Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Size exclusion behavior of polymers in amide solvents

Summary The abnormal behavior of acrylonitrile polymers shown by size exclusion chromatography (SEC) in N,N-dimethylformamide (DMF) was investigated by using model polymers having variable degrees of sulfonated moieties as electric charged groups. The unexpected small retention volume and very high UV absorption at 280 nm were observed in the case of the samples with ionic sulfonate groups even in very small amounts, as chain ends. The abnormal behavior was confirmed to be due to impurities of DMF decomposition which interact with charged groups in the polymers.     

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.     

Local polydispersity detection in size exclusion chromatography: Method assessment

Local polydispersity is the term describing the variety of molecules present at the same retention volume in size exclusion chromatography (SEC) analysis. In the analysis of a linear homopolymer, local polydispersity is generally attributed to the effect of axial dispersion: it can cause molecular size variety (i.e., imperfect resolution) at each retention volume and thus local polydispersity in the molecular weight. In the analysis of polymer blends (copolymers and branched polymers), it is possible to have local polydispersity, even when the resolution is perfect, because molecules of different compositions (or degrees of branching) can have the same molecular size in solution. Conventional SEC interpretation assumes no local polydispersity if the axial dispersion effects are negligible. Three methods are currently available for detecting local polydispersity by using a combination of differential refractive index, light scattering, and viscometer detectors: the chromatogram comparison method, the conventional calibration curve comparison method, and the universal calibration comparison method. Here we experimentally assess these three methods using polymer blends and emphasize the chromatogram comparison method. All three are shown to be useful for assessing triple detector systems, but they are capable of detecting local polydispersity due to molecular heterogeneity only for very large differences in specific refractive index increments in the blend components. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 370–383, 2001     

Characterization of branched polymers by SEC coupled with a multiangle light scattering detector. II. Data processing and interpretation

This study deals with the characterization of branched polymers by means of size-exclusion chromatography coupled with a multiangle light scattering detector (SEC-MALS). The application of SEC-MALS is demonstrated on several randomly branched polystyrene and star-branched poly(benzyl methacrylate) samples. Various methods of the data processing are compared. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 454–460, 2001     

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.     

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.     

Influence of shearing history on the rheological properties and processability of branched polymers. III. An amorphous long-chain branched polymer

Viscoelastic properties of branched polymers vary with their shearing history; notwithstanding, their primary molecular parameters do not change. According to a recent study, such viscoelastic variation was believed to be observed only with crystalline long-chain branched polymers such as low-density polyethylene or polyacetal. That is, the origin of the viscoelastic variation was attributed to the presence of specific entanglements at the branching points, which was formed during the crystallization process. However, the viscoelastic variation of the long-chain branched polymers is the phenomenon at temperatures well above their melting points, namely, it is considered that whether the long-chain branched polymers are crystalline or not is not essential for the occurrence of the viscoelastic variation. Thus, the influence of the shearing history on the rheological properties of an amorphous long-chain branched polymer was investigated in this paper, and it was found that, irrespective of their crystallinity, the viscoelastic properties of long-chain branched polymers vary according to their shearing history.     

Comments on the measurement of long chain branching by size exclusion chromatography

Summary A technique for measuring long chain branching as a function of polymer molecular weight uses SEC with a low angle laser light scattering (LALLS) detector to compare M_W of an eluting species with the molecular weight of the linear counterpart that has the same retention time. This technique is correct only if all species in the SEC detector cells have the same constitution. Evidence is presented that indicates that this condition prevails for low density, high pressure polyethylene and polyvinyl alcohol. Alternative forms of data representations are suggested. A major uncertainty in the data treatment is the value to be assigned to the ratio of radii of gyration of linear and branched polymers with the same molecular weight. A method is suggested to measure this ratio directly, as a function of molecular weight, if the eluting species at any instant are uniform in branching character.     

Elution behaviour of diolmodified epoxides in size exclusion chromatography

The reaction of bisphenol A-diglycidyl ether (BADGE) with butane-1,4-diol (BD) in the presence of Mg(ClO₄)₂ leads to linear and branched oligomers. The formation ratio of these products depends on the reaction temperature. In experiments at 100°C, an epoxide consumption of up to 70% can be observed using HPLC. In this range all products show good solubility in THF, so that it is possible to follow the increasing molar mass by using SEC. A characteristic relation of the molar mass against the conversion rate is derived and SEC data of a branched product are discussed.     

Size-exclusion chromatography with two-angle laser light-scattering (SEC-TALLS) of high molecular weight and branched polymers

The accuracy and precision of results obtained from light-scattering detection at two angles (TALLS) for size-exclusion chromatography (SEC) are examined for linear narrow molecular weight distribution polystyrenes between 1,290,000 and 20,000,000 MW and for branched polyesters. The ratio of light-scattering intensities at 15° and 90° is used to calculate weight-average molecular weight, M?_w, and an average root-mean-square radius, r?_gu, equivalent to the z-average radius. A shape for the polymer molecule is assumed and an analytical relationship for the particle-scattering function is required. It is shown that analysis of the data using the particle-scattering function for a random coil is valid for both high molecular weight, linear polystyrenes and long-chain branched polyesters. The radius, r?_gu, is determined with high precision by using the ratio of light-scattering signals, which is insensitive to errors in sample concentration and changes in the eluent flow rate. The correct average radius for the whole polymer is obtained despite using low-efficiency, large-particle diameter SEC columns; however, axial dispersion significantly affects molecular weights and radii calculated at each retention volume that can limit the utility of plots used to deduce polymer conformation. © 1995 John Wiley & Sons, Inc.     

