Light scattering detectors and methods for the same

Methods for determining a radius of gyration of a particle in solution using a light scattering detector are provided. The method may include passing the solution through a flowpath in a sample cell, determining respective angular normalization factors for first and second angles of the detector, obtaining a first scattering intensity of the particle in solution at the first angle, obtaining a second scattering intensity of the particle in solution at the second angle, obtaining a 10° scattering intensity of the particle in solution at an angle of about 10°, determining a first particle scattering factor, determining a second particle scattering factor, plotting an angular dissymmetry plot, fitting a line to the angular dissymmetry plot, determining a slope of the line at a selected location on the line, determining the radius of gyration of the particle in solution from the slope of the line, and outputting the radius of gyration.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Stage application of PCT/US2019/012095 filed 2 Jan. 2019, the entire disclosure of which is incorporated herein by reference.

BACKGROUND

Conventional light scattering detectors are often utilized in conjunction with chromatographic techniques to determine one or more physical attributes or characteristics of various molecules or solutes suspended in solutions. For example, light scattering detectors are often utilized with gel permeation chromatography (GPC) to determine a molecular weight and a radius of gyration of various particles, such as polymers. In light scattering detectors, a sample or effluent containing molecules (e.g., polymers) is flowed through a sample cell from an inlet to an outlet disposed at opposing ends thereof. As the effluent is flowed through the sample cell, the effluent is illuminated by a collimated beam of light (e.g., laser). The interaction of the beam of light and the polymers of the effluent produces scattered light. The scattered light is then measured and analyzed for varying attributes, such as intensity and angle, to determine the physical characteristics of the polymers.

While conventional light scattering detectors have proven to be effective for determining the physical attributes of a wide variety of molecules, conventional light scattering detectors are limited in their ability to analyze small molecules. For example, conventional light scattering detectors often lack the sensitivity and/or resolution to measure Rg of molecules having a radius of gyration of less than about 10 nm. In view of the foregoing, conventional light scattering detectors often incorporate lasers having relatively greater power or energy to increase the sensitivity of the detectors. Incorporating lasers with greater power, however, is cost prohibitive and often requires larger instruments due to the relatively larger footprint of the lasers. Alternatively, the volume of the sample cells in conventional light scattering detectors can been increased to increase the intensity of scattered light. Increasing the volume of conventional sample cells, however, leads to excessive peak broadening.

What is needed, then, are improved light scattering detectors and sample cells thereof, methods for increasing the sensitivity and/or resolution of the light scattering detectors without increasing peak broadening, and improved methods for determining a radius of gyration of a particle.

BRIEF SUMMARY

This summary is intended merely to introduce a simplified summary of some aspects of one or more implementations of the present disclosure. Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. This summary is not an extensive overview, nor is it intended to identify key or critical elements of the present teachings, nor to delineate the scope of the disclosure. Rather, its purpose is merely to present one or more concepts in simplified form as a prelude to the detailed description below.

The foregoing and/or other aspects and utilities embodied in the present disclosure may be achieved by providing a method for determining a radius of gyration (Rg) of a particle in solution using a light scattering detector. The method may include passing the particle in solution through a flowpath in a sample cell, wherein the flowpath has a centerline aligned with a beam of light of the detector. The method may also include determining an angular normalization factor (Nθ1) for a first angle of the detector and an angular normalization factor (Nθ2) of a second angle of the detector, wherein the first angle is about 90° relative to the centerline, and wherein the second angle is about 170° relative to the centerline. The method may also include obtaining a first scattering intensity (Iθ1) of the particle in solution at the first angle. The method may also include obtaining a second scattering intensity (Iθ2) of the particle in solution at the second angle. The method may also include obtaining a 10° scattering intensity (I10) of the particle in solution at an angle of about 10°. The method may also include determining a first particle scattering factor (Pθ1) with the first scattering intensity (Iθ1), the 10° scattering intensity (I10), and the angular normalization factor (Nθ1) for the first angle. The method may also include determining a second particle scattering factor (Pθ2) with the second scattering intensity (Iθ2), the 10° scattering intensity (I10), and the angular normalization factor (Nθ2) for the second angle. The method may also include plotting an angular dissymmetry plot, wherein the angular dissymmetry plot comprises the first particle scattering factor (Pθ1) and the second particle scattering factor (Pθ2). The method may also include fitting a line to the angular dissymmetry plot. The method may also include determining a slope of the line at a selected location on the line. The method may also include determining the radius of gyration (Rg) of the particle in solution from the slope of the line. The method may also include outputting the radius of gyration (Rg).

In at least one implementation, determining the angular normalization factor of the first and second angles of the detector may include passing each of a plurality of known particles in solution through the flowpath of the sample cell. Determining the angular normalization factor of the first and second angles of the detector may also include obtaining scattering intensity values for each of the plurality of known particles in solution at an angle of about 10°, at the first angle, and at the second angle. Determining the angular normalization factor of the first and second angles of the detector may also include determining the angular normalization factor (Nθ1) for the first angle with a plot of a ratio of the scattering intensity values of each of the plurality of known particles at the first angle to the scattering intensity values of each of the plurality of known particles at an angle of about 10°. Determining the angular normalization factor of the first and second angles of the detector may also include determining the angular normalization factor (Nθ2) for the second angle with a plot of a ratio of the scattering intensity values of each of the plurality of known particles at the second angle to the scattering intensity values of each of the plurality of known particles at an angle of about 10°.

In at least one implementation, each of the plurality of known particles in solution have a known molecular weight.

In at least one implementation, the first particle scattering factor (Pθ1) is in the form

Pθ1=(Iθ1/I10)Nθ⁢1,
where: Iθ1is the scattering intensity of the particle in solution at the first angle; I10is the scattering intensity of the particle in solution at an angle of about 10°; and Nθ1is the angular normalization factor for the first angle.

In at least one implementation, the second particle scattering factor (Pθ2) is in the form

Pθ2=(Iθ2/I10)Nθ2,
where: Iθ2is the scattering intensity of the particle in solution at the second angle; I10is the scattering intensity of the particle in solution at an angle of about 10°; and Nθ2is the angular normalization factor for the second angle.

In at least one implementation, plotting the angular dissymmetry plot comprises: plotting a first point on a plane, the first point comprising a first coordinate and a second coordinate, wherein the first coordinate of the first point is the first particle scattering factor (Pθ1), and wherein the second coordinate of the first point is in the form

μθ⁢12=(4⁢π⁢n0⁢sin⁢θ12λ)2,
where: n0is a refractive index of the solution; θ1is the first angle; and λ is a wavelength of the beam of light; plotting a second point on the plane, the second point comprising a first coordinate and a second coordinate, wherein the first coordinate of the second point is the second particle scattering factor (Pθ2), and wherein the second coordinate of the second point is in the form

μθ⁢22=(4⁢π⁢n0⁢sin⁢θ⁢22λ)2,
where: n0is a refractive index of the solution; θ2is the second angle; and λ is the wavelength of the beam of light.

In at least one implementation, fitting the line to the angular dissymmetry plot comprises a least squares fitting. The line may include a polynomial degree of less than three.

