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Gel permeation chromatography (GPC) or also named size exclusion chromatography (SEC) is the most often used method for determining the molecular weight of natural and synthetic macromolecules. One specific strength of this method lies in the fact that by the separation process the whole molecular weight distribution is obtained. The molecular weight distribution contains much larger information for the characterization of polymer samples compared to a single value.
When GPC started was the concentration detector the only detector used for the determination of the molecular weight distribution. calculation the molecular weight from the concentration chromatogram needs the elaborate calibration of the columns by polymer standards. If sample and standard are different only relative molecular weights are obtained. The combination of concentration, viscosity and light scattering detection established a standard because of its superior information content.
Fig. 1: Principle of conventional calibration. Polymer standards with a narrow distribution are used to build up a calibration curve. This is then used to calculate the average molecular weight and polydispersity of the sample.
The conventional method for calibration of the GPC columns uses commercially available polymer standards with low polydispersity. The molecular weight is plotted versus the elution volume (see figure 1). The polymer is usually detected by a refractive index (RI) detector  or a UV detector, if the polymer contains UV absorbing groups. The molecular weight of an unknown sample is then calculated by dividing the area below the curve in small fractions (slices) and projecting the retention volume of each slice on the calibration curve.
Usually only relative molecular weights are obtained because of the different chemical composition of sample and standard. This is a consequence of the separation of the molecules on the columns by size (more precise: their hydrodynamic volume) and not by molecular weight. The hydrodynamic volume of a polymer molecule depends on the chemical constitution, its structure (linear or branched) and also from concentration. Thus, two polymer molecules can elute, despite of the same molecular weight, at different retention volume and therefore alter the calculated molecular weight.
Universal calibration was first described 1967 by Benoit et al.  and allows to the determination of the exact molecular weight even for samples that are different in chemical composition or structural properties. This Calibration is based on the fact that the product of intrinsic viscosity  and molecular weight is directly proportional to the hydrodynamic volume. With the development of the four-capillary viscometer by Haney  this method was introduced to GPC. This patented differential viscometer detector allowed for the first time to measure the intrinsic viscosity on-line without the drawback of earlier viscometers (low sensitivity, influenced by pump pulsation, Lesec effect).
Fig. 2: Principle of the 4-capillary viscometer. The capillaries 1 and 2 divide the flow symmetrically. The sample in the lower branch builds up a back pressure whereas the sample in the upper branch flows without pressure in a reservoir. The intrinsic viscosity is calculated from the pressure difference (DP) together with the inlet pressure (IP).
If one takes into account that GPC is a separation technique by size the advantage of a online viscometer is directly visible. By using the universal calibration of the chromatographic columns a calibration curve giving the size of the molecules over the retention volume is obtained and thus is independent of chemical composition or structure of the used polymer standards. The real molecular weight of the sample is easily calculated, by measuring the intrinsic viscosity of the sample as well. Thus universal calibration goes not rely on a certain type of polymer standard.
By using a viscometer detector and universal calibration a comprehensive characterisation of the unknown sample is possible. Besides the determination of absolute molecular weight further important variables are measures like the intrinsic viscosity and the radius of gyration and for both parameters the distribution over the whole sample.
By using the Mark-Houwink-equation = K*M^a and calculating the parameters a and K further information is collected. For ideal coil conformations is the a-value in the range of 0.6-0.8; more compact structures (e.g. branched polymers, proteins) values below 0.5 are typical; stiff polymer chains deliver values in the range of 1-2. The theory from Zimm and Stockmayer allows the calculation of the degree of branching by comparing the intrinsic viscosity of branched and linear polymers.
Very often light scattering is used to determine the molecular weight by GPC. One big advantage is that the molecular weight is measured without the need for a calibration curve because of the proportionality of the light scattering signal direct to the molecular weight. The Rayleigh equation (1) describes the relation of the scattered light of the dissolved polymer molecules by the so-called Raleigh ratio Rθ, of the polymer concentration c and the weight average molecular weight Mw .
K is an optical constant, A2 the second virial coefficient and P(θ) the static structure factor.
Looking at “small” macromolecules a isotropic scattering in all directions is observed, thus P(θ) = 1 for all angles θ (figure 3). The size of the macromolecules is here compared to the wave length of the used laser light. Molecules with a diameter less than 1/20 of the laser wave length are “small”. Using a typical wave length of 670 nm all molecules with a diameter less than 15 nm show no angular dependence. Linear synthetic molecules reach this border if their molecular weight surpasses 150.000 g/mol. For branched molecules the molecular weight must be even higher.
Fig. 3: Angle dependency of the Rayleigh light scattering. “Small” molecules (radius < ca. 15 nm scatter the light isotropically, for larger molecules is the intensity of the scattered light in forward direction higher. At 7° almost the full scattered light is detected for all polymers accessible with GPC.
