Equal Reactivity Hypothesis Research Articles

Santosh K. Gupta: Professor extraordinaire and inspiration to several generations

Santosh K. Gupta: Professor extraordinaire and inspiration to several generations

Autoacceleration in Free Radical Polymerization. 2. Molecular Weight Distributions

Molecular weight distributions during autoacceleration in free radical polymerization are calculated within the framework developed in part 1. Most macroradicals (living chains) are so immobilized by entanglements that they terminate with short mobile unentangled chains with rate constants independent of their own lengths. In some respects, Flory's equal reactivity hypothesis is recovered, leading to a Flory (exponential) distribution of the living population for most chain lengths N. The instantaneous distribution of the polymer product, $& is a copy of the living one. Its mean length is Nd - 1/Ri where & is the initiation rate. For the shortest chains, $d exhibits power law behavior with exponents determined by short chain termination kinetics and vanishes at N = 0. It follows that $d is peaked at N = z, the characteristic short chain length.

Polymerization kinetics of poly(p-phenylene-cis-benzobisoxazole)

The kinetics of polycondensation of terephtalic acid with diaminoresorcinol in the nematic phase appear to be independent of molecular weight, in good agreement with Flory's equal reactivity hypothesis. The results suggest that, for well-mixed reactive mixtures, translational diffusion does not appear to control the polymerization rates

Olefins polymerization on titania and titania-supported rhodium

The adsorption of ethene and propene on titania and titania-supported rhodium has been studied, observing a continuous adsorption even after 24 h. The samples have been reduced at 623 or 773 K, but no difference was observed, whichever the reduction temperature or the presence of rhodium, on the amount of gas adsorbed per unit of surface area of the solid. A study of the polymerization has been done following the “equal reactivity hypothesis”, and it has been concluded that the role played by the rhodium particles is to facilitate adsorption of the gaseous molecule, that is then transfered to the surface of the support, where it polymerizes.

Kinetics of transesterification of dimethyl terephthalate with poly(tetramethylene ether) glycol and 1,4-butanediol catalyzed by tetrabutyl titanate

The kinetics of tetrabutyl titanate catalyzed transesterification of dimethyl terephthalate with poly(tetramethylene ether) glycol of various molecular weight has been studied in the presence and absence of 1,4-butanediol. Detailed analysis of experimental data with a proposed kinetic model indicates that the equal reactivity hypothesis for functional groups is valid within a wide range of experimental conditions studied. It is also found that the reactivity of hydroxyl groups of macrodiols such as poly(tetramethylene ether) glycol is independent of the chain length of the polymer. Effect of various reaction parameters on the transesterification rate and the resulting product composition is also discussed.

Kinetics of transesterification of dimethyl terephthalate with 1,4‐butanediol catalyzed by tetrabutyl titanate

AbstractThe kinetics of tetrabutyl titanate catalyzed transesterification of dimethyl terephthalate (DMT) with 1,4‐butanediol (BD) is investigated. Detailed analysis of experimental data indicates that equal reactivity hypothesis for functional groups is valid for [BD]/[DMT] molar ratios greater than 2 up to 75% conversion. Effects of reaction temperature and catalyst concentration are also discussed.

Modeling of melamine formaldehyde polymerization. II. Development of a simpler model

AbstractThe kinetic modeling of melamine–formaldehyde polymerization presents a relatively formidable mathematical challenge because of the simultaneous presence of several types of deviations from Flory's equal reactivity hypothesis. A molecule of melamine has six reactive amide hydrogens, which can react with the CH2OH groups of formaldehyde in solution. The reactivity of the secondary hydrogens on the melamine is about 61% of that of the primary hydrogens (induced asymmetry). There is a shielding effect present, i. e., the reactivity of the hydrogens near the outside of a multiringed polymer molecule is higher than that of the hydrogens inside the coiled molecules. Two bound CH2OH groups on the polymer molecules can self‐condense to give methylene linkages, the reactivity depending upon the location of the two groups. And, to confound modeling effort still further, all these reactions are reversible. An earlier attempt at molding this system considered the reactions between 36 “basic” species. This model was far too detailed and failed to acount for the reverse reactions. In the present study, a simpler model has been proposed which involves fewer “basic” species. An improved model for intramolecular reactions is also developed. Several important characteristics of the polymerization have been obtained as a function of time. Results from this model have been compared with those obtained from the earlier model, and also compared with the short‐time experimental results. The present model can be extended to account for the reverse reactions quite easily.

