Polymer coupling and theory of on-random crosslinking: an analytical solution

Gel formation is an important feature in free-radical polymer coupling. Due to the different possible combination reactivities of each polymer backbone radical, polymer chains are crosslinked in a non-random manner. Equations of the moments have been derived to predict the pregel molecular weight development and the crosslink density at gel point. This work provides an analytical solution for the differential equations. The model agrees with the Flory-Stockmayer gelation theory under the condition of random crosslinking. The magnitude of deviations from the classical theory for non-random crosslinking depends on the product of the radical termination reactivity ratios (r₁r₂), the ratio of the rate constants of backbone radical generation (k), the ratio of the weight-average chain lengths of primary polymers (y), and the polymer weight fractions (w₂).     

Polymerization of (p‐vinylphenyl)hydrogalvinoxyl and formation of a stable polyradical derivative

4‐[(3,5‐Di‐tert‐butyl‐4‐hydroxyphenyl)(3,5‐di‐tert‐butyl‐4‐oxo‐cyclohexa‐ 2,5‐dienylidene)methyl]styrene (abbreviated as (p‐vinylphenyl)hydrogalvinoxyl) was polymerized using AIBN as an initiator to give a bright yellow polymer with M w = 3.2 × 10⁴. The polymer was oxidized to give the corresponding polyradical derivative, whose spin concentration could be increased up to about 70 mol % depending on oxidative conditions. ESR signal line‐width in the solid state was greatly increased below 200 K for the polyradical with a high spin concentration (> 50 mol %). The magnetization and magnetic susceptibility indicated weak antiferromagnetic interaction among the radical sites. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 189–198, 1999     

The network gel polymer electrolyte based on poly(acrylate-co-imide) and its transport properties in lithium ion batteries

Poly (acrylate-co-imide)-based gel polymer electrolytes are synthesized by in situ free radical polymerization. Infrared spectroscopy confirms the complete polymerization of gel polymer electrolytes. The ionic conductivity of gel polymer electrolytes are measured as a function of different repeating EO units of polyacrylates. An optimal ionic conductivity of the poly (PEGMEMA₁₁₀₀-BMI) gel polymer electrolyte is determined to be 4.8 × 10^–3 S/cm at 25 °C. The lithium transference number is found to be 0.29. The cyclic voltammogram shows that the wide electrochemical stability window of the gel polymer electrolyte varies from −0.5 to 4.20 V (vs. Li/Li⁺). Furthermore, we found the transport properties of novel gel polymer electrolytes are dependent on the EO design and are also related to the rate capability and the cycling ability of lithium polymer batteries. The relationship between polymer electrolyte design, lithium transport properties and battery performance are investigated in this research.     

Gel growth in free radical crosslinking copolymerization: Effect of inactive gel radicals

A kinetic model is presented for the post‐gelation period of free‐radical crosslinking copolymerization. The model takes into account the trapped radical centers in the gel forming system. It was shown that the weight fraction of sol, W_s, relates to the number of crosslinked units per weight‐average primary molecule, ε, through the equation where n = 2 for Flory's most probable molecular weight distribution, and n = 3 for primary molecules formed by radical combination. Calculation results demonstrate that the existence of trapped radicals significantly affects the growth rate of the gel molecule. It increases the total radical concentration and accelerates the gel growth. The difference in the predictions with and without considering the trapped radicals becomes significant as the crosslinker concentration decreases or, as the vinyl group reactivity on the crosslinker or on the polymer decreases.     

