J. Phys. Chem. 1987, 91, 6048-6055
6048
The biradical which is formed in tetrahydrofuran decomposition (reaction l ) , (CH2)2-0, decomposes according to the reaction’ (CH2)2-0
-+
+ CH3 + CO
H
-+
+ CH3 + HCN
H
(13)
Since reaction 7 has the highest rate in the pyrolysis, the large quantities of HCN found in the shocked samples support the conclusion that reaction 13 is the main supplier of hydrogen cyanide. The second largest nitrogen-containing product is acetonitrile. The question is whether the latter can be formed via the rearrangement of the biradical (CH2)2-NH
-
CH3-CH=NH
(14)
1 CH3CN f t i 2
or whether it is formed by a reaction between methyl radicals and hydrogen cyanide, both reaction products:
CH3 + HCN
-+
CH3CN
+H
(15)
The equivalent of reaction 14 with (CH2)2-0 would be its rearrangement to acetaldehyde: (CH2)2-0
-+
CH3CHO
’3CH2-’2CH2
(12)
where the methyl radicals are the source for the large quantities of methane found in tetrahydrofuran decomposition. A similar reaction in pyrrolidine would be (CH2)2-NH
Whether reaction 14 takes place or not, can be determined by using a specifically labeled pyrrolidine:
(16)
As has been discussed in our tetrahydrofuran pyrolysis article,’ no t r a m of acetaldehyde were found among the reaction products, thus ruling out completely the existence of reaction 16.
1
“CH2 N‘
’‘&I2
H
’
Acetonitrile with two isotopically identical carbon atoms would then rule out reaction 14. Unfortunately, we were unable to obtain such a labeled pyrrolidine and the question of reaction 14 remains an open question until such a molecule can be made available. The production mechanism of the additional two nitriles which are found among the reaction products, acrylonitrile and ethane nitrile, has been described in a previous articleSdealing with the thermal reactions of acetonitrile. Since a similar environment prevails under the experimental conditions of the present study, their production mechanism may be assumed to be the same. Similar to the observations in tetrahydrofuran decomposition we did not observe any products resulting from isomerization reactions of pyrrolidine. It should be mentioned that preliminary results on the reactions of pyrrole (C4H4NH)show a number of isomerization products resulting from the ring opening of the latter.5 Similar reactions in furan could not be established.2 B. The Pyrolysis Scheme. The overall pyrolysis of pyrrolidine can be summarized in Scheme I. It contains the major reactions that participate in the pyrolysis. Some of the later reactions in the pyrolysis are given as overall (schematic) processes for simplicity.
Acknowledgment. This research was sponsored by the Stiftung Volkswagenwerk. We thank Prof. Thomas Just for very valuable discussions. Registry No. Pyrrolidine, 123-75-1.
Scattering Anisotropy of Partially Oriented Samples. Turbidity Flow Linear Dichroism (Conservative Dichrolsm) of Robshaped Macromolecules Nabil Mikati,? Jerker Nordh, and Bengt Nordh* Department of Physical Chemistry, Chalmers University of Technology, S-412 96 Gothenburg, Sweden (Received: July 7, 1986; In Final Form: March 8, 1987)
Light-scattering anisotropy of partially oriented macromolecules or particles is important in several contexts; however, owing to the generally rather complex forms of both the scattering expressions and the orientational distributions that these have to be integrated over, very few calculationshave been made. We calculate here the scattering flow h e a r dichroism (“conservative dichroism”) of rodlike, nonabsorbing and noninteracting particles of varying size and shape that are partially oriented in a Couette flow cell and observed along a radial optical direction. The scattering is calculated according to the RayleighGans-Debye approach and the flow orientation described by the Peterlin-Stuart theory for rigid particles. It is found convenient to define a “reduced turbidity linear dichroism”,LD: = (T,,- ~ ~ ) / analogous 7 i ~ to the ordinary, absorptive reduced dichroism, LDX. Unlike LDX, however, LD: is generally not factorizable into separate “optical” and ”structural” terms but is expected to depend on higher moments of the orientational distribution. The scattering anisotropy at complete orientation varies with particle geometry and increases monotonically with the length of particles whose diameter is small compared to the wavelength of light. Measured linear dichroism of very long, rod-shaped aggregates of the protein tubulin, oriented in Couette flow, shows fair agreement with the calculated dependence of LD: with gradient and, furthermore, allows comparison between turbidity dichroism and absorptive dichroism to be made.
