An experimental investigation on the evolution of the molecular weight distribution in styrene emulsion polymerization

Styrene ab initio emulsion polymerizations were conducted at 70°C in an automated reaction calorimeter. Two polymerizations were performed, one above and the other below the critical micelle concentration (CMC) of the surfactant, thus ensuring differing polymerization kinetics between the two: the system below the CMC gave large particles that were expected to follow pseudobulk kinetics, while that above the CMC gave small particles that were expected to follow zero-one kinetics. The evolutions of the molecular weight distributions (MWDs) were characterized by removing samples periodically during the course of the reactions and analyzing with gel permeation chromatography. Interpretation of the data used average molecular weights, the GPC MWDs, and the number MWDs, as functions of conversion. It was found that all of the number MWDs (plotted as ln (number of polymer chains) vs. molecular weight of polymer chains) were concave-up at low molecular weights and become nearly linear at molecular weights (≥3−4 × 10⁶); this linearity is expected from theory. The slope of the high molecular weight region was consistent with theory for the dominant mode for chain stoppage: termination and transfer for the pseudobulk system and (predominantly) chain transfer to monomer for the zero-one system. The most likely explanation for the concavity of the number MWDs is a heterogeneity of radicals: some surface anchored with sulfate end groups and others (with hydrogen end groups arising from transfer to monomer and/or reentry) being more mobile. Thus, two types of termination are proposed: slow reaction-diffusion for the less mobile surface anchored chains, and rapid short-long (center of mass) termination for the more mobile hydrogen-terminated chains. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 989–1006, 1997     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

Molecular Weight Development during Simultaneous Chain Scission,Long‐Chain Branching and Crosslinking, 1

A general matrix formula is proposed for the weight‐average molecular weights of the polymer systems formed through simultaneous scission, branching and crosslinking of N types of chains, assuming the chain connection statistics are Markovian. For the polymerization systems in which chains are generated consecutively, such as for free‐radical polymerization, the present theory can be applied by increasing the number of chain types N to infinity, by considering the chains formed at different times as different types of chains. The gel point determination reduces to the eigenvalue problem and the present theory extends the classical gelation theory to non‐random, history‐dependent reaction systems. From the mathematical point of view, this theory is capable of describing complex molecular build‐up processes through end‐linking, T‐ and H‐shaped chain connections, irrespective of reaction/reactor types used.

Schematic representation of the 0^th generation segment and the connection to the 1^st generation segments.     

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     

Multisensitive polymers based on 2‐vinylpyridine and N‐isopropylacrylamide *

Poly(2‐vinylpyridine) (P2VP) containing functionalized end groups was synthesized using nitroxyl‐mediated radical polymerization with a hydroxy‐functionalized stable free radical. It was shown that P2VP could be synthesized with variable molar masses and low polydispersities. The transformation of the hydroxy groups to an acrylic ester led to the formation of macromonomers. A free‐radical copolymerization of these macromonomers with N‐isopropylacrylamide gave a graft copolymer with a poly(N‐ispopropylacrylamide) backbone and P2VP side chains. Polymers containing different amounts of the monomers were synthesized. It was possible to vary both the amount of P2VP side chains at a constant chain length of the macromonomer and the chain length at a nearly constant chain number. The behavior of the multifunctional macromolecules at different temperatures and pH values was investigated using dynamic light scattering and DSC. The macromolecules were found to retain the specific properties of the homopolymers. The hydrodynamic radii of the synthesized graft copolymers were both dependent on the temperature and pH value. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3797–3804, 2001     

Molecular Weight Development in Free‐Radical Polymerization with Polyfunctional Chain‐Transfer Agents, 1. Equal Reactivity Model

The analytic expression for the weight‐average molecular weight development in free‐radical polymerization that involves a polyfunctional chain‐transfer agent is proposed. Free‐radical polymerization is kinetically controlled; therefore, the probability of chain connection with a polyfunctional chain‐transfer agent as well as the primary chain‐length distribution changes during the course of polymerization. We consider the primary chains formed at different times as different types of chains, and the heterochain branching model is used to obtain the weight‐average chain length at a given conversion level in a matrix formula, described as P_w = W { D _w + ( I + T ) SP ( I – TSP )^–1 D_f }. Because the primary chains are formed consecutively, the number of chain types N is extrapolated to infinity, but such extrapolation can be conducted with the calculated values for only three different N values. The criterion for the onset of gelation is simply described as a point at which the largest eigenvalue of the product of matrixes, TSP reaches unity, i. e., det  ( I – TSP ) = 0. The present model can readily be extended for the star‐shaped polyfunctional initiators, and the relationships between the model parameters and kinetic rate expression for such reaction systems are also shown.     

