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Resonant Raman spectroscopic study of biphenyl glutarate diacetylene polymer
Volume 45, number 3
CHEMICAL PHYSICS LETTERS
i Fe5cuary 1977
RESONANT RAMAN SPECTROSCOPIC STUDY OF BIPHENYL GLUTARATE DIACETYLENE POLYMER
D. BLOOR”, W. HERSEL Physrkolisches Institut der Universltat Stuttgart, 7000 Stuttgart-Vaihingen, 80, W-Germany
Teil3,
and D.N. BATCHELDER Deprtment of Physics, Queex Mary College. London El 4N.7, UK Received 29 September
1976
The resonantly enhanced Raman spectra of biphenyl glutarate diacetylene polymer chains in fully radiation pofymerfzed and partially thermally polymerized samples are reported. Details of the resonant enhancement in the region of the polymer electronic absorption were studied in partially polymerized sampIes. The rofe of defects in producing fluorescent emission and in broadening the optical absorption for radiation polymerized samples is briefly discussed.
Raman spectroscopy has proved to be a valuable tool in the study of the electronic and vibrational states of single crystaldiacetylene polymers [l-S] _Macroscopic single crystal of these conjugated polymers can be obtained by solid-state polymerization 16-91. The optical absorption of the conjugated chains is extremely intense and strong resonantly enhanced Raman scattering is observed. The Raman spectra are simple, despite the presence of complex side groups, since only vibrational modes which couple with the n-electron system are enhanced. Thus, the most intense Raman lines are due to the in plane stretching vibrations of the all-trans planar backbone, The use of a dye laser enables the variation of the Raman scattering intensity to be observed throughout the region of the electronic absorption peak. Thus, the details of the interrelation of the electronic and vibrational states of the polymer chain can be studied. We have reported previously such a study of the polymer * Permanent address: Department College, London, UK.
of Physics, Queen Mary
obtained from the his@-toluene sulphonate) of 2,4hexadiyne-1,6diol, TSHD [S] _ For this polymer the electronic absorption is split at low temperatures [ IO,1 1] and vibrational modes coupled to one electronic state, but not the other, were clearly identified. We here report similar studies of the poiymer obtained from biphenyl gbrtarate diacetyIene, BPG [12,13] _ The partially and fully polymerized BPG crystaIs, which were also used for optical absorption measurements [14], were obtained from Professor G. Wegner of the Institute for Macromolecular Chemistry at the University of Freiburg. The partially poiymerized samples -were thermally polymerized at room temperature while fully polymerized samples were obtained by -y-irradiation of the monomer crystals. The structure of the monomer molecule and the proposed structure of the polymer chain 112,131 are shown in fig. I. Raman spectra were recorded at a resolution of I cm-L using a rhodamine 6G dye laser. A photon counting system and a cooled-selected photomultiplier were used so that good signal to noise ratios could be obtained with Low laser power incident on the sample, thus preventing sample decomposition. Samples were mounted in a con411
CHEMICAL PHYSICS LETTERS
Volume 45, number 3
pqi o\ C-C-C-C-~
0
_p
k k k
0
Q-c-c-c&~ (4 Fig. 1. (a) Molecular structure of BPC monomer. (b) Polymer chain structure of BPG polymer, the biphenyl glutarate linkages are shown schematically. tinuous flow cryostat so that the sample temperature could be varied between 300 K and 4 K. The optical spectrum of BPG is simpler than that of TSHD polymer since the electronic absorption is not split at low temperatures. For partially polymerized BPG, where we assume there are long polymer chains distributed in the monomer matrix (cf. TSHD refs [9,1 l]), the absorption peak is at 16 592 cm-* at 2 K and the lineshape is as expected for a onedimensional van Hove singularity, i.e. an inter-band transition [ 141. The radiation polymerized samples have an absorption starting at about 16 600 cm-l with the first broad absorption peak at 17 160 cm-l ai 2 K. Large ESR signals are observed in these samples so that it appears likely that defects produced during irradiation are responsible for the loss of detail in the optical spectrum. A typical Raman spectrum for a fully polymerized BPC crystal, with excitation at 16 500 cm-*, at 4 K is shown in fig. 2. The frequencies of the Raman lines and the vibrational sidebands, observed in the optical spectra, at liquid helium temperatures for both partially and fully polymerized samples are compiled in table 1. The comparison of Raman and sideband frequencies is poor for the fully polymerized crystals,
WAVENUMBER
[em+]
Fig. 2. Raman spectrum of a fully radiation polymerized crystal of BPG. recorded with an excitation frequency of 16 500 cm-’ and a sample temperature of 4 K.