Introduction Among current methods for studying macroscopically oriented samples, linear dichroism is fiiding increasing use. An advantage to dispersive phenomena, such as polarized scattering and birefringence, is that linear dichroism can often be directly related to structure, through the directional properties of the light-abPresent address: CEA-Verken, S-152 00 StrHngnils, Sweden.
0022-3654/87/2091-6048$01.50/0
sorbing electronic or vibrational transition^.'-^ In addition, linear dichroism is today very sensitively measured by modulation as has been exploited extensively, for example, for (1) Thulstrup, E. W.Aspects of the LD and MCD of Planar Organic Molecules; Springer: Berlin, 1980. ( 2 ) Nordh, B. Appl. Spectrosc. Rev. 1978, 14, 157-248. (3) Michl, J., Thulstrup, E. Spectroscopy with Polarized Lighr; VCH Verlagsgesellschaft: Weinheim, FRG,1986.
0 1987 American Chemical Society
Scattering Anisotropy of Partially Oriented Samples studying flow-oriented biopolymers, such as DNA2*6v7and its complexes with small m o l e c ~ l e smetal , ~ ~ ~ions,lOJ’and even proteins.12 In connection with recent flow dichroism measurements on microtubules, which are fiberlike protein aggregate^,'),'^ the problem of quantitative interpretation of turbidity anisotropy of partially oriented particles in flow fields was found not to have been satisfactorily solved before. The aim of the present report is thus to cnsider the anisotropic forward scattering, within the Rayleigh-Gans-Debye (RGD) approximation, of elongated, locally isotropic cylindrical particles subject to flow orientation in the usual Couette flow apparatus with radial measuring geometry. Measurements of turbidity linear dichroism of microtubules, and its dependence on flow gradient, are also carried out and the experimental and theoretical results compared. Scattering anisotropy and birefringence due to anisotropy of local fields (*form anisotropy”) have been considered occasionally in the literature. Peterlin and Stuart, in an early theory for flow birefringence of elliptical particles,15 found the macroscopic birefringence to be proportional to an optical factor (dependent on the indices of refraction of the particle and the surrounding solvent) and an orientation factor;1sJ6the flow birefringence of flexible polymers has been shown to factorize analogo~sly.’~A similar factorization into optical and orientation factors is also anticipated for “form dichroism”, which is the anisotropic attenuation of the light absorption of randomly oriented or cubic chromophores due to the anisotropy of the local fields.18 The light scattering of either perfectly oriented or randomly oriented particles has been considered by several authors, both for cases of infinitely thin isotropic disks or rods,19v20and for cylindrical particles with comparable length and thickness.2’-25 Anisotropic light scattering of flow oriented dispersions, measured as anisotropic turbidity (conservative dichroism) has been studied extensively by Heller and Conservative dichroism of c ~ - w o r k e r s and ~ ~ by ~ ~ other^.^^,^' ~-~~
(4) Jensen, H.P.; TroTell, T.; Schellman, J. A. Appl. Spectrosc. 1978,32, 192. (5) NordCn, B.; Seth, S. Appl. Spectrosc. 1985, 39, 647-655. (6) Hofrichter, J.; Schellman, J. A. Quantum Chem. Biochem. 1973, 5, 787. (7) Matsuoka, Y.; Norden, B. Biopolymers 1982, 22, 1731-1746. (8) Norden, B.; Tjerneld, F. Chem. Phys. Lett. 1977, 50, 508-512. (9) NordCn, B.; Tjerneld, F. Biopolymers 1982, 21, 1713-1734. (10) Nordtn, B.; Matsuoka, Y.; Kurucsev, T. Biopolymers 1986, 25, 1531-1 545. (11) Htird, T.; NordCn, B. Biopolymers 1986, 25, 1209-1228. (12) Kubista, M.; HBrd, T.; Norden, B. Biochemistry 1985,24,6336-6342. (13) Nordh, J.; Deinum, J.; NordCn, B. Eur. Biophys. J . 1986, 14, 113-122. (14) Wallin, M.; Nordh, J.; Deinum, J. Biochim. Biophys. Acta 1986,880, 189-1 96. (15) Peterlin, A.; Stuart, H. A. Z . Phys. 1939, 112, 1-19. (16) Peterlin, A.; Stuart, H. A. In Hand- und Jahrbuch der chemischen Physik, Eucken, A., Wolf, K. L., a s . ; Adadem; Verlagsgesellschaft: Leipzig, 1943; Vol 8, Sektion I.B, p 1. (17) Copic, M. J. Chem. Phys. 1957, 26, 1382-1390. (18) Norden, B.; Davidsson, A. Chem. Phys. 1978, 30, 177-186. (19) Horn, P. Ann. Phys. 1956, 10, 386-396. (20) Picot, C. J. Colloid Interface Sci. 1968, 27, 360-365. (21) Van Aartsen, J. J. Eur. Polym. J . 