Mass transfer effects in polycondensation reactors wherein functional groups are not equally reactive

AbstractThree simplified models of polycondensation reactors are considered in which the condensation product is continuously removed by application of vacuum. Reversible polycondensation reactions of monomers violating the equal reactivity hypothesis have been simulated in these reactors. The effect of various rate and reactor design variables on the molecular weight distribution (MWD) and its moments is studed. It is observed that when the reverse reactions are rapid, the results are fairly sensitive to the level of vacuum applied and to the mass transfer resistance; whereas when the forward reactions predominate, results lie very close to earlier plots for the corresponding irreversible polymerizations. These reactor variables then have relatively small influence on the MWD. Splitting of the MWD curves for odd and even values on n is observed under certain conditions, the effects being more pronounced in the presence of mass transfer than in its absence.

Condensation polymerisations with unequal reactivity in segregated continuous‐flow stirred tank reactors

AbstractA parametric study of the molecular weight distribution and its moments has been made on the irreversible condensation polymerisation of ARB type monomers which do not obey the equal reactivity hypothesis. The reactions are simulated for a continuous‐flow stirred‐tank reactor with distributed residence times, the mean residence time being the operating variable. Two different kinetic schemes have been proposed which represent the limiting cases of the actual situations (models I and II) which are usually encountered and the effect of segration in a CSTR has been studied. The molecular weight distributions, number average chain lengths and the polydispersity indices have been computed. Results are found to lie intermediate between batch reactors and homogeneous, continuous‐flow stirred tank reactors. Plots between the poly dispersity index and the monomer conversion with the reactivity ratio, R, and the number average chain length as parameters indicate that results are far more sensitive to variations in R for model II than for model I.

Condensation polymerization of ARB type monomers in CSTRs wherein the monomer is R times more reactive than other homologues

Molecular weight distributions ( MWDs) and their moments for the polycondensations of ARB-type monomers which do not obey the equal reactivity hypothesis, in ideal continuous-flow stirred tank reactors (CSTRs), have been studied. The model assumes that monomers react with monomers and higher homologues at a rate which is R times that of all other reactions in the system. It is found that the polydispersity indices are much higher than for the batch reactor. The MWD has been found to split into two curves, one for even-ordered homologues and one for odd-ordered ones. For R < 1, these curves merge for higher homologues, whereas for R > 1, firstly there is a fall in the mass fraction from monomer to the dimer, then a rise to a broad maxima after which they decay slowly. Results are also compared with those for a different kinetic scheme in which the monomer reacts only with a monomer at a rate R times that characterizing all other species.

Condensation polymerizations in ideal continuous‐flow‐stirred tank reactors of monomers violating the equal reactivity hypothesis

AbstractMolecular weight distributions, moments and the polydispersity indices were computed for AB‐type condensation polymerization in an ideal continuous‐flow‐stirred tank reactor for monomers not following the equal reactivity hypothesis. The model considers the rate of reaction between monomer and monomer to be R times that characterizing the reaction between any other species in the reaction mass. It is found that the polydispersity indices in these reactors are substantially larger than values obtained in batch reactors. Also, the molecular weight distribution splits into two curves—one for odd‐order homologs and the other for even‐order ones for R &gt;1. For R &lt; 1, substantial amounts of unreacted monomer are present in the exit stream, and curve splitting does not occur.

Molecular weight distributions and moments for condensation polymerizations characterized by two rate constants

Molecular weight distributions (MWD) and moments have been computed for condensation polymerizations of ARB-type monomers wherein the reactions involving the monomer are characterized by a rate constant k 11 and those involving other species, by k p . For k 11/ k p < unity, the MWD curves are found to split into two, one for even n and one for odd values of n. Substantial amounts of unreacted monomer are found in the reaction mass for this case and so moments and the polydispersity index computed without the monomer are better representations of the distributions. For k 11/ k p > unit, conventional MWDs are observed with dispersions different from those representing polymerizations satisfying the equal reactivity hypothesis.