Deterministic Solutions for a Step-growth Polymerization

Chain topology, including branch node, chain link and cross-link dynamics that contribute to the number of elastically active strands and junctions, are calculated using purely deterministic derivations. Solutions are not coupled to population density distributions. An eigenzeit transformation assists in the conversion of expressions derived by chemical reaction principles from time to conversion space, yielding transport phenomena type expressions where the rate of change in the molar concentrations of branch nodes with respect to conversion is expressed as functions of the fraction of reactive sites on precursors and reactants. Analogies are hypothesized to exist in cross-linking space that effectively distribute branch nodes with i reacted moieties between cross-links having j bonds extending to the gel. To obtain solutions, reacted sites on nodes or links with finite chain extensions are examined in terms of stoichiometry associated with covalent bonding. Solutions replicate published results based on Miller and Macosko’s recursive procedure and results obtained from truncated weighted sums of population density distributions as suggested by Flory

Reaction Kinetics Analysis of Urethane Polymerization to Gelation

A chemical reaction analysis of a thermosetting, urethane resin formulated from a triol and a diisocyanate is reported. Population density distributions of oligomeric molecules, monomer concentration, the cumulative molar concentration of intramolecular bonds, the resin\u27s average molecular weights, and extent of reaction were determined as a function of time. Rate expressions for intermolecular reactions were first order with respect to the concentration of each reactant and were proportional to the functionality of their respective chemical moieties. Rate expressions for intramolecular reactions were first order with respect to the concentration of the reactant and were proportional to the functionality of the limiting chemical moiety on the reactant. The initial ratio of the chemical equivalents and effects of dilution were incorporated into numerical simulations. Stanford and Stepto\u27s experimental data were analyzed. Gel points and the concentration of intramolecular bonds were correlated as a function of conversion. Intramolecular reaction rate expressions derived with the aid of Gaussian chain statistics require the molar concentrations of all chemical isomers of a specified chemical composition. The present reaction rate expression allows chemical isomers to be lumped into a single population density distribution variable, substantially reducing the dimensions of the simulation. Numerical results demonstrate that the simplified rate expression is an excellent

Preventive medicine of von Hippel-Lindau disease-associated pancreatic neuroendocrine tumors

Pancreatic neuroendocrine tumors (PanNETs) are rare in von Hippel-Lindau disease (VHL) but cause serious morbidity and mortality. Management guidelines for VHL-PanNETs continue to be based on limited evidence, and survival data to guide surgical management are lacking. We established the European-American-Asian-VHL-PanNET-Registry to assess data for risks for metastases, survival and long-term outcomes to provide best management recommendations. Of 2330 VHL patients, 273 had a total of 484 PanNETs. Median age at diagnosis of PanNET was 35 years (range 10-75). Fifty-five (20%) patients had metastatic PanNETs. Metastatic PanNETs were significantly larger (median size 5 vs 2\u2009cm; P\u20091.5\u2009cm in diameter were operated. Ten-year survival was significantly longer in operated vs non-operated patients, in particular for PanNETs <2.8\u2009cm vs 652.8\u2009cm (94% vs 85% by 10 years; P\u2009=\u20090.020; 80% vs 50% at 10 years; P\u2009=\u20090.030). This study demonstrates that patients with PanNET approaching the cut-off diameter of 2.8\u2009cm should be operated. Mutations in exon 3, especially of codons 161/167 are at enhanced risk for metastatic PanNETs. Survival is significantly longer in operated non-metastatic VHL-PanNETs

First Shell Substitution Effects: Diglyeidyl Ether of Bisphenol A cured with 4,4\u27-Diaminodiphenylmethane

First shell substitution effects were incorporated into a kinetic reaction model descriptive of the polymerization of an epoxy resin formulated from diglycidyl ether of bisphenol A and 4,4\u27-diaminodiphenylmethane. Analysis of populaiion density distribution dynamics for the hardener and several oligomers in the sol fraction showed that the reactivity of secondary amino hydrogens is less than the reactivity of primary amino hydrogens

Kinetic Analysis of Competing Intramolecular and Intermolecular Polymerization Reactions

