On the kinetics of styrene emulsion polymerization above CMC. I. A mathematical model

A detailed mathematical model of the kinetics of styrene emulsion polymerization has been proposed. Its main features/assumptions are compartmentalization, micellar and homogeneous nucleation, particle formation by both initiator‐derived and desorbed radicals, dependence on the particle size of the rate coefficients, thermodynamic considerations, and aqueous phase kinetics. The model predicts that micellar nucleation dominates over homogeneous nucleation and that the evolution of the nucleation rate reaches a maximum, where desorbed radicals have an important contribution. Initiator‐derived radicals with only one monomeric unit have also a significant contribution on the rate of capture in particles. The results suggest that the correctness of the instantaneous termination approach depends not only on the size of the particle, but also on the type of entering radical (initiator‐derived or monomeric). © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2201–2218, 2000     

Effect of the presence of polymer in miniemulsion droplets on the kinetics of polymerization

Solution of polystyrene in styrene were dispersed in an aqueous gel phase comprising sodium lauryl sulfate, cetyl alcohol, and water using an emulsification process known to produce monomer droplet sizes inthe submicron size range (referred to as miniemulsion droplets). The shelf-life stabilities of these miniemulsions were studied to determine their relative droplet sizes, and the emulsions were concommitantly polymerized in an isothermal batch reaction calorimeter. The polymerization kinetics and final particle sizes produced were compared with miniemulsion and conventional emulsion polymerizations prepared using equivalent recipes without the addition of polystyrene. The results indicate that polymerization of miniemulsions prepared from polymer solutions produce significantly different kinetics than both miniemulsion and conventional emulsion polymerizations. In general, a small amount of polymer greatly increases the rate of polymerization and the final number of particles produced in the polymerization to the extent where even conventional polymerizations carried out above the critical micelle concentration of the surfactant polymerize more slowly. The results are explained by considering the system to be comprised of small, stable pre-formed monomer-swollen polymer particles which are able to efficiently capture aqueous phase radicals. This enables the system to produce a large final number of particles, similar to the initial number of pre-formed polymer particles, as opposed to miniemulsions and micelles in which only a relatively small fraction of the initial number of species (droplets or micelles) become polymer particles. © 1994 John Wiley & Sons, Inc.     

Photochemical initiated polymerization of single microdroplets

The production of polymeric microspheres via aerocolloidal processing is explored. A droplet consisting of a mixture of 1,6-hexanediol diacrylate and trimethylolpropane ethoxy triacrylate monomers was levitated electrodynamically in the path of an argon ion laser beam (=488 nm). The laser beam served as the source of illumination for elastic and inelastic light-scattering measurements. The reaction was followed by Raman spectroscopy, and polymerization was initiated with an -amino acetophenone derivative which undergoes -cleavage upon exposure to the laser light. The diameters of the suspended droplets were typically 20–80 m, producing polymeric microspheres of approximately the same size. The size and refractive index of the product microspheres were determined by elastic light-scattering. The Raman data show the elimination of carbon-carbon double bonds and the formation of C–H bonds as rapid polymerization proceeded.     

Estimation of morphological characteristics of single particles from light scattering data in flow cytometry

Numerical methods for solving the reverse problem of light scattering for single particles and a variety of experimental results have been reviewed. In particular, the two-dimensional Mie scattering method for the estimation of sizes and refractive indices of single particles has been developed. The method of triple two-dimensional Mie scattering has been elaborated, which extends the range of particle sizes with correct solutions of the reverse light scattering problem. The flying light scattering indicatrix method, which allows the estimation of the parameters of spherical particles, is presented. The results of the use of a flow cytometer of standard design for the anaysis of milk microflora and for an AIDS immunoassay by latex agglutination are given. The design of a scanning flow cytometer is considered. The results of measuring the light scattering from polystyrene latex particles are given.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1181–1190, July, 1994.The author is grateful to A. K. Petrov and M. A. Kamkhe for supporting the work on cytometry, E. G. Saprykin for useful discussion and comments, G. Alm (Swedish Agricultural Univ.) for initiating the interest to immunological studies, and A. V. Chernyshev, T. S. Mashnin, V. I. Prots, and A. A. Doroshkin for cooperation.     