1979, 6, 1095-1 104. (22) Heller, W. Reu. Mod. Phys. 1959, 31, 1072-1077. (23) Meeten, G. H. J. Colloid Interface Sci. 1981, 84, 235-239. (24) Van De H u h . Light Scattering by Small Particles; Wiley: New York, 1957. (25) Kerker, M. The Scattering of Light and other Electromagnetic Radiation; Academic: New York, 1969. (26) Nakagahi, M.; Heller, W. J. Polym. Sci. 1959, 38, 117-131. Tabibian, R.; Nakagaki, M.; Papazian, L.J. Chem. Phys. (27) Heller, W.; 1979, 52,4294-4305. (28) Nakagaki, M.; Heller, W. J. Chem. Phys. 1975, 62, 333-340. (29) Nakagaki, M.; Heller, W. J . Chem. Phys. 1976, 64, 3797-3801.
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 6049
i
Figure 1. Geometric notations. Polar and azimuthal angles defining orientation of rod-shaped particle (P): 8,4 referring to scattering theory, and e,, 4, to hydrodynamic theory. The velocity gradient vector G is directed along the Z axis (flow direction = Y axis). Light is incident along -2 and scattered along the direction denoted S at the angles a and
P. electrically (or by other cylindrically symmetrical fields) oriented ensembles of scattering, nonabsorbing particles has been considered theoretically more recer~tly.~*,~~ Mayfield and Bendet, in a study of anisotropic light scattering of tobacco mosaic virus, oriented in capillary flow, exploited the symmetry of the flow geometry to obtain an analytical expression of the distribution function allowing a rather direct computation of the anisotropic turbidity.)’ A revival of conservative dichroism measurements is found in recent studies of dynamics of colloidal solutions subject to time-dependent flow fields;34however, this is an approach assuming other boundary conditions and, furthermore, neglects Brownian motion (rotational diffusion). Nakagaki and Heller,Z8v29 and also Okano and Wada,30 have made extensive computations of anisotropic scattering based upon the Peterlin-Stuart theory, which is the only rigorous theory for the distribution of rigid particles in a constant flow gradient that includes rotational diffusion. However, their treatments assumed unpolarized incident light or a flow or measuring geometry different from that of the common Couette cell used today, which has a radial light propagation. As has been noticed by Nakagaki and Heller,29 the anisotropic scattering problem requires the computation of a considerable number of additional coefficients of the distribution function than is needed for birefringence or (absorptive) linear dichroism measurement^.)^ We have recently performed a calculation of the complete Peterlin-Stuart distribution, in a limited range of flow gradient^,)^ solving the appropriate flow differential equation by numerical methods. Excellent agreement with all the Peterlin-Stuart coefficients needed for the scattering problem was obtained for low and intermediate gradients (rapidly accelerating computation costs limited the study to reduced gradients C/O I 10). In the present study we shall base our calculation on the coefficients tabulated by Nakagaki and Heller in a wider gradient interval (0 I C / O I 60).29
Theory The basic principle of the Rayleigh-Gans-Debye (RGD) approximation is to treat the scattering of any volume element of a particle of arbitrary shape as a Rayleigh s ~ a t t e r e r ,unper~~,~~ turbed by other, surrounding elements. The particle is assumed to consist of a dielectric whose optical permittivity is essentially isotropic (on a molecular level) and does not differ very much from that of the surrounding medium. The scattering is determined as the sum of all waves from the independent scattering centers, (30) Okano, K.; Wada, E. J. Chem. Phys. 1961, 34, 405-408. (31) Mayfield, J. E.; Bendet, I. Biopolymers 1970, 9, 655-668. (32) Stoimenova, M.; Labaki, L.; Stoylov, S . J. Colloid. Interface Sci. 1980, 77, 53-56. (33) Ravey, J. C. J. Polym. Sci. Symp. 1974, 42, 1131-1145. (34) Frattini, P. L.; Fuller, G. G. J. Colloid Interface Sci. 1984, 100, 506-518. (35) Wada, A. Appl. Spectrosc. Rev. 1972, 6, 1-30. (36) Andersson, L.;Norden, B., unpublished.
