considerable assistance in carrying out a direct characterization of the topology of the PES(s) involved in which use would be made of an inversion method such as that developed by LeRoy et for determining potential energy functions from boundcontinuum spectra. In this vein, a procedure has recently been adopted to derive the potential energy curves for the bound electronically excited B 3 h Ustate of molecular 123233,83*84 and the A 3 n l state of I C P from real-time measurements, in which the appropriate potential functions were obtained by Fourier transformation of the FTS data followed by application of the wellknown RKR integrals. In a similar manner, for a known functional form of the reactive PES(s), measurements over a range of prohe laser wavelengths X2 at a fixed XI would provide an (81) Patel, D.; Pritt Jr., A. T.; Coombe, R. D. J . Chem. Phys. 1982, 76, 6449. (82) LeRoy, R. J.; Keogh, W. J.; Child, M. S.J . Chem. Phys. 1988,89, 4564. (83) Gruebele, M.; Roberts, G.; Dantus, M.; Bowman, R. M.; &wail, A. H. Chem. Phys. Lett. 1990, 166,459. (84) Bernstein, R. B.; Zewail, A. H. Chem. Phys. Lett. 1990, 170, 321.
4647
invaluable aid to determining the shapes of the high-lying molecular states V2(r)populated by the probe laser and the nature of interactions between them. Clearly, the assumptions regarding the exponentiality of the PESs V2(r)and the nature of the long-range regions of Vl(r)and Vl,(r) need to be strengthened, and we hope that future experiments will provide a better description of the PESs.
Acknowledgment. This work was supported by the Air Force Office of Scientific Research under grant number AFOSR 900014. We are grateful to Drs. P. P. Sorokin and R. E. Walkup for sending us a preprint of ref 70 and for their thoughtful and careful reading of this paper. G.R. thanks SERC for the award of a NATO Postdoctoral Fellowship. Note Added in Proof. A recent theoretical treatment of time-resolved absorption spectra (Walkup, R. E.; Misewich, J. A.; Glownia, J. H.; Sorokin, P. P. J. Chem. Phys. 1991,94, 3389) has been applied to the dissociation of Bi2 (Walkup, R. E., private communication): good agreement was obtained with the results of Figures 4 and 5 by using a repulsive length parameter L, = 0.3 A and a van der Waals difference potential with a coefficient of 2 X lo* cm-’ A6. As discussed here and previously,16 the long-range region of the potential is important in governing the dissociation dynamics, and the value L,= 2 A of Sorokin and c o - w ~ r k e r sused ~ ~ in this work is only an indication of the less repulsive nature of the reactive potentials Vxr)at large internuclear separations. When further experiments (involving tuning of XI and A,) are completed and ab initio calculations (Morokuma, K., private communication) become available, it should be possible to deduce the key features of the PESs that contribute to the interesting dynamics of Bi2 fragmentation.
Low-Frequency Raman-Active Modes In a-Methyl,o-hydroxyollgo(oxyethy1ene)s Carl Campbell,+Kyriakos Viraq*J Andrew J. Masters, John R. Craven,%Zhrng Hao,I Stephen G. Yeates,ll and Coiin Booth Manchester Polymer Centre and Department of Chemistry, University of Manchester, Manchester, MI 3 9PL, UK (Received: August 14, 1990; In Final Form: November 29, 1990) Low-frequency Raman spectra were recorded for a-methy1,w-hydroxyoligo(oxyethylene)s,CIEmOHwith m in the range 4-16, Le., 14-50 chain atoms. Longitudinal acoustical mode (LAM) frequencies were identified and compared with those determined previously for a-hydro,whydroxyoligo(oxyethylene)s and a-methy1,o-methoxyoligo(oxyethy1ene)s. On the basis of the linear crystal model of Minoni and Zerbi, the two most prominent bands in the low-frequency spectra were assigned to the LAM-1 and LAM-3 modes of the H-bonded dimer crystallized in a bilayer structure.
