Differential refractometer

This invention measures the change of a fluid's refractive index with changes in the concentration of a solute dissolved therein. A determination of this quantity is required for many types of chemical analyses especially for the determination of molecular weights. The fluid is restricted to a thin capillary channel (11) within a transparent material (10) such as glass. A fine light beam (18) is incident upon the capillary at an angle close to the critical angle. The axes of the light beam and capillary intersect at a point within the capillary defining thereby a plane within which the refraction occurs. A position sensing (27) device is placed to measure the displacement of the beam twice refracted during its passage through the capillary channel, said measure being used to generate a numerical value of the ratio dn/dc, where dc is the change of solute concentration resulting in a change dn of the solution's refractive index.

tted through the fluid strikes the rods at approximately the critical angle 
of the fluid. As the refractive index of the fluid changes, the amount of 
light reaching the detector will change, permitting thereby the deduction 
of said fluid refractive index change. 
DISCLOSURE SUMMARY OF THE INVENTION 
It is the major objective of my invention to monitor the refractive index 
of a fluid stationary within or flowing through a capillary channel 
surrounded by a transparent medium. This is accomplished by detecting the 
deviation of a fine beam of light after it has passed through the 
capillary, said displacement from the incident beam being due to the 
difference between the refractive index of the fluid and the transparent 
medium surrounding it. The transparent medium surrounding the capillary is 
of a refractive index higher than that of the fluid and the passage of the 
light beam is from said transparent medium into the capillary at angle 
obtuse to the capillary axis and then exiting the capillary back into said 
transparent medium. The deviation of the light beam from its straight line 
path is due to the differences of the corresponding refractive indices of 
the fluid and surrounding medium. The deviation will be greatest as the 
incident beam impinges on the capillary at an angle (measured with respect 
to the normal to the capillary axis) slightly less than the critical 
angle. 
It is a further objective of my invention to provide a means for measuring 
the change of refractive index of a fluid at essentially the same physical 
position from which the fluid's light scattering properties are measured. 
This spatially coincident measurement is particularly important in the 
field of liquid chromatography, especially when applied to the technique 
of size exclusion or gel permeation chromatography. 
Another objective of my invention is the deduction of the concentration of 
dissolved substances in the fluid, since a changing concentration of a 
dissolved solute will cause corresponding changes in the refractive index 
of the resulting solution. Such changes in concentration can be 
quantitated by converting said beam deviation into corresponding changes 
in concentration. 
My invention will be particularly useful when applied to a light scattering 
cell similar to those described in the above referenced U.S. Pat. No. 
4,616,927 of which I am a co-inventor. Said patent, hereinafter called the 
"927" patent, describes an important type of light scattering cell 
permitting measurement of the light scattering properties of solutions 
with minimal interference from light scattered at the cell interfaces.

MODES FOR CARRYING OUT THE INVENTION 
FIG. 1 presents a diagram of the refraction and reflection of a light ray 1 
in a transparent medium of refractive index n.sub.1, striking the plane 
interface 4--4 at an angle .theta..sub.1, and entering a medium of 
refractive index n.sub.2. The ray 2 is reflected at an angle .theta..sub.1 
and the ray 3 is refracted into medium 2 at an angle .theta..sub.2. The 
relationship between the angles .theta..sub.1 and .theta..sub.2 is given 
by Snell's Law 
EQU n.sub.1 sin .theta..sub.1 =n.sub.2 sin .theta..sub.2. (1) 
Snell's Law was derived by Huygens in the 17th Century from his wave 
description of light and more rigorously may be derived directly from 
Maxwell's equations. The resultant equations of refraction and reflection 
between media for which the refractive indices may be complex are often 
referred to as the Fresnel equations. FIG. 1 has been drawn for the case 
where n.sub.2 &gt;n.sub.1. Consider for that case, the situation where the 
ray 1 just grazes the plane interface, i.e. 
EQU .theta..sub.1 =.pi./2. (2) 
Equation (1) may be rewritten, therefore, as 
EQU .theta..sub.2 =.theta..sub.c =sin.sup.-1 (n.sub.1 /n.sub.2).(3) 
Equation (3) so-written defines the critical angle .theta..sub.c so-named 
because reversing the ray direction from 3 defines an angle of incidence 
at the plane 4--4 from medium n.sub.2 which represents the limiting angle 
in that medium. Any ray incident on the interface 4--4 from medium n.sub.2 
at an angle greater than .theta..sub.c will be perfectly reflected and no 
energy will be refracted into medium n.sub.1. At the critical angle, a 
surface wave is said to be launched between the media and that surface 
wave is exponentially attenuated in the medium n.sub.1. These surface or 
evanescent waves have been shown to have most interesting properties and 
are of importance for a number of devices and inventions in common use. A 
textbook by N. J. Harrick on "Internal Reflection Spectroscopy" on his 
article in volume 17 of Applied Spectroscopy (1987) should be consulted 
for some further explanations and interesting applications. 
