A New Apparatus for Light Scattering Studies

H. G. Jerrard and D. B. Sellen

An instrument which is suitable for investigating the light scattering properties of macromolecules insolution in the angular range 200 to 160° is described. A null modulation method is used to measurethe ratio of the intensity Io of the light scattered at an angle 0 to the direction of the incident light tothat (Is) incident on the scattering volume. This is accomplished by attenuating I until it equals Io,this condition being found by an electronic detector. The value of I is known from a calibration ex-periment. Details are given of the optical arrangement, the detector, and the calibration and methodof use of the apparatus. Adequate sensitivity, accuracy, and stability are demonstrated.

Introduction

A number of instruments designed for light scatteringmeasurements have been developed in the last twentyyears. Visual" 2 and photographic recording have beenused but modern instruments usually employ photo-electric detection'-' which gives high precision andaccuracy. In this paper an apparatus is describedwhich, although developed primarily for detecting thesmall changes in scattered intensity that occur whenmacromolecular solutions are subjected to an appliedelectric field, is suitable for conventional light scatteringmeasurements. The purpose for which it was designednecessitated higher sensitivity and accuracy than ispossessed by other instruments. The instrument alsohas a wide angular range, an optical system producinga well defined, intense primary light beam of uniformcross section, a high degree of freedom from stray light,and good angular resolution. It is easy to operate.

Principle of Instrument

The function of a light scattering apparatus is tomeasure the ratio of the intensity of the light scatteredfrom a solution in a cell to the intensity of the incidentbeam. In the present apparatus this is achieved bycombining the two beams and allowing the resultantcombination to fall on a single photomultiplier tube sothat a null modulation method of detection can berealized. Such methods have been described byHardy' 5 and their merits discussed by Kovalevskii.17The principle is illustrated in Fig. 1. One beam, shown

Both authors were at the Department of Physics, SouthamptonUniversity, Southampton, England. D. B. Sellen is now atNatural Rubber Producers Research Association, WelwynGarden City, England.

Received 28 November 1961.

as the primary beam, is linearly polarized by a polaroidPi in a direction at 900 to that of the second beam whichcomprises the scattered light. The latter is polarizedby P2. Both beams traverse a polarizing disk P3 whichrotates with an angular velocity co. If the intensitiesof the two beams, when incident on P 3 , are I, and I2respectively, then the resulting intensity incident onthe photomultiplier cathode is I where, ignoring absorp-tion losses in the rotating disk,

I = (11 ±2) (1 -I2)+ cos2wt. (1)

Thus there is a steady component equal to the averageof the two incident intensities and an alternatingcomponent of twice the frequency of disk rotation andof peak to peak amplitude equal to the difference of thetwo incident intensities. When the intensities I, and I2are equal the alternating component disappears butonly if the two beams are linearly polarized accuratelyat right angles.

The state of polarization of the scattered light isdependent upon the angle at which it is scattered. Itis totally linearly polarized in directions at 900 tothe incident beam, unpolarized for zero-angle scattering,and partially linearly polarized for all other angles.Thus the effect of P2 will not only be to render the lightincident on P linearly polarized but will attenuatethe beam by an amount which varies with the angle ofscattering. To overcome this a quarter-wave plateis inserted in front of P2 and set with its vibrationdirections at 450 to the plane of partial polarization.The linearly polarized component is thus turned intocircularly polarized light so that no preferential direc-tion of polarization exists, and hence the attenuation byP2 of the linearly polarized component is th seame as

May 1962 / Vol. 1, No. 3 / APPLIED OPTICS 243

PM

Axis

Fig. 1. Principle of apparatus. N-neutral filter, P-rota-table polarizer, PI and P 2-fixed polarizers, P3-rotatory polaroiddisk, PM-photomultiplier, Q-quarter-wave plate.

for unpolarized light. In practice the intensity of the

primary beam is some 106 times that of the scatteredintensity so that initially the primary beam intensityis attenuated by a neutral filter N in order to make the

orders of magnitude of the two beams the same.Equality of intensity is then effected by rotating a

polaroid P the attenuation thus produced beingproportional to cos2 k, where q5 is the angle between the

vibration directions of P and P,. The apparatus iscalibrated in terms of 0.

Description of Apparatus

The apparatus is shown in Figs. 2 and 3. For the

purpose of description it may be conveniently dividedinto the optical system, the electrical system, and the

light scattering cell.

