Theory of chromatography of linear and cyclic polymers with functional groups

We discuss the chromatographic behavior of linear polymers and rings having specific (functional) adsorption-active groups. Functionalized eight-shaped, daisy-like and theta-shaped macromolecules are considered as well. By using a model of an ideal chain with point-type defects in a slit-like pore we derive equations for the distribution coefficient covering all modes of chromatography of functionalized polymers of any molar mass in both narrow and wide pores. Additionally simple approximate formulae are obtained for a number of important modes of chromatography; chromatograms are simulated for model mixtures of polydisperse non-functional and functional polymers. By using the theory we analyze separation of polymers by molar mass, functionality and topology. Although there is a principal possibility to use adsorption chromatography or size-exclusion chromatography (SEC), we conclude that the liquid chromatography at the critical condition (LCCC) is especially efficient for separation of polydisperse polymers by both functionality and topology. The theory predicts that functionalized linear and cyclic polymers can be separated from each others by LCCC even better than non-functionalized ones. The LCCC behavior of some other types of polymers such as comb-like and semicyclic ones is discussed as well.     

Topological separation of linear and star-shaped polystyrenes by off-line 2D chromatography. Stars having high molar mass arms and quantification of the star fraction

Off-line 2D separations on mixtures of linear and star-shaped polymers were performed using temperature gradient interaction chromatography (TGIC) as a first and SEC as a second dimension. The experiments resulted in clear separations of the linear and star shaped-structures for arm molar masses up to 42,000 g/mol. The resolution is nearly independent of the molar masses of the arms and depends only on the number of star arms. From the 2D chromatograms it is possible to determine the molar mass of the first branched structure, i.e. the three arm star. The evaluation of the relative peak volume allows a reliable estimation of the amount of branched structures in the complex mixture.     

Characterization of branched polymers by size exclusion chromatography coupled with multiangle light scattering detector. I. Size exclusion chromatography elution behavior of branched polymers

The elution behavior of branched macromolecules during their separation by size exclusion chromatography (SEC) was studied. The elution behavior of branched polymers was investigated using samples of randomly branched polystyrene and star branched poly(benzyl methacrylate) of different levels of branching by means of a SEC chromatograph coupled with a multiangle light scattering detector. Abnormal SEC elution behavior was found to be typical for highly branched polymers. After a normal elution at small elution volumes the molar mass and root mean square radius of the eluting molecules increased with increasing elution volume. Several SEC experiments were carried out to find explanation for this effect and SEC separation was compared with the separation by thermal field flow fractionation. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1588–1594, 2001     

Molar mass distributions of polymers from size exclusion chromatography and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry: Methods for comparison

Equations are presented for calculating molar mass averages and molar mass distributions from matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) data and from size exclusion chromatography (SEC) data. The utility of polydispersity is examined as an indicator of the expectation of MALDI‐TOF MS mass discrimination effects. Cumulative distributions are found to be rich in information for comparing the two techniques and are easily obtained from both SEC and MALDI‐TOF MS data. Analyses of a series of narrow molar mass distribution poly(methyl methacrylate) (PMMA) standards and one polydisperse sample have been performed with both methods. MALDI‐TOF MS did not detect dimer and trimer in the PMMA samples, and it often indicated lower amounts of high‐molar‐mass polymers than did SEC. The results showed that the distribution breadth, as evidenced by the standard deviation of the distribution (calculated from the polydispersity and number‐average molar mass), correlated well with the molar mass range observed in the MALDI‐TOF MS spectra, whereas the polydispersity alone did not. Ratioing the extremes in the molar mass concentrations measured with the SEC differential refractometer, which were necessary to adequately define molar mass distributions, showed that detector dynamic range values as high as approximately 370,000 were required for the polydisperse samples. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 627–639, 2005     

SEC-Gradients, an alternative approach to polymer gradient chromatography: 1. Proof of the concept

A new approach to gradient chromatography of polymers is presented, in which the sample is introduced at the end of the gradient and elutes within the elution volume range typical for size exclusion chromatography (SEC). Due to the gradient the samples are retarded and elute nearly independent of molar mass at the adsorption threshold. The concept was proven for a series of narrowly distributed poly(methy methacrylate)s (PMMA) in a chloroform-tetrahydrofuran (THF) SEC-gradient. The application of the SEC-gradient to a blend of PMMA and polystyrene standards of similar molar masses, which could not be separated by SEC due to their similar hydrodynamic sizes, resulted in a clear separation according to chemical composition. Since SEC-gradients allow dissolving the sample in strong eluents, which might result in breakthrough peaks in conventional gradients, the new approach is a valuable alternative to conventional gradient chromatography.     

