B. NordBn, G. Lindblom, and I. Jon55
2086
Linear Dichroism Spectroscopy as a Tool for Studying Molecular Orientation in Model Membrane Systems Bengt Nordin,” Goran Llndblom, and Ivan Jon55 Department of Inorganic Chemlstry 1 and Department of Physical Chemistry 2, University of Lund, 5-22007 Lund, Sweden (Received May 9, 1977)
Ordinary linear dichroism (LD) spectroscopy with rectangular optics is not applicableto thin uniaxial samples having the optical axis perpendicular to the plane of the sample. A method has been developed to study such samples at inclined optical incidence and a general relation derived between the LD (corrected for polarized reflection) and the average orientation of the absorbing transition dipole. For molecules of C2”,D2h, or higher symmetry the usual order parameters can be obtained. The method has been tested on anthracene in a polyethylene standard slab of perfectly axial symmetry. The estimated orientation agreed with previous reports on anthracene in stretched polyethylene sheets. A number of chromophoric molecules solubilized in macroscopically aligned lamellar mesophases of the systems sodium octanoate/decanol/water and sodium di2-ethylhexylsulfosuccinate(Aerosol OT)/water have also been studied. In the first system rodlike molecules (diphenylethyne, anthracene, retinal) are oriented with their long axes parallel to the hydrocarbon chains of the amphiphile, while an extremely long molecule (&carotene) as well as water-soluble planar cationic dyes are on the average oriented parallel to the lamellar planes. In the Aerosol OT system all molecules studied were oriented parallel to the lamellar planes.
Introduction With water, amphiphilic molecules frequently form liquid crystalline phases with structures depending on temperature and composition. Most notably, they can form lamellar mesophases built up of molecular bilayers separated by water. The resemblance to biological membranes has led to a great interest in the physical properties of lyotropic liquid crystalline phases.l Wellknown physical methods such as x-ray diffraction and differential scanning calorimetry have given evidence about the structure and the phase stability of such systems. Molecular motion has also been studied by NMR and ESR.lv3 However, knowledge about the orientation of partly or completely solubilized molecules in the bilayer membrane is still quite limited, probably due to the lack of specific and unambiguous methods for these kinds of studies. The technique of linear dichroism (LD), nowadays sensitively measured using the phase modulation techn i q ~ ehas , ~ been successfully employed in a number of cases where the sample molecules can be given a certain degree of ~ r i e n t a t i o n . ~ Since various membranes may themselves be easily aligned (e.g., by “spreading”6on a plane, by flow gradients? or magnetic fields6)there appear to be possibilities of applying linear dichroism spectroscopy to elucidate the orientation, e.g., of an embedded protein in the lipid matrix, provided the orientation of some chromophore within the protein is known. However, a problem arises since the thin membranes do not permit light of sufficient intensity to be propagated through themselves in the direction parallel to the membrane plane. On the other hand, if the light impinges perpendicularly to the membrane plane, that is, along the optical axis, no dichroism results since the distribution of the molecules around this axis is cylindrically symmetric. The obvious way to obtain an observable LD of such a sample is to tilt the optical axis with respect to the direction of the incident light. In Figure l a a sample which is uniaxially symmetric (around the z axis) is tilted around a “hinge”, the laboratory-fixedX axis. In this way unequal interaction probabilities can arise between light rays with The Journal of Physlcal Chemistry, Voi. 8 1, No. 22, 1977
mutually orthogonal polarizations (Xand 2) and an absorbing transition dipole oriented in the sample. Inclined incidence has been employed on several occasions before to study thin uniaxial samples: e.g., Bateman and Covington8discussed the orientation of the carbon chains of fatty acid multilayers on the basis of polarized reflection studies, and Yannas et alS9estimated elements of the rotivity tensor of collagen from measurements of the optical activity under inched incidence on a dried collagen film. No detailed analysis has been reported on the method of studying polarized transmission of such samples, but previously employed relations between measureable entities and molecular properties have been based on special assumptions about the orientational distributions and the symmetries of the molecules.6,10 Basic Theory Intrinsic Linear Dichroism Due to Molecular Orientation. The perturbation producing ordinary electronic spectra is an interaction of the electric field, E, of the radiation and the electric dipole moment, p, of the molecule. The decadic extinction coefficient e (M-l cm-l) due to a single transition o m is
-
where p denotes a normalized band shape function and E is a unit vector along E, the other symbols having their usual meaning.ll The linear dichroism is defined as (where C is the concentration in mol dm-3 and d is the optical path length in centimeters) that is the difference in absorption when the light is polarized parallel and perpendicular, _respectively, to the laboratory 2 axis in Figure 1 (Le., E is parallel and perpendicular to 2, respectively). The averages are over the distribution function appropriate to the method of orientation. The averages are conveniently handled by employing a spherical tensor formalism12 and it is then shown (Appendix, eq Al-A6)
Dichroism of Membranes
Since LD/A is approximatelylinear in cos2w a preliminary LDW=O is easily obtained (Figure 2e) and the following expression can be used (we have dropped the conicity factor, which is justifiable for small a ) LD j A
-=
+ (LDjW'O/3)
cos2 0
3s, nZ(1 - (cos w /n)")"2
(6)
We stress by the index i that the relation is between the LD from the transition moment 1.1, and the average orientation of that direction in the molecule. In the case of overlapping bands with differing polarizations, S, can be replaced by (cXSx+ tyS, + E ~ S ~ )+/ E(, E ~E,) for a symmetric m01ecule.l~ Reflection Dichroism. In the derivation above we have only considered the LD effect from molecular orientation in the membrane. In order to experimentally obtain that LD, however, we shall have to first subtract a generally strong contribution, LDR, from polarized reflections at the various boundaries. In the present experiments we have thick samples and LDRcan be extrapolated from the LD level observed in the transparent regions surrounding the absorption band. However, for the sake of completeness when presenting this method, we give the expression which must be used to correct for LDR in case of thin (d < cm) or strongly absorbing (lo4cm-l < A ) samples. This point has hitherto been ignored in polarized studies of membranes. The boundaries are the following: air/supporting plate = 12, supporting plate/membrane = 23. The supporting plate is generally transparent and thick as compared to the wavelength of light. The LD contribution from the two ambient boundaries 12 can be expressed by, e.g., following the outline of ref 15.
