An Experimental Evaluation of a New Commercial Viscometric Detector for Size-Exclusion Chromatography (SEC) Using Linear and Branched Polymers

Abstract

Herein are reported some findings on the application of a new type of continuous automatic viscometer, in parallel with a differential refractometer, as a detector system for SEC. A universal calibration is required for the instrument and two methods of construction are applicable. The first is the customary peak-position calibration using polymer standards of narrow molecular-weight distribution and the second uses a single broad standard of known [Mbar]_w and [Mbar]_n. The two types of calibration are shown to give nearly-identical values of molecular weight when used to process chromatograms obtained from various linear homopolymer standards of varying chemical composition. These values compare favourably with those quoted by the suppliers of the polymer standards. One of the more powerful features of this instrumentation, namely its potential for estimating accurate molecular weights of branched polymers, is demonstrated by analysis of a series of branched polyvinylacetates prepared by a conventional bulk, free-radical polymerisation procedure. The calculation of the degree of chain branching is discussed. Another particular feature of the viscometer detector, its ability to indicate the presence of low concentrations of high-molecular-weight impurity in polymer samples, is also shown.     

Long chain branching indices of low density polyethylenes from size exclusion chromatography and 13C-NMR spectroscopy

Size exclusion chromatography (SEC) and ¹³C-NMR analyses have been used to measure long chain branching indices in low density, free radical-polymerized polyethylenes. Calculation of long chain branching frequency from SEC data requires the assumption of a molecular model. Generally, a randomly branched polymer is assumed, with branches originating at trifunctional branch points. Long chain branch concentrations determined by SEC analysis alone appear to be valid only in a relative sense. The parameters used in the model assumptions vary from polymer to polymer. Despite these limitations, SEC analyses appear to be internally consistent when applied to polyethylenes made by a single manufacturer and process. Comparisons of absolute values of long branch frequency between products from different reactor types require NMR as well as SEC data.     

STUDY ON CATIONIC RING-OPENING POLYMERIZATION MECHANISM OF 3-ETHYL-3-HYDROXYMETHYL OXETANE

ABSTRACT

Cationic ring-opening polymerization of 3-ethyl-3-hydroxylmethyl oxetane was carried out using BF₃·O(C₂H₅)₂ as initiator, and a branched polyether was formed. Typical SEC curves show that the polymer consists of two fractions: one has higher molecular weight (11.7×10⁴～ 9.2×10⁴) and the other has lower molecular weight (3.8×10³～4.0×10³). This probably resulted from the chain-tran sfer reaction of two propagating polymer chains. The structure of the polyEHMO formed was characterized by ¹H and ¹³C NMR spectra. The degree of branching is mainly affected by the propagation mechanism. As the molar ratio of [I]₀/[EHMO]₀ in feed increased, the degree of branching also increased.     

Synthesis of Amphiphilic Azobenzene Functionalized Branched-Type Copolymer Based on Branched Poly(2-(Dimethylamino) ethyl methacrylate) and Investigation of Its Drug Release Properties

Here, we reported the synthesis of branched poly(2-(dimethylamino) ethyl methacrylate) (PDMAEMA) via a combination of activator generated by electron transfer atom transfer radical polymerization (AGET ATRP) and self-condensing vinyl polymerization (SCVP) techniques. The typical linear kinetics of the AGET ATRP of DMAEMA with the initiation of 2-(2-bromoisobutyryloxy) ethyl methacrylate (BIEM) was observed. The molecular weight (M_n ) of the branched PDMAEMA increased with the monomer conversion. The GPC traces of these polymers were unimodal and the molecular weight distributions (M_w/M_n ) were in the range of 1.30–2.10. The degree of branching (DB) determined by NMR spectra agreed with theoretical value. The branched amphiphilic copolymer functionalized with azobenzene was then prepared via AGET ATRP chain-extension of branched PDMAEMA with azobenzene monomer, 6-[4-(4-methoxyphenylazo)phenoxy]hexyl(meth)acrylate as the second monomer. The GPC traces of these branched copolymers showed the mono-peaks, which proved the successful preparation of copolymers. The properties of this branched copolymer in controlling drug release were also investigated. It was found that the drug release rate of chlorambucil can be controlled by various factors, such as polymer structure, light, temperature and pH values.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Branched polystyrene with abundant pendant vinyl functional groups from asymmetric divinyl monomer

