6 SIZE-EXCLUSION CHROMATOGRAPHY Yuri Kazakevich and Rosario LoBrutto 6.1 SEPARATION OF THE ANALYTE MOLECULES BY THEIR SIZE Size-exclusion chromatography (SEC) separates polymer molecules and bio- molecules based on differences in their molecular size.The separation process in simplified form is based on the ability of sample molecules to penetrate inside the pores of packing material and is dependent on the relative size of analyte molecules and the respective pore size of the absorbent. The process also relies on the absence of any interactions with the packing material surface. Two types of SEC are usually distinguished: 1. Gel permeation chromatography (GPC)—separation of synthetic (organic-soluble) polymers. GPC is a powerful technique for polymer characterization using primarily organic solvents. 2. Gel filtration chromatography (GFC)—separation of water-soluble biopolymers. GFC uses primarily aqueous solvents (typically for aqueous soluble polymers, proteins, etc.). Physical and chemical properties of polymers are dependent on their molec- ular weight and molecular weight distribution.The separation principle in SEC is based on the forced transport of the polymer molecules through the porous stationary-phase media under the conditions of suppressed interactions of the 263 HPLC for Pharmaceutical Scientists, Edited by Yuri Kazakevich and Rosario LoBrutto Copyright © 2007 by John Wiley & Sons, Inc. polymer analyte with the surface. The mobile-phase eluent is selected in such way that it interacts with the surface of packing material stronger than the polymer.Under these conditions, the smaller the size of the molecule, the more it is able to penetrate inside the pore space and the movement through the column is retarded. On the other hand, the bigger the molecular size, the higher the probability the molecule will travel around the particles of the packing material and, thus, is eluted earlier. The molecules are separated in order of decreasing molecular weight, with the largest molecules eluting from the column first and smaller molecules eluting last (Figure 6-1). Molecules larger than the pore size do not enter the pores and elute together as the first peak in the chromatogram and this is called total exclu- sion volume which defines the exclusion limit for a particular column. Mole- cules that can enter the pores diffuse into the internal pore structure of the gel to an extent depending on their size and the pore size distribution of the 264 SIZE-EXCLUSION CHROMATOGRAPHY Figure 6-1. Illustrative description of separation in SEC . gel. The molecules will have an average residence time in the particles that depends on the molecules size and shape in the particular mobile phase.There- fore, different molecules have different total residence times in the column. This portion of a chromatogram is called the selective permeation region (the effective volume in which separation can occur). Molecules that are smaller than the pore size can enter all pores, have the longest residence time on the column, and will elute all together as the last peak in the chromatogram. This last peak in the chromatogram determines the total permeation limit for a par- ticular column. The largest elution volume (retention volume) in any given SEC column is equal to the total mobile-phase volume in the column (known as the void volume, V 0 ).The exclusion range indicates the molecular weight of solutes above which all solutes having a molecular weight greater than the exclusion limit.These analytes will elute at the same retention time as a single peak. A specific column can be used for separation of solutes with molecular weights that are within the molecular weight window between the exclusion and permeation limits (Figure 6-2). Separation process in SEC is based on the actual size of the molecules, which in turn reflects the molecular weight of the polymer.The resulting SEC SEPARATION OF THE ANALYTE MOLECULES BY THEIR SIZE 265 Figure 6-2. Elution of analytes in SEC . (Reprinted with permission from reference 1.) chromatogram reflects the size distribution of the polymer sample, and its rela- tionship with the molecular weight distribution which lays the foundation of the SEC theory. 