FIG. 2 shows the structure of a conventional split prism device used to 
measure the difference of the refractive indices of two liquids contained, 
respectively, in triangular shaped regions 5 and 6. The incident ray 1 
passes through medium 5, strikes the interface at 8 and is refracted in 
medium 6. The refracted ray leaves medium 6 at 9 where it appears 
displaced and parallel to the undeviated ray 7. For small refractive index 
differences between the liquids, it may be shown that 
EQU d=L(n.sub.1 -n.sub.2)/(2n.sub.1) (4) 
where L is the width of the square structure. Note that the change in the 
displacement d is directly proportional to the difference of the 
refractive indices of the solutions. 
With these preliminaries, the details of my invention will be clearly 
understood by those skilled in the art. FIG. 3 presents the refraction of 
a ray of light passing through a liquid containing capillary channel. The 
ray 1 begins in transparent medium 10, strikes a capillary channel 11 at 
the point 12, is refracted by the difference of refractive indices between 
the medium 10 and liquid 11, strikes the opposite side of the capillary, 
and is refracted again as the ray 3 emerges at 13 into the medium 10 once 
again. The path of the indeviated ray 14 is indicated by the dotted line. 
The deviation, d, of the refracted ray with respect to the undeviated ray 
is also shown. For this figure, the geometry corresponds to all rays and 
the capillary lying in the same plane. If the refractive index of 11 were 
the same as that of the surrounding transparent medium 10, the beam 3 
would be undeviated and superimposed on the undeviated ray 14. 
Let us now examine further the case where the liquid is of a refractive 
index less than the surrounding medium. For ease of discussion, we shall 
consider the transparent medium to be glass and the liquid to be a 
transparent fluid such as water or toluene or tetrahydrofuran or other 
so-called mobile phases used in forms of liquid chromatography. 
Alternatively, these liquids are more commonly called solvents. This 
glass/mobile phase dichotomy is intended for illustrative purposes only. 
There are many other transparent solids and liquids by which means this 
invention is equally operative. For the discussion and explanation that 
follows we shall assume 
EQU n.sub.g &gt;n.sub.s (5) 
where n.sub.g is the glass refractive index and n.sub.s is the refractive 
index of the solvent. The direction of the displacement d of FIG. 3 is 
characteristic of the relation of Eq. (5). As the refractive index of the 
liquid (solvent) increases because of the increased concentration of 
dissolved substances (solutes), the displacement of the refracted ray 3 
will decrease and the refracted ray will approach co-linearity with the 
undeviated ray as n.sub.s approaches n.sub.g. Since, characteristically, 
the capillary channel will be of finite length, it is important to select 
the incident angle so that the ray displacement is not so great as to 
remove the ray completely, or so that it strikes ends of the capillary or 
the supporting structure. For example, if the angle of incidence from the 
glass was the critical angle per Eq. (3), then there would be no capillary 
traversing ray whatsoever. 
Referring now to FIG. 4, we see the refractions and displacement of the ray 
1 as it passes through the capillary 11, beginning and ending in the glass 
10. The capillary channel is shown of diameter 2r in the plane containing 
all rays. The incident ray 1 makes an angle .theta.' to the capillary 
axis. For this geometry, the conventional angle of incidence is 
.pi./2-.theta.'. The undeviated ray would appear as ray 14, ray 3 
corresponds to the ray displaced by the pure solvent, and ray 15 displaced 
a distance .DELTA. from ray 3 toward 14 is the ray corresponding to 
changes occurring due to a dissolved solute in the solvent causing a 
refractive index change .DELTA.n. 
