Electric Birefringence A Simple Apparatus for Determining Physical Parameters of Macromolecules and Colloids Harold H. Trimm, Kevin Parslow, and Barry R. Jennings Electro-Optics Group, Physics Department, Brunel University, Uxbridge, Middlesex, UK UB8 3PH
The importance of macromolecules and colloids in industrial processes and biological interactions is reflected in the recent rapid increase in both information and research on these materials. On the molecular scale, both macromolecules and colloidal particles1 are huge. Hence much of the fundamental interest in these systems relates to the determination of their physical parameters in solution. Research techniques such as lieht scattering. -. ultracentrifueation. electron microscopy, and X-ray diffraction are c~mmoklyused to determine the molecular mass and dimensions of macromolecules (I),yet both the complexity of the experimental procedures and the cost of even simple equipment prevents the inclusion of these methods in underGaduate teaching lahoratories. Hence, many graduates are leaving school with little experience in practical characterization of these systems. A novel, rapid method for the determination of the optical, electrical, and geometrical parameters of macromolecules has recently been gaining- popularity a t the research level. I t is .. transient electric birefringence ( 2 )and overcomes the aforementioned shortcomings of other characterization methods. I t is straightforward, hoth experimentally and conceptually, and thus provides an ideal teaching method by which students can gain experience with practical systems. A research-grade electric birefringence apparatus, suitable for the analysis of a wide range of polymer, biopolymer, and colloidal systems and capable of yielding comprehensive data on the size. ~.shaoe.,dipole moments. electrical oolarizabilitv. ". and optical anisotropy of macromolecules, represents a considerable capital investment (3).In this paper, we describe a simplified form that can be assembled for less than $100 and can be used to measure hoth the dimensions and dipole moments of many macromolecules. Details are given of the construction and maniodation of the apparatus. Illustrative re.. sults are presented for a polymer latex emulsion (polytetrafluoroethylene (PTFE) in water), a biopolymer solution (DNA in water) and a clay sol (aqueous sepiolite). The method thus provides a realistic vehicle for undergraduate familiarization with macromolecular and colloidal systems. ~
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Theory Light is an electromagnetic wave motion, whose speed of tra\&e through a mnt&ial is relitrained hy successi;.e electriral interactitma with the electronic and atomic array of the material structure. This velocity-limiting property is embraced in the concept of the refractive index. The majority of macromolecules have an anisotropic structure, as the atomic array differs along the principal molecular axes. Hence, the refractive index varies with their axial directions and the material is birefringent. However, the property cannot be analvzed a t the level of a sinele molecule. A crvstal of. the material would exhibit the doihle refracting characteristics of the individual mulecules, but such crystals are difficult to
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Hereaner the term macromolecule will be used: the additional applicability of the text and the descr:bed method to colloids being understood. 1114
Journal of Chemical Education
Figure 1. Diagamatic rspesentation of anisampic molecules in: (a)* of an arieming field, and (b) in an orienting field.
absence
grow t o a suitable size, especially the biological macromolecules. The approach, is therefore, to produce a "dilute" C N S ~ ~ .
In solution, solute molecules adopt a random arrangement as represented in Figure la, and the information obtainable from the anisotropy of a single molecule is lost due to a spatial averaging of all the possible orientations of the constituent chaotic molecules. The solution is then isotropic, and light polarized in anv plane encounters the same index of refraction "pon transmis&n through the sample. If, however, the solute molecules can be aligned, then the solution as a whole becomes anisotropic (Fig. 1b) and birefringence (An) results. This is defined as the difference between the indices of refraction for light polarized parallel and perpendicular to the orienting field vector, respectively (4). A plane-polarized beam of light can be visualized as being composed of two, equiphase and equiamplitude, linearly polarized components at 45O t o the incident heam polarization azimuth. If one of these components lies in the orienting field direction, then the optical phase difference S introduced between the components due to the variable light velocities associated with each is related to An via the expression
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for lieht of waveleneth A traversine a birefrineent medium of " lengk 1. T o auantifv 6 and hence An. the beam from a lieht source is passed thrlugh an optical polkzer in zero azimuti; and then into a sample cell across which the electric field is applied a t 45' azimuth. The elliptically polarized emergent light falb on a further polarizer (referred to as the analyzer) which is crossed with respect to the polarizer (Fig. 2). For polymer solutions, which have a small induced birefringence, the intensity la of the light transmitted through the system is given by
Figwe 2. Relathe wlematiml setling of i b optical cnnponenta, viewed along h e light beam. nl and n l represent the indices of refraction parallel and perpendicular to the applied field direction (€), respedively. The shaded regions indicate the elecbodes.
