Diffusion control in radiation graft polymerization with varying dependence of rate on monomer concentration

The quantitative effect of diffusion control on the rate of radiation-initiated graft polymerization has been studied theoretically for systems in which the diffusion-free reaction may show various dependencies of rate on monomer concentration other than the usual first-order dependence. The study is also very general in that it can be applied to systems involving a variety of different modes of initiation and termination. Whether the grafting process is diffusion-free or diffusion-controlled has been analyzed in terms of the interaction of the initiation rate R_i, the propagation and termination rate constants k_p and k_t, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, the diffusivity D of the monomer in the polymer, and the diffusion-free kinetic order of dependence v of the grafting rate on monomer concentration. The dependence of the grafting rate for both the diffusion-free and diffusion-controlled reactions on these parameters is expressed both by mathematical experssions and graphically. Diffusion control is shown to occur at a critical value of the parameter A which is proportional to L(k_pR_i^w/k_t^zD)^1/2M^(ε?1)/2 where w, z, and v have different values depending on the specific modes of initiation, propagation and termination in a particular grafting system. The grafting rate is shown to vary with the value of A according to specific mathematical expressions. In comparing diffusion-free to diffusion-controlled reaction, it is shown that the former is independent of L and D while the latter is directly dependent on L and inversely on D^1/2. Further, the change from diffusion-free to diffusion-controlled reaction involves a change in the dependence of rate on monomer from v-order to [(v ? 1)/2]-order. The nonsteady-state as well as the steady-state reaction rates have been analyzed.     

Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problem can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the v power of the monomer concentration C, in which the proportionality constant a = k_pR/k, where k_p and k_t are the propagation and termination rate constants, respectively, and R_i is the initiation rate. The values of v, w, and z depend on the particular reaction system. The results of our earlier work were generalized by allowing a non-Fickian diffusion rate, obtained from an extension of the Fujita free-volume theory, which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D₀ [exp(δC/M)], where M is the saturation concentration. It was shown that a reaction system is characterized by the three dimensionless parameters v, δ, and A = (L/2)[aM^(v?1)/D₀]^1/2, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of δ and v cause a reaction system to behave closer to the diffusion-free regime. The transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, v order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. The dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system.     

Diffusion-controlled reaction. VI. Radiation graft polymerization of styrene to polyethylene

The radiation graft polymerization of styrene to polyethylene was studied under diffusion-controlled conditions of radiation intensity I, monomer concentration M₁, and polymer sample thickness L. The results of the present study together with previous work under diffusion-free conditions verify our theoretical model for the diffusion-controlled reaction. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The order of dependence of grafting rate on radiation intensity for diffusion-controlled reaction is one-half that for diffusion-free reaction. Diffusion control leads to a decrease in the order of dependence of grafting rate on monomer concentration. The decrease is greater than theoretically predicted; possible reasons for this effect are described.     

Diffusion-controlled reaction. VI. Radiation graft polymerization of 4-vinylpyridine to polyethylene

The radiation-initiated graft polymerization of 4-vinylpyridine to high-density polyethylene was studied over a wide range of reaction conditions of radiation intensity I, monomer concentration M₁, and polymer film thickness L. The conditions included both diffusion-free and diffusion-controlled graft polymerizations. The results corroborate our previous theoretical predictions on the effect of I, M₁, and L on the experimental grafting rate. The grafting rate is inverse first order in L for diffusion-controlled reaction and independent of L for diffusion-free reaction. The dependence of grafting rate on radiation intensity decreases from 1/2 to 1/4 order for diffusion-controlled reaction. Diffusion control results in a decrease in the dependence of rate on monomer concentration. The observed decrease is somewhat greater than theoretically predicted.     

