CA1247399A - Sample cell for light scattering measurements - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
A sample cell is described that permits the measurement of the light scattering properties of very small liquid-borne samples with negligible background interference from the illumination source. A
technique is described whereby the cell construction permits the mea-surement of the illumination intensity at the scattering sample itself, permitting, thereby, the normalization of each detected scattered sig-nal. The cell structure and detection method incorporated therein also permit measurement of extremely small angle scattered intensities with-out interference of the incident light beam itself.

Description

~ ~73~3 SAMPLE CELL FOR LIGHT SCATTERING MEASUREMENTS
Steven D. Phillips, ~effrey M. Reece, and Philip J. Wyatt RELATED PATENTS
The present invention is a new type of light scattering cell and as such will find broad utility in various fields of light scattering determinations. Among some of the most important are those o~ the type discussed at length in the following patents by some of the inventors of the present cell and techni~ue, namely:
U.S~ Patent No. 4,490,042 Title: Method for determining the Properties of Wine Inventor: Philip J. W~att Date of Issue: December 25, 1984 U.S, Patent No. ~,541,719 Title: Method and Appratus for Characterizing Micro-Particles and Measuring Their Response to Their Environment Inventor: Philip J. Wyatt Date of Issue: September 17, 1985 U.S. Patent No. 4,548,500 Title: Process and Apparatus for Identifying or Characterizing Small Particles Inventor: Philip J. Wyatt and Gregory M. Quist Date of Issue: October 2~, 1985.

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DEFINITIONS
The term "light" shall mean electromagnetlc radiation, either monochromatic or of a broader frequency range, either unpolarized or polarized.
The term "size parameter" shall mean p, where p = 2~ a/~, a is the mean particle radius, and ~ is the wave-length of the incident electromagnetic radiation in the medium in which the particles are measured.
The term "very small partlcle" shall mean any particle whose size parameter is less than one.
The term "small particle" shall mean any particle whose size parameter is less than six.
The term "large particle" shall mean a particle whose size parameter is greater than s~x.
The term "beam" shall mean light propagating in a parallel or nearly parallel direckion.
The term "beam diameter" of an incident light source, ~ith a Gaussian intensity profile, such as a laser, shall refer to the diameter

- 2 of the beam measured betweell the poin~s at which the intensity has fallen to l/e2 the intensity at the center of the beam.
The term "forward scattering direction" shall mean all rays, i.e. directed line segments, propagating at an angle less than 90 degrees with respect to the direction of the incident beam.
The term '~ackward scattering direction" shall mean all rays, i.e. directed line segments, propagating at an angle greater than 90 degrees with respect to the direction of the incident beam.
For plane polarized light, the plane perpendicular to the direction of the wave's electric field is called the V-plane and said plane polarized light is vertically polarized with respect to said perpendicular plane. The corresponding H-plane-is perpendicular to the V-plane and contains the incident wave's electric field.
The terms '~ackground effects" and '~ackground contributions"
shall mean any source of light detected by an instrument which is not due to the scattering of light from the sample. We will be concerned solely with background contributions arising from interactions of the incident beam with the sample cell and related apparatus. We will assume any background produced by light scattering from a pure solvent itself is neyligible.

SU~URY OF TffE INVENTION
A new type of cell is disclosed for making light scattering measurements on very small liquid samples. The preferred embodiment of the invention comprises a right cylinder with a hole bored through a diameter. The cylinder and hole are optically polished and the cylinder is surrounded ky an array of detectors lying in the plane of the hole and parallel to the base. Means are provided for introducing and remov-~ 2~

ing a particle-bear mg sample fluid. The sample introduoed into the hole, thereby, is illuminat~d by a collimated light beam whose diameter is much smaller than the diameter of the hole. This beam passes direct-ly through the hole and enters and leaves the cell by means of special windows mounted externally to the oe ll. ~ecause of the slight differen oe of refractive lndex ~etween the fluid and the surrounding glass oe ll, very little stray or background light enters the detectors, even at very small scattering angles. The Lnvention also pxovides means for attenuating small angle scattered int~nsities which are a source of detector saturation in conventional light scattering instruments. Other cell structures are disclosPd together with a novel method for normaliz-ing the detected scattered intensities to the incident beam intensity.