The foregoing and/or other aspects and utilities embodied in the present disclosure may be achieved by providing a method for determining a radius of gyration (Rg) of a particle in solution using a light scattering detector. The method may include passing the particle in solution through a flowpath in a sample cell, wherein the flowpath has a centerline aligned with a beam of light of the detector. The method may also include determining an angular normalization factor (Nθ1) for a first angle of the detector, wherein the first angle is either about 90° or about 170° relative to the centerline. The method may also include obtaining a first scattering intensity (Iθ1) of the particle in solution at the first angle. The method may also include obtaining a 10° scattering intensity (I10) of the particle in solution at an angle of about 10° or less. The method may also include determining a first particle scattering factor (Pθ1) with the first scattering intensity (Iθ1), the 10° scattering intensity (I10), and the angular normalization factor (Nθ1) for the first angle. The method may also include plotting an angular dissymmetry plot, wherein the angular dissymmetry plot comprises the first particle scattering factor (Pθ1). The method may also include fitting a line to the angular dissymmetry plot. The method may also include determining a slope of the line at a selected location on the line. The method may also include determining the radius of gyration (Rg) of the particle in solution from the slope of the line. The method may also include outputting the radius of gyration.

In at least one implementation, determining the angular normalization factor (Nθ1) for the first angle of the detector comprises: passing each of a plurality of known particles in solution through the flowpath of the sample cell; obtaining scattering intensity values of each of the plurality of known particles in solution at an angle of about 10° and at the first angle; and determining the angular normalization factor (Nθ1) for the first angle with a plot of a ratio of the scattering intensity values of each of the plurality of known particles at the first angle to the scattering intensity values of each of the plurality of known particles at an angle of about 10° with respect to a respective weight average molecular weight of each of the plurality of known particles in solution.

In at least one implementation, each of the plurality of known particles in solution have a known molecular weight.

In at least one implementation, the first particle scattering factor (Pθ1) is in the form

Pθ1=(Iθ⁢⁢1I10)Nθ⁢1,
where: Iθ1is the scattering intensity of the particle in solution at the first angle; I10is the scattering intensity of the particle in solution at an angle of about 10°; and Nθ1is the angular normalization factor for the first angle.

In at least one implementation, plotting the angular dissymmetry plot comprises: plotting a first point on a plane, the first point comprising a first coordinate and a second coordinate, wherein the first coordinate of the first point is the first particle scattering factor (Pθ1), and wherein the second coordinate of the first point is in the form

μθ⁢12=(4⁢π⁢n0⁢sin⁢θ⁢12λ)2⁢,
where: n0is a refractive index of the solution; θ1is the first angle; and λ is a wavelength of the beam of light.

In at least one implementation, the line of the angular dissymmetry plot is a straight line.

In at least one implementation, the radius of gyration (Rg) of the particle in solution is less than 10 nm.

In at least one implementation, the method may further include: obtaining an angular normalization factor (Nθ2) of a second angle of the detector, wherein second angle is either about 90° or about 170° relative to the centerline, and wherein the second angle is different from the first angle; obtaining a second scattering intensity (Iθ2) of the particle in solution at the second angle; and determining a second particle scattering factor (Pθ2) with the second scattering intensity (Iθ2), the 10° scattering intensity (I10), and the angular normalization factor (Nθ2) for the second angle. The angular dissymmetry plot may further comprise the second particle scattering factor (Pθ2).

In at least one implementation, determining the angular normalization factor of the second angle of the detector comprises: obtaining scattering intensity values of each of the plurality of known particles in solution at the second angle; and determining the angular normalization factor (Nθ2) for the second angle with a plot of a ratio of the scattering intensity values of each of the plurality of known particles at the second angle to the scattering intensity values of each of the plurality of known particles at an angle of about 10° with respect to a respective weight average molecular weight of each of the plurality of known particles in solution.

In at least one implementation, the second particle scattering factor (Pθ2) is in the form

Pθ2=(Iθ⁢⁢2I10)Nθ2,
where: Iθ2is the scattering intensity of the particle in solution at the second angle; I10is the scattering intensity of the particle in solution at an angle of about 10°; and Nθ2is the angular normalization factor for the second angle.

In at least one implementation, plotting the angular dissymmetry plot further comprises: plotting a second point on the plane, the second point comprising a first coordinate and a second coordinate, wherein the first coordinate of the second point is the second particle scattering factor (Pθ2), and wherein the second coordinate of the second point is in the form μθ22=

(4⁢π⁢n0⁢sin⁢θ22λ)2⁢,
where: n0is a refractive index of the solution; θ2is the second angle; and λ is the wavelength of the beam of light.

In at least one implementation, the line of the angular dissymmetry plot is a curved line.

In at least one implementation, the radius of gyration (Rg) of the particle in solution is less than 100 nm, optionally greater than 10 nm.

DETAILED DESCRIPTION

The following description of various typical aspect(s) is merely exemplary in nature and is in no way intended to limit the disclosure, its application, or uses.

As used throughout this disclosure, ranges are used as shorthand for describing each and every value that is within the range. It should be appreciated and understood that the description in a range format is merely for convenience and brevity, and should not be construed as an inflexible limitation on the scope of any embodiments or implementations disclosed herein. Accordingly, the disclosed range should be construed to have specifically disclosed all the possible subranges as well as individual numerical values within that range. As such, any value within the range may be selected as the terminus of the range. For example, description of a range such as from 1 to 5 should be considered to have specifically disclosed subranges such as from 1.5 to 3, from 1 to 4.5, from 2 to 5, from 3.1 to 5, etc., as well as individual numbers within that range, for example, 1, 2, 3, 3.2, 4, 5, etc. This applies regardless of the breadth of the range.

Additionally, all numerical values are “about” or “approximately” the indicated value, and take into account experimental error and variations that would be expected by a person having ordinary skill in the art. It should be appreciated that all numerical values and ranges disclosed herein are approximate values and ranges, whether “about” is used in conjunction therewith. It should also be appreciated that the term “about,” as used herein, in conjunction with a numeral refers to a value that may be ±0.01% (inclusive), ±0.1% (inclusive), ±0.5% (inclusive), ±1% (inclusive) of that numeral, ±2% (inclusive) of that numeral, ±3% (inclusive) of that numeral, ±5% (inclusive) of that numeral, ±10% (inclusive) of that numeral, or ±15% (inclusive) of that numeral. It should further be appreciated that when a numerical range is disclosed herein, any numerical value falling within the range is also specifically disclosed.

All references cited herein are hereby incorporated by reference in their entireties. In the event of a conflict in a definition in the present disclosure and that of a cited reference, the present disclosure controls.

As used herein, the term or expression “sensitivity” may refer to the ratio of signal to noise. It should be appreciated by one having ordinary skill in the art that increasing laser power does not necessarily improve the sensitivity.