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
6050
with phases referring to a common origin. In analogy with the (absorptive) linear dichroism, LD = All we shall define the turbidity linear dichroism (equivalent to conservative dichroism"), LD,, as the differential turbidity of orthogonal forms of linearly polarized light: LD, = AT = 711 - 7 1 (1)
In analogy with the reduced linear dichroism,2 LD' = LD/Aiso, we also define a reduced turbidity linear dichroism
with 7im being the turbidity of the corresponding isotropic solution. Consider a particle in a flow field as defined in Figure 1. The particle is assumed to have a cylindrical symmetry and an orientation which is determined by a pair of angles 4, 8 (or, alternatively, as will be explained, +p, OP). Light is incident along the -2 direction and scattered along the direction denoted S,defined by the angles a and /3. The two notations for-the particle orientation refer to the scattering and the hydrodynamic theories, respectively (p for Peterlin-Stuart); they are interrelated according to eq A1-A2 in the Appendix. Following the matrix formulation of Van de H ~ l s t the ,~~ scattered electric fields are given by
Mikati et al. entation of rigid ellipsoidal particles is described by the Peterlin-Stuart distribution function, fl$ ,ep),expanded in Legendre polynomials as outlined elsewhereltzs
where G/B is the so-called reduced gradient, G being the flow gradient and 6 the rotational diffusion constant around the minor axis of the ellipsoid or rod. The coefficients ahk and bhk are functions of the axial ratio,p (major to minor axes) of the ellipsoid and the reduced gradient. Many of the coefficients have been tabulated long ago by Scheraga et al." for selected particle dimensions and shear gradients. A number of additional coefficients have more recently been computed by Nakagaki and Heller.2* Averaging the turbidity linear dichroism of eq 7 over the disand the unpolarized turbidity of eq tribution function fl+,,O,)! 8 over a random distribution, respectively, one has
sin3 /3 sin O f ( + , O ) R2(P,a) (IO)
sin 8 (1
(3)
+ cos2 P)R2(/3,a) (1 1)
= r b of eq 2, we may obtain the reduced turbidity Since ( 7JrandOm where L and r denote the directions parallel and perpendicular linear dichroism as the ratio between eq 10 and 11. to the scattering plane SOZ. The Si's are the amplitude functions, In the Appendix a few additional expressions needed are derived. depending on the geometry of the particle and the scattering angle. With standard algebra, used elsewhere for similar p u r p o ~ e s , ~ ' * ~ ~Calculations one obtains the intensity of the scattered light from perfectly The integrals of eq 10 and 11 were solved numerically by using oriented particles, when the incident beam has parallel and perthe rectangular rule;38 the equations were approximated by the pendicular polarization relative to the orientation direction, refollowing summations spectively ( A T ) F= Z,,= HZ&2(/3,a)[cos2 a cos2 /3 sin2 a] (4) 1 P Q R S c f l A , B ) AZ(A,B,Al,Bl) sin(B).G.H.Gl.Hl (12) Z1 = HZ,,R2(/3,a)[sin2 a + cos2 /3 cos2 a] 4 r k = I/=lm=ln=l (5)
+
where R2(/3,a) denotes the square of the amplitude of the form vector, defined and evaluated by Van de HulstZ4for particles of varying geometry (see Appendix for further details). For cylinders one hasz4 R(6,a) = F(KD sin /3/2 sin y ) E ( K L sin p / 2 cos y) ( 6 ) with
F(u) =
;( 7- y ) 2 sin u
cos u
+
E ( u ) = sin u / u cos y = sin 8 cos /3/2 cos (4 - a) - sin /3/2 cos 0
+
where D is the diameter of the cylindrical particle and L is its length. K is the modulus of the wave vector. For very thin rods, KD
