Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 1. Molecular weight calculations for linear copolymers

The moment equations for binary copolymerization in the context of the terminal model have been solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights were compared with those found using pseudo-kinetic rate constants with the method of moments and with the instantaneous property method for homopolymerization. With the pseudo-kinetic rate constant method under polymerization conditions where number-average molecular weights (M̄_n) are below about 10³ the error in calculating M̄_n exceeds 5%. The error increases rapidly with decrease in molecular weight for M̄_n < 10³. M̄_n measured experimentally for polymer chains (homo- and copolymers) have error limits of greater than ±5% at the 95% confidence level. Therefore, for all practical purposes, the pseudo-kinetic rate constant method is valid for M̄_n greater than 10³. Errors in calculating weight-average molecular weights (M̄_w) or higher averages are always smaller than those for M̄_n when applying the pseudo-kinetic rate constant method. The assumptions involved in molecular weight modelling using the pseudo-kinetic rate constant approach are thus proven to be valid, and therefore it is recommended that the pseudo-kinetic rate constant method be employed with the instantaneous property method to calculate the full molecular weight distribution and averages for linear chains synthesized by multicomponent chain growth polymerization.     

Modelling free-radical copolymerization kinetics, 3. Molecular weight calculations for copolymers with crosslinking

A comprehensive model for molecular weight calculations of free-radical crosslinking copolymerizations was developed using the pseudo-kinetic rate constants and the method of moments. The moments of copolymer chain distributions are defined in such a way so that the molecular weight averages of crosslinking copolymers can be calculated using the moments. The present model is based on a general crosslinking copolymerization scheme, accounting for chain transfer to small molecules and polymer, bimolecular termination, and crosslinking reactions. The influence of crosslinking reactions on molecular weight development is discussed. The effects of the reactivity of pendant double bonds on the moments development were further demonstrated using model simulations. The simulations results suggest that the higher-order molecular weight averages are very sensitive to the reactivity of pendant double bonds. It was found that chain transfer to polymer affects the gelation point significantly. The radical fractions must be calculated accounting for chain transfer reactions in addition to propagations in order to properly evaluate pseudo-kinetic rate constants. The present model was used to predict kinetic behavior and molecular weight development of styrene/m-divinylbenzene and styrene/ethylene dimethacrylate free-radical crosslinking copolymerizations in benzene solution at 60°C. It was found that the present model is in excellent agreement with the experimental data published in the literature. Model predictions and experimental data show that the reactivity of pendant double bonds is much lower than that of vinyl and divinyl monomers. The simulation results suggest that the assumption of the same reactivity of functional groups is likely not valid for many free-radical crosslinking copolymerizations. The present model based on a kinetics approach can be used to predict molecular weight development for vinyl/divinyl free-radical crosslinking copolymerizations and to estimate kinetic parameters in the pre-gelation period.     

Kinetic theory of anionic copolymerization with constant monomer ratio, 2 . Molecular weight distribution

The kinetic differential equations for the anionic copolymerization with constant monomer ratio are treated by Laplace transformation and a graphical technique. A theoretical method is established by which all molecular parameters of the copolymers, such as the molecular distribution (MWD), the average molecular weight and the polydispersity, can be calculated from reaction rate constants, initial conditions and polymerization time. Three-dimensional plots obtained by numerical computation are presented to illustrate the influence of the reaction conditions on the MWD's of the copolymers.     

Molecular weight distribution of metallocene polymerization with long chain branching using a binary catalyst system

In metallocene polymerization, termination by β-hydride elimination generates polymer chains containing unsaturated vinyl groups at their chain ends. Further polymerization of these macromonomers produces branched polymers. Material properties of the branched polymers not only depend on molecular weight and branching density, but also on chain structure. This work presents analytical expressions to predict the bivariate distribution of molecular weight and branching density for polymer chains having dendritic and comb structures. It is shown that when a single metallocene catalyst is used the formation of dendritic polymers is favored with only a very small fraction of highly branched chains assuming comb structure. The use of a binary catalyst system is therefore proposed to obtain high content of comb polymers. One catalyst generates macromonomers and the other yields in-situ branching. It is found that the comb polymers give much narrower molecular weight distributions than dendritic polymers with same branching densities.     