412
1 February
1977
either because of the large optical absorption linewidths or the possibility that the optical absorption is due to defects, as discussed later. The comparison is good for the partially polymerized samples, which have sharp optical absorptions. Small differences are observed between the Raman and sideband frequencies, these are expected since (a) the sidebands give excited state frequencies while the Raman lines have ground state frequencies and (b) the sidebands reflect the vibrational density of states while the Raman lines are due to the specific vibrational modes. The relative Raman scattering intensities for both types of samples are similar. For excitation frequencies within 800 cm-l of the electronic absorption peak there are only small changes in the relative intensities of the high frequency Raman lines (frequencies above 700 cm-l). However, the low frequency Raman lines (frequencies below 700 cm-l) showed a marked increase in intensity relative to the high frequency lines as the excitation frequency is increased across the quoted range. The resonant enhancement was studied in detail for the partially polymerized samples since, unlike fully poly;nerized crystals, the reflectivity and refractive index do not change significantly in the region of the electronic absorption [ 11 ,15,16] . Thus, the scattering intensity needs to be corrected only for the sample absorption [5], which can be obtained from transmission measurements [14], and the v4 frequency dependence. The behaviour of the lines at 128 1 cm-l is shown in fig. 3a and that of the pair of lines at 2 114 and 2 124 cm-l, in the t%C stretching region, is shown in fig. 3b. These frequency dependences can be compared with the electronic absorption lineshape shown in fig. 3c. The rise in intensity of the 1281 cm-l line is similar to, but less asymmetric than, the absorption line profile. While the 2 114 cm-l line has a similar behaviour the 2 124 cm-l line has maximum intensity about 400 cm-l above the electronic absorption, in the region of the first pronounced vibrational sideband, see fig. 3c. In this region the intensity variations of the two lines indicate that there is interference between the scattering processes. Close examination of the Raman spectra reveals small frequency shifts of several lines in the same region suggesting the occurrence of similar secondary resonant enhancements but with frequency differences too small to be clearly resolved. These effects are similar to but less pronounced than those observed for TSHD polymer [S] . However,
Volume 45, number 3
CHEMiCAL PHYSICS LETTERS
E February I977
Table 1 Vibrational frequencies of BPG polymer observed by optical and Raman spectroscopy, aU frequencies quote+ in cm-r Optical spectroscopy fully radiation polymerized
Raman spectroscopy partially ~erm~y polymerized
fully radiation polymerizeda)
partiaiiy tbermaBy polymerized b!
1421
174 320 430 548 702,725 744,766 862,925,1019 1049, llil 1195 I255,1281 1405,1439 1452,1497
43.49, s9 73 125 178 323 433 549 702,723 742,758 862,924, Lot.8 I@%, 1112 1 I92 1256,1281 1402,1436 1449, I496
2098
2112
2114.2124
184C) 404,453 555
330
753
1287 1460 1740 2240
a) Excitation frequency 16 500 cm-‘, Raman lines below 150 cm-’ not recorded. b) Excttation frequency 17 100 cm-‘. C) These bands can only be seen in spectra recorded on a more extended scale than that of fig. 3c.
