Molecular weight distributions in radiation-induced polymerization. V. A simultaneous kinetic and molecular weight distribution analysis of the liquid-state polymerization of styrene

The γ-ray initiated polymerization of styrene in the liquid state was investigated over the temperature range 0 to ?29°C at constant dose rate. The kinetics and molecular weight distributions were studied for samples prepared by standard techniques and samples subjected to exhaustive drying to remove residual water. In the former case, the rates of reaction were comparable to those for purely free radical polymerization, however, the resulting molecular weight distributions were distinctly bimodal, indicating an additional contribution from the cationic mechanism. On the other hand, the rates of polymerization for rigorously dried samples were 2 to 3 orders of magnitude greater than accepted free-radical values, and the molecular weight distributions were unimodal in nature. The experimental results were compared with theoretical kinetic data and molecular weight distribution data generated from a kinetic scheme taking into consideration polymerization via free-radical, cationic, and radical-cationic species, resulting in the evaluation of a number of quantities of interest. Substitution of determined values for the rate constants and G values results in good agreement between theoretically generated and experimentally determined kinetic data and molecular weight distribution data over the range of experimental conditions studied.     

Molecular weight distributions in radiation-induced polymerization. III. γ-Ray-induced polymerization of styrene at low temperatures

The kinetics of the γ-radiation-induced polymerization of styrene was studied at radiation intensities of 8 × 10⁴, 2.4 × 10⁵, 3.1 × 10⁵, and 8.3 × 10⁵ rad/hr over a temperature range of ?10°C to 30°C. The water content of the irradiated samples varied from 1.0 × 10^?3 to 7.5 × 10^?3 mole/l. The power dependence of the rate of polymerization on the dose rate at ?10°C varied from 0.53 to 0.71 as the water content of the sample varied from 7.5 × 10^?3 to 1.0 × 10^?3 mole/l. A value of 3.1 kcal/mole was determined for the overall activation energy. Molecular weight distribution studies by gel-permeation chromatography indicated the presence of two distinct peaks. The contribution of each peak was dependent on specific experimental parameters. Kinetic data and molecular weight distribution data indicate the coexistence of two propagating species. Analysis of the data strongly suggests that a free-radical mechanism and a cationic mechanism are involved.     

Molecular weight distribution in radiation-induced polymerization. I. γ-radiation-induced free-radical polymerization of liquid styrene

The kinetics of γ-radiation-induced free-radical polymerization of styrene were studied over the temperature range 0–50°C at radiation intensities of 9.5 × 10⁴, 3.1 × 10⁵, 4.0 × 10⁵, and 1.0 × 10⁶ rad/hr. The overall rate of polymerization was found to be proportional to the 0.44–0.49 power of radiation intensity, and the overall activation energy for the radiation-induced free-radical polymerization of styrene was 6.0–6.3 kcal/mole. Values of the kinetic constants, k_p²/k_t and k_trm/k_p, were calculated from the overall polymerization rates and the number-average molecular weights. Gelpermeation chromatography was used to determine the number-average molecular weight M?_n, the weight-average molecular weight M?_w, and the polydispersity ratio M?_w/M?_n, of the product polystyrene. The polydispersity ratios of the radiation-polymerized polystyrene were found to lie between 1.80 and 2.00. Significant differences were observed in the polydispersity ratios of chemically initiated and radiation-induced polystyrenes. The radiation chemical yield, G(styrene), was calculated to be 0.5–0.8.     

Molecular weight distributions in radiation-induced polymerization. VII. γ-ray-induced polymerization of “wet” styrene in the solid state

In the present paper kinetic and molecular weight distribution results are reported for the γ-ray-initiated polymerization of styrene in the solid state. “In-source” polymerization over the temperature range ?35°C to ?55°C and post-polymerization at ?35°C have been investigated for “wet” styrene samples (water concentration ≈ 10^?3 mole/l.). An interesting feature of the solid-state polymerization of styrene is the bimodal nature of the molecular weight distribution. On a qualitative basis the results resemble those obtained previously for the polymerization of rigorously dried (“dry”) styrene. However, there are noticeable differences on a quantitative basis resulting from the considerable difference in the water content between wet and dry samples. On the basis of these studies, the kinetic and molecular weight distribution data have been interpreted as being indicative of polymerization occurring simultaneously via free-radical and cationic mechanisms.     