ABSTRACT: Kinetic reaction theory was used to model a step-growth, thermoset polymerization of a monomer of even functionality/. Intermolecular additions were represented by second-order and intramolecular reactions were expressed by first-order rate expressions. All functional groups were assumed to react with equal reactivity. Independent variables are degree of polymerization i, extent of cross-linking j, and conversion p. The normalized rate constant for intramolecular reactions is c. The solution for the normalized population density distribution............ subj Formulae for the number-, mass-, and cross-link-average molecular weights were derived

Chemical/Mechanical Analyses of Anhydride-Cured Thermosetting Epoxys: DGEBA/NMA/BDMA

The chemical state of cure in a thermosetting resin was used to predict the resin’s equilibrium modulus. High performance liquid chromatography analyses of the sol fraction yielded molar dynamics for monomeric, oligomeric, and polymeric molecules. Their population density distributions were compared with theoretical predictions based on a chain-growth polymerization mechanism. The resulting chemical estimates of the state of cure were integrated into calculations yielding concentrations of network structures within the gel that contribute to the density of elastically active strands and junctions. The theory of rubber elasticity was then used to predict the equilibrium modulus. Measurements incorporated dynamic mechanical analysis. A comprehensive understanding of the polymerization mechanism and cure history are required for accurate simulations of contributions from branch nodes and chain links. Deterministic models based solely on chemical reaction analysis were used to estimate chain connectivity with the gel. Results were interpreted using stochastic-based reasoning

Kinetic Reaction Analysis of an Anhydride-Cured Thermoplastic Ep-oxy:PGE/NMA/BDMA

A comprehensive reaction analysis of a linear epoxy resin cured with an anhydride was performed to evaluate the reaction rate expressions. Monomers included phenyl glycidyl ether and methyl- 5-norbornene-2,3-dicarboxylic anhydride or nadic methyl anhydride; the catalyst was N,N-dimethylbenzylamine; the initiator was n-propanol. Emphasis was initially placed on the molar dynamics of monomeric and oligomeric molecules. Molecular fractionations were achieved using reversed phase, high performance liquid chromatography. Chemical reaction rate constants were examined as a function of degree of polym-erization. For the chain-initiated polymerization, the initiation rate constant was observed to be approximately 3 times greater than the propagation constant associated with oligomeric molecules. Both Poisson and Gold distributions were used to fit data. Examinations of polymeric fractions obtained by gel permeation chromatography in conjunction with a multiangle laser light scattering photometer revealed a minor side reaction that broadened the polydispersity index and resulted in the reduc-tion of the cumulative, molar concentration of molecules as a function of conversion

Reaction Kinetics Analyses of Amine-Cured Epoxies: First Shell Substitution Effects

Kinetic reaction theory was used to model first shell substitution effects for several amine-cured epoxy resins, subject to the constraint of intermolecular reactions. Moment analysis will allow numerical simulations to be extended beyond the gel point. Functionalities for several chemical moieties were correlated as a function of conversion. Simulations also incorporated population density distribution dynamics. Analyses of several oligomers clearly demonstrated the dependency of oligomeric weight fractions on first shell substitution effects and conversion. The ratio of rate constants for reactions of secondary amino hydrogens relative to reactions of primary amino hydrogens ranged from 0.5 to 1.2 for the resins analyzed

Michaelis–Menten Kinetics for Enzymatic Depolymerization of a Linear Polyester Synthesized from Z-Protected Glutamic Acid

A biodegradable polyester resin was polymerized from N-benzyloxycarbonyl- L -glutamic acid and ethylene glycol. Rhizopus delemar lipase was used as a biocatalyst for the rupture of ester bonds during the hydrolysis studies. Depoly-merization was observed to followa Michaelis–Menten mechanism, with the maximumrate of monomer formation dP/dtmax = 1.12 x 10-8 mol/s and the rate constant Km x 2.03 x 10-4 mol. Subject to initial conditions described by the most probable distribution and Michaelis–Menten–type depolymerization rate expressions, population density distribu-tion dynamics of the polymeric molecules that formed the resin were explicitly described using a deterministic ap-proach