Fig. 2. Diagrammatic view of apparatus. S-mercury-arclamp, LI-condensing lens, H-circular diaphragm, F 1-heatabsorbing filter, L2-collimating lens, a, b, c-rectangular slits,F2 -interference filter, SC-light-scattering cell. The scatteredlight collecting system, which rotates about an axis through SC,includes lenses L3, L4 , and L5, diaphragms Al and A2, reflecting

prisms R1, R2, and R3, quarter-wave plate Q, and polaroid P2.The transmitted light collecting system, which is fixed, has a neu-

tral filter N, polaroid P rotatable in divided circle, fixed polaroidPi, reflecting plates G1, G2, and G3, and lens L6 . P3 is rotating

polaroid driven by motor M; C-commutator, PM-photo-multiplier. Polarizers can be placed on the optical bench atP' and on end of collecting system at P" for depolarization

measurements.

A. The Optical System

This system consists essentially of a collimatingarrangement to produce an intense incident beam andtwo collecting optical units mounted on a box. Oneunit, inside the box, brings the scattered light onto thephotomultiplier and the second unit, mounted outsidethe box, collects the transmitted light. One side ofthe box can be removed to allow of easy access to theinterior. Light from a mercury lamp S (G.E.C.250 watts ME/D Compact Source) is condensed by alens LI (focal length 10 cm; aperture 5 cm) upon, acircular diaphragm H (diam 2.5 mm). The lamp is

Fig. 3. Photograph of apparatus. At the center is seen thecircular scale on top of the box below the photomultiplier housing.The transmitted light collector is on the right of the housing.

run on a stabilized dc supply. An image of H isproduced near the center of the cell by a lens L2 (focallength 6 cm; aperture 4 cm). Between H and L2 isa heat absorbing filter, and between L2 and thecell are an interference filter F2 and three verticalrectangular slits a, b, and c each 2 mm wide and 1 cmhigh. This arrangement gives a well-defined uniformbeam. A polarizer, whose axis can be adjusted tohorizontal or vertical orientation, can be inserted be-tween L2 and a.

The scattered light is received by a collector unitcontaining prisms R1, R2 , and R3. This unit can berotated about a vertical axis through the center of thebox so as to receive light scattered at various anglesin the horizontal plane, as in the apparatus of M'Ewenand Pratt.' The position of the unit relative to theincident beam of light can be read from a circular scalegraduated in 0.50 intervals on top of the box. Thelight passes to the photocathode of the photomultiplierafter total internal reflection in the prisms R1, R2, andR3. All three prisms can be rotated about a horizontalaxis and R3 can also move about a vertical axis. Thelens L3 is focused for parallel light upon the circular

aperture A2 (diam 1.5 mm) which constitutes a field

244 APPLIED OPTICS / Vol. 1, No. 3 / May 1962

.I., 5-:SC P11

�,IGYl

stop. The distance L3A2 is 5 cm. The aperture A,(diam 4.5 mm) is an aperture stop. The angularresolving power of the unit is about 1. Lens L4has its focus at Al and lens L5 is placed so that an imageof A, of about 9 mm diameter is formed on the photo-cathode which has a stop of 7 mm diameter in frontof it. The image of Al is of uniform intensity and thestopping down of the photocathode area eliminates anyerror arising from any possible precession of the imageabout the axis of rotation due to misalignment. Thusthe photomultiplier response is always independent ofthe angular position of the viewing unit. The unitmay be extended between L and R2 to accommodatelarger cells when necessary without altering the opticsof the system. The quarter-wave plate Q and thepolaroid P2 are placed in the positions shown. Thepolaroid is of high quality and can be rotated from out-side the box. It is adjusted so that the scattered light,after passing through the glass plate G, is linearlypolarized in the plane of the diagram. Mica quarterplates mounted between glass cover slides are used, onefor wavelength 5461 A and another for 4358 A. Pro-vision is made for orienting the plate correctly. Toensure that a plate could not introduce an error greaterthan 1%, the wavelength for which it is quarter-wavemust be correct to 30 A and its azimuth must notdepart from 450 by more than 0.5'. The platesused conformed to these limits and were selected afterexamination by the channeled spectrum method de-scribed by Jerrard. 1 For depolarization measurementsa polaroid can be mounted on the viewing unit in frontof the lens L, and the mounting was arranged so as tomake it possible to transmit first the vertical and thenthe horizontal components of the light beam.

