Emulsion polymerization. V. Lowest theoretical limits of the ratio kt/kp

It is assumed that the propagating polymeric radicals have no diffusive mobility in the very highly viscous medium within latex particles. Chain growth takes place on a lattice when the polymeric radical reacts with a monomer present on a lattice site adjacent to that occupied by the reactive chain end. For termination, two radical chain ends must be positioned on adjacent lattice sites at the same instant. The k_t/k_p ratios calculated with this model are either similar to or somewhat lower than the values determined in emulsion polymerization experiments. A minimum value of k_t/k_p can be calculated with the aid of the rate equation of Part III by assuming that only “living” polymer is produced during emulsion polymerization. This value of k_t/k_p is significantly lower than that calculated by the lattice model. Since the value corresponding to the lattice model gives the slowest practically achievable termination rate, it is concluded from these calculations that emulsion polymerization cannot be carried out under conditions in which chain termination is completely suppressed.     

Photopolymerization of methyl methacrylate with the use of tetrahydrofuran–bromine charge-transfer complex as the photoinitiator

The polymerization of MMA was kinetically studied in the presence of visible light (using a 125-W high-pressure mercury vapor lamp with fluorescent coating, without a filter), a THF—bromine charge-transfer complex being used as the photoinitiator. The initiator exponent was 0.5 in bulk polymerization. The monomer exponent varied from about 1.2 to about 2.5, depending on the nature of the solvent used; the initiator exponent also varied in diluted systems, depending on the nature and proportion of the solvent, the variation being from a value of 0.5 in bulk system to zero or almost zero at about 25% (v/v) solvent concentration. Other kinetic parameters, viz., k_p²/k_t and the activation energy for polymerization, were determined and are reported. Kinetic and other evidence indicates that the photopolymerization takes place by a radical mechanism and termination is bimolecular in nature in bulk systems; in dilute systems, termination by initiator complex assumes predominance, particularly at high solvent concentrations (≥25% v/v).     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.     

Effect of pyridine on the kinetics of polymerization of methyl methacrylate initiated by benzoyl peroxide and azobisisobutyronitrile at 60°C

Solution polymerization of MMA, with pyridine as the solvent and BZ₂O₂ and AIBN as thermal initiators, was studied kinetically at 60°C. The monomer exponent varied from 0.45 to 0.91 as [BZ₂O₂] was increased from 1 × 10^?2 to 30 × 10^?2 mole/liter in a concentration range of 8.3-4.6 mole/liter for MMA. For AIBN-initiated polymerization the monomer exponent remained constant at 0.69 as [AIBN] varied from 0.4 × 10^?2 to 1.0 × 10^?2 mole/liter in the same concentration range for MMA. The k²_p/k_t Value increased in both cases with an increase in pyridine concentration in the system. This was explained in terms of an increase in the k_p value, which was due presumably to the increased reactivity of the chain radicals by donor-acceptor interaction between the molecules of solvent pyridine and propagating PMMA radicals and in terms of lowering the k_t value for the diffusion-controlled termination reaction due to an increase in the medium viscosity and pyridine content.     

Photopolymerization of Methyl Methacrylate Using the Benzil-Dimethylaniline Combination as the Photoinitiator

Benzil (BZL)-dimethylaniline (DMA) exciplex interaction has been utilized to initiate the photopolymerization of methyl methacrylate at 40°C in bulk and in solution. Depending on the nature of the solvent used, the monomer exponent values varied between 0.47 to 2.76. Initiator exponent values were found to be 0.29 and 0.15 with respect to [BZL] and [DMA], respectively. A low value of k_p ²/k_t and the high initiator transfer constant values indicated significant initiator-dependent termination. The semipinacol radical formed during irradiation is thought to be mainly responsible for primary radical termination while the generated ion radicals are presumed to participate in degradative initiator transfer.     

Photopolymerization of methylmethacrylate using triethylamine-benzoylperoxide redox initiator system

Photopolymerization of MMA was studied kinetically at 35° using TEA-BZ₂O₂ redox system as initiator. The initiator exponent is 0.34 but the monomer exponent depends on the solvent. Solvents (acetonitrile, pyridine and bromobenzene) giving negative or fractional monomer exponent show a rate enhancing effect through actively influencing the initiation step; benzene and chloroform give first order dependence of rate on [monomer] and behave as normal (inert) diluents. Initiation of polymerization takes place through radicals generated by photodecomposition of TEA-BZ₂O₂ complex formed in situ, the radical generation step being solvent or monomer dependent. Kinetic non-idealities are interpreted in terms of significant initiator dependent termination via degradative chain transfer.     