Effect of polyfunctional chain transfer agents on molecular weight distribution in free-radical polymerization, 2. The case C ≤ 1

In this part of the series, the influence of polyfunctional chain transfer agents with transfer constant C ≤ 1 on the molecular weight distribution was studied. The analytical expressions for the number- and weight-average degree of polymerization, and dispersion index were derived by kinetic and statistical methods. The expression for the molecular weight distribution can only be obtained by statistical methods. Some numerical examples on the dependence of distribution parameters as a function of the functionality of transfer agents f and transfer constants are illustrated. A critical value of the chain transfer constant was found to exist, which permits the synthesis of linear (for f = 2) or branched polymers (f > 2) with DP _w/DP _n approximately equal to 2 during the entire course of the polymerization.     

Chain‐length dependent termination in rotating sector polymerization, 1. The evaluation of the rate constant of chain propagation kp

The chain‐length distributions (CLDs) of polymers prepared by rotating‐sector (RS) techniques under pseudostationary conditions were simulated for the case of chain‐length dependent termination and analysed for their suitability of determining the rate constant of chain propagation k_p from the positions of their points of inflection. The tendency to underestimate k_p is a little more pronounced than in pulsed‐laser polymerization (PLP) but, interestingly, the situation improves in the presence of chain‐length dependent termination. The estimates also were found to be more precise a) for smaller rates of initiation, b) for higher order points of inflection, c) if termination is by combination, d) if the role played by the shorter one of the two chains becomes less dominant. Taken in all, the determination of k_p from the points of inflection in the CLD of RS‐prepared polymers may well compete with the more famous PLP method, especially if some care is taken with respect to the choice of experimental conditions.     

Chemiluminescence simulation method for the evaluation of the termination rate constant for 2-cyanopropyl peroxy and α-phenyl-ethyl peroxy radicals

An iterative method has been devised for the simulation of chemiluminescence data during the oxidative decomposition of αα′ azobisisobutyronitrile in the presence of ethylbenzene. From this simulation the cross termination rate constant of the two types of peroxy radicals present has been estimated.     

Multichannel RRKM-TST and CVT rate constant calculations for reactions of CH2OH or CH3O with HO2

The kinetics and mechanism of the gas-phase reactions between hydroxy methyl radical (CH(2)OH) or methoxy radical (CH(3)O) with hydroproxy radical (HO(2)) have been theoretically investigated on their lowest singlet and triplet surfaces. Our investigations indicate the presence of one deep potential well on the singlet surface of each of these systems that play crucial roles on their kinetics. We have shown that the major products of CH(2)OH + HO(2) system are HCOOH, H(2)O, H(2)O(2), and CH(2)O and for CH(3)O + HO(2) system are CH(3)OH and O(2). Multichannel RRKM-TST calculations have been carried out to calculate the individual rate constants for those channels proceed through the formation of activated adducts on the singlet surfaces. The rate constants for direct hydrogen abstraction reactions on the singlet and triplet surfaces were calculated by means of direct-dynamics canonical variational transition-state theory with small curvature approximation for the tunneling.     

Bimolecular rate constant and product branching ratio measurements for the reaction of C2H with ethene and propene at 79 K