Polymerization of free secondary amine bearing monomers by RAFT polymerization and other controlled radical techniques

This work describes the polymerization of the free secondary amine bearing monomer 2,2,6,6‐tetramethylpiperidin‐4‐yl methacrylate (TMPMA) by means of different controlled radical polymerization techniques (ATRP, RAFT, NMP). In particular, reversible addition‐fragmentation chain transfer (RAFT) polymerization enabled a good control at high conversions and a polydispersity index below 1.3, thereby enabling the preparation of well‐defined polymers. Remarkably, the polymerization of the secondary amine bearing methacrylate monomer was not hindered by the presence of the free amine that commonly induces degradation of the RAFT reagent. Subsequent oxidation of the polymer yielded the polyradical poly(2,2,6,6‐tetramethylpiperidinyloxy‐4‐yl methacrylate), which represents a valuable material used in catalysis as well as for modern batteries. The obtained polymers having a molar mass (M_n) of 10,000–20,000 g/mol were used to fabricate well‐defined, radical‐bearing polymer films by inkjet‐ printing. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Basic gel permeation chromatography studies. III. Mathematical analysis of peak spreading

Peak spreading in gel permeation chromatography has been studied with a range of gels including those whose permeation limit corresponded to about 10³, 10⁶, 10⁸, and 10⁹ molecular weight polystyrene. Peak spreading conformed to the equation Y_V ² = Y_M ² + Y_A ² + Y_I ² + Y_D ² + Y_S ², where Y_V is the peak width of a normal chromatogram, Y_M is the contribution due to the true molecular weight of the sample, Y_A is due to peak spreading in the apparatus, Y_I is spreading in the interstitial volume, Y_D is diffusional spreading due to time spent in the gel, and Y_S is due to sorption. Evaluating the appropriate parts of the equation leads to measures of the true molecular weight distribution and the contribution due to diffusion into and out of the gel. The data also allowed estimates as to the diffusional spreading with small molecules. With polystyrene having 100 000 molecular weight, diffusional spreading accounts for 80% of Y_V ,² but with small molecules the contribution due to diffusion was not detected.     

Density functional theory study of the magnetic properties of rare earth complexes: the magnetic coupling mechanism in YIII and GdIII complexes with nitronyl nitroxide

The magnetic coupling interactions of the nitronyl nitroxide radicals bound to diamagnetic (Y^III) and paramagnetic (Gd^III) rare earth ions in two model magnetic systems based on novel rare earth organic radical complexes Ln(hfac)₃(NITPhOCH₃)₂ (Ln = Y^III 1, Gd^III 2; hafc = hexafluoroacetylacetonate; NITPhOCH₃ = 4′-methoxyo-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) have been investigated by density functional theory (DFT). The magnetic coupling mechanisms were also explored from the viewpoint of molecular orbital and spin density populations. DFT calculations show that the empty 4d-orbitals of Y^III and 5d-orbitals of Gd^III play an important role in the antiferromagnetic coupling between the two nitronyl nitroxide radical ligands, and that the ferromagnetic coupling between the Gd^III ion and the radical magnetic centers can be attributed to the nearly complete localization of the isotropic 4f-shell and singly occupied magnetic orbital (Π^*) of the nitronyl nitroxide.     

Metal Complexes of Free Radicals. Part II: Identification and structures of radical complexes of alkaline earth metals and zinc

The formation of chelate complexes between free radicals and closed-shell metal ions is observed by ESR. spectroscopy. High resolution spectra of 1:1 complexes formed between the radical anion of glyoxal-bis-(N-t-butylimine) (GLIR) and Mg²⁺, Ca²⁺ and Zn²⁺ are completely analysed. The complexes formed in dimethoxyethane or tetrahydrofuran solutions are Ca(GLIR)⁺, Mg(GLIR)X, Zn (GLIR)X and Zn(GLIR)Y^?₂, where X = Cl^?, Br^?, I^?, and Y = CN^?, NCS^?. The formation of the heterometallic, binuclear cyanide-bridged complex Zn(GLIR)Fe(CN)₆^3? is also described. Isotropic coupling constants are given for protons and ¹⁴N in GLIR as well as for the metal nuclei and magnetic nuclei in the groups X and Y. Stabilities, structures and ESR. parameters of these radical complexes are discussed.     