The various distances to the right of the perpendicular through the point 
of incidence 12 are labeled in the figure. Combining these results, the 
displacement .DELTA. transverse to the ray 3 may be expressed simply in 
the form 
EQU .DELTA.=2r(cot .theta..sub.2 -cot .theta..sub.1) sin .theta.'.(6) 
The angles .theta.', and .theta..sub.1 are related by Snell's Law 
EQU n.sub.g sin (.pi./2-.theta.')=n.sub.s sin (.pi./2-.theta..sub.2)(7) 
EQU or 
EQU n.sub.g cos .theta.'=n.sub.s cos .theta..sub.2. (8) 
Further 
EQU cot .theta..sub.2 =cos .theta..sub.2 /(1-cos.sup.2 .theta..sub.2).sup.1/2=( 
n.sub.g /n.sub.s) cos .theta.'/[1-(n.sub.g /n.sub.s).sup.2 cos.sup.2 
.theta.'].sup.1/2 (9) 
and similarily, 
##EQU1## 
Equation (6) may be readily evaluated given .theta.',n.sub.g, .DELTA.n and 
n.sub.s. Note furthermore that 
EQU .theta.'&gt;cos.sup.-1 (n.sub.s /n.sub.g), (11) 
since the right hand side of Eq. (11) corresponds to .pi./2-.theta..sub.c, 
where .theta..sub.c is the critical angle of Eq. (3). If .theta.' is less 
than or equal to cos.sup.-1 (n.sub.s /n.sub.g), then no ray enters the 
capillary 11. 
In the limit 
##EQU2## 
Eq. (6) may be written in the approximate form 
##EQU3## 
Note that Eq. (13) confirms a linear displacement change, .DELTA., with a 
linear refractive index change .DELTA.n, since .theta.', r, p, and n.sub.s 
are fixed quantities. For .DELTA.n much above 10.sup.-4 and .theta.' 
within 1.degree. of the critical angle, this linear variation requires 
correction to second order. 
FIG. 5 shows a cross sectional view of the cylinder cell 10 of the "927" 
Patent. The capillary 11 is bored along a cylinder diameter and polished. 
In its conventional configuration, a light source is incident through the 
capillary fluid from 16, exiting at 17. Scattered light detectors are 
placed circumfrentially about the cylinder and lie in the plane of the 
capillary. These detectors are aimed toward the center of the capillary, 
and placed with faces parallel to the cylinder curved surface closest to 
them. Details are presented in the "927" Patent. For purposes of the 
present refractometer invention, a secondary source of light 18 lying in 
the plane of the detectors, or otherwise above or below such plane, is 
directed toward the center of the capillary through which it would pass 
were it not for the refractions of the liquid within the capillary 11. The 
path of an undeviated ray is shown at 14, while the fluid has created the 
ray displaced therefrom by the liquid at 13. As the refractive index of 
the fluid within the glass capillary increases, the refracted ray will 
emerge at 15 and move towards coincidence with 14. 
We will now examine Eqs. (6) and (10) for angles satisfying Eq. (11). As an 
example, let us take n.sub.g =1.61655 and n.sub.s =1.3333. Here n.sub.g is 
the refractive index of Hoya F2 glass at a wavelength of 632.8 nm. Such 
glass is of frequent use in optical fibers as well as the refraction cells 
of my co-invention "927" Patent. F2 glass is commonly manufactured by 
Schott and Hoya Glass companies, among others. Let the solvent refractive 
index, n.sub.s, correspond to water, a common solvent/mobile phase in 
liquid chromatography, and let the incident wavelength be 632.8 nm. This 
is the wavelength of the most common He-Ne laser. For the stated glass and 
liquid, the incident ray must strike the capillary at an angle .theta.' 
greater than 
EQU cos.sup.-1 (1.333/1.61655)=34.4.degree.. (15) 
For purposes of subsequent calculation, we shall take the diameter of the 
capillary, 2d, to be 1.5 mm, a commonly found dimension of the refraction 
cell above referenced. 
Table 1 presents the displacement in mm of the refracted ray 3 of FIG. 4 
from the undeviated ray 14 for the aforementioned values of n.sub.g and 
n.sub.s. Also listed are the calculated transmittances of the ray 3 for 
vertical and horizontal polarizations of the incident ray. Vertically 
polarized light corresponds to plane polarized light for which the 
electric field is polarized perpendicular to the plane of the figure. 