BRIEF DESCRIPTIoN OF THE FIGURES
Figure 1 ~hcws a top ~iew o~ a cylindrical scattering oell surxc~uxled by a set o collimated detectors and illuminated by a colli-matad light beam.
Figure 2 presents a perspective view of a preferred embodiment of the scattering cell showing the illumination source, th flow chan-nel, the cell windows, an~ the fittlngs for introducing samples.
Figure 3 shc,ws a flow fixture that is attached to the cylin-dric~l sample cell to calry liquld-borne s~,~les into or out of it.
Figure 4 shows the application of Snell's Law at the Ln~exfa oe between two media.
Figure 5 is a top view of a pre~erred embodiment showing the sa~ple oe ll, the normalization beam monitor, several typical detector mEans, and the illumunation source.

'lLt~?~P3~!

BA~KGE~)UND
Many important la~oratory and industrial prcgrams are invDl~ad with the measurement of fine particles in suspension by light scat~ering techniques. Fon~nDst among them is the light scattering procedure for the determination of mnlecular weights of unknown solutes suspended in various types of solvents. W~thout going into the details of this procedure, which is described in n~ny texts such as Kerker's book Ihe Scattering of ~ht and Other Electrcma~ne~ic Radiation, the general nY#uLrement inv~lves the preparation of a suspension of the unknown material fDllowed by its illlDmnatiQn by a collimated beam of ~Dnochrc, matic light. The intensity of the light scatbered by the suspension is then measured as a function of ~ngle and solute ODn oe ntration. S mce the scattering prop~rties of the s~mple cell or cuvette containing the solution may interfere with this determination, it is important to use a cell whose so-call~d "bac~ground" oantributions will be m ~ and affect the determ~nations least~ ~deally, the ce.ll will permit the mPasurement of the sc~ttering prGperties of the solute particles or molecules at incre~sin~ly lower concentrations, Many types of assays and bioassays, such as described by Wyatt in his chapter in the book edited by Charalambcus entitled Analysis of Fbods and Beverages, involve the preparation of aqueous suspensions. Subsequent re~sule~ent of these s ~ sions by light scattering me~ns invslves detect-ing v y ~mall changes in the measured light scattering properties of the solutions. Often, the aocuracy of the results will be af~ected by back-ground effects created by the scattering oell itself. Even the ~ery simplest determinations of transmission or aptical density, such as performed ~y o~nv~ntional spectrDphDtomet~rs of the type m~nufactured by Bausch and Lomb, depend critically on the bacXground contributions of the liquid-containing cell. Furthermore, some compounds, such as those separated by means of liquid chromatography, are obtained in such small volumes that the cell containing them also must have a very small vol-ume, ~ypically on the order of microliters or less. ~hus, '~ackground"
effects become increasingly important because of the close proximity of the sample cell liquid and air interfaces to the field of view of the detection system.
While studying many of the aforementioned measurements, we have discovered a cell structure and method of measurement that permits the exa~nination by l1ght scattering means of extremely small volumes of liquid-borne samples at virtually all scattering angles, no matter how small, without introducing significant background artifacts from the containing sample cell itself. This cell structure permits, in addi-tion, the determination of the actual light flux incident upon the sample being examined, an o~ten important re~uirement for many light scattering applications.

