The drive to develop synthetic rubber during World War II spurred the first research efforts into theory and practice of light scattering for characterization of macromolecules in solution. Since then light scattering technology has evolved into the sophisticated, robust instruments developed – and continually refined - by Wyatt Technology. Absolute analysis of synthetic polymers to determine molecular weight, size, branching and conformation remains one of the primary applications of multi-angle light scattering.
Sample and reference polymers with the same hydrodynamic volume elute from a GPC column at the same time, but do not have the same molecular weights. SEC-MALS determines polymer molar mass independently of elution time.
Absolute molar mass & size
Only multi-angle light scattering (MALS) can determine the absolute molar mass and size distributions of heterogeneous polymers independently of retention time and molecular standards, and regardless of non-ideal column interactions. That's because MALS measures molecular weight and rms radius (a.k.a. radius of gyration) directly from first principles. All you need is a convenient means of size-based separation preceding the on-line MALS detector.
Couple a DAWN® MALS detector and an Optilab® refractive index concentration detector to your favorite size exclusion chromatography (SEC) or gel permeation chromatography (GPC) system to create a SEC-MALS absolute characterization tool for polymers. Wyatt detectors interface with HPLC systems from all major vendors.
For more advanced separation capabilities consider the advantages of field-flow fractionation coupled to MALS detectors – FFF-MALS. Wyatt's Eclipse™ DualTec™ and Eclipse AF4 FFF systems separate nanograms to milligrams over sizes from 1 to 1000 nm, without shear or non-ideal column interactions.
Design and control of polymer branching permit the creation of synthetic materials with novel mechanical, thermal and rheological properties. The most reliable means of evaluating branching in all types of polymers is multi-angle light scattering, as described by Dr. Stepan Podzimek in 'Branching Revealed: Characterizing Molecular Structure in Synthetic and Natural Polymers by Multi-Angle Light Scattering' (Application Note and On-Demand Webinar).
Branching ratio is determined through the relationship between molar mass and size; both are determined simultaneously and independently via multi-angle light scattering coupled to size exclusion chromatography (SEC-MALS) or field-flow fractionation (FFF-MALS). Molecules smaller than 10 nm in radius require a ViscoStar® differential viscometer to determine size or else a WyattQELS dynamic light scattering module embedded in the MALS detector for size measurements.
Figure 1. Analysis of branching by comparing conformation plots of linear and branched polystyrene.
While SEC-MALS is suitable for a wide variety of polymers, FFF-MALS using the Eclipse DualTec or Eclipse AF4 offers many advantages over SEC. FFF-based separation is imperative for certain large, highly branched polymers that elute abnormally from SEC columns.
Figure 2. RMS radius vs. elution volume plot of acrylic copolymer. Separation by SEC-MALS exhibits abnormal elution (non-monotonic in molar mass).
Figure 3. FFF-MALS (plotted in blue) overcomes abnormal elution and anomolous conformation plots exhibited by certain large, highly branched polymers in SEC-MALS (plotted in red).
Even if the polymer is not branched, information regarding conformation is available in the relationship between molar mass and size, or between the ratio of rms radius Rg to hydrodynamic radius Rh.
Figure 4. Polystyrene, PMMA, cellulosic rods and hyaluronic acid exhibit different slopes corresponding to different conformations.
Figure 5. Theoretical relationship between mass and radius for different conformations.
Co-polymers are not generally amenable to standard GPC analysis because no reference standards are available to represent elution time vs. molar mass. Even with standard SEC-MALS it is difficult or even impossible to analyze heterogeneous distributions of co-polymers, since in general dn/dc – a property that depends on the chemical composition but not the structure of the polymer, and a requisite parameter in MALS analysis – varies across the chromatogram unpredictably.
However, it is possible to carry out co-polymer analysis via the triple-detection system: SEC + UV-MALS-RI, or in some cases SEC + NIR-MALS-RI, if the two polymer components exhibit significantly different responses to the two concentration signals. In this scenario, the ASTRA® software acquires concentration data from two distinct concentration detectors (ultraviolet UV and refractive index RI, or near-infrared NIR and RI). RI is measured via an Optilab differential refractometer, MALS is measured via a DAWN multi-angle light scattering detector, and UV or NIR via third-party online detectors.
Figure 1. Plots of styrene fraction versus molar mass for copolymers of styrene-butyl acrylate prepared by emulsion polymerization. The feed styrene fraction: 23%, 48% and 73%.
Given known polymer responses to each of the two concentration detection signals it is possible to calculate the ratio of concentrations of the two; this information is combined with the MALS signal to determine the molar mass of each polymer in the complex. Hence at each elution time this analysis provides the overall molar mass as well as the total molar masses of each constituent in the co-polymer.
Unfractionated Measurements: Zimm Plots
Some polymers are too fragile to run through a gel permeation chromatography (GPC) column without degradation, e.g., a macroligand which can dissociate from labile metals. Others, such as large PMMA molecules, may be too large for GPC. These materials can still be characterized by means of batch MALS, which determines weight-average molecular weight Mw and Z-averaged rms radius rg,z. Accurate determination of these values requires a 'Zimm plot' analysis, i.e., a measurement of light scattering intensity as a function of angle and concentration, without separation.