b
17ma
WAVENUMEER
tern+ 1
nmo
WQa
WAVENUMBER
km3
Fig. 3. (a) Variation of the Raman scattering intensity at 4 K of the 1231 cm-’ vibration of BPG poiymer in a partially thermaiIy polymerized crystal in the region of the electronic absorption. @I)As (a) for the 2114 and 2124 cm-’ vibrations. Cc) Biectronic absorption lineshapes of BPG polymer in a partially polymerized crystal at 2 K. 4I.3
Volume 45. number 3
CHE,MICALPHYSICSLElTERS
whereas for TSHD the effects are associated with two electronic absorptions here they are associated with an electronic and a vibronic peak. The spectrum of BPG is rich in lines in the C=C stretching region, in comparison TSHD has only one intense and one weak peak in this region [ 1,9] . Possible causes of the additional lines are (a) conjugation between the polymer chain and the adjacent phenyl rings,(b) t&c occurrence of a non-centrosymmetric structure rendering more vibrations Raman active, (c) vibrations of the bis phenyi glutarate linkages giving finite vibrational amplitude in the polymer cham and, (d) Fermi resonances of backbone combination bands with the C=C stretching vibration. Conjugation appears unlikely since molecular models of the monomer and polymer place the phenyl rings orthogonal to the plane of the backbone. This has recently been confirmed by the X-ray structural data of Day [ 171. However, these structural results did not show clearly a centric structure so that suggestion (b) cannot be eliminated. Coupling between the glutarate links and diacetylene chain is likely. The occurrence of low frequency Raman lines attributable to accordion modes of the glutarate links supports this interpretation. Several combination frequencies fall into the C=C region, indeed so many that unambiguous identification of possible Fermi resonances is impossible. The line at 1439 cm-l in the fully polymerized sarnpies cannot be observed at room temperature while its equivalent in partially polymerized samples r.xnains in the spectrum though it is somewhat broadened. These observations are compatible with a Fermi rcsonance modified by the different temperature shifts of the fundamental vibrations in the two types of sample. In addition to the Raman spectrum the radiation polymerized samples exhibited a broad fluorescence at low temperatures. The observed vibrational structure and the dependence on excitation frequency show clearly that the electronic absorption at 17 160 cm-l is an aliowed zero-phonon transition. However, the fluorescence of the highly defective radiation polymerized BPG contrasts strongly wi*h the absence of fluorescence in partially thermally polymerized BPC and thermally polymerized TSHD, which have much greater perfection. This suggests that the defects act as traps, which are only populated at low temperatures, from which radiative decay is favoured. The equivalence of the Raman spectra of fully and partially polymerized BPG shows that the 414
1 February 1977
polymer chains have nearly the same conformation in both sarrples. This contrasts with the apparently large difference in electronic absorption energies quoted above. However, the radiation polymerized samples have an absorption edge at the same energy as the peak position in the partially polymerized samples. Thus the presence of defects may produce a distribution of absorptions at energies above the infinite chain limit with the higher energy peak reflecting either a maximum in the distribution of chain lengths or the absorption of the defects. The latter explanation accords with the interpretation of the fluorescence given above. Further studies of the defects by ESR are in hand in an effort to resolve these problems. This work was supported by grants from the SRC and the SFB. One of us (D.B.) thanks the Humboldt Foundation for a Fellowship and Professor H.C. Wolf for his hospitality during the course of this work. References 1I] A.J. hlelveger and R.H. Baughman,J. Polymer Sci. A2
11 (1973) 604. [2] R.H. Baughman,J.D. Witt and K.C. Yee, J. Chh=m. Phys. 60 (1974) 4755. [31 G.J. Exarhos, W.M. Risen Jr. and R-H. Baughman, 3. Am. Chem. Sot. 98 (1976) 481. [4] D. Bloor, D.J. Ando, F.H. Preston and D.N. Batchelder, in: Structural studies of macromolecules by spectroscopic methods, ed. K.J. Ivin (Wiley, New York, 1976) p. 91. [S] D.N. Batchelder and D. Bloo:, Chem. Phys. Letters 38 (1976) 37. [6] G. Wegner, Z. Naturforsch. 24b (1969) 824. [7] G. Wegner. Makromol. Chem. 1.54 (1972) 35. [8J C. Wegner, Mcthoden der Organischen Chemie, Vol. 4/Sb, Part II (Thieme, Stuttgart, 1976) p. 1499. [91 D. Bloor, L. Koski, G-C. Stevens, F.H. Preston and D.J. Ando, J. Mater. Sci. 10 (1975) 1678. [ 101 D. Bloor, D.J. Ando, F.H. Preston and G.C. Stevens, Chem. Phys. Letters 24 (1974) 407. [l 11 D. BJoor and F.H. Preston, Chem. Phys. Letters 38 (1976) 33. (121 H.-J. Graf, Diplomarbeit, University of Mainz (1974). (131 R.H. Baughman and KC. Yee, J. Polymer Sci. Polymer Chem. Ed. 12 (1974) 2467. 1141 D. Bloor. Chem. Phys. Letters 42 (1976) 174. [ 151 D. Btoor and F.H. Preston, Phys. Stat. Sol., to be published. [ 161 B. Reinter, H. Brissler, J. Hesse and G. Weiser, Phys. Stat. Sol. 73b (1976) 709. [ 171 D. Day, M.Sc. Thesis, Case Western Reserve University (1976).