6.2 MOLECULAR SIZE AND MOLECULAR WEIGHT A polymer molecule in solution has a certain shape that strongly depends on the type of polymer, type of solvent, temperature, and other conditions. Usually a polymer forms some kind of globular species whose size is depen- dent on the degree of solvation by solvent molecules. This globe could be described by its volume (v) and hydrodynamic radius (R). Hydrodynamic radius (radius of gyration) of the polymer in the solution could be expressed in the form (6-1) where [η] is intrinsic viscosity and M is molecular weight. For some polymers that are not flexible, the effective R is used to represent the radius of the sphere. The parameter R is equivalent to the mechanical behavior of the polymer in solution. Viscosity is the simplest parameter of the polymer solution. From the Stokes and Einstein equations, the volume of the equivalent sphere is proportional to the product of intrinsic viscosity and polymer molecular weight: (6-2) where [η] is intrinsic viscosity, M is molecular weight, N A is Avogadro’s number, and v is the volume of the equivalent sphere.As one could see, the intrinsic vis- cosity is an important parameter related to the molecular weight of the polymer and its molecular volume. By definition, intrinsic viscosity is a limit of the ratio of the specific viscosity of the polymer solution to its concentration at c → 0, or it is the y-intercept of the dependence of η sp versus concentration. Polymer molecules of a different nature but with the same molecular weight usually have different hydrodynamic radii.This is due to the differences in coil flexibility, intramolecular interactions, and, most importantly, the differences in their interactions with the solvent. This essentially means that if two differ- ent polymers analyzed at identical SEC conditions show similar peaks with identical elution volume, it does not confirm that the molecular weights of these polymers are identical. It only indicates that at the given conditions the gyration radii of the molecules are the same, causing similar elution. The nature of the solvent also has a significant effect on the polymer conformation and thus on its gyration radius and molecular volume. If the h [] =MNv A 25. RM= [] 3 4 1 3 ph 266 SIZE-EXCLUSION CHROMATOGRAPHY solvent–polymer interactions are favorable or essentially prevailing over the interactions between different segments of the same polymer, then we can expect a high degree of solvation and the polymer globe will swell. For instance, if polystyrene is dissolved in toluene, due to the similar nature of the solvent and polystyrene monomer, toluene will solvate polymer molecules and their gyration radius increases. On the contrary, if the same polystyrene is dissolved in tetrahydrofuran (THF), then interactions between polystyrene segments prevail over the interactions with THF. As a consequence, the size of the polymer globe in THF is relatively small, especially in comparison to that in toluene. From equation (6-2), one can conclude that intrinsic viscosity is propor- tional to the polymer molecular volume. On the other hand, the effective mol- ecular volume is also the function of the molecular weight and the type of used solvent (or the nature of the solvent–polymer and polymer–polymer interac- tions). The intrinsic viscosity is an exponential function of the molecular weight with fixed coefficients for any specific polymer and solvent. (6-3) This expression is known as the Mark–Houwink equation, and K and α are constants for any given pair of polymer and solvent. These constants are tabulated and could be found for most known polymers in reference 2. 6.3 SEPARATION MECHANISM Eluent flow through the chromatographic column packed with porous packing material has a velocity distribution depending on the pathway. Flow around the adsorbent particles is the fastest. Flow through the pore space is much slower. Since the smallest molecules can penetrate all of the pores, they can be distributed in the whole liquid volume of the column and their average migration speed is therefore the slowest. Molecules of intermediate size may penetrate into the pore space but may not come close to the pore walls, so their center of mass will be allocated closer to the center of the pores where flow velocity is higher. Their average migration speed is higher. The biggest molecules experience steric hindrance in permeation inside the packing pore space and move through the column primarily around the particles with the fastest possible speed. As a result, the biggest molecules come out of the column first, and the smallest ones come out last. Obviously, all molecules that are not able to penetrate into the pore space, move with the same velocity. Retention volume of all these molecules is the same and is called exclusion volume, also known as total exclusion. The total exclusion volume is a characteristic of a particular column which determines its upper separation limit. h [] =⋅KM α SEPARATION MECHANISM 267 6.4 CALIBRATION SEC calibration establishes the relationship of a particular