Branched polystyrenes with abundant pendant vinyl functional groups were prepared via radical polymerization of an asymmetric divinyl monomer, which possesses a higher reactive styryl and a lower reactive butenyl. Employing a fast reversible addition fragmentation chain transfer (RAFT) equilibrium, the concentration of active propagation chains remained at a low value and thus crosslinking did not occur until a high level of monomer conversion. The combination of a higher reaction temperature (120 °C) and RAFT agent cumyl dithiobenzoate was demonstrated to be optimal for providing both a more highly branched architecture and a higher polymer yield. The molecular weights (M_ws) increased with monomer conversions because of the controlled radical polymerization characteristic, whereas the M_w distributions broadened showing a result of the gradual increase of the degree of branching. The evolution of branched structure has been confirmed by a triple detection size exclusion chromatography (TRI‐SEC) and NMR technique. Furthermore, the double bonds in the side chains were successfully used for chemical modification reactions. ¹H NMR and FTIR measurements reveal that the great mass of pendant vinyl groups were converted to the corresponding objective end‐groups. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6023–6034, 2008     

On-line viscometry combined with gel permeation chromatography. II. Application to branched polymers

Gel permeation chromatography (GPC) combined with on-line flow time measurements have been applied to the analysis of branching in polymers. Three sets of branched polymers were examined: polybutadienes lightly crosslinked by high energy radiation, a styrene-divinyl benzene copolymer and several of its fractions, and polyvinyl acetates branched by polymer transfer reactions during polymerization. The reduction in intrinsic viscosity due to branching was determined for each GPC fraction of the polybutadiene samples. The branching frequency in these fractions was known from other information, so the results were used to establish a relationship between viscosity ratio G and the theoretical size ratio g. This relationship was then used to calculate the distribution of branching and M _w in the styrene copolymers and the polyvinyl acetates. The results were compared with independent information on these polymers. The agreement was generally good.     

Naphthalene Complexation by β-Cyclodextrin: Influence of Added Short Chain Branched and Linear Alcohols

Naphthalene forms 1 : 1 complexes with -cyclodextrin (-CD)in water. The binding constant is 377 ± 35 M^-1. Addition of linear or branched alcohols causes a reduction in the apparent strength of naphthalene binding (K_app) compared to the value in the absence of additives. For example, 1% 1-pentanol reduces K_app to 184 ± 31 M^-1. Branching does not alter K_app much for a given number of carbon atoms, e.g., it is 113 ± 9 M^-1for 2-pentanol and 116 ± 8 M^-1for 3-pentanol. The exception to this is tert-butanol for which K_app is 577 ± 40 M^-1. The variation in K_app as a function of [1-pentanol] yields values for the individual equilibrium constants contributing to K_app. This reveals that a ternary complex forms involving naphthalene, the CD and 1-pentanol. The constant for formation of the ternary complex is 99 ± 29 M^-2. NaI quenching of naphthalene fluorescence indicates that the CD cavity partially protects the naphthalene excited state fromthis water phase quencher. Interestingly, the Stern–Volmer constant is lower in the presence of 1-pentanol than in its absence, although there should be more unbound (and therefore more NaI accessible) naphthalene in the former system than in the latter. These apparently contradictory results are discussed in terms of ternary complex formation.     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

Randomly branched bisphenol A polycarbonates. I. Molecular weight distribution modeling,interfacial synthesis,and characterization