Comparative study of kinetics and reactivity indices of free radical polymerization reactions

Density functional theory calculations are used to determine the kinetics and reactivity indices of the first propagation steps of the polyethylene and poly(vinyl chloride) polymerization. Transition state theory is applied to evaluate the rate coefficient from the microscopically determined energies and partition functions. A comparison with the experimental Arrhenius plots validates the level of theory. The ability of reactivity indices to predict certain aspects of the studied propagation reactions is tested. Global softnesses of the reactants give an indication of the relative energy barriers of subsequent monomer additions. The correlation between energy and hardness profiles along the reaction path confirm the principle of maximum hardness. Local indices predict the regioselectivity of the attack of the growing radical to vinyl chloride. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Reactive surfactants in heterophase polymerization. Part XXI—kinetics of styrene dispersion polymerization stabilized with poly(ethylene oxide) macromonomers

The kinetics of styrene dispersion polymerization, using poly(ethylene oxide) macromonomers as precursors for the stabilization, has been studied. The conversions of both styrene and macromonomers have been determined. The effects of various parameters such as the polarity of the medium, the nature and the amount of macromonomer and the concentrations of the reactants have been studied. A strong gel effect was observed, the main polymerization process taking place inside the particles where the average number of radicals per particle may be more than a thousand. © 1997 John Wiley & Sons, Ltd.     

Synthesis of saccharidic polymer colloids via free radical mini‐emulsion polymerization

Polymer colloids based on 3‐O‐methacryloyl‐1,2:5,6‐di‐O‐isopropylidene‐α‐D ‐glucofuranose (3‐MDG) and butyl acrylate (BA) were prepared via free radical mini‐emulsion polymerization. The kinetic and colloidal features of the copolymerization were investigated. The final particle size (D) of the sugar latexes is inversely proportional to the concentration of the anionic emulsifier (sodium dodecyl sulphate, SDS) and the non‐ionic one (alkyl polyglucoside, APG). It was also found that D is independent of the concentration of either the water‐soluble initiator (potassium persulfate, KPS), or the oil‐soluble initiator (2,2′‐azobisisobutyronitrile, AIBN). The rate of mini‐emulsion polymerization is lower in comparison with the conventional emulsion polymerization under the same conditions. The polymerization rate (R_p) and the total number of particles (N_p) are proportional to the 0.72th and 0.93th power of the SDS, and to the 1.40th and 2.22th of the APG concentration. Following reaction orders, 0.79/0.06 were obtained for R_p/N_p versus the concentration of KPS, and 0.22/?0.01 for AIBN, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Mechanism and kinetics of the imidazolidinone nitroxide‐mediated free‐radical polymerization of styrene

Styrene radical polymerizations mediated by the imidazolidinone nitroxides 2,5‐bis(spirocyclohexyl)‐3‐methylimidazolidin‐4‐one‐1‐oxyl (NO88Me) and 2,5‐bis(spirocyclohexyl)‐3‐benzylimidazolidin‐4‐one‐1‐oxyl (NO88Bn) were investigated. Polymeric alkoxyamine (PS‐NO88Bn)‐initiated systems exhibited controlled/living characteristics at 100–120 °C but not at 80 °C. All systems exhibited rates of polymerization similar to those of thermal polymerization, with the exception of the PS‐NO88Bn system at 80 °C, which polymerized twice as quickly. The dissociation rate constants (k_d) for the PS‐NO88Me and PS‐NO88Bn coupling products were determined by electron spin resonance at 50–100 °C. The equilibrium constants were estimated to be 9.01 × 10^?11 and 6.47 × 10^?11 mol L^?1 at 120 °C for NO88Me and NO88Bn, respectively, resulting in the combination rate constants (k_c) 2.77 × 10⁶ (NO88Me) and 2.07 × 10⁶ L mol^?1 s^?1 (NO88Bn). The similar polymerization results and kinetic parameters for NO88Me and NO88Bn indicated the absence of any 3‐N‐transannular effect by the benzyl substituent relative to the methyl substituent. The values of k_d and k_c were 4–8 and 25–33 times lower, respectively, than the reported values for PS‐TEMPO at 120 °C, indicating that the 2,5‐spirodicyclohexyl rings have a more profound effect on the combination reaction rather than the dissociation reaction. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 327–334, 2003     