Theory of chromatography of complex cyclic polymers: eight-shaped and daisy-like macromolecules

A theory of chromatography of eight-shaped, trefoil-shaped and daisy-like polymers is developed. For a model of an ideal chain in a slit-like pore exact equations and a number of approximate formulae for the distribution coefficient K of these polymers are derived. All modes of chromatography of complex macrocycles of arbitrary molar mass in both narrow and wide pores are covered by the theory. It is shown that complex macrocycles always elute after linear polymers and rings of the same contour length. The effective chromatographic radius of eight-shaped and daisy-like macromolecules, which determines retention in size-exclusion chromatography are calculated. The increase in the retention with molar mass is predicted for all types of macrocycles at the critical interaction condition. Non-monotonous molar mass dependences of K are found at pre-critical interaction. We simulate separation of complex cyclic polymers from linear and ring precursors, discuss possibilities to separate symmetric and asymmetric eights, and speculates on the use of chromatography for separating knotted and unknotted polymer rings. According to the theory, the chromatography under the critical and pre-critical interaction conditions is expected to be especially efficient in these and similar problems. Boundary conditions for the theory and its applicability to real systems are discussed.     

New analytical methods for epoxy resins, 2. Two-dimensional chromatography

In order to gain information on the functionality type distribution and molar mass of bisphenol A based epoxy resins, on-line coupled two-dimensional chromatography was used. In the first chromatographic dimension, liquid chromatography at the critical point of adsorption separated the samples with respect to functionality. The functionality fractions were automatically transferred into size exclusion chromatography as the second dimension, where the fractions were separated with respect to their molar mass distribution. As a result of the two-dimensional experiment, the samples were mapped in contour plots, providing quantitative information on the interconnected parameters functionality, molar mass, and branching.     

Z-RAFT star polymerization of styrene: Comprehensive characterization using size-exclusion chromatography

Reversible addition-fragmentation chain transfer (RAFT) polymerizations of styrene in bulk at 80 °C using tri-, tetra-, and hexafunctional trithiocarbonates, in which the active RAFT groups are linked to the core via the stabilizing Z-group, were studied in detail. These Z-RAFT star polymerizations of styrene showed excellent molecular weight control up to very high monomer conversions and star sizes of more than 200 kDa. The application of high pressure up to 2600 bar was found to significantly increase the relative amount of living star polymer. Not even at very high monomer conversions and for large star molecules, a shielding effect of growing arms hampering the RAFT process could be identified. Absolute molecular weights of star polymers using a conventionally calibrated SEC setup were determined with high precision by using a mixture of linear and star-shaped RAFT agents. When using phenylethyl as the leaving R-group, well-defined star polymers that perfectly match the theoretical predictions were formed. However, when using benzyl as the leaving group, a pronounced impact of monomer conversion on the star polymer topology was observed and pure star polymers with the expected number of arms could not be obtained.     

Use of gradient,critical, and two‐dimensional chromatography in the analysis of styrene‐ and methyl methacrylate‐grafted epoxidized natural rubber

The growing number of heterogeneous polymeric species that are being synthesized places increasing demands on existing analytical techniques. Although size‐exclusion chromatography (SEC) has established itself as a powerful analytical tool, it has its limits when complex polymers, e.g., graft copolymers, must be analyzed. In this case, complementary techniques such as gradient HPLC and liquid chromatography at critical conditions (LCCC) are more favorable. The present study describes the synthesis and analysis of methyl methacrylate‐ and styrene‐grafted epoxidized natural rubber by different chromatographic techniques. The grafting efficiency was evaluated by gradient HPLC under normal and reversed phase conditions. Methyl methacrylate‐grafted ENR50 was further analyzed by LCCC, where separation of the rubber and grafted rubber occurred according to chemical composition but was independent of the molar mass of the methyl methacrylate homopolymers. This was followed by the combination of LCCC and SEC, where separation was achieved in two dimensions. Relevant deductions were made of both the chemical composition distribution and the molar mass distribution of the functional groups of methyl methacrylate‐grafted ENR50. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2530–2538, 2003     