Introduction of low-frequency Raman spectra of crystalline oligo(oxyethy1ene)s have yielded information on the longitudinal vibrations of helical chains, particularly on the large effect of end forces on the frequency of the longitudinal mode. A recent study’ by Raman spectroscopy of a series of uniform oligo(oxyethy1ene) dimethyl ethers, CIEmCI,with oxyethylene chain lengths in the range m = 2-25, has served to reinforce conclusions that ‘ h n t addrm: European Vinyls Corp. (UK) Ltd., Research and Technology, The Heath, Runcorn, Cheahire, WA7 4QD. UK. Present address: Physical Chemistry Laboratory, University of Athens, 13A Navarinou Street, Athens 106 80, Greece. ‘Present address: Albright and Wilson Ltd., Petroleum Additives Group, Whitehaven. Cumbria CA28 9QQ, UK. Present address: Institute of Applied Chemistry, Academia Sinica, Changchun, PRC. ‘Present address: IC1 Chemicals and Polymers Ltd., Research and Technology, The Heath. Runcorn, Cheshire, WA7 4QD, UK.
0022-3654/91/2095-4647$02.50/0
van der Waals end forces significantly increase the frequency of the single-node longitudinal acoustical mode (LAM-]) of oligo(oxyethy1ene)s. The effect is greatly enhanced by strong hydrogen bonds at the chain ends of oligo(oxyethy1ene) diols, HE,,,OH: in this case, the observed LAM-1 frequency approaches twice that anticipated for an oligo(oxyethy1ene) chain with free ends.’V2 Direct comparison of the Raman spectra of a short uniform oligo(oxyethy1ene) dimethyl ether with that of its corresponding diol is not straightforward, since the chain ends of the short oligomers are very restricted by hydrogen bonding in the end-group planes of their layer crystals’J and the longitudinal mode may (1) Campbell. C.; Viras. K.; Booth, C. J . Polym. Scl., Polym. Phys. Ed., in press. (2) Viras, K.; Teo, H. H.; Marshall. A.; Domszy, R. C.; King, T. A,; Booth, C. J. Polym. Sei., Polym. Phys. Ed. 1983, 21, 919. (3) Viras, K.; King, T. A.; Booth, C. J. Polym. Sei.,Polym. Phys. Ed. 1985, 23, 41 1.
0 1991 American Chemical Society
4648 The Journal of Physical Chemistry. Vol. 95, No. 12, 1991
Campbell et ai.
SCHEME I C,&OH-
TosCl
C~QOTOSwo% KOH C,E,OH
I
&OH
/ KOH
ClE60H
1
Toscl
CIEsOTos
-1
HESOH/ KOH
TosCl
CIEIOOTOS
1
ClEloOH
HbOH'KoH
CIEISOH
not be Raman active. In the present work we have observed the low-frequency Raman spectra of a series of uniform amethyl,w-hydroxyoligo(oxyethylene)s, CIE,OH, thereby ensuring that the LAM-1 mode can be detected, though much modified by the disparate forces at the two ends of the chain. Samples of a-methyl,whydroxypoly(oxyethylene) [trivial name: methoxypolyethyleneglycol, methoxy-PEG] are available commercially, but t h a e materials have distributions of chain lengths. The distributions may be narrow, though is not true of all commercially available samples, but any distribution of chain lengths complicates the interpretation of LAM frequencies, particularly so for samples of short chain length. The LAM bands are broadened by the crystal-stem-lengthdistribution, while samples with average chain lengths shorter than about 20 oxyethylene units (M,N 1OOO) may undergo fractionation (Le., rejection of short chains) on crystallization. This difficulty is avoided in the present work by the use of specially synthesized uniform oligomers. A further advantage of the use of uniform oligomers is uniformity of environment of a given end group in the end plane of its layer crystal. In contrast, the chain ends in polyethylene glycols have a variety of environments in the rough end surfaces of their lamellar crystals, including hydrogen bonding with both hydroxy and ether oxygen.'