丙烯酰胺基偶氮苯的RAFT聚合反应动力学

以丙烯酰胺基偶氮苯(AAAB)为单体,二硫代苯甲酸异丙苯酯(CDB)为链转移剂,偶氮二异丁腈(AIBN)为引发剂,N,N-二甲基甲酰胺(DMF)为溶剂,利用可逆加成-断裂链转移(RAFT)聚合法合成了侧链含有偶氮苯基团的聚丙烯酰胺基偶氮苯(PAAAB),同时考察了反应温度、引发剂浓度、链转移剂浓度等因素对聚合反应的影响。利用FT-IR、1H NMR、GPC等对其结构进行了表征。结果表明,聚合反应动力学曲线呈良好的线性关系,分子量分布窄;随着[CDB]/[AIBN]比例的增大,聚合速率、分子量和分子量分布均下降。     

Synthesis and characterization of oxazoline-functional polymer particles by free radical nonaqueous dispersion polymerization

A novel oxazoline-functional methacrylate was prepared and employed as comonomer to produce nonaqueous dispersions of oxazoline-functional polymer particles. In nonaqueous free radical dispersion copolymerization of methylmethacrylate in the presence of oxazoline-functional methacrylate, ethyleneglycoldimethacrylate crosslinking agent, AIBN initiator, and polystyrene-block-poly(ethene-alt-propene) dispersing agent, the average polymer particle size, varying between 100 and 500 nm, was controlled by the dispersing agent contents. According to titration with HClO₄ all oxazoline groups regardless of their location at particle surface or bulk, were accessible. Glass transition temperature decreased from 120 to 0°C when oxazoline functional methacrylate was increased from 0 to 95 mol %. As imaged by atomic force microscopy incorporation of the new oxazoline-functional methacrylate improved film formation. Oxazoline-functional polymer particles were easy to redisperse in a variety of other diluents. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2539–2548, 1997     

Composite cure kinetic analysis of unsaturated polyester free radical polymerization

Curing kinetics of unsaturated polyester resin system exhibiting apparent induction periods was investigated by modeling free radical initiation and propagation processes. The isothermal curing induction time as well as the maximum-rate time provided the same activation energy in the Arrhenius relation, and therefore, the isothermal curing master curve was constructed by using the reduced time method. Two model elementary rate equations for radical and monomer were proposed to describe the free radical polymerization of unsaturated polyester resin systems. The power law was adopted to express the conversion dependence function of the initiation efficiency and the monomer reaction rate. Demonstrating the capability of the developed model, the agreement between experimental and predicted data was excellent in both isothermal and dynamic-heating conditions, even with the same model parameters in different thermal conditions. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2447–2456, 1997     

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran

Free radical dispersion polymerization of styrene in a mixture of 2-propanol and tetrahydrofuran was carried out at 70°C up to high conversions. The influence of the change of the critical chain length on the evolution of the insoluble polymer component was examined. Monomer conversion and the formation of the insoluble polymer component were measured in order to test a mathematical model presented in our previous article. The critical polymer chain length i₀, the initiation rate constant k_d, and the ratio k_p/k, where k_p and k_t are propagation and termination rate constants, respectively, have been obtained and compared with those reported in the literature. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2757–2761, 1998     

R12 hydrate formation kinetics based on laser light scattering technique

Gas hydrates are non-stoichiometric crystalline compounds of water with gas at a certain temperature and pressure. Compared to the thermodynamics of hydrate formation, our knowledge on the kinetics aspect is rather immature. It is well known that the kinetics of hydrate formation/dissociation plays an important role in many industrial cases, such as the exploitation of methane hydrate underground, the storage and transportation of natural gas in solid hydrate state, the inhibition of hydrate i…     