Separating ethylene-propylene-diene terpolymers according to the content of diene by HT-HPLC and HT 2D-LC

The separation of ethylene-propylene-diene terpolymers (EPDM) according to the three monomer units is an important task to understand the macroscopic properties of these technically important elastomers. In particular a separation with regard to the content of diene is of extreme value because the distribution of the latter along and across the molar mass axis determines the cross-linking behavior. In this study we show that high-temperature liquid chromatography (HT-HPLC) can be used for this purpose: the chromatographic retention of EPDM on porous graphite using a gradient of 1-decanol→trichlorobenzene is a function of both the content of ethylene and diene. The contribution of the diene alone to the chromatographic retention can be quantified by calculating the difference in elution volume between the EPDM and an EP copolymer having an equivalent content of ethylene. The chromatographic separation of fully hydrogenated EPDM indicates that the additional retention due to diene is the result of its geometrical nature. Coupling the HPLC separation according to the chemical composition with size exclusion chromatography (SEC) enables to reveal for the first time the complete molecular heterogeneity, i.e. the relationship between the chemical composition distribution and the molar mass distribution of EPDM.     

Strain-promoted azide-alkyne cycloaddition “click” as a conjugation tool for building topological polymers

Strain-promoted azide-alkyne cycloaddition “click” reaction (SPAAC) was successfully used as a tool in synthesis of star polymers by grafting onto approach. The application of SPAAC method in star polymer synthesis was investigated for coupling reaction of the dibenzocyclooctyne (DIBO) end group of polystyrene (PS) and poly(ethylene glycol) (PEG) with coupling agents bearing 2, 3, or 4 azido groups. Firstly, well-defined linear DIBO-terminated PS was obtained by atom transfer radical polymerization (ATRP) of styrene using a DIBO containing ATRP initiator and linear DIBO-terminated PEG was obtained by terminal functionalization of PEG monomethyl ether (PEG-OH). Then a series of star PS and PEG bearing two, three and four arms were prepared respectively by subjecting SPAAC coupling reaction between the linear polymer-DIBO and the azido tethered core molecules at 30 °C without catalyst. The obtained star PS showed a well-defined structure after fractional precipitation to remove slightly excess linear polymers, and all the star polymers were characterized via Fourier transform infrared spectroscopy (FTIR), ¹H nuclear magnetic resonance spectroscopy (¹H NMR), size exclusion chromatography (SEC) and matrix-assisted laser desorption ionization-time-of-flight mass spectrometry (MALDI-TOF MS).     

Field-flow fractionation: New and exciting perspectives in polymer analysis

The development of advanced polymeric materials requires state-of-the-art synthesis and molecular characterization protocols. Only the precise knowledge of molecular structure–property correlations allows achieving optimum performance properties of novel materials. The analysis of the molecular composition of a complex polymeric material requires the determination of its molar mass, chemical composition, functionality and molecular topology among other (less important) parameters.A number of column-based fractionation methods, including size exclusion chromatography (SEC) and high performance interaction chromatography (HPLC) are the standard techniques for the analysis of complex polymers. These methods work well as long as the molar mass is not too high and/or the macromolecules do not exhibit undesired interactions with the stationary phase (column). Certain polymers form large aggregates or other entities (micelles, liposomes) in solution that typically cannot be analyzed by column-based fractionation methods.One alternative for the fractionation of such complex materials is field-flow fractionation (FFF), an open-channel technique which does not use a stationary phase. In FFF, all problems related to the stationary phase such as undesired adsorption, shear degradation of large macromolecules, co-elution of linear and branched macromolecules, can be avoided. Different sub-techniques of FFF render the fractionation of complex polymer systems according to molecular size, chemical composition or molecular topology.In this review article, most recent developments of FFF in polymer analysis are addressed. Natural and synthetic polymers, polyolefins and polymeric nanocomposites are embraced. The most important FFF sub-techniques in polymer analysis include asymmetric flow field-flow fractionation (AF4) and thermal field-flow fractionation (ThFFF). Major developments in these very topics since 2008 are critically discussed following a previous review article that summarized earlier work (see Prog. Polym. Sci. 2009; 34: 351–68). The potentials and limitations of the different FFF sub-techniques for polymer analysis are elaborated and most recent methods of hyphenating FFF with other techniques are highlighted.     