Looking at larger macromolecules the scattered light intensity towards higher angels is reduced, thus P(θ) depends on the measuring angle. To measure the right molecular weight the scattered light at θ = 0° must be measured. This is experimentally impossible because of the primary beam of the laser.
There exist several approaches to solve this dilemma: the most consequent way is to measure the scattered light at an angle as close as possible to 0°. This is the only method to avoid extrapolation or correction of the measured values. This approach called low angle light scattering (LALS) is complicated by the proximity of the primary beam and reflections on the glass-air surface and was therefore rarely used in the past. Nowadays these problems are solved by a clever design of the sample cell and by fading out the primary beam by a tilted mirror. The scattering light at 7° is even for the largest polymers accessible by gel permeation chromatography only about 1 % less compared to the scattered light at 0°.
In general a second parameter can be calculated by light scattering on polymers: the radius of gyration. This radius is calculated from the angular dependence of the scattered light. For molecules with a radius below 15 nm no angular dependence is observed and thus it is for many polymer samples impossible to determine the radius of gyration by static light scattering.
Triple detection means the combination of 3 detectors with different information. That is a concentration detector (RI or UV), a light scattering detector (measures molecular weight), and a viscosity detector (sensitive to the molecular density in solution). With these three detectors the distribution of molecular weight, intrinsic viscosity, and size (radius) of the polymers over the whole molecular weight range accessible by GPC can be determined.
Plotting the intrinsic viscosity over molecular weight on a logarithmic scale gives the Mark-Houwink-Plot log  = alog M + log K. this is the central structure plot in polymer analytics. It shows structural variations by branching as well as the coiling behaviour of the polymer chain and its stiffness. With this method the physical properties of the polymer sample are measured directly and independent from the elution volume, this makes the method robust to chromatographic conditions as flow rate irregularities, peak broadening and column degradation.
There are two further advantages of triple detection: The flexibility of the system. Is it impossible to use one of the detectors for a certain analysis, the others can still be used to precisely measure the molecular weight. Further leads the comparison of different methods very often to a better understanding of the polymer structure.
Development and synthesis of even more special polymers and their application in industrial and pharmaceutical applications leads to an enhanced complexity of polymer analytics. Using two or more different monomers during the synthesis leads to the formation of copolymers. Homogeneous statistic copolymers can in GPC be treated as homopolymers. This is not possible for inhomogeneous polymers with varying contents of monomer A and B over the molecular weight distribution.
With the application of two concentration detectors (RI and UV) that give different responses to the comonomers A and B the calculation of the true concentration profile and the content of each monomer is possible. Equation 2 displays this dependency. KRI and KUV are instrument constants, dn/dc is the refractive index increment and dA/dc is the UV absorption of the monomers A and B at the wavelength λ:
Combination of the two concentration detectors with a viscometer and a light scattering detector gives the distribution of all polymer specific parameters as described for homopolymers. The same approach can be used for other two component systems as e.g. protein/polymer complexes.
Fig. 4: Triple chromatogramm of two narrow distributed polystyrene standards.
Linear Polystyrene (PS) is commercially available with narrow and broad molecular weight distribution. Polystyrene samples in tetrahydrofuran are a very good example to show the responses of the three detectors.
Figure 4 shows the triple chromatogramm of a mixture of two narrow polystyrene standards (MW = 850,000 und 30,000 g/mol). The use columns show a good separation and the peaks are baseline separated. The RI chromatogramm shows that the PS with the lower molecular weight is about 4 times as concentrated as the high molecular weight PS. Despite this difference in concentration the signals of the viscosity and light scattering detector of the high molecular weight PS are much larger. The reason for this lies in the molecular weight dependent signal of the viscometer and light scattering detector.
Fig. 5: Triple chromatogram of a broad polystyrene: Mw = 254.000 g/mol, PDI = 2,5, IV = 0,843 dL/g.
Figure 5 shows the triple chromatogramm of a broad (polydisperse) PS sample. The signals of the light scattering detector and the viscometer are shifted towards higher molecular weight (lower elution volume) compared to the RI signal. This shift is the result of the different response of the detectors. The shift caused by the volume offset between the detectors is already corrected by the software. The RI signal is independent of molecular weight whereas the viscometer and light scattering detector react much more sensitive to high molecular weight contents and therefore leading to a much faster rise of the signals on the left side of the chromatogramm. This apparent shift of the viscosity and light scattering signal compared to the RI detector is also a measure for the polydispersity of the sample.