Experimental Section Materials. The a-methy1,whydroxy oligomers were prepared from commercially available oligoethylene glycols, H(OCH2CHd,0H, where n = 2-5, and the monomethyl ethers of the lower two glycols, CH3(OCH2CH2)OH, where n = 2 and 3. The method used, described for related syntheses, involved ascending the homologous series of oligomers by reaction of the tosylate (Ts, CH3C6H4S02-)of a methyl ether with the monopotassium salt of a glycol: i.e. CH3(OCH2CHJxOH TsCl- C H ~ ( O C H ~ C H ~ ) , O T S
+
+
CH~(OCH~CH~),OTS H(OCH2CH2)yO-K++ CH3(OCH2CH2),+,OH
+ KOTS
Examples of the synthetic routes are outlined in Scheme I. The required products were separated from small amounts of higher oligomers and residues of reactants by solvent extraction and/or preparative gel-permeation chromatography. The purified products were characterized by a number of methods: Chemical Analysis. C and H analyses were consistent with molecular formulas. 'HNMR Spectroscopy: Bruker 300 MHz spectrometer,CDC13 solvent, TMS reference. Spectra showed the expected resonances at d = 3.35 (CH30CH2CH20-), 3.35 (CH30C&CH20-), 6 = 3.75 (HOCH2CH20-) and 3.65 (interior CHJ. (4) Tw, H. H.; Marshall, A.; Booth. C. Makromol. Chem. 1982, 183,
2265.
( 5 ) Ytatcs, S.G.; TW,H. H.; Mobbs, R. H.; Booth, C. Makromol. Chem. 1984, 185. 1559. (6) Craven, J. R.; Mobbs, R. H.; Booth, C.; Goodwin, E. J.; Jackson, D. Makromol. Chem. 1989. 190, 1207.
1
0
50
-
100
15
frequency / cm-1
Figure 1. Low-frequency Raman spectra of a-methy1,whydroxyoligo(0xyethylene)s at 173 K (a) C,E40H, (b) CIE$,OH, (c) CIEI60H.The intensity scales and zeros are arbitrary.
Analytical GPC. GPC curves, obtained by using a system suited to oligomers' with tetrahydrofuran eluent at 30 OC, showed narrow singlet peaks with no indication of oligomeric impurities. Mass Spectroscopy. (Kratos MS-25 with chemical ionization, NH4+, M < 700. Spectra showed molecular ions (M 1 and M 18) corresponding to the molecular formulas and with no indication of higher oligomers. Raman Spectroscopy. Raman scattering at 90° to the incident beam was recorded by means of a Spex Ramalog spectrometer fitted with a 1403 double monochromator and a 1442U third monochromator in the scanning mode. The operation of the instrument was controlled by a DMl B Spectroscopy Laboratory Coordinator computer. The light source was a Coherent Innova 90 argon ion laser operated at 514.5 nm and 500 mW. Typical operating conditions for low frequencies (5-300 cm-I) were bandwidth = 1.5 cm-I, scanning increment = 0.1 cm-I, integration time = 2 s. On occasion, for very low frequencies, the conditions were bandwidth = 0.8 cm-I, scanning increment = 0.05 cm-I, integration time = 5 s. The frequency scale was calibrated by reference to the spectra of L-cystine and n-hexacosane, the latter being used immediately before recording a spectrum. Generally, high-frequency spectra were recorded immediately after the low-frequency spectra, in order to confirm that samples were unchanged by exposure to the laser beam. Liquid samples were enclosed in a capillary tube and cooled to a given temperature (to f l K) in the range 143-293 K by means of a Harney-Miller cell (Spex Industries Inc.). The intensity of a Raman band was observed over a period of time to ensure equilibration of the sample at a given temperature. X-ray Diffraction and Differential Scanning Calorimetry. One of the oligomers, C1EI60H,was investigated by X-ray diffraction and another, ClE80H,was investigated by differential scanning calorimetry (DSC). The methods used were those described elsewhere.8
+
+
Results and Discussion The oligomers are denoted CIE,OH, where m is the number of oxyethylene units in the chain. (7) Craven, J . R.; Tyrer, H.; Li, S. P. L.; Booth, C.; Jackson, D. J. Chromatogr. 1987, 387, 233. (8) Craven, J. R.; Zhang, H.; Booth, C. Makromol. Chem., submittal for publication.