FIG. 1Aillustrates a schematic view of an exemplary light scattering detector (LSD)100including an exemplary sample cell102, according to one or more implementations. The LSD100may be operably coupled with a sample source or device104, and capable of or configured to receive a sample or effluent therefrom. For example, as illustrated inFIG. 1A, the LSD100may be fluidly coupled with the sample source or device104via line106and configured to receive the effluent therefrom. Illustrative sample sources or devices104may include, but are not limited to, a chromatography instrument capable of or configured to separate one or more analytes of a sample or eluent from one another. For example, the sample source or device104may be a liquid chromatography instrument capable of or configured to separate the analytes of the eluent from one another based on their respective charges (e.g., ion exchange chromatography), sizes (e.g., size-exclusion or gel permeation chromatography), or the like. In an exemplary implementation, the LSD100is operably coupled with a liquid chromatography instrument configured to separate the analytes from one another based on their respective sizes. For example, the LSD100is operably coupled with a liquid chromatography instrument including gel permeation chromatography columns.

The LSD100may include the exemplary sample cell102, a collimated beam of light source, such as a laser108, and one or more detectors110,112,114(three are shown) operably coupled with one another. The detectors110,112,114may be any suitable detector capable of or configured to receive analyte scattered light. For example, any one or more of the detectors110,112,114may be a photo-detector, such as a silicon photo-detector. The LSD100may include one or more lenses116,118,120,122,124(five are shown) capable of or configured to refract, focus, attenuate, and/or collect light transmitted through the LSD100, and one or more mirrors126,128(two are shown) capable of or configured to reflect or redirect the light transmitted through the LSD100.

In at least one implementation, a first lens116and a second lens118may be disposed on opposing sides or axial ends of the sample cell102and configured to refract, focus, attenuate, and/or collect light transmitted therethrough. In another implementation, a body130of the sample cell102may define recesses132,134configured to receive the first and second lenses116,118. For example, as illustrated inFIG. 1Aand further illustrated in detail inFIG. 1B, the body130of the sample cell102may define a first recess132and a second recess134extending longitudinally or axially therethrough, and configured to receive the first lens116and the second lens118, respectively. As illustrated inFIGS. 1A and 1B, each of the first and second lenses116,118may define a convex surface along respective first or outer end portions136,138thereof. While the first end portions136,138of the first and second lenses116,118are illustrated as defining convex surfaces, it should be appreciated that any one of the respective first end portions136,138of the first and second lenses116,118may alternatively define a flat surface. As further illustrated inFIG. 1A, each of the first and second lenses116,118may define a flat surface along respective second or inner end portions140,142thereof. As further described herein, the respective second end portions140,142of the first and second lenses116,118may seal and/or at least partially define a channel or flowpath144extending through the sample cell102.

The laser108may be any suitable laser capable of or configured to provide a beam of light146having sufficient wavelength and/or power. For example, the laser108may be a diode laser, a solid state laser, or the like. The laser108may be configured to emit the beam of light146through the sample cell102. For example, as illustrated inFIG. 1A, the laser108may be arranged or disposed about the LSD100such that the beam of light146emitted therefrom is transmitted through the sample cell102. As further illustrated inFIG. 1A, a third lens120may be interposed between the sample cell102and the laser108and configured to focus the beam of light146directed to and through the sample cell102.

In at least one implementation, at least one of the mirrors126,128may be associated with a respective detector110,112, and configured to reflect or redirect the light (e.g., scattered light or analyte scattered light) towards the respective detector110,112. For example, as illustrated inFIG. 1A, a first mirror126may be disposed proximal the first lens116and configured to reflect at least a portion of the light from the first lens116towards a first detector110. In another example, a second mirror128may be disposed proximal the second lens118and/or interposed between the second and third lenses118,120, and configured to reflect at least a portion of the light from the second lens118towards a second detector112. In at least one implementation, one or more lenses122,124may be interposed between the first and second mirrors126,128and the first and second detectors110,112to focus, refract, or otherwise direct the light from the mirrors126,128to the detectors110,112. For example, as illustrated inFIG. 1A, a fourth lens122may be interposed between the first detector110and the first mirror126, and a fifth lens124may be interposed between the second detector112and the second mirror128.

In at least one implementation, at least one of the detectors110,112,114may be configured to receive the light (e.g., scattered light or analyte scattered light) from the sample cell102without the aid or reflection of one of the mirrors126,128. For example, as illustrated inFIGS. 1A and 1B, a third detector114may be disposed adjacent to or coupled with the sample cell102and configured to receive the light (e.g., scattered light) from the sample cell102at an angle of about 90° with respect to the beam of light146. As further discussed herein, an optically transparent material or a sixth lens186may be configured to refract or direct the scattered light toward the third detector114.

As illustrated inFIG. 1A, at least one of the sample cell102, the first, second, and third lenses116,118,120, and the first and second mirrors126,128may be disposed parallel, coaxial, or otherwise aligned with one another along a direction of the beam of light146emitted by the laser108. As further illustrated inFIG. 1A, each of the first and second detectors110,112may be disposed or positioned to receive light (e.g., scattered light or analyte scattered light) from the respective mirrors126,128in a direction generally perpendicular to the beam of light146emitted by the laser108. Each of the first and second mirrors126,128may define a respective bore or pathway150,152extending therethrough. For example, the first mirror126may define a bore150extending therethrough in a direction parallel, coaxial, or otherwise aligned with the beam of light146. Similarly, the second mirror128may define a bore152extending therethrough in the direction parallel, coaxial, or otherwise aligned with the beam of light146. It should be appreciated that the bores150,152extending through the respective mirrors126,128may allow the beam of light146emitted from the laser108to be transmitted through the first and second mirrors126,128to thereby prevent the beam of light146from being reflected towards the first and second detectors110,112.

FIG. 1Dillustrates an enlarged view of the portion of the exemplary LSD100indicated by the box labeled1D ofFIG. 1C, according to one or more implementations. As previously discussed, the body130of the sample cell102may at least partially define the channel or flowpath144extending therethrough. For example, as illustrated inFIG. 1D, an inner surface154of the body130may at least partially define the flowpath144extending therethrough. The flowpath144may define a volume of the sample cell102. The flowpath144may include a central axis or centerline156extending therethrough and configured to define a general orientation of the flowpath144. As illustrated inFIG. 1B, the flowpath144and the central axis156thereof may be aligned or coaxial to the beam of light146emitted from the laser108. The flowpath144of the sample cell102may be interposed between the first and second lenses116,118. In at least one implementation, the first and second lenses116,118may sealingly engage the body130of the sample cell102on opposing sides thereof to thereby prevent a flow of the sample or effluent from the flowpath144via the interface between the body130and the respective first and second lenses116,118. In another implementation, a seal (e.g., gasket, O-ring, etc.) (not shown) may be disposed between the body130and the first and second lenses116,118to provide a fluid tight seal therebetween.

The flowpath144may include an inner section158and two outer sections160,162disposed along the centerline156thereof. As illustrated inFIG. 1D, the inner section158may be interposed between the two outer sections160,162. The inner section158may be fluidly coupled with and configured to receive a sample or effluent from the sample source104. For example, as illustrated inFIG. 1Dwith continued referenced toFIG. 1A, the body130of the sample cell102may define an inlet164extending therethrough and configured to fluidly couple the sample source104with the inner section158via line106. In a preferred implementation, the inlet164is configured such that the sample from the sample source104is directed to the middle or center of the flowpath144or the inner section158thereof.