Molecular weight distributions in radiation-induced polymerization. VI. γ-ray-induced polymerization of “dry” styrene in the solid state

The γ-ray-initiated polymerization of styrene in the solid state has been studied over the temperature range ?35°C to ?55°C for samples exhaustively purified and dried to remove residual water (“dry” samples). Comparison with kinetic results previously reported for dry samples in the liquid state indicates a sharp decrease in the rate of polymerization resulting from the liquid to solid state transition. The molecular weight distributions for in-source polymerization at ?35°C and ?40°C are bimodal in nature, and the appearance of a third peak is noticeable at ?47°C and ?55°C. In the case of postpolymerization at ?35°C the molecular weight distribution is bimodal as in the case of in-source samples. In the former case, however, the high molecular weight peak is predominant whereas the low molecular weight peak predominates in the latter. These results have been tentatively attributed to the postulated coexistence of two distinct propagating species which are radical and cationic in nature.     

Radiation-induced polymerization of tetraoxane in the solid state. II. Molecular weight distribution

In order to investigate the mechanism of the radiation-induced postpolymerization of tetraoxane in the solid state, the polymer was fractionated, and the fractions were characterized by reduced viscosity. The molecular weight of polymer formed in vacuo decreased drastically after the introduction of oxygen under conditions such that the polymer yield increased. The decrease in the molecular weight in the postpolymerization of tetraoxane is attributed to degradation of the polymer in the presence of oxygen. It is suggested that at least peroxides formed by preirradiation contribute to both the increase in polymer yield and the decrease in molecular weight of the polymer.     

Molecular weight distribution and molecular structure of polyethylene produced by radiation-induced polymerization

The molecular weight distribution of polyethylene produced by radiation was calculated according to a kinetic scheme. The calculated molecular weight distribution was compared with the results deduced from gel-permeation chromatography. The observed distribution curve from GPC was broader and showed a lower degree of polymerization than the calculated one. Discrepancies between observed and calculated curves can be explained if the polymer contains nonsteady-state products and if the reaction mechanism includes chain transfer to dead polymer. By this reaction long-chain branching would occur. Several long-chain branches per polymer molecule were indeed found, as inferred from solution properties.     

A kinetic approach to homogeneous Ziegler type polymerization. Steady state

In this paper we present a kinetic approach to the analysis of steady-state homogeneous Ziegler-Natta polymerization activity data. The influence of the number of monomeric species that are coordinated to the active site on the apparent rate law is discussed and the equations are fitted to the experimental results.     

A kinetic approach to homogeneous Ziegler type polymerization. Transient state

In this paper we present a kinetic approach to the analysis of transient-state homogenous Ziegler-Natta polymerization activity data. The main features of the experimental data are discussed and fitted to transient kinetic models.     

Cationic polymerization of formaldehyde in liquid carbon dioxide. Part II: A kinetic study of the polymerization

The kinetic behavior on the polymerization of formaldehyde with and without acidic catalyst, in liquid carbon dioxide, in the temperature range of 30 to 50°C. was investigated. In the polymerization without catalyst both the polymer yield and the degree of polymerization increased with reaction time and also with rising temperature. With acidic catalyst, such as acetic acid and dichloroacetic acid, both the polymer yield and the degree of polymerization increased more than that in the polymerization without catalyst. The overall rate of polymerization with and without acidic catalyst was expressed by the first-order rate equation with respect to monomer concentration. From the results it was concluded that the polymerizations belonged to a type of successive polymerization with rapid initiation and no termination. The rate constant and the activation energy of each elementary process of polymerization were estimated on the basis of the results.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

Molecular weight distribution in nonlinear emulsion polymerization

A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1515–1532, 1997     

Molecular weight distribution in emulsion polymerization. II. The copolymer case

A model for evaluating instantaneous degree of polymerization distribution and the chain composition distribution of copolymers produced in emulsion is developed. The approach adopted is based on the mathematics of Markov processes and represents an extension of the one developed for homopolymers in Part I. As in the homopolymer case, the main aspect of the theoretical treatment is the definition of the proper one step transition probability matrix through the so called subprocess-main process procedure. The model accounts for monomolecular and bimolecular termination (both by combination and disproportionation) and, in principle, it can be applied to any number of reacting monomer species as well as to any number of active chains per particle. However, only the 0–1–2 and 0–1–2–3 emulsion copolymerization systems are discussed in detail. In the case of the chain composition distribution, the model allows the calculation of its moments only, through the method of the Generating Function associated with the probability density function. The expression obtained for the instantaneous probability density functions, as well as for the corresponding cumulative distributions, are all in explicit form and involve only algebraic operations among matrices. Efficient numerical procedure for their application are reported in the Appendix. Illustrative calculations are reported for a 0–1–2–3 copolymerization system, simulating the copolymer styrene–methylmethacrylate. The effect of the various termination mechanisms on the distribution of degrees of polymerization and on the first two moments of the chain composition distribution is discussed in detail. Finally, the three dimensional overall distribution function of both chain length and composition is shown under the assumption of Gaussian type chain composition distribution.     