Grafting onto wool. V. Kinetics of graft copolymerization of methyl methacrylate in the viscous media of wool fibers

The graft copolymerization of methyl methacrylate in S-carboxymethylated wool fibers was investigated in the aqueous LiBr-K₂S₂O₈ system. The rate of grafting, the degree of polymerization of graft polymer, and the number of grafting sites were determined on varying the thiol content at a constant concentration of monomer. Kinetic considerations lead to the following expression in agreement with the experimental results: Z/DP = {(k_td + k_tc)/k_p²[M]²} R_p, where Z is the number of DNP endgroups of polymer; DP is the average degree of polymerization; k_p, k_td, and k_tc are the rate constants of propagation, termination by disproportionation, and termination by recombination, respectively; [M] is the concentration of monomer in fibers, and R_p is the overall rate of grafting. For wool fibers in media sufficiently high viscosity, the rate constants k_td and k_tc of diffusion-controlled termination are approximately equal and not affected by the change in cross-link density, provided that the thiol and disulfide interchange occurs. The possibility of occurrence of mechanical bond scission through a radical mechanism is involved in systems with extremely small amounts of thiol groups.     

Solvent effect on the radical polymerization of di-n-butyl itaconate

Solvent effect on the polymerization of di-n-butyl itaconate (DBI) with dimethyl azobisisobutyrate (MAIB) was investigated at 50 and 61°C. The solvents used were found to affect significantly the polymerization. The polymerization rate (R_p) and the molecular weight of the resulting polymer are lower in more polar solvents. The initiation rate (R_i) by MAIB, however, shows a trend of being rather higher in polar solvents. The stationary state concentration of propagating poly(DBI) radical was determined by ESR in seven solvents. The rate constants of propagation (k_p) and termination (k_t) were evaluated by using R_p, R_i, and the polymer radical concentration observed. The k_p value decreases fairly with increasing polarity of the solvent used, whereas k_t is not so influenced by the solvents. The solvent effect on k_p is explained in terms of a difference in the environment around the terminal radical center of the growing chain. Copolymerization of DBI with styrene (St) was also examined in three solvents with different physical properties. The poly(DBI) radical shows a lower reactivity toward St in a more polar solvent.     

Comparative study of the absolute reactivity of vinyl monomers: Kinetics of polymerization of vinyl monomers initiated by Mn3+–thiodiglycolic acid redox system

The kinetics and mechanism of polymerization of methacrylic acid (MAA) and ethyl acrylate (EA) initiated by the redox system, Mn³⁺–thiodiglycolic acid (TDGA) were investigated in the 15–35°C temperature range. The polymerization kinetics of both the monomers followed the same mechanism, viz., initiation by primary radical and termination by Mn³⁺–thiodiglycolic acid complex. The rate coefficients k_i/k₀ and k_p/k_t were related to the monomer reactivity and polymer radical reactivity, respectively. It was observed that both monomer reactivity and polymer radical reactivity followed the same order, viz., EA > MAA. The polymer radical reactivity varied inversely with the Q values of the monomers.     

Effects of macromolecular matrix on the process of radical polymerization of ionizable monomers

Radical polymerization of methacrylic acid (MAA) and acrylic acid (AA) in the presence of a positively charged macromolecular matrix was studied. In the presence of a matrix, the rates of polymerization were remarkably increased, especially in high pH region. This suggests that electrostatic interaction between the macromolecular matrix and the growing chains and/or the monomer molecules plays an important role in the process of polymerization reaction. The kinetic orders were greatly influenced by the relative matrix concentration (PC) as follows: for (PC)₀ > [M]₀, R_p = k[M]^0.9 [PC]_0.3 [I]^0.8≤ [M]₀ R_p = k[M]^0.3[PC]⁰[I]^0,8 where [M] and [I] are monomer and initiator concentration, respectively, and k is a constant. The mechanism of the interaction of matrix with monomer and/or growing chains in the process of the propagation is discussed. The complex formed in the matrix polymerization could be easily made into fiber by spinning.     