Size exclusion chromatography of polyelectrolytes in dimethylformamide

A study of the size exclusion chromatographic behavior of styrene–methacrylic acid and epoxyacrylic polymers has been made. These polymers exhibit strong “ion-exclusion” effects in DMF, similar to that found for water-soluble polyelectrolytes such as sodium polystyrene sulfonate. The addition of lithium bromide, at a concentration of 0.1M, overcomes ion exclusion on a set of silicabased, “deactivated” duPont SEC columns. Calibration of both the duPont columns and a set of styrene–divinyl benzene based columns (μ-Styragel) is complicated by absorption of polystyrene standards in DMF and DMF/salt mobile phases. The absorption of monomeric solutes on the duPont columns in DMF/salt mobile phases is different from that of their corresponding polymers.     

Gel permeation chromatography on branched polymers

In gel permeation chromatography on long-chain branched polymers, calibration with linear samples leads to incorrect results. There are, however, several ways in which the data can be treated correctly. All of them call for the use of extra experimental information, such as viscosity or light scattering data of the whole polymer or the GPC eluent. The Drott—Mendelson method, using [η] of the whole polymer and GPC data, has been employed for analysing three low density polyethylene samples. The potentialities of viscometry and light-scattering measurements in the GPC effluent have also been examined. From [η], M_w and GPC data the long-chain branching index g′ can be derived in three ways, although it should be stated that the average g′-values so found for polydisperse samples are different.     

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.     

Unperturbed dimensions of branched chain,star and ring polymers

A novel Monte Carlo method has been applied to the calculation of the unperturbed dimensions of various monodisperse polymers, e.g. star polymers, branched polymers formed by the crosslinking of linear primary chains, and linear chains with some intramolecular cycles. Where results for the parameters h^?1 and g (representing the effect of branching upon the hydrodynamic radius and the radius of gyration, respectively) were known previously, agreement is good. The method can, however, be applied to furnish other statistical averages for polymers of any arbitrary branched structure, and the effects of polydispersity may also be included.     

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.     

Synthesis and characterization of well-defined comb-like branched polymers

Well-defined comb-like branched polymers having one branch in each repeating unit have been successfully synthesized by the coupling reaction of living polystyrene (PS) and polyisoprene (PI) anions with 1, 1-diphenylethenyl (DPE) groups along PS backbone prepared via atom transfer radical polymerization (ATRP) of 4-vinylbenzyloxy benzophenone (Sc) followed by Wittig reaction. The resulting comb-like branched polymers were characterized by IR, ¹H-NMR, gel permeation chromatography (GPC) and static light scattering (SLS) in detail. The effect of living chains and DPE group molar ratio on grafting efficiency was discussed. The results show the coupling reaction of living chains and DPE groups was highly effective, and the coupling efficiency can be controlled via the feed molar ratios of living chains and DPE groups. Moreover, the effect of molecular weights of backbone (PSe) and PSLi or PILi on grafting efficiency was also discussed. The results show that when excess living polymers were used, the almost quantitative grafting efficiency could be achieved. __________ Translated from Acta Polymerica Sinica (China), 2007, (3): 203–208 [译自: 高分子学报]     

Synthesis and characterization of well-defined comb-like branched polymers

Well-defined comb-like branched polymers having one branch in each repeating unit have been successfully synthesized by the coupling reaction of living polystyrene (PS) and polyisoprene (PI) anions with 1, 1-diphenylethenyl (DPE) groups along PS backbone prepared via atom transfer radical polymerization (ATRP) of 4-vinylbenzyloxy benzophenone (Sc) followed by Wittig reaction. The resulting comb-like branched polymers were characterized by IR, ¹H-NMR, gel permeation chromatography (GPC) and static light scattering (SLS) in detail. The effect of living chains and DPE group molar ratio on grafting efficiency was discussed. The results show the coupling reaction of living chains and DPE groups was highly effective, and the coupling efficiency can be controlled via the feed molar ratios of living chains and DPE groups. Moreover, the effect of molecular weights of backbone (PSe) and PSLi or PILi on grafting efficiency was also discussed. The results show that when excess living polymers were used, the almost quantitative grafting efficiency could be achieved.     

Novel biocidal polymers based on branched and linear poly(hydroxystyrene)

New biocidal polymers based on branched as well as linear poly(p-hydroxystyrene) were synthesized. Biocidal polymers were synthesized in two steps by creation of active centers via chloroacetylation of linear and branched poly(p-hydroxystyrene) using chloroacetyl chloride. The second step involves the immobilization of onium salts onto the chloroacetylated polymers. All the prepared polymers were characterized using elemental microanalysis, FT-IR, ¹H NMR spectra, and TGA. Antimicrobial activity of the prepared polymers was tested against various pathogenic microorganisms. The antimicrobial activity was found to be affected by the active group and the tested microorganism. The phosphonium salts showed higher activity than ammonium salts.     

Number-average molecular weight by size exclusion chromatography

It is now theoretically possible to obtain absolute accurate values of number-average molecular weight of complex polymers (e.g., branched polymers or copolymers) using size exclusion chromatography (SEC) with only a detector that measures the difference between the eluting polymer solution viscosity and the viscosity of the pure mobile phase (a differential viscometer [DV] detector). However, both precision and accuracy of these “DV M?_n” values are of concern. In this work, the precision of NBS 706 polystyrene was found to be two to three times worse for the DV M?_n than for the conventionally calculated M?_n. Also, regarding accuracy, the DV M?_n values were affected by the location of the universal calibration curve along the retention volume axis (a problem intimately associated with the problem of specifying the correct interdetector volume), the sensitivity of the DV detector to low molecular weights present in the sample, and axial dispersion. Each of these sources of error are examined in turn and two methods of calculating M?_n values are proposed. © 1994 John Wiley & Sons, Inc.