CHEMICAL PHYSICS LETTERS
i Fe5cuary 1977
RESONANT RAMAN SPECTROSCOPIC STUDY OF BIPHENYL GLUTARATE DIACETYLENE POLYMER
D. BLOOR”, W. HERSEL Physrkolisches Institut der Universltat Stuttgart, 7000 Stuttgart-Vaihingen, 80, W-Germany
Teil3,
and D.N. BATCHELDER Deprtment of Physics, Queex Mary College. London El 4N.7, UK Received 29 September
1976
The resonantly enhanced Raman spectra of biphenyl glutarate diacetylene polymer chains in fully radiation pofymerfzed and partially thermally polymerized samples are reported. Details of the resonant enhancement in the region of the polymer electronic absorption were studied in partially polymerized sampIes. The rofe of defects in producing fluorescent emission and in broadening the optical absorption for radiation polymerized samples is briefly discussed.
Raman spectroscopy has proved to be a valuable tool in the study of the electronic and vibrational states of single crystaldiacetylene polymers [l-S] _Macroscopic single crystal of these conjugated polymers can be obtained by solid-state polymerization 16-91. The optical absorption of the conjugated chains is extremely intense and strong resonantly enhanced Raman scattering is observed. The Raman spectra are simple, despite the presence of complex side groups, since only vibrational modes which couple with the n-electron system are enhanced. Thus, the most intense Raman lines are due to the in plane stretching vibrations of the all-trans planar backbone, The use of a dye laser enables the variation of the Raman scattering intensity to be observed throughout the region of the electronic absorption peak. Thus, the details of the interrelation of the electronic and vibrational states of the polymer chain can be studied. We have reported previously such a study of the polymer * Permanent address: Department College, London, UK.
of Physics, Queen Mary
obtained from the his@-toluene sulphonate) of 2,4hexadiyne-1,6diol, TSHD [S] _ For this polymer the electronic absorption is split at low temperatures [ IO,1 1] and vibrational modes coupled to one electronic state, but not the other, were clearly identified. We here report similar studies of the poiymer obtained from biphenyl gbrtarate diacetyIene, BPG [12,13] _ The partially and fully polymerized BPG crystaIs, which were also used for optical absorption measurements [14], were obtained from Professor G. Wegner of the Institute for Macromolecular Chemistry at the University of Freiburg. The partially poiymerized samples -were thermally polymerized at room temperature while fully polymerized samples were obtained by -y-irradiation of the monomer crystals. The structure of the monomer molecule and the proposed structure of the polymer chain 112,131 are shown in fig. I. Raman spectra were recorded at a resolution of I cm-L using a rhodamine 6G dye laser. A photon counting system and a cooled-selected photomultiplier were used so that good signal to noise ratios could be obtained with Low laser power incident on the sample, thus preventing sample decomposition. Samples were mounted in a con411
CHEMICAL PHYSICS LETTERS
Volume 45, number 3
pqi o\ C-C-C-C-~
0
_p
k k k
0
Q-c-c-c&~ (4 Fig. 1. (a) Molecular structure of BPC monomer. (b) Polymer chain structure of BPG polymer, the biphenyl glutarate linkages are shown schematically. tinuous flow cryostat so that the sample temperature could be varied between 300 K and 4 K. The optical spectrum of BPG is simpler than that of TSHD polymer since the electronic absorption is not split at low temperatures. For partially polymerized BPG, where we assume there are long polymer chains distributed in the monomer matrix (cf. TSHD refs [9,1 l]), the absorption peak is at 16 592 cm-* at 2 K and the lineshape is as expected for a onedimensional van Hove singularity, i.e. an inter-band transition [ 141. The radiation polymerized samples have an absorption starting at about 16 600 cm-l with the first broad absorption peak at 17 160 cm-l ai 2 K. Large ESR signals are observed in these samples so that it appears likely that defects produced during irradiation are responsible for the loss of detail in the optical spectrum. A typical Raman spectrum for a fully polymerized BPC crystal, with excitation at 16 500 cm-*, at 4 K is shown in fig. 2. The frequencies of the Raman lines and the vibrational sidebands, observed in the optical spectra, at liquid helium temperatures for both partially and fully polymerized samples are compiled in table 1. The comparison of Raman and sideband frequencies is poor for the fully polymerized crystals,
WAVENUMBER
[em+]
Fig. 2. Raman spectrum of a fully radiation polymerized crystal of BPG. recorded with an excitation frequency of 16 500 cm-’ and a sample temperature of 4 K.