Horizontally polarized light corresponds to plane polarized light whose 
electric field lies in the plane of the figure. The light transmitted 
through the capillary channel into the glass along ray 3 has a 
transmittance T that may be derived from the Fresnel relations presented, 
for example, by C. W. Ditchburn in his book "Light." At each glass/liquid 
interface, there is a reflected fraction R of the incident power. Thus, 
the light transmitted through the capillary is 
EQU T=(1-R). (16) 
The reflectance R for the case of horizontally polarized light (electric 
field lies in the plane of the capillary channel axis) is 
EQU R.sub.H =tan.sup.2 (.theta.'-.theta..sub.1)/tan.sup.2 
(.theta.'+.theta..sub.1). (17) 
For vertically polarized incident light (electric field polarized 
perpendicular to the capillary channel axis), 
EQU R.sub.v =sin.sup.2 (.theta.'-.theta..sub.1)/sin.sup.2 
(.theta.'+.theta..sub.1). (18) 
TABLE 1 
______________________________________ 
Ray displacement in mm for water filled 
capillary channel in F2 glass. 
.THETA.' (degrees) 
Displacement T.sub.V T.sub.H (%) 
______________________________________ 
35 6.10 24 40 
36 3.23 45 67 
37 2.30 58 79 
38 1.81 66 86 
39 1.49 72 91 
40 1.27 76 94 
45 0.71 88 99 
______________________________________ 
Note that the closer the incident ray 1 lies to the critical angle of 
34.4.degree., the greater is the displacement and the smaller is the 
transmitted fraction for either polarization. 
Next, consider the effect of a refractive index change in the capillary 
fluid of 0.0005, i.e. let the liquid refractive index increase to 1.3338. 
This is a change that might be encountered for a peak concentration of 5 
mg/ml in a size exclusion chromatography experiment. The utility of a 
differential refractometer is directly related to its ability to monitor 
such changes in refractive index. The calculations of Table 2, which 
follow, include another column, viz. the displacement change .DELTA. with 
respect to the position of the pure water displacement. 
TABLE 2 
______________________________________ 
Ray displacement and displacement changes (in mm), .DELTA., 
caused by a capillary solvent (water) refractive index 
increase of 0.0005 in F2 channel glass. 
.THETA.' (degrees) 
Displacement 
.DELTA. T.sub.V (%) 
T.sub.H (%) 
______________________________________ 
35 5.90 0.194 25 42 
36 3.19 0.043 46 67 
37 2.28 0.021 58 80 
38 1.79 0.013 66 87 
39 1.48 0.009 72 91 
40 1.26 0.007 76 94 
45 0.70 0.002 88 99 
______________________________________ 
Again we see that the most pronounced effects occur closest to the critical 
angle. 
Consider now a second example where instead of F2 glass, we choose Schott 
K5 glass whose refractive index at 632.8 nm is 1.52064. The critical angle 
(measured with respect to the capillary axis) is now 28.74.degree. per Eq. 
(11). Table 3 presents the displacement in mm of the refracted ray 3 of 
FIG. 4 from the undeviated ray 14 for the case of water in a K5 cell. 
TABLE 3 
______________________________________ 
Ray displacement in mm for water filled 
capillary channel in K5 glass. 
.THETA.' (degrees) 
Displacement T.sub.V T.sub.H (%) 
______________________________________ 
29 8.98 16 24 
30 3.44 46 60 
31 2.30 60 75 
32 1.75 69 84 
33 1.42 76 89 
35 1.03 83 94 
40 0.58 92 99 
______________________________________ 
Introducing a refractive index change of 0.0005 now yields the values shown 
in Table 4: 
TABLE 4 
______________________________________ 
Ray displacement and displacement changes (in mm), .DELTA., 
caused by a capillary channel solvent (water) refractive index 
increase of 0.0005 in K5 glass. 
.THETA.' (degrees) 
Displacement 
.DELTA. T.sub.V (%) 
T.sub.H (%) 
______________________________________ 
29 8.28 0.698 18 26 
30 3.37 0.071 46 61 
31 2.27 0.030 61 76 
32 1.74 0.017 70 84 
33 1.41 0.012 76 89 
35 1.02 0.007 84 94 
40 0.58 0.003 92 99 
______________________________________ 
As a final example, consider the solvent toluene whose refractive index is 
about 1.49, in F2 glass. The critical angle from Eq. (3) is now 22.82 
degrees. Tables 5 and 6 present the corresponding data. 
TABLE 5 
______________________________________ 
Ray displacement in mm for toluene filled 
capillary channel in F2 glass. 