In at least one implementation, the inner section158may be cylindrical or define a cylindrical volume, and may have a circular cross-sectional profile. It should be appreciated, however, that the cross-sectional profile may be represented by any suitable shape and/or size. For example, the cross-sectional profile may be elliptical, rectangular, such as a rounded rectangle, or the like. The inner section158may have any suitable dimension. In at one implementation, the inner section158may have a length extending between the two outer sections160,162of from about 4 mm to about 12 mm or greater. For example, the inner section158may have a length of from about 4 mm, about 5 mm, about 6 mm, about 7 mm, or about 7.5 mm to about 8.5 mm, about 9 mm, about 10 mm, about 11 mm, about 12 mm, or greater. In another example, the inner section158may have a length of from about 4 mm to about 12 mm, about 5 mm to about 11 mm, about 6 mm to about 10 mm, about 7 mm to about 9 mm, or about 7.5 mm to about 8.5 mm. In a preferred implementation, the inner section158may have a length of from about 7 mm to about 9 mm, preferably about 7.5 mm to about 8.5 mm, more preferably about 8 mm. In at least one implementation, the inner section158may have a diameter of from about 1.2 mm to about 2.0 mm or greater. For example, the inner section158may have a diameter of from about 1.2 mm, about 1.3 mm, about 1.4 mm, about 1.5 mm, or about 1.55 mm to about 1.65 mm, about 1.7 mm, about 1.8 mm, about 1.9 mm, about 2.0 mm, or greater. In another example, the inner section158may have a diameter of from about 1.2 mm to about 2.0 mm, about 1.3 mm to about 1.9 mm, about 1.4 mm to about 1.8 mm, about 1.5 mm to about 1.7 mm, or about 1.55 mm to about 1.65 mm. In a preferred implementation, the inner section158may have a diameter of from about 1.5 mm to about 1.7 mm, preferably about 1.55 mm to about 1.65 mm, more preferably about 1.6 mm.

The outer sections160,162of the flowpath144may be fluidly coupled with the inner section158and configured to receive the sample or effluent therefrom. In at least one implementation, at least one of the first and second outer sections160,162may be cylindrical or define a cylindrical volume, and may have a circular cross-sectional profile. For example, at least one of the first and second outer sections160,162may be sized and shaped similar to the inner section158ofFIG. 1D. In another implementation, at least one of the first and second outer sections160,162may be conical or frustoconical such that a cross-sectional area at a respective first end portion or inlet166,168thereof may be relatively less than a cross-sectional area at a respective second end portion or outlet170,172thereof. In a preferred implementation, the first and second outer sections160,162may both be frustoconical or define a frustum, where the respective first end portions or inlets166,168are configured to receive the sample from the inner section158, and the respective second end portions or outlets170,172are configured to deliver the sample to a waste line174(seeFIG. 1A).

The inner surface154of the body130may at least partially define respective taper angles (θ1, θ2) of the first outer section160and the second outer section162. For example, as illustrated inFIG. 1D, the portion of the inner surface154defining or forming the first outer section160of the flowpath144and the centerline156of the flowpath144may define the respective taper angle (θ1) of the first outer section160. In another example, the portion of the inner surface154defining or forming the second outer section162of the flowpath144and the centerline156of the flowpath144may define the respective taper angle (θ2) of the second outer section162. The first and second outer sections160,162may have any taper angles (θ1, θ2) capable of or configured to allow the LSD100and the detectors110,112,114thereof to receive scattered light at any desired angle. WhileFIG. 1Dillustrates the taper angles (θ1, θ2) of the first and second outer sections160,162to be relatively equal to one another, it should be appreciated that one of the taper angles (θ1, θ2) may be relatively greater than the other. It should further be appreciated that than any one or more attributes (e.g., length, taper angle, diameter, shape, size, etc.) of the first and second outer sections160,162may be different. In a preferred implementation, the attributes (e.g., length, taper angle, diameter, shape, size, etc.) of the first outer section160and the second outer section162are the same or substantially the same.

Each of the outer sections160,162may be fluidly coupled with the waste line174. For example, as illustrated inFIGS. 1A and 1D, the body130may define a first outlet176and a second outlet178extending therethrough and configured to fluidly couple the first outer section160and the second outer section162with the waste line174via a first outlet line180and a second outlet line182, respectively. As further illustrated inFIG. 1D, the first and second outlets176,178may be fluidly coupled with the respective second end portions170,172of the outer sections160,162. It should be appreciated that the orientation (e.g., circumferential orientation) or location of the inlet164and the first and second outlets176,178may vary. For example, the inlet164may be circumferentially aligned with at least one of the first and second outlets176,178. In another example, the inlet164may be circumferentially offset from at least one of the first and second outlets176,178. In yet another example, the first and second outlets176,178may be circumferentially aligned with one another or circumferentially offset from one another.

As illustrated inFIG. 1D, the body130of the sample cell102may define an aperture184extending through at least a portion thereof, and configured to allow light (e.g., scattered light) from the inner section158to be directed or transmitted to the third detector114. The aperture184may be sealed with an optically transparent material186, such as a quartz crystal, to thereby allow the light from the inner section158to be directed to the third detector114. In an exemplary implementation, illustrated inFIGS. 1B and 1D, the optically transparent material186may be shaped to refract a portion of the light towards the third detector114. For example, the optically transparent material186may be the sixth lens (e.g., a ball lens) configured to seal the aperture184and at least partially refract the light towards the third detector114.

In an exemplary operation of the LSD100, with continued reference toFIGS. 1A-1D, the sample source104(e.g., a liquid chromatograph including a gel permeation chromatography column) may inject or direct the sample or effluent (e.g., dilute particle and/or polymer solution) to and through the flowpath144of the sample cell102via line106and the inlet164. As illustrated inFIG. 1D, the sample from the sample source104may be directed toward a center or middle of the flowpath144and/or the inner section158of the sample cell102. As the sample flows to the center of the inner section158, the flow of the of sample may split such that a first portion of the sample flows towards the first outer section160, and a second portion of the sample flows towards the second outer section162. The portions of the sample in the first and second outer sections160,162may then be directed out of the sample cell102and to the waste line174via the first and second outlets176,178and the first and second outlet lines180,182, respectively.

The rate of flow of the sample through the first outer section160and the second outer section162may be modified or adjusted (i.e., increased or decreased) by adjusting the respective lengths of the first outlet line180and the second outlet line182. In at least one implementation, a rate of flow of the first and second portions of the sample through the first and second outer sections160,162may be the same or substantially the same. For example, the rate of flow of the first portion of the sample through the first outer section160is the same or substantially the same as the rate of flow of the second portion of the sample through the second outer section162. In another implementation, the rate of flow of the first and second portions of the sample through the first and second outer sections160,162may be different. It should be appreciated, however, that a time correction may be applied if the rate of flow is different through the first and second outer sections160,162.