Randomly branched bisphenol A polycarbonates (PCs) were prepared by interfacial polymerization methods to explore the limits of gel‐free compositions available by the adjustment of various composition and process variables. A molecular weight distribution (MWD) model was devised to predict the MWD, G, and weight‐average molecular weight per arm (M_w /arm) values based on the composition variables. The amounts of the monomer, branching agent, and chain terminator must be adjusted such that the weight‐average functionality of the phenolic monomers (F_OH ) was less than 2 to preclude gel formation in both the long‐ and short‐chain branched (SCB) PCs. Several series of SCB and long‐chain branched PCs were prepared, and those lacking gels showed molecular weights measured by gel permeation chromatography–UV and gel permeation chromatography–LS consistent with model calculations. In SCB PCs, the minimum M_w /arm that could be realized without gel formation depended on both composition (molecular weight, terminator type) and process (terminator addition point, coupling catalyst) variables. The minimum M_w /arm achieved in the low molecular weight series studied ranged from ∼3300 to ∼1000. The use of long chain alkyl phenol terminators gave branched PCs with lower glass‐transition temperatures but a higher gel‐free minimum M_w /arm. SCB PCs where M_w /arm was less than ∼M_c spontaneously cracked after compression molding, a result attributed to their lack of polymer chain entanglements. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 560–570, 2000     

One‐pot inimer promoted ROCP synthesis of branched copolyesters using α‐hydroxy‐γ‐butyrolactone as the branching reagent

An array of branched poly(?‐caprolactone)s was successfully synthesized using an one‐pot inimer promoted ring‐opening multibranching copolymerization (ROCP) reaction. The biorenewable, commercially available yet unexploited comonomer and initiator 2‐hydroxy‐γ‐butyrolactone was chosen as the inimer to extend the use of 5‐membered lactones to branched structures and simultaneously avoiding the typical tedious work involved in the inimer preparation. Reactions were carried out both in bulk and in solution using stannous octoate (Sn(Oct)₂) as the catalyst. Polymerizations with inimer equivalents varying from 0.01 to 0.2 were conducted which resulted in polymers with a degree of branching ranging from 0.049 to 0.124. Detailed ROCP kinetics of different inimer systems were compared to illustrate the branch formation mechanism. The resulting polymer structures were confirmed by ¹H, ¹³C, and ₁H‐₁₃C HSQC NMR and SEC (RI detector and triple detectors). The thermal properties of polymers with different degree of branching were investigated by DSC, confirming the branch formation. Through this work, we have extended the current use of the non‐homopolymerizable γ‐butyrolactone to the branched polymers and thoroughly examined its behaviors in ROCP. © 2016 The Authors. Journal of Polymer Science Part A: Polymer Chemistry Published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1908–1918     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Visible-Light-Mediated Controlled Radical Branching Polymerization in Water

Hyperbranched polymethacrylates were synthesized by green-light-induced atom transfer radical polymerization (ATRP) under biologically relevant conditions in the open air. Sodium 2-bromoacrylate (SBA) was prepared in situ from commercially available 2-bromoacrylic acid and used as a water-soluble inibramer to induce branching during the copolymerization of methacrylate monomers. As a result, well-defined branched polymethacrylates were obtained in less than 30 min with predetermined molecular weights (36 000<M_n<170 000), tunable degree of branching, and low dispersity values (1.14≤Đ≤1.33). Moreover, the use of SBA inibramer enabled the synthesis of bioconjugates with a well-controlled branched architecture.     

Theory of Multiple‐Detection Size‐Exclusion Chromatography of Complex Branched Polymers

SEC separates complex branched polymers by hydrodynamic volume, rather than by molecular weight or branching characteristics. Equations relating the response of different types of detectors are derived including band broadening, by defining a distribution function N′(M,V_h), the number of chains with molecular weight M and hydrodynamic volume V_h. While the true molecular weight distribution of complex polymers cannot be determined by SEC, irrespective of the detector used, the formalism enables multiple detection SEC data to be processed to both analyze the polymer sample and reveal mechanistic information about polymer synthesis. The formalism also shows how the true weight‐ and number‐average molecular weight, and , can be obtained from correct processing of the hydrodynamic volume distributions.