A comparison of the absolute reactivity of vinyl monomers. I. Kinetic studies on radical polymerization of vinyl monomers initiated by a Mn3+–diglycolic acid redox system

The kinetics of polymerization of acrylamide (AM), acrylic acid (AA), and acrylonitrile (AN) initiated by the redox system Mn³⁺–diglycolic acid (DGA) was studied. All three systems followed the same mechanism; namely, initiation by an organic free radical arising from the oxidation of diglycolic acid and termination by the interaction of polymer radicals with Mn³⁺ ion. The rate coefficients k_i/k₀ and k_p/k_t were related to monomer and polymer radical reactivity, respectively. An inverse relation between monomer and polymer radical reactivity was observed. Monomers with higher Q values gave higher k_i/k₀ values but lower k_p/k_t values. The e values of the monomers were important in determining the reactivities of monomers with nearly the same Q values.     

Plasma polymerization investigated by the substrate temperature dependence

Plasma polymerization of tetra fluoroethylene (TFE), perfluoro-2-butyl-tetrahydrofuran (PFBTHF), ethylene, and styrene were investigated in various combinations of monomer flow rates and discharge wattages for the substrate temperature range of ?50 to 80°C. The polymer deposition rates can be generally expressed by k₀ = Ae^?bt, where k₀ is the specific deposition rate given by k₀ = (deposition rate)/(mass flow rate of monomer), A is the preexponential factor representing the extrapolated value of k₀ at zero absolute temperature, and b is the temperature-dependence coefficient. It was found that the value of b is not dependent on the condensibility of monomer but depends largely on the group of monomer; that is, perfluorocarbons versus hydrocarbons. The values of A are dependent on domains of plasma polymerization. In the energy deficient region A is given by A = α(W/FM)ⁿ, where α is the proportionality constant, W is discharge wattage, FM is the mass flow rate, and n is close to unity. In the monomer deficient region A becomes a constant. The kinetic equation is discussed in view of the bicyclic rapid step-growth polymerization mechanisms.     

Radiation-induced graft polymerization of styrene to poly(vinyl chloride)

The radiation-induced graft polymerization of styrene to poly(vinyl chloride) (PVC) was investigated. Relations between the rate of grafting and the dose rate when the polymer is irradiated in liquid monomer or in monomer vapor, and between the rate of grafting and monomer concentration absorbed in the polymer have been investigated. The rate of grafting in monomer vapor was found to be far larger than that in liquid monomer. A high rate of grafting in monomer vapor was thought to result from a lower concentration of monomer in PVC during irradiation. An experiment carried out on PVC containing the monomer at various concentrations showed that the rate is largest at a monomer concentration of about 3.5 mole/l. and is smaller for higher and lower concentrations. On the assumption that the theory of homogeneous homopolymerization can be applied to this grafting reaction, the value of k_p²/k_t has been obtained, where k_p and k_t are propagation constant and termination constant, respectively. The value of k_t greatly increases when the monomer concentration exceeds 3.5 mole/l. This increase of k_t can be accounted for if it is assumed that the monomer absorbed in the polymer works as a plasticizer and increases the molecular motion of the polymer. A measurement of the elastic modulus of PVC containing the monomer at various concentrations showed that this is, in fact, the case.     

Mechanism of styrene emulsion polymerization during interval II

A systematic study of the kinetics of styrene emulsion polymerization in the postnucleation stage by the way of seed particle growth of monodisperse latices was undertaken, in which the colloidally important parameters were varied: R_p was independent (within limits) of (a) ionic strength, (b) pH, (c) initiator concentration (potassium persulfate), and (d) surfactant (sodium dodecyl sulfate) concentration; R_pp was independent (within limits) of (a) seed particle number concentration N, (b) oil:water phase ratio, and (c) monomer:polymer ratio; R_p was directly proportional to seed-particle surface area. The viscosity average molecular weight of the polymer formed during interval II, M_v(i–j), was approximately constant and increased linearly with N. Log M_v(i–j) was inversely proportional to reaction temperature; M_v(i–j) was inversely proportional to initiator concentration. The overall activation energy of polymerization E′_p was equal to the activation energy of propagation E_p during interval II. The value of k_p at 60°C was 615 dm³ mol^?1 s^?1. Trace of oxygen seems to affect the average number of radicals per particle ī during interval II polymerization.     