As the sample flows through the flowpath144of the sample cell102, the laser108may emit the beam of light146along and through the centerline156of the flowpath144via the bore152of the second mirror128. In at least one implementation, illustrated inFIG. 1A, the beam of light146may be transmitted through the third lens120, which may at least partially focus the beam of light146along the centerline156of the flowpath144. In another implementation, the third lens120may be omitted. In at least one implementation, an optional screen or diaphragm188may be disposed between the laser108and the sample cell102, and configured to “cleanup,” segregate, or otherwise filter stray light (e.g., halo of light) from the beam of light146. For example, the diaphragm188may define a hole or aperture (e.g., adjustable aperture/iris) capable of or configured to filter out stray light from the beam of light146.

At least a portion of the beam of light146may travel or be transmitted from the laser108to and through the sample cell102, the first lens116, the bore152of the second mirror128, and/or an optional diaphragm196. For example, at least a portion of the beam of light146may be transmitted unhindered or without interacting with any of the analytes in the sample from the laser108to and through the sample cell102, the first lens116, the bore152of the second mirror128, and/or the optional diaphragm188. The remaining portion of the beam of light146transmitted through the flowpath144may interact or otherwise contact analytes suspended, dispersed, or otherwise disposed in the sample and/or flowing through the sample cell102.

The contact between the beam of light146and the analytes in the sample may generate or induce scattered light or analyte scattered beams190,192,194(seeFIGS. 1A and 1B). For example, contact between the beam of light146and the analytes contained in the sample or flowing through the flowpath144of the sample cell102may generate forward and back analyte scattered beams190,192. In another example, contact between the beam of light146and the analytes contained in the sample or flowing through the flowpath144of the sample cell102may generate right angle (e.g., about 90° relative to the centerline156) scattered beams194in a direction generally perpendicular to the beam of light146.

It should be appreciated that the flow of the sample to the center of the flowpath144via the inlet164allows the sample to interact immediately with the beam of light146, thereby minimizing peak broadening. For example, flowing the sample directly to the center of the flowpath144allows the sample to interact with the beam of light146without flowing through at least half the length or volume of the sample cell102(e.g., in a lateral or axial direction) and the flowpath144thereof. Flowing the sample directly to the center of the flowpath144also minimizes the amount of time necessary for the sample to interact with the beam of light146and generate the analyte scattered beams190,192,194. It should further be appreciated that one or more components of the LSD100are configured such that only light scattered from the center of the flowpath144are collected by the detectors110,112,114. For example, at least one of the first lens116, the first mirror, and the fourth lens122may be configured to segregate forward light scattering190that originates from the center of the flowpath144from forward light scattering190that originates from other regions of the flowpath144, such that the first detector110only receives forward light scattering190that originates from the center of the flowpath144. Similarly, at least one of the second lens116, the second mirror128, and the fifth lens124may be configured to segregate back light scattering192that originates from the center of the flowpath144from back light scattering192that originates from other regions of the flowpath144, such that the second detector112only receives back light scattering192that originates from the center of the flowpath144.

As illustrated inFIG. 1A, the forward analyte scattered beams or forward scattered light190may be directed towards the first detector110via the first lens116, the first mirror126, and the fourth lens122. At least a portion of the forward scattered light190may be at least partially refracted by the convex surface defined along the first end portion136of the first lens116. As illustrated inFIG. 1A, the forward scattered light190may be refracted by the convex surface toward the first mirror126, and the first mirror126may reflect the forward scattered light190toward the first detector110via the fourth lens122. The fourth lens122may collect the forward scattered light190, and direct and/or focus the forward scattered light190toward the first detector110.

The forward scattered light190may be scattered at varying angles of from greater than 0° to less than 90°, relative to the beam of light146emitted from the laser108and/or the centerline156of the flowpath144. For example, the forward scattered light190may be scattered at any angle of from greater than 0°, about 5°, about 10°, about 15°, about 20°, about 25°, about 30°, about 35°, about 40°, or about 45° to about 50°, about 55°, about 60°, about 65°, about 70°, about 75°, about 80°, about 85°, or less than 90°. In another example, the forward scattered light190may be scattered at any angle of from about 5°, about 6°, about 7°, about 8°, about 9°, or about 9.5° to about 10.5°, about 11°, about 12°, about 13°, about 14°, or about 15°, relative to the beam of light146emitted from the laser108and/or the centerline156of the flowpath144. In yet another example, the forward scattered light190may be scattered at an angle of from about 5° to about 15°, about 6° to about 14°, about 7° to about 13°, about 8° to about 12°, about 9° to about 11°, or about 9.5° to about 10.5°. It should be appreciated that the LSD100and any component thereof may be configured to receive the forward scattered light190scattered at any angle greater than 0° and less than 90°. For example, any one or more attributes (e.g., shape, location, orientation, etc.) of the first detector110, the first lens116, the first mirror126, the fourth lens122, and/or any additional optional diaphragms may be adjusted, modified, or otherwise configured such that the first detector110may receive any of the forward scattered light190. In a preferred implementation, the LSD100and the first detector110thereof is configured to receive or collect the forward scattered light190at an angle of from about 9° to about 11°, preferably about 9.5° to about 10.5°, and more preferably at an angle of about 10°, relative to the beam of light146and/or the centerline156of the flowpath144.

As illustrated inFIG. 1A, the back analyte scattered beams or back scattered light192may be directed towards the second detector112via the second lens118, the second mirror128, and the fifth lens124. At least a portion of the back scattered light192may be at least partially refracted by the convex surface of the second lens118. As illustrated inFIG. 1A, the back scattered light192may be refracted by the convex surface toward the second mirror128, and the second mirror128may reflect the back scattered light192toward the second detector112via the fifth lens124. The fifth lens124may collect the back scattered light192, and direct and/or focus the back scattered light192toward the second detector112.

The back scattered light192may be scattered at varying angles of from greater than 90° to less than 180°, relative to the beam of light146emitted from the laser108and/or the centerline156of the flowpath144. For example, the back scattered light192may be scattered at any angle of from greater than 90°, about 95°, about 100°, about 105°, about 110°, about 115°, about 120°, about 125°, about 130°, or about 135° to about 140°, about 145°, about 150°, about 155°, about 160°, about 165°, about 170°, about 175°, or less than 180°. In another example, the back scattered light192may be scattered at any angle of from about 165°, about 166°, about 167°, about 168°, about 169°, or about 169.5° to about 170.5°, about 171°, about 172°, about 173°, about 174°, or about 175°, relative to the beam of light146emitted from the laser108and/or the centerline156of the flowpath144. In yet another example, the back scattered light192may be scattered at an angle of from about 165° to about 175°, about 166° to about 174°, about 167° to about 173°, about 168° to about 172°, about 169° to about 171°, or about 169.5° to about 170.5°. It should be appreciated that the LSD100and any component thereof may be configured to receive the back scattered light192scattered at any angle greater than 90° and less than 180°. For example, any one or more attributes (e.g., shape, location, orientation, etc.) of the second detector112, the second lens118, the second mirror128, the fifth lens124, and/or any additional optional diaphragms may be adjusted, modified, or otherwise configured such that the second detector112may receive any of the back scattered light192. In a preferred implementation, the LSD100and the second detector112thereof is configured to receive or collect the back scattered light192at an angle of from about 169° to about 171°, preferably about 169.5° to about 170.5°, and more preferably at an angle of about 170°, relative to the beam of light146and/or the centerline156of the flowpath144.