Star poly(2‐ethyl‐2‐oxazoline)s—synthesis and thermosensitivity

A series of star‐shaped poly(2‐ethyl‐2‐oxazoline)s was prepared by cationic polymerization. The polymerization was initiated by dipentaerythrityl hexakis(4‐nitrobenzene sulfonate) and a tosylated hyperbranched polymer of glycidol. The polymerization proceeded in a controlled manner. The star structure of the products was determined by nuclear magnetic resonance. The molar mass distributions that were measured by gel permeation chromatography with multiangle laser light scattering were narrow, and the experimental values of the molar masses were close to those predicted. The very compact structure of the polymers obtained (compared with the linear counterparts) confirmed the star formation. The star poly(2‐ethyl‐2‐oxazoline)s show a phase transition temperature in the range 62–75 °C. Comparison of this phase transition temperature with that of the linear poly(2‐ethyl‐2‐oxazoline)s with the same molar masses indicates the influence of molar mass and topological structure of the macromolecule on temperature behavior. The prepared copolymers are spherical, which might be useful for the controlled transport and release of active compounds. Copyright © 2011 Society of Chemical Industry     

Molar mass distribution by size exclusion chromatography: Comparison of multi-angle light scattering and universal calibration

Series of polymers of various molar mass, chemical composition, and molecular architecture was analyzed by size exclusion chromatography (SEC) coupled with a multi-angle light scattering (MALS) photometer and an online viscometer. The molar mass averages were determined from the signal of MALS or calculated from the intrinsic viscosity and universal calibration. The comparison of the obtained results showed significant differences between the two methods. The MALS detection was shown to be more accurate for the determination of the weight-average molar mass and less vulnerable to the spreading of polymer peak by band broadening. The universal calibration can yield more accurate estimation of the number-average molar mass of branched polymers. It is also significantly more accurate for the characterization of fluorescent polymers than MALS with a regular laser of 660 nm. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47561.     

Characterization of star-shaped poly(l-lactide)s by liquid chromatography at critical conditions

A series of linear and star-shaped poly(l-lactide)s (PLA's) have been prepared by living polymerization of l,l-dilactide (LA) and analyzed by liquid chromatography at critical conditions (LC-CC). For the analysis of the PLA's LC-CC conditions have been used corresponding to silica gel as the stationary phase and a mixture of 1,4-dioxane/n-hexane (56.25/43.75 by vol%) at 50 °C as the mobile phase. At the critical point of adsorption, a series of linear C₄H₉-PLA-OH's having molar masses (M_n) in the range from 2.3×10³ to 7.4×10⁴, prepared by ring-opening polymerization of LA initiated with Sn(OC₄H₉)₂ (THF, 80 °C), showed no dependence of the elution volumes on molar mass. In subsequent experiments, star-shaped PLA's bearing various numbers of PLA-OH arms (R-(PLA-OH)_x) have been prepared in a controlled synthesis starting from various polyols (R-(OH)_x) containing exclusively primary hydroxyl groups: diethyleneglycol (x=2), trimethylolpropane (x=3), di(trimethylolpropane) (x=4), dipentaerithritol (x=6), and poly(3-ethyl-3-hydroxymethyloxetane) (〈x〉=13.4) and LA monomer. As coinitiator/catalyst tin(II) octoate (Sn(Oct)₂) has been used (bulk polymerization, 120 °C). ¹H NMR analysis of the resulting star-shaped polymers revealed that all OH-groups in the polyols started growth of the PLA chains. The series of star-shaped PLA's have been analyzed by LC-CC as well as by two-dimensional (2D) chromatography (i.e. LC-CC versus size exclusion chromatography (SEC)) with regard to possible structural imperfections. It has been shown, that the LC-CC elution volumes of the resulting R-(PLA-OH)_x increase with the number of PLA-OH arms, allowing discrimination of the individual R-(PLA-OH)_x's in their mixture. An exponential increase of the retention volume as a function of the number of arms has been found. Eventually, LC-CC measurements of the elution volumes carried out for acetylated star-shaped PLA's (R(PLA-OOCCH₃)_x) have shown that for the interactions of the R-(PLA-OH)_x macromolecules with the column packing the hydroxyl end-groups are mostly responsible.     