Chain length‐dependent termination in pulsed‐laser polymerization. VIII. The temperature dependence of the rate coefficient of bimolecular termination in the bulk polymerization of styrene

The photosensitized polymerization of styrene in bulk was investigated in the temperature range of 25–70°C with respect to the average rate coefficient of bimolecular chain termination k̄_t, especially its chain length dependence at low conversions, by means of pulsed laser polymerization (PLP). Three methods were applied: two of them were based on equations originally derived for chain length independent termination taking the quantity k_t contained therein as an average k̄_t, while the third one consisted in a nonlinear fit of the experimental chain length distribution (CLD) obtained at very low pulse frequencies (LF‐PLP) to a theoretical equation. The exponent b characterizing the extent of chain length dependence was unanimously found to decrease from about 0.17–0.20 at 25°C to 0.08–0.11 at 70°C, slightly depending on which of the three methods was chosen. This trend toward more “ideal” polymerization kinetics with rise of polymerization temperature is tentatively ascribed to a quite general type of polymer solution behavior that consists in a (slow) approach to a lower critical solution temperature (LCST), which is associated with a decrease of the solvent quality of the monomer toward the polymer, an effect that should be accompanied with a decrease of the parameter b. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 697–705, 2000     

Modeling termination kinetics in free‐radical polymerization using a reduced number of parameters

An approach for modeling chain‐length dependent termination rate coefficients is presented. The method is based on the assumption that free‐radical chain length may be considered as a continuous variable. As compared to discrete numerical methods, in continuous modeling the number of independent dimensionless parameters can be significantly reduced. As a consequence, for a wide variety of monomers the conversion dependence of k_t can be predicted without extensive numerical calculations. The method may also be used to determine polymerization conditions under which simpler models of k_t (which neglect effects arising from the dependence of k_t on chain length) may be applied. Calculations for methyl methacrylate, styrene, and butyl acrylate bulk polymerizations up to high degrees of monomer conversion show that the impact of chain length on termination varies with conversion and strongly depends on the type of monomer.     

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.     

Effect of viscosity on termination rate constant in radical polymerization at low conversion

By using the expression, k_t = A₁D_s for the chain termination rate constant (where A₁ is a constant and D_s is the diffusion constant of radical chain end), a familiar chain termination rate constant, k_t = A₂/η_s (where A₂ is a constant and η_s is solvent viscosity) was examined with variation of conversion x. It was found that the proportionality of chain termination rate constant and solution viscosity is a valid relation at conversion 0 but is approximate at conversion x_c ≥ x > 0. Here x_c denotes a critical conversion under the average distance around spherical polymers formed in polymerization solution is zero. At conversions above x_c, the inverse relation between chain termination rate constant and solution viscosity is not correct.     

Determination of Chain Transfer Constant for Solvent When the Viscosity of the Polymerizing System Is Considered Important

Abstract

The chain transfer constant of the polymethyl methacrylate radical for N,N-dimethylaniline was determined in two solvents, benzene and dimethyl phthalate. Plots were made using1/P_n=k_t°R_p/k_p ²[M]²η + C_S1 [S₁]/[M] + C_S2 [S₂]/[M] +C_M where η=viscosity of monomer-solvents mixture, k_t°=rate coefficient of termination when η=1 cP, S₁=benzene or dimethyl phthalate, S₂=N,N-dimethylaniline, and other symbols have their usual meanings. The plots agreed well for the two solvents. If the plots were made without considering the viscosity term, two separate lines resulted for the two solvents. Thus it is essential to consider the viscosity of the polymerizing system in the analysis of chain transfer reactions when the termination reaction is diffusion-controlled and the viscosities of the monomer and solvent differ markedly.     

Relationship between chain termination rate constant and conversion in radical polymerization

At low and high conversions, the chain termination rate constant for bimolecular termination between polymeric radicals given by k_t = A_tD_s, where A_t is a constant and D_s is the diffusion constant of radical chain end, is completely correct. This termination rate constant does not depend on solution viscosity, but conversion.     

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.     

Radical polymerization of methyl methacrylate in the presence of isotactic poly(methyl metacrylate). VII. Determination of the rate constants for template polymerization

The separate rate constants k_p and k_t for propagation and termination of radical template polymerization of methyl methacrylate along isotactic poly(methyl methacrylate) as a polymer template have been determined. The polymerizations were carried out in the strongly complexing solvent dimethylformamide at 5°C. For the evaluation of k/k_t from stationary kinetic experiments, the rates of initiation were determined by employing a scavenger method. The nonstationary experiments yielding k_p/k_t were performed by means of the rotating sector technique. As the template rate effects increased with decreasing initiator concentration, the rotating sector curves were corrected for variation in light intensity. It appeared that the radical lifetime increases from 8.4 sec for normal or blank polymerization to 64 sec for template polymerization. The calculated values of k_p are 26.6 and 5.9 l./mole-sec and of k_t 140 × 10⁴ and 1.7 × 10⁴ l./mole-sec for blank and template polymerization, respectively. The changes in k_p and k_t, due to the presence of template polymer, are explained in terms of an extra loss of activation entropy in the stereoselective propagation step and a strong hindrance of segmental diffusion for the termination reaction of the chains growing along the polymer template.     

