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.     

A theory of topological separation of linear and star-shaped polymers by two-dimensional chromatography

Topology influences the size of macromolecules, but polymers are usually distributed with respect to molar mass, which also results in the size distribution within a polymeric sample. Due to this fact size-exclusion chromatography (SEC) is not able to separate even moderately polydisperse polymers by topology; the same is also true for the adsorption chromatography (AC). The full separation by molar mass and topology is not possible by any single mode of chromatography. These problems can be solved by means of two-dimensional chromatography which combines SEC and AC mechanisms. A theory of interactive chromatography of linear and star-shaped ideal-chain polymers is used to analyze two-dimensional chromatographic separation of polydisperse linear and star polymers. Basing on this theory, we simulate 2D-chromatograms for model mixtures of polydisperse linear and star-shaped polymers of equal average molar mass, and demonstrate that 2D-separation of such polymers by topology is possible. A possibility to separate symmetric and very asymmetric stars by 2D-chromatography is predicted. The influence of the molar-mass heterogeneity, pore size and adsorption interaction parameter on the 2D chromatographic pattern is analysed, and the conditions for a good separation of linear and star polymers are formulated. The theoretical results are in a qualitative agreement with the experimental data, which have been reported previously by Gerber and Radke.     

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.     

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.     

Molecular characterization of α,β-poly(N-2-hydroxyethyl)-dl-aspartamide derivatives as potential self-assembling copolymers forming polymeric micelles

A family of graft copolymers derivatives obtained from α,β-poly(N-2-hydroxyethyl)-dl-aspartamide (PHEA) have been studied as potential self-assembling macromolecules forming stable polymeric micelles at low critical micellar concentration. These polymers are obtained grafting on PHEA poly(ethylene glycol) (PEG) (M_w 5000 g/mol) (PHEA-PEG), hexadecylamine (PHEA-C₁₆) or both moieties (PHEA-PEG-C₁₆). The PHEA derivatives were characterised by a multi-angle light scattering (MALS) photometer on line to a size exclusion chromatography system in obtaining the molar mass distribution of the polymers. In addition, to investigate the capacity to form micellar aggregates in aqueous medium the MALS photometer was used in off-line batch mode in obtaining molar mass and dimension of the polymeric aggregates.     

Fast determination of critical eluent composition for polymers by gradient chromatography

Gradient chromatography was applied in order to calculate the composition at elution for different methacrylates on normal phase columns. In addition the composition at elution was determined for polyethyleneoxide on a reverse phase column. It is shown that high molar mass polymers elute for a given homopolymer irrespective of their molar mass at the same eluent composition, which varies only slightly with gradient slope. In general the composition at elution in gradient chromatography is expected to be slightly lower than the true critical composition. For high molar mass polymers we found this composition to be close to the critical composition determined by isocratic experiments. The difference between the composition at elution and the true critical composition for a variety of polymethacrylates and for polyethyleneglycol was found to be only between 0.2 and 5%. Thus, after estimating the composition at elution, only a small number of additional isocratic experiments is needed to find the exact critical composition.     

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.     

Theory of chromatography of ring-shaped block copolymers

A theory is developed for describing liquid chromatography of ring diblock and multiblock copolymers. The chromatographic behavior of ring block copolymers at different adsorption interactions is analyzed theoretically and compared with that of linear block copolymers; typical chromatograms are simulated by using the theory. In particular, it is shown that under the critical interaction condition for one block the chromatographic retention of a ring diblock copolymer is dependent of the length of the ‘critical’ block; this behavior differs qualitatively from that of a linear diblock copolymer. Ring copolymers are always more retained than linear ones, therefore such copolymers can be separated. Especially good separation of heterogeneous ring and linear block copolymers is predicted at near-critical interaction conditions. According to the theory, ring diblocks and multiblocks can be separated as well, if one component of a copolymer is adsorbing, while the other one is not adsorbing.     