Kinetics of polymerization rate based on the dependence of termination rate on chain length

When the structure of a primary radical resembles that of the chain end of the polymer radical, the rate of the primary radical termination is approximately the same as the termination rate between the oligomer radical and the polymer radical. The rate constant of termination between polymer radicals of chain length n and s, which involve the primary radicals, is k_t,ns = const.(ns)^?a. In the polymerization of methacrylonitrile initiated by 2,2′-azobisisobutyronitrile in dimethylformamide at 60.0°C, the value of a is found to be 0.091. From data obtained previously in the bulk polymerization of styrene initiated by 1-azobis-2-phenylethane at 60.0°C, the value of a is found to be 0.167. Because such a values are so large that they are not estimated by the excluded volume, the termination rates are discussed by adding the dependence of the diffusion of the segments to that for chain length.     

Molecular weight distribution in emulsion polymerizations

A mathematical formulation is given which describes the evolution of the number distribution of the molecular weight (MWD) of linear polymer chains that grow in emulsion polymerization systems. The resulting set of coupled ordinary differential equations takes into account the microscopic events of free radical entry, exit, chain annihilation, bimolecular termination (by combination and disproportionation), and chain transfer in a mono- or polydisperse system. Simple analytic solutions are presented for systems in which the number of particles, as well as the average number of free radicals per particle, is constant and in which the rate coefficients are size independent. These solutions indicate that compartmentalization of the free radicals in the latex particles results in a significant increase in the polydispersity of the polymer produced by emulsion polymerization, compared with that in bulk systems. The theory shows that significant mechanistic information may be obtained from experimental MWDs and that, in principle, experimental conditions may be prescribed to grow a desired MWD. The MWDs are presented in a novel manner that facilitates the comparison of theory with experiment.     

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Literature data are summarized for the chain‐length‐dependence of the termination rate coefficient in dilute solution free‐radical polymerizations. In essence such experiments have yielded two parameter values: the rate coefficient for termination between monomeric free radicals, kequation/tex2gif-stack-1.gif, and a power‐law exponent e quantifying how k_t values decrease with increasing chain length. All indications are that the value e ≈ 0.16 in good solvent is accurate, however the values of kequation/tex2gif-stack-2.gif which have been deduced are considerably lower than well‐established values for small molecule radicals. This seeming impasse is resolved by putting forward a ‘composite’ model of termination: it is proposed that the value e ≈ 0.16 holds only for long chains, with e being higher for small chains – the value 0.5 is used in this paper, although it is not held to dogmatically. It is then investigated whether this model is consistent with experimental data. This is a non‐trivial task, because although the experiments themselves and the ways in which they are analyzed are elegant and not too complicated, the underlying theory is sophisticated, as is outlined. Simulations of steady‐state polymerization experiments are first of all carried out, and it is shown that the composite model of termination both recovers the e values which have been found and beautifully explains why these experiments considerably underestimate the true value of kequation/tex2gif-stack-3.gif. Simulations of pulsed‐laser polymerizations find the same, although not quite so strikingly. It is therefore concluded that our new termination model, which retains the virtue of simplicity and in which all parameter values are physically reasonable, is consistent with experimental data. Taking a wider view, it seems likely that the situation of the exponent e varying with chain length will not just be the case in dilute solution, but will be the norm for all conditions, which would give our model and our work a general relevance.

Normalized chain length distributions from PLP simulations.     