As illustrated inFIG. 1D, the right angle analyte scattered beams or right angle scattered light194may be directed towards the third detector114via the aperture184extending between the third detector114and the inner section158of the flowpath144. In at least one implementation, the third detector114may be disposed in the aperture184adjacent the inner section158. In another implementation, illustrated inFIG. 1D, the optically transparent material186may be disposed in the aperture184to seal the inner section158of the flowpath144. The optically transparent material186may be any suitable material capable of allowing the right angle scattered light194to be transmitted to the third detector114. The optically transparent material186may be shaped to refract at least a portion of the right angle scattered light194toward the third detector114. For example, as previously discussed, the optically transparent material186may be a ball lens shaped to refract the right angle scattered light194toward the third detector114.

The right angle scattered light194may be scattered in a direction generally perpendicular to the beam of light146and/or the centerline156of the flowpath144. For example, the right angle scattered light194may be scattered at an angle of from about 87°, about 88°, about 89°, about 89.5°, or about 90° to about 90.5°, about 91°, about 92°, or about 93°. In another example, the right angle scattered light194may be scattered at an angle of from about 87° to about 93°, about 88° to about 92°, about 89° to about 91°, or about 89.5° to about 90.5°. It should be appreciated that the LSD100and any component thereof may be configured to receive the right angle scattered light194scattered in a direction generally perpendicular to the beam of light146and/or the centerline156of the flowpath144. For example, the shape, location, orientation, or any other attributes of the optically transparent material186(e.g., the sixth lens) and/or the third detector114may be adjusted, modified, or otherwise configured such that the third detector114may receive any of the right angle scattered light194. In a preferred implementation, the LSD100and the third detector114thereof is configured to receive or collect the right angle scattered light194at an angle of from about 89° to about 91°, preferably about 89.5° to about 90.5°, and more preferably at an angle of about 90°, relative to the beam of light146and/or the centerline156of the flowpath144.

The present disclosure may provide methods for determining a radius of gyration (Rg) of a particle (e.g., nanoparticle, microparticle, etc.) in solution using a light scattering detector, such as the LSD100disclosed herein. The particle may be, for example, a polymer, a protein, a protein conjugate, or a DNA fragment. For example, the present disclosure may provide methods for determining the radius of gyration (Rg) of a particle in solution by analyzing data (e.g., via an electronic processor or computer system) from the light scattering detector (e.g., the LSD100). While reference may be made to the LSD100and the components thereof described herein, it should be appreciated that the methods for determining the radius of gyration (Rg) may be conducted or performed with any suitable light scattering detector.

The method for determining a radius of gyration (Rg) of a particle in solution using a light scattering detector (e.g., the LSD100) may include passing or flowing the particle in solution through a flowpath144in a sample cell102of the LSD100, where the centerline156of the flowpath144is aligned with the beam of light146of the LSD100. The method may also include normalizing one or more angles of the light scattering detector (e.g., the LSD100) or determining an angular normalization factor (Nθ) for the one or more angles of the light scattering detector. For example, the method may include determining an angular normalization factor (Nθ) for a first angle. In another example, the method may include determining an angular normalization factor (Nθ) for a first angle and a second angle. As further discussed herein, the first angle may be either about 90° or about 170° relative to the centerline156of the flowpath144, and the second angle may be either about 90° or about 170° and different from the first angle. The method may also include obtaining a first scattering intensity (Iθ1) of the particle in solution at the first angle. The method may also include optionally obtaining a second light scattering intensity (Iθ2) of the particle in solution at the second angle. The method may further include obtaining a 10° scattering intensity (I10) of the particle in solution at an angle of about 10° or less. The method may also include determining a first particle scattering factor (Pθ1) with the first scattering intensity (Iθ1), the 10° scattering intensity (I10), and the angular normalization factor (Nθ1) for the first angle. The method may also include optionally determining a second particle scattering factor (Pθ2) with the second scattering intensity (Iθ2), the 10° scattering intensity (I10), and the angular normalization factor (Nθ2) for the second angle. The method may also include plotting an angular dissymmetry plot, fitting a line to the angular dissymmetry plot, and determining a slope of the line of the angular dissymmetry plot at a selected location. The method may also include determining the radius of gyration (Rg) of the particle in solution from the slope of the line, and optionally, outputting or displaying the radius of gyration.

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may include normalizing the one or more angles of the light scattering detector or determining an angular normalization factor (Nθ) for the one or more angles of the LSD100. Determining an angular normalization factor (Nθ) for one or more angles of the LSD100may be performed to account for scattering volume differences of the LSD100or varying sensitivities of any one or more of the detectors110,112,114.

In at least one implementation, only one angle of the LSD100is normalized. For example, one or a first angle of the LSD100that may be normalized may include either an angle of about 90° or about 170°. In another implementation, two or first and second angles of the LSD100are normalized. For example, a first angle at about 90° and a second angle at about 170° are normalized. The number of angles normalized may be at least partially determined by a size or radius of gyration of the particle. For example, only one or the first angle of the LSD100may be normalized for determining the Rg of a particle having an Rg of less than or equal to about 10 nm. In another example, two or first and second angles of the LSD100may be normalized for determining the Rg of a particle having an Rg of about 10 nm or greater to about 100 nm. It should be appreciated that the first and second angles of the LSD100may also be normalized for determining the Rg of a particle having an Rg of less than 10 nm.

Normalizing an angle (e.g., 90°, 170°, etc.) of the LSD100or determining an angular normalization factor (Nθ) for the angle may include passing a plurality of known particle standards (e.g., known polymer standards) in solution through the flowpath144of the sample cell102, passing the beam of light146through the centerline156of the flowpath144, collecting the analyte scattered light192,194at the angle, and determining a scattering intensity (Iθ) at the angle with the analyte scattered light192,194collected at the angle. For example, determining the angular normalization factor (Nθ) for an angle of about 90° or about 170° may include passing a plurality of known particle standards in solution through the flowpath144of the sample cell102, passing the beam of light146through the centerline156of the flowpath144, collecting the analyte scattered light192,194at the angle of about 90° or about 170°, respectively, and determining a scattering intensity (Iθ) at the angle of about 90° (I90) or about 170° (I170) with the analyte scattered light192,194collected at the angle of about 90° or about 170°, respectively.

Determining the angular normalization factor (Nθ) for the angle (e.g., 90°, 170°, etc.) may also include collecting the analyte scattered light190at an angle (e.g., 0°) close to or incident with the beam of light146and determining a scattering intensity (I0) at the angle close to or incident with the beam of light. It should be appreciated that collecting the analyte scattered light190at an angle of about 0° relative to the centerline156is not possible, as the signal from the beam of light146is relatively greater than any analyte scattered light at the angle of about 0°; and thus, would mask any analyte scattered light at the angle of about 0°. As such, the analyte scattered light190is collected at an angle close to the beam of light146. For example, it is assumed that analyte scattered light190collected at an angle of about 10° or less is equivalent to the analyte scattered light collected at about 0°. As such, the scattering intensity at an angle of about 10° (I10) is equivalent or substantially equivalent to the scattering intensity at about 0° (I0).