Diffusion of liquids in molten polymers: Mutual diffusion coefficient dependence on liquid miscibility and polymer molar mass

This paper addresses two important features of the diffusion of liquids into a molten polymer matrix: the dependence of the mutual diffusion coefficient on the liquid miscibility and molar mass of polymers. In addition, a rheological approach is chosen for its capacity to support modeling, and the mutual diffusion coefficient expressed with the free-volume theory, is estimated by an inverse method. For that purpose, the diffusion process of 2,3-epoxypropyl-phenylether (EPPE) and the N-ethylaniline (NEA) in three molten poly(ethylene-co-vinyle acetate) elastomers (EVA) having different molar masses is examined. The NEA is fully miscible with EVA and its diffusion process is not dependent on the molar mass of the polymer. On the other hand, the diffusion process of EPPE, that is partially miscible with EVA, is strongly influenced by the molar mass of the EVA. Furthermore, the evolution of the concentration gradient during the diffusion process of EPPE is driven by the necessity for the mixture to form a two-phase system with an EVA-rich phase and an EPPE-rich phase. In this case, the concentration gradient through the sample is not continuous at a macroscopic scale. Consequently, the calculation procedure is only applied during the early stages of the diffusion. For EPPE, the variation of the mutual diffusion coefficient with the molar mass of EVA is taken into account through the variation of the interaction parameter. Actually, despite the imperfections of the model, our experimental observations and rheological inverse calculation of the diffusion process are in agreement with the findings of the free volume theory of the diffusion.     

Macrocycle-functionalized polystyrene beads as specific absorbers

Crosslinked polystyrene beads were first functionalized with phenacyl ester linkers, and a series of four macrocycles with different ring sizes were synthesized from these linkers. The macrocycles were built from amide-linked monomers coupled by conventional peptide-synthesis methods. Annulation was achieved by copper(I)-catalyzed intramolecular azide–alkyne cycloaddition to give triazole linked macrocycles. The macrocycles were cleaved from the polymer beads with hydrazinolysis or saponification. The structures of macrocycles were confirmed by high-resolution nuclear magnetic resonance (NMR) and liquid chromatography–mass spectrometry (LC–MS) analysis. The ability of the polymers to selectively bind compounds from a mixture of aromatic derivatives in ethanol was tested. The prepared polystyrene supported macrocycles were found to selectively bind bromophenol blue and bromocresol green non-covalently with an association constant of 160–490 M⁻¹.     

Multidimensional mass spectrometry methods for the structural characterization of cyclic polymers

Several synthetic methods have been developed for the tailored preparation of cyclic macromolecules due to their unique physical and chemical properties. Unequivocal characterization of the macrocyclic architectures has remained challenging, however, because isomeric linear structures often exist, or the spectral features of linear vs. cyclic chains are similar. To address this problem, multidimensional mass spectrometry (MS) techniques have been evaluated for the separation and identification of polymeric macrocycles. Tandem mass spectrometry (MS²) is found to be ideally suitable for the differentiation of linear and cyclic architectures whose molecular ions exhibit distinct fragmentation characteristics. Conversely, differences in macromolecular sizes and shapes can be exploited to identify the correct architecture by ion mobility mass spectrometry (IM-MS). A third option, chromatographic separation (LC) before MS analysis, is available for the detection of cyclics in complex mixtures. The capabilities of these techniques and combinations thereof are demonstrated with specific covalent or supramolecular (co)polymers.     

Synthesis of dihydroxy poly(ethylene-co-butadiene) via metathetical depolymerization: Kinetic and mechanistic aspects

We investigate the synthesis of dihydroxytelechelic poly(ethylene-co-1,3-butadiene) via metathetical depolymerization of the corresponding high molar mass copolymers in the presence of first generation Grubbs catalyst and butene diacetate as functionalizing chain transfer agent, followed by hydrolysis of the acetoxy chain ends. Formation of telechelic oligomers is complicated by a fast back-biting reaction leading to cyclohexene and macrocycles production. The thermodynamically favored formation of unsaturated six membered ring results from the presence of 1,7-dienic unsaturations in the starting copolymer. Macrocycles also rapidly and almost quantitatively form in the first reaction stage. Opportunely they can re-open in the presence of functionalizing transfer agent, owing that the later is introduced in molar excess with respect to the macrocycle, finally yielding linear dihydroxytelechelic oligomers.     

