Another absolute instrumental approach was also possible with the development of light scattering theory by Albert Einstein, Chandrasekhara Venkata Raman, Peter Debye, Bruno H. Zimm, and others. The problem with measurements made using membrane osmometry and sedimentation was that they only characterized the bulk properties of the polymer sample. Moreover, the measurements were excessively time consuming and prone to operator error. In order to gain information about a polydisperse mixture of molar masses, a method for separating the different sizes was developed. This was achieved by the advent of size exclusion chromatography (SEC). SEC is based on the fact that the pores in the packing material of chromatography columns could be made small enough for molecules to become temporarily lodged in their interstitial spaces. As the sample makes its way through a column the smaller molecules spend more time traveling in these void spaces than the larger ones, which have fewer places to "wander". The result is that a sample is separated according to its hydrodynamic volume. As a consequence, the big molecules come out first, and then the small ones follow in the eluent. By choosing a suitable column packing material it is possible to define the resolution of the system. Columns can also be combined in series to increase resolution or the range of sizes studied.
The next step is to convert the time at which the samples eluted into a measurement of molar mass. This is possible because if the molar mass of a standard were known, the time at which this standard eluted should be equal to a specific molar mass. Using multiple standards, a calibration curve of time versus molar mass can be developed. This is significant for polymer analysis because a single polymer could be shown to have many different components, and the complexity and distribution of which would also affect the physical properties. However this technique has shortcomings. For example, unknown samples are always measured in relation to known standards, and these standards may or may not have similarities to the sample of interest. The measurements made by SEC are then mathematically converted into data similar to that found by the existing techniques.
The problem was that the system was calibrated according to the Vh characteristics of polymer standards that are not directly related to the molar mass. If the relationship between the molar mass and Vh of the standard is not the same as that of the unknown sample, then the calibration is invalid. Thus, to be accurate, the calibration must use the same polymer, of the same conformation, in the same eluent and have the same interaction with the solvent as the hydration layer changes Vh.
Benoit et al. showed that taking into account the hydrodynamic volume would solve the problem. In his publication, Benoit showed that all synthetic polymers elutes on the same curve when the log of the intrinsic viscosity multiplied by the molar mass was plotted against the elution volume. This is the basis of universal calibration which requires a viscometer to measure the intrinsic viscosity of the polymers. Universal calibration was shown to work for branched polymers, copolymers as well as starburst polymers.
For good chromatography, there must be no interaction with the column other than that produced by size. As the demands on polymer properties increased, the necessity of getting absolute information on the molar mass and size also increased. This was especially important in pharmaceutical applications where slight changes in molar mass (e.g. aggregation) or shape may result in different biological activity. These changes can actually have a harmful effect instead of a beneficial one.
To obtain molar mass, light scattering instruments need to measure the intensity of light scattered at zero angle. This is impractical as the laser source would outshine the light scattering intensity at zero angle. The 2 alternatives are to measure very close to zero angle or to measure at many angle and extrapolate using a model (Rayleigh, Rayleigh–Gans–Debye, Berry, Mie, etc.) to zero degree angle.
Traditional light scattering instruments worked by taking readings from multiple angles, each being measured in series. A low angle light scattering system was developed in the early 1970s that allowed a single measurement to be used to calculate the molar mass. Although measurements at low angles are better for fundamental physical reasons (molecules tend to scatter more light in lower angle directions than in higher angles), low angle scattering events caused by dust and contamination of the mobile phase easily overwhelm the scattering from the molecules of interest. When the low-angle laser light scattering (LALLS) became popular in the 1970s and mid-1980s, good quality disposable filters were not readily available and hence multi-angle measurements gained favour.
Multi-angle light scattering was invented in the mid-1980s and instruments like that were able to make measurements at the different angles simultaneously but it was not until the later 1980s (10-12)[clarify] that the connection of multi-angle laser light scattering (MALS) detectors to SEC systems was a practical proposition enabling both molar mass and size to be determined from each slice of the polymer fraction.
Applications
Light scattering measurements can be applied to synthetic polymers, proteins, pharmaceuticals and particles such as liposomes, micelles, and encapsulated proteins. Measurements can be made in one of two modes which are un-fractionated (batch mode) or in continuous flow mode (with SEC, HPLC or any other flow fractionation method). Batch mode experiments can be performed either by injecting a sample into a flow cell with a syringe or with the use of discrete vials. These measurements are most often used to measure timed events like antibody-antigen reactions or protein assembly. Batch mode measurements can also be used to determine the second virial coefficient (A2), a value that gives a measure of the likelihood of crystallization or aggregation in a given solvent. Continuous flow experiments can be used to study material eluting from virtually any source. More conventionally, the detectors are coupled to a variety of different chromatographic separation systems. The ability to determine the mass and size of the materials eluting then combines the advantage of the separation system with an absolute measurement of the mass and size of the species eluting.