Determining the angular normalization factor (Nθ) for the angle (e.g., 90°, 170°, etc.) may also include plotting a ratio of the scattering intensity values of each of the plurality of known particles at the angle (e.g., 90°, 170°, etc.) to the scattering intensity values of each of the plurality of known particles at an angle of about 10° (I10), namely a ratio of (Iθ/I10), versus a respective weight average molecular weight of each of the plurality of known particles. An illustrative plot of the ratio (Iθ/I10) versus the respective weight average molecular weight of each of the plurality of known particles is shown inFIG. 2. For example, determining the angular normalization factor (N90) for an angle of about 90° may include plotting the ratio (I90/I10) of the scattering intensity (I90) values of each of the plurality of known particles at an angle of about 90° to the scattering intensity values (I10) of each of the plurality of known particles at an angle of about 10° versus the respective weight average molecular weight of each of the plurality of known particles. In another example, determining the angular normalization factor (N170) for an angle of about 170° may include plotting the ratio (I170/I10) of the scattering intensity (I170) values of each of the plurality of known particles at an angle of about 170° to the scattering intensity (I10) values of each of the plurality of known particles at an angle of about 10° versus the respective weight average molecular weight of each of the plurality of known particles.

Determining the angular normalization factor (Nθ) for the angle (e.g., 90°, 170°, etc.) may also include fitting a line to the plot of the ratio (Iθ/I10) versus the respective weight average molecular weight of each of the plurality of known particles. For example, as illustrated inFIG. 2, determining the angular normalization factor (N90) for the angle at about 90° may include fitting a line202to the plot of the ratio (I90/I10) versus the respective weight average molecular weight of each of the plurality of known particles. In another example, illustrated inFIG. 2, determining the angular normalization factor (N170) for the angle at about 170° may include fitting a line204to the plot of the ratio (I170/I10) versus the respective weight average molecular weight of each of the plurality of known particles.

Determining the angular normalization factor (Nθ) for the angle (e.g., 90°, 170°, etc.) may further include extrapolating the respective lines202,204of each of the plots to determine the angular normalization factor (Nθ). It should be appreciated that the angular normalization factor (Nθ) for the angle may be the extrapolated value at a molecular weight or x-value of 0. For example, the angular normalization factor (Nθ) for the respective angle may be the value at a respective y-intercept206,208of each of the lines202,204. For example, as illustrated inFIG. 2, the angular normalization factor (N90), as determined by the y-intercept206, for the angle at about 90° is about 1.0099. As further illustrated inFIG. 2, the angular normalization factor (N170), as determined by the y-intercept208, for the angle at about 170° is about 0.7807.

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may include obtaining a first light scattering intensity (Iθ1) of the particle in solution (e.g., the unknown particle in solution) at the first angle (e.g., 90°, 170°, etc.), and optionally obtaining a second light scattering intensity (Iθ2) of the particle in solution at the second angle. For example, the method may include passing the particle in solution through the flowpath144in the sample cell102, collecting the analyte scattered light192,194at the first angle and/or the second angle, and determining the scattering intensity of the first angle (Iθ1) and/or the second angle (Iθ2).

The method may also include obtaining a scattering intensity (I0) of the particle in solution at an angle close to or incident with the beam of light146by collecting the analyte scattered light190at an angle of about 0° relative to the centerline156. As discussed above, collecting the analyte scattered light190at an angle of about 0° relative to the centerline156is not possible, as the signal from the beam of light146is relatively greater than any analyte scattered light at the angle of about 0°; and thus, would mask any analyte scattered light at the angle of about 0°. As such, the analyte scattered light190of the particle in solution is collected at an angle close to the beam of light146. For example, it is assumed that analyte scattered light190collected at an angle of about 10° or less is equivalent to the analyte scattered light collected at about 0°. As such, the scattering intensity (I10) of the particle in solution at an angle of about 10° is equivalent to the scattering intensity (I0) of the particle in solution at about 0°.

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may include determining a first particle scattering factor (Pθ1) with or utilizing the first scattering intensity (Iθ1), the 10° scattering intensity (I10), and the angular normalization factor (Nθ1) for the first angle. The method for determining the radius of gyration (Rg) of the particle in solution may also, optionally, include determining a second particle scattering factor (Pθ2) with or utilizing the second scattering intensity (Iθ2), the 10° scattering intensity (I10), and the angular normalization factor (Nθ2) for the second angle.

In at least one implementation, the particle scattering factor (Pθ) may be represented by equation (1):

Pθ=(IθI10)Nθ,(1)
where:Iθmay be the scattering intensity of the particle in solution at a respective angle (e.g., about 90° or about 170°);I10is the scattering intensity of the particle in solution at an angle of about 10° or less; andNθis the angular normalization factor for the respective angle.
It should be appreciated that the particle scattering factor (P0) at 0° may be assumed to be the same particle scattering factor (P10) at about 10°, which is equal to one (1).

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may further include plotting an angular dissymmetry plot. Illustrative angular dissymmetry plots are shown inFIGS. 3 and 4. The angular dissymmetry plot may include one or more points on a plane. For example, the angular dissymmetry plot may include one, two, three, four, or more points on a plane. As illustrated inFIG. 3, the angular dissymmetry plot may include a first point302and a second point304. As further illustrated inFIG. 4, the angular dissymmetry plot may include a first point402, a second point404, and a third point406. Each of the points302,304,402,404,406may include a first coordinate, such as an x-coordinate, and a second coordinate, such as a y-coordinate. The first or x-coordinate may be represented by μ2, which may be expressed by equation (2):

μθ2=(4⁢π⁢n0⁢sin⁢θ2λ)2,(2)
where:n0is a refractive index of the solution in which the particle is contained;θ is the respective angle (e.g., about 90° or about 170°); andλ is a wavelength of the beam of light.
The second or y-coordinate may be represented by the respective particle scattering factor (Pθ). It should be appreciated that the beam of light may have any suitable wavelength. In at least one implementation, the wavelength may be from about 400 nm to about 600 nm. For example, the wavelength of the beam of light may be from about 400 nm, about 450 nm, or about 500 nm to about 550 nm, or about 600 nm. In a preferred implementation, the wavelength of the beam of light may be from about 450 nm to about 550 nm, about 500 nm to about 530 nm, or about 515 nm. In one implementation, the wavelength of the beam of light may exclude wavelengths of about 600 nm or greater to about 700 nm.