     

DETERMINATION OF BRANCHING DISTRIBUTION IN HIGH cis-1,4-POLYBUTADIENE BY GPC AND AUTOMATIC VISCOMETRY

Based on the methods reported by Ambler and Kraus, a method has been developed for the determination of long-chain branching distribution in polymers by the combined use of GPC and intrinsic viscosity data of polymer fractions. In this method, g_i, λ_i, G_i, m_i, the weight percentage of polymer that is branched, etc. can be used simultaneously to characterize the distribution, degree and content of branching in polymers. Some relations between molecular weight polydispersity and branching polydispersity in Nickel-based high cis-1,4-polybutadiene samples are discussed. It was found that the number of long branches λ. per unit molecular weight is a function of molecular weight and all of the samples are highly branched at a molecular weight of about 10~6.     

Mean‐Field Calculation of MZ for Randomly Branched Condensation Polymers

The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of M_Z via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents to control the chain length between branch points, multiple branching agents, and arbitrary stoichiometries. M_Z closely approximates the largest branched polymer in the system and is therefore a key parameter describing static scaling behavior near the gel point. Nonuniversal static scaling of M_Z is illustrated with examples from the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1415–1422     

Branched versus linear polyisoprene: Fractionation and phase behavior

Branched polyisoprene (PI) was prepared from PI-macromonomers. Linear byproducts of the synthesized polymer were removed by means of inverse spin fractionation, using the solvent cyclohexane (CH) and the precipitant acetone (AC). A well-defined fraction (M_w = 17.5 kg/mol, M_w/M_n = 1.8) of the branched polyisoprene obtained in this manner was used to determine different phase diagrams with branched and/or linear PI in the mixed solvent CH/AC at 25 °C. For comparable molar masses of the polymers the two-phase area is smallest for the branched PI and slightly larger for the linear PI; in the case of the unfractionated original sample of the branched polymer one observes a pronounced peninsula of immiscibility extending into the region of high CH concentrations. This feature is attributed to a large miscibility gap between the branched and the linear polymer, which was studied in more detail for the ternary system CH/branched PI/linear PI.     

Synthesis of branched polymers by means of anionic polymerization. 11. anionic synthesis of densely branched polystyrenes carrying double branches in each repeating unit

We have demonstrated the first successful synthesis of well-defined densely branched polystyrenes carrying double branches in each of all repeating unit of backbone polymer by the coupling reaction of 1,1-diphenylethylene-end-capped polystyryllithiums with novel polystyrene derivatives having two benzyl bromide moieties in each monomer unit. The coupling reaction efficiently and quantitatively proceeded without any steric limitations to introduce two polystyrene branches in each repeating unit under certain conditions in THF at −40°C. Thus, a series of 36.4- and 181-arm densely branched polystyrenes were synthesized (M_w = 365 ∼ 2 000 kg/mol, M_w/M_n = 1.01 ∼ 1.03). In the 36.4-arm branched polystyrenes thus synthesized, the maximum M_w value of the introduced polystyrene as a branch segment was 55.1 kg/mol. The experimental g‘ values of the 36.4-arm branched polystyrenes deterimined in the range of 0.14 ∼ 0.15 were very close to the value of 0.13 calculated from the empirical equation previously reported by Roovers.     

Long‐chain branched ROMP polymers

This article describes the construction of branched ROMP‐polymer architectures via polycondensation of AB_n‐type macromonomers. For this convergent strategy, a polymer was synthesized that carries several hydroxyl‐groups along the polymer chain and one carboxylic acid group at the chain end. An esterification reaction between these functional groups yielded long‐chain branched polymers. The polymers were analyzed by NMR and SEC to monitor the condensation reaction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Influence of molecular weight distribution and long chain branching on the glass transition temperature of polycarbonate

Molecular weight distribution and long chain branching were taken into account for the glass transition temperature (Tg)-molecular weight (M) relationships for bisphenol-A polycarbonate. A new form of the four-variable equation for Tg is proposed for polydisperse branched polymers. The extended equations were compared with the experimental results on Tg and M averages; they were also applied for characterization of branched polymer by the combined GPC/V and DSC methods.