Sorption and swelling of semicrystalline polymers in supercritical CO2

The equilibrium sorption and swelling behavior of four different polymers—poly(methyl methacrylate), poly(tetrafluoroethylene), poly(vinylidene fluoride), and the random copolymer tetrafluoroethylene–perfluoromethylvinylether–in supercritical CO₂—are studied at different temperatures (from 40 to 80 °C) and pressures (up to 200 bar). Swelling is measured by visualization, and sorption through a gravimetric technique. From these data, the behavior of amorphous and semicrystalline polymers can be compared, particularly in terms of partial molar volume of CO₂ in the polymer matrix. Both poly(methyl methacrylate) and the copolymer of tetrafluoroethylene exhibit a behavior typical of rubbery systems. On the contrary, polymers with a considerable degree of crystallinity, such as poly(tetrafluoroethylene) and poly (vinylidene fluoride), show larger values of partial molar volume. These can be related to the limited mobility of the polymer chains in a semicrystalline matrix, which causes the structure to “freeze” during the sorption process into a nonequilibrium state that can differ significantly from the actual thermodynamic equilibrium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1531–1546, 2006     

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.     

Dendronized Polymers via Macromonomer Route in Supercritical Carbon Dioxide

Radical polymerizations from third to fifth generation macromonomers were conducted in supercritical carbon dioxide (scCO₂). It was found that all monomers were not soluble in such a medium, and reactions occurred in the CO₂‐swollen monomer matrices. Despite the expected severe diffusion limitations, very high conversions and molecular weights were obtained. It is believed that the plasticization effect induced by the CO₂ plays a key role in these surprising findings. Scanning force microscopical analyses confirmed that mainly linear dendronized polymers were obtained and therefore chain transfer to polymer is virtually irrelevant.

     

Polycondensation Kinetics of Lactic Acid

The direct polycondensation of D ,L ‐lactic acid in the absence and presence of different catalysts at various temperatures has been studied experimentally. Two types of reactions were carried out, one under closed conditions to estimate the equilibrium constant and the other under flow of nitrogen to estimate the polymerization rate constant. A mathematical model was developed based on a suitable kinetic scheme for polycondensation reaction accounting for the rate of water removal. The effects of different operating conditions (temperature and pressure) on the average molecular weight of the polymer have been explored through experiments and model simulations.

     

GMRES physics-based preconditioner for all Reynolds and Mach numbers: numerical examples

This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. The assumptions were set on laminar flows and Newtonian fluids. The goal of this research is to show the capabilities of the present code to treat a wide range of problems appearing in laminar fluid dynamics towards the unification from incompressible to compressible and from inviscid to viscous flow codes. Several authors with different approaches have tried to attain this target in CFD with relative success. At the beginning the methods based on operator splitting and perturbation were preferred, but lately, with the wide usage of time-marching algorithms, the preconditioning mass matrix (PMM) has become very popular. With this kind of relaxation scheme it is possible to accelerate the rate of convergence to steady state solutions with the modification of the mass matrix under certain restrictions. The selection of the mass matrix is not an easy task, but we have certain freedom to define it in order to improve the condition number of the system. In this paper we have used a physics-based preconditioner for the GMRES implicit solver developed previously by us and an SUPG formulation for the semidiscretization of the spatial operator. In sections 2 and 3 we present some theoretical aspects related to the physical problem and the mathematical model, showing the inviscid and viscous flow equations to be solved and the variational formulation involved in the finite element analysis. Section 4 deals with the numerical solution of non-linear systems of equations, with some emphasis on the preconditioned matrix-free GMRES solver. Section 5 shows how boundary conditions were treated for both Euler and Navier–Stokes problems. Section 6 contains some aspects about vectorization on the Cray C90. The performance reached by this implementation is close to 1 Gflop using multitasking. Section 7 presents several numerical examples for both models covering a wide range of interesting problems, such as inviscid low subsonic, transonic and supersonic regimes and viscous problems with interaction between boundary layers and shock waves in either attached or separated flows. © 1997 John Wiley & Sons, Ltd.     

Dispersion Polymerization of Methyl Methacrylate in Supercritical Carbon Dioxide: Control of Molecular Weight Distribution by Adjusting Particle Surface Area

Summary: Experiments of methyl methacrylate dispersion polymerization are carried out in a reaction calorimeter using PDMS-mMA as surfactant. Different stabilizer concentrations from 0 to 10 wt% with respect to monomer have been considered in order to control particle morphology. The analysis by scanning electron microscopy reveals a definite decrease of the total particle surface area at decreasing stabilizer concentration. At the same time, the analysis of the polymer microstructure by gel permeation chromatography shows a trend of the average molecular weight towards smaller values. In particular, a second mode at low molecular weights has been observed leading to bimodal molecular weight distributions. The experimental results are compared with simulation results obtained through a detailed kinetic model developed in previous studies. 1 The key role of the radical exchange between continuous and dispersed phases is confirmed.     

Ab Initio Calculation of the Propagation Kinetics in Free Radical Polymerization: Chain Length and Penultimate Effects

Summary: In this work, Quantum Chemistry is applied to investigate the propagation kinetics in free radical polymerization. Energies, structures and transition state geometries are determined using density functional theory, which combines good accuracy with reasonable computational demand. In particular, B3LYP functional is used to evaluate the exchange and correlation energy with the 6-311+G(d,p) basis sets. The capabilities of the approach with respect to the prediction of the kinetic constants of elementary processes relevant to polymeric systems (propagation reactions) is first tested using literature experimental data as reference values. 1 Namely, two different monomers of industrial relevance have been selected, acrylonitrile and styrene. For such systems, the effect of chain-length on the propagation rate coefficient is examined. Finally, for the selected monomer pair, the relative reactivity (so-called reactivity ratios) is also analyzed, in particular considering the penultimate effect.     

Prediction of competitive adsorption on coal by a lattice DFT model

Adsorption is one of the main mechanisms involved in the ECBM process, a technology where CO₂ (or flue gas, i.e. a CO₂/N₂ mixture) is injected into a deep coal bed, with the aim of storing CO₂ by simultaneously recovering CH₄. A detailed understanding of the microscopic adsorption process is therefore needed, as the latter controls the displacement process. A lattice DFT model, previously extended to mixtures, has been applied to predict the competitive adsorption behavior of CO₂, CH₄ and N₂ and of their mixtures in slit-shaped pores of 1.2 and 8 nm width. In particular, the effect of temperature, bulk composition and density on the resulting lattice pore profiles and on the lattice excess adsorption isotherms has been investigated. Important insights could be obtained; when approaching near critical conditions in the mesopores, a characteristic peak in the excess adsorption isotherm of CO₂ appears. The same effect could be observed neither for the other gases nor in the micropores. Moreover, in the case of mixtures, a depletion of the less adsorbed species close to the adsorbent surface is observed, which eventually results in negative lattice excess adsorption at high bulk densities.     

Intracellular pH measurements made simple by fluorescent protein probes and the phasor approach to fluorescence lifetime imaging

A versatile pH-dependent fluorescent protein was applied to intracellular pH measurements by means of the phasor approach to fluorescence lifetime imaging. By this fit-less method we obtain intracellular pH maps under resting or altered physiological conditions by single-photon confocal or two-photon microscopy.