412
1 February
1977
either because of the large optical absorption linewidths or the possibility that the optical absorption is due to defects, as discussed later. The comparison is good for the partially polymerized samples, which have sharp optical absorptions. Small differences are observed between the Raman and sideband frequencies, these are expected since (a) the sidebands give excited state frequencies while the Raman lines have ground state frequencies and (b) the sidebands reflect the vibrational density of states while the Raman lines are due to the specific vibrational modes. The relative Raman scattering intensities for both types of samples are similar. For excitation frequencies within 800 cm-l of the electronic absorption peak there are only small changes in the relative intensities of the high frequency Raman lines (frequencies above 700 cm-l). However, the low frequency Raman lines (frequencies below 700 cm-l) showed a marked increase in intensity relative to the high frequency lines as the excitation frequency is increased across the quoted range. The resonant enhancement was studied in detail for the partially polymerized samples since, unlike fully poly;nerized crystals, the reflectivity and refractive index do not change significantly in the region of the electronic absorption [ 11 ,15,16] . Thus, the scattering intensity needs to be corrected only for the sample absorption [5], which can be obtained from transmission measurements [14], and the v4 frequency dependence. The behaviour of the lines at 128 1 cm-l is shown in fig. 3a and that of the pair of lines at 2 114 and 2 124 cm-l, in the t%C stretching region, is shown in fig. 3b. These frequency dependences can be compared with the electronic absorption lineshape shown in fig. 3c. The rise in intensity of the 1281 cm-l line is similar to, but less asymmetric than, the absorption line profile. While the 2 114 cm-l line has a similar behaviour the 2 124 cm-l line has maximum intensity about 400 cm-l above the electronic absorption, in the region of the first pronounced vibrational sideband, see fig. 3c. In this region the intensity variations of the two lines indicate that there is interference between the scattering processes. Close examination of the Raman spectra reveals small frequency shifts of several lines in the same region suggesting the occurrence of similar secondary resonant enhancements but with frequency differences too small to be clearly resolved. These effects are similar to but less pronounced than those observed for TSHD polymer [S] . However,
Volume 45, number 3
CHEMiCAL PHYSICS LETTERS
E February I977
Table 1 Vibrational frequencies of BPG polymer observed by optical and Raman spectroscopy, aU frequencies quote+ in cm-r Optical spectroscopy fully radiation polymerized
Raman spectroscopy partially ~erm~y polymerized
fully radiation polymerizeda)
partiaiiy tbermaBy polymerized b!
1421
174 320 430 548 702,725 744,766 862,925,1019 1049, llil 1195 I255,1281 1405,1439 1452,1497
43.49, s9 73 125 178 323 433 549 702,723 742,758 862,924, Lot.8 I@%, 1112 1 I92 1256,1281 1402,1436 1449, I496
2098
2112
2114.2124
184C) 404,453 555
330
753
1287 1460 1740 2240
a) Excitation frequency 16 500 cm-‘, Raman lines below 150 cm-’ not recorded. b) Excttation frequency 17 100 cm-‘. C) These bands can only be seen in spectra recorded on a more extended scale than that of fig. 3c.