.THETA.' (degrees) 
Displacement T.sub.V T.sub.H (%) 
______________________________________ 
23 10.04 15 19 
24 3.18 51 60 
25 2.06 66 75 
26 1.54 75 84 
27 1.24 81 89 
30 0.76 90 96 
35 0.44 95 99 
______________________________________ 
TABLE 6 
______________________________________ 
Ray displacement and displacement changes (in mm), .DELTA., 
caused by a capillary channel solvent (toluene) refractive 
index increase of 0.0005 in F2 glass. 
.THETA.' (degrees) 
Displacement 
.DELTA. T.sub.V (%) 
T.sub.H (%) 
______________________________________ 
23 8.81 1.228 18 22 
24 3.10 0.084 52 61 
25 2.03 0.034 67 76 
26 1.53 0.020 76 84 
27 1.22 0.013 81 89 
30 0.75 0.006 90 96 
35 0.44 0.003 96 99 
______________________________________ 
Measurement of the displacement change, .DELTA., may be achieved quite 
easily. Using a split photodiode, for example, of the type manufactured by 
United Detector Technology, changes less than 0.1 micrometer may be 
detected. Such a refractive change would correspond to a concentration 
change of the order of 10.sup.-4 ng/ml. Referring to the examples 
presented, we note the following: 
1) The greatest displacement changes occur for incident light beam angles 
approaching the critical angle. The displacement change becomes smaller 
quite rapidly as the incident beam moves away from this critical angle. 
2) The displacement change increases with increasing glass/liquid 
refractive index difference. 
3) The transmission change, for both V and H incident polarizations, 
dT/d.theta.', decreases as the liquid refractive index increases. 
Note that a narrow beam of light of finite cross section X passing through 
a capillary channel of circular cross section will produce a flaired 
oblong refracted beam transverse to the refraction plane upon emerging 
from the capillary structure of FIG. 5. FIG. 6 presents a side view of a 
finite beam of diameter X passing through a capillary whose refractive 
index is less than that of the surrounding medium. Since the capillary 
refractive index is less than that of the glass, the capillary will act as 
a negative cylindrical lens. A split photodiode detector would be placed 
preferentially with its face nearly perpendicular to the emerging beam and 
its division axis along the flair direction. 
FIG. 7 is a drawing of the cylinder refraction cell and manifold structure 
described in the "927" Patent. The cylindrical glass cell 10 is shown with 
the fine capillary channel 11 attached at either end by inlet and outlet 
manifolds 30 and 17, respectively. The fluid sample is introduced at 31, 
pumped into the cell, and leaves the cell at 19. Each manifold is fitted 
with a laser beam entrance or exit window, 20 or 21, respectively. The 
laser source is incident from 22 used for scattering experiments produces 
a beam entering at 20, passing along the capillary 11 axis, and exiting 
through window 21. An array of detectors, not shown, lie circumferentially 
about the cylinder cell in a plane parallel to the cylinder ends and 
coplanar with the capillary channel 11. Other manifold configurations 
include an integrated structure such as illustrated by the design patent 
application by Wyatt and Shuck referenced earlier. 
The actual shape of the transparent region through which the capillary 
passes may be of many different forms, each form selected on the basis of 
the geometry and function of the region into which the differential 
refractometer is to be located. For example, for one preferred embodiment 
of the invention, the glass region would be in the form of the refraction 
cell disclosed in the previously referenced "927" Patent by Phillips et 
al. and shown schematically and in cross section in FIG. 5. However, such 
an orientation of the incident light beam to the capillary axis could be 
effected equally well by positioning the source 18 above the scattering 
detection plane 23 by using a spherical glass cell 24 in the manner 
indicated in FIG. 8, the preferred embodiment of the invention. Here the 
light beam 18 is incident on the surface at 28, passes through the 
capillary 11, is refracted thereby as has been discussed earlier, and then 
emerges through the opposite surface at 26 to be detected at 27. Note that 
the position sensing detector 27 and the incident light source 18 lie out 
of the conventional detection plane 23 of the aforereferenced "927" 
patent. 
The refractometer light source 18 should be contrasted with the second 
light source 22 whose beam passes through and parallel to the capillary 11 
and scatters from the solution entrained therein. While the light source 
22 and capillary 11 lie in the scattered light detector plane 23, the 
refractometer light source 18 and the corresponding position sensing 
detector 27 lie in general in a different plane containing also the 
capillary axis 11. 