elution volume with specific molecular weight of the polymer (Figure 6-3) [3]. For calibration the elution volume of the solutions of polymer standards with known narrow molecular weight distributions are measured. An example of a separation is shown in Figure 6-4 [4]. In SEC, hydrodynamic volume of the polymer mole- cules is being measured rather than the actual mass of a particular species.The hydrodynamic volume is the space a particular polymer molecule occupies when it is in solution. The molecular weight can be approximated from SEC data from the relationship between molecular weight and hydrodynamic volume for particular known standards. However, the relationship between hydrodynamic volume and molecular weight is not the same for all polymers, so only an approximate measurement can be obtained. A series of commercially available polystyrene standards can be used for calibration. The elution volume (elution time multiplied by flow rate) corre- sponding to a particular peak in the chromatogram is related to the molecu- lar weight of a particular polystyrene. After assignment of the molecular weight for each component to its elution volume, the logarithms of the mole- cular weight of the standards are plotted against their elution volumes in order to construct a calibration curve (Figure 6-3). Each combination of column, polymer, and solvent has its own calibration curve. The same polymer molecules could have different sizes in different solvents, and two molecules of different polymers might have the same size despite their 268 SIZE-EXCLUSION CHROMATOGRAPHY Figure 6-3. Calibration curves for a set of AquaGel (Polymer Laboratories) columns designed for the separation of water soluble polymers. Calibration using PEO and PEG standards. (Reprinted from reference 3, with permission from Polymer Laboratories Inc.) different molecular weight. So the calibration curve for the certain polymer is valid only if the standards used are of the same nature and used eluent was of the same type. If two different polymers in the same solvent have the same intrinsic viscosity, then their molecular weights are related as (6-4) This makes it possible to use standards of one polymer for characterization of another if the corresponding Mark–Houwink constants are known. For most known polymers, Mark–Houwink constants are tabulated. For example, a polystyrene (PS)-based calibration could be used for characterization of polymethylmethacrylate (PMMA). Retention volume in SEC is proportional to the size of the polymer molecules in solution. In addition, as discussed in Section 6.2, equation (6-2), the product of the intrinsic viscosity of the polymer and its molecular weight is proportional to the hydrodynamic molecular volume. These relationships allowed Benoit et al. [5, 6] to introduce a universal molecular weight calibration. KM KM 1 1 2 2 12 ⋅=⋅ aa CALIBRATION 269 Figure 6-4. Example of a separation of calibration mixture of polystyrene standards. (Reprinted from reference 4, with permission from Phenomenex.) In conventional molecular weight calibration, the dependence of the reten- tion volumes of a series of narrow molecular weight distribution standards with known average masses is plotted against the logarithms of their molecu- lar weights. In universal calibration, the logarithm of the product of the intrin- sic viscosity [η] and molecular weight M (essentially hydrodynamic volume) is plotted against retention volume. Hydrodynamic molecular volume is directly related to the retention volume if only the steric separation mecha- nism is involved. Benoit et al. [5, 6] found that plots of the logarithm of hydro- dynamic volumes versus corresponding retention volumes for a series of narrow standards of different polymers in different solvents resulted in a single calibration curve, as shown in Figure 6-5. The combination of the differential refractive index (RI) detector and on-line viscometer allows the direct use of the universal calibration and thus true molecular weight determination. The RI detector is concentration- sensitive, and the viscometer records specific viscosity.The ratio of the specific viscosity to the concentration is equivalent to intrinsic viscosity (as discussed in Section 6.1), and the continuous dependence of this ratio versus the reten- tion volume could be related to the universal calibration curve, thus allowing the correlation of each point on the chromatogram with the true molecular weight. More detailed information on this type of GPC analysis can be found in the book by Yau et al., Modern Size-Exclusion Liquid Chromatography [7]. 