Effect of chain length on rates of diffusion-limited small molecule-polymer and polymer-polymer reactions: Phosphorescence quenching studies

Model interactions have been studied by phosphorescence quenching to obtain a better understanding of the chain length dependence of interpolymeric chain end-chain end reactions such as those involved in the termination step of free radical polymerization. For small molecule-polymer interactions in dilute cyclohexane solution, quenching rate constant (k_q) data agree with the Smoluchowski equation prediction that k_q scales as polymer molecular weight (MW) to the -½ power, confirming self-diffusion control. For polymer-polymer interactions in dilute solution, the chain length dependence is weaker than that predicted by translational diffusion control, as described by the Smoluchowski equation, but is stronger than that predicted by renormalization group theory. For interactions between 70000 MW benzil-end-labeled polystyrene and varying MWs of anthracene-end-labeled polystyrene at 300 g/L polymer, k_q decreases by a factor of 10 in going from MWs of 100 to 1000 g/mol; beyond 1000 g/mol, k_q is nearly independent of chain length. Such effects indicate that the importance of oligomeric radical self-diffusion and polymer radical chain-end segmental mobility must be carefully considered in understanding the termination process in free radical polymerization. © 1996 John Wiley & Sons, Inc.     

Evolution of molecular weight distributions in the catalytic chain transfer polymerization of methyl methacrylate up to high monomer conversions

The evolution of molecular weight distributions (MWDs) with monomer conversion in the catalytic chain transfer (CCT) polymerization of methyl methacrylate at 60 °C is investigated by simulation (via the program package PREDICI®) and experiment. A Co(III)‐based complex is used as the precursor for the CCT agent, which is formed in situ by initiator‐derived (2,2′‐azobisisobutyronitrile) radicals to yield the catalytically active Co(II) species. The small shifts seen in the MWD toward lower molecular weights with increasing monomer conversion are shown to be of the same order of magnitude as the associated changes in the MWD in non‐CCT controlled free‐radical polymerization, indicating that no significant change in the MWD with monomer conversion is associated with the CCT process. These results are compared to the evolution of MWDs in conventional chain transfer polymerizations with thiols as transfer agents. A clear shift toward higher molecular weights is seen with increasing monomer conversion, indicating disparate rates of thiol and monomer consumption. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3303–3312, 2000     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

One‐pot synthesis of heterograft copolymers via “graft onto” by atom transfer nitroxide radical coupling chemistry

Heterograft copolymers poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ ethylene oxide)‐graft‐polystyrene and poly(tert‐butyl acrylate) (poly (GTEMPO‐co‐EO)‐g‐PS/PtBA) were synthesized in one‐pot by atom transfer nitroxide radical coupling (ATNRC) reaction via “graft onto.” The main chain was prepared by the anionic ring‐opening copolymerization of ethylene oxide (EO) and 4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl (GTEMPO) first, then the polystyrene and poly (tert‐butyl acrylate) with bromine end (PS‐Br, PtBA‐Br) were prepared by atom transfer radical polymerization (ATRP). When three of them were mixed each other in the presence of CuBr/N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) at 90 °C, the formed secondary carbon radicals at the PS and PtBA chain ends were quickly trapped by nitroxide radicals on poly(GTEMPO‐co‐EO). The heterograft copolymers were well defined by ¹H NMR, size exclusion chromatography, fourier transform infrared, and differential scanning calorimetry in detail. It was found that the density of GTEMPO groups on main chain poly(GTEMPO‐co‐EO), the molecular weights of PS/PtBA side chains, and the structure of macroradicals can exert the great effects on the graft efficiency. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6770–6779, 2008     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Chain collapse by lattice simulation

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(In N)^3/11, as predicted by the renormalization group theory.     

Macromolecular Architecture Based on Anionically Prepared Poly(ethylene oxide) Macromonomers

Synthesis of poly(ethylene oxide) (PEO) macromonomers carrying a methacyloyl group in one end, and N, N-dimethyl amino, thiophene, styryl and vinyl ether functional groups in the other end was desribed. The general synthetic strategy is based on the living anionic polymerization of ethylene oxide initiated with functional potassium alcoholates, followed by reaction with methacyloyl chloride. These macromonomers were further utilized in various macromolecular architectures through via concurrent or selective thermal free radical, oxidative and photoinitiated free radical and cationic polymerization methods. The use of this synthetic route to prepare graft copolymers possessing completly and perfectly alternating PEO side chains using charge-transfer-complex polymerization was also demonstrated.     