The traditional method for making Zimm plots involves manual preparation of a series of aliquots with increasing concentrations. Batch MALS measurements are made in a scintillation vial using the Batch Conversion Kit. Alternatively, in the microbatch method the aliquots are injected into the MALS flow cell. In either case ASTRA software analyzes the data via a global fit of all angles and concentrations to a single light scattering equation. The results include Mw, rg,z and the second virial coefficient A2 which indicates solute-solute and solute-solvent interactions.
Several convenient methods for making Zimm plots utilize automation to create a series of dilutions from a single stock solution, injecting the samples into the MALS and RI flow cells, acquiring the concentration and light scattering data automatically and calculating the three parameters. This automation may be carried out with the Calypso composition-gradient system or by programming an autosampler with a large injection loop.
Differential Refractive Index Determination
The differential refractive index dn/dc quantifies the change of refractive index of a solution with concentration of the analyte. There are at least three reasons for measuring dn/dc of a polymer sample:
- In order to use a differential refractometer to measure concentration online with GPC – dn/dc represents the instrument response
- Analysis of MALS data requires knowledge of dn/dc at the MALS wavelength
- The fraction of each monomer in a co-polymer solution can be estimated if the dn/dc values of the two monomers differ significantly
Manual measurements of dn/dc are readily carried out on the Optilab® differential refractometer by means of the WISH Injection Module. Automated measurements may be carried out by combining the Optilab with a Calypso® composition-gradient system.
SEC-IV and Universal Calibration
SEC-IV utilizes intrinsic viscosity and empirically determined Mark-Houwink parameters to determine polymer molar masses. The Mark-Houwink parameters depend on the polymer, solvent and conformation.
Though not as rigorous as SEC-MALS, Universal Calibration (UC) is commonly utilized in the analysis of molecular weights of linear polymers. UC determines hydrodynamic volume from retention time on the column, and calculates molar mass at each elution volume from the ratio of hydrodynamic volume and intrinsic viscosity (this analysis is less accurate than SEC-MALS because it ignores the possibility of non-ideal sample-column interactions, and requires reference standards compatible with the mobile phase).
The ViscoStar on-line differential viscometer and Optilab differential refractometer operate in tandem along with ASTRA software to analyze molar mass and intrinsic viscosity distributions of a polymer sample by means of SEC-IV or UC.
These techniques are particularly useful when the refactive indices of the polymer and solvent are closely matched, making the polymer essentially invisible since it will not scatter appreciable quantities of light (dn/dc~0).
Measuring Mark-Houwink parameters
The relationship between molar mass and intrinsic viscosity for a given type of polymer, indicative of molecular conformation, is described by the Mark-Houwink parameter. This value may be obtained in two ways:
- by purely viscometric means, using UC to characterize both molar mass and intrinsic viscosity.
- by SEC-MALS-IV-RI wherein molar mass is determined by the combination of a DAWN® MALS detector and Optilab, while intrinsic viscosity is determined with a ViscoStar® and Optilab. The analysis is carried out in the ASTRA® software.
Kinetics of Reactions and Degradation
Since light scattering intensity is directly proportional to molar mass, it is an excellent means of monitoring the progression of a polymerization reaction. The angular dependence of multi-angle light scattering indicates size for additional diagnostics, and dynamic light scattering may be included for further characterization.
When reaction time scales are significantly longer than the time required to perform a separation (typically 30 minutes), the ideal means of characterizing the polymerization process is regular withdrawal of aliquots from the reaction vessel and analysis by means of SEC-MALS. Reactions over shorter times must necessarily be evaluated in batch (unfractionated) mode which provides average molar masses and sizes rather than full distributions. The Calypso composition-gradient system is a convenient means of preparing, mixing and injecting multi-component solutions into a MALS system such as the DAWN.
Abbas, S.; Lodge, T. P. Depletion interactions: effects of added homopolymer on ordered phases formed by spherical block copolymer micelles. Macromolecules 2008, 41, 8895-8902.
Bielawski, C. W.; Benitez, D.; Grubbs, R. H. An "endless" route to cyclic polymers. Science 2002, 297, 2041-2044.
Podzimek, S. Importance of multi-angle light scattering in polyolefin characterization. Macromol. Symp. 2013, 330, 81-91.
Striegel, A. M. Influence of chain architecture on the mechanochemical degradation of macromolecules. J. Biochem. Bioph. Meth. 2003, 56, 117-139.
Striegel, A. M., Pitkanen L. Detection orthogonality in macromolecular separations: role of the on‑Line viscometer in characterizing polymers at conditions of “spectroscopic invisibility”. Chromatographia 2015, 78, 743-751.
Tarazona, M. P; Saiz, E. Combination of SEC/MALS experimental procedures and theoretical analysis for studying the solution properties of macromolecules. J. Biochem. Bioph. Meth. 2003, 56, 95-116.