Truths and myths about the determination of molar mass distribution of synthetic and natural polymers by size exclusion chromatography

This article discusses various aspects of the determination of molar mass distribution by means of size exclusion chromatography (SEC) in various application modes. The effects of erroneous specific refractive index increment (dn/dc), branching, column performance, and enthalpic interactions on the results obtained by different SEC techniques are discussed. Combination of SEC and a light scattering detector represents the most direct way to the molar mass distribution of all natural and synthetic polymers as it completely eliminates the need for column calibration and to a certain extent eliminates the dependence of the obtained results on some operational variables such as flow rate, temperature, or injected mass. A multiangle light scattering (MALS) photometer has become the most frequently used light scattering detector capable of determination of molecular size as another important polymer characteristic. This article contrasts SEC‐MALS method with other application modes of SEC from the viewpoint of some frequent confusions and misunderstandings. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40111.     

System development for size exclusion chromatography of starch hydrolysates

A system for the aqueous size exclusion chromatography (SEC) of starch hydrolysates has been developed. Sepharose CL is the chromatographic support material, and aqueous sodium hydroxide solution is the eluent. Various factors affecting the resolution of the proposed system are discussed. Support materials having small particle size and narrow particle size distribution are necessary for maximizing separation efficiency. The ionic strength of the eluent, however, has a negligible effect on separation efficiency. The fractionation range of the system has been broadened by connecting in series columns containing two different Sepharose-CL gel types according to the bimodal pore size distribution concept. Well-characterized sodium polystyrene sulfonate and dextran standards are used to calibrate this SEC system. The Coll–Prusinowski calibration procedure leads to a linear calibration curve over a wide molecular weight domain.     

Liquid chromatography at critical conditions of polyethylene

Olefin copolymers are of increasing scientific interest due to their important application potential. Liquid chromatography can deliver important information, especially on their molecular structure. In particular, liquid chromatography at critical conditions (LCCC) is of interest because, in this chromatographic mode, the elution is molar mass independent for a given repeat unit. LCCC is conducted at conditions where the entropic effect of size exclusion is equal to the enthalpic effect of interaction between the macromolecules and the stationary phase and can be used to separate copolymers as well as some homopolymers containing one single repeat unit but having different end groups. For the first time, critical conditions for linear PE were experimentally identified by using porous graphite (Hypercarb™) as the stationary phase, and either 1-decanol/ortho-dichlorobenzene (ODCB), 1-decanol/1,2,4-trichlorobenzene (TCB), n-decane/ODCB, or n-decane/TCB as the mobile phase at 160 °C. The identified critical conditions for PE using the above approach in the above solvents have been verified to be correct, barring slight deviations, by two different techniques which were previously used to determine critical conditions for polymers soluble at ambient temperature. The critical conditions for polyethylene were applied to separate statistical copolymers of ethylene/1-octene with similar molar mass.     

Depolarization behaviour of dilute polymer solutions: II. Angular dependence and analyzer absorption

Study of the depolarization behaviour of dilute polymer solutions leads to determination of the Cabannes factor, necessary for correcting the Rayleigh ratio used in light‐scattering calculations for deviations due to anisotropy. We present here a method to determine the Cabannes factor for polymers as a simultaneous function of both scattering angle and molar mass, accomplished by coupling size‐exclusion chromatography with depolarization multi‐angle light scattering (SEC/D‐MALS). The depolarization behaviour of brominated polystyrene (PSBr), previously studied at a right‐angle geometry, is seen to possess a non‐trivial angular dependence in addition to being a function of molar mass. We also demonstrate initial attempts at correcting SEC/D‐MALS results for absorption of light by the Polaroid filters that act as analyzers in the optical train of the system. Copyright © 2003 Society of Chemical Industry     

A one-pot approach to dendritic star polymers via double click reactions

A class of well-defined dendritic star polymers with poly (ε-caprolactone) (PCLs) on the periphery has been prepared via one-pot double click reactions (Cu-catalyzed azide/alkyne click chemistry, i.e., CuAAC and Diels–Alder [4+2] cycloaddition reactions). The predecessors for Diels–Alder reaction, maleimide end-functionalized PCLs were produced by ring-opening polymerization (ROP). Obtained dendritic star polymers were characterized by ¹H NMR, size exclusion chromatography (SEC), UV/vis, and fluorescence spectroscopy.