a-Meth yl,o-h ydroxyoligo(oxyethy1ene)s
The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 4649
TABLE I: Lon-Frequency Raman Bands of Uniform a-MetLyL~Lydroxy-digo(oxycUykae)s
freauencv/cm-' other low-frequency ~~
sample
T/K
ClEdOH CIEsOH
173 253 173 243 173 263 173 263 173 263 173 263 173 263 173 173 263 173
CIE60H
CIE7OH ClEBOH
ClbOH ClEloOH ClEllOH ClElZOH CIEl60H
i 34.6 27.9 31.2 25.0 27.6 22.7 24.6 19.7 21.5 18.3 19.4 16.4 17.2 15.7 16.7
-
12.2 12.5
ii
~
bands 23, 52, 61, 76, 105 57,70, 105 20, 60. 75. 105 50,75 20, 46, 75 16, 35, 77, 108 18, 37, 83, 108 79 16, 37, 66, 83 34, 59, 80, 106 14, 37, 68, 84, 106 79, 106 81, 106 80, 106 82, 106 63, 85, 105 84 85
u u u 54.1 57.3 52.3 55.3 47.5 49.4 42.7 45.4 38.3 39.4 33.0 36.0 32.5 25.3 26.4
#Band (ii) overlaps the broad band centered on 70-76 cm-I.
7 .
B
I
0
0.00
0.02
m
0.04
0.06
0.08
(chain length).'
Figure 2. Frequency versus reciprocal chain length for a-methyl,@hydroxyoligo(oxyethy1ene)s (C,E,,,OH) at 173 K: ( 0 )band (i) and (B) band (ii).
Raman Spectroscopy. The high-frequency Raman spectra (100-1800 cm-l) of the oligomers were examined for evidence of the conformation of the oxyethylene chain. Following recent work by Matsuura and Fukuhara? the indicators used were the bands at 291,936, and 1231 cm-I. The spectra of the samples (oxyethylene chain length, m 1 4) were consistent with crystallization of chains in the helical conformation, i.e., the tgt sequence of bonds O-CH2-CH2-0. Examples of low-frequency spectra (5-1 50 cm-I, samples CIE40H,C&OH, and CIE160Hat 173 K) are shown in Figure 1. Spectra of all samples were generally recorded several times in order to define the band frequencies as precisely as possible. The values obtained are listed in Table I. The spectra generally showed the usual features observedv in the low-frequency Raman spectra of low-molecular-weight poly(oxyethylene)s, Le., weak bands at 34, 61, and 106 cm-I and a broad band in the region 70-90 cm-! see the spectra of C1&OH and C I E I 6 0 Hin Figure 1. Weak bands at 20-23 and 14-18 cm-I were observed in certain spectra (see Table 1); these bands have also been described beThe bands of major interest in this work are seen particularly well in the spectrum of oligomer ClE90H; see Figure 1, sample at 173 K, prominent bands of comparable intensity at 19.4 and 45.4 cm-'. The frequencies of these bands, which are picked out in Table I as (i) and (ii), are markedly dependent on the chain lengths of the oligomers (Figure 2). As illustrated in Figure 1, the two bands are not equally prominent throughout the range of the chain lengths investigated. When the chain is
0.00
0.06
0.08
(chain length)-'
Figure 3. Frequency versus reciprocal chain length for a-methyl,@hydroxyoligo(oxyethy1ene)s (CIE,OH) at 173 K: ( 0 )band (i) and (B) band (ii). The dashed curve represents the results for a-methyl,* methoxy-oligo(oxyethy1ene)s (CIEmCl) at 173 K taken from ref 1. The dotted curve represents the results for a-hydr0.w-hydroxyoligo(oxyethy1ene)s (HE,OH) at 173 K, also taken from ref 1. "'e
*..
-"'c
"'h
fe
fc
+-
....