Radical polymerization of vinyl acetate with primary radical termination

Vinyl acetate was polymerized at high initiation rate with 2,2′-azobis(2,4-dimethyl valeronitrile) as initiator at 50°C. In this polymerization, the power dependence of polymerization rate on the initiation rate is smaller than at lower concentration of monomer. This dependence was kinetically analyzed at each given concentration of monomer. Average degree of polymerization of polymer formed depends on the concentration of initiator. This dependence was explained by considering chain and primary radical terminations and transfer to monomer of polymer radical, and the initiator efficiency (=0.503) was deduced. It was found that the chain termination is inversely proportional to solvent viscosity, but the primary radical termination is not inversely proportional to solvent viscosity. Further, the value of the primary radical termination rate constant (=1.4 × 10⁹l./mole-sec) was estimated.     

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.     

Collision between polymeric radicals for termination rate constants

The motion of each polymeric radical during a collision between the polymeric radicals with the same radius is treated as completely random motion. The result obtained is: k_t = 0.250k_s (where k_t is the chain-termination rate constant and k_s is the reaction rate constant between radical chain ends). On taking the motion of the primary radical during a collision between a primary radical and a large polymeric radical to be completely random, the result obtained is: k_ti = 0.250k_si (where k_ti is the primary radical termination rate constant and k_si is the reaction rate constant between primary radical and radical chain end). On substituting k_s for k_si in the second equation, the rate constant obtained becomes the chain termination rate constant between the very small polymeric radical and the very large polymeric radical, and identical to the former equation. This identity indicates that the effect of the difference of the size of the polymeric radicals on the collision process relating to the chain termination rate constant should not be large.     

Determination of absolute rate constants for free radical polymerization of ethyl α-fluoroacrylate and characterization of the polymer

The absolute rate constants for propagation (k_p) and for termination (k_t) of ethyl α-fluoroacrylate (EFA) were determined by means of the rotating sector method; k_p = 1120 and k_t = 4.8 × 10⁸ L/mol.s at 30°C. The monomer reactivity ratios for the copolymerizations with various monomers were obtained. By combining the k_p values for EFA from the present study and those for common monomers with the monomer reactivity ratios, the absolute values of the rate constants for cross-propagations were also evaluated. Reactivities of EFA and poly(EFA) radical, being compared with those of methyl acrylate and its polymer radical, were found to be little affected by the α-fluoro substitution. Poly(EFA) prepared with the radical initiator was characterized by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Although the glass transition temperature obtained by DSC for poly(EFA) resembled that of poly(ethyl α-chloroacrylate), its TGA thermogram showed fast chain de polymerization to EFA that was distinct from complicated degradation of poly(ethyl α-chloroacrylate).     

Scaling and structural properties of a polymer in a simple solvent: A study based on integral equations

We present a statistical mechanical theory for polymer–solvent systems based on integral equations derived from the polymer Kirkwood hierarchy. Integral equations for pair monomer–monomer, monomer–solvent, and solvent–solvent correlation functions yield polymer–solvent distribution, chain conformation in three dimensions, and scaling properties associated with polymer swell and collapse in athermal, good, and poor solvents. Variation of polymer properties with solvent density and solvent quality is evaluated for chains having up to 100 bonds. In good solvents, the scaling exponent v has a constant value of about 0.61 at different solvent densities computed. For the athermal solvent case, the gyration radius and scaling exponent decrease with solvent density. In a poor solvent, the chain size scales as N^v with the value of the exponent being about 0.3, compared with the mean field value of ⅓. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3025–3033, 1998     

Radiation-induced polymerization of acrylic acid in aqueous solution

Aqueous acrylic acid in the presence of cupric chloride has been subjected to γ-irradiation under various reaction conditions and the molecular weights of the resultant poly(acrylic acid) measured. The results, taken in conjunction with previous findings on the dependence of the rate of polymerization on intensity, monomer concentration, and cupric chloride concentration, indicate chain termination solely by cupric ion (rate constant k_tCu) and chain transfer to polymer (rate constant kf). Values have been obtained for k_tCu/k_p, k_f/k_p and G(radical) of acrylic acid. On the basis of these data a theoretical chain-length distribution has been derived which agrees well with distribution measured by gel-permeation chromatography.