+
b
z Figure 1. Geometrical parameters of membrane model system and optics: (a) transition dipole p and its coordinates ( 4 , 8); (b) conical angle of light beam and tilting angle of sample.
that the LD due to the molecular orientation, divided by the absorption of the sample at random orientation, is given by the very simple equation LD/A, = 3s cos2 o
(3)
where w is the angle between the laboratory Y axis (the direction of light propagation) and the membrane plane, and S is the order parameterT3representing the average orientation of y with respect to the director of the uniaxial membrane system (see the Appendix). If we assume that A, be determined at normal incidence we have to adjust for the fact that LD refers to a longer pathlength, by the factor [l - (cos w / n ) 2 ] - T / z( n is the refractive index of the sample). Further, a sample tilt as defined in Figure 1corresponds to a true angle arcsin (sin u ) / nwithin the sample (Snellius' law). Finally, one may take into account the conicity of the light pencil, implying a tilt (cull or aI)of the electric vector with respect to the laboratory axes. We assume circular conicity (one angle 2a) and an even intensity distribution. Incorporating these corrections one obtains instead of eq 3:
sin a
2a
(4)
Generally an absorbance, A, of the oriented sample with nonpolarized radiation at normal incidence, is more easily obtained than A,. A relation between A and A, is, however, easily derived; the absorbance at random orientation is equal to one third of the trace of the absorbance tensor of the sample: A , = ' / J A , , + A,, + Azz). A,, is the absorption when E is polarized parallel to the x axis, etc. The absorbance of the oriented sample for nonpolarized light is equal to A = (A,, + Ayy)/2.Furthermore, the LD extrapolated to w = 0 is given according to the definition LDW=O = A,, - AXx.The cylindrical symmetry of the sample implies that A,, = A,, and we have A, = A
+ LDW='/3
(5)
where the Fresnel coefficients (R = rr*) are defined as Rlij = [(nj2COS' $ j - nj2 COS' $ j - kj2 cos2 $j)2 4Jzj2ni2cos2 $i cos2 $j]/[(ni cos (#Jj + nj COS $j)' kj2 COS' @j12 Rlljj = [(nj2 COS' $ j - ni2 cos2 @ j kj2 COS' $ j ) 2 4kj2nj2 cos2 Pi cos2 $ j ] / [ (nj cos $ j ni cos $j)2 kj2 cos2 q+]2
+
+
+
+
+ + (8)
RLT2and Rl12are obtained by inserting nl = 1, n2 = refractive index of the supporting plate at the relevant wavelength, 61 = ~ / - 2w , cj2 = arcsin [(sin 6 J / n 2 ]and k2 = 0. To obtain the contribution from the reflections 23 at the absorbing thin sample we must take into account the effect of interference in the transmitted intensity, and of a complex refractive index ii3 = n3 + ik3. As a reasonable approximation isotropic n3and k3 = A In 10/4rvdo may be assumed in eq 8 to get R123 and We insert q53 = arcsin [sin ( ~ / -2 w ) / n 3 ] . The effect of interference is governed by the phase coefficient cos 26, where 6 = 2adn3 cos +3/X. By following the derivation methods of any standard textbook on opticsT6one obtains 2LD23 = 2 1% (1- Ri23)/(1 - R1123) [l - R123 exp(-Ad/do)]' + 4R123exp(-Ad/d,) cos 6 log [l - R1123exp(-Ad/d0)l2+ 4R1lZ3exp(-Ad/do) cos 6 (9) For very large absorptions eq 9 has the form of eq 7 and the effect of the interference is negligible. On the other hand, when A = 0 and 6 = (2N + 1 ) ~ / 2we , have LD23= The Journal of Physical Chemistry, Vol. 81, No. 22, 1977
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B. Nord6n, G. Lindblom, and I. Jon65
I
-01
1 1 / , , 1 , , , , 1 1 , 1 3 00
~
LD
400
400
nm
rn
n : /
-00;
, I
J
nm
e
LD 0
376 nrn 0,051 005-
cos2LJ
-i I
I
I
0.5
0.5
0
Figure 2. LD and A of anthracene in a polyethylene slab (diameter 8 mm, thickness 0.15 mm) in which the hydrocarbon chains are aligned perpendicularly to the plane. The slab was arranged at different incidence angles according to Figure 1: (a) longitudinal band region (concentration 1.4 X M); (b) transverse band region (concentration 4.6 X M); (c) sketched preferred orientation of anthracene in the polyethylene slab; @,e) dependence of LD of the two anthracene bands on the angular factor in eq 8.
0. Thus a varying 6, e.g., due to the wavelength dependence of n3, can cause large LDR variations. Since the LD in eq 6 decreases with A, a simultaneously increasing ambiguity in LDR (due to uncertainty in 6) may prevent the accurate determination of Si. However, when k3 is small (k3may be neglected in eq 8 when