........ fh
Figure 4. Infinite one-dimensional crystal model of Minoni and Zerbi.Io The subscripts c, e, and h indicate chain, methyl-end and hydroxy-end groups, respectively.
long (m > lo), band (i) can be difficult to define as its frequency approaches the lower limit of measurement. When the chain is short ( m < 6), band (ii) overlaps the bands in the 60-80-cm-* region and cannot be defined with any certainty. Spectra were generally recorded at two to four temperatures in the range 143-293 K. No significant changes were observed in the high-frequency spectra, showing that the crystal structure was unchanged across the temperature range. The frequencies of bands (i) and (ii) decreased as temperature increased at a rate of -1 to -3 cm-' per 100 K (Table I). In Figure 3, the present results for bands (i) and (ii) are compared with those obtained' for a-methyl,@-methoxy-oligo(oxyethylene)s, CIE,CI, and a-hydro,@-hydroxyoligo(oxyethylene)s, HE,OH. The earlier results are represented by theoretical curves obtained by fitting data' according to Minoni and Zerbi.'O The frequencies of band (ii) lie between those expected for CIE,CI and HE,OH oligomers. The most striking feature of Figure 3 is the relatively low frequency of band (i). Our interpretation is that these bands arise from the longitudinal vibration of hydrogen-bonded dimers in a layer crystal; as pursued in detail in the next section. Calculations. Minoni and Zerbi'O have suggested that a relatively simple linear model chain can be used to interpret the longitudinal vibrations of crystalline oligomers with significant interchain end forces. In the present case we needed to predict the vibrational frequencies of H-bonded dimers in a layer crystal where they are subject to van der Waals end forces. The a p propriate equations were derived by extending Minoni and Zerbi's treatment of an infinite one-dimensional crystal with a unimeric (single oligomer) repeat unit to the case where the repeat unit is an H-bonded dimer. The notation used is indicated in Figure 4. The CH2 chain groups and the CH3 and OH end groups are represented by point masses, m,, me, and mh,respectively, and the interactions between them are represented by force constantsf,,f,, a n d k respectively. The phase angle (e) of the longitudinal vibration centered on the H bond was calculated by adapting the method of Minoni and Zerbi'O to this slightly more complex case. For purposes of computation, the equations were used in the form X'J22
-Xd2l = 0
where ~
(9) Matruura, H.; Fukuhara, K. J . f h y s . Chem. 1987, 91, 6139.
0.04
0.02
~
~
~
~~~
(10) Minoni, G.; Zcrbi, 0. J. fhys. Chem. 1982. 86, 4791.
4650 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991
Campbell et al.
XI, = 2&(cos 6 - l ) ( m e / m c )sin 6 -&(sin 26 - sin 8) + 2L sin 6 XI2 = 2&(cos 6 - l ) ( m e / m c )cos 6 -&{cos 26 - cos 6) + 2L cos 6
80 7
X 2 , = 2fc(cos 6 - l ) ( m h / m c )sin x6 &{sin (x - 1)6 - sin (x0)) + 2fh sin (x6)
40 a
-
0-
?!
X2, = 2&(cos 6 - I ) ( m h / m c )cos x6 &{COS (X
- i)e - COS (xe)l+ 2fh
COS
60
6 .