The reactions of the ethynyl radical (C(2)H) with ethene (C(2)H(4)) and propene (C(3)H(6)) are studied under low temperature conditions (79 K) in a pulsed Laval nozzle apparatus. Ethynyl radicals are formed by 193 nm photolysis of acetylene (C(2)H(2)) and the reactions are studied in nitrogen as a carrier gas. Reaction products are sampled and subsequently photoionized by the tunable vacuum ultraviolet radiation of the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory. The product ions are detected mass selectively and time-resolved by a quadrupole mass spectrometer. Bimolecular rate coefficients are determined under pseudo-first-order conditions, yielding values in good agreement with previous measurements. Photoionization spectra are measured by scanning the ALS photon energy while detecting the ionized reaction products. Analysis of the photoionization spectra yields-for the first time-low temperature isomer resolved product branching ratios. The reaction between C(2)H and ethene is found to proceed by H-loss and yields 100% vinylacetylene. The reaction between C(2)H and propene results in (85 ± 10)% C(4)H(4) (m/z = 52) via CH(3)-loss and (15 ± 10)% C(5)H(6) (m/z = 66) by H-loss. The C(4)H(4) channel is found to consist of 100% vinylacetylene. For the C(5)H(6) channel, analysis of the photoionization spectrum reveals that (62 ± 16)% is in the form of 4-penten-1-yne, (27 ± 8)% is in the form of cis- and trans-3-penten-1-yne and (11 ± 10)% is in the form of 2-methyl-1-buten-3-yne.     

Ab initio MO and TST calculations for the rate constant of the HNO+NO2→HONO+NO reaction

Potential-energy surfaces for various channels of the HNO+NO₂ reaction have been studied at the G2M(RCC,MP2) level. The calculations show that direct hydrogen abstraction leading to the NO+cis-HONO products should be the most significant reaction mechanism. Based on TST calculations of the rate constant, this channel is predicted to have an activation energy of 6–7 kcal/mol and an A factor of ca. 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at ambient temperature. Direct H-abstraction giving NO+trans-HONO has a high barrier on PES and the formation of trans-HONO would rather occur by the addition/1,3-H shift mechanism via the HN(O)NO₂ intermediate or by the secondary isomerization of cis-HONO. The formation of NO+HNO₂ can take place by direct hydrogen transfer with the barrier of ca. 3 kcal/mol higher than that for the NO+cis-HONO channel. The formation of HNO₂ by oxygen abstraction is predicted to be the least significant reaction channel. The rate constant calculated in the temperature range 300–5000 K for the lowest energy path producing NO+cis-HONO gave rise to © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 729–736, 1998     

Statistical evaluation of an analytical GC/MS method for the determination of long chain fatty acids

In-depth evaluation of an analytical method to detect and quantify long chain fatty acids (C₈-C₁₆) at trace level concentrations (25-1000 μg/l) is presented. The method requires derivatization of the acids with methanolic boron trifluoride, separation, and detection by gas chromatography-mass spectrometry. The calibration experiments passed all the tested performance criteria such as linearity, homoscedasticity, and ruggedness. The detection limits and related quantities were computed by applying the method detection limit, and the calibration line approximation. The values obtained by applying the latter approach were more reliable and consistent with the actual statistical theory of detection decisions and yielded the following concentrations: C₈, 87.6 μg/l; C₁₀, 45.2 μg/l; C₁₁, 39.9 μg/l; C₁₂, 37.7 μg/l; C₁₄, 41.4 μg/l and C₁₆, 40.6 μg/l. Two different gas-liquid chromatographic columns were tested and similar results achieved, which shows the ruggedness of the method.     

Molecular modeling, theoretical calculations and property evaluation of three muscarinic agonists. X-ray structures of LU 25-109 and WAL 2014

LU 25-109 (II) and WAL 2014 (talsaclidine, III) are two M1 muscarinic agonists chemically related to the natural substance arecoline (I). All these compounds have beneficial effects on memory and cognition in animals and humans, and they have been proposed in the treatment of Alzheimer's disease, but only III will likely find a place in therapy. In this work we have investigated the solid state structures of II and III, and the X-ray structures of the two molecules and of the parent compound I have been used to input a series of computational chemistry efforts.

In particular, the X-ray geometries have been manipulated to model 20 molecular structures (1–20) which have been submitted to ab initio, semiempirical quantum mechanics and molecular mechanics calculations. The conformational space accessible to the 20 structures has been assessed by means of potential energy maps. The reactivities of 1–20 have been estimated by examining at the graphics terminal the composition and the extension of the frontier orbitals (HOMOs and LUMOs) and of the molecular electrostatic potential. The information obtained has been interpreted to explain the different degrees of activity shown by I–III. Our data indicate that III has better in vivo activity for its intermediate size, less polar surface, conformational rigidity and orientation of reactive domains.     