270 SIZE-EXCLUSION CHROMATOGRAPHY Figure 6-5. Universal Benoit calibration. (Reprinted from reference 5, with permission.) 6.5 COLUMNS Polymer-based packing materials are the main type of adsorbent used in size-exclusion HPLC. Most SEC analyses of synthetic organic polymers are performed on rigid or semirigid crosslinked polystyrene gel materials (styrene–divinylbenzene copolymers with different degree of crosslinkage). These materials require careful selection of separation conditions and solvent, since they can shrink and swell in different solvents and temperatures, thus changing their separation power. A major requirement of size-exclusion separation is the complete absence of any interactions between analyzed com- ponents and the surface of packing material in the column. Polymeric pack- ings do not have any active surface groups and could be synthesized with controlled porosity. For the separation of biopolymers in aqueous media, gel- filtration chromatography is used with stationary phases that have a mildly hydrophilic surface, which is usually required to avoid noticeable hydropho- bic interactions with the surface. These types of stationary phases for GFC include (a) dextrans, agaroses, polyacrylamide, or mixtures of these compo- nents which are suitable for low- or medium-pressure chromatography and (b) porous silica-based media which are more suitable for higher-pressure applications. The separation range in size-exclusion chromatography for a particular column is relatively narrow, and it lies between the total volume of the liquid phase in the column (void volume) and the exclusion volume, V e . The differ- ence between these two volumes is the total pore volume of the packing mate- rial in the column. Indeed, if some molecules of studied polymers are small enough to penetrate inside all pores of the packing material, they will elute with the column void volume. On the other hand, polymers with significant molecular size that cannot penetrate inside the particles will all travel together around the particles and elute early with exclusion volume. To obtain wider separation range, longer and wider column dimensions are used. The greater the amount of packing material in the column, the higher the total pore volume and the higher the difference between void and exclu- sion volumes. Another important parameter is the ability of the column to discriminate different ranges of molecular masses. This range is dependent on the size of the pores of packing material and pore size distribution. Column manufac- turers usually provide the standard calibration curves of polystyrene standards in THF for each column, as shown in Figure 6-6 [8]. One of the most important requirements for the GPC column is the absence of the specific interactions with the studied polymer. The more inert the surface of the packing material, the better. Early applications of GPC separa- tion were sometimes performed on porous glass particles with controlled porosity [9]. The ease of the manufacturing of the controlled porosity par- ticles had determined this choice, but it was not always possible to find an COLUMNS 271 eluent that would suppress interactions of the polymer with the glass surface. Modern GPC columns are primarily made of styrene–divinylbenzene copolymer. Increased technological advances allow preparation of the rigid porous particles with relatively narrow pore size distribution from this copolymer. The presence of the aromatic rings in the body of the packing material is prone to π–π-type interactions, which could be a problem for the separation of polymers with significant aromaticity, like polyimids. Traditional reversed-phase columns appear to offer the most inert surface since the alkyl-type bonded ligands at high bonding density can only partici- pate in weak dispersive interactions, which could be suppressed by practically any organic solvent. An example of the calibration curve made on a commer- cial reversed-phase column is shown in Figure 6-7. For the analysis of water-soluble polymers (such as surfactants, oligosac- charides, PEGs, lignosulfonates, polyacrylates, polysaccharides, PVA, cellulose derivatives, PEO, polyacrylic acids, polyacrylamides, hyaluronic acids, CMC, starches, gums) and for separations of oligomers and small molecules, columns that are comprised of macroporous material with hydrophilic functionalities may be used. The requirement for these columns in SEC mode is to eliminate or minimize ionic and hydrophobic effects that make aqueous SEC (otherwise known as GFC) very demanding. The interaction of analytes with neutral, ionic, and hydrophobic moieties must be suppressed. It is often necessary to modify the eluent (addition of salt) in order to avoid sample-to-sample and sample-to-column interactions that can result in poor aqueous SEC separa- tions and low recoveries. 