20
(xe) n
and x is the chain length of the oligomer (C,E,OH) in chain atoms (C and 0). The LAM frequency (v) was obtained from ( 2 7 ~ =) ~(2fc/m,)(1 - cos 6 ) The values of the parameters used in applying the equations to the oligo(oxyethy1ene)s were as follows: m, = 2.4385 X kg (an average value over the oxyethylene unit, CH2CH20);me = 2.4967 X kg; mh = 2.8243 X kg;fc = 55 N m-';f, = 2.5 N m-l;fh = 12 N m-I. The values of the force constants are based on those used earlier' to fit the LAM-1 frequencies of homologous series of a,w-dimethyl and a,o-dihydroxy oligo(oxyethylene)s. The force constant used for the chain bonds Cr, = 55 N m-l) is equivalent to a longitudinal modulus for helical poly(oxyethy1ene) of E = 2.5 X lokoN m-2, as found earlier.2,3 Song and Krimm"J2 have calculated LAM-I frequencies for oligo(oxyethy1ene)svia normal-coordinate analysis and shown that lateral interchain forces contribute to E. Here we assume that the effect of lateral forces can be subsumed into the composite chain force constant&. The value used for the force constant of the H bond (fh = 12 N m-I) is that used earlier' to fit the results for a,o-dihydroxy-oligo(oxyethy1ene)s. The value of the force constant for the methyl-methyl interaction Cr, = 2.5 N m-I) was adjusted slightly from that used earlier' (Le.,& = 3 N m-I) in order to slightly improve the fit to the present results; this probably reflects the greater sensitivityof the longitudinal vibration centered on the H bond compared to that of a vibration centered in the oligo(oxyethy1ene) chain. The comparison of frequencies made in Figure 5 shows excellent correspondence between of observed and calculated results. The calculation yields the series of longitudinal vibrations centered on the H bond. The wave profiles of the first two modes are indicated in Figure 6. The numbers of nodes per dimeric repeat unit are 2 for mode (i) and 4 for mode (ii); i.e., they are LAM-2 and LAM-4 of the crystal repeat unit. Discounting the node centered in the van der Waals interaction permits the usual nomenclature to be used: i.e., LAM-I of the dimer for mode (i) and LAM-3 of the dimer for mode (ii). If, for mode (ii), the node centred in the H bond is also discounted, then it can be denoted LAM-1 of the monomer. The most acceptable nomenclature is LAM-I and LAM-3 of the dimer. Supporting Results from X-ray Diffraction and DSC. Investigation of the layer structure of the oligomers by X-ray scattering was not possible across the full range of oligomers, because of their low melting points. However, the structure of crystalline oligomer CIEI60Hwas investigated in this way. The sample was crystallized slowly under a small temperature gradient, Le., directionally crystallized as described elsewhere.8 High-order reflections from the long spacing were apparent in the diffraction photograph, from which the long spacing itself was found to be 1, = 9.60 nm. The increment per chain atom in crystalline oligo(oxyethy1ene)s has been found8 to be 0.0967 nm, from which an approximate molecular length of 1, = 4.84 nm can be calculated ( C I E I 6 0 H ,49 chain atoms). Hence / , / I 2, indicative of a bilayer and in keeping with crystallization of H-bonded dimers. It is noted that the sample investigated by X-ray diffraction was crystallized very slowly, whereas a relatively fast cooling rate (2 K m i d ) was used in crystallizing oligomer C I E I 6 0 Hfor Raman
-
( I I ) Song, K.; Krimm, S.J. Polym. Sci., Polym. Phys. Ed. 1990,28, 35. (12) Song, K.;Krimm, S.J . Polym. Sci., Polym. Phys. Ed. 1990, 28, 63.
0.00
0.02
0.04
0.06
0.08
(chain length)-'
Figure 5. Comparison of calculated and observed frequencies. The curves represent (a) LAM-I and (b) LAM-2 frequencies calculated for hydrogen-bonded dimers with force constants (Minoni-Zerbi model) of f, = 5 5 N m-',fc = 2.5 N m-l, andfh = 12 N m-I, and with appropriate lengths (see Table I) and group masses (see text). The experimental results are for a-methyl,w-hydroxyoligo(oxyethy1ene)s(C,E,OH) at 173 K: ( 0 )band (i) and (m) band (ii).
H-bond
Figure 6. Sketch of the vibrational displacements in (a) mode (i) and (b) mode (ii). The longitudinal displacementsare represented as tran-
sverse.
t %
Q
-30
-20 -10 0 temperature / "C
10
Figure 7. DSC curves obtained with heating rate 4 K min-l for amethyl+-hydroxyocta(oxyethy1ene) (ClE80H): quenched from the melt to -40 OC; crystallized slowly from the melt at 0 OC and then cooled to
-40 OC.
spectroscopy, with the possibility of a less-perfect morphology. DSC was used to investigate the effect of crystallization rate on the crystal structure of a second oligomer, CIE80H. When quenched from the melt to -40 OC, the DSC curve showed a broad melting peak with a maximum at 0.5 O C (Figure 7). The enthalpy of fusion, by the baseline method, was AHfu 120 J g-I. Values of the peak width at half-height, determined at several heating rates, extrapolated to ATll2 4 K at zero heating rate, whereas a value of ATllz