b
17ma
WAVENUMEER
tern+ 1
nmo
WQa
WAVENUMBER
km3
Fig. 3. (a) Variation of the Raman scattering intensity at 4 K of the 1231 cm-’ vibration of BPG poiymer in a partially thermaiIy polymerized crystal in the region of the electronic absorption. @I)As (a) for the 2114 and 2124 cm-’ vibrations. Cc) Biectronic absorption lineshapes of BPG polymer in a partially polymerized crystal at 2 K. 4I.3
Volume 45. number 3
CHE,MICALPHYSICSLElTERS
whereas for TSHD the effects are associated with two electronic absorptions here they are associated with an electronic and a vibronic peak. The spectrum of BPG is rich in lines in the C=C stretching region, in comparison TSHD has only one intense and one weak peak in this region [ 1,9] . Possible causes of the additional lines are (a) conjugation between the polymer chain and the adjacent phenyl rings,(b) t&c occurrence of a non-centrosymmetric structure rendering more vibrations Raman active, (c) vibrations of the bis phenyi glutarate linkages giving finite vibrational amplitude in the polymer cham and, (d) Fermi resonances of backbone combination bands with the C=C stretching vibration. Conjugation appears unlikely since molecular models of the monomer and polymer place the phenyl rings orthogonal to the plane of the backbone. This has recently been confirmed by the X-ray structural data of Day [ 171. However, these structural results did not show clearly a centric structure so that suggestion (b) cannot be eliminated. Coupling between the glutarate links and diacetylene chain is likely. The occurrence of low frequency Raman lines attributable to accordion modes of the glutarate links supports this interpretation. Several combination frequencies fall into the C=C region, indeed so many that unambiguous identification of possible Fermi resonances is impossible. The line at 1439 cm-l in the fully polymerized sarnpies cannot be observed at room temperature while its equivalent in partially polymerized samples r.xnains in the spectrum though it is somewhat broadened. These observations are compatible with a Fermi rcsonance modified by the different temperature shifts of the fundamental vibrations in the two types of sample. In addition to the Raman spectrum the radiation polymerized samples exhibited a broad fluorescence at low temperatures. The observed vibrational structure and the dependence on excitation frequency show clearly that the electronic absorption at 17 160 cm-l is an aliowed zero-phonon transition. However, the fluorescence of the highly defective radiation polymerized BPG contrasts strongly wi*h the absence of fluorescence in partially thermally polymerized BPC and thermally polymerized TSHD, which have much greater perfection. This suggests that the defects act as traps, which are only populated at low temperatures, from which radiative decay is favoured. The equivalence of the Raman spectra of fully and partially polymerized BPG shows that the 414
1 February 1977
polymer chains have nearly the same conformation in both sarrples. This contrasts with the apparently large difference in electronic absorption energies quoted above. However, the radiation polymerized samples have an absorption edge at the same energy as the peak position in the partially polymerized samples. Thus the presence of defects may produce a distribution of absorptions at energies above the infinite chain limit with the higher energy peak reflecting either a maximum in the distribution of chain lengths or the absorption of the defects. The latter explanation accords with the interpretation of the fluorescence given above. Further studies of the defects by ESR are in hand in an effort to resolve these problems. This work was supported by grants from the SRC and the SFB. One of us (D.B.) thanks the Humboldt Foundation for a Fellowship and Professor H.C. Wolf for his hospitality during the course of this work. References 1I] A.J. hlelveger and R.H. Baughman,J. Polymer Sci. A2
11 (1973) 604. [2] R.H. Baughman,J.D. Witt and K.C. Yee, J. Chh=m. Phys. 60 (1974) 4755. [31 G.J. Exarhos, W.M. Risen Jr. and R-H. Baughman, 3. Am. Chem. Sot. 98 (1976) 481. [4] D. Bloor, D.J. Ando, F.H. Preston and D.N. Batchelder, in: Structural studies of macromolecules by spectroscopic methods, ed. K.J. Ivin (Wiley, New York, 1976) p. 91. [S] D.N. Batchelder and D. Bloo:, Chem. Phys. Letters 38 (1976) 37. [6] G. Wegner, Z. Naturforsch. 24b (1969) 824. [7] G. Wegner. Makromol. Chem. 1.54 (1972) 35. [8J C. Wegner, Mcthoden der Organischen Chemie, Vol. 4/Sb, Part II (Thieme, Stuttgart, 1976) p. 1499. [91 D. Bloor, L. Koski, G-C. Stevens, F.H. Preston and D.J. Ando, J. Mater. Sci. 10 (1975) 1678. [ 101 D. Bloor, D.J. Ando, F.H. Preston and G.C. Stevens, Chem. Phys. Letters 24 (1974) 407. [l 11 D. BJoor and F.H. Preston, Chem. Phys. Letters 38 (1976) 33. (121 H.-J. Graf, Diplomarbeit, University of Mainz (1974). (131 R.H. Baughman and KC. Yee, J. Polymer Sci. Polymer Chem. Ed. 12 (1974) 2467. 1141 D. Bloor. Chem. Phys. Letters 42 (1976) 174. [ 151 D. Btoor and F.H. Preston, Phys. Stat. Sol., to be published. [ 161 B. Reinter, H. Brissler, J. Hesse and G. Weiser, Phys. Stat. Sol. 73b (1976) 709. [ 171 D. Day, M.Sc. Thesis, Case Western Reserve University (1976).