Looking closely to the 3 curves one observes that the shift of the light scattering signal is larger compared to the viscometer signal. The reason therefore lies in the behaviour of intrinsic viscosity. The light scattering signal is proportional with molecular weight but the viscosity grows according to the Mark-Houwink  = K Ma equation with the power of a. The exponent a is for linear polymers that form an ideal statistic coil in solution smaller than one (e.g. 0.7 in the case of PS in THF), thus the viscosity signal grows slower compared to the light scattering signal. This effect is also observed for the narrow Ps samples in figure 4. The curve of Log M over retention volume (figure 5) shows a linear behaviour and therefore an ideal separation by size exclusion mechanism.
Fig. 6: Schematic picture of the bromination of polystyrene.
The performance of triple detection is demonstrated on the example of PS compared to brominated polystyrene (BrPS, used in flame retardants) with the same chain length. Bromination of PS leads to the substitution of Hydrogen (1 amu) by Bromine (80 amu). This leads to an increase of molecular weight whereas the size of the polymer coil is almost unaffected, as shown schematically in figure 6.
Fig. 7: Comparison of the detector signals before and after the bromination.
Comparing the chromatogramms (figure 7) shows almost no alteration of the RI chromatogram. Using conventional calibration would result in almost the same molecular weight for both samples. The signal of the light scattering detector much larger and therefore a 2.5 times larger molecular weight is calculated (table 1). The reduction of the viscosity signal confirms as an independent detector the increase of density of the brominated polymer.
| Table 1: Molecular weight of polystyrene before and after the bromination
Fig. 8: Triple chromatogramm of a maltodextrine sample. Mw = 468.000 g/mol, PDI = 3,48, IV = 0,117 dL/g.
Natural Macromolecules – Maltodextrine
Maltodextrins are produced by the enzymatic degradation of starch. They are use as food additives to improve the rheologic properties or as flavour enhancer. By differences in the used starch, the enzymes or processing parameters are the resulting maltodextrines different in molecular weight and degree of branching.
Figure 8 shows the triple chromatogram of a maltodextrine sample. Already from the peak shapes is a high degree of branching visible in the high molecular weight range. At low retention volume an intense LALS signal and a small viscosity signal is observed. This means a high molecular weight combined with a high density (low viscosity) and therefore a highly branched structure.
Fig. 9: Mark-Houwink plot of the maltodextrine sample. The dotted line shows the expected curve for a linear maltodextrine sample.
The increasing degree of branching can nicely be followed in the Mark-Houwink plot (figure 9). Linear polymer samples result in a linear Mark-Houwink curve from that the slope is calculated and information about the coiling properties are derived. For the maltodextrine sample a significant downwards curvature is observed. This curvature shows the inhomogeneous structure of the sample and that the number of side chains increase towards the high molecular weight region. Quantitative calculation of the number of branches and the branching frequency is possible. Other example that have been successfully analyzed by GPC are: starch, cellulose, nitrocellulose, pectin, xanthan, heparin, hyaluronic acid, chitosan, pullulan, dextran, careageenan, proteins, antibodies, RNA, DNA ...
The utilisation of multiple detectors enhances the available information from the GPC analysis significantly. Especially for the determination of structural properties of the polymer samples offers triple detection the ideal solution. Triple detection allows, besides measuring the absolute molecular weight, the determination of coil dimensions and other physical parameters that otherwise must be measured with additional instruments.
One of the biggest advantages of triple detection is the fact that no elaborate calibration are necessary and certain non-perfect conditions as flow rate fluctuations, separation not by size exclusion or column degradation have no impact on the results. this is because the retention volume is not used for the calculation of molecular weight, intrinsic viscosity, coil dimensions and degree of branching.
Analysis of the results can be done on different levels. The raw triple chromatogramm allow already to extract qualitative information of the sample. In a easy way average values of the physical parameters can be calculated. The calculation of the distributions of molecular weight and intrinsic viscosity gives the most comprehensive information about the sample and its branching. Do you see the complete picture of your macromolecules?
 M. A. Haney, Principles of Triple Detection GPC/SEC: The Deflection Refractometer (RI), Laboratory Equipment, March 2003
 Z. Grubisic, P. Rempp, H. Benoit, A Universal Calibration for Gel Permeation Chromatography, J. Polym. Sci. B: Polym. Lett. 5, 753 (1967)
 M. A. Haney, The Differential Viscometer. II. On-line Viscosity Detector for Size-Exclusion Chromatography, J. Appl. Polym. Sci. 30, 3037 (1985)
 B. H. Zimm, W. H. Stockmayer, The Dimensions of Chain Molecules Containing Branches and Rings, J. Chem. Phys 17, 1301 (1949)
 S. Mori, H. G. Barth, Size Exclusion Chromatography, Kapitel 8.1, Springer Verlag Berlin (1999)