Absolute molar mass
Encyclopedia
Absolute Molar Mass is a process to determine the characteristics of molecules.

History

The first absolute measurements of molecular weights (i.e. made without reference to standards) were based on fundamental physical characteristics and their relation to the molar mass. The most useful of these were Membrane Osmometry and Sedimentation
Sedimentation
Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained, and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration...

.

Another absolute instrumental approach was also possible with the development of light scattering
Light scattering
Light scattering is a form of scattering in which light is the form of propagating energy which is scattered. Light scattering can be thought of as the deflection of a ray from a straight path, for example by irregularities in the propagation medium, particles, or in the interface between two media...

 theory by Einstein, Raman
Chandrasekhara Venkata Raman
Sir Chandrasekhara Venkata Raman, FRS was an Indian physicist whose work was influential in the growth of science in the world. He was the recipient of the Nobel Prize for Physics in 1930 for the discovery that when light traverses a transparent material, some of the light that is deflected...

, Debye
Peter Debye
Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

, Zimm
Bruno H. Zimm
Bruno Hasbrouck Zimm was an American chemist. He was a professor emeritus of chemistry and biochemistry from University of California, San Diego, and a leading polymer chemist and DNA researcher.-Early life:...

, and others. The problem with measurements made using membrane osmometry and sedimentation was that they only characterized the bulk properties of the polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...

 sample. Moreover, the measurements were excessively time consuming and prone to operator error. In order to gain information about a polydisperse
Polydisperse
A collection of objects is called polydisperse or polysized if they have a broad range of size, shape and mass characteristics. A sample of objects that have a uniform size, shape and mass distribution are called monodisperse. In practice, polydisperse collections are common because it is...

 mixture of molar masses, a method for separating the different sizes was developed. This was achieved by the advent of Size exclusion chromatography
Size exclusion chromatography
Size-exclusion 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...

 (SEC). SEC is based on the fact that the pores in the packing material of chromatography columns
Chromatography
Chromatography is the collective term for a set of laboratory techniques for the separation of mixtures....

 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 elute. 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
Calibration curve
In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration...

 of time versus molar mass was 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 were always measured in relation to known standards, and these standards may or may not have had any similarities to the sample of interest. The measurements made by SEC were 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
Molar mass
Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

 (e.g. aggregation
Particle aggregation
Particle aggregation in materials science is direct mutual attraction between particles via van der Waals forces or chemical bonding....

) or shape may result in different biological activity
Biological activity
In pharmacology, biological activity or pharmacological activity describes the beneficial or adverse effects of a drug on living matter. When a drug is a complex chemical mixture, this activity is exerted by the substance's active ingredient or pharmacophore but can be modified by the other...

. 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) 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 polymer
Synthetic polymer
Synthetic polymers are often referred to as "plastics", such as the well-known polyethylene and nylon. However, most of them can be classified in at least three main categories: thermoplastics, thermosets and elastomers....

s, protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s, pharmaceuticals and particles such as liposome
Liposome
Liposomes are artificially prepared vesicles made of lipid bilayer. Liposomes can be filled with drugs, and used to deliver drugs for cancer and other diseases. Liposomes are composite structures made of phospholipids and may contain small amounts of other molecules...

s, 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.

Multi Angle (Laser) Light Scattering (MALS) Method

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.
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