Although the preferred and most common configuration of the capillary will 
be of cylindrical cross section, other forms may be used to equal 
advantage. For example, the cross section could be rectangular, being 
formed by combining planar polished transparent elements to yield a 
capillary void through which the fluid may flow, or in which it may be 
placed, of rectangular cross section. Rectangular boxes may be drilled 
easily by means of ultrasonic machining such as performed by machines 
manufactured by Bullen Ultrasonics of Ohio. In addition, the capillary 
need not be straight since a slightly curving capillary, whose radius of 
curvature is large compared to its transverse dimensions, may be useful 
for certain types of geometries. 
Having described the elements of my invention together with some examples 
of glass-capillary structures that might be employed therein, I now 
discuss further some preferred embodiments of the invention. 
The ability to determine the refractive index change of a fluid in which a 
solute has been dissolved requires the following elements: 
A) A collimated light beam oriented with respect to the fluid bearing 
capillary channel 11 at an angle somewhat less than the critical angle 
defined by the refractive indices of the entraining transparent medium 
(higher refractive index) and the solute-absent fluid (lower refractive 
index) given by Eq.(11). Preferentially, the illuminating light beam will 
be a laser unpolarized or polarized. Incident polarization can be plane or 
circular or combination thereof; 
B) Attachment means whereby the light beam of A may be positioned with 
respect to and rigidly attached to 
C) A transparent refraction cell containing a finely polished capillary 
channel carrying said fluid therethrough; and 
D) Position sensing means whereby the displacement of the refracted 
transmitted beam caused by a fluid refractive index change may be detected 
and quantified. 
It is important to note that if the solute has a negative refractive index 
increment dn/dc with concentration, the angle of the incident beam 
preferentially would be oriented at a smaller angle than if dn/dc is 
positive. This will prevent the refracted beam from approaching the 
critical angle too closely thereby preventing any light from being 
refracted. For the Broerman device, described earlier, this type of an 
adjustment cannot be effected. In addition, the Broerman device is 
directed to detecting intensity differences whereas the present device 
detects both displacement and intensity variations with most emphasis on 
the former. 
In a preferred embodiment of the invention, the refraction cell would be of 
a spherical shape and form claimed in the "927" patent. The light source 
would be a fine laser beam oriented normal to the spherical face, and 
entering the fluid bearing capillary channel at an angle (measured with 
respect to the normal to the capillary channel axis) slightly less than 
the critical angle defined by Eq.(3). After refraction through the 
capillary channel in the manner shown in FIG. 4 and emerging through the 
opposite face of the sphere as detailed in FIG. 8, the beam is centered 
upon a position sensing element 27. The reference position of the beam 
with respect to said sensing element preferentially corresponds to the 
refracted position 3 of FIG. 4 caused by the pure solvent alone. Any 
change in refractive index of the solvent would cause a shift of the beam 
15 from said reference position 3 which in turn would cause a change in 
the output signal of the position sensing device, such as shown at 27 in 
FIG. 8. 
The output signal could be generated in different manners. For example, 
with a split photodiode of the type described previously, each half of the 
photodiode would be subjected to different levels of incident light flux 
caused by changes in the centering of the beam as well as intensity 
variations transverse to the beam due to different transmissivities of the 
refracted elements of the beam arising from its finite cross section and 
the corresponding slight differences of incident angles. A typical output 
would be generated by the difference of the two corresponding output 
currents or voltages. Since light sources of considerable short term 
stability are required for increased precision, the difference signal 
could be referenced to the light power incident on the structure. Said 
incident light power may be obtained from a reference beam incident on a 
different photodiode. For example, as many lasers have a small amount of 
light energy leaking out through their rear laser mirror, said light being 
easily detected by the simplest of photodetectors fastened to the rear of 
the laser. As the laser output varies, so too would the rear beam power. 
Alternatively incident reference power could be monitored with respect to 
a beam splitter at the emitting forward end of the laser. Such monitoring 
systems have been described in considerable detail in the copending 
application earlier referenced in this description. Another type of dual 
output device is a continuous photodiode structure manufactured by Silicon 
Detector Corporation. This device produces an output at each of its ends 
proportional to the distance from the center of the device of the beam. 