Instationary polymerization technique – an alternative route for the direct determination of the rate constant of chain propagation

Instationary polymerization technique (IPT) is a combination of nonstationary polymerization conditions and the controlled deactivation of all active radicals present in the system by reaction with an inhibitor at a certain time span after initiation. The special features of the resulting molecular weight distribution can be used for the direct determination of k_p in analogy to the pulsed‐laser polymerization (PLP) method. Furthermore, a qualitative information about the prevailing termination mechanism – i.e. disproportionation or combination – is also feasible from the distribution at a first glance.     

Much improved upper limit for the rate constant for the reaction of O2+ with N2

The rate constant for the reaction of O2+ with N2 to produce NO+ plus NO has been measured at 423, 523, and 623 K in a turbulent ion flow tube. Much improved upper limits for this reaction at the three temperatures are 2, 4, and 10x10(-21) cm3 s-1, respectively. These results should render this reaction irrelevant when modeling all plasmas involving atmospheric gases.     

Room‐temperature RAFT copolymerization of 2‐chloroallyl azide with methyl acrylate and versatile applications of the azide copolymers

A new vinyl azide monomer, 2‐chlorallyl azide (CAA), has been synthesized from commercially available reagent in one step. The reversible addition fragmentation chain transfer (RAFT) copolymerization of CAA with methyl acrylate (MA) was carried out at room temperature using a redox initiator, benzoyl peroxide (BPO)/N,N‐dimethylaniline (DMA), in the presence of benzyl 1H‐imidazole‐1‐carbodithioate (BICDT). The polymerization results showed that the process bears the characteristics of controlled/living radical polymerizations, such as the molecular weight increasing linearly with the monomer conversion, the molecular weight distribution being narrow, and a linear relationship existing between ln([M]₀/[M]) and the polymerization time. Chain extension polymerization was performed successfully to prepare block copolymer. Furthermore, the azide copolymers were functionalized by Cu^I‐catalyzed “click” reaction with alkyne‐containing poly(ethylene glycol) (PEG) to yield graft copolymers with hydrophilic PEG side chains. Surface modification of the glass sheet was successfully achieved via the crosslinking reaction of the azide copolymer under UV irradiation at ambient temperature. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1348–1356, 2010     

(2,6-Diphenyl) phenyl methacrylate—2. Radical copolymerization with methyl methacrylate. The Tgs of its copolymers with an addendum on the polymerization of (2,6-diphenyl) phenyl acrylate

The radical copolymerization of (2,6-diphenyl) phenyl methacrylate (1) with methyl methacrylate in DMF with AIBN at 70°C has the reactivity ratios r₁ = 0.071 and r₂ = 1.42, from which Q₁ = 1.45 and e₁ = 1.20. The copolymers had M_ns in the range of 10,000–40,000 and T_gs ranging from 406 to 480 K from which the hypothetical T_g for poly-1 was deduced as 500 K (227°C). Unlike 1, (2,6-diphenyl) phenyl acrylate could be polymerized to oligomers with M_n of the order of 2500.     

Gas chromatographic—mass spectrometric studies of long chain hydroxy acids.—III.1 The mass spectra of the methyl esters trimethylsilyl ethers of aliphatic hydroxy acids. A facile method of double bond location

Trimethylsilylation has proved to be extremely useful in the gas chromatography and the mass spectrometry of hydroxy acid methyl esters. The characteristic mass spectral fragmentation patterns have shown these derivatives to be superior in some respects to others for structural elucidation; in particular, hydroxylation followed by trimethylsilylation provides a useful method of double bond location in unsaturated fatty acid esters.

1 A preliminary presentation of this method has been given by G. Eglinton at the Lecture etting in Combined Gas Chromatography—Mass Spectrometry at the school of Pharmacy, London, August 9, 1967. It has come to the authors' attention that this method simultaneously developed by Dr. P. Capella, Institute di Industria Agrarie, University of Bologna, Italy^1c (P. Capella and C. M. Zorzut, Anal. Chem. 41 , 1458 (1968).)