The incident light, after transmission through thecell, is received by the second collector unit whichdirects the beam to the photocathode by glass coverslips G, G2, and G. These can be rotated about theirhorizontal axes and G2 also about its vertical axis. Thelens L6 forms an image of c on the photocathode. Thelight leaving G will be almost completely linearlypolarized with its vibration direction perpendicular tothe plane of the diagram. This linear polarization isassured by the insertion of the polaroid P which issuitably oriented. The neutral filter N and polaroidP are placed as shown. P is mounted on a dividedcircle readable to 2 min of arc and which can be extrap-olated to one minute. N was oriented at 450 to theprimary beam so as not to reflect light back throughthe cell. This means that the transmitted light will bepartially polarized, the vibration direction which is inexcess being in the plane of incidence, i.e., in this casehorizontal. Thus the attenuation as P is rotated is notproportional to cos24, but to f(o), where

f(o) = cos2ok{1 - [1 - cos(i - r)] sin240.

In this expression i and r are the angles of incidence andrefraction, respectively. For i = 450 and a glass ofrefractive index 1.52 as used here,

f(o) = cos2o(1 - 0.169 sin2o).

The beam is stopped down to a height of 2 mm afterleaving N.

On leaving G3 both beams pass through the rotatingpolarizing disk P3 which serves simply as a modulator;the quality of the polaroid used for this is not important.The disk is driven by a small dc motor.

B. The Electrical System

Examination of Eq. (1) shows that the photo-multiplier current consists of a steady component andan alternating component. In addition there is photo-electric shot noise associated with the signal, togetherwith some dark current which is made up of a steadycomponent and varying thermionic shot noise. Ofthese only the noise associated with the signal issignificant. The detector unit is required to detectthe alternating component and to determine the con-ditions when it is zero. For this purpose it is necessaryto have a signal to noise ratio which is as high aspossible. This ratio is proportional to the square rootof the product of the light intensity, the photocathodesensitivity, and the time constant of the detectingsystem.

A block diagram of the system is shown in Fig. 4.An EMI photomultiplier type 9502 is used. This hasgood stability, an over-all sensitivity for an appliedpotential of 1650 volts of 2000 amp per lumen, and adark current of 0.002 ua. Power is supplied from astabilized supply. Output currents of up to 1 a areobtained, which with a 10 megohm load give outputpotentials up to 10 volts peak value. The output ispassed through a low gain selective amplifier having aQ factor that is variable from 4 to 20. The frequencyof the alternating component that is to be detected is

Fig. 4. Block diagram of electrical system.

May 1962 / Vol. 1, No. 3 / APPLIED OPTICS 245

Performance Data

Once the apparatus is calibrated, and after the liquidunder examination is in the cell, it is only necessaryto adjust to have no alternating component in thephotomultiplier output. This is done by rotating Puntil no alternating component is visible on the C.R.O.trace, and the homodyne, when set for a small time con-stant, gives zero output. A finer adjustment for Pis then obtained by increasing the values of time con-stant so that finally a reliable value for 0 results.

Fig. 5. The light-scattering cell.

110 cps, corresponding, for a Q factor of 20, to a time

constant of about 0.2 sec. The amplifier output is

displayed on a cathode-ray oscilloscope and also passesinto a phase-sensitive (homodyne) rectifier. The homo-

dyne is supplied with a reference signal and if thisis in the same phase and has the same frequency as the

signal from the selective amplifier, then the homodynerectifier produces a dc output voltage which is pro-

portional to the product of the amplitudes of the inputand reference signals. This voltage is fed through a

filter which removes voltages, due to noise or similarextraneous causes, which are not identical in frequency

with the reference signal. The filter output is displayed

on a meter. The filter can be adjusted for various

times of response. The circuit used is a version of thatgiven by Miller et al.'9 modified for the frequencies and

response times required here. The latter are 1, 3, 8,

and 40 sec. The reference signal for the homodyne has

a frequency of twice the frequency of rotation of the

polarizing disk P 3 and is obtained from a commutatormounted on the same shaft as P3 . This delivers a

square wave of the appropriate frequency which then

passes through a low-pass filter, an amplifier, and a

phase adjuster so that the phase of the reference signal

can be made the same as that of the signal to be de-

tected. From the phase adjuster the signal is fed intothe homodyne rectifier.

C. The Cell

The light-scattering cell shown in Fig. 5 is a semi-

cylindrical type. The cylindrical part was ground from

a piece of good quality glass so that there were nostriations. The adhesive used is Araldite 103 with

hardener 951. The side extensions are necessary as

otherwise light scattered from the entrance windowand suffering multiple reflections between the circular

face and plane back face will emerge through the cell

center into the viewing unit. With this cell arrange-ment these parasitic reflections are not visible. The

use of black glass prevents internal reflections at the

glass-air face of the back wall of the cell and reduces

stray light in general.