272 SIZE-EXCLUSION CHROMATOGRAPHY Figure 6-6. Typical calibration curves for a set of SEC columns. (Reprinted from reference 8, with permission.) [...]... SIZE-EXCLUSION CHROMATOGRAPHY technique is most suitable for quality control and polymer screening, as well as for troubleshooting during the analysis of pharmaceutical samples 6.11 AQUEOUS SEC APPLICATIONS For aqueous SEC, ionic interactions need to be suppressed and the eluent usually modified by the addition of salt and/or the adjustment of pH For water-soluble polymers with hydrophobic character,... SOLVING MASS BALANCE ISSUES SEC can be used to solve mass balance issues that may be encountered in reversed-phase chromatography applications for example, if the area% does not agree with the assay% value for pharmaceutical analysis of a particular active pharmaceutical ingredient or intermediate The discrepancy in mass balance could be due to species that are not observed at the wavelength of detection... N 2 i i i i = ∑M j ∑j i i (6 -6) i The ratio of weight average to number average molecular weight is called the polydispersity, rd The wider is the molecular weight distribution the higher the polydispersity value The rd for unimolecular polymer is equal to 1 All natural polymers, such as peptides, DNA, and saccharides, have polydispersity equal to 1 6.7 EFFECT OF ELUENT For the method development of... solvent needs to be considered Tetrahydrofuran is the most common solvent used for most GPC separations, although for polyimids and other high-temperature polymers the use of special solvents such as n-methylpyrrolidone may be necessary The development of GFC methods generally has similar considerations, with much higher requirements for the packing material GFC deals with water-soluble polymers; thus the... approach for the separation of the aqueous polymeric samples is shown in Figure 6-8 In biological separations, the choice of mobile phase is critical and must consider both column performance and the maintenance of biological function of the sample and the aim of separation Figure 6-9 represents a preparative separation of a mixture of proteins at pH 7 in phosphate buffer Typical buffers used for classical... polystyrenes of known structure, J Chim Phys 63 (19 66), 1507–1514 6 Z Grubisic, P Rempp, and H J Benoit, Universal calibration for gel permeation chromatography, Polymer Sci B, Polymer Lett 5 (1967), 753–759 7 W W Yau, J J Kirkland, and D D Bly, Modern Size-Exclusion Liquid Chromatography, Wiley-Interscience, New York, 1979 8 Waters Catalog, Waters Inc., Milford, MA, 2006 9 B G Belenkii and L Z Vilenchik,... Dekker, 2004 12 J Wen, T Arakawa, and J S Philo, Review: Size exclusion chromatography with on-line light scattering, absorbance, and refractive index detectors for studying proteins and their interactions, Anal Biochem 240 (19 96), 155 13 M.-I Aguilar, HPLC of Peptides and Proteins, Vol 251, Humana Press, Totowa, NJ, 2004 ... acceptable for gel filtration These include denaturing buffers (6 M guanidine hydrochloride or 8 M urea) and those containing nonionic detergents (Tween-20, Brij-35 at concentrations from 0.01 to 0.1% v/v) All silica-based gel filtration columns possess a slight negative charge This charge is likely due to unreacted Figure 6-8 Principles of the selection of acceptable column type and mobile-phase type for the... pH values above 8.5 does cause a slow base-catalyzed dissolution of the silica packing, but can be tolerated for short periods at the expense of reduced column life Other types of GFC columns are chemically modified crosslinked polystyrene gels with sulfo groups on the surface They are suitable for the 278 SIZE-EXCLUSION CHROMATOGRAPHY Figure 6-10 Example of a separation of dietary fiber mix on GPC column... of magnitude lower than UV) Very sensitive to pressure, flow, and temperature fluctuations Two specialized detectors have been developed with specific applications for SEC The first is the laser light-scattering detector, which has been around for almost 20 years but now has new electronics and computer data acquisition capabilities Substitution of bulky He–Ne gas lasers with small, inexpensive diode lasers . chromatography applications for example, if the area% does not agree with the assay% value for pharmaceutical analysis of a particular active pharmaceutical ingredient. interactions of the 263 HPLC for Pharmaceutical Scientists, Edited by Yuri Kazakevich and Rosario LoBrutto Copyright © 2007 by John Wiley & Sons, Inc.