Molecular weight distribution in emulsion polymerization. I. The homopolymer case

A model for evaluating the instantaneous degree of polymerization distribution of homopolymers produced in emulsion, based on the mathematics of the Markov chains, is developed. The model accounts for any number of active chains per particle, as well as for the two fundamental mechanisms of chain termination: mono- and bi-molecular, both by combination and by disproportionation. The core of the model is the so called subprocessmain process treatment, which allows us to correctly evaluate the degree of polymerization of the chains growing in the polymer particles, by distinguishing between the events experienced by the polymer chain which imply a change of its degree of polymerization (subject transitions) and those which imply only a change in the particle state (environment transitions). This is obtained by properly defining the one-step transition probability matrix of the relevant Markov process. Once this is done, the evaluation of the distribution of the degrees of polymerization reduces to a few simple operations among matrices. Explicit expressions for the instantaneous probability density functions and the relative cumulative distributions are obtained. The application of such relationships is facilitated by the numerical procedures reported in the Appendices. The results of the model developed in this work are in agreement with those of earlier models in the range of parameter values of practical interest. In the limit of very low molecular weights, only the model developed in this work provides the correct answer. Moreover, a much more significant result is its applicability to the case of emulsion copolymerization, as it is shown in Part II.     

Polymerization in the crystalline state. IX. Relation between the velocity of radiation-induced in-source polymerization and post-polymerization

A general relation is derived between the polymerization velocities to be expected for crystalline monomers during irradiation at a polymerization temperature and the post-polymerization observed in samples irradiated at very low temperatures and subsequently warmed outside the irradiation source. For acrylamide, the experimental data are in satisfactory agreement with the theoretical relationship. The possible reasons for a deviation from this relationship are discussed.     

Molecular weight distribution in thermal polymerization of styrene

The molecular weight distribution in thermal polymerization, for which the termination rate is comparable with the transfer rate, is analyzed by assuming that (1) the termination rate is independent of chain length; (2) the rate is translational diffusion-controlled; and (3) the rate is influenced by the excluded volume. The theoretical distribution, based on the assumption that the rate is translational diffusion-controlled, is the best fit to the experimental data at high temperature. The dependence of the rate on chain length is stronger at higher temperature (>80°C). The ratio of the termination rate to the transfer rate increases with increasing temperature.     

Molecular weight development in constant-rate styrene emulsion polymerization

Continuously uniform latices were applied in an experimental study of molecular weight development in constant-rate styrene emulsion polymerization. The formulation around which this study centered exhibited Smith-Ewart, case II kinetics from zero to about 60% conversion with a constant conversion rate of 13 ± 2%/hr and a final particle diameter of 2300 Å. By utilizing an inhibitor perturbation technique, we directly confirmed that free radicals are generated from K₂S₂O₈ by a first-order process with 100% efficiency. We further confirmed that, in contrast to current theories for constant rate polymerization, both the instantaneous values of M?_n and M?_v may increase 6- to 9-fold. Little or no chain branching is evidenced. We interpret these findings to mean that radicals are not utilized with 100% efficiency in emulsion polymerization.     

Polymerization of aromatic nuclei. VIII. Molecular weight control in benzene polymerization

The molecular weight of p-polyphenyl prepared from benzene—aluminum chloride—cupric chloride, was affected by solvent, concentration, and temperature. Relative molecular weights were measured by polymer solubility in chloroform, and positions of the infrared para band and ultraviolet reflectance λ_max. The order of effectiveness of the solvents in reducing molecular weight was: o-C₆H₄Cl₂ > 1,2,4-C₆H₃Cl₃ > SnCl₄ ～ CS₂ > [C₆H₆]. Degradative oxidation revealed that o-dichlorobenzene solvent was incorporated as an endgroup to only a minor extent. In general, the molecular weight of p-polyphenyl decreased with increasing temperature and with decreasing concentration. The theoretical aspects are treated.     

A systematic scheme of qualitative analysis for anions.IV

A comprehensive investigation has been undertaken to ascertain how the basic radicals that pass into the sodium carbonate filtrate arc distributed among the various groups for the detection of anions. Methods for the detection of these basic radicals in the presence of the anions have been worked out in detail. It was found that the scheme for the detection of anions put forward previously remains unaffected by the presence of these basic radicals. It has been shown that the scheme for the detection of anions can be integrated with the comprehensive schemes for the detection of basic radicals and insoluble substances.