Note that the differential response of the position sensor as well as the 
light beam monitor should be converted to a numerical or analog 
representation for practical use. Thus a preferred output of the 
instrument would be a numerical representation of the change of refractive 
index of the solution relative to a previously measured or stored 
reference value. The most accurate values so-displayed would be generated 
internally or by external computer means to yield a value dn proportional 
to the ratio of the differential detector output divided by the incident 
light beam intensity. Since Eq. (6) suggest a proportionality which 
generally may not be quite linear as shown in Eq. (13), the 
proportionality factor as a function of .DELTA. may be stored in computer 
means connected to the instrument for subsequent reference, may be 
generated and stored by means of a calibration procedure, and/or may be 
generated by external computer means. If the unit is to be used on-line, 
for example with a simultaneous light scattering measurement as shown in 
plane 23 of FIG. 8, then the analog signals generated by the instrument 
would be transmitted directly into an analog-to-digital multiplexing 
converter for on-line use in another preferred embodiment of the 
invention. 
Since the displacement, .DELTA., is a monotonic function of the refractive 
index change, dn, and said refractive index change will be directly 
proportional to the concentration change of the dissolved substance, the 
said displacement may be referred directly to the actual concentration of 
said dissolved substance. Thus referred to the displacement, d, of the 
pure liquid, the measured displacement which induces a monotonic response 
in a detecting position sensing means may be used to generate a solute 
concentration value, c. Each displacement will correspond, therefore, to a 
specific concentration from the relation 
EQU n=n.sub.o +(dn/dc)c, (19) 
EQU or 
EQU n-n.sub.o =.DELTA.n=(dn/dc)c (20) 
EQU and 
EQU c=.DELTA.n/(dn/dc), (21) 
where n.sub.o is the refractive index of the pure fluid absent dissolved 
substance and n is the refractive index of the fluid plus solute. dn/dc is 
easily measured by making a measurement of .DELTA.n caused by a 
concentration change .DELTA.c, then extrapolating to the limiting value of 
.DELTA.n/.DELTA.c, i.e. 
EQU (dn/dc)=lim (.DELTA.n/.DELTA.c)as .DELTA.c.fwdarw.0 (22) 
FIG. 9 shows the result of an early experimental confirmation of the 
invention. A 5 W plane polarized laser beam was attached to a structure 
holding a cylindrical refraction cell of the type described in the "927" 
patent. The wavelength of the laser was 632.8 nm, the cell refractive 
index was 1.61655, and the capillary was filled with water of refractive 
index 1.333. Injected into the capillary and pumped therethrough by means 
of a 510 chromatography pump of the type manufactured by the Waters 
Company was a 20 microliter aliquot of a 0.1% dextran (in NaCl buffer) of 
approximate molecular weight 600,000. The change of refractive index with 
respect to concentration, dn/dc, was about 0.10. The difference of the two 
signals produced by the United Detector Technology split photodiode was 
amplified to produce the plot of FIG. 9 of voltage versus time. Since the 
pump was operating at a speed of 0.5 ml/minute, the time scale also 
corresponds to the so-called retention volume obtained by multiplying time 
by the factor 0.5 ml/min. The small spikes superimposed on the curve arose 
from pump pulsations causing the structure to move slightly relative to 
the laser and detector source. These are easily removed by incorporating 
said refraction cell elements into a stationary structure. The breadboard 
configuration used to make these early measurements was assembled without 
particular attention to structural stability. 
Although the impressive results of FIG. 9 were generated using a continuous 
wave laser, further signal enhancement would be achieved by modulating the 
laser beam by electrical or chopper means. At a frequency above the cutoff 
frequency of the standard multi-angle detectors of the "927" device, the 
modulated refractive index signal would not be detected by the multi-angle 
detectors. Thus, the multi-angle scattering as well as the refractive 
index changes could be monitored simultaneously even though both were 
performed at the same wavelength using different laser sources. 
Alternatively, both sets of measurements could be interspersed, turning 
one laser off while the other was on. A further variation of the dual 
measurement could be perform using light sources of different wavelengths 
in combination with filters covering the multi-angle scattering detectors 
and permitting thereby the selective detection of the appropriate signals 
with a narrow band pass filter covering the position sensitive detector 
corresponding to the wavelength of the refractometer light source and 
covering the multi-angle scattered light detectors with narrow band pass 
filters at the wavelength of the scattering light source. Many variations 
of these detection strategies will be clearly evident to those skilled in 
the art of light detection from sources fixed in space. 