DETAII.S OF THE INVENTION
A typical detection system is shown in Fig. 1. An incident light source, usually a monochromatic beam 1 such as produced by a laser passes through the sample cell. Also shot~n in this figure is a set of discrete detectors 2 spaced circumferentially about this ce~l. Each detector is collimated so that its field of view includes only a very small volume at ~he center of the cell.
Figure 2 presents a perspective view of the scattering cell of the preferred embodiment of our invention. 1~ consists of a cylinder 3 of glass or o~her transparent material of refractive index generally chosen close to the index of the solve~t carrying the sample. Through the cylinder, a hole 4 is drilled along a diameter of the cylinder and lying in the plane of the detector array. The outer diameter of the cylinder and the hole interior surfaces are optically polished to remove any surface irregularities. Attached to each aperture of the cylinder is a fixture 5 containing an optical window 6 and a bore 7 to carry the sample into or out of the cell.
Figure 3 shows a greater detail of the fixtures S which, in the preferred embodiment of this invention, contains a tube 9 to convey the liquid-borne sample into or out of the cell hole 4. Note that the light beam that passes through the cell must, in th~ preferred embodiment of this invention, b~ of even smaller cross section than the hole 4. ~ typical cell would have a hole diameter of 2.0 mm and be illuminated with a laser beam diameter of 0.4 mm such as is produced by a special He-Ne laser manufactured by Melles Griot. As should be evi-dent from Figs. 1-3, were ~he refractive index of the cylinder the same as the refractive index of the li~uid passing through the cell, the set-up would correspond to the geometry of the large radius of curvature structure of Fig. l; yet the beam passing through the cell of the present invention does not strike any surface within the field of view of any detector. As seen in Fig. 2, the beam entrance and exit windows 6 are far removed from the center of the cell, which eliminates the background contributio~s associated with the beam traversing an air/
glass/liquid interface. In addition, the sample volume contained within this cell is ex~remely small relative ~o the volume required for the traditional cell of such large radius of curvature. The actual volume of the sample would depend on the diameter of the hole 4 ~ut into the

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cylinder. Light scattered from this small sample volume will not be attenuated significantly as it passes through the glass cell region to the detectors. This also permits the examination of samples of greater particle d~nsity without the usual multiple scattering degradations that would be caused by the intervening particles in a comparably sized scattering cell, i.e. a cell where the glass region of the present invention were replaced by an additional liquid sample.
The difference of refractive index between the solvent fluid passing through hole 4 ~nd that of ~he glass cylindrical cell 3 surrounding it results in another important feature of our invention.
We have already stated that these refractive indices will be quite close. As long as they are different, it will be possible to obtain measurement~ of light scattered at very small angles by particles or molecules illuminated by the highly collimated lig~t source with negli-gible background contributions, as shall soon be demonstrated. Typical-ly, the refractive index of the liquid nl will be that of water, 4/3, while that of the glass n2 will be about 3/2. Applying Snell'F, Law (see Fig.
41 to determine the refraction of a ray 1 striking the water-glass interface 8 at an angle ~ yields the result n1 sin (2 ~ ~) = n2 sin (2 - ~

where the angle of incidence is ~/2 - ~ and t~e angle of refraction is ~J2 - ~' Expanding the sine functions in Eq. (1) and collecting terms, immediately results in n2 cos ~' = nl cos ~, (2) ~ote that point 9, for the case of the scattering cell of the preferred 3~

embodiment, lies a~ead, i.e. to the left, of the center of the cell 10, and is on the interface. A detector means detecting light at an angle ~' would be collimated to be centered on point 10.
It is interesting to note that as the scattering angle ~ be-comes very small, i.e. approaches zero, the source of the scattering event 11 whose refracted rays are detected at ~'moves to the right of the center of the cell 10. In the limit at ~ = O, a~ = cos 1 (8/9) =
27.27. Thus, no matter how small the scattering angle ~ , the re-fracted ray will be detected at an angle ~' sufficiently distant from all interfaces to permit said detector means to avoid receiving any direct contributions from the incident beam 1.
The scattering angle ~ of F'ig. 4 represents the most important independent variable of a light æcattering measurement. Accordingly, in the preferred embodiment of our invention, the detector means ~ of Fig.
1 should be placed 60 that there i8 a one-to-one correspondence with the set of ~-angles selected for an experiment. An often used set of scattering angles ~ is selected ~uch that the angles are equally spaced in sin ~/2. The latter choice is particularly convenient for certain types of measurements related to molecular weight determinations or small particles whose refractive indices are very close to that of the medium surrounding them. If the detectors surrounding the glass cell were spaced equidistantly in a~ or sin ~'/2, the interpretation of the data ~o-detected in terms of the physically important scattering angle would require the complex mathematical inversion of Eq. (1) for each measurement. Instead, in a preferred embodiment of our invention, we place ~he detector means about the cell at those angles ~' that corres-pond to the selected set of scattering angles ~. For example, for equidistant spacing in sin ~/2 such ~hat 0.2 < sin ~/2 < 0.9, (3) which is a range frequently found in scattering measurements, Eq. (1) may be solved for ~'in terms of sin ~/2 as follows:

n2 cos ~' = nl cos ~ = n~ 2 sin2 e/2). (4) Hence ~' = cos 1 ~ n (1 - 2 sin2 ~/2)]. ~5) For a typical case where the cell is optical glass of refractive index 3/2 and ~he sample is in a liquid of refractive index 4/3, a set of detectors at angle ~' would be placed according to the transforma~ion table below:

Table oE Transformed Scattering Angles ~in ~2 ~ ~~

.2 23.07 35.13 .2$ 28.96 38.95 .3 34.92 43.21 .35 40.97 47.84 .4 47.16 52.81 .45 53.49 58.07 .5 60.00 63.61 .55 66.73 69.44 .6 73.74 75.59 .65 81.08 g2.0~
.7 æ~.85 88.98 .75 97.18 96.38 .~ 106.26 104.41 .85 116.42 113.30 .9 128.32 123.45 To maXe a measurement at a very small scattering angle in the forw~rd direction will require a very precise placement and oollimation of the detector means, since refraction causes a small range of ~'values to correspond o a larger range of ~-values, for ~ near 0. For a 1~

measurement at, say, 0 - 5.73, the detector means would have to be placed at 27.82~, a scant 30' of arc from the limiting ~ = 0 value, where ~ = 27.27. ~evertheless, light scattered in this direction may be precisely intercepted by the carefully set detector means.
As the average particle si~e parameter P becomes larger, the relative intensity of light scattered in the forward direction to that scattered into the b~ckward direction becomes very large. For many types of instruments de~ecting scattered light at small angles, this becomes a troublesome problem as large forward scattering contributions may overwhelm and saturate the ~etector means monitoring forward scat-tering events. This is not true for our invention because o the unique attenuation of such forward scattered light. As ~ ~0, the fraction of scattered light flux refracting into angle ~' becomes progressively smaller and becomes ~.ero when ~ = O. In Fig. 4, the fraction of scattered light flux re~lected at the water ~lass interface 8 in terms of the angle o incidence, ~ , may b~ determined from Fresnel's rela-tions discussed, or example, in the textbook ~ by R.W. Ditchburn~
For the case of vertically polarized incident light, the re~lected fraction Pw from liquid to glass is given by the relation p 5 talll2 ~ 0 ) ( ~j ) tan (~' + ~) where 9 is given by E~. (2). Note that as ~ ~ Pw-~1 , i.e. most of the light is reflected and only a decreasing fraction 1-- w is transmitted to the small angle detector means. In the case of normal incidence ~ and ~ /2. Taking this limiting case and applying Snell's law, we obtain (nl ~ n2~ ~632 = 0,34~ (7) wgoo ~nl ~ n2)2 ~17/6) Thus by plac mg the scattering particles in a medium of refrac*ive index less than that of the ~urrcun~ing scattering cell, which is a natural procedure ~henever particles are measured in solution, our invention permits the detection of light scattered at small angles wlthout sah~rating the small angle detector means.
Although we have explained the key el~ments of our invention by me~ns of a preferred cylindrical eu~cdinent diEculs~d ak~ve, it wlll be clear to those skilled in the art of light scattering that cur invention a~plies e~ually to many other geometries and oell structures.
qhe latter is of yarticular signi~cance as it represents the hydrosol equivalent of a single particle ~erosol p~rticle analyser. ~ighly irreqLlar particles will scatter light as a cc~plex function of both the polar angle ~ and the azimuthal angle ~, The variation of intensity with ~ t a ~ixed ~ ~or a sæh*rically s~mmetric particle, on the other h~nd, is a simple function of cos2 ~ and s ~ d. The detection, cLassification, and neasuren~nt of particles pf oomplex structure requires, therefore, that me~surements be performsd At n~ny C3~ ~1 locations that do not lie in a plane. If the incident light be plane polarized vertically ~ith respect to a s~,t of detectors lying along a great circl~ of the sphere/air interface, then there is another great cir de at right angles to this with respect to which t~e incident light is harizont lly polariz3d.
Nbte also that a sphere is not the only three dimensional s ~ e for which our invention will ~pply/ t~Dugh it cert2inly provides tbe g~eatest 1~