Radical polymerization behavior of ethyl ortho-formylphenyl fumarate involving intramolecular hydrogen abstraction

The radical polymerization behavior of ethyl ortho-formyl-phenyl fumarate (EFPF) using dimethyl 2,2′-azobisisobutyrate (MAIB) as initiator was studied in benzene kinetically and ESR spectroscopically. The polymerization rate (R_p) at 60°C was given by R_p = k[MAIB]^0.76[EFPF]^0.56. The number-average molecular weight of poly(EFPF) was in the range of 1600–2900. EFPF was also easily photopolymerized at room temperature without any photosensitizer probably because of the photosensitivity of the formyl group of monomer. Analysis of ¹H? and ¹³C-NMR spectra of the resulting polymer revealed that the radical polymerization of EFPF proceeds in a complicated manner involving vinyl addition and intramolecular hydrogen-abstraction. The polymerization system was found to involve ESR-observable poly(EFPF) radicals under the actual polymerization conditions. ESR-determined rate constant (2.4–4.0 L/mol s) of propagation at 60°C increased with decreasing monomer concentration, which is mainly responsible for the observed low de-pendency of R_p on the EFPF concentration. Copolymerizations of EFPF with some vinyl monomers were also examined. © 1995 John Wiley & Sons, Inc.     

KINETICS OF POLYMERIZATION OF METHYL METHACRYLATE INITIATED BY COPPER POLYPROPYLENE-BASED POLYAMIDOXIME-SODIUM SULFITE SYSTEM*

The aqueous polymerization of methyl methacrylate initiated by copper polypropylene-based polyamidoxime (PPAO-Cu) -sodium sulfite system was investigated. The overall rate of polymerization (R_p) isR_p=9.7 x 10~(12) e~(-21.200/RT) [MMA]~(O.88)[Na_2 SO_3]~(0.50)The length of the induction period (τ) is inversely proportional to the concentration of sodium sultite and independent of the amount of polymer supported copper and the concentration of monomer. It could be expressed as follows:1/τ=1.2x10~(12)e~(-15.600/RT)[Na_2SO_3]=K_τR_iThe polymerization is initiated by a primary radical generated from the redox reaction rather than induced by "coordination-proton transfer" mechanism.     

Kinetics of the Copolymerization of Methyl Vinyl Ketone and Acrylamide Initiated by the Adduct of Methyl Vinyl Ketone and Imidazole

N-(Butyl-3-one)imidazole acts as an initiating adduct which is formed in the anionic polymerization of methyl vinyl ketone (MVK) induced by imidazole (Im) and is directly formed from Im and the MVK monomer. The kinetics of the anionic homopolymerization of MVK and acrylamide (AAm) under argon in the presence of the adduct were investigated in tetrahydrofuran (THF). The rate of polymerization for the MVK system is expressed as R_p = k[Adduct] [MVK], where k = 3.1 × 10^?6 L/(mol·s)in THF at 30°C. The overall activation energy, E_a , was found to be 5.34 kcal/mol. The R_p for the AAm system is expressed as R_p = k[Adduct] [AAm], where k = 6.8 × 10^?6 L/(mol·s) in THF at 30°C, with E_a 7.78 kcal/mol. The mechanism of the polymerization induced by the initiator adduct is discussed on the basis of these results.     

Long-lived polymer radicals. VI. Polymerization of N-methylmethacrylamide with formation of living propagation radicals

The polymerization of N-methylmethacrylamide (NMMAm) with azobisisobutyronitrile (AIBN) was investigated kinetically in benzene. This polymerization proceeded heterogeously with formation of the very stable poly(NMMAm) radicals. The overall activation energy of this polymerization was calculated to be 23 kcal/mol. The polymerization rate (R_p) was expressed by: R_p = k[AIBN]^0.63-0.68[NMMAm]^1?2.5. Dependence of R_p on the monomer concentration increased with increasing NMMAm concentration. From an ESR study, cyanopropyl radicals escaping the solvent cage were found to be converted to the living propagating radicals of NMMAm in very high yields (ca. 90%). Formation mechanism of the living polymer radicals was discussed on the basis of kinetic, ESR spectroscopic, and electron microscopic results.     