Synthesis of an optically active helical poly(1,3-phenyleneethynylene) bearing stable radicals and its chiroptical and magnetic properties

We synthesized an optically active helical poly(1,3-phenyleneethynylene) with pendant galvinoxyl residues and dimethyl(10-(1S)-pinanyl)silyl groups. The hydrogalvinoxyl precursor polymer was given by polymerization of (1,3-diiodophenyl)hydrogalvinoxyl and 1,3-diethynyl-5-[dimethyl(10-(1S)-pinanyl)silyl]benzene using Pd(PPh₃)₄ catalyst (M_w = 1.7 × 10⁵, M_w/M_n = 3.7). In the CD spectrum taken in ethyl acetate solution, clear Cotton effects were observed in the absorption region of the backbone and hydrogalvinoxyl chromophore, indicating an excess of one-handed helical foldamer conformation. The polymer yielded the corresponding polyradical with high spin concentration by treatment of the polymer solution with PbO₂. The Cotton effects appeared in CD spectra of the polymer and polyradical by addition of methanol to the chloroform solution, although the Cotton effects were hardly observed in chloroform. On the other hand, in the MCD spectra of the polymer and polyradical taken in chloroform solution, Faraday effects were observed in the absorption region of the backbone and galvinoxyl chromophore. The static magnetic susceptibility of the chiral polyradical was measured using a SQUID magnetometer, and showed the antiferromagnetic interaction.     

Synthesis of isotactic,syndiotactic, and heterotactic poly(tributyltin methacrylate) and poly(tributyltin methacrylate-co-styrene)

Pure isotactic and enriched syndiotactic poly(tributyltin methacrylate) were synthesized by the reaction of the respective poly(methacrylic acid) with tributyltin oxide. The heterotactic polymer was prepared in a similar manner and from free radical initiated (AIBN or BPO) polymerization of tributyltin methacrylate. In each case, polymer configuration was confirmed by ¹H-NMR of the hydrolyzed/esterfied product. The relatively large ¹¹⁹Sn-NMR linewidth of the isotactic tributyltin containing polymer suggests an intra-molecular exchange of the pendant tin groups. T_g, T_d, and M _v data are also reported. Poly(tributyltinmethacrylate-co-styrene) was prepared by free radical polymerization and reactivity ratios [r(styrene) = 0.51, r(TBTM) = 0.49] and Q-e values for TBTM (0.78, 0.38) were determined.     

EFFECT OF GAMMA RAYS IN THE PREPARATION OF POLYMER AND HYDROGEL FROM ACRYLAMIDE MONOMER

The formation of polymer and hydrogel from aqueous solutions having 20, 30 and 40% concentrations ofacrylamide monomer by γ-ray irradiation processing in the dose range 0.06-30 kGy using a Co-60 source and theircharacterization have been observed. Polymer conversion and gel fraction are found to depend on radiation doses. Polymerconversion increases with the increase of dose, depending on the solution concentration, where maximum conversion isachieved at 0.18, 0.16 and 0.10 kGy for 20%, 30% and 40% concentrations, respectively. On the other hand, gel fractionincreases with dose from the gel point (0.12 kGy) for all concentrations, where 100% conversion of gel occurs at doses≥5 kGy. Tensile strength, viscosity and molecular weight (M_w) of polymer samples increase with both the dose and theconcentration, showing a high value of M_w up to≈10~8. Swelling of hydrogels under water with respect to time varies due tothe variation of cross-linking density formed in the gels and the maximum swelling mainly occurs within 24 h. A remarkable change of surface morphology reveals characteristic features of monomer, polymer and hydrogel films.     

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.     

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     

Kinetics of emulsion polymerization of methyl methacrylate

The kinetics of the emulsion polymerization of methyl methacrylate at 50°C have been studied in seeded systems using both chemical initiation and γ-radiolysis initiation. Both steady-state rates and (for γ-radiolysis) the relaxation from the steady state were observed. The average number of free radicals per particle was quite high (e.g., ～0.7 for 10^?3 mol dm^?3 S₂O²₈ initiator). The data are quantitatively interpreted using a generalized Smith–Ewart–Harkins model, allowing for free radical entry, exit, biomolecular termination within the latex particles, and aqueous phase hetero-termination and re-entry. From this treatment, there results (i) the dependence of the termination rate coefficient (k_t) on the weight fraction of polymer (w_p), (ii) lower bounds for the dependence of the entry rate coefficient on initiator concentration, and (iii) the conclusion that most exited free radicals undergo subsequent re-entry into particles rather than hetero-termination. The results for k_t(w_p) are consistent with diffusion control at temperatures below the glass transition point. Comparisons are presented of the behavior of methyl methacrylate, butyl methacrylate, and styrene in emulsion polymerization systems.     