A mathematical model for Modulated Differential Scanning Calorimetry

Reading and co-workers introduced a new technique a few years ago called Modulated Differential Scanning Calorimetry or MDSC. Here the first part of a theoretical analysis for this technique is given. A simple mathematical model for modulated differential scanning calorimetry in the form of an ordinary differential equation is derived. The model is analysed to find the effect of a kinetic event in the form of a chemical reaction. Some possible sources of error are discussed. A more sophisticated version of the model allowing for spatial variation in a calorimeter is developed and it is seen how it can be reduced to the earlier model. Some preliminary work on a phase change is also presented.Dedicated to Prof. Menachem Steinberg on the occasion of his 65th birthday     

Kinetics of nanoconfined benzyl methacrylate radical polymerization

The effect of nanoconfinement on the kinetics of benzyl methacrylate radical polymerization is investigated using differential scanning calorimetry. Controlled pore glass (CPG), ordered mesoporous carbons, and mesoporous silica are used as confinement media with pore sizes from 2 to 8 nm. The initial polymerization rate in CPG and mesoporous silica increases relative to the bulk and increases linearly with reciprocal pore size; whereas, the rate in the carbon mesopores decreases linearly with reciprocal pore size; the changes are consistent with the rate being related to the ratio of the pore surface area to pore volume. Induction times are longer for nanoconfined polymerizations, and in the case of CPG and carbon mesopores, autoacceleration occurs earlier, presumably due to the limited diffusivity and lower termination rates for the confined polymer chains. The molecular weight of the polymer synthesized in the nanopores is generally higher than that obtained in the bulk except at the lowest temperatures investigated. The equilibrium conversion under nanoconfinement decreases with decreasing temperature and with confinement size, exhibiting what appears to be a floor temperature at low temperatures.     

Mechanism and kinetics of polymerization of propylene in a microwave plasma

Flowing microwave plasma of propylene and propylene with argon was studied by mass spectrometry. Plasma composition was investigated as a function of external parameters such as pressure, argon/propylene ratio, and microwave-induced power. It was found that the propylene broke down to C₂H₂ and CH₄, or reacted further with propylene. Two main products, leading to the determination of three main chain reactions for the polymerization of propylene by ion-molecule interactions, were observed, namely, C₂H₂ and CH₄. These were the propylene, acetylene, and ethylene chain reactions. It was also found that the propylene disappeared in a pseudo-first-order reaction. Consequently an overall rate constant for the polymerization was determined (50 sec^–1 at 1 torr pressure for propylene plasma). This constant is found to be linearly dependent upon the propylene percent concentration, and nonlinearly dependent upon plasma pressure.Partly presented at the 157th meeting of the Electrochemical Society, St. Louis, Missouri, May 11–16, 1980.     

Free radical exit in emulsion polymerization. I. Theoretical model

The exit or desorption of free radicals from latex particles is an important kinetic process in an emulsion polymerization. This article unites a successful theory of radical absorption (i.e., initiator efficiency), based on propagation in the aqueous phase being the rate determining step for entry of charged free radicals, with a detailed model of radical desorption. The result is a kinetic scheme applicable to true “zero-one” systems (i.e., where entry of a radical into a latex particle already containing a radical results in instantaneous termination), which is still, with a number of generally applicable assumptions, relatively simple. Indeed, in many physically reasonable limits, the kinetic representation reduces to a single rate equation. Specific experimental techniques of particular significance and methods of analysis of kinetic data are detailed and discussed. A methodology for both assessing the applicability of the model and its more probable limits, via use of known rate coefficients and theoretical predictions, is outlined and then applied to the representative monomers, styrene and methyl methacrylate. A detailed application of the theory and illustration of the methodology of model discrimination via experiment is contained in the second article of this series. © 1994 John Wiley & Sons, Inc.     

Kinetics of radical polymerization of dimethylphenyl methacrylates

The kinetics of free radical polymerization of all six existing isomeric dimethylphenyl methacrylates were studied in bulk at 60°C, initiated by dilauroyl peroxide, using dilatometry. The different polymerization rates observed, resulting from the different monomer structures, are discussed in terms of steric and other effects, considering also the previous results for tolyl methacrylates. © 1993 John Wiley & Sons, Inc.