Monte Carlo simulation of size exclusion chromatography for branched polymers formed through free‐radical polymerization with chain transfer to polymer

The elution curves of size exclusion chromatography (SEC) for branched polymers formed through free‐radical polymerization that involves chain transfer to polymer were theoretically investigated by using a Monte Carlo method. We considered two types of measured molecular weight distribution (MWD), (1) the calibrated MWD relative to standard linear polymers, and (2) the MWD obtained by using a light scattering photometer (LS) in which the weight‐average molecular weight of polymers within the elution volume is determined directly. It was found that the calibrated MWD clearly underestimates the high molecular weight tail, and the measured distributions are narrower than the true MWD. On the other hand, the present simulation results showed that the LS method gives reasonable estimates of the true MWDs. The mean square radius of gyration of the polymer molecules having the same molecular weight was also investigated. The radii of gyration showed clear deviation from the Zimm‐Stockmayer equation^[1] because of the non‐random nature of branched structure and the difference in the primary chain length distribution.     

Size exclusion chromatography of branched polymers: Star and comb polymers

Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight‐average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb‐branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD.     

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

Molecular weight distribution in random branching of polymer chains

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight-average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T-shaped junctions) without assistance of crosslinkages (H-shaped junctions).     

Theoretical description of unconstrained thermally induced shape‐memory recovery in crosslinked polyethylenes

A new theoretical approach based on the modified three‐element Eyring‐Halsey model was developed for the derivation of an equation describing the thermally induced recovery of predeformed and crystallized crosslinked polymers. The proposed approach takes into account the influence of crystallizable covalent network and of entangled slipped molecular chains. Modeling of thermally induced shape‐memory (SM) recovery strain and SM recovery rate detected at constant heating rate has been successfully performed for nearly linear and two short‐chain branched polyethylenes, which were crosslinked by peroxide. The values of material constants determined by fitting agree with the estimations existing in literature. Fitting results have shown that increase of degree of branching and crosslink density accompanied with reducing crystallinity results in increasing contribution of the entangled slipped chains to the total stored SM strain. The physical sense of main fitting parameters and their dependences on the material constants such as crystallinity are discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 815–822     

Rheological properties of HyperMacs—long‐chain branched analogues of hyperbranched polymers

HyperMacs are long chain branched analogues of hyperbranched polymers, differing only in the sense that they have polymer chains, rather than monomers between branch points. Although the building blocks for HyperMacs and AB₂ macromonomers can be well defined in terms of molecular weight and polydispersity, the nature of the coupling strategy adopted for the synthesis of the HyperMacs results in branched polymers with a distribution of molecular weights and architectures. Melt rheology showed polystyrene HyperMacs to be thermorheologically simple, obeying William–Landel–Ferry behavior. Zero shear viscosities of the polymers were shown to increase with average molecular weight and the melts display shear‐thinning behavior. HyperMacs showed little evidence for relaxation by reptation and the rheological behavior agreed well with the Cayley tree model for hierarchical relaxation in tube models of branched polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2762–2769, 2007     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

Liquid chromatography at the critical condition: Thermodynamic significance and influence of pore size

Liquid chromatography at the critical condition (LCCC) is a high performance liquid chromatography (HPLC) technique that lies between size exclusion chromatography and adsorption-based interaction chromatography, where the elution of polymers becomes independent of polymer molecular weight. At LCCC, the balance between the entropic exclusion and the enthalpic adsorption interactions between polymers and stationary phases results in the simultaneous HPLC elution of polymers regardless of molecular weight. Using C18-bonded silica chromatographic columns with 5 μm particle size and different average pore size (diameter = 300 Å, 120 Å, 100 Å, and 50 Å), we report (1) the thermodynamic significance of LCCC conditions and (2) the influence of column pore size on the determination of critical conditions for linear polymer chains. Specifically, we used mixtures of monodisperse polystyrene samples ranging in molecular weight from 162 to 371,100 g/mol and controlled the temperature of the HPLC columns at a fixed composition of a mobile phase consisting of 57(v/v)% methylene chloride and 43(v/v)% acetonitrile. It was found that, at the fixed mobile phase composition, the temperature of LCCC (T_LCCC) is higher for C18-bonded chromatographic columns with larger average pore size. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2533–2540, 2009     

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     

Polystyrene with dendritic branching by convergent living anionic polymerization. II. Approach using vinylbenzyl chloride