As illustrated inFIG. 3, the angular dissymmetry plot may include the first point302corresponding to the angle at 0°, or about 10° based on the assumption discussed above, and the second point304corresponding to either an angle of about 90° or an angle of about 170°. A first or x-coordinate of the first point302is equal to μ2, which according to equation 2 is equal to zero (0). A second coordinate of the first point302is equal to the particle scattering factor (P10), which is equal to one (1). Similarly, a first or x-coordinate of the second point304is equal to μ2calculated at either about 90° or about 170°, and a second or y-coordinate of the second point304is equal to the respective particle scattering factor (Pθ). As illustrated inFIG. 4, the angular dissymmetry plot may include the first point402corresponding to the angle at 0°, or about 10° based on the assumptions discussed above, the second point404corresponding to the angle at about 90°, and the third point406corresponding to the angle at about 170°. The respective first and second coordinates of each of the first, second, and third points402,404,406of the angular dissymmetry plot ofFIG. 4may be determined as discussed above.

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may also include fitting a line306,408to the angular dissymmetry plot. Fitting the line306,408to the angular dissymmetry plot may include a least squares fitting. The line306,408may include a polynomial degree of less than three. The line306,408may be a straight line or a curved line. For example, as illustrated inFIG. 3, the line306may be a straight line and have a polynomial degree of one. In another example, illustrated inFIG. 4, the line408may be curved line that may have a quadratic relationship and a polynomial degree of two.

As discussed above, the method for determining the radius of gyration (Rg) of the particle in solution may include determining a slope of the line306,408at a selected location on the line306,408. The selected location on the line306,408may be anywhere along the line. In at least one implementation, the selected location on the line306,408may be at a y-intercept or where the x-value is zero.

The method for determining the radius of gyration (Rg) of the particle in solution may also include calculating or determining the radius of gyration (Rg) of the particle in solution with or from the slope of the line306,408at the selected location. The radius of gyration (Rg) of the particle in solution may be represented by equation (3):
Rg2=−3×b(3),
where b is slope of the line at the selected location.

The method for determining the radius of gyration (Rg) of the particle in solution may also include outputting or displaying the radius of gyration (Rg). For example, the method may include outputting the radius of gyration (Rg) on a display (e.g., computer display), a readout, a report, or a disk storage of a computing system, such as the computing system described herein.

FIG. 5illustrates a computer system or electronic processor500for receiving and/or analyzing data from the LSD100, according to one or more implementations. The computer system or electronic processor500may be a general purpose computer, and may allow a user or chromatographer to process data, analyze data, interpret data, store data, retrieve data, display data, display results, interpret results, store results, or any combination thereof. The results may be graphical in form and/or tabular in form. It should be appreciated that, while the electronic processor500is shown operably and/or communicably coupled with the LSD100ofFIG. 1A, the electronic processor500may be operably and/or communicably coupled with any suitable light scattering detector known in the art.

The computer system or electronic processor500may be capable of or configured to operate, communicate with (e.g., send/receive data), modify, modulate, or otherwise run any one or more components of the LSD100. For example, the electronic processor500may be operably and/or communicably coupled with and capable of or configured to operate, communicate with, modify, modulate, or otherwise run a pump (not shown), the laser108, the sample source104, any one or more of the detectors110,112,114, or any other component of the LSD100.

In at least one implementation, illustrated inFIG. 5, the electronic processor500may be operably and/or communicably coupled with the detectors110,112,114and capable of or configured to send and/or received signals and/or data502therefrom. The data502from the one or more detectors110,112,114may be or include analog data, such as fluctuating analog voltage. In at least one implementation, the electronic processor500may be capable of or configured to convert the analog data to digital data. For example, the electronic processor500may include an analog to digital converter (not shown). In another implementation, an analog to digital converter may be interposed between the LSD100or the detectors110,112,114thereof and the electronic processor500.

The electronic processor500may be capable of or configured to receive, collect, record, and/or store data502from any one or more components of the LSD100. For example, as illustrated inFIG. 5, the electronic processor500may receive data502from the one or more detectors110,112,114of the LSD100, optionally convert the data502, and record and/or store the data502in a computer memory, such as a local drive or network drive (e.g., cloud drive).

The electronic processor500may be capable of or configured to analyze, process, display, and/or output data502. For example, the electronic processor500may include software capable of or configured to analyze, process, display, and/or output data502. The software may also be capable of or configured to process the data502and output or display the data502on a workstation or display504. The software may include any one or more of the algorithms, equations, methods, steps, processes, or formulas disclosed herein. The electronic processor500may process and/or extract information from the data502to prepare results, and present the data502and/or the results, such as in a report or on the display504. The electronic processor500may include a graphical user interface (GUI) that allows a user or the chromatographer to interact with all systems, subsystems, and/or components of the electronic processor500and/or the LSD100.

FIG. 6illustrates a block diagram of the computer system or electronic processor500ofFIG. 5that may be used in conjunction with one or more light scattering detectors, including the LSD100, and/or one or more methods disclosed herein. For example, the computing system500(or system, or server, or computing device, or device) may represent any of the devices or systems described herein that perform any of the processes, operations, or methods of the disclosure. Note that while the computing system500illustrates various components, it is not intended to represent any particular architecture or manner of interconnecting the components as such details are not germane to the present disclosure. It will also be appreciated that other types of systems that have fewer or more components than shown may also be used with the present disclosure.

As shown, the computing system500may include a bus602which may be coupled to a processor604, ROM (Read Only Memory)608, RAM (or volatile memory)610, and storage (or non-volatile memory)612. The processor604may store data502(seeFIG. 5) in one or more of the memories608,610,612. The processor604may also retrieve stored data from one or more of the memories608,610, and612. The one or more memories608,610,612may store the software disclosed therein, which may include instructions to perform any one or more of the processes, operations, or methods described herein. The processor604may also retrieve stored software or the instructions thereof from one or more of the memories608,610, and612and execute the instructions to perform any one or more of the processes, operations, or methods described herein. These memories represent examples of a non-transitory computer-readable medium (or machine-readable medium) or storage containing instructions which when executed by a processor604(or system, or computing system), cause the processor604to perform any one or more of the processes, operations, or methods described herein. The RAM610may be implemented as, for example, dynamic RAM (DRAM), or other types of memory that require power continually in order to refresh or maintain the data in the memory. Storage612may include, for example, magnetic, semiconductor, tape, optical, removable, non-removable, and/or other types of storage that maintain data even after power is removed from the computer system500. It should be appreciated that storage612may be remote from the system500(e.g. accessible via a network).

A display controller614may be coupled to the bus602in order to receive data to be displayed on a display504, which may display any one of the user interface features or implementations described herein and may be a local or a remote display device504. The computing system500may also include one or more input/output (I/O) components616including mice, keyboards, touch screen, network interfaces, printers, speakers, and other devices. Typically, the input/output components616are coupled to the system500through an input/output controller618.

Modules620(or program code, instructions, components, subsystems, units, functions, or logic) may represent any of the instructions, subsystems, steps, methods, equations, calculations, plots, or engines described above. Modules620may reside, completely or at least partially, within the memories described above (e.g. non-transitory computer-readable media), or within a processor604during execution thereof by the computing system500. In addition, Modules620may be implemented as software, firmware, or functional circuitry within the computing system500, or as combinations thereof.

The present disclosure has been described with reference to exemplary implementations. Although a limited number of implementations have been shown and described, it will be appreciated by those skilled in the art that changes may be made in these implementations without departing from the principles and spirit of the preceding detailed description. It is intended that the present disclosure be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.