RANDOM
ORIENTATION
RELAXATION
F b p e 3. The optical rspms.3 (lowtn bace) to a puls.4 applied field (upperIraca) shown as a function of time. Three separate states of molecular order are designated. Areas A, and A2 are indicated for the calculation of paramater 0.
where K represents light loea from other processes and 10 is the incident light intensity. These can he found by recording the light intensity transmitted through the system, I,, with no hirefringence induced in the medium in the cell, and the analyzer offset by angle a.The following then holds I, = nIo sin2ru
(3)
For the special case, with polarizer and analyzer set parallel, a = a12 and the light intensity I,,z is equal to KIO Hence, A . I In A. = -mn (4) rl which is ohtained hy direct substitution. Molecular alignment is achieved by the interaction of an nermanent (u) electric field intensitv. .( E.)with anv. . - . or induced dipole moment arising from the anisotropy (An) in the electrical darizabilitv of the moli.~.ules.Brownian forces comoete and oppose such ordering. Hence, the degree of alignment achieved is a function of the thermal energy (kT) with k and T, the Boltzmann constant and the absolute temperature, respectively. I t is convenient to apply the field in the form of a short duration pulse. This has the advantages of (1)making the method extremely fast, (2) minimizing the unwanted heating effects that accompany the application of continuous electric fields and (3) enabling one to study the rates of orientation and disorientation and hence to obtain a measure of the molecular size. The optical transmitted intensity in response to the applied field pulse is transient in nature (Fig. 3). The field excitation is accompanied by an exponential-type estahlishment of the hirefringence a t a steady value. This is where the molecules align to their equilibrium degree, hut a t a rate dependent upon the size, shape, and electrical properties of the molecules and the viscosity ( 7 ) of the medium. Upon termination of the pulse, the hirefringence and, hence, the transmitted intensity reduces hack to zero at a rate characterized by the rotary diffusion coefficient ( D ) of the molecules. For a monodisperse
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Figure 4. Electric birefringence apparatus, (a) schematic represemation, corn panents are designated as follows: (PG) pulse generator, (0)oscilloscope, (R)
solution of rigid molecules, this field-free decay of the hirefringence has the form (5). An = Ano exp(-6Dt) (5) w i t h Ano the birefringence amplitude a t the instant of field
termination. Hence, a value of 6D can he calculated from the value o f t ohtained when An has fallen to approximately 0.37 of An0 (i.e., e-1 of Ano). Once obtained, D can he interpreted in terms of the major molecular dimension (L) as (6) For snheres of diameter L. d is unitv. hut for rods of leneth L and k i d ratio p, 6 has the value 3 ilk 2p - 0.8). With rgds, 4 is not sensitive to the choice of p. Also, q can he taken as the viscosity of the solvent. Similar equations exist for discs, ellipsoids (6), and the major tumbling motion of polymer coils 17) ,. Finallv. some information on the electrical characteristics of the moiecules can he estimated. With ever-increasing field intensitv 8.'. An is a direct funrtion of X2at low E. This is the Kerr law (8)region. With increasing field strength, this quadratic dependence on E is lost. Within this Kerr law region, the shape of the hirefringence transient indicates the dipolar nature of the molecules. If one measures the relative areas of the regions above the rise and below the fall of the birefringence trace, i.e., A1 and Az of Figure 3, then, for a system with predominantly induced dipole moments, the rise and decay of the transient hirefringence trace are symmetric (4) and the ratio Q = AJAz = 1. This is not true for molecules with predominantly permanent dipoles, for which Q = 4. \.
The Apparatus
The complete system for teaching purposes is shown in Figure 4. A brief outline is given below, followed by a detailed description. Ideally one needs a hright, stable, and collimated light Volume 61 Number 12 December 1984
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beam. This may he ohtained from a high-intensity, lightemittine diode (LED). The light is then incident upon a polarize~i; contact with a rectangular glass cell holding the test samrde. Within the cell and transverse to the light beam, an difference electric field is applied by means of a across a pair of oarallel metal electrodes. The field direction is set a t 450 to the angle of polarization of the incident beam. An analyzer crossed with respect to the initial polarizer is in contact with the external exit face of the cell. This is then followed hv a photodetector whose response is linearly proportional & the light intensity. As explained ahove, s k h a system gives a photodetector response proportional to the square of the hirefringence induced in the sample. The applied field pulses ideally need to he variahle in amplitude and length. The smaller the molecules, the larger the field strength, hut shorter the duration needed for the required molecular orientation. This simplified apparatus, however, uses a fixed field strength of 25,000 Vlm hut allows variable oulse leneths to he chosen. The transient r&ponse of the photodetector is recorded on a storaee oscillosco~e.Permanent recording- can he ohtained by the displayed trace. Detailed Descrlptlon
A high-intensity red LED of peak wavelength 670 nm forms the lieht source. Because the LED output is not well collimated it is positioned as closely as p&sihle to the cell to minimize light loss due to the divergence of the optical beam. The LED is powered from a 9-Vbattery in conjunction with a series resistor, whose value is determined from the expression where V is the battery potential, Vfthe forward voltage, and I,, the maximum recommended forward current. Although greater illumination could be achieved by a white light source (e.g., tungsten filament) the large amount of infrared radiation emitted inhibits the action of the ohotodetector. The alternative would he to use a white source and a good quality infrared cut-off filter. This is a more expensive combination. The polarizer and analyzer are simply pieces of Polaroidm sheet obtainable from most ohotomaohic suooliers. Care must be taken to ensure that thioptic-ax& are &rectly oriented as exolained oreviouslv. The oolarizer and analvzer are cut to the same shape as thecell faces and glued (at theedges only) directlv onto the cell faces to leave an unobscured ootical oath. The angle of the optic axis of the polaroid is usually marked. If not. it must he ascertained hv one of the well-known orocedurks (9). Once the polarize; has been fixed, the coirect oosition for the analvzer can be located bv rotatine it with respect to the polarizer until complete extinction of transmitted lieht can he ohtained. Althoueh the material is imperfect, extinction ratios in excess of