For each type of fluid of different refractive index, there will be a 
unique optimal angle at which the incident light beam should be set. Thus, 
unless said fluid be always the same, means should be provided to adjust 
the angle of the incident beam with respect to the capillary. Optimally, 
this angle will lie close to the critical angle, perhaps one or two 
degrees therefrom. Alternatively, the light source may be fixed and the 
capillary channel containing refraction cell rotated so that the 
beam/capillary channel angle setting may be adjusted thereby. Means should 
also be provided, as required, to orient the position sensing element that 
monitors the position of the refracted beam. Once the light beam/capillary 
channel angle has been set for the solvent selected, the adjustment of the 
position sensing element is straightforward: with the capillary channel 
filled with the pure solvent, the position sensing element is set at a 
position that will yield a null electrical signal. Alternatively, it could 
be placed at a position yielding a small signal relative to those it would 
generate with increasing solute concentration. Depending upon the actual 
physical structure of the position sensing element, there could be many 
similar orientations thereof, as will be readily apparent to those skilled 
in the art. 
In closing this discussion of my invention, some further features are 
disclosed. The light beam, which would be preferably a laser beam, should 
be of a cross section less than the cross section of the capillary channel 
since only those elements of the beam striking the capillary will be 
refracted and, in a preferred embodiment, all elements of the incident 
light beam should be affected by refraction in the capillary channel. 
Further, as has been alluded to earlier, the best orientation of the 
capillary channel and light beam should be such that their center lines 
intersect. Any other orientation would correspond to a partial grazing by 
the incident beam. The symmetric spatial intersection of the two axes will 
insure further the symmetrical refraction of the incident light beam by 
the capillary channel with respect to the plane defined by these two 
lines. 
We note, furthermore, from Eq. (6) that the displacement of the refracted 
beam, .DELTA., with respect to the incident beam, increases as the 
capillary channel diameter, 2r, increases. The capillary channel itself, 
therefore, must be long enough to accommodate both the refracted beam as 
well as the internally reflected beam without said beams striking the 
capillary terminations or any other similar obstacles. Such obstacles 
would result in secondary reflections by said beams and these reflections 
are generally unwanted sources of stray light. Since the sensitivity of 
the refractometer increases as the diameter of the capillary, the optimal 
cell may be larger than the standard refraction cell, which is about 22 
mm. However, from the chromatography point of view, a larger capillary 
volume will result in a greater band broadening of the solute contained 
therein. Thus a judicious tradeoff of design parameters must be made. 
In this preferred embodiment of the invention, the refractometer structure 
would serve a dual purpose as indicated in FIG. 8. Surrounded by detectors 
27 coplanar with the capillary 11 and illuminated through the capillary by 
a light source 22, the structure will function by measuring the angular 
variation of light scattered by the particles flowing through the 
capillary according to the cited "927" patent. Adding the second light 
source 18 and displacement detector 27, the structure will function as a 
concentration sensitive detector as described in this present application. 
In order that neither light source interfere with the detectors associated 
with the other, it may be necessary to turn one off while the other is 
being used. This may be achieved by mechanical, shutter means or, in the 
case of certain classes of lasers, the light sources themselves may be 
modulated. In either event, the time delay between such successive 
measurements may be reduced to a time period small relative to the 
displacement of the particles entrained in the fluid flowing through the 
capillary 11. In this manner, the measurement of the scattered light 
variations with detector angular position from an ensemble of 
particles/molecules may be measured from essentially the same physical 
particles whose concentration is simultaneously monitored. This may be 
achieved with the preferred embodiment of the invention, as shown in FIG. 
8. 
INDUSTRIAL APPLICABILITY 
This invention of a flow through differential refractometer will have 
significant industrial application for chemistry and in particular polymer 
chemistry wherein the physical characteristics of large molecules are 
sought. Combined with the technique of size exclusion chromatography the 
preferred embodiment of my invention will permit the measurements of 
molecular size and weight of each separated fraction irrespective of the 
constancy of flow rate since both light scattering and concentration 
measurement may be performed on the same flowing volume element of 
effluent. Used with another form of concentration detector, such as 
ultraviolet absorption or evaporative mass detection, the invention will 
permit deduction of the differential refractive index increment dn/dc with 
concentration. In this manner, the physical parameters of co-polymers may 
be derived by combining the measurements of differential refractometer, 
light scattering array, and concentration sensitive detector. 
While there has hereinbefore been presented what is at present considered 
to be the preferred embodiments of the method and apparatus for measuring 
the refractive index changes within the fluid bearing capillary, it will 
be apparent to those of ordinary skill in the art that many modifications 
and variations may be made therefrom without departing from the true 
spirit and scope of the invention. All such variations and modifications, 
therefore, are considered to be a part of the invention.