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flexibilit~ for scattering measurements. Other useful three dimen-sional struct,ures include cubes and many resular and irregulax polyhedra.
It is interesting to note that the transformed detector locations discussed above for the cylindrical oell embodhment of our mvention apply egyally well to a sp~erical oe ll. The angle of m cidence of the scattered ray ~epends only on ~ insofar as the application of 5nell's law is ccncerned ~nd is independent of ~. The azimuthal ~ttering angles ~ would be selecbed to define different æts of detec*ors, each lying on a great c.ir~le, It should be noted that the hole 4 through the c~ll can contain additional structures such as a small spheri al cavity at the center of the cel].. This c~vity wculd allow scattered light originating at the c~lter of the c~ll to proce~d along a radial l.ine out of the cell ~d into the detec~o~s. Thi5 ~uld elimun~te the refraction problem at ~he liquld~glass interface ~rising ran the non-perpendicularity of thR.
scattered ray ~t the inter~ace. Hence, ~11 de ~ ors, except tho æ
whose field of view is obscured ~y hole ~, will be s~umultanec~lsly view~
ing t~P center o~ the cavity. Such sn arrang~ment would be important when, ~or example, vlewing a single particle is desired, which requires many detectors viewnng the sa~e particle at the s~me location at the same time. The spherical cavity within the spheric21 c~ll could ke easily fakricated, for example, by assembling the spherical cell from two hemisp~eres ground on a lens gri~ding mach~ne. ~fter cutting a ! ~ 2 ~ 7 3 9 ~

sample introduction channel in each hemisphere and a central hemispheri-cal cavity in each hemisphere, the two hemispheres and cavities would be p~lished and joined together by index matching cement.
Figure 5 shows a perspective view of the assembled cell com-plete with fixtures and surrounded with an array of detectors. Consider the beam monitor 12. It will monitor the beam intensity after passing through the sample. If n is the number of particles per ml and ~ is the average scattering cross section per particle, then in a path length X, the intensity I of the illumination source will be attenuated accord-ing to Beer's Law as:

~ = Io exp-~n oX), (8) where, Io ~ the incident intensity. For many types of measurements, it is important that the scattered intensities detected be normalized to the intensity of the illumination incide~t upon the scattering parti-cles. This normalization is particularly important in the measurement of molecular weights or monitoring critical growth processes. Some instruments split the incident beam and use the fraction removed thereby as this normalizati.on factor Io~ However, this value, so-obtained, may not well present the actual intensity at the sample because of the attenuation of the intervening sample and reflections at the cell inter-faces. Furthermore, this attenuation will vary from sample to sample.
~y introducing a beam monitor such as shown in Fig. 5, we are able to obtain very accurate representations of the normalized scattered inten-sities as follows.
Consider that ~he total sample pa~h through the cell hole 4 is ~X and that the detectors 2 are collimated to view only the small volume at the center of the hole, a distance X from the beam entrance window 6 3~
in Fig. 5. The Lnbensity at the beam monitor 12 relative to the inci-dent intensity at the entranoe window is given by application of Eeer~s law with the mcorporation of the Fresnel reflec~ion fraction f, at eash air-glass interfaoe and Fresnel reflection fraction g at each glass/li-quid interface. 9enoe, t~e total reflection fraction is F = f ~ g - fg I2 Y Io (l-F) exp-(2n ~ X). (9) Ihe intensity at the oenter of the sample, Il, on the other hand7 is just Il - Io (l-F) exp-(n a x). (10) Instead of normalizing the scattered intensities by Io, we should n~r-malize by the factor oi Il of Eq. (10). Hbwever, the normalization fa~tor N = I ~ I (l-F) e~(n c5 X) ~ (11) E~tl~re, any normalization ~actor which is p~oportional to N is an ~u~lly suitable n~nnalization factor. We are o~ly con~erm3d ~th the relative in'censity at the o~ntsr of the oell which varies ~rn s~unple-anple ~ue to differences in turbidit~es u~ fran time-to-time due to the time varying inte~sity of the light source.
Let N2 = J~ ~ (12) ~ere I3 ~ X Io, o~K~l He~ce, b~ rrr~nitoring a s ~ l frac~ion, X, of the in~i ~ nt ~3e ~n~sity at the ext~T~ source n~itor l3~ and lrDnitoring I2 at the beam ~Dniu~r 12~ one obta ms N2 via ~t~