In situ radical polymerization of methyl methacrylate in a solution of surface modified TiO2 and nanoparticles

Surface modified TiO₂ nanoparticles dissolved in toluene were encapsulated in PMMA by in situ radical polymerization of methyl methacrylate initiated by 2,2′-azobisisobutyronitrile. The surface modification of the TiO₂ nanoparticles (average diameter of 4.5 nm) was achieved by the formation of a charge transfer complex between TiO₂ nanoparticles and 6-palmitate ascorbic acid. The surface modified TiO₂/nanoparticles were characterized using UV−Vis and FTIR spectroscopy, while the obtained polymer nanocomposites were characterized using reflection and ¹H NMR spectroscopy, as well as gel permeation chromatography. The influence of the TiO₂ nanoparticles on the thermal properties of the PMMA matrix was investigated using thermo-gravimetric analysis and differential scanning calorimetry. The glass transition temperature of the polymer was not influenced by the presence of the nanoparticles while the thermal stability was significantly improved.     

Heterochain model for simultaneous long‐chain branching and crosslinking. II. Application to free‐radical polymerization

The matrix formula developed in the context of hetrochain theory, M?_w = M?_wp + WF ( I ? M )^?1 S , was applied to describe the molecular weight development during free‐radical homopolymerization. All of the required probabilistic parameters are expressed in terms of the kinetic‐rate constants and various concentrations. In free‐radical polymerization, the primary chains are formed consecutively, and the number of heterochain types, N, is extrapolated to infinity. Practically, such extrapolation can be conducted on the basis of the calculated values for only three different N values with sufficient accuracy. This matrix formula is valid regardless of the chemical and reactor systems used, as long as the primary chain‐connection statistics is considered Markovian. The gel point can be determined simply by solving an equation det( I ? M ) = 0. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2791–2800, 2004     

Electrochemical and chemical polymerization of acrylamide

The electrochemical and chemical polymerization of acrylamide (AA) has been studied. The electrolysis of the monomer in N,N-dimethylformamide (DMF) containing (C₄H₉)₄NClO₄ as the supporting electrolyte leads to polymer formation in both anode and cathode compartments. The cathodic polymer dissolves in the reaction mixture and the anodic polymer precipitates during the course of polymerization. A plausible mechanism for the anodic and cathodic initiation reaction has been given. The chemical polymerization of acrylamide that has been initiated by HClO₄ is analogous to its anodic polymerization. The polymer yield increases with an increase in concentration of the monomer and HClO₄. Raising the reaction temperature also enhances the polymerization rate. The overall apparent activation energy of the polymerization was determined to be ca. 19 kcal/mole. The copolymerization of acrylamide was carried out with methyl methacrylate (MMA) in a solution of HClO₄ in DMF. The reactivity ratios are r₁ (AA) = 0.25 and r₂ = 2.50. The polymerization with HClO₄ appears to be by a free radical mechanism. When the polymerization of acrylamide is carried out with HClO₄ in H₂O, a crosslinked water-insoluble gel formation takes place.     