Vinylbenzyl chloride (VBC) has been used as a coupling agent in Convergent Living Anionic Polymerization to produce polymers with dendritic branching. The slow addition of a stoichiometric amount of VBC to living polystyrene chains allows the coupling to proceed through macromonomer formation followed by vinyl addition. Changing the reaction conditions produced two types of structures. Star‐shaped polymers with a hyperbranched core were made by the continuous slow addition of VBC alone, and chain‐extended hyperbranched structures with varied molecular weight between branch points were produced by the slow addition of VBC mixed with different amounts of styrene monomer. The extent of growth of the two different types of structures ranged from 2.4 to 2.6 generations for the case of VBC added alone, corresponding to an average of 5.3 to 6.1 arms attached to the hyperbranched core, and from 3.2 to 4.2 generations for polymers produced from the addition of VBC mixed with styrene. Relatively low polydispersities were obtained for all samples. The highly branched nature of the polymers was reflected in the low intrinsic viscosity relative to linear polystyrene and in the dependence of glass‐transition temperature on the molecular weight relative to the number of end groups. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4289–4298, 2000     

Radical polymerization in the presence of peroxide and reducing agent monomer for branched polymers

In this article, we report the radical polymerization in the presence of peroxide and commercially available or designed reducing agent monomer (RAM) for the preparation of branched poly(methyl methacrylate)s (PMMAs). The reaction behavior of the RAM was studied by NMR. Triple‐detection SEC (TD‐SEC) analysis was used to confirm the branching structure of the prepared PMMAs and to investigate the influence of peroxide concentration and RAM concentration on molecular weight and branched structure. The obtained branched PMMAs exhibited high molecular weights and relatively narrow polydispersities at high conversion of MMA. Interestingly, a significant increase in molecular weight and degree of branching of the obtained polymers are observed in higher BPO concentration, these results are quite different from that reported in the literature. The unique radical polymerization mechanism in the RAM/BPO redox‐initiated radical polymerization system resulted in branched PMMAs with high molecular weights at relatively high RAM and BPO concentrations. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 833–840     

Structure of interpenetrating polymer networks

A possible model for the formation of interpenetrating polymer networks is suggested. Phase separation is assumed to be faster than gelation. This implies that domains rich in either component grow first until late stages of spinodal decomposition. In these domains, short linear chains are crosslinked, leading to large branched macromolecules. Growth of the domains is slowed down by the presence of crosslinked polymers. It is assumed that it is stopped when the sizes of the domains and of the branched macromolecules are comparable. The resulting domains are significantly larger than the average distance between crosslinks. These results are supported by recent neutron scattering results on a poly(carbonate-urethane)/polyvinyl pyridine interpenetrating network. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1507–1512, 1998     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906     

Stimuli-responsive star polymers

Stimuli-responsive star polymers gain more and more interest over the last decades due to their unique properties compared to their linear counterparts. The branched structure for instance has influence on the responsive behavior of these polymers. This review offers an overview of stimuli-responsive star polymers generated by different polymerization techniques, e.g. anionic and controlled radical polymerization (CRP). Beside conventional branched homopolymers different other types like block copolymers, miktoarm star copolymers, core crosslinked star polymers (CCS) and comb polymers are also presented. Furthermore their responsive behavior in solution or immobilized on a substrate, and their applications are outlined. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2980–2994     

Postgel properties in the statistical crosslinking of heterochains. II. Free‐radical crosslinking copolymerization

The heterochain crosslinking theory is applied to postgel behavior in the free‐radical crosslinking copolymerization of vinyl and divinyl monomers. In this context, the crosslinked polymer formation can be viewed as a system in which the primary chains formed at different times are combined in accordance with the statistical chain‐connection rule governed by the chemical reaction kinetics. Because the primary chains are formed consecutively, the number of chain types N must be extrapolated to infinity, N → ∞. Practically, such extrapolation can be conducted with the calculated values for only three different N values. The analytical expressions for the weight fraction and average molecular weights of the sol fraction are derived for the general primary chain length distribution function in free‐radical polymerization. Illustrative calculations show that the obtained results agree with those from the Monte Carlo method, and that the postgel properties in free‐radical crosslinking copolymerization systems could be significantly different from those in randomly crosslinked systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2342–2350, 2000     

One‐step synthesis of ladder‐type fused poly(benzopentalene) derivatives with tunable energy levels by variable substituents

Novel ladder‐type conjugated polymers, fused poly (benzopentalene) derivatives, were synthesized from the readily accessible 1,4‐dibromo‐2,5‐diethynylbenzene derivatives by the Pd‐catalyzed self‐polycondensation in one‐step with high yields. The low solubility of the ladder structure was suggested when the triisopropylsilyl substituents were selected. However, when longer alkyl chains were introduced into the peripheral moieties, such as the dialkylanilino (DAA) and alkyloxyphenyl groups, a high solubility was achieved and the number‐average molecular weight (M_n) reached 18,000. The UV‐Vis absorption spectral shapes of the polymers were similar to the reported dibenzopentalene derivatives, except for the bathochromically shifted end absorptions. This result suggests an extension of the π‐conjugated systems due to the polymerization. Moreover, the almost defect‐free structure of the ladder‐type polymers was confirmed by the quantitative tetracyanoethylene (TCNE) addition to the DAA‐activated alkynes. The titration experiments of TCNE to the polymers revealed the number of terminal alkynes, which enabled us to calculate the molecular weight of the polymers. The calculated molecular weight was consistent with that determined by GPC. After the TCNE addition, the polymer band gaps reasonably decreased as suggested by the UV‐Vis‐NIR absorption and electrochemical measurements. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Obtaining aliphatic branched polycarbonates via simple copolymerization of trimethylene carbonate with cyclic carbonate containing pendant ester groups