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     

Characterization of polydihydrosilane by SEC-MALLS and viscometry

Silicon hydride compounds consisting of silicon and hydrogen constitute a fascinating class of silicon-based polymers because of their ability to form high-quality silicon film by solution-based process. In this study, we synthesize polydihydrosilane by photo-induced ring-opening polymerization of cyclopentasilane, and determine the molar mass, radius of gyration, and intrinsic viscosity of it in cyclohexene by size-exclusion chromatography combined with multi-angle laser light scattering and viscometry. It was found that the molar mass of polydihydrosilane ranges broadly from 10² to 10⁶ g/mol. Both the intrinsic viscosity and radius of gyration exhibited a scaling behavior with respect to the molar mass with the intrinsic viscosity exponent α = 0.206 and radius of gyration exponent ν = 0.410. Classification of the polymer structure based on the α value suggests that the polydihydrosilane forms a branched-chain structure with a particle-like compact shape rather than a straight chain.     

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.     

Solution properties of comb‐like polymers consisting of dimethylsiloxane monomer units

A series of comb‐like polymers consisting of dimethylsiloxane monomer units and differing by side‐chain length have been studied in hexane solution using analytical ultracentrifugation, translational diffusion and viscometry. Analysis of the hydrodynamic parameters and their molar mass dependences based on the Fixman–Stockmayer theory or wormlike spherocylinder model shows that with side chain lengthening, the Kuhn segment length A of the polymers under study increases from the value of A for linear polydimethylsiloxane to values typical for semi‐rigid chain polymers A = 8–10 nm. © 2016 Society of Chemical Industry     

How does sequence length heterogeneity affect the dilute solution conformation of copolymers?

Sequence length heterogeneity (SLH) is defined as the change, as a function of copolymer molar mass (M), in the average number of continuous monomers of a given repeat unit. SLH can influence polymeric properties such as thermal stability, mechanical behavior, transparency, and the ability of copolymers to reduce interfacial surface tension. Here, we demonstrate the relation between SLH and the change as a function of molar mass of a dimensionless size parameter, the ratio of the viscometric radius and the radius of gyration, irrespective of chemical heterogeneity or molar mass polydispersity. Multi-detector size-exclusion chromatography (SEC) provides for a convenient method by which to experimentally establish this relation and, consequently, a method by which to determine whether SLH is present in a copolymer, whether the degree of randomness of a copolymer changes across the molar mass distribution (MMD), or whether two copolymers differ from each other in degree of randomness at a given M and/or across their MMDs. Results from our SEC and FT-IR measurements of block, random, alternating, and gradient copolymers of styrene (S) and methyl methacrylate (MMA) and their respective homopolymers agree with results from a probability theory based model of SLH in linear random copolymers. The multi-detector SEC method employs instrumentation available in most polymer separations laboratories and the relations developed should be applicable to copolymers other than the S-MMAs studied here.     

Lithium naphthalenides in non-polar or in low-polarity media: some insights regarding their use as initiators in anionic polymerizations

The synthesis of bidirectional anionic initiators by the reaction between metallic lithium (Li) and naphthalene (Naph), under mild conditions, in non-polar (benzene) or low-polarity media (benzene/THF mixtures) is reported. The efficiency of these initiators to provide macromolecules with well-defined structures was demonstrated. Model linear homopolymers from styrene (S) or hexamethyl(ciclotrisiloxane) (D₃) monomers were synthesized using classical anionic polymerization (high-vacuum techniques). The model polymers obtained were analyzed using the conventional analytical techniques, and showed narrow molar mass distributions, a broad range of molar masses (from 3000 to 1,000,000 g/mol) and polydispersity indexes (M _w/M _n) lower than 1.1. High molar mass polymers were obtained using pure benzene as solvent, whereas lower molar masses were obtained in benzene/THF mixtures in which the concentration of THF was lower than 10 % v/v. The ratio [Li]/[Naph] and the nature of the reaction medium are the experimental parameters to be controlled to obtain the desired lithium naphthalenides.