The addition of an SLS detector coupled downstream to a chromatographic system allows the utility of SEC or similar separation combined with the advantage of an absolute detection method. The light scattering data is purely dependent on the light scattering signal times the concentration; the elution time is irrelevant and the separation can be changed for different samples without recalibration. In addition, a non-size separation method such as HPLC or IC can also be used. As the light scattering detector is mass dependent, it becomes more sensitive as the molar mass increases. Thus it is an excellent tool for detecting aggregation. The higher the aggregation number, the more sensitive the detector becomes.
Low-angle (laser)-light scattering (LALS) method
LALS measurements are measuring at a very low angle where the scattering vector is almost zero. LALS does not need any model to fit the angular dependence and hence is giving more reliable molecular weights measurements for large molecules. LALS alone does not give any indication of the root mean square radius.
MALS measurements work by calculating the amount of light scattered at each angle detected. The calculation is based on the intensity of light measured and the quantum efficiency of each detector. Then a model is used to approximate the intensity of light scattered at zero angle. The zero angle light scattered is then related to the molar mass.
As previously noted, the MALS detector can also provide information about the size of the molecule. This information is the Root Mean Square radius of the molecule (RMS or Rg). This is different from the Rh mentioned above who is taking the hydration layer into account. The purely mathematical root mean square radius is defined as the radii making up the molecule multiplied by the mass at that radius.
B.H. Zimm, R.S. Stein and P. Dotty, Pol. Bull. 1,(1945), 90
M. Fixman, J. Chem. Phys. 23 (1955), 2074
A.C. Ouano and W. Kaye J. Poly. Sci. A1(12) (1974), 1151
Z. Grubisic, P. Rempp, and H. Benoit, J. Polym. Sci., 5 (1967), 753
Flow Through MALS detector, DLS 800, Science Spectrum Inc.
P.J. Wyatt, C. Jackson and G.K. Wyatt Am. Lab 20(6) (1988), 86
P.J. Wyatt, D. L. Hicks, C. Jackson and G.K. Wyatt Am. Lab. 20(6) (1988), 106
C. Jackson, L.M. Nilsson and P.J. Wyatt J. Appl. Poly. Sci. 43 (1989), 99
Related Research Articles
The molecular mass (m) is the mass of a given molecule: it is measured in daltons. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quantity relative molecular mass, as defined by IUPAC, is the ratio of the mass of a molecule to the unified atomic mass unit and is unitless. The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of a substance and is expressed in g/mol. That makes the molar mass an average of many particles or molecules, and the molecular mass the mass of one specific particle or molecule. The molar mass is usually the more appropriate figure when dealing with macroscopic (weigh-able) quantities of a substance.
Size-exclusion chromatography (SEC), also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their size, and in some cases molecular weight. It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers. Typically, when an aqueous solution is used to transport the sample through the column, the technique is known as gel-filtration chromatography, versus the name gel permeation chromatography, which is used when an organic solvent is used as a mobile phase. The chromatography column is packed with fine, porous beads which are commonly composed of dextran, agarose, or polyacrylamide polymers. The pore sizes of these beads are used to estimate the dimensions of macromolecules. SEC is a widely used polymer characterization method because of its ability to provide good molar mass distribution (Mw) results for polymers.
In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsistent size, shape and mass distribution is called non-uniform. The objects can be in any form of chemical dispersion, such as particles in a colloid, droplets in a cloud, crystals in a rock, or polymer macromolecules in a solution or a solid polymer mass. Polymers can be described by molecular mass distribution; a population of particles can be described by size, surface area, and/or mass distribution; and thin films can be described by film thickness distribution.
Gel permeation chromatography (GPC) is a type of size-exclusion chromatography (SEC), that separates analytes on the basis of size, typically in organic solvents. The technique is often used for the analysis of polymers. As a technique, SEC was first developed in 1955 by Lathe and Ruthven. The term gel permeation chromatography can be traced back to J.C. Moore of the Dow Chemical Company who investigated the technique in 1964. The proprietary column technology was licensed to Waters Corporation, who subsequently commercialized this technology in 1964. GPC systems and consumables are now also available from a number of manufacturers. It is often necessary to separate polymers, both to analyze them as well as to purify the desired product.
Gas chromatography (GC) is a common type of chromatography used in analytical chemistry for separating and analyzing compounds that can be vaporized without decomposition. Typical uses of GC include testing the purity of a particular substance, or separating the different components of a mixture. In preparative chromatography, GC can be used to prepare pure compounds from a mixture.
The molar mass distribution describes the relationship between the number of moles of each polymer species (Ni) and the molar mass (Mi) of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation.