Kinetic and EPR studies on radical polymerization. Radical polymerization of di-2[2-(2-methoxyethoxy)ethoxy]ethyl itaconate

The polymerization of di-2[2-(2-methoxyethoxy)ethoxy]ethyl itaconate (1) with dimethyl 2,2-azobisisobutyrate (2) was studied, in benzene, kinetically and spectroscopically with the electron paramagnetic resonance (EPR) method. The polymerization rate (R _p) at 50°C is given by the equation:R _p=k[2]^0.48 [1]^2.4. The overall activation energy of polymerization was calculated to be 34 kJ·mol^–1. From an EPR study, the polymerization system was found to involve EPR-observable propagating polymer radicals of 1 under the actual polymerization conditions. Using the polymer radical concentration, the rate constants of propagation (k _p) and termination (k _t) were determined. With increasing monomer concentration,k _p(1.54.3 L·mol^–1·s^–1 at 50°C) increases andk _t (1.0·10⁴4.2·10⁴ L·mol^–1·s^–1 at 50°C) decreases, which seems responsible for the high dependence ofR _p on the monomer concentration. The activation energies of propagation and termination were calculated to be 11 kJ·mol^–1 and 84 kJ·mol^–1, respectively. For the copolymerization of 1(M ₁) and styrene (M ₂) at 50°C in benzene the following copolymerization parameters were found:r ₁=0.2,r ₂=0.53, Q₁=0.57, ande ₁=+0.7.     

Propagation rate coefficients of isobornyl acrylate,tert‐butyl acrylate and 1‐ethoxyethyl acrylate: A high frequency PLP‐SEC study

Pulsed laser polymerization (PLP) coupled to size exclusion chromatography (SEC) is considered to be the most accurate and reliable technique for the determination of absolute propagation rate coefficients, k_p. Herein, k_p data as a function of temperature were determined via PLP‐SEC for three acrylate monomers that are of particular synthetic interest (e.g., for the generation of amphiphilic block copolymers). The high‐T_g monomer isobornyl acrylate (iBoA) as well as the precursor monomers for the synthesis of hydrophilic poly(acrylic acid), tert‐butyl acrylate (tBuA), and 1‐ethoxyethyl acrylate (EEA) were investigated with respect to their propagation rate coefficient in a wide temperature range. By application of a 500 Hz laser repetition rate, data could be obtained up to a temperature of 80 °C. To arrive at absolute values for k_p, the Mark‐Houwink parameters of the polymers have been determined via on‐line light scattering and viscosimetry measurements. These read: K = 5.00 × 10⁵ dL g⁻¹, a = 0.75 (piBoA), K = 19.7 × 10⁵ dL g⁻¹, a = 0.66 (ptBA) and K = 1.53 × 10⁵ dL g⁻¹, a = 0.85 (pEEA). The bulky iBoA monomer shows the lowest propagation rate coefficient among the three monomers, while EEA is the fastest. The activation energies and Arrhenius factors read: (iBoA): log(A/L mol⁻¹ s⁻¹) = 7.05 and E_A = 17.0 kJ mol⁻¹; (tBuA): log(A/L mol⁻¹ s⁻¹) = 7.28 and E_A = 17.5 kJ mol⁻¹ and (EEA): log(A/L mol⁻¹ s⁻¹) = 6.80 and E_A = 13.8 kJ mol⁻¹. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6641–6654, 2009     

Self‐entanglement of a single polymer chain confined in a cubic box

We study the self‐entanglement of a single linear polymer chain with N monomers confined to a cubic box (L × L × L) using the bond‐fluctuation lattice model and primitive path analysis. We probe chains with N between 30 and 750 and vary the degree of confinement L/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We find that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p is the average primitive path length, collapse onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/R_g0 < 1, we find that R_g/R_g0 ～ (L/R_g0)^0.8 and (L_p/R_g0) ～ (L/R_g0)^?2. We verify that the simulation methodology used is quantitatively consistent with experimental data, and the Colby‐Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of L_p with monomer density ?; L_p ～ ?^5/9, in the former, and L_p ～ ?^2/3, in the latter. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1283–1290