Testing and CalibrationThe geometry and alignment of the instrument were

tested by measuring the angular dependence of fluores-cent intensity exhibited by a dilute aqueous solutionof fluorescein. The intensity should be independentof the angle at which it is seen.20 Fluorescence wasexcited with light of wavelength 4358 A and a yellowfilter was placed in front of the viewing unit to stop thepassage of any other scattered light and stray reflec-tions. After correcting for cell geometry2" by multiply-ing by sin 0, where 0 is the angle between the incidentbeam direction and the direction of observation, the

fluorescent intensity was found to be constant to within40.35%. This was carried out with a time constant of8 sec. This constancy of intensity does not mean,however, that the quarter-wave (X/4) plate is function-ing correctly since fluorescent light is unpolarized.

The correct setting and action of the X/4 plate waschecked, and the calibration of the apparatus wascarried out by measuring the scattering and turbidityof a colloidal suspension of silica (Ludox*) in distilledwater. This solution was centrifuged for 1 hr at 15,000 gand then put into the scattering cell using a hypo-dermic syringe which, after being filled, had a Milliporetcellulose filter unit attached to it. The filter had apore size of 1.2 /i. Filtration alone of the Ludox wasnot sufficient. Polarizer settings 0 were obtained for anumber of values of 0. The measured backgroundscattering of distilled water was subtracted and theresultant values multiplied by sin 0/(1 + cos20). A

small correction was applied to allow for the fact thatthe lengths traveled in the solution in the cell by theincident and scattered light were different.22 In the60°-150° range the values of 0 were constant to within

0.7%, indicating the correct functioning of the X/4plate. Below 600 a small rise (less than 4%) wasdetected and this was thought to be due to insufficient

* Prepared by E. I. du Pont de Nemours and Co., Delaware,U.S.A. English agents: Durham Raw Materials Ltd., London,England.

t Obtainable from Millipore Filter Corporation, Bedford,Massachusetts, U.S A. English agents V. A. Howe and Co. Ltd.,

London, England.

246 APPLIED OPTICS J Vol. 1, No. 3 / May 1962

clarification of the Ludox. The depolarization Pu at90° was measured and extrapolated to zero concentra-tion: its value was 0.0065 at 4358 A.

The calibration constant C of the instrument is de-fined by the equation

2.303 D l67r 16,r-3R90 f ( )

in which is the turbidity, Rgo the Rayleigh ratio at90°, D is the optical density, is the path length, andf(4) is as previously defined. The turbidity of Ludoxsolutions of concentration 0.5% was measured withcells giving a value of of 4 cm, in a Unicam SP500spectrophotometer. In the range 4300 to 6000 A, Dwas found to be porportional to X-4, which indicatesthat the measured values correspond to turbidity onlyand not to absorption.

A block of turbid glass for which R90 = 5.3 X 10-4

cm-' at 5461 A was used as a substandard to check theconstancy of the value C. The standard deviation wasnever greater than 2% which was less than the accuracywith which C was determined.

Typical Results

A number of solutions have been studied with theapparatus described-a typical set of results being givenby bovine plasma albumin. All measurements weretaken at 20'C. This was dissolved in distilled water,centrifuged for 2 hr at 20,000 g and then passedthrough Millipore filters of sizes 1.2 /u and 0.1 . Nodissymmetry of scattering was observed. From the-ory 2 the Rayleigh ratio R0, the concentration c (gmcm- 3 ), and the weight-average molecular weight MIfor a solution of refractive index n at wavelength X invacuo are related by the equation

Kc(1 + cos0) 1

Ro Ml +2Bc,

where

K 27r2fn2(n/?Jc)2X4NA

in which NA is Avogadro's number and B is a factordependent on the type of macromolecule. A graph ofKc( + cos2 0)/Ro against c should give a straight lineof intercept 1/Mw and slope 2B. The value of n/acwas found from measurements with a Rayleigh inter-ference refractometer. The graph is shown in Fig. 6from which values of the slope and M, of -3.5 X 10-4and 69,000 respectively were found. The depolariza-tion was measured (u = 0.018) and the molecularweight, corrected by use of the Cabannes factor,2 3

was finally calculated to be 67,000. The results arein satisfactory agreement with those of Dandliker.2 4

The authors are grateful to A. M. Taylor for anumber of suggestions and to S. W. Punnett for his

1-6T

0

ID-

-Z__

1*01-

0 2 4 6 8 10CONCENTRATION c,(IO3g.cm3 )

Fig. 6. Light scattering of bovine plasma albumin at 4358 A and200 C centrifuged and measured in water.

advice on the electronics. Thanks are also due toJ. H. Freeland who made most of the apparatus.One of us (D.B.S.) is indebted to the Department ofScientific and Industrial Research for the award of aresearch studentship.

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