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer.
Elastic recoil detection analysis (ERDA), also referred to as forward recoil scattering, is an ion beam analysis technique in materials science to obtain elemental concentration depth profiles in thin films. This technique is known by several different names. These names are listed below. In the technique of ERDA, an energetic ion beam is directed at a sample to be characterized and there is an elastic nuclear interaction between the ions of beam and the atoms of the target sample. Such interactions are commonly of Coulomb nature. Depending on the kinetics of the ions, cross section area, and the loss of energy of the ions in the matter, ERDA helps determine the quantification of the elemental analysis. It also provides information about the depth profile of the sample.
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon auto-correlation function. In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions.
An integrating sphere is an optical component consisting of a hollow spherical cavity with its interior covered with a diffuse white reflective coating, with small holes for entrance and exit ports. Its relevant property is a uniform scattering or diffusing effect. Light rays incident on any point on the inner surface are, by multiple scattering reflections, distributed equally to all other points. The effects of the original direction of light are minimized. An integrating sphere may be thought of as a diffuser which preserves power but destroys spatial information. It is typically used with some light source and a detector for optical power measurement. A similar device is the focusing or Coblentz sphere, which differs in that it has a mirror-like (specular) inner surface rather than a diffuse inner surface.
Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A2, can be calculated.
Low-angle laser light scattering or LALLS is an application of light scattering that is particularly useful in conjunction with the technique of Size exclusion chromatography, one of the most powerful and widely used techniques to study the molecular mass distribution of a polymer.
Particle size analysis, particle size measurement, or simply particle sizing, is the collective name of the technical procedures, or laboratory techniques which determines the size range, and/or the average, or mean size of the particles in a powder or liquid sample.
Field-flow fractionation, abbreviated FFF, is a separation technique which does not have a stationary phase. It is similar to liquid chromatography as it works on dilute solutions or suspensions of the solute. Separation is achieved by applying a field perpendicular to the direction of transport of the sample which is pumped through a long and narrow channel. The field exerts a force on the sample components concentrating them towards one of the channel walls, which is called accumulation wall. The force interacts with a property of the sample on which then the separation occurs, in other words on their differing "mobilities" under the force exerted by the field. As an example, for the hydraulic, or cross-flow FFF method, the property driving separation is the translational diffusion coefficient or the hydrodynamic size. For a thermal field, it is the ratio of the thermal and the translational diffusion coefficient.
Polymer characterization is the analytical branch of polymer science.
Multiangle light scattering (MALS) describes a technique for measuring the light scattered by a sample into a plurality of angles. It is used for determining both the absolute molar mass and the average size of molecules in solution, by detecting how they scatter light. A collimated beam from a laser source is most often used, in which case the technique can be referred to as multiangle laser light scattering (MALLS). The insertion of the word laser was intended to reassure those used to making light scattering measurements with conventional light sources, such as Hg-arc lamps that low-angle measurements could now be made. Until the advent of lasers and their associated fine beams of narrow width, the width of conventional light beams used to make such measurements prevented data collection at smaller scattering angles. In recent years, since all commercial light scattering instrumentation use laser sources, this need to mention the light source has been dropped and the term MALS is used throughout.
A chromatography detector is a device used in gas chromatography (GC) or liquid chromatography (LC) to detect components of the mixture being eluted off the chromatography column. There are two general types of detectors: destructive and non-destructive. The destructive detectors perform continuous transformation of the column effluent with subsequent measurement of some physical property of the resulting material. The non-destructive detectors are directly measuring some property of the column eluent and thus affords greater analyte recovery.
A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item under study and the referenced unit of measurement. Measuring instruments, and formal test methods which define the instrument's use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error and measurement uncertainty. These instruments may range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators. Virtual instrumentation is widely used in the development of modern measuring instruments.
Brookhaven Instruments Corporation is a Nova Instruments company established in the late 1960s. Brookhaven Instruments designed modern techniques in characterizing nanoparticles, proteins, and polymers using light scattering techniques such as dynamic, static, electrophoretic, and phase analysis for: particle size, zeta potential, molecular mass, and absolute molar mass analysis.
Asymmetrical flow field-flow fractionation (AF4) is most versatile and most widely used sub-technique within the family of field flow fractionation (FFF) methods. AF4 can be used in aqueous and organic solvents and is able to characterize nanoparticles, polymers and proteins. The theory for AF4 was conceived in 1986 and was established in 1987 and first published by Wahlund and Giddings. AF4 is distinct from symmetrical Flow FFF because it contains only one permeable wall so the cross-flow is caused only by the carrier liquid. The cross-flow is induced by the carrier liquid constantly exiting by way of the semi-permeable wall on the bottom of the channel.
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