Eq. (12). The value of K need not be known as N2 is only a relative normalization factor.
It is to be understood that while 13A is the preferred position of the monitor, the alternative position shown at 13B is still operable.
This final normalization obtained as the s~uare root of the product of relative intensities at the beam monitor 12 and an external monitor 13A or 13B represents, therefor, the optimum normalization constant since it is always proportional to the real time value at the sample.
While there has hereinbefore been presented what is at present considered to be the preferred embodiment and process of oux invention which has described a scattering cell and technique or measuring the scattered light intensities from small particles and molecules in solution over a broad range of scattering angles including those near zero degrees, it will be apparent to thG~e o ordinary skill in the art of light scattering that many modifications and variations may be made thererom without departing rom the true spirit and scope of the invention. All such variations and modifica-tions, therefore, are considered to be part of the invention.
Some of the developments and studies associated with this invention were performed under Contract #DAMD17-84-C-4155 from the U.S. Army Medical Research & Devel~pment Command. The Government has certain non-e~cclusive rights under the terms of this contract.

Claims (9)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A method for normalizing the scattered intensities of light from particles suspended in a solvent and illuminated by a collimated light beam comprising the steps of a) measuring the intensity of light transmitted straight through the sample and external to the sample containing cell, Is;
b) measuring a fraction of the incident light source intensity before entering the cell, If;
c) dividing all subsequently measured scattered intensities at specified scattering angles by the quantity , where Is is the intensity value measured in step a and If is the intensity value measured in step b.

2. The method of claim 1 where the sample is confined to a channel and the illuminating light beam has a diameter much smaller than the diameter of the channel.

3. The method of claim 1 where the light beam is from a laser.

4. The method of claim .3 where the laser is polarized.

5. The method of claim 1 where the fractiion of the incident light source intensity is measured directly at the source itself.

6. The method of claim 1 where the light transmitted straight through the cell is I2 = Io(1-F)2exp-(2n.sigma.X), where Io is the incident light intensity entering on the cell, 2X is total distance through the cell, n is the number of particles per ml in the sample, .sigma. is the average scattering cross section per particle, and F = f+g-fg, where f is the Fresnel reflection fraction and each air/glass interface through which the incident light beam passes and g is the Fresnel reflection fraction at each glass/liquid interface through which said light beam passes.

7. The method of claim 1 where the fraction of the incident light source intensity is obtained from a beam splitter, said beam splitter dividing the incident beam into a source beam which illuminates the sample and a reference beam which illuminates the reference beam monitor.

8. An incident beam monitor comprised of:
a) an illumination source monitor means;
b) a transmitted beam monitor means;
c) a multiplication means that forms a value proportional to the product of the signals from said source monitor means and said transmitted beam monitor means; and d) a square root means that forms a value proportional to the square root of the product signal from step c.

9. The incident beam monitor of claim 8 where the illumination source monitor means is comprised of a beam splitter and split beam detector.