Different possibilities for obtaining branched, functional carbonate copolymers are presented in this study. Copolymers were synthesized according to the ring‐opening polymerization (ROP) of the cyclic carbonate monomers, containing pendant ester groups. As an example, we chose copolymerization of ethyl 5‐methyl‐2‐oxo‐1,3‐dioxane‐5‐carboxylate (MTC‐Et) with trimethylene carbonate (TMC), using zinc (II) and lanthanum (III) acetylacetonates as ROP initiators. The transesterification processes of ester groups in pendant, short chains, appearing during conducted copolymerization, led to the establishment of two different fractions: first‐branched and high molecular weight fraction and second‐linear and low molecular weight. The content of this high‐molecular‐weight fraction increased with both: the amount of MTC‐Et in started reaction mixture and the time of conducted copolymerization. Reactivity constants in studied reaction were determined. It was possible to obtain the copolymer fraction (ca. 30%) with molecular weight of up to a million g/mol, with a highly branched chain microstructure using lanthanum (III) acetylacetonate as initiator. Conclusions were based on detailed NMR analysis, determining microstructure of the copolymer chains and additionally on GPC and DSC measurement. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 808–819     

Kinetics of the styrene emulsion polymerization using n‐dodecyl mercaptan as chain‐transfer agent

The kinetics of the styrene emulsion polymerization using n‐dodecyl mercaptan as chain‐transfer agent was studied. It was found that the chain‐transfer agent (CTA) had no effect on polymerization rate but substantially affected the molecular weight distribution (MWD). The efficiency of the CTA in reducing the MWD was lowered by the mass‐transfer limitations. The process variables affecting CTA mass transfer were investigated. A mathematical model for the process was developed. The outputs of the model include monomer conversion, particle diameter, number of polymer particles, and number‐average and weight‐average molecular weights. The model was validated by fitting the experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4490–4505, 2000     

Synthesis of arborescent styrene homopolymers and copolymers from epoxidized substrates

The synthesis of arborescent styrenic homopolymers and copolymers was achieved by anionic polymerization and grafting. Styrene and p‐(3‐butenyl)styrene were first copolymerized using sec‐butyllithium in toluene, to generate a linear copolymer with a weight‐average molecular weight M_w = 4000 and M_w/M_n = 1.05. The pendant double bonds of the copolymer were then epoxidized with m‐chloroperbenzoic acid. A comb‐branched (or arborescent generation G0) copolymer was obtained by coupling the epoxidized substrate with living styrene‐p‐(3‐butenyl)styrene copolymer chains with M_w ≈ 5000 in a toluene/tetrahydrofuran mixture. Further cycles of epoxidation and coupling reactions while maintaining M_w ≈ 5000 for the side chains yielded arborescent copolymers of generations G1–G3. A series of arborescent styrene homopolymers was also obtained by grafting M_w ≈ 5000 polystyrene side chains onto the linear and G0–G2 copolymer substrates. Size exclusion chromatography measurements showed that the graft polymers have low polydispersity indices (M_w/M_n = 1.02–1.15) and molecular weights increasing geometrically over successive generations. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Round‐robin experiment in high‐temperature gel permeation chromatography

The results of an interlaboratory or round‐robin experiment in high‐temperature gel permeation chromatography (HT‐GPC) analysis are presented. The intention was to determine and raise awareness of interlaboratory reproducibility of HT‐GPC techniques. Fifteen laboratories performed analyses of five polyethylene samples and standards SRM 1475 and 1476. Reproducibility, as measured by the interlaboratory standard deviation (s_LAB), was greatly influenced by the breadth of the molecular weight distribution (MWD) and branching. The s_LAB values for the weight‐average molecular weight (M_w) of linear polyethylenes of narrow and broad MWDs were 4 and 14%, respectively. For branched polymers, GPC viscometry methods are shown to measure significantly higher molecular weights than the noncoupled GPC method, with higher variance. For branched polyethylenes measured with GPC viscometry, the reproducibility of M_w was characterized by s_LAB = 18%. Reproducibility of the SRM 1475 standard was better than for unknowns. The results for branched standard SRM 1476 emphasize the important role of the detection method in GPC but call into question the use of this material as a molecular weight standard. For single‐site polyethylene, only a handful of labs measured an MWD that closely matched the Flory distribution. Qualitatively, the responses indicate that many variations in instrument and analytical methods exist among laboratories; this is partly a reflection of the development and refinements that this technique must yet undergo before a truly standard method is widely accepted and practiced. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 905–921, 2002