Photoinitiated free radical polymerization of vinyl compounds in aqueous solution

A new method for the photochemical initiation of polymerization of vinyl compounds in aqueous solution is described. The photochemically active species is an ion pair complex of the formula Fe³⁺X⁻(X⁻ = OH⁻, CI⁻, N⁻₃, etc.). The light absorption by the ion pair leads to an electron transfer causing reduction of the cation and oxidation of the anion to an atom or free radical X. The latter leads to the initiation of polymerization in accordance with X + CH₂CHR→XCH₂ CHR . The kinetics of the reaction were studied by the measurement of: (a) ferrous ion formed (colorimetrically), (b) monomer disappearance (by titration and by weighting the polymer), (c) the chain length of the polymer (in the case of methyl methacrylate). The dependence of the quantum yield on the light intensity, light absorption fraction, and the concentration of vinyl monomer and ferrous ion added initially was investigated. A complete mechanism, both with regard to the formation of free radicals and the polymerization reaction, was put forward involving: (1) light absorption, (2) a primary dark back reaction, (3) dissociation of the primary product, (4) a secondary dark back reaction, (5) initiation of polymerization by free radicals, (6) propagation of polymerization, and (7) termination by recombination of active polymer endings. The mechanism was verified by the experimental results and some constant ratios were estimated quantitatively.     

Aging and degradation of polyolefins. I. Peroxide-initiated oxidations of atactic polypropylene

Efficiencies of polymer radical production by thermal decomposition of di-tert-butylperoxy oxalate (DBPO) have been measured in bulk atactic polypropylene (PP) at 25–55°C; they range from 1 to 26%, depending on [DBPO], temperature, and presence of oxygen. Most of the polymer radicals thus produced disproportionate in the absence of oxygen but form peroxy radicals in its presence. Most of the pairs of peroxy radicals interact by a first-order reaction in the polymer cage. The fraction that escapes gives hydroperoxide in a reaction that is half order in rate of initiation. In interactions of polymer peroxy radicals, in or out of the cage, about one-third give dialkyl peroxides and immediate chain termination, two-thirds give alkoxy radicals. About one-third of the later cleave at 45°C; the rest abstract hydrogen to give hydroxy groups and new polymer and polymer peroxy radicals. The primary peroxy radicals from cleavage account for the rest of the chain termination. Cleavage of alkoxy radicals and crosslinking of PP through dialkyl peroxides nearly compensate. Up to 70% of the oxygen absorbed has been found in hydroperoxides. The formation of these can be completely inhibited, but cage reactions are unaffected by inhibitors. Concentrations of free polymer peroxy radicals have been measured by electron spin resonance and found to be very high, about 10^?3M at 58–63°C. Comparison with results on 2,4-dimethylpentane indicate that rate constants for both chain propagation and termination in the polymer are much smaller than those for the model hydrocarbon but that the ratio, k_p/(2k_t)^½, is about the same.     

Physico-chemical properties of the copper(II)-poly-4-vinylpyridine complexes

Water-soluble Cu(II) complexes of poly-4-vinylpyridine, partially quaternized by methyl bromide or dimethylsulphate (PP, Mt) and of the analogue (4-ethylpyridine) were studied by physicochemical technique such as visible spectrophotometry, viscosity, speed sedimentation and EPR spectroscopy. Peculiarities of the complex formation reaction were observed for the polymer compared to the analogue. The predominant formation of tetrapyridinate-Cu(II) species [(CuL₄)]²⁴ was found to take place in aqueous solution for PP, Mt with degree of quaternization (β) 20,24,37,49,57,65 per cent over a wide range of P_YJ Cu(II) molar ratios. In addition, not all the free polymer pyridine residues are capable of forming [Cu L4 ]² complexes even though there is a large excess of Cu(II) ions. The maximum value of the pyridine fraction forming [Cu L₄ ]²¹ in PP_YMt-20, 24, 37, 49 (obtained by spectroscopic titration) was found to be 45–50 per cent. Addition of Cu(NO₃)₂ to the aqueous polymer solution causes strong reduction of specific viscosity and increase of sedimentation coefficient from - 1 S to - 6 S. These data lend to the suggestion of the existence of macromolecular associates bound by Cu(II) ions and approximate estimation of their average molecular weight. It was shown also that Bjerrum's procedure cannot be used to account for the polymer stability constants. The differences between complex formation for polymer pyridine and monomer pyridine seem to be due to the high local pyridine concentration in the coil of the macromolecule and the hydration effects of the polymer chain on the characteristics of the pyridine residues.