Synthesis of Structurally Well‐Defined Telechelic Polymers by Organostibine‐Mediated Living Radical Polymerization: In Situ Generation of Functionalized Chain‐Transfer Agents and Selective ω‐End‐Group Transformations

Several organostibine chain‐transfer agents possessing polar functional groups have been prepared by the reactions of azo initiators and tetramethyldistibine ( 1 ). Carbon‐centered radicals thermally generated from the azo initiators were trapped by 1 to yield the corresponding organostibine chain‐transfer agents. The high yields observed in the synthesis of the chain‐transfer agents strongly suggest that distibines have excellent radicophilic reactivity. As the reactions proceeded under neutral conditions, functional groups that are incompatible with ionic conditions were incorporated into the chain‐transfer agents. The chain‐transfer agents were used in living radical polymerization to synthesize the corresponding α‐functionalized polymers. As the functional groups in the chain‐transfer agents did not interfere with the polymerization reaction, well‐controlled polymers possessing number‐average molecular weights (M_ns) predetermined by the monomer/transfer agent ratios were synthesized with low polydispersity indices (PDIs). The organostibanyl ω‐polymer ends were transformed into a number of different functional groups by radical‐coupling, radical‐addition, and oxidation reactions. Therefore, it was possible to synthesize well‐controlled telechelic polymers with the same and also with different functional groups at their α‐ and ω‐polymer ends. Distibine 1 was also found to increase PDI control in the living radical polymerization of styrene and methyl methacrylate (MMA) using a purified organostibine chain‐transfer agent. Well‐controlled poly(methyl methacrylate)s with M_n values ranging from 10 000 to 120 000 with low PDIs (1.05–1.15) were synthesized by the addition of a catalytic amount of 1 . The results have been attributed to the high reactivity of distibine 1 towards polymer‐end radicals, which are spontaneously deactivated to yield organostibine dormant species.     

Chain transfer to solvent in the radical polymerization of N‐isopropylacrylamide

Chain transfer to solvent has been investigated in the conventional radical polymerization and nitroxide‐mediated radical polymerization (NMP) of N‐isopropylacrylamide (NIPAM) in N,N‐dimethylformamide (DMF) at 120 °C. The extent of chain transfer to DMF can significantly impact the maximum attainable molecular weight in both systems. Based on a theoretical treatment, it has been shown that the same value of chain transfer to solvent constant, C_tr,S, in DMF at 120 °C (within experimental error) can account for experimental molecular weight data for both conventional radical polymerization and NMP under conditions where chain transfer to solvent is a significant end‐forming event. In NMP (and other controlled/living radical polymerization systems), chain transfer to solvent is manifested as the number‐average molecular weight (M_n) going through a maximum value with increasing monomer conversion. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Studying the Fundamentals of Radical Polymerization Using ESR in Combination with Controlled Radical Polymerization Methods

Electron spin resonance (ESR) spectroscopy can contribute to understanding both the kinetics and mechanism of radical polymerizations. A series of oligo/poly(meth)acrylates were prepared by atom transfer radical polymerization (ATRP) and purified to provide well defined radical precursors. Model radicals, with given chain lengths, were generated by reaction of the terminal halogens with an organotin compound and the radicals were observed by ESR spectroscopy. This combination of ESR with ATRPs ability to prepare well defined radical precursors provided significant new information on the properties of radicals in radical polymerizations. ESR spectra of the model radicals generated from tert-butyl methacrylate precursors, with various chain lengths, showed clear chain length dependent changes and a possibility of differentiating between the chain lengths of observed propagating radicals by ESR. The ESR spectrum of each dimeric, trimeric, tetrameric, and pentameric tert-butyl acrylate model radicals, observed at various temperatures, provided